Dec 16, 2015 - achieved by exploring which flood-generating processes control the seasonality and mag- nitude of ...... Observ. Lur-evskogo, Univ. Tartu ...
Bringing structure to catchment-scale hydrological diversity around the world By W OUTER R EINIER B ERGHUIJS
Department of Civil Engineering U NIVERSITY OF B RISTOL
A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of D OCTOR OF P HILOSOPHY in the Faculty of Engineering.
2016
Word count: 45357
A BSTRACT
n this dissertation we use data from many locations around the world to bring structure to the catchment-scale hydrological diversity around the world. We investigate catchment-scale hydrology at various time-scales, whereby we explore how seasonal conditions influence overall catchment response. First, we develop a framework that allows synthesising most of the global seasonal climatology using indices that are straightforward to interpret. Second, we show how seasonal climatic conditions are strongly connected to seasonal hydrologic conditions. Third, we show how the influence of seasonal hydrologic conditions on long-term average streamflow undermines recent assessments of the dominant drivers of streamflow changes. Subsequently, we partly resolve these shortcomings. Fourth, we focus on how short-term hydrological responses are compounded by seasonal hydroclimatic conditions, and how this provides insights in the dominant drivers of low river flows and floods. Because not all catchment-scale hydrological diversity can be explained by seasonal hydroclimatic conditions, we conclude with a parsimonious model that describes how catchments release stored water as streamflow. Overall, the exposed hydrological patterns provide novel insight in the regional differences of hydrologic response. The seasonal climatic patterns dominate seasonal hydrologic response, and influence the hydrology over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). The rest of the unexplained catchment-scale hydrological diversity appears to be at least partly explained by regional differences in how catchments filter available water storage into streamflow.
I
i
D EDICATION AND ACKNOWLEDGEMENTS
riting this thesis would not have been possible without the generous support of many people. First of all, I would like to thank Ross Woods for being a tremendous supervisor. We have had many fun, motivating and fruitful discussions that have helped me to shape my work. I thank colleagues from the University of Bristol and collaborators from other institutes that supported my work, challenged it when needed, and helped me to improve: Christopher Hutton, Susanna Almeida, Thorsten Wagener, Ida Westerberg, Andreas Hartmann, Nicholas Howden, Peter Greve, Ralph Trancoso, David Rupp, Josh Larsen, Tim van Emmerik, Emma Aalbers, Murugesu Sivapalan, and Anne van Loon. I thank my friends and family for their unconditional support and encouragement. Thank you Rachael, for all your love and support.
W
iii
A UTHOR ’ S DECLARATION
declare that the work in this dissertation was carried out in accordance with the requirements of the University’s Regulations and Code of Practice for Research Degree Programmes and that it has not been submitted for any other academic award. Except where indicated by specific reference in the text, the work is the candidate’s own work. Work done in collaboration with, or with the assistance of, others, is indicated as such. Any views expressed in the dissertation are those of the author.
I
SIGNED: .................................................... DATE: ..........................................
v
TABLE OF C ONTENTS
Page List of Tables
xi
List of Figures 1
xiii
Introduction
1
1.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Basics principles of hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Prediction at the catchment scale . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.3
Dealing with diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.4
Different approaches to classification . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.5
Learning from data of many catchments . . . . . . . . . . . . . . . . . . . . .
5
1.2
Research objective and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.3
Chapters and research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
I
Seasonal hydroclimatology
13
2
Climate similarity and differences
15
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2.1
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2.2
Sinusoidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2.3
Calibration and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.3.1
Global monthly climatology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.3.2
Assessment of errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.3.3
Comparison of framework and data-derived climate characteristics . . . .
25
2.4
The framework as a classification tool . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.5
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.5.1
28
2.3
Is the sinusoidal function suitable to describe monthly climatology? . . . . vii
TABLE OF CONTENTS
2.5.2 2.6 3
What insight can the similarity indices give? . . . . . . . . . . . . . . . . . .
31
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Patterns of seasonal water balances
35
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.2.1
Constructing the seasonal water balances . . . . . . . . . . . . . . . . . . . .
38
3.2.2
Constructing a similarity framework and forming coherent clusters . . . .
42
3.2.3
Comparison of streamflow signatures at a range of time scales . . . . . . .
42
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.3.1
Regional patterns of the seasonal water balance . . . . . . . . . . . . . . . .
43
3.3.2
Similarity framework for seasonal water balance . . . . . . . . . . . . . . .
45
3.3.3
Grouping of catchments into coherent clusters . . . . . . . . . . . . . . . . .
49
3.3.4
Connection to similarity of streamflow signatures . . . . . . . . . . . . . . .
55
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3.4.1
On the similarity of seasonal water balance . . . . . . . . . . . . . . . . . . .
62
3.4.2
On the link of seasonal water balance to other streamflow signatures . . .
64
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.3
3.4
3.5
II Long-term mean hydrology
67
4
Spatial vs. temporal patterns of the long-term water balance
69
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.3
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.3.1
Space-time asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.3.2
Climate seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.3.3
Non-linearity of wetness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.3.4
Unexplained forest effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.4 5
Drivers of changing water balances
75
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
5.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.2.1
Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.2.2
Water balance framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.2.3
Typical rates of change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.2.4
Relative sensitivity to aridity changes . . . . . . . . . . . . . . . . . . . . . .
80
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.3
viii
TABLE OF CONTENTS
5.4
Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
III Event-scale hydrology
83
6
Flood patterns and mechanisms
85
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
6.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
6.2.1
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
6.2.2
Hypothesized flood-generating mechanisms . . . . . . . . . . . . . . . . . . .
87
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
6.3.1
Seasonality of floods and flood predictors . . . . . . . . . . . . . . . . . . . .
90
6.3.2
Interannual variability of floods and flood predictors . . . . . . . . . . . . .
92
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
6.4.1
On exposing controls of flood response . . . . . . . . . . . . . . . . . . . . . .
94
6.4.2
Implications for flood prediction and trend analysis . . . . . . . . . . . . . .
94
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
6.3
6.4
6.5 7
8
Changes in global flood conditions
97
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
7.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
7.2.1
Streamflow data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
7.2.2
Quantifying changes in floods . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
7.3
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Low flow patterns and mechanisms
105
8.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.3
8.2.1
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2.2
Seasonality indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2.3
Testing hypothesized low flow controls . . . . . . . . . . . . . . . . . . . . . . 109
8.2.4
Quantifying the contribution of water balance components . . . . . . . . . . 110
8.2.5
Quantifying the role of climate and landscape for low flow variability . . . 111
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 8.3.1
Timing of low flow events and hypothesized controls . . . . . . . . . . . . . 112
8.3.2
Contribution of water balance components . . . . . . . . . . . . . . . . . . . 115
8.3.3
The role climate and landscape on LAF variability . . . . . . . . . . . . . . . 116
8.4
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 ix
TABLE OF CONTENTS
9
Storage sensitivity of streamflow
121
9.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9.2
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9.3.1
Storage sensitivity of streamflow . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3.2
Analytical approximation ²S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3.3
Comparison of ²S with historical flow variability . . . . . . . . . . . . . . . . 124
9.4
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.5
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
10 Conclusions and outlook
131
10.1 Short summary of chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.2 Outlook and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 A Supporting information Chapter 2
137
B Supporting information Chapter 5
141
B.1 The dependence of partial derivatives to the climatic input . . . . . . . . . . . . . . 141 B.2 The attribution of 20 th century runoff changes to aridity and other factors . . . . . 143 C Supporting information Chapter 6
145
C.1 Seasonality metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 D Supporting information Chapter 9
147
D.1 Calculating ²S for any Q vs. dQ/dt relationship . . . . . . . . . . . . . . . . . . . . . 147 D.2 Correspondence between streamflow sensitivity and catchment attributes . . . . . 149 E Additional publication: Snow’s role for the mean annual water balance
153
F Additional publication: Creating community for early career geoscientists
161
G Overview PhD related activities
165
Bibliography
169
x
L IST OF TABLES
TABLE 2.1
Page
Correspondence between of temperature based, precipitation based, and combined characteristic of the analytical model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
26
Water balance equations for the various stores, constitutive relationships and description of symbols. We refer to Figure 3.1 for the model structure and the organization of the stores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
The
K RSR M
39
values of the catchment clusters. The first row contains the M clusters
K and the first column the K clusters. The results show that the estimates of RSR M
are the lowest along the diagonal of the Table, which represent the variance within, whereas the off-diagonal terms that represent variance between are all larger. . . . . 3.3
52
Characteristics of the 10-catchment clusters. The table contains the cluster name, amount of catchment of within-cluster catchments (n), the clusters-boundary conditions and associated minimum, average and maximum values within the clusters. Additionally a short description of the catchments is included. . . . . . . . . . . . . . .
54
A.1 A description of the precipitation pattern for regions where X p exceeds 0.3. . . . . . . 138
xi
L IST OF F IGURES
F IGURE 1.1
Page
Overview of the various hydrological processes that may occur in a given area and the components of the surface energy balance. . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
2
A description of catchment functioning (here depicted as a butterfly) is often trapped in space and time; the uniqueness of place and time does not allow the description to be reliably applied in other locations or future conditions. . . . . . . . . . . . . . . . . .
1.3
A short overview of the three Parts, eight Chapters, and their connections, that represent the research chapters of this thesis. . . . . . . . . . . . . . . . . . . . . . . . .
2.1
4
7
Conceptual description of monthly climate according the framework; example of a precipitation regime (a), a temperature regime (b), several precipitation regimes for a range of seasonal precipitation amplitudes (c), and correction factor C r as a function of the seasonal precipitation amplitude (δP ) (d). . . . . . . . . . . . . . . . . . . . . . . .
2.2
The mean temperature (T), the seasonal temperature amplitude (∆T ), the phase shift (s T ), and the monthly temperature error (X T ). . . . . . . . . . . . . . . . . . . . . . . . .
2.3
19
23
The mean precipitation rate (P), the dimensionless seasonal temperature amplitude (δP ), the phase shift (s P ), and the monthly precipitation error (X P ). . . . . . . . . . . .
24
2.4
The phase difference between the precipitation and temperature regime (s d ). . . . . .
24
2.5
MERRA-Land observation (bar) and analytically approximated (dashed line) monthly temperature and precipitation climatology of the individual grid-cells that fall at 25th percentile, median, and 75th percentile values of different δP and ∆T intervals. . . . .
2.6
27
Climate classification of the world based on the five climatic indices. Observations are divided into tertiles with equal membership for every index. The figure shows class boundary conditions (bottom right), and the spatial distribution of classes. The phase shift s d is delineated into two classes: high (H) and low (L) values are merged into one group (L) because of the cyclic behaviour of s d . Classes with less then 250 grid-cells are not presented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
29
L IST
OF
F IGURES
3.1
Structure of the extended FLEX I conceptual rainfall-runoff model used in this study (adapted from Fenicia et al. [87]). This model structure should be evaluated in conjunction with the model governing equations presented in Table 3.1. The model consists of five coupled stores representing snow (C R ), vegetation interception (I R ), unsaturated zone (UR ), saturated groundwater (S R ), and a store representing fast runoff (FR ). . .
3.2
40
Three examples of simulated and measured seasonal discharge regimes and associated Nash-Sutcliffe efficiencies (NS). The catchments on the left and middle have been accepted for further study (NS > 0.80). The discharge regime on the right is one of the 51 eliminated catchments because the model predictions had an unacceptable fit with the observed data (NS < 0.80). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
41
Diversity of the seasonal water balance across the U.S. represented by 17 catchments. Most of the seasonal regimes that are not displayed can be considered an interpolation of the displayed ones. Note that all y-axes have the same scale. . . . . . . . . . . . . . .
3.4
45
The proposed framework consisting of three hydroclimatic indices. δP expresses the seasonality and timing of precipitation, f s the fraction of precipitation falling as snow, and φ the aridity index. The figure includes descriptions of how key processes of the seasonal water balance change as a function of the indices. . . . . . . . . . . . . . . . .
3.5
46
The values of the hydro-climatic indices δ∗P (measure of precipitation timing with respect to potential evaporation), f s (snowiness, fraction of total annual precipitation that falls as snow), and φ (aridity index, ratio of annual potential evaporation to annual precipitation) for the 321 study catchment catchments. . . . . . . . . . . . . . .
3.6
48
Overview of the fluxes and storage regimes of the 10-catchment clusters. Regimes included are (first row) the precipitation, (second row) streamflow, (third row) snowmelt, (fourth row) snow storage, (fifth row) evaporation, (sixth row) storage, and (seventh row) deficit. The thin coloured-lines display values of the individual catchments. The thicker black lines display the within-cluster average values. (Note that some values are not shown because they plot above the top of the vertical scale). . . . . . . . . . . .
3.7
51
The organization of the 321 MOPEX study catchments into 10 hydrologically similar catchment clusters. The dotted boxes contain the description of the catchment classes, index ranges δ∗P , f s , φ, and the hydroclimatic character. Arrows describe changes in the hydroclimatic controls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8
53
The organization of the ecosystem regions, main plant formations, and soil orders across the U.S. overlain by the locations of catchments belonging to the 10 catchment clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9
57
(top) The annual runoff ratio, (middle) the coefficient of variation of the annual runoff ratio, (bottom) and the long-term water balances presented in context of the Budyko Hypothesis for the 10-catchment clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
58
L IST
OF
F IGURES
3.10 (top) The rising limb density and (bottom) base flow index values of the 10-catchment clusters displayed in whisker plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
3.11 Overview of the various signature values of the 10-catchment clusters. Signatures included are (first row) the Parde coefficients, (second row) the flow duration curve, (third row) the flood growth curve, (fourth row) the flood frequency curve, (fifth row) the timing of annual maximum flows, (sixth row) the decline curve, (seventh row) the low flow frequency curve, and (eight row) the timing of the low flow occurrences. The thin colored-lines display values of the individual catchments. The thicker black lines display the within-cluster average values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1
61
Spatial sensitivity of water yield (x-axis) and temporal sensitivity of water yield (yaxis) for 420 watersheds located in the United States, and the spatial pattern of their differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1
71
Global hydro-climatic characteristics of the Budyko framework. The spatial pattern of the evaporative index, E/P (top), the aridity index, φ (middle), and the parameter, ω (bottom), based on the EU-WATCH data of the period 1901-2001. . . . . . . . . . . . .
5.2
77
The relative and absolute sensitivity of freshwater availability to changes in aridity and other factors. (a) The relative sensitivity of aridity changes compared to all other factors expressed by Θφ/ω , (b) the sensitivity of mean annual runoff to changes in the ˆ ∂φˆ , and (c) the sensitivity of mean annual runoff to changes in the aridity index ∂Q/ ˆ ∂ω∆ω/∆φˆ . . . . . . . . . . . . . . . . . . . . . other factors scaled by typical changes ∂Q/
5.3
79
The relative and absolute sensitivity of freshwater availability to changes in aridity and other factors for dryland areas versus other regions (a) The relative occurrence of the sensitivity to aridity changes compared to all other factors expressed by Θφ/ω for dryland areas versus all other regions, and (b) the absolute sensitivity of mean annual ˆ ∂φˆ . High φ-values have similar ∂Q/ ˆ ∂φˆ values runoff to changes in the aridity index ∂Q/ for a relative wide range of ω-values, leading to the distinct peak. . . . . . . . . . . . .
6.1
82
Mean day of (a) maximum annual daily flow, (b) maximum daily precipitation, (c) maximum weekly precipitation, (d) maximum precipitation excess, and (e) maximum snowmelt and associated standard deviations (right column). Black crosses indicate that the data were not calculated due to an absence of significant snow ( E) and evaporation-dominated (E > P) low flow generation. . . . . . . . . . . . . . 116
8.5
Spatial pattern of the coefficient of variation of LAF (top), the coefficient of variation of water storage (middle), and storage sensitivity of streamflow ²S (α, β,Q LAF ) (bottom).117
8.6
Scatterplot of the variability of annual minimum flows expressed as the coefficient of variation of LAF (y-axis), climate variability expressed as the coefficient of variation of catchment storage (x-axis left), and storage sensitivity of streamflow ²S (α, β,Q LAF ) (x-axis right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 xvi
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OF
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The α (mm1−β dayβ−2 ) and β (-) values for the 725 catchments. (NB: no physical interpretation can be placed on the spatial patterns of α). . . . . . . . . . . . . . . . . . 125
9.2
Storage sensitivity of streamflow (²S ) for different three different flow values: Q = 0.1 (mm/d) (left), Q = 0.5 (mm/d) (center), and Q = 1.0 (mm/d) (right). The catchments’ α (mm1−β dayβ−2 ) and β (-) values are indicated by black markers. (NB: it is only
meaningful to compare α values between catchments when their β values are the same).126 9.3
The storage sensitivity of streamflow (²S ) for low flow (Q 85 ), median (Q 50 ), and high flow (Q 15 ) conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.4
Scatterplot of the storage sensitivity to streamflow (²S ) for low flow (²S (Q 85 )), median (²S (Q 50 )), and high flow (²S (Q 15 )) conditions, and associated slopes of the flow duration curves for low (S FDC (Q 75 ,Q 95 )), median (S FDC (Q 40 ,Q 60 )), and high (S FDC (Q 5 ,Q 25 )) flow conditions.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.1 Range of the time average P(t)/P values that occur for different δP values because the inaccuracy of the correction factor C r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 A.2 Delineation of the land surface in regions according to the precipitation error (X P ), precipitation seasonality (δP ), and mean precipitation rate (P). . . . . . . . . . . . . . . 139 B.1 Visualization of Fuh’s equation F(φ,ω), the partial derivative ∂F , ∂ω
and the relative strength
∂F ∂F / ∂φ ∂ω
∂F , ∂φ
the partial derivative
using climate aridity (φ=EP /P) as the climate
input (top row). Visualization of Fuh’s equation F(ψ,ω), the partial derivative partial derivative
∂F , ∂ω
and the relative strength
∂F ∂F / ∂ψ ∂ω
∂F , ∂ψ
the
using climate wetness (ψ= φ1 )
as the climate input (bottom row). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 ∆Q b, and ∆ω for each grid cell. . . . . . . . . . . . . . . . . . . . . . 144 B.2 Visualization of Q , ∆φ D.1 An example of a log(− dQ/dt) vs log(Q) plot used to derive ²S values for an individual catchments. The graph shows all the original data points from hydrograph recessions, the linear Brutsaert and Nieber approximations, and the smoothed relationship. This numerical approximation of the smoothed relationship relaxes the assumption that a single α and β parameter can describe the log(− dQ/dt) vs log(Q) characteristics; instead the relationship of log(− dQ/dt) vs log(Q) can now take in principle any shape 148 D.2 Comparison of the Analytical approximation of ²S as quantified in the main article using the Brutsaert and Nieber [1977] hydrograph recession characteristics (α, β), and the Numerical approximation which relaxes the assumption that only single α and β parameter are needed to describe the log-log plot characteristics . . . . . . . . . 149 D.3 Correspondence of storage sensitivity of streamflow (²S ) for median flows and several catchment characteristics quantified by the Spearman correlation coefficient (r s ) and the Pearson correlation coefficient (r p ). The catchment characteristics include catchment area, mean elevation, mean catchment slope, annual precipitation, and mean temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 xvii
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D.4 Correspondence of storage sensitivity of streamflow (²S ) for median flows and several catchment lithographic characteristics [126], quantified by the Spearman correlation coefficient (rs) and the Pearson correlation coefficient (rp). The lithographic characteristics include the percentage of unconsolidated sediments (su), siliciclastic sedimentary rocks (ss), pyroclastics (py), mixed sedimentary rocks (sm), carbonate sedimentary rocks (sc), acid volcanic rocks (va), intermediate volcanic rocks (vi), basic volcanic rocks (vb), acid plutonic rocks (pa), intermediate plutonic rocks (pi), basic plutonic rocks (pb), metamorphics (mt), water bodies (wb), ice and glaciers (ig), and no data available (nd). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 E.1 Mean annual streamflow and streamflow anomaly in the context of the Budyko hypothesis, stratified by snow fraction. The observed long-term streamflow and precipitation measurements are placed in the context of the Budyko hypothesis. The Budyko hypothesis states the mean streamflow is primarily a function of the catchment’s annual precipitation and potential evaporation as shown by the black line in a. Departures below the Budyko curve for catchments with a significant fraction of the precipitation falling as snow indicate that an increased fraction of precipitation as snowfall is associated with higher streamflow, as clarified by the linear regression in b.155 E.2 Sensitivity of annual streamflow to the fraction of annual precipitation falling as snowfall. The histogram shows the change in normalized streamflow (Q/P) per unit change of the annual snow fraction ( f s ) for 97 snow-affected catchments ( f s > 0.15). Positive values of sensitivity indicate that the annual streamflow of catchments varies (between years) directly with the annual f s . Years with higher snow fraction, f s , tend to have higher values of annual streamflow. . . . . . . . . . . . . . . . . . . . . . . . . . 156
xviii
HAPTER
C
1
I NTRODUCTION
Small parts of this chapter are adapted from a "Review Article" that is in preparation for EarthScience Reviews (ISSN: 0012-8252), an “Article" that is published in the Dutch Journal of Physics [20], and a published blogpost [122]. The text in this chapter is written by W.R. Berghuijs, but has benefited from suggestions of co-authors S. Harrigan and P. Greve.
1.1
Background
Earth’s fresh water is essential for life as we know it. However, too much or too little water leads to floods and droughts, often with catastrophic consequences. The terrestrial water cycle also plays a central role in environmental sciences, as it shapes energy and vapour fluxes to the atmosphere, regulates biogeochemical processes, and shapes the Earth’s landscape. Thus, understanding the terrestrial water cycle is not only societally important, but also essential to understanding the Earth system more generally. Hydrology is the science that should facilitate this understanding; it is the study of the movement and storage of water on Earth and other planets [43, 76, 235].
1.1.1
Basics principles of hydrology
Movement and storage of water can occur via a wealth of processes (See Figure 1.1) and is in many regions affected by human activity. Storage can consist of various components such as soil moisture, ground water, canopy storage, surface water, ice, snow and reservoirs. Precipitation can take place in various forms, most commonly as rain or snow. Evaporation includes transpiration, interception, bare soil evaporation, sublimation and evaporation from surface water. Runoff processes 1
CHAPTER 1. INTRODUCTION
can consist of river discharge, various forms of overland flow, and various forms of subsurface flow.
Figure 1.1: Overview of the various hydrological processes that may occur in a given area and the components of the surface energy balance.
The water balance is the conceptualisation that uses the principle of mass conservation to summarise all these processes for a control volume: (1.1)
dS = P −E −Q dt
where S stands for water stored in the control volume, t for time , P for precipitation rate, E for evaporation rate, and for the rate at which the various runoff processes recharge or drain the control volume. The land water balance is strongly coupled to the surface energy balance; most precipitation never ends up in the river, but is evaporated instead. Globally over 60% of terrestrial precipitation is evaporated [247] and the fraction of landsurface where evaporation exceeds runoff is ∼77% [122]. The energy balance that summarises these processes for a given control area: (1.2)
dH = R n − S h − λE − G dt 2
1.1. BACKGROUND
where H is the energy stored within the surface layer, t is time, R n is the net radiation, λE is the latent heat flux (evaporation), S h is the sensible heat flux, and G is the ground heat flux to deeper ground layers. The land water balance and surface energy balance are strongly coupled [264], yet universally applicable laws capturing the behaviour of this feedback and interaction at larger spatial scales remain rare and description of this behaviour often relies on highly parameterised and place-specific models [271].
1.1.2
Prediction at the catchment scale
In hydrological sciences, equations describing water movement are available for individual processes at small scales [e.g. 55, 88, 204, 227, 242]. Many hydrological models have been developed that use these equations to describe individual components of the water balance (for an overview read [43]) or to combine multiple components of the water balance [e.g., 70–75]. A widely used method to describe the response of a catchment is by upscaling these small-scale equations; catchments are split into elements that are assumed small and homogeneous enough that the equations of water movement are applicable. These models are reliable when the assumptions underpinning their theories apply. However, the assumptions that these equations often rely on, such as homogeneity, uniformity and time invariance of flow paths, are virtually non-existent in nature, especially at the scale of interest to many hydrologists: a catchment [271]. In addition, the distributed description of the catchment is often not considered realistic; we cannot observe all the relevant properties across the entire catchment, with the consequence that we do not have the data to underpin reliable parameters of model grid-cells. This leads to equifinality [30], and poor understanding of the catchment [30, 271]. In the quest to better understand movement of water at the catchment scale, Dooge [63], among others [e.g. 184, 271] advocates that, instead of describing the increasing complexity of a catchment (upscaling of small-scale theories), understanding can be generated by acknowledging the simplicity of how catchments filter the climate signal. Improved understanding should focus on new theories that go beyond the mechanics of run-off generation and focus on understanding the underlying climatic and landscape properties that control those mechanics at the catchment scale. The catchment is thereby considered an entity, having certain characteristics and controls that can be quantified and are useful for understanding and predicting the response at a catchment scale.
1.1.3
Dealing with diversity
No two catchments are completely identical, and individual catchments are subject to change. Each catchment is a unique composition of climate, a river network, soils, geology, topography, vegetation, the catchments shape and size, and human influences on the system. The fact that between catchment differences of all these components can be very large, makes it difficult to 3
CHAPTER 1. INTRODUCTION
produce descriptions of catchment response that are applicable beyond an individual catchment [28, 184, 269]. As a consequence the bulk of hydrological science literature consist of case studies describing the complex behavior at individual sites. Yet, the uniqueness of individual sites makes it difficult to transfer findings to new locations and facilitate understanding and prediction in other catchments. All these spatially unique catchments are in the meanwhile subject to change [197, 322], which makes it difficult to transfer findings to future conditions (Figure 1.2).
Figure 1.2: A description of catchment functioning (here depicted as a butterfly) is often trapped in space and time; the uniqueness of place and time does not allow the description to be reliably applied in other locations or future conditions.
Does this mean every catchment needs to be extensively measured, studied, and modelled before we can present any understanding of it? In other sciences similar challenges have led to frameworks that help to identify and predict first order differences between study objects [186]; e.g. biology has Linnaean classification [175], chemistry holds the periodic table [190], in limnology water bodies are classified by mixing regime, or by nutrient status [332], and fluid mechanics uses continuous dimensionless numbers to describe the character of flow [17]. Although such classifications are not a panacea to all problems these sciences face, they are extremely important to generate new understanding, identify transferability of understanding, organise understanding, and communicate understanding. Attempts for classifications in hydrology have not been unanimously successful; hydrology does not yet possess a generally agreed upon catchment classification system, nor does it possess many well established principles of similarity for catchment behaviour. 4
1.1. BACKGROUND
1.1.4
Different approaches to classification
Olden et al [216] identified two fundamentally different approaches in hydrologic classification. The inductive approach classifies regions according to properties of hydrological observations (e.g. streamflow characteristics). Inductive approaches can be considered clustering exercises where no a-priori understanding of the controls of hydrologic response is required. The deductive approach classifies regions according to aspects of the environment that are thought to control the hydrologic response (e.g. landscape, anthropogenic and/or climate conditions). The deductive approach (contrary to the inductive approach) aims at exposing why a region has particular hydrologic behaviour and therefore reflects some degree of understanding of the system. As long as the assumptions underpinning the deductive approach apply, it is (in theory) suitable to predict or describe hydrologic conditions at varying spatial scales, for changing climate and landscape conditions, and for other datasets. Yet simple universally applicable laws capturing the behaviour of the water balance at the catchment scale remain rare and description of this behaviour often relies on highly parameterised and place specific models [271]. For example, in hydrological science there is no quantitative classification framework to globally order regions with different seasonal water balance behaviour while the framework provides a rigorous but simple deductive inquiry into the causes of hydrologic similarities and differences between places. Attempts to classify hydrological behaviour at shorter timescales have been limited by the difficulty of producing concise, transferable, and easily understood explanations of different basin behaviour [e.g. 260, 344]. Consequently, descriptions of regional hydrological differences often have a qualitative (e.g., dry/wet, forest/pasture) [e.g. 222, 327], local (framework only applies regionally) [e.g. 23, 327], and/or inductive character [e.g. 222, 260]. Therefore it is currently difficult to summarise and simplify the differences, and causes of differences of the temporal variability of the terrestrial water balance globally.
1.1.5
Learning from data of many catchments
Typical datasets available for hydrological studies of catchments consist of streamflow, precipitation, temperature series, land cover, main soil types, and topographic indices derived from digital elevation models of the catchment. This amount of data can not easily unveil controls on how the catchment functions. For extensively gauged headwater-scale catchments it is difficult to generate general understanding that remains applicable at other sites [114]. Controlled experiments at the catchment scale are generally not feasible to perform. Consequently much can be gained from comparisons of a large set of catchments. Comparing catchments across a wide diversity is the hydrological surrogate for a collection of test tubes in a controlled experiment in laboratory tests. Using a large amount of catchments, the data can be presented such that we learn from patterns that express the similarity and differences between catchments. This can subsequently be used to derive hypotheses about how the catchments function [80, 114, 121, 269, 271]. Measures of 5
CHAPTER 1. INTRODUCTION
similarity can be descriptors of hydrological variability, but also suitable modelling approaches of a catchment. Using this approach the available data can expose patterns that would not be unveiled when studying a catchment in isolation. Additionally hypotheses can be tested among a large amount of catchments, which allows testing whether findings are applicable for a wide range of catchments, with the chance of creating generalisations at the catchment scale.
1.2
Research objective and scope
In this thesis I will make steps that help to better understand the similarity and difference between different catchments. (Such approaches should use (when possible) deductive approaches to express the similarity and difference of places, rather than that they are clustering exercises that do not reflect understanding of the system. Catchments are not described by upscaling small scale theories, but rather by finding appropriate descriptions for the catchment as an entity. This will be done by comparing the spatial and temporal hydrologic patterns of many catchments, rather than studying one place in detail. The broad objective of this thesis is to better map and understand the diversity of hydrologic conditions around the world. We do not aim to outcompete detailed descriptions (e.g. extensively calibrated hydrological models) of individual catchments, but rather to provide insight into how catchments behave in context of other catchments. These comparisons may (i) reveal catchment behavior that was previously unknown, (ii) provide a reference for detailed case studies, and (iii) help to organize the plethora of hydrologic conditions around the world. The specific focus and novelty will vary per Chapter, and will depend on data availability, current status of the hydrologic literature, and serendipity. Hydrologic characteristics and the associated most important climate and landscape characteristics that determine how a catchment functions are time scale dependent [10, 23, 36]. At short-time scales, rainfall intensity, topography, and antecedent wetness conditions are important factors controlling streamflow generation [32, 69, 94, 304, 305]. At longer time-scales, historical observations of the multi-annual water balance of catchments all over the world reveal a tight relationship between the surface water balance and the ratio of potential evaporation to precipitation [e.g. 45, 215]. Because the primary controls on hydrologic response vary across temporal scales our investigations will be done for various time-scales. Recent hydrologic synthesis efforts have presented evidence that the seasonal water balance is at the core of overall catchment responses, and understanding it will assist in predicting signatures of streamflow variability at other time scales [37]. In this thesis we follow this central role by starting with hydrology descriptions at the seasonal time-scale (Part I), and use these seasonal patterns to understand the hydrology at longer timescales (Part II) and shorter timescales (Part III) (Figure 1.3). For 6
1.2. RESEARCH OBJECTIVE AND SCOPE
each timescale we address the following three questions: • What are the main between catchment differences and how can they be described parsimoniously? • To what novel hydrologic insight do these patterns of between catchment differences lead? • What are the physical characteristics controlling the between catchment differences?
Figure 1.3: A short overview of the three Parts, eight Chapters, and their connections, that represent the research chapters of this thesis.
This thesis consists of three main parts, eight research chapters, a concluding chapter and supplementary Material. Chapters 2-9 consists of five published articles, and three chapters of which manuscripts are in preparation for, or in review at, various journals. All chapters are included as individual scientific contributions and each contains an abstract, introduction, main part and conclusions. While the chapters can be read as individual scientific contributions, they are linked to one another as indicated in Figure 1.3, and they ask the same fundamental questions listed above (only at different time-scales). In Chapter, 10 we conclude with an overall reflection on the work. The Appendices A-D present supplementary material supporting Chapters 2-9. Appendix E presents a published peer reviewed paper that has been largely prepared before my PhD studies, and is therefore only included in the Appendix. Appendix F presents a peer reviewed publication that does not cover the main topic of my PhD thesis, and is therefore only 7
CHAPTER 1. INTRODUCTION
included in the Appendix. Appendix G gives an overview of the academically relevant activities of the author conducted during his PhD studies.
1.3
Chapters and research questions
The above listed research objective and scope only provides a broad description of what is covered in this thesis. Here, we list the specific research questions per chapter, and provide the abstract of the chapter to provide more context. Part I: Seasonal hydroclimatology Chapter 2 Can simple mathematical functions help to more informatively summarize the global mean monthly climatology than currently available approaches? Summary for context: Climate descriptors and classifications are vital for ordering past, current and future climatic conditions. Yet, these parsimonious descriptors of climatic conditions only capture specific aspects of this climate signal, and lose all other information available in the observations. As a result, climate descriptions are often not physically insightful when they are applied in other studies. In this study, we show that a sinusoidal function with an annual period can adequately describe the vast majority of monthly precipitation and temperature climates around the world. This finding allows us to synthesise intra-annual monthly precipitation and temperature climatology using 5 indices that are easy to interpret. The indices describe (i) the mean precipitation rate (P), (ii) the mean temperature (T), (iii) the seasonal precipitation amplitude (δP ), (iv) the seasonal temperature amplitude (∆T ), and (v) the phase difference between the precipitation and temperature regimes (s d ). The combination of the 5 indices describes the relative time series of precipitation and temperature climatology, in contrast to earlier proposed similarity indices that only capture specific aspects of these time series. We demonstrate how the framework can reproduce many earlier proposed indices and classifications, and provide an example how the framework can be used to classify regions. We argue that the framework provides comprehensive insight into global climatology and can function as a quantitative conceptual basis for climate descriptions among different sciences. Chapter 3 Do seasonal climatic conditions control the between catchment differences in seasonal hydrologic conditions, and how do these seasonal conditions in turn relate to the hydrology at other time-scales? Summary for context: Recent hydrologic synthesis efforts have presented evidence that the seasonal water balance is at the core of overall catchment responses, and understanding 8
1.3. CHAPTERS AND RESEARCH QUESTIONS
it will assist in predicting signatures of streamflow variability at other time scales, including inter-annual variability, the flow duration curve, low flows, and floods. In this study, we group 321 catchments located across the continental U.S. into several clusters with similar seasonal water balance behavior. We then delineate the boundaries between these clusters on the basis of a similarity framework based on three hydroclimatic indices that represent aridity, precipitation timing, and snowiness. The clustering of catchments based on the seasonal water balance has a strong relationship not only with regional patterns of the three climate indices but also with regional ecosystem, soil, and vegetation classes, which point to the dependence of these physiographic characteristics on seasonal climate variations and the hydrologic regimes. Building on these catchment clusters, we demonstrate that the seasonal water balance does have an imprint on signatures of streamflow variability over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). The seasonal water balance is well integrated into variability at seasonal and longer time scales, but is only partly reflected in the signatures at shorter time scales, including flooding responses. Overall, the seasonal water balance has proven to be a similarity measure that serves as a link between both short-term hydrologic responses and long-term adaptation of the landscape with climate. Part II: Long-term mean hydrology Chapter 4 What is wrong with the current way we characterise which factors are dominant in controlling changes of global mean runoff? Summary for context: Understanding the effects of climate and land-cover on water yield is a challenging component in assessments of future water resources. Zhou et al. [2015] [354] (hereafter Z15) use Fu’s water balance model that in their opinion provides a globally unifying framework that can quantify water yield sensitivity to climate and land-cover change. We show that key assumptions underpinning their application of the framework are contradicted by observations of many watersheds located in diverse climates and landscapes; Z15 ignore the space-time asymmetry of the co-variation of climate wetness and water yield, climate intra-annual variability, and typical rates of change of climate and landscape. Additionally, the framework does not provide the claimed explanation for increases in water yield associated with increases in forest cover. All these aspects undermine Z15’s application of the framework, and should be considered to draw robust conclusions on the effects of climate and land-cover on water yield. Chapter 5 If we resolve some of these issues of previous assessments, what are now the dominant drivers of changes in global mean runoff? Summary for context: Unraveling the main drivers of hydrological change is key for 9
CHAPTER 1. INTRODUCTION
the prediction and management of global freshwater resources [197]. Precipitation and potential evaporation are commonly studied drivers [15, 86, 93, 103, 140, 219, 249, 267], as aridity (the ratio of potential evaporation to precipitation) explains ∼90% of the spatial differences in mean annual runoff across the globe [45]. However, it is unclear if reported changes in aridity over time also explain most of the temporal changes in freshwater resources across the Earth’s land surface. We resolve new global patterns on the importance of aridity to changes in runoff by evaluating its relative sensitivity to change in combination with observed trends. This reveals runoff is most sensitive to changes in aridity across only ∼20% of the land surface, meaning other factors dominate for the remaining 80%. We confirm water resources in dryland regions are highly sensitive to aridity changes [15, 219], but in addition show the sensitivity of runoff to changes in other factors is far higher. The burden of these other factors therefore falls on the more poorly constrained roles of changing climatic variability, CO2 - vegetation feedbacks and anthropogenic modifications to the landscape. The influence of these factors upon future runoff is further compounded in dryland regions by sparse hydrological information, signifying a need to improve monitoring and modeling of the dominant runoff drivers in these regions. Part III: Event-scale hydrology Chapter 6 What are the dominant hydrologic mechanisms responsible for generating maximum flows across the United States? Summary for context: River flooding can have severe societal, economic and environmental consequences. However, limited understanding of the regional differences in floodgenerating mechanisms results in poorly understood historical flood trends and uncertain predictions of future flood conditions. Through systematic data analysis of 420 catchments we expose the primary drivers of flooding across the contiguous United States. This is achieved by exploring which flood-generating processes control the seasonality and magnitude of maximum annual flows. The regional patterns of seasonality and inter-annual variability of maximum annual flows are, in general, poorly explained by rainfall characteristics alone. For most catchments soil-moisture dependent precipitation excess, snowmelt, and rain-on-snow events are found to be much better predictors of the flooding responses. The continental-scale classification of dominant flood-generating processes we generate here emphasizes the disparity in timing and variability between extreme rainfall and flooding, and can assist predictions of flooding and flood risk within the continental US. Chapter 7 Are globally the largest floods changing in frequency and magnitude? Summary for context: Analyses of trends in observed floods often focus on relatively frequent events, whereas changes in rare floods are only studied for a small number of 10
1.3. CHAPTERS AND RESEARCH QUESTIONS
locations that have exceptionally long observational records. Understanding changes in rare floods is especially relevant as these events are often extremely damaging, influence the design of major structures, and shape the riparian environment. Here we assess changes in the largest flood events (∼0.033 annual exceedance probability) observed during the period 1980-2009 for 1778 catchments ( 0.5 if (s P − s T ) < −0.5
s d can range from -0.5 (completely out of phase, P peaks before T), to 0 (completely in phase), to 0.5 (completely out of phase, P peaks after T). For the climate displayed in Figure 2.4a,b s d equals -0.40 [year]. The time-averaged value of P(t) can deviate from P because C r is numerically approximated (see Figure A.1). The 5 indices needed to characterize the climate now are: (i) the mean precipitation rate (P), (ii) the mean temperature (T), (iii) the seasonal precipitation amplitude (δP ), (iv) the seasonal temperature amplitude (∆T ), and (v) the phase difference between the precipitation and temperature regimes (s d ). 2.2.2.1
Derivation of other climate characteristics
The 5 indices can be used to derive any climate characteristic that is a function of the mean within year pattern of precipitation and temperature. Derived characteristics can, for example, consist solely of temperature characteristics such as the duration that the temperature is below a certain threshold temperature (T c ): −2 sin−1
(2.6)
tT =
³
T c −T ∆T
2π 20
´
+π
2.2. METHODS
Similarly, the duration that the seasonal precipitation is below a certain threshold temperature (P c ) can be approximated by: −2 sin−1
tP =
(2.7)
³
P c −P P ·δ P
´
+π
2π
These equations can be used to derive climate characteristics such as the number of frost days [77], number of tropical days [209], number of dry months [298], number of wet months [298]. Similar expressions can be derived for indices such as precipitation seasonality [323], precipitation concentration index [217], degree-day factor [134], and cooling degree month [286]. Temperature and precipitation characteristics can be combined to express how much precipitation falls while a certain temperature condition is met. Examples are annual snowfall, the fraction of precipitation that falls as snow [26, 341], and the precipitation in the growing season [348]. Woods [341] showed how the fraction of precipitation falling below a certain temperature threshold (T0 ) is calculated as follows: ∗
(2.8)
f s = f s (T ∗ , δ∗P ) =
1 sin−1 (T ∗ ) δP − − 2 π π
q 1 − T ∗ , for δP ≤ 1
where, δ∗P = δP · sgn(∆T ) · cos(2π · s d )
(2.9)
T − T0 |∆ T |
T∗ =
(2.10)
Because the indices describe the character of widely used sinusoidal functions, analytical solutions can be derived for other precipitation, temperature or combined characteristics. Widely adopted classifications [3, 45, 135, 163, 165, 225, 295, 300] can also be reproduced, but this requires more laborious expressions, sometimes including calculation of potential evaporation based on mean monthly temperature [e.g., 119].
2.2.3
Calibration and evaluation
To test the adequacy of the sinusoidal function with an annual period for the description of the precipitation and temperature climate we define two objective functions that express the goodness of fit for the temperature and precipitation approximations: (2.11)
XT =
(2.12)
XP =
12 |T(t) − T | X t 12 t=1
12 |P(t) − P | X t
t=1
21
P
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
where X P expresses the mean monthly precipitation error normalized by the average precipitation rate (-). When the error, X P , is 0 the sinusoidal function is a perfect fit to the observed precipitation value P t . The value of X P expresses to what degree the monthly precipitation deviates relative to the mean monthly value observed at that location. X T expresses the mean monthly temperature error ( o C), which is the mean absolute error in the temperature approximation. The coefficients of Equation 2.1 and 2.2 are obtained by the Simplex search method [210] of MATLAB’s fminsearch to minimize X T and X P [172]. For both the optimizations P and T are fixed according to the longterm average observed values; solely the seasonal amplitude and phase shift are calibrated. The objective functions are chosen because they have the same units as the observed and described signal, and they can be interpreted without information on the variance in the observations.
2.3
Results
We first provide an overview of the global monthly climatology according to the description by the sinusoidal functions. Subsequently we evaluate in more detail the appropriateness of the sinusoidal function to describe the monthly precipitation and temperature climatology. Finally we assess the correspondence of characteristics of the climate derived from the 5 indices and characteristics of the climate directly derived from the observations.
2.3.1
Global monthly climatology
Figure 2.2 displays the global occurrence of the mean temperature (T), the seasonal amplitude of temperature (∆T ), the phase shift of the temperature regime compared to January 1st (s T ), and the temperature error (X T ) in approximating the observed data by a sinusoidal function. The mean temperature for the assessed grid cells varies between -28.1 and 37.1 o C. The seasonal temperature amplitude also varies strongly across the grid cells with a maximum ∆T of 32.5 o C. The approximation of the monthly temperature signal gives an average temperature error (X T ) of 0.85 o C, with a standard deviation of 0.44 o C. This error is relatively small compared to the mean seasonal amplitude of temperature, ∆T , of 12.8 o C (median = 12.8 o C). The regions where the temperature error is large coincide with the regions where the seasonal temperature amplitude (∆T ) is also large or with regions with a highly seasonal precipitation regime. In the areas with a seasonal precipitation regime the seasonal change in soil moisture can be a strong control on the surface energy balance, thereby affecting the intra-annual temperature pattern; this is one possible cause of the larger errors. Figure 2.3 displays the global occurrence of the mean precipitation rate (P), the seasonal precipitation amplitude (δP ), the phase shift (s p ), and the precipitation error (X P ). The precipi22
2.3. RESULTS
Figure 2.2: The mean temperature (T), the seasonal temperature amplitude (∆T ), the phase shift (s T ), and the monthly temperature error (X T ).
tation rate ranges from a minimum of 4 mm/y, to a maximum of 10561 mm/y. The global mean precipitation rate is 706 mm/y (median = 501 mm/y). The seasonality of the precipitation varies regionally; δP has an average value of 0.80 (-) (median = 0.63), but can locally be as high as 4.7 (-). The approximation of the seasonal precipitation signal, on average, leads to a mean absolute error of the monthly precipitation of δP = 0.17 (-), with a standard deviation of 0.12. With a mean seasonality of precipitation (δP ) equal to 0.80 this suggests that, on average, the within-year seasonality of precipitation is largely captured by the sinusoidal description. Figure 2.4 displays the phase difference between the precipitation and temperature regimes (s d ). This phase difference is for most regions relatively close to 0 indicating that precipitation amounts are the highest during the warmer months at the given location. In some regions of all the continents the precipitation amounts are highest during the cool season.
2.3.2
Assessment of errors
To improve understanding of the ability of the sinusoidal function to describe the precipitation regime we highlight how well the description works as a function of precipitation characteristics, and how the errors vary between regions. 23
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
300
350
Figure 2.3: The mean precipitation rate (P), the dimensionless seasonal temperature amplitude (δP ), the phase shift (s P ), and the monthly precipitation error (X P ).
500
450
400
350
300
250
200
150
100
50
-0.4
50
-0.2
100
0
150
0.2
200
0.4
250
sd [year]
Figure 2.4: The phase difference between the precipitation and temperature regime (s d ).
24
2.3. RESULTS
The regional differences in errors indicate that the sinusoidal function is not always an informative description of the monthly precipitation regime as the approximation can show relatively high error values (see map of X P in Figure 2.3). The percentage of grid cells where X P is larger than 0.30 (-) is 12.6%. Of these grid cells 69.0% are located in dry regions with annual precipitation below 300 mm/y. The regions with very low precipitation rates ( 1.0). Figure A.2 (Appendix A) delineates the grid cells in discrete classes based on the X P , δP , and P values.
The grid cells where X P is larger than 0.3 are only located in a limited number of regions (See Figure A.2). Reasons for these high X P values vary regionally. Table A.1 gives a point wise description per region that shows high (X P > 0.3) values. These descriptions indicate the regional reasons for the higher error value and should improve understanding of the regional adequacy of the hypothesis that the monthly precipitation pattern can be described with the sinusoidal function. The sinusoidal approximation is not informative in regions with a bimodal rainfall pattern such as southwestern United States and the Horn of Africa. Figure 2.5 gives an overview of the measured and modelled temperature and precipitation regimes, to give qualitative understanding how well the approximations describe the observed regimes. For different ranges of precipitation seasonality we have selected individual gridcells whose error value is the 25th percentile, median and 75th percentile for that category, in order to view seasonal regimes where the sinusoidal functions produce high, medium and low errors. For the temperature regimes the 75th percentile and better fits all have a very good correspondence between the sinusoidal function and the actual observations. Hence the sinusoidal functions also visually appear very suitable for describing the monthly temperature pattern. For the precipitation patterns the correspondence between the sinusoidal function and the actual observations is lower. Although we visually inspected the measurements of all grid cells, we were not able to identify a more suitable simple mathematical function to describe the measured precipitation regime in a similar parsimonious manner.
2.3.3
Comparison of framework and data-derived climate characteristics
We evaluate the ability of the framework to reproduce specific climatic characteristics. This gives an indication of the suitability of the framework to provide a common reference for studies that are interested in specific climate characteristics. We compare characteristics of the climate as assessed by the 5 similarity indices and characteristics of the climate directly derived from the data. The derived indices include temperature-based, precipitation-based and combined 25
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
Table 2.1: Correspondence between of temperature based, precipitation based, and combined characteristic of the analytical model. Climate descriptor
Description
Definition
Duration frost season Duration growing season Cooling degree month
Period that mean temperature is below freezing point [77]. Period that mean temperature is above a certain threshold, here set at 8 ( o C). Combined influence of winter temperature and duration expressing the sum the duration times the anomaly [286]. Period that the mean precipitation rate is lower than 20 (mm/month) [225]. Period that the mean precipitation rate is higher than 60 (mm/month) [225].
P P
Dry period
Wet period
Precipitation seasonality Fraction of precipitation falling as snowfall Growing season precipitation Holdridge aridity index
KöppenGeiger mainclass
Mean deviation of monthly precipitation compared to the mean annual precipitation [323]. Precipitation falling as snowfall (as derived by a temperature threshold) divided by the total amount of precipitation [341]. Annual amount of precipitation falling when growing season conditions (T(t)> 8 o C). Climatic water availability in each part of the year, defined as the ratio of the temperature to the annual precipitation [135]. Percentage of grid-cells that are assigned to the correct Köppenclass according to the definitions of [225].
26
R2
P ( t(T ( t) < 0)/ ( t)
Slope linear regression 0.997
0.9889
P ( t(T ( t) > 8)/ ( t)
1.0115
0.9899
0.998
0.999
P
(T c − T ( t))/ T ( t) < T c
P
t, if
P
P ( t(P ( t) < 20)/ ( t)
1.0337
0.967
P
P ( t(P ( t) > 60)/ ( t)
0.9671
0.968
P
( t) |P ( t)− P12 | P P ( t)
0.9473
0.9609
1.046
0.899
1.036
0.9262
1.012
0.984
-
0.998
P
(P ( t) < 1)/
P
(P (T ( t) > 8)
58.93
P
P
P
T ( t(T >0)) P
See Table 1 in [225].
2.3. RESULTS
Figure 2.5: MERRA-Land observation (bar) and analytically approximated (dashed line) monthly temperature and precipitation climatology of the individual grid-cells that fall at 25th percentile, median, and 75th percentile values of different δP and ∆T intervals.
temperature and precipitation characteristics. The characteristics of the climate assessed, and their definitions are listed in Table 2.1. Given the large number of grid cells involved, the correspondence between the analytically derived and the data-derived values is summarised by the slope of a linear regression (indication of accuracy), and the R 2 -value of the linear regression (indication of precision). The analytically derived value is used as the explanatory variable. The combination of the linear regression slope and the R 2 -value expresses how all the information contained in these similarity indices can be reproduced with the reference framework. The slopes of the linear regression approach one for most climate indices, with R 2 -values also approaching one (see Table 2.1). This indicates enough information is captured within the framework to accurately and relatively precisely reproduce a variety of widely used climate indices. Temperature indices (duration frost season, duration growing season, cooling degree month) have the highest R 2 -value, which is also expected considering the good fit between 27
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
temperature observations and descriptions. The R 2 -value for precipitation characteristics (dry period [225], wet period [225] and precipitation seasonality [323]) decrease slightly, but slopes still are close to one with R 2 also close to one. One variable to highlight is the precipitation seasonality index as defined by Walsh & Lawer [323]. The slope of the linear regression gives a value of 0.90 which confirms that most of the precipitation variability is captured by the sinusoidal function. For combined characteristics (fraction of precipitation falling as snowfall [341], growing season precipitation [348], Holdridge aridity index [135] the performance decreases again, but still R 2 -values are around 0.94 and the slope of the linear regression still approaches one. The correspondence with the Köppen main class according to the definitions used in Peel et al. [225] gives a 99.81% correspondence between derived classes, indicating that this widely used classification scheme can be reproduced as well.
2.4
The framework as a classification tool
The framework can be used as a classification tool to characterize or cluster climate based on the five indices using the notation: [P, T, δP , ∆T , s d ]. An example grid-cell in New Zealand [43.5300 o S, 172.6203 o E] has the characteristics [662.9, 6.8, 0.30, 6.86, -0.01]. When regions with comparable climates are defined, the single values can be replaced by the associated minimum and maximum value, e.g. [600/800, 5/10, 0.1/0.4, 4/8, -0.25/0.25]. Another type of classification can make the different components dependent on another, e.g. [(600+30T)/(800+30T), 5/10, 0.1/0.4, 4/8, -0.25/0.25]. As an example, we classify the land surface into different climatic regions. The four indices [P, T, δP , ∆T ] are divided into tertiles with an equal number of grid-cells per group; per index there is a group of low, medium and high values. The 5th index (s d ) is divided into a group of small and large phase differences, again with an equal number of grid-cells. Climate classes are constructed based on the combination of the above-mentioned groups, leading to 34·2 = 162 climate classes. However, not all combinations of groups occur, resulting in 120 classes with grid-cells assigned. Figure 2.6 displays the class boundary conditions (bottom right), and the spatial distribution of classes with more than 250 grid-cells. Although the current example classification does not have a specific purpose beyond providing an example, the framework allows classifying climate groups quantitatively, while maintaining the qualitatively easy to interpret character (e.g. cold, wet, high rainfall seasonality, medium temperature seasonality, out of phase).
2.5 2.5.1
Discussion Is the sinusoidal function suitable to describe monthly climatology?
We aimed to develop descriptors of the intra-annual precipitation and temperature climate that maintain most of the monthly information that is present in the observed signal, while using a 28
2.5. DISCUSSION
Figure 2.6: Climate classification of the world based on the five climatic indices. Observations are divided into tertiles with equal membership for every index. The figure shows class boundary conditions (bottom right), and the spatial distribution of classes. The phase shift s d is delineated into two classes: high (H) and low (L) values are merged into one group (L) because of the cyclic behaviour of s d . Classes with less then 250 grid-cells are not presented.
limited number of descriptors to characterise the climate. By identifying that most of the climates around the world can be described by a sinusoidal pattern with an annual period, both for monthly precipitation and temperature, simple analytical functions appear to be very suitable for this purpose. The most parsimonious description that still acknowledges intra-annual variation of precipitation and temperature consist of 5 indices: here described by P, T, δP , ∆T and s d . More parsimonious descriptors integrate these dimensions and therefore by definition lose information.
The systematic comparison of the analytical model performance with the observed data indicates regional differences in the adequacy of the sinusoidal function for describing the observed monthly regimes. For the temperature climatology, Figure 2.5 shows that the seasonal pattern is well described by the sinusoidal function, as the mean absolute error (X T ) is much smaller than the within-year variability of the temperature regime (∆T ). Considering that the climatic descrip29
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
tors should be parsimonious and easily understandable, we have not identified an opportunity to improve on the sinusoidal description to describe the monthly temperature pattern, while still maintaining the parsimony and simplicity of the current sinusoidal description.
The goodness of fit (X P ) of the precipitation regimes indicates that the sinusoidal function for most regions provides a reasonable approximate for the precipitation regimes. High errors, with few exceptions, occur either in the very dry places (P 1). The significant percentage of grid cells with a hyper seasonal precipitation regime indicates that previous characterizations with an upper bound of 1.0 for the seasonality [23, 37, 130, 196, 234, 341] are not suitable for characterising the global monthly precipitation climatology, though it can be applied in some regions.
For the precipitation pattern the error in the sinusoidal approximation can be regionally relatively high, and there is more room for a refined mathematical description, especially in regions with a clear bimodal monthly precipitation regime. In dry regions the monthly precipitation rates are based on a limited number of precipitation events, so there is often no smooth mean monthly pattern. Improvement of the parsimonious precipitation description will consequently be very difficult for regions with low precipitation rates. The data we used for the fitting of our framework are interpolated, which may impact the performance of the framework. This may be particularly important in arid data poor regions, where there is the possibility of poor performance due to inaccurate data interpolation.
The balance between providing an appropriate and detailed description of the climate and providing a simple parsimonious understandable description depends on the purpose of the frameworks. Earlier studies used more detailed sinusoidal functions to describe regional climatic gradients [136], or suggested to regionally change the period of the seasonal cycle to half a year [196]. Although such refinements may improve the correspondence of the analytical function and the observed climate signal, they also require more indicators to describe the climate and are physically less easy to interpret. The most detailed description of monthly precipitation and temperature values, are the actual observed values. However, description of this information requires two numbers for every month to characterise the climate, and thus is inappropriate to characterise the climate in a quickly understandable way when the climate of many different locations needs to be characterised or compared.
Whether the errors introduced by the approximation are problematic completely depends on the purpose the framework is used for. In context of studies that use other climate indices or climate classes, the suitability of the mathematical approximation is underpinned by the high correspondence between derived climate characteristics with the framework and climate charac30
2.5. DISCUSSION
teristics based on measurements. This indicates the amount of information lost by summarising the monthly climate with the 5-indices is very small as the reproduction of other variables is well maintained. Comparison with the precipitation seasonality index of Walsh & Lawler [323] indicates that on average most of the variability of mean intra-annual precipitation is captured within the description. However, some information (the error) is lost and not available for detailed assessments when only the 5 climate descriptors are used. Evaluation of the descriptors of the monthly climate is only performed for grid-scale precipitation and temperature, which does not take into account sub-grid variability. Hence the hypothesis is not tested at sub-grid scales. Further testing and mapping for sub-grid variability is left for future work. Yet as the hypothesis originates from applications at local sites, it is not expected that at sub-grid scales the performance will change significantly. The proposed description is scale-independent in its application and hence a potentially useful way to characterise any place at any scale or to characterise the variability or mean of a single unit, at other than grid-scales (e.g. a river basin).
2.5.2
What insight can the similarity indices give?
By identifying that the mean monthly climatology in many parts of the world can be described by a sinusoidal pattern we simplified the mean climate signal into five dimensions, which has multiple uses, and limitations. A clear limitation of the framework is the loss of detail available in the observed signal, such as between year variability, short-term variability etc. A description of mean seasonal climate does not incorporate, but can be expanded by, descriptors that characterize precipitation characteristics such as storminess and inter-annual variability. The 5 indices are thus currently not adequate for forcing mechanistic models or studies that require detailed data (e.g. daily) of the temporal climate conditions. Additionally the error of precipitation and/or temperature can be too large to highlight climatic differences in regional studies that compare climatologically almost equivalent sites. Therefore the descriptors will not always be suitable for local assessments that require as much detailed information as possible. These limitations are intrinsic properties of any climate classification and climate descriptors. The framework is rather intended as a tool to order global dominant features of monthly precipitation and temperature climatology. Because our description provides a good approximation to the time series of observed climatology, our framework can provide a much more comprehensive understanding on what monthly climate patterns are occurring globally compared to earlier parsimonious climate descriptors. This more comprehensive way of describing monthly climatology has multiple distinct advantages compared to the classifications and indices that describe only specific characteristics of the monthly climatology but lose all other information obtained in the observations. 31
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
The framework makes it conceptually much easier to describe the actual physical gradients of monthly climatology between two places. The similarity indices we propose all have a well-defined, unambiguously interpretable definition. Many previous similarity indices and classifications[e.g. 163, 165, 225] are rather a combination of numerical indices where the physical gradient between places cannot be expressed within a quantitative manner or sometimes even conceptual manner. Expressing these physical gradients between places in a conceptually easy manner is not only valuable for education purposes but also can assist in exposing physical gradients that underpin differences and similarity between places for research purposes.
Sanderson [255] advocated for a novel classification of the world climates. Modern textbooks continue to use the 100-year old Köppen classification of climates [163], which is based on de Candolle’s vegetation groups, themselves based on the five climatic zones of the ancient Greeks.he limited physical information contained in the similarity indices systems remains a barrier to give insight into the climatic similarity and differences between places. Additionally, because all classification systems have their specific purpose (e.g. cluster vegetation similarity) it is difficult to use the indices across different studies and sciences. For example, the limited quantitative information on the intra-annual climate conditions that is contained in Köppen classification makes it unsuitable as a common reference framework for many different studies. Because of the much smaller loss of information in our framework and the ability to reproduce previous classifications we argue our framework can generate a conceptual step forward in characterising the within year variations of the climate, where climatic differences between places are easily expressed.
We argue that our framework can provide a quantitative conceptual basis for climate descriptions among different sciences. Because the analysis of section 3.3 indicates the approximated regimes can accurately reproduce other climate descriptors, the framework can provide a holistic picture of the monthly precipitation and temperature climatology. Goals of previous climate indices [e.g. 77, 209, 298, 323] and classifications have been to organize the climate such that specific climate-dependent characteristics occur in a region [3, 45, 135, 163, 165, 225, 295, 300]. In contrast, our framework provides five climate dimensions that in a simple manner can characterize under which monthly precipitation and temperature climatology the case specific assessments occur. Many climate indices and climates of classification schemes are derived from the mean intra-annual precipitation and temperature pattern. Consequently, these indicators can all be expressed in terms of the 5 proposed climate indices. The framework can thus provide a common reference scheme to describe climatic conditions, and thereby better highlight climatic similarity and differences between places.
32
2.6. CONCLUSIONS
Classification, the delineation of groups with similar characteristics, is always case specific, except when there are discrete differences between the observed items, such as classes in Linnaean taxonomy [175], elements of the periodic table [190], and turbulent and laminar flow in fluid mechanics [17]. Our framework rather uses continuous numbers to describe the character of climate where discrete classes are based on more purpose-specific conditions. The 5-dimensions form a continuum in which we can only subdivide by putting in artificial boundaries. We provided an example based on arbitrarily chosen class boundaries, which classified the land surface into different climatic regions. Although this classification does not have a specific purpose beyond providing an example, it shows how the framework allows classifying climate groups quantitatively, while maintaining a qualitatively easy to interpret character. The fact that the full within-year climatology is described using the indices means that the indices can force mechanistic models [e.g., 234, 340, 341].This characteristic, combined with the notion that the indices can express the climatic gradients between several places, make it potentially a powerful tool to combine simple mechanistic and falsifiable models and large scale climate classifications. Additionally, the framework may provide an useful tool to characterize past of future climatic change or variations in a holistic, physically easily interpretable way compared to using changes in the discrete Köppen climate classes [50, 252], changes in speed of change of Köppen climate classes [181], changes in precipitation concentration [179], and changes in mean climatology [102].
2.6
Conclusions
Climate is a key factor in many sciences and determines the diversity of many biotic and abiotic factors around the world. Climate descriptors and climate classifications are widely used tools to synthesise climatic conditions in a parsimonious manner and are vital for understanding, ordering and describing the global climatic diversity. The diversity of climates around the world makes it difficult to produce parsimonious descriptors of climatic conditions that still maintain most of the information present in the observed signal. Consequently, climate descriptors and classifications only describe a specific aspect of the climate signal, or they have a qualitative character. As a result, climate descriptions are often physically not very insightful when they are applied in other sciences or studies. In this study we showed that a sinusoidal function with an annual period can describe most of the monthly precipitation and temperature patterns. The mean absolute temperature error of the sinusoidal function is 0.85 ( o C), which is an order of magnitude smaller than the mean intra-annual variation of temperature. Similarly, the mean monthly error of precipitation is on average below 0.18 [-]; high error values mainly occur in regions with low precipitation rates or 33
CHAPTER 2. CLIMATE SIMILARITY AND DIFFERENCES
in regions with a very seasonal precipitation regime. This finding allows us to synthesize most of the monthly precipitation and temperature patterns using 5 indices that are physically easy to interpret. The indices describe (i) the mean precipitation rate (P), (ii) the mean temperature (T), (iii) the seasonal precipitation amplitude (δP ), (iv) the seasonal temperature amplitude (∆T ), and (v) the phase difference between the precipitation and temperature regime (s d ). The combination of the 5 indices summarises the relative time series of mean monthly precipitation and temperature. Quantitative comparison of characteristics of the climate as assessed by the 5 similarity indices and directly derived from the original climatic data shows good correspondence. This indicates the framework is able to give a holistic picture of climatic conditions, but also indicates its ability to provide a common reference framework for studies that are interested in more specific climate characteristics. As an example, we classify the land surface into different climatic regions based on the five indices. Although this classification does not have a specific purpose beyond providing an example, it shows how the framework allows classifying climate groups quantitatively, while maintaining a qualitatively easy to interpret character. Hence the proposed framework provides a basis to summarise the global diversity of monthly precipitation and temperature climatology within a 5-dimensional space. This allows expressing the climatic diversity in a simple and understandable manner, while the quantitative character of the monthly climate signal is maintained. Because a wide range of climatic classification and similarity indices can be brought back to the 5-dimensional space the framework can be used as a common reference scheme among different sciences.
34
HAPTER
C
3
PATTERNS OF SEASONAL WATER BALANCES
This chapter is published a "Research Article" in Water Resources Research (ISSN: 1944-7973). This publication has been slightly modified to improve consistency throughout this thesis. This chapter benefited from the comments of two anonymous reviewers, A. Montanari, S. Gharari, M. Yaeger, and S. Ye. Initial analyses presented in this chapter have been made available previously [19]. Citation: Berghuijs, W. R., M. Sivapalan, R. A. Woods, and H. H. G. Savenije (2014), Patterns of similarity of seasonal water balances: A window into streamflow variability over a range of time scales, Water Resources Research, 50, 5638-5661, doi:10.1002/2014WR015692.
Abstract Recent hydrologic synthesis efforts have presented evidence that the seasonal water balance is at the core of overall catchment responses, and understanding it will assist in predicting signatures of streamflow variability at other time scales, including inter-annual variability, the flow duration curve, low flows, and floods. In this study, we group 321 catchments located across the continental U.S. into several clusters with similar seasonal water balance behavior. We then delineate the boundaries between these clusters on the basis of a similarity framework based on three hydroclimatic indices that represent aridity, precipitation timing, and snowiness. The clustering of catchments based on the seasonal water balance has a strong relationship not only with regional patterns of the three climate indices but also with regional ecosystem, soil, and vegetation classes, which point to the strong dependence of these physiographic characteristics on seasonal climate variations and the hydrologic regimes. Building on these catchment clusters, we demonstrate that the seasonal water balance does have an imprint on signatures of streamflow 35
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
variability over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). The seasonal water balance is well integrated into variability at seasonal and longer time scales, but is only partly reflected in the signatures at shorter time scales, including flooding responses. Overall, the seasonal water balance has proven to be a similarity measure that serves as a link between both short-term hydrologic responses and long-term adaptation of the landscape with climate.
3.1
Introduction
The well-known heterogeneity and complexity associated with catchments make it difficult to produce generalizations of their streamflow response beyond individual catchments [28, 63, 184]. Yet, despite the heterogeneity and complexity present in individual catchments, it is generally believed that they hold some level of internal organization and simplicity of responses, which should permit a degree of predictability of their functional behavior [63, 184, 259, 270]. One example of generalized predictive behavior is that the mean-annual partitioning of precipitation into evaporation and streamflow is primarily a function of the relative atmospheric supply and demand of water, expressed by the aridity index, the ratio of the mean available energy (potential evaporation) to mean available water (precipitation) at the annual scale [45, 231]. This understanding of the process control of the annual water balance would allow a priori prediction, albeit to first order, of long-term average streamflows for catchments where no streamflow measurements are available [187]. It has been shown that the energy versus water competition, as per the Budyko hypothesis, can even extend to the inter-annual variability of the annual water balance [48, 198]. Additionally, it would provide a framework for catchment intercomparisons [80], for uncovering additional secondary controls, and for studying changes to the long-term water balance of catchments in response to climate and land cover change [e.g. 64, 96, 353].
The dominant climatic and landscape controls on hydrologic responses are time scale dependent [10, 81]. Therefore, a natural extension of the Budyko-type framework would be one that might help to understand the physical controls on the similarity and differences of streamflow variability at shorter time scales. In this paper, we focus on developing a similarity framework for seasonal water balance behavior and the imprint of such seasonal water balance on signatures of streamflow variability at a range of other time scales. In the past, similarity metrics to group catchments with similar seasonal water balance behavior have been based on streamflow characteristics themselves [116, 120, 222, 223, 229, 328], climate characteristics [163, 225], catchment characteristics [42, 173], hybrids of both climate and catchment characteristics [340, 350], and combinations of streamflow and climate characteristics [52]. In this paper, we extend the similarity analysis beyond streamflow variability alone, and to explicitly include the fullness of the seasonal water balance. 36
3.1. INTRODUCTION
Classification studies based on observed streamflow data alone help us to cluster catchments together on the basis of their similarity and even produce regional maps, but without explicit consideration of the underlying process controls (be they climate or landscape factors) they are unable to be used to make predictions in ungauged basins across noncontiguous regions. While spatial proximity can be used as a surrogate for catchment similarity [4] under some circumstances, ideally, a similarity framework should be process based, and yet provide a foundation for comparative studies aimed at learning from observed data. The key process that underpins seasonal streamflow behavior is the storage variation that results in response to timing differences between water availability (rainfall plus snowmelt) and energy availability (potential evaporation) [296, 334, 343].
The development of a similarity framework for the comparative analysis of the seasonal water balance would be of particular interest as these seasonal variations impact streamflow variability not just seasonally, but at other time scales as well. For example, in cold regions, accumulation during winter and subsequent melting of the snowpack and ice during spring produce strong seasonal streamflow variations. Because the seasonal water balance impacts the variations of soil moisture or snow storage and more generally, antecedent wetness conditions, it can have a major impact on runoff variability at event scales, and in this way affect streamflow variability at all time scales and states [37]. At shorter time scales, for example, the seasonal water balance has been shown to control the middle part of the flow duration curve and thereby forms the connection between high flows and low flows [344, 347, 349]. Over longer time scales, the seasonal water balance leaves an imprint not only on the annual water balance and inter-annual variability, but is also reflected in the vegetation types that become established [281], and more generally, in ecosystem productivity [123, 246]. Consequently, the seasonal water balance behavior may provide ecohydrological insights into regional patterns of climate-soil-vegetation dynamics and help to delineate regions with fundamentally different hydrologic regimes [251].
The aim of this paper is to develop a similarity framework to characterize seasonal water balance behavior, specifically including storage variations as well as the more general seasonal streamflow variations. The development of such a similarity framework, and the testing of hypotheses regarding the central role of the seasonal water balance in streamflow variability at all time scales, can provide deep insights that may enable parsimonious descriptions of catchment rainfall-runoff responses [145, 184], and achieve generalizations beyond individual catchments [80, 271]. The focus of the study is not necessarily to seek more detailed physically based understanding of individual processes, but to generate broader insights into the nature of streamflow variability at a holistic level through the development of an organized hydrological perspective [158] based on a synthesis of what is already known and built into standard conceptual models of 37
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
catchment response. In this paper, we use rainfall-runoff data from over 300 catchments across the U.S., and through a combination of data analysis and conceptual rainfall-runoff modeling we aim to: (i) bring out the diversity of the seasonal water balance of catchments located across the continent, (ii) develop a framework to characterize similarity and differences of seasonal water balance behavior amongst these catchments, (iii) use this framework to group the observed seasonal water balances into clusters exhibiting similar behavior, and (iv) test and elucidate the central role of the seasonal water balance in underpinning and linking several signatures of streamflow variability across a wide range of time scales and system states. This study may be considered as an extension and also a synthesis of the previous work of Kennard et al. [154], Sawicz et al. [260], Coopersmith et al. [52], and Ye et al. [347]. Sawicz et al. [260] used a Bayesian clustering scheme to group 280 U.S. catchments into nine homogeneous, hydrologically similar classes on the basis of a combination of six streamflow signatures. Kennard et al. [154] also used Bayesian clustering scheme and hydrological signatures to obtain hydrologically coherent clusters in Australia. Coopersmith et al. [52] developed a classification system to group a large and diverse population of catchments within the U.S. into homogeneous groups of similar seasonal streamflow variations. Ye et al. [347] explored the dominant process controls of seasonal water balance in different parts of the U.S. through the use of a top-down modeling approach. In this paper, we extend the work of Coopersmith et al. [52] and Ye et al. [347] to arrive at a process-based similarity framework that includes the components of the seasonal water balance, including (model-predicted) seasonal variations of storage. The development of the similarity framework based on the seasonal water balance allows the clustering of similar catchments, supported by a deeper understanding of what makes these catchments similar. Consequently, the proposed delineation of hydrologically similar clusters extends from a purely empirical study [52, 154, 260], or a modeling study [347], to one based on holistic process understanding.
3.2 3.2.1
Methods Constructing the seasonal water balances
Through the use of a conceptual and parsimonious rainfall-runoff model, we reconstruct seasonal water balances of some 372 catchments located across the entire U.S. These catchments, which belong to the Model Parameter Estimation Experiment (MOPEX) data set [67, 261], span a wide diversity of climatic and physiographic characteristics and range in size from 67 to 10,329 km2 . Precipitation, temperature, potential evaporation, and streamflow are all available on a daily basis. Perennial snow cover is absent for most catchments and does not exceed 3% of the surface area for individual catchments [26]. The MOPEX catchments are characterized by limited 38
3.2. METHODS
human influence [261], which allows this study to focus on natural variability. The impact of anthropogenic factors, such as dams, is considered beyond the scope of this study. Storage and evaporation components of the seasonal water balance are obtained through the implementation of the previously published FLEX I water balance model [87], now expanded with the snow module. The model is of a lumped conceptual type and consists of stores representing the saturated and unsaturated soil zones, canopy interception and snow, and a surface store representing fast flow. Figure 3.1 presents the structure of the extended FLEX I model used here and Table 3.1 provides the coupled set of water balance equations included in the model, the associated constitutive relationships, and the definitions of the parameters.
Table 3.1: Water balance equations for the various stores, constitutive relationships and description of symbols. We refer to Figure 3.1 for the model structure and the organization of the stores. Water balance equation
Constitutive relationships
Description symbols
dS c = Rc − Pc dt
R c = P , if T ≤ T crit
β = shape parameter [-] E IR = interception evaporation [L/T] E p = potential evaporation [L/T] EU R = unsaturated zone evaporation [L/T]
P c = min(max(T − T crit , 0) · f dd , S c /∆T dS i = R i − E IR dt
E IR = min(E p , S i /∆T )
D = partitioning coefficient [-] f dd = degree-day factor [L/T2 ] I r = storage capacity interception res. [L] K f = timescale fast reservoir [1/T] K s = timescale groundwater reservoir [1/T] L p = evaporation threshold [-]
P i = min(S i − I r , 0)/∆T R i = P ; if T > T crit dS u = R u − EU R dt
C r = 1 + exp
−
−1 Su +1 S uc 2 β
P = precipitation [L/T] P i = precipitation excess interception [L/T] P m = max. percolation rate [L/T] R i = recharge interception reservoir [L/T] R c = recharge snow reservoir [L/T] R f = recharge fast reservoir [L/T]
Pe = Pi + Pc R u = (1 − C r ) · P e EU R = (E p − E IR ) · (1, SS L1 ) uc p
R s = recharge groundwater reservoir [L/T] R u = recharge unsaturated reservoir [L/T]
dS s = R s − EQ s dt
R S = (P e − R u ) · D + P m · (S u /S uc ) Q s = S s /K s
dS f = R f − EQ dt f
S c = snow reservoir storage [L] S i = interception storage [L] S u = unsaturated reservoir storage [L] S s = groundwater reservoir storage [L] S f = fast reservoir storage [L]
R f = (P e − R u ) · (1 − D )
S uc = storage capacity unsaturated reservoir [L] t = time [days] T = temperature [ o C] T crit = threshold temperature [ o C] Q f = discharge fast reservoir [L/T] Q s = discharge groundwater reservoir [L/T]
Q f = S s /K f
The model is calibrated in each of the 372 catchments using the MOSCEM-UA algorithm [320] with 10,000 iterations. The model is calibrated for the period 1972-1977 using as objective functions the Nash-Sutcliffe efficiency of the flow duration curve and the Nash-Sutcliffe efficiency of the logarithm of the flow. Because of the focus on seasonal water balance, the parameter sets with the best Nash-Sutcliffe fit to the observed regime curves (45 day moving average mean within-year variation of streamflow) for the 10 year period (1972-1982) are selected for further 39
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Figure 3.1: Structure of the extended FLEX I conceptual rainfall-runoff model used in this study (adapted from Fenicia et al. [87]). This model structure should be evaluated in conjunction with the model governing equations presented in Table 3.1. The model consists of five coupled stores representing snow (C R ), vegetation interception (I R ), unsaturated zone (UR ), saturated groundwater (S R ), and a store representing fast runoff (FR ).
analysis. The 45 day time window is chosen to filter out most of the short-term and inter-annual variability of the observed hydrographs, but preserve most of the distinct seasonal behavior. For longer time periods, shorter time windows have been used to construct the regime curve [e.g. 347]. Similar time windows provide noisy seasonal hydrographs when only 10 years of data are used. Most of the catchments produce a relatively smooth regime curve using the 45 day window that we have used. Of the 372 catchments, 51 catchments for which the Nash-Sutcliffe efficiency of the regime curves are smaller than 0.80 are removed from further consideration, in order to eliminate unrealistic and uncertain seasonal patterns. Figure 3.2 displays three examples of simulated and measured seasonal discharge regimes and associated Nash-Sutcliffe efficiencies (NS). The examples represent a good and clearly acceptable regime fit (NS = 0.95), a marginally acceptable regime fit (NS = 0.81), and a catchment with a poor fit, which was therefore rejected from any further consideration (NS = 0.54). In general, catchments in the agricultural mid west and in the relatively more arid zones have poorer model performances, and are the ones removed from contention. At the multi-annual scale, because carry-over of soil water and frozen water storage over several years can be assumed negligible, especially when the water year is used, 40
3.2. METHODS
calibrated model predictions of evaporation can be deemed accurate enough. On the other hand, although no storage or evaporation measurements are available to validate model predicted within-year variations of storage and evaporation, the spatial variations of seasonal water storage change between the months appear, to first order, to be in line with results of earlier studies [112]. Clearly, the outcomes of this paper will rely critically on the performance and robustness of the model predictions, and for this reason, they can be considered a plausible hypothesis that can continue to be refined in the future with further refinements to the model, improved estimation of parameters, and through conditioning with independent measurements, such as evaporation rates from flux towers, up-scaled to catchment scale [294] and water storage variations from satellite gravimetry [177].
Figure 3.2: Three examples of simulated and measured seasonal discharge regimes and associated Nash-Sutcliffe efficiencies (NS). The catchments on the left and middle have been accepted for further study (NS > 0.80). The discharge regime on the right is one of the 51 eliminated catchments because the model predictions had an unacceptable fit with the observed data (NS < 0.80).
With the available data and the internal dynamics simulated by the model, we characterize the first-order seasonal water balance dynamics of the remaining 321 catchments: how much water is stored and what part is released, using the 10 year mean of the 45 day moving average of a simple mean seasonal water balance equation: (3.1)
dS u dS s + = Pn + Ps − Q − E dt dt
Where P n stands for rainfall (mm/d), P s for snowmelt (mm/d), Q for river discharge (mm/d), E for evaporation (mm/d), S u for storage in the unsaturated zone and groundwater reservoir (mm), S s for storage in the snow reservoir (mm) and t for time (d). In addition, we also define the water deficit D (mm/d), which is the difference between potential evaporation, E p , and actual evaporation, E. Evaporation is a lumped flux combining all evaporative processes, including interception, soil evaporation, and transpiration. Combined storage in the unsaturated zone and in the groundwater reservoir is expressed as a relative storage of the catchment compared to the value on the first of January, which is fixed arbitrarily at 150 (mm) to allow intercomparison of 41
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
catchment storage variations. Note that the model outcomes are solely used for the construction of seasonal water balances for the purpose of formation of clusters of similar catchments; the analysis of other signatures of streamflow variability will be based on measured streamflow data, not model predictions. The reconstruction of Equation 3.1, through the use of multiyear model simulations, thus leads to the quantification of seven components of the mean seasonal water balance: P n ; Q; P s ; S s ; E; S u g ; D; as defined above. The mean within-year variations of these seven components will be the basis for defining similarity of seasonal water balances.
3.2.2
Constructing a similarity framework and forming coherent clusters
Upon completion of the modeling and the quantification of the mean seasonal water balance for each of the catchments as per Equation 3.1, the next tasks, using these model outputs, are the organization of these catchments into coherent groups on the basis of seasonal water balance similarity, followed by the identification of key physical controls of the seasonal water balance, to underpin the development of a quantitative similarity framework. These key tasks are undertaken in several steps. First, all the individual seasonal water balances are presented on a national map. This map is used to visually explore the presence of coherent patterns in the seasonal water balances, and to compare these to results of previous classification studies [e.g. 52, 229, 347]. Guided by the previous studies and the characteristics of the clusters formed here, we look for climatic variables that may govern broad-scale patterns of the seasonal water balance dynamics. We then test the ability of several hydroclimatic indices (see later for details) governing both annual and seasonal water balances that have been previously proposed, i.e., by Budyko [45] and by Woods [341], to distinguish between classes of seasonal water balance behavior generated by the model. Finally, we experiment with variations of cluster boundaries through different combinations of the hydroclimatic indices and in this way form 10 hydrologically coherent clusters. This is done manually in an iterative manner until catchment clusters are formed that satisfy the key criteria of similarity within cluster (minimum within-cluster variance) and differences between (maximum between-cluster variance). The variance measure used here is the RMSE-observations standard deviation ratio [205].
3.2.3
Comparison of streamflow signatures at a range of time scales
Using the clusters formed on the basis of the seasonal water balance, we subsequently investigate if and how the seasonal water balance is related to, underpins, or explains other streamflow signatures, looking for evidence of within-cluster similarity and between-cluster variability. These signatures reflect the functioning of catchments over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). The signatures considered are the flow duration curve, the flood frequency and growth curves, the low flow frequency curve and decline 42
3.3. RESULTS
curve, the base flow index, the rising limb density, the annual streamflow and inter-annual variability, and the long-term water balance in the context of the Budyko hypothesis [45]. Note that these signatures are not explicitly accounted for in the previous clustering analysis but, together as a group, can be considered composite measures of the overall hydrologic functioning of the catchments [260]. Note again that this comparative analysis of the various signatures is performed using actual streamflow observations, not model predictions.
3.3 3.3.1
Results Regional patterns of the seasonal water balance
We begin with a presentation of the diversity of the mean seasonal water balances across the U.S., as predicted by the model. For illustration purposes, we present in Figure 3.3 the mean seasonal water balance regimes for just 17 selected catchments, distributed across the country. The remainder of the 321 catchments not displayed (purely due to space limitations) can be considered, with a few exceptions, as interpolations between the chosen 17 catchments. The inset at the bottom left corner and the caption illustrates the kind of information that is used to describe the seasonal water balance regime. These include: the main input to the system (rainfall+snowmelt: red line), potential evaporation (dashed black line), snow storage (blue line), and soil water storage (bold black line). The magnitude of actual evaporation is represented by the size of the dark blue shading, and the magnitude of streamflow is represented by the size of the green shading. Note that all of the quantities presented above are ensemble means, over the 10 years of model simulation. Also note that the soil water storage is a relative magnitude, set to 150 (mm) on 1 January. We now use this template to interpret physically the mean seasonal water balance regimes for the 17 chosen catchments, in order to gain insights into the nature of variability across the continental U.S. In the western part of the U.S., the catchments have a seasonal precipitation regime, with the peak of precipitation during winter (out of phase with potential evaporation). Consequently, these catchments have a large storage variation over the year. High winter precipitation is partially stored and released later and hence streamflow is seasonal. In the Pacific Northwest, the water deficit (the difference between potential and actual evaporation) is only present during the months with low precipitation and additionally, there is a significant influence of snow. In central and southern California, the aridity index is higher and the seasonality of streamflow is also stronger, and significant discharge is only observed during the winter period. In arid catchments, streams may fall dry during summer and have a large water deficit throughout most of the year.
43
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Moving east, the mountainous catchments in the Rocky Mountains, Cascade Range, and Sierra Nevada have a very distinct snow influence. Again aridity and water deficit increase when moving south, and are experienced throughout most of the year. Water availability and potential evaporation are more in phase, and snow accumulation on the surface and subsequent melt means less (and delayed) recharge to the soil below, leading to smaller soil water storage variation compared to the catchments in the western coastal states.
In the more arid catchments of the Great Plains, precipitation and evaporation are in phase, leading to very small storage variations and much smaller streamflows. In the interior lowlands east of the Great Plains, relatively small storage variation persists; however, catchments are less arid, leading to more streamflow. Overall, smaller storage fluctuations and reduced seasonal accumulation indicate that soil moisture storage is concentrated at the surface, and combined with random storm event occurrences, thus contributing to much temporal and spatial variability.
In the south-eastern part of the U.S., precipitation is seasonal. In Florida, a distinct increase in precipitation is observed during the summer months. A part of this water results in streamflow, but evaporation is high as well. Overall this increase in streamflow and evaporation does not match the precipitation and significant change in storage can be observed. In other south-eastern U.S. catchments, the presence of two small peaks in precipitation and lower precipitation during summer months leads to seasonality in discharge and significant storage variation. Catchments are relatively humid, and water deficit remains small during the summer months.
The eastern and north-eastern parts of the U.S. have relatively constant precipitation throughout the year, with a distinct increase of snow in the northern parts and parts of the Appalachian Mountains. These catchments do not have much water deficit, and the variation of water storage is relatively small. Discharge in Northern catchments is increasingly seasonal and out of phase with potential evaporation, but this is due to a combination of snowmelt and the phenology associated with deciduous forests [347].
The above assessment of seasonal water balance has highlighted several facets of the enormous variability seen across the continental U.S.: total runoff volume, seasonal flow regime, seasonal soil water storage regime, snow storage, and snowmelt. Preliminary assessment of the seasonal water balances of not just the 17 catchments, but all 321 catchments, indicate that, similar to Coopersmith et al. [52] and Ye et al. [347], spatial variations of climate seasonality and aridity underpin much of the wide diversity of the seasonal regimes exhibited by the MOPEX catchments. Aridity determines the partitioning of precipitation into evaporation and discharge. The timing of precipitation in relation to potential evaporation has a large impact on seasonal soil water storage and the discharge regime. Additionally, snowmelt and accumulation processes 44
3.3. RESULTS
Figure 3.3: Diversity of the seasonal water balance across the U.S. represented by 17 catchments. Most of the seasonal regimes that are not displayed can be considered an interpolation of the displayed ones. Note that all y-axes have the same scale.
provide a distinct streamflow peak and delay in soil water recharge in the mountainous catchments in the west. Vegetation phenology (which, like snow, is partly temperature driven [294]) contributes to the strong seasonality of streamflows in the north-east [347]. Overall, we identify the role of climate aridity, precipitation timing, snow, and phenology (also governed by temperature), as the primary controls of the seasonal water balances. Therefore, they are potential candidates to serve as quantitative indices to define similarity of seasonal water balances.
3.3.2
Similarity framework for seasonal water balance
On the basis of the assessment of the computed seasonal water balances, we propose three dimensionless indices that account for the key physical controls identified above: aridity, precipitation timing, and snowiness. To allow simple forms for these indices, we assume that the seasonal variability of precipitation, potential evaporation, and air temperature can be modelled as simple sine curves [25, 196, 234, 341]. This assumption holds well for most regions in the U.S., although catchments in the south and south-west of the U.S. may be exceptions. (3.2)
P(t) = P[1 + δP · sin(2π(t − s P )/τP )] 45
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
(3.3)
E p (t) = E p [1 + δE · sin(2π(t − s E )/τE )]
(3.4)
T(t) = T + ∆T · sin(2π(t − s T )/τT )
where t is the time (y), s is a phase shift (y), τ is the duration of the seasonal cycle (y), δ is a dimensionless seasonal amplitude, ∆ is the seasonal amplitude, and the subscripts T, P, E p stand for temperature, precipitation and potential evaporation (mm/d) . Duration τ of the seasonal cycle is one year (τT = τE = τP ). P(t) is the precipitation rate (mm/d) as a function of t, with the time-averaged mean value P. E(t) is the potential evaporation rate (mm/d) at as a function of t, with the time-averaged mean value E p . The temperature, T(t), has a time-averaged mean value T ( o C), and seasonal amplitude ∆T ( o C). Using a least squares optimisation we obtain the parameters of Equations 3.2, 3.3 and 3.4. Using these equations we adopt simple expressions for the seasonality and timing precipitation, the aridity, and the fraction of precipitation fallen as snow. From these equations, we adopt simple expressions for the seasonality and timing of precipitation, the aridity, and the fraction of precipitation falling as snow. With the variables presented in Equations (3.2, 3.3 and 3.4), we now define three dimensionless similarity indices, whose ability to characterize the similarity of seasonal water balances will be tested subsequently.
Figure 3.4: The proposed framework consisting of three hydroclimatic indices. δP expresses the seasonality and timing of precipitation, f s the fraction of precipitation falling as snow, and φ the aridity index. The figure includes descriptions of how key processes of the seasonal water balance change as a function of the indices.
46
3.3. RESULTS
3.3.2.1
Seasonality and timing of precipitation
The similarity index governing the seasonality and timing of precipitation is defined as [341]: δ∗P = δP · sgn(∆T ) · cos(2π(s p − s T )/τ)
(3.5)
The dimensionless variable δ∗P summarises if precipitation is seasonal, and if the precipitation is in phase with the potential evaporation and temperature regime (s E ≈ s T ). δ∗P can range from -1 to 1, and expresses the following scenario’s: • δ∗P = -1, for strongly winter-dominant precipitation. • δ∗P = 0, for uniform precipitation. • δ∗P = +1, for strongly summer-dominant precipitation. 3.3.2.2
Fraction of precipitation falling as snow
The fraction of precipitation falling as snow is the second similarity index. This fraction is both a function of temperature and δ∗P , and is approximated by Woods [341] as: f s (T
(3.6)
∗
∗
, δ∗P ) =
∗ 1 sin−1 (T ) δ p − − 2 π π
q
1−T
∗2
∗
where T is a dimensionless measure of the mean temperature: ∗
T =
(3.7)
T − T0 |∆ T |
where T0 is the critical temperature below which precipitation falls as snow, set at 1 o C. 3.3.2.3
Aridity index
The dimensionless aridity index is defined by Budyko as: (3.8)
φ=
Ep P
where E p is the mean potential evaporation rate (mm/d) and P is the mean precipitation rate (mm/d), where the mean is estimated over many years. φ can range from 0 to (in theory) infinity. 3.3.2.4
Overview of the similarity framework
The three proposed hydro-climatic indices (δ∗P , f s , φ) span a three-dimensional space, which is presumed to accommodate most of the spatial variability in the observed seasonal water balances. Figure 3.4 displays the framework, including a qualitative description of how some of the key components of the seasonal water balance change due to gradients in the proposed indices. To 47
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
first order, the aridity index determines the long-term partitioning of incoming precipitation into streamflow and evaporation. The timing and seasonality of precipitation, in relation to those of potential evaporation, determines not only the within-year variation of streamflow, but also rates of accumulation and subsequent release of soil moisture and groundwater storage. An increased fraction of precipitation falling as snow contributes to the accumulation of snow during the cold winter period, a delay in contributions to soil moisture and recharge to groundwater, and the subsequent melting during spring, which contributes to higher delayed streamflows during this time of the year. In the east and north-east, a high value of f s also coincides with the presence of deciduous vegetation, which responds to the wide variations of temperature through large changes of phenology: dropping of leaves and minimal evaporation during winter and greening up and vigorous evaporation during spring and summer.
Figure 3.5: The values of the hydro-climatic indices δ∗P (measure of precipitation timing with respect to potential evaporation), f s (snowiness, fraction of total annual precipitation that falls as snow), and φ (aridity index, ratio of annual potential evaporation to annual precipitation) for the 321 study catchment catchments.
The spatial distributions of δP , f s , φ are displayed in Figure 3.5. Each of the three indices exhibits distinct regional patterns, generally independent of each other. Most of the catchments 48
3.3. RESULTS
in the east and in the north-west tend to be generally humid, with low values of the aridity index, φ, whereas catchments in the midsection of the continent as well as in the south-west are generally semiarid to arid with higher values of φ. In the case of precipitation timing, catchments in the east tend to have low precipitation seasonality with values of δ∗P in the range [-0.4, 0.4], whereas the catchments in the midsection of the continent (Great Plains, Central Plains) exhibit in-phase seasonality with δ∗P values approaching 1.0, and catchments in the west exhibit strong out of-phase seasonality with δ∗P values approaching 1.0. Finally, the patterns of f s show that catchments in the north-east and mountainous catchments along the Rockies, Cascade Range and Sierra Nevada have snowfalls exceeding 50%, whereas most of the rest of the catchments have lower to negligible snowfall as a fraction of total precipitation. The ability of these three independent hydro-climate indices to characterize the similarity and differences of the computed seasonal water balances of the 321 study catchments is explored next.
3.3.3
Grouping of catchments into coherent clusters
The objective here is to group the 321 study catchments into a small number of hydrologically coherent clusters on the basis of the seven components of the mean seasonal water balance, namely, P n ;Q; P s ; S s ; E a ; S u ; and D. In this study, the grouping is done manually through a trial and error procedure based initially on visual observations, which is then refined by an iterative procedure. This is achieved by progressively adjusting the boundaries between the resulting clusters in terms of the three climatic similarity indices defined before, through the application of objective criteria (minimum within-cluster variance and maximum between-cluster variance). Here only the results relating to the final cluster configurations are presented. Figure 3.6 presents the seasonal variations of these same seven components for catchments belonging to each of the resulting final 10 catchment clusters. Regimes of individual catchments are displayed using thin lines, while the average value within the cluster is presented using a thicker black line. These displays can already be used to visually assess the degree to which these seven components of seasonal water balance show similarity and differences, both within and between the clusters. There is much that can be learned from Figure 3.6 about the richness of seasonal water balances across the U.S.: not only the differences between the clusters, but in some cases even the variability within some of the clusters themselves. One way to frame this discussion is to chart how the variability in the precipitation propagates through the catchments and ends up in the observed streamflow variability. First row of Figure 3.6 shows that there is considerable variation in the seasonal precipitation regime between the clusters: from a large snowmelt component (B1, B2), out-of-phase seasonality of P with E p (A1, A2, and A3), in-phase seasonality (C1, C2), mild to no seasonality (D2, D3) to mild out-of-phase seasonality (D1). These propagate to wide variations in the snow and soil water storage and streamflow. In B1 and B2, snow storage is more dominant than soil water storage, and spring snowmelt dominates 49
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
streamflow. A1, A2, and A3 experience large seasonal soil water storage variations, and winter flows dominate streamflow. Due to in-phase seasonality, the range of seasonal soil water storage is very low in C1 and C2, and streamflow is mildly seasonal with dominant winter flows. There is also considerable within-cluster variability in C1 and C2 compared to the more western clusters, perhaps pointing to the dominance of local, event-scale responses, and potentially also caused by differences in soils, or land cover and land management in these major agricultural regions. Clusters D2 and D3 show that the slightly (or no) in-phase seasonality of precipitation is transformed to strong out-of-phase seasonality of streamflow. This is a combined result of snowiness and a strong impact of vegetation phenology. Finally, D1 represents a more straightforward transformation from out-of-phase precipitation to out-of phase seasonality of streamflow. In spite of these large variations across the continent, the seasonal regimes of actual evaporation show considerable similarity in both shape and magnitude amongst all clusters, less so for the dry catchments (e.g., A2, A3). This is interesting, considering that the clusters cover a broad range of climates and landscape properties, including vegetation. Granted, this is a model predicted result, yet these rates when aggregated to the annual time scale are still correct, because the model is calibrated against observed streamflows. This comes across as an emergent pattern, and raises the question as to whether any of this can be explained by adaptation of the catchment (and vegetation) with climate. This calls for further detailed study, with the use of not only measured evaporation rates in different parts of the continent but also estimates of vegetation cover and net primary productivity, guided by large-scale theories governing long-term water balances and vegetation behavior, including the Budyko and Horton Hypotheses [45, 303]. Even though visual inspection of the results presented in Figure 3.6 indicate remarkable similarity within, and significant differences between, the 10 catchment clusters, can this be objectively confirmed? In order to assess this quantitatively, we estimated the RMSE-observations standard deviation ratio (abbreviated as RSR) [205] for the seven different components of the seasonal water balance (P n ;Q; P s ; S s ; E a ; S u ; D) of individual catchments, compared to the mean regimes of that component of a certain cluster, given by:
(3.9)
K RSR M
P365 q
m,n
(X i − Yim )2 1 1 i =1 = = q n n=1 7 m=1 P365 (X m,n − Y m )2 N X
7 X
i =1
i
where n is the catchment under consideration, N is the number of catchments present in that cluster, M is the cluster under consideration (M = 1 : 10; A1, A2, A3, B1, B2, C1, C2, D1, D2, D3), K is the cluster to which a catchment from cluster M is compared (K = 1 : 10; A1, A2, A3, B1, B2, C1, C2, D1, D2, D3), m is the regime of consideration (m = 1 : 7; P n ;Q; P s ; S s ; E a ; S u ; D), i is the day of year (i = 1 : 365), X nm i is the value of the regime m from catchment n on day i from cluster M, Yim is the mean of the N regime curves from cluster K and Y m is the mean K value of Yim . The resulting RSR M is a measure of how large is the average variance between
50
3.3. RESULTS
Figure 3.6: Overview of the fluxes and storage regimes of the 10-catchment clusters. Regimes included are (first row) the precipitation, (second row) streamflow, (third row) snowmelt, (fourth row) snow storage, (fifth row) evaporation, (sixth row) storage, and (seventh row) deficit. The thin coloured-lines display values of the individual catchments. The thicker black lines display the within-cluster average values. (Note that some values are not shown because they plot above the top of the vertical scale).
51
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
K cluster M and the mean of cluster K. Values of the RSR M for each of the 100 cluster pairs are K presented in Table 3.2. The results show that indeed the estimates of RSR M are the lowest along
the diagonal of Table 3.2, which represent the variance within, whereas the off-diagonal terms that represent variance between are all larger. This confirms that the 10 chosen clusters are indeed hydrologically coherent and possibly having distinct characteristics, both visually and objectively. Of course there is still considerable variability within some of the clusters. Likewise, K both visual inspection and the magnitudes of the off diagonal terms in the RSR M table show
that differences between the clusters D1, D2, and D3 are relatively small, even though they are still larger than the diagonal values. There is also a discrepancy in that D2 and D3 appear to be similar in terms of these metrics: both are affected by phenology and snow, yet to different degrees.
K Table 3.2: The RSR M values of the catchment clusters. The first row contains the M clusters K and the first column the K clusters. The results show that the estimates of RSR M are the lowest along the diagonal of the Table, which represent the variance within, whereas the off-diagonal terms that represent variance between are all larger.
A1 A2 A3 B1 B2 C1 C2 D1 D2 D3
A1 0.58 0.82 1.00 0.91 1.06 1.14 1.12 1.22 1.27 1.33
A2 0.88 0.65 0.80 0.94 1.22 1.31 1.53 1.07 1.49 1.52
A3 0.98 0.92 0.53 1.02 1.23 1.68 1.34 1.01 1.17 1.17
B1 0.88 0.81 1.11 0.39 0.98 1.63 1.41 1.33 1.56 1.78
B2 0.98 0.94 1.08 0.72 0.52 1.17 1.28 1.17 1.37 1.42
C1 0.92 0.93 0.95 0.92 0.97 0.75 0.82 0.96 0.91 0.87
C2 0.89 0.91 1.01 0.88 0.95 0.95 0.58 0.88 0.8 0.82
D1 0.82 0.85 0.91 0.89 1.05 1.07 1.00 0.54 0.87 0.96
D2 0.85 0.87 0.96 0.90 1.02 0.99 0.82 0.69 0.55 0.65
D3 0.87 0.91 0.99 0.90 1.01 0.97 0.8 0.75 0.64 0.53
In order to place the 10 catchment clusters within the similarity framework proposed above, based on the three similarity indices, δ∗P , f s , φ, as part of the clustering procedure, we determined the combinations of the ranges of values of (δ∗P , f s , φ) that apply to each of the 10 distinct clusters. These are presented in Table 3.3, which also contains a brief description of the nature of the within-cluster seasonal water balance, including, in each case, our initial interpretation of the dominant feature that controls the seasonal patterns of hydrological response. Figure 3.7 shows the geographic spread and organization of the 10 catchment clusters obtained in this way; they exhibit remarkable spatial coherence. Figure 3.7 also displays the ranges of the climatic similarity indices (δ∗P , f s , φ) that delineate the clusters, which emphasizes the role of seasonal climate in underpinning the seasonal water balances and associated dominant processes, regardless of landscape properties.
Having established the coherence and geographic location of the 10 chosen clusters and their 52
3.3. RESULTS
Figure 3.7: The organization of the 321 MOPEX study catchments into 10 hydrologically similar catchment clusters. The dotted boxes contain the description of the catchment classes, index ranges δ∗P , f s , φ, and the hydroclimatic character. Arrows describe changes in the hydroclimatic controls.
connection to the three climatic indices, we next explore whether the locations and geographic spread of the clusters are mirrored in any on-ground features. Figure 3.8 presents the wellestablished ecosystem regions, soil orders, and locations of broad-scale plant formations across the continental U.S., in each case overlain by the locations of the 321 catchments and the clusters to which they belong. The results show a remarkable match between the locations and regional spread of the catchment clusters and the physiographic regions and plant formations, which not only supports the notion that the formation of local soils and vegetation is climate dependent, but also that vegetation and soils both contribute to and are a reflection of the seasonal water balance regime. The dominant features attributed to each of the catchment clusters in Table 3.3, can thus be deemed as mechanisms through which vegetation and soils adapt to and modify the seasonal water balance in each case. It must also be noted that although MOPEX catchments are characterized by limited anthropogenic influences [261], some of the catchments in classes C1 and C2 are partly covered by cropland and pasture. 53
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Table 3.3: Characteristics of the 10-catchment clusters. The table contains the cluster name, amount of catchment of within-cluster catchments (n), the clusters-boundary conditions and associated minimum, average and maximum values within the clusters. Additionally a short description of the catchments is included. Cluster Vegetation Ecoregion
Soil order Dominant process n δ∗ P
Observed fs Observed φ
Observed Description
Cluster Vegetation
A1 Coniferous Marine mountains/ Mediterranean regime mountains Andisols, inceptisols Seasonal soil water storage 9 -1/-0.4 -0.99/-0.83/-0.59 0/0.45 0/0.25/0.44 0.35/0.75 0.36/0.41/0.64 Humid catchments where precipitation and evaporation are out of phase. Consequently large soil water and streamflow variations occur and streamflow is perennial.
A2 Coniferous /Shrubs Mediterranean regime mountains
A3 Shrubs Mediterranean regime mountains
B1 Coniferous Temperate steppe regime mountains
B2 Coniferous Temperate steppe regime mountains
Alfisols, inceptisols Seasonal soil water storage 5 -1/-0.4 -0.99/-0.94/-0.90 0/0.45 0/0.12/0.38 0.75/1.75 0.76/1.00/1.54 Semi-arid catchments where precipitation and evaporation are out of phase. Consequently large soil water and streamflow variations occur and streamflow can be perennial or intermittent. C2 Short grass prairie
Mollisols Seasonal soil water storage 7 -1/-0.4 -0.99/-0.83/-0.68 0/0.45 0/0.15/0.41 1.75/5 1.83/2.60/4.10 Arid catchments where precipitation and temperature are out of phase. Consequently soil water and streamflow variations occur and streamflow can be intermittent.
Andisols Snow storage
Entisols, inceptisols Snow storage
6 -1/0 -0.90/-0.63/-0.35 0.45/1 0.52/0.56/0.59 0.4/0.75 0.42/0.57/0.73 Mountainous humid catchments where snow storage causes a delay in the streamflow and soil water recharge peak. Catchments have perennial stream flow
13 -1/0 -0.99/-0.39/-0.02 0.45/1 0.46/0.54/0.69 0.75/1.75 0.83/1.32/1.74 Mountainous semiarid catchments where snow storage causes a delay in the streamflow and soil water recharge peak. Catchments have perennial stream flow
D1 Mixed deciduous coniferous
D2 Deciduous
D3 Deciduous
Steppe
Subtropical
Hot continental (Mountains) Alfisols/ Inceptisols/ Spodosoils Phenology
Warm continental (Mountains) Aridisols
Ecoregion
C1 Some short grass prairie, but mainly long grass prairie Prairie
Soil order
Mollisols
Mollisols/ Utisols
Alfisols
Dominant process
Event scale response
Event scale response
Soil water storage
n δ∗p
48 0/1 0.02/0.47/0.73 0/0.25 0/0/14/0.21 0.9/1.5 0.91/1.13/1.43 Semi-arid catchments where precipitation and evaporation are in phase. Streamflow and storage variations of both soil water and snow are small. Streams may fall dry but can be perennial
30 0/1 0.15/0.56/0.90 0/0.25 0/0.07/0.17 1.5/5.3 1.56/2.38/5.29 Arid catchments where precipitation and evaporation are in phase. Seasonal streamflow and storage variations of both soil water and snow are very small. Streams are intermittent
69 -0.4/0.3 -0.26/-0.03/0.21 0/0 0/0/0 0.5/0.9 0.53/0.68/0.71 Humid catchments where precipitation and evaporation are slightly out of phase. Catchment have soil water storage variations and a slightly seasonal streamflow regime with low flows during summer
Observed fs Observed φ
Observed Description
54
83 -0.1/0.3 -0.07/0.17/0.28 >0/0.20 0.02/0.12/0.20 0.5/0.9 0.51/0.74/0.90 Humid catchments where precipitation and evaporation are slightly in phase. Catchments have small soil water storage variations and a fairly constant seasonal streamflow regime.
Phenology and snow storage 51 -0.1/0.4 -0.01/0.25/0.39 0.2/0.45 0.20/0.25/0.39 0.4/0.9 0.46/0.64/0.89 Humid catchments where precipitation and evaporation are slightly in phase. Catchments have soil water and snow storage variations with a soil water and streamflow increase in spring.
3.3. RESULTS
3.3.4
Connection to similarity of streamflow signatures
Now that we have formed coherent clusters of catchments based on the seasonal water balance, each with distinct dominant seasonal processes, we explore their possible imprint on signatures of streamflow variability at a range of time scales. The variability of each signature within and between the clusters is examined, including any connections between these various signatures and aspects of the seasonal water balance. Note again that these signatures are derived directly from streamflow observations and not model predictions. The results are presented in descending order of time scales (annual, seasonal, daily), and extreme states (floods and low flows). While one would expect to see the manifestation of only the net effects of seasonality at the annual scale, the nature of climate seasonality can be expected to be explicitly manifested in streamflow variability at the seasonal scale. On the other hand, not all local (spatial) or short time scale variability can be accommodated in mean seasonal water balance behavior, and therefore is likely to show up as additional variability or noise. 3.3.4.1
Mean annual water balance and inter-annual variability of streamflow
Figure 3.9 presents (top) the mean annual runoff ratio, and (middle) the coefficient of variation (CV ) of the annual runoff ratio, i.e., the standard deviation of the annual runoff ratio divided by the mean runoff ratio. Note that clusters are organized here from the left to the right through a combination of aridity and seasonality (wet-dry-wet, out-of-phase, in-phase, no seasonality), in order to capture the gradient in dominant processes (and therefore, the order is different from what appears in Figures 3.6 and 3.11). Due to this organization, the results in Figure 3.9 (top) indicate that the mean annual runoff ratio initially decreases from the left to the right, hitting a minimum for cluster C2, and then increasing again toward the right. Correspondingly, the mean CV of annual runoff ratio shows an opposite trend: initially increasing from the left to the right and then decreasing again. These changing but consistent patterns between the clusters are mostly due to change in aridity: clusters A3 and C2 (both arid regions) exhibit the smallest mean annual runoff ratio and largest mean CV . In addition, the within-cluster variability also exhibits the same or similar pattern as the mean CV : it first increases from left to right, and then decreases. Clusters A3 and C2 both exhibit the largest within-cluster variability. These trends are a consequence of a combination of aridity and intra-annual variability of precipitation timing, and the presence or absence of snow. To separate the effects of aridity, precipitation timing, and snow, we present in Figure 3.9 (bottom) the mean annual water balances of the study catchments on the Budyko curve [45] as a function of the aridity index, but organized by cluster. The results in Figure 3.9 (bottom) shows that the mean annual water balances of individual catchments do indeed fall around the Budyko curve, but with large deviations. There is considerable organization to this scatter, however, in terms of the positions of the various clusters. Similar to previous studies [130], we find that 55
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
timing of precipitation does have an impact on mean annual water balance. While clusters C1, D1, and D2 fall right on the Budyko curve or close to it, clusters A1, A2, A3, B1, B2, and D3 fall away (below) from the Budyko curve, producing more runoff (to different degrees) than predicted by Budyko. Differences between D1, D2, and D3 are due to differences in phenology and snowiness. Deviations from the Budyko curve are greatest for the mountainous clusters B1 and B2. In other words, the presence of snow increases annual runoff, (i.e., B1; B2: f s > 0 : 45; D3: f s > 0.2) which is in line with the earlier findings [26]. The semiarid and arid clusters with seasonal precipitation and precipitation in phase with potential evaporation, i.e., C1; C2: φ > 0.9; δ∗P > 0 , have significantly less runoff (i.e., more evaporation) compared to Budyko’s prediction. This is in contrast to catchments with precipitation out of phase with potential evaporation, i.e., A1; A2; A3: δ∗P < −0.4, which generate slightly more runoff than predicted. 3.3.4.2
Base flow index and the rising limb density
The rising limb density is defined as the ratio of the number of rising limbs to the total length of time the hydrograph is rising [266]. A high rising limb density value indicates flashy hydrographs. The base flow index is the ratio of long-term base flow to total streamflow; in this case, the base flow is estimated from the observed streamflow hydrograph through the application of a low-pass filter [7, 318]. In a sense these are complementary features, the rising limb density is an indicator of frequency of fast flows, and base flow index is a measure of the importance of slow flows. We use the one-parameter single-pass digital filter method and associated parameters based on previous studies [e.g. 78, 260] to estimate the base flow index. Figure 3.10 displays the rising limb density and base flow index for the 10 catchment clusters. The base flow index is highest in the catchments dominated by snowmelt only (B1; B2: f s > 0.45) and lowest in the flat, semiarid, and arid catchments where small storage variability occurs C1; C2: φ > 0.9; δ∗P > 0.3. Catchments with a high rising limb density also have a low base flow index, and vice versa. Landscape controls play a vital role in determining both the base flow index and rising limb density, with strong differences between the mountainous catchments in the west and the flatter catchments in the mid west and the east. The results on the base flow index here agree with the regional patterns presented in Beck et al. [16]. 3.3.4.3
Seasonal flow regime and Parde coefficient
Figure 3.11 presents several signatures of variability at a range of time scales, from seasonal to daily, including floods and low flows. Figure 3.11 (first row) displays the Parde coefficients [222] that express the non-dimensionalized seasonal flow regime of the catchments. The catchments with most precipitation falling as snow (B1; B2: f s > 0.45) have a distinct streamflow peak during spring. Arid and semiarid catchments, with precipitation and potential evaporation in phase, C1; C2: φ > 0.9; δ∗P > 0, have the greatest within-class variability of flow regimes. Maximum flow in many catchments occurs in different winter or spring months, but for the arid catchments of C2, 56
3.3. RESULTS
Figure 3.8: The organization of the ecosystem regions, main plant formations, and soil orders across the U.S. overlain by the locations of catchments belonging to the 10 catchment clusters.
this peak in some cases observed during summer as well. This is not surprising, given the high variability of the precipitation regime shown in Figure 3.6, for these clusters. For catchments where precipitation and evaporation are out of phase (A1; A2; A3: δ∗P < 0.3) the streamflow is highly seasonal (mostly winter flows), with the seasonal variability becoming increasingly skewed with increasing aridity. The seasonal flow regimes of clusters D1, D2, D3 are relatively similar, but for different reasons. The seasonal patterns of D1 simply reflect the precipitation pattern (which is mildly seasonal and out of phase with potential evaporation), whereas the seasonal flow regimes of D2 and D3 are more a reflection of vegetation phenology and snow storage. Overall, one can see that there is a clear imprint of the seasonal water balance in the Parde coefficients, which is to be expected. 3.3.4.4
The flow duration curve
The flow duration curve (FDC) is a representation of the frequency distribution of streamflow defined for a specific time step, usually daily [317]. Figure 3.11 (second row) presents the FDCs 57
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Figure 3.9: (top) The annual runoff ratio, (middle) the coefficient of variation of the annual runoff ratio, (bottom) and the long-term water balances presented in context of the Budyko Hypothesis for the 10-catchment clusters.
58
3.3. RESULTS
for individual catchments (thin lines) and the average value within the cluster (thicker black line) for the daily discharge values. Note that the FDC is a frequency domain representation of daily flow variability, and the timing of flow is lost during its presentation. Nevertheless, in most of the clusters, a clear imprint of the seasonal water balance is still present in the FDCs. The catchments with most precipitation falling as snow (B1; B2: f s > 0.45) show compact FDCs with a distinct inflection point. This inflection represents the differences between the period in spring when the winter snowpack is melting and the rest of the year. Arid and semiarid catchments, with precipitation and potential evaporation in phase, C1; C2: φ > 0.9; δ∗P > 0, may become dry during part of the year because there are marginal soil water storage variations that can buffer dry periods. These two clusters also show significant variability within the clusters, reflecting the seasonal variability of precipitation regimes (Figure 3.6) and flow regimes (Figure 3.11). In semiarid and arid catchments where precipitation and evaporation are out of phase, A2; A3: φ > 0.75; δ∗P < 0.3; the river dries out during the summer period because the soil water storage
recharged during winter and the winter snowpack cannot provide sufficient base flow for the entire arid summer period. Overall, several clusters show remarkable similarities of the FDCs, e.g., D1, D2, D3. Also, sometimes it is hard to distinguish the cluster to which a catchment may belong on the basis of the FDC alone. This equifinality is a consequence of the frequency domain representation of the FDCs: two different types of within-year variability can give rise to very similar FDCs, as shown previously by others [344]. Where there is considerable variability within clusters (e.g., C1, C2), the variability is probably due to the role of the landscape properties, as well as event-scale responses that are not captured by the similarity framework but which would require extension of the model to include additional sources of variability in climate and/or catchment characteristics.
3.3.4.5
Flood frequency curve and the flood growth curve
Figure 3.11 presents the growth curve (third row), the flood frequency curve (fourth row) and the timing of annual maximum flow (fifth row), using all available historical data, which in this case includes up to 54 years of daily flow data. Note that the flood growth curve is a plot of the ratio of annual maximum streamflow to the mean annual flood (linear scale) as a function of the Gumbel reduced variate. The flood frequency curve is the plot of the actual (non-normalized) annual maximum streamflow (in this case, presented at a logarithmic scale) also as a function of the Gumbel reduced variate. Note that the analysis of floods here has been carried out based on daily flows only, which has obvious limitations for flood frequency analysis. Nevertheless, both signatures are valuable indicators of the variability of extreme (annual maximum) flows. The results show significant similarity and differences between and within the clusters, and once again an imprint of the seasonal water balance can be seen in both signatures. For example, the growth curves for A1 and B1 show remarkable Extreme Value Type I (EV-I or Gumbel)-like behavior (straight line), whereas the arid clusters, (A3; C2), show more nonlinear, EV-II-like behavior, 59
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Figure 3.10: (top) The rising limb density and (bottom) base flow index values of the 10-catchment clusters displayed in whisker plots.
in line with the findings of Farquharson et al. [83]. Catchments with high snowfall, (B1; B2; f s > 0.45), show very low within-cluster variability, whereas the arid catchments belonging to A3 and C2 show increasing within-cluster variability with increasing return period. Of the remaining clusters, the humid catchments belonging to D1, D2, and D3 show a common, compact (and linear) behavior up to a threshold value of return period, after which there is substantial within-cluster variability. This suggests a mix of flood producing processes (rainfall or snowmelt driven) and a change of process with increasing return period, partly contributed to by seasonality. Absolute flood values show considerable between-cluster variability mainly reflecting the wetness of the catchments (a function of aridity), and considerable within-cluster variability for catchments with a high aridity and low seasonal variability, i.e., (C1; C2: φ > 0.9), but also for the more humid catchments D1, D2, and D3. Most clusters show strong seasonality in the timing of maximum flows, which is linked to the timing of maximum storage, although there is considerable variability between the clusters. Catchments in which storage variations are the smallest (C1, C2) also have the highest uncertainty in the timing of peak flows. 60
3.3. RESULTS
Figure 3.11: Overview of the various signature values of the 10-catchment clusters. Signatures included are (first row) the Parde coefficients, (second row) the flow duration curve, (third row) the flood growth curve, (fourth row) the flood frequency curve, (fifth row) the timing of annual maximum flows, (sixth row) the decline curve, (seventh row) the low flow frequency curve, and (eight row) the timing of the low flow occurrences. The thin colored-lines display values of the individual catchments. The thicker black lines display the within-cluster average values. 61
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
3.3.4.6
Low flow frequency curve and decline curve
Figure 3.11 presents the decline curve (sixth row), the low flow frequency curve (seventh row), and the timing of the minimum flows (eighth row). The decline curve expresses the annual minimum discharge of 15 consecutive days, as a fraction of the mean annual minimum discharge, as a function of the Gumbel reduced variate. On the other hand, the low flow frequency curve expresses the minimum discharge of 15 consecutive days as a function of the Gumbel reduced variate. Both curves are constructed using all available historical data per catchment. Figure 3.11 indicates that generally the between-year variability of low flows increases with climatic aridity. Catchments with high winter precipitation A1; A2; A3: δ∗P < 0.3 and snowmelt influence (B1; B2: f s > 0.45) have a low between-year variability of low flows, as both catchment types experience recharge of soil water storage before the summer period begins. Arid and semiarid catchments with precipitation and evaporation in phase (C1; C2: φ > 0.9; δ∗P > 0.3) fall dry during part of the year, because marginal soil water storage variations are unable to buffer dry periods. The timing of low flows also shows considerable variability between clusters, since seasonal climate determines the soil water storage patterns, which are largely in line with the timing of minimum flow.
3.4 3.4.1
Discussion On the similarity of seasonal water balance
The patterns displayed in Figure 3.7 indicate that the grouping procedure used in the study has produced coherent spatial clusters of similar seasonal water balances that satisfy the set criteria of minimum within-cluster variance and maximum between-cluster variance. Admittedly, the clustering presented here is based on seasonal water balance predictions by a conceptual model calibrated to observed streamflows. Without independent information on evaporation, soil moisture, and snow storage, the results are likely to include some degree of equifinality, i.e., there could be more or less evaporation (or storage) than is predicted by the model. Until more information is available, the clustering of catchments can be deemed as a hypothesis that remains to be tested. The clusters of hydrologically similar basins are not only hydrologically coherent [e.g. 229, 260], but are also physiographically and climatically coherent. The spatial pattern of catchment clusters is largely overlapping with previous classification studies based on streamflow signatures [52, 260] or dominant process controls [347]. Compared to these studies, we exposed hydrological coherence at a wider range of time scales (daily to decadal), a wider range of states (low flows to floods), and a wider range of processes (water balance components). Clusters are characterized by the magnitudes of three climatic indices relating to aridity, precipitation timing, and snowiness. Compared to Coopersmith et al. [52], the amount of similarity indices to distinguish between different classes is reduced, and now only depends on climatic variables. Our indices account 62
3.4. DISCUSSION
for the role of snow. Snow is not explicitly included in the indices of Coopersmith et al. [52] and Petersen et al. [229].
In general, classes with more catchments naturally have larger within-class variability of hydrologic regimes. This larger range of variability can be due to the larger number of catchments within the cluster, but can also be due to the larger diversity of physiographic, anthropogenic, or climatic factors within a cluster. Attribution of the larger within-cluster variability requires further detailed study of individual clusters or regions. Similar to Coopersmith et al. [52], these results may suggest that the seasonal water balance is primarily controlled by climate. However, as shown in Figure 3.8 , the clusters also coincide very well with well-known ecosystem, soil, and vegetation classes. This not only lends credence to the grouping achieved on the basis of the seasonal water balance, but indicates a codependence of vegetation with seasonal water balance, i.e., the type of vegetation and its dynamics impact the seasonal water balance, but on the other hand the vegetation type and dynamics also reflect the water balance. The seasonal water balance thus provides ecohydrological insights into the regional patterns of climate-soil-vegetation dynamics and helps to delineate regions with fundamentally different hydrologic regimes [251]. This study also confirms previous results from ecological studies that have shown that it is not annual precipitation but seasonal precipitation and timing that govern vegetation types and functioning, and their geographic distribution [246, 281].
The seasonal water balances presented in Figure 3.6 also reveal differences in certain dominant features that drive or reflect the seasonality of the water balance. Snowmelt and snow storage, driven by snowiness of precipitation are the dominant features in clusters B1 and B2. Carry-over of soil moisture and groundwater storage, in response to a strong out-of-phase seasonality, is the dominant driver in clusters A1, A2, and A3. Surface soil moisture variations, likely driven by storm events, appear to be the main drivers of the seasonal water balance in clusters C1 and C2. Finally, vegetation phenology driven by seasonal variations of energy (and possibly soil moisture storage) is the main driver of seasonal water balance in clusters D2 and D3. These dominant processes are consistent with both the seasonal climate and the types of vegetation that are present: A1, B1, B2 (coniferous), A2 (coniferous forest and shrubs), B3 (shrubs), C1, C2 (short grass prairie and long grass prairie), D2, D3 (deciduous), and D1 (mixed deciduous/coniferous). The close association between the seasonal water balances, as reflected in these dominant features, and the types and functioning of the vegetation present, along with the patterns of seasonal variation of actual evaporation seen in Figure 3.6 , bring attention to the different mechanisms that vegetation may have adopted to respond to and also reflect the seasonal water balance behavior. Examples of such adaptation include the carry-over of storage from wet to dry periods in clusters A1 and A2, and seasonal phenology changes in clusters D2 and D3. 63
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
Thus, in spite of the fact that the similarity framework used quantitative measures of similarity based on climate, it is still relying heavily on adaptation of the landscape, especially vegetation, to the climate. There is no guarantee that another place in the world with the same climate factors will evolve in the same way, in the presence of a different topography and geology (or parent material). To be universally applicable, the similarity framework must find a way to explicitly account for the role of landscape factors. A similarity framework based on a combination of climate and landscape characteristics is feasible in theory [e.g. 349], but suffers from the inability to specify the controlling landscape properties in an unambiguous manner for a large number of catchments. Evidence is emerging that model parameters relating to landscape properties are dependent upon climatic factors [196, 301]. This codependence is an issue that requires focused research efforts in the future before we can complete the development of universal catchment classification schemes, and is beyond the scope of the present empirical study. The framework proposed here also suffers from the fact that local climate variations are not fully represented in the formulation, e.g., the bimodal rainfall patterns present in some southern states.
3.4.2
On the link of seasonal water balance to other streamflow signatures
Now that the catchment grouping has revealed catchment clusters which exhibit strong similarities of seasonal water balance, including clear and unique features, how much of an imprint of the nature of seasonality is present in other signatures of streamflow variability? Addressing this question might help to highlight secondary controls, and generate a more holistic understanding of streamflow variability. Results presented in Figure 3.9 clearly indicated that at the annual scale, the nature of seasonality introduces a distinct element to the Budyko curve, in the way the classes organize themselves. Out-of-phase seasonality and snowiness have the effect of reducing the annual evaporation (and increasing annual streamflow) compared to Budyko’s predictions. Likewise, in-phase seasonality has the effect of increasing annual mean evaporation (and reducing annual mean streamflow). On the other hand, while inter-annual variability of annual streamflow is mostly affected by aridity, there is also a significant contribution due to climate seasonality, especially in semiarid and arid basins with in-phase seasonality (e.g., C1 and C2). The effects of seasonality are also mediated by landscape factors, as reflected in the base flow index (BFI): higher BFI works together with strong seasonality to reduce inter-annual variability, as shown in the results of Figure 3.9 . It is to be noted that mountainous catchments (clusters B1, B2) have a higher BFI than flatter catchments (clusters C1 and C2). This may be an artefact of the higher snowmelt component. 64
3.5. CONCLUSIONS
Results presented in Figure 3.11 indicate that the remaining signatures show a combination of the effects of seasonality and landscape properties. The timing of flood peaks and low flows is strongly affected by seasonality, which then impacts on the shapes of both flood frequency curves and low flow frequency curves. Aridity impacts the slope of the FFC (growth curves are more nonlinear with increasing aridity), clusters that include out-of-phase seasonality and snowiness show strong within-cluster compactness. The presence of in-phase seasonality and storminess contributes to significant within-cluster variability. The patterns of streamflow signatures, and their link to climatic indices, can potentially be used to predict streamflow signatures when no streamflow measurements are available. Additionally, it may help to identify or interpret changes of hydrological behavior in response to climate change. Coopersmith et al. [51] used the similarity indices of Coopersmith et al. [52] to classify temporal shifts in seasonal streamflow. Our similarity indices can be used in a similar fashion, but now to describe hydrological shifts for a wider range of time scales, conditions, and processes. Vegetation [251] and the composition of the landscape [258] in combination with geology [336] are clearly significant controls on observed hydrological behavior. At long time scales and large space scales some of these factors have been implicitly factored into the grouping of catchments through their imprint in the observed seasonal water balances. An example is BFI, which is largely determined by landscape characteristics and in some cases by snowiness, as in the case of mountainous catchments in the western U.S. [257]: clearly, it is of major importance under low flow conditions, but has been found to also impact the shape of the flood growth curve [113]. On the other hand, at small time and space scales, the landscape characteristics that matter are those that determine the responsiveness of a catchment to precipitation inputs. Including such landscape characteristics in the similarity framework will very likely improve the prediction of these signatures. Until truly universal similarity frameworks are developed that capture streamflow variability at a range of time scales, streamflow observations and signatures of streamflow variability remain the best objective and holistic metrics of catchment similarity: this has been the rationale of previous catchment classification studies [52, 154, 260, 321].
3.5
Conclusions
In this study, we have used a conceptual rainfall-runoff model to compute the seasonal water balance behavior of over 300 catchments across the continental U.S., and to bring out interesting coherent spatial patterns. Using the computed seasonal water balances, we grouped catchments into 10 coherent clusters having similar behavior, satisfying the criteria of minimum variance within clusters and maximum variance between clusters. We developed a similarity framework 65
CHAPTER 3. PATTERNS OF SEASONAL WATER BALANCES
based on three climate indices alone, i.e., climatic aridity, timing of seasonal precipitation, and a temperature-based measure of snowiness, that provide a backdrop to, and explanations for, the observed similarities and differences. While the clustering of catchments is based on the seasonal water balance, and has a strong relationship to regional patterns of the three climate indices, both of these spatial patterns have been shown to map on to well-known regional ecosystem, soil, and vegetation classes. These results suggest that the dominant soil orders and vegetation types are not only climate dependent, but also that vegetation and soils both contribute to and are a reflection of the seasonal water balance regime. The dominant processes attributed to each of the catchment clusters can thus be deemed as different mechanisms through which vegetation and soils adapt to and modify the seasonal water balance in each case. A major element of the adaptation of the landscape with the seasonal climate is manifested differently in the processes or seasonal water balance behavior in different places: carry-over of soil moisture in California, snow storage and melt in the Rocky Mountains, and phenology in north-east U.S. The paper has also demonstrated that the seasonal water balance patterns provide a useful backdrop to the streamflow variability over a wide range of time scales (daily to decadal) and states (low flow to floods). On seasonal to longer (mean annual and inter-annual variability) time scales, streamflow variability either directly, or indirectly through adaptation of landscape features with climate, reflects the nature of seasonal water balance. On shorter time scales, streamflow variability is a result of the interaction of climate directly with the landscape, including topography, vegetation and soil. Until these landscape factors are included, the similarity framework will remain incomplete and not universally applicable. All the signatures of streamflow variability considered here are outward manifestations of both short-term hydrologic responses and long-term adaptation of the landscape with climate, and therefore reflect as well as impact patterns of seasonal water balances, which are normally unobserved internal dynamics of catchments.
66
Part II
Long-term mean hydrology
67
HAPTER
C
4
S PATIAL VS . TEMPORAL PATTERNS OF THE LONG - TERM WATER BALANCE
This chapter is published as a "Correspondence" in the Nature Communications (ISSN: 1097-0088). This publication has been slightly modified to improve consistency throughout this thesis. Citation: Berghuijs, W.R. & Woods. R.A. (2016), Correspondence: Space-time asymmetry undermines water yield assessment Nature Communications, 7, 11603, doi:10.1038/NCOMMS19332
Abstract Understanding the effects of climate and land-cover on water yield is a challenging component in assessments of future water resources. Zhou et al. [2015] [354] (hereafter Z15) use Fu’s water balance model [92] that in their opinion provides a globally unifying framework that can quantify water yield sensitivity to climate and land-cover change. We show that key assumptions underpinning their application of the framework are contradicted by observations of many watersheds located in diverse climates and landscapes; Z15 ignore the space-time asymmetry of the co-variation of climate wetness and water yield, climate intra-annual variability, and typical rates of change of climate and landscape. Additionally, the framework does not provide the claimed explanation for increases in water yield associated with increases in forest cover. All these aspects undermine Z15’s application of the framework, and should be considered to draw robust conclusions on the effects of climate and land-cover on water yield. 69
CHAPTER 4. SPATIAL VS. TEMPORAL PATTERNS OF THE LONG-TERM WATER BALANCE
4.1
Introduction
Z15 use Fu’s equation [92, 354], based on the widely used Budyko framework [45], to quantify the spatial differences of mean water yield normalized by precipitation (Q/P) as a function of the wetness index (precipitation/potential evaporation P/E P ) and watershed characteristic (ω). Z15 subsequently derive the sensitivity of Q/P to both wetness (∂Q/P/∂P/E P ) and watershed characteristics (∂Q/P/∂ω) to understand the role of climatic and land-use changes on water yield. Although similar approaches have been applied before [248], Z15 ignore several crucial assumptions that undermine their use of the framework.
4.2
Methods
Z15 used the partial derivate of Fu’s equation [92] to calculate the water yield sensitivity to wetness index: (4.1)
∂(Q/P)
P = ∂(P/E P ) EP µ
¶−2
P − EP µ
¶−ω−1 · µ ¶ ¸ P −ω (1−ω)/ω · 1+ EP
where P, E P , and ω denote the long-term average values of precipitation, potential evaporation and watershed characteristics. We calculate water yield sensitivity to climate based on temporal differences is calculated using the slope (α): P (Q/P) i = α · EP µ
(4.2)
¶
+β i
where (Q/P) i is the water yield of year i, and (P/E P ) is the wetness index of year i. The α is approximated by the slope terms of least squares estimators. Annual values used in the analysis are from 1 September to 31 August to minimise the effects of carry over of water storage. Repeating the analysis for 5-year values yields similar results. Data are from 420 watersheds of the MOPEX dataset [67, 261]. Identical to an earlier study [26] 11 of the 431 watersheds of the MOPEX dataset for which less than 15 years of data are available are eliminated.
4.3 4.3.1
Results and discussion Space-time asymmetry
Z15 analyze how three variables (Q/P, P/E P , ω) co-vary in space, to approximate their connection in time. Thereby Z15 implicitly assume there is symmetry between spatial (between-watershed) and trends of temporal (between-years) precipitation partitioning into streamflow and evaporation. This is not necessarily the case for watersheds [178, 228]. To test if this assumption is valid we compare ∂Q/P/∂P/E P , as approximated by Z15’s equation (see Methods Equation 4.1, that is based on spatial differences) and the ∂Q/P/∂P/E P calculated using interannual water balances (see Methods Equation 4.1, that is based on temporal differences). Figure 4.1 shows a 70
4.3. RESULTS AND DISCUSSION
scatterplot of the spatial vs. temporal sensitivities for the widely used MOPEX dataset [67, 261] consisting of 420 watersheds located in diverse climates and landscapes. The sensitivity metrics are significantly correlated (R 2 = 0.502, p < 0.001), but on average the difference between the two metrics is 27.9%. There are distinct regional patterns (Figure 4.1) in to what degree spatial and temporal approximations differ. This suggests that in certain landscapes space is tradable for time. However, in other landscapes, this assumption leads to systematic under or overestimation of the sensitivity to climate change. Understanding why there are regional differences between spatial and temporal precipitation partitioning, and how these differences can change when the landscape coevolves with climate [302] are open questions that need to be answered.
Figure 4.1: Spatial sensitivity of water yield (x-axis) and temporal sensitivity of water yield (yaxis) for 420 watersheds located in the United States, and the spatial pattern of their differences.
71
CHAPTER 4. SPATIAL VS. TEMPORAL PATTERNS OF THE LONG-TERM WATER BALANCE
4.3.2
Climate seasonality
Z15 attribute any effects of ω to landscape characteristics. However, both empirical evidence and modelling studies [23, 26, 196, 234, 339] indicate that climate intra-annual variability is a major factor in determining the Q/P of a watershed, and thereby it also strongly affects ω. When Roderick and Farquhar [248] first introduced the sensitivity framework, they acknowledged that this watershed parameter encodes all factors other than climate wetness that change the partitioning of precipitation between evaporation and streamflow. Therefore ω also includes effects of precipitation seasonality, timing, and form (e.g. snow-vs.-rain). Ignoring this role of climate intra-annual variability can bias the attribution of ω towards landscape properties, prevents landscape effects from being strictly separated from intra-annual climate effects, overestimates the importance of landscape effects, and ignores the role of part of the climate effects on water yield.
4.3.3
Non-linearity of wetness
Z15 claim to identify the critical values of P/E P and ω that define ranges where either climate or landscape changes are more important for water yield. In addition to the earlier identified issues of the framework, Z15’s so-called “critical values" are misleading for two reasons. Sensitivity to wetness (∂Q/P/∂P/E P ) and watershed characteristics (∂Q/P/∂ω) are both dimensionless metrics and therefore potentially comparable. However, comparison of these metrics is not meaningful for assessing water yield changes (∆Q/P) unless it is combined with typical changes of climate (∆P/E P ) and watershed parameter (∆ω). Additionally, the wetness index can vary orders of magnitude between watersheds [See Z15 Figure 7]. Because climate change (∆EP/E P ) is proportionally related to the occurring wetness index, a 10% increase in precipitation can lead to orders of magnitude difference in ∆P/E P values. Z15’s methods and conclusions on the relative importance of climate and landscape sensitivity do not take these aspects into account. Therefore Z15 are not able to identify the real relative importance of climate and landscape on water yield.
4.3.4
Unexplained forest effects
Finally, Z15 state that the pattern of ω, P/E P values and their correlation with landscape properties can explain the diverse effects of forest cover changes on water yield. This implies that Fu’s equation can predict both negative and positive streamflow changes in response to increase in forest; however, this implication is not correct. Z15’s proposed explanation for positive sensitivity is independent of the Fu’s equation. They instead rely on their assertion that E P over forests is lower than E P over grassland in the same location, because of the lower temperatures observed over forests [226]. However, the use of any E P equation that relies only on temperature is clearly inappropriate for this question, since forest and grassland have very different partitioning of energy between latent and sensible heat. Lower temperatures over forest are not sufficient to 72
4.4. CONCLUSIONS
estimate changes in forest E P , and even if they were, this would not be a consequence of Fu’s equation; as a result we do not agree that Z15 have provided an explanation for cases where water yield from forest exceeds that from grassland.
4.4
Conclusions
In summary, we disagree with the main conclusion of Z15 that their study exposes the relative role of climate and landscape on water yield. Four major issues all related to the asymmetry of temporal and spatial conditions constrain the current validity of the framework. First, data indicates that the central assumption of tradability of space and time is not valid for all landscapes. Secondly, the landscape parameter ω is, using Z15’s approach, not separable from important and ignored intra-annual climate conditions. Thirdly, the critical values of P/E P and ω identified by Z15 only provide mathematical guidance on the importance of climate and landscape, but the connection with real world changes is still to be clarified. Finally, the framework does not provide the claimed explanation for increases in water yield associated with increases in forest cover. We therefore recommend acknowledging these limitations and emphasise that a unifying framework of climate and landscape sensitivities needs to be more conservative in its assumptions, or needs to better address space-time asymmetry of the co-variation of P/E P and Q/P, climate intra-annual variability, and typical rates of change of climate and landscape.
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5
D RIVERS OF CHANGING WATER BALANCES
An extended version of this chapter will be submitted as a "Research Article" to Water Resources Research. The current version represents a "Letter" that was submitted to Nature Climate Change. Co-authors for this chapter are J.R. Larsen, T.H.M. van Emmerik, and R.A. Woods.
Abstract Unraveling the main drivers of hydrological change is key for the prediction and management of global freshwater resources [197]. Precipitation and potential evaporation are commonly studied drivers [15, 86, 93, 103, 140, 219, 249, 267], as aridity (the ratio of potential evaporation to precipitation) explains ∼90% of the spatial differences in mean annual runoff across the globe [45]. However, it is unclear if reported changes in aridity over time also explain most of the temporal changes in freshwater resources across the Earth’s land surface. We resolve new global patterns on the importance of aridity to changes in runoff by evaluating its relative sensitivity to change in combination with observed trends. This reveals runoff is most sensitive to changes in aridity across only ∼20% of the land surface, meaning other factors dominate for the remaining 80%. We confirm water resources in dryland regions are highly sensitive to aridity changes [15, 219], but in addition show the sensitivity of runoff to changes in other factors is far higher. The burden of these other factors therefore falls on the more poorly constrained roles of changing climatic variability, CO2 - vegetation feedbacks and anthropogenic modifications to the landscape. The influence of these factors upon future runoff is further compounded in dryland regions by sparse hydrological information, signifying a need to improve monitoring and modeling of the dominant runoff drivers in these regions. 75
CHAPTER 5. DRIVERS OF CHANGING WATER BALANCES
5.1
Introduction
Global freshwater availability is vital for both societies and ecosystems [214, 319]. The availability of renewable freshwater resources is largely determined by river flow [214], as groundwater abstractions often exceed aquifer replenishment [98]. Potential evaporation (E P ) and precipitation (P) (often summarized by the aridity index, E P /P) are the dominant climatic factors that determine differences between catchments in how precipitation is partitioned between mean-annual runoff (Q) and evaporation (E) [23, 45]. The Budyko framework [45] utilizes this prominent role of aridity and, in its most commonly used parametric form [92], states that the mean annual balance of E and Q can be expressed as a function of aridity and other factors: (5.1)
F(φ, ω) = E/P = 1 − Q/P = 1 + φ − (1 + φω )1/ω
where φ is aridity, and ω is a parameter that accounts for all other factors that influence the partitioning of rainfall (e.g. climate seasonality, soils, vegetation, topography). Aridity (φ) is strongly established as the dominant factor determining the spatial differences in mean runoff and evaporation across the globe. Changes in mean precipitation and potential evaporation are consequently considered to be of primary relevance for changes to the terrestrial water cycle [15, 86, 93, 103, 140, 219, 249, 267, 354]. However, it is uncertain [15, 219] whether documented changes to mean precipitation and potential evaporation also translate to aridity being the dominant driver of changes in water availability (Q) over time, and how this dominance varies across the land surface. Other factors (summarized by ω) potentially play a more important role in controlling temporal changes in mean water availability at regional and local scales, including changes in climatic variability (e.g. climate seasonality [23], snow conditions [26], storminess [196]), CO2 - vegetation feedbacks (e.g., CO2 -fertilization [307], water use efficiency change [308]), and anthropogenic modifications (e.g. land use change [342], irrigation [146], reservoir construction [146]). In recent years, the Budyko framework has been increasingly used to quantify the role of aridity and other factors in changing water availability [107, 354]. These studies assume that E and Q change approximately according to the Budyko curve (Equation 5.1) when φ changes, which allows the sensitivity of E or Q to changes in aridity and other factors to be evaluated analytically. Current global assessments of this sensitivity to aridity changes [107, 354] analyze how the long-term means of φ and ω co-vary between locations, to approximate how F responds to these changes. An important constraint of this approach is that it implicitly assumes that spatial differences in runoff and evaporation translate directly into how this partitioning should change in time [24]. This assumption is not necessarily unreasonable, as the Budyko framework often predicts temporal changes in runoff and evaporation as well or better than land-surface models [250]. However, this assumption can lead to both over- and under-estimation of the sensitivity of runoff to aridity changes, and potentially biases the relative importance of φ and ω by not 76
5.1. INTRODUCTION
accounting for their observed magnitudes of change [24]. In combination this diminishes our predictive capacity of the relative runoff sensitivity to changes in aridity over time.
Figure 5.1: Global hydro-climatic characteristics of the Budyko framework. The spatial pattern of the evaporative index, E/P (top), the aridity index, φ (middle), and the parameter, ω (bottom), based on the EU-WATCH data of the period 1901-2001.
We introduce a method that removes many of these current limitations to obtain more robust sensitivities to aridity changes. First we determine ω for all land-surface grid cells based on decadal variations in ω and F instead of long-term average values (see Methods). The derived global pattern of F, φ and ω is based on WATCH data for the period 1901-2000 (Figure. 5.1) [326]. Furthermore, as the choice of climatic input may vary (i.e. aridity E p /P versus wetness index 77
CHAPTER 5. DRIVERS OF CHANGING WATER BALANCES
P/E p ) we introduce the partial derivative of the change in normalized runoff (∂Qˆ = ∂Q/Q) to the change in normalised aridity (∂φˆ = ∂φ/φ, see Methods Equation 5.2-5.3) based on Fu’s equation ˆ ∂φˆ produces the same result for each climatic index, our approach avoids (Equation 5.1). As ∂Q/ the erroneous pitfall that the global pattern of relative sensitivities is an artefact of whichever ˆ ∂φˆ and index is chosen (see Appendix B). Finally, in order to make a direct comparison of ∂Q/ ˆ ∂ω informative, we include representative changes in φˆ and ω based on their trends over the ∂Q/ periods 1901-1950 and 1951-2000 (Methods Equation 5.6 and Equation 5.7). This is important because changes in ω during the 20th century have on average been eight times larger than changes in φˆ ; this has not been taken into account in previous global assessments [107, 354]. While these observed centennial trends may not necessarily hold for the coming decades [140], they highlight that relative changes in aridity are typically much smaller than the changes in ω across the globe, which our approach now incorporates to allow an equitable comparison of the relative roles of aridity versus other factors on changing global freshwater resources (Methods Equation 5.8).
5.2 5.2.1
Methods Data description
We use the WATCH model ensemble data for the period 1901-2000 to determine the global pattern of the aridity index φ, and the ω parameter for the period 1901-2000 (http://www.eu-watch.
org). Data are monthly values of evaporation, precipitation, and potential evaporation. Grid-cells have a 0.5 o by 0.5 o spatial resolution. Aridity φ is derived based on long-term mean values of precipitation and potential evaporation for the period 1901-2000. ω is determined fitting Equation 5.1 through the cloud of 10 points of 10 year values of E/P and φ based on the minimised root mean square error of the equation to the data points. Although there are accuracy limitations in using the multi-model derived fluxes for E, the dataset remains useful for evaluating the first order sensitivities to φ and ω. Alternative derivations based on global gridded Q datasets are also possible, however given similar limitations in accuracy they would not significantly change the results presented here.
5.2.2
Water balance framework
Based on Fu’s equation (Equation 5.1) [92] the partial derivative of normalised runoff changes with respect to φˆ is:
(5.2)
³ ¡ ω ¢ 1 −1 ´ ω−1 ω φ 1 − φ φ + 1 ˆ ∂Q = ¡ ¢1 b ∂φ −φ + 1 + φω ω
78
5.2. METHODS
Figure 5.2: The relative and absolute sensitivity of freshwater availability to changes in aridity and other factors. (a) The relative sensitivity of aridity changes compared to all other factors ˆ ∂φˆ , expressed by Θφ/ω , (b) the sensitivity of mean annual runoff to changes in the aridity index ∂Q/ and (c) the sensitivity of mean annual runoff to changes in the other factors scaled by typical ˆ ∂ω∆ω/∆φˆ . changes ∂Q/
79
CHAPTER 5. DRIVERS OF CHANGING WATER BALANCES
and the partial derivative of normalised runoff changes with respect to ω is: ¡ ¢ ¶ ¡ ω ¢1 µ ω ¡ ¢ φ ln φ ln φω + 1 φ +1 ω ¡ ¢− =− ¡ ¢1 · ω ∂ω ω2 −φ + 1 + φω ω ω φ + 1
∂Qˆ
(5.3) where
b= ∂φ
(5.4)
∂φ φ
and ∂Q ∂Qˆ = Q
(5.5)
5.2.3
Typical rates of change
To permit a meaningful comparison of the partial derivatives (Equation 5.2-5.3) we calculate how large the changes in both ω and φˆ have been during the 20th century. (5.6)
∆ω = mean (|ω1901−1950 −ω1951−2000 |)
(5.7)
b = mean ∆φ
µ
|φ1901−1950 −φ1951−2000 |
¶
φ1901−2000
WATCH data of the 20th century suggests that the mean relative change in aridity (∆φˆ ) over the 20th century has been 0.0263, while the mean change in specific parameter (∆ω) during this period has been 0.2091. We do not find any significant correlation between these typical rates of change and mean φˆ or mean ω values.
5.2.4
Relative sensitivity to aridity changes
The comparison on the relative sensitivity to aridity changes is now given by: ˆ
Θφ/ω =
(5.8)
b ∂Q ∆φ b ∂φ ˆ
Q ∆ω ∂∂ω
where aridity is considered dominant when Θφ/ω > 1 and other factors are considered dominant when Θφ/ω < 1.
5.3
Results
We can now provide a more realistic global assessment on the sensitivity of runoff to changes in aridity (Figure 5.2a). For 19.8% of the land surface, runoff is more sensitive to changes in aridity (Θφ/ω > 1), see Methods Equation 5.8) while changes in the catchment parameter ω (representing all other factors) dominate 80.2% of the land surface (Θφ/ω < 1). Consistent with these sensitivity 80
5.4. DISCUSSION AND CONCLUSIONS
values, we find changes in aridity can explain only 25% of the global changes in total runoff that have occurred over the 20th century (see Appendix B). These percentages and their spatial pattern either differ substantially or are almost the direct reciprocal of previous global assessments [107, 354], emphasizing the need for caution in applying the Budyko framework to questions of temporal runoff sensitivity. Interestingly, freshwater availability is most sensitive to aridity changes within the equatorial tropics (i.e.: Amazon, Congo, and archipelagos of the Western Pacific), large areas of the North American continent, eastern parts of continental Asia, New Zealand, northern Europe, and around the Pampas of South America. For most other regions, changes in factors other than aridity are more likely to dominate runoff sensitivity. The secondary influence of changes in aridity (Θφ/ω < 1) for the majority of the land surface is further accentuated within many dryland regions (E P /P > 1.5) of the world (Figure 5.1b), where the relative sensitivity to other factors is exceptionally high (Θφ/ω T crit )
where P snow is the snowmelt rate, P is the precipitation rate for days when the daily average temperature T exceeds the temperature threshold T crit set at 1 ( o C). f dd is the melt rate set at 2.0 (mm/d/K) [341], and S snow is the snow storage: (6.4)
S snow (t) = S snow (t − 1) + P(t(T(t) < 1) − P snow (t)
Since there is no data available on snowmelt, snow storage, and rain-on-snow events, the absolute value of P snow is a rough approximation of snowmelt dynamics.
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6.2. METHODS
Figure 6.1: Mean day of (a) maximum annual daily flow, (b) maximum daily precipitation, (c) maximum weekly precipitation, (d) maximum precipitation excess, and (e) maximum snowmelt and associated standard deviations (right column). Black crosses indicate that the data were not calculated due to an absence of significant snow ( E) and evaporation-dominated (E > P) low flow generation.
storage depletion causes LAF. In these places streamflow exceeds evaporation, and is therefor the primary contributor to LAF. This scenario is only observed in two of the 420 catchments. For the vast majority of catchment (418/420) evaporation exceeds streamflow during the LAF generation period. The distance of the scatter plot from the origin indicates how large the sum of evaporation and streamflow are compared to total precipitation during the LAF period. For most catchments evaporation by itself already exceeds precipitation. This indicates that evaporation is the largest flux contributing to low flow conditions. The role of evaporation dominated water storage depletion is consistent with the results from the seasonality analysis.
8.3.3
The role climate and landscape on LAF variability
There are spatial differences in the variability of climatic conditions (here summarised by Eq. 8.18: CV∆S ) and the sensitivity of the streamflow of catchments to storage changes (here summarised by Eq. 8.19: ²S (α, β,Q LAF )) and the associated variability of the magnitude of minimum annual flows (here summarized by Eq. 8.18: CVQ ) (Figure 8.5). The coefficient of variation of LAF of (CVQ ) has regional differences; on average CVQ is highest in the central part of the US, with the exception of many of the snow dominated catchments in the Rocky Mountains. The inter-annual variability of water storage magnitude (CV∆S ) shows less strong regional patterns; relatively large inter-annual variation of water storage occurs in catchments spread over different areas. The sensitivity of the streamflow of catchments to storage changes ²S (α, β,Q LAF ) shows similar regional patterns to CVQ with the most sensitive regimes located in the central part of the 116
8.3. RESULTS
continent.
Figure 8.5: Spatial pattern of the coefficient of variation of LAF (top), the coefficient of variation of water storage (middle), and storage sensitivity of streamflow ²S (α, β,Q LAF ) (bottom).
Scatterplot of ²S (α, β,Q LAF ), CVQ , and CV∆S (Figure 8.6) indicates there is significant correlation (R 2 = 0.73, p < 0.001) between the inter-annual variability of LAF magnitude and landscape sensitivity of low flows, while the correlation between storage variability and low flow conditions 117
CHAPTER 8. LOW FLOW PATTERNS AND MECHANISMS
(R 2 = 0.12) is minimal. This suggests that landscape much rather than climate determines the regional differences in annual low flow variability. This indicates that catchment functioning, rather than climate variability, dominates the inter-annual variability of the magnitude of LAF.
Figure 8.6: Scatterplot of the variability of annual minimum flows expressed as the coefficient of variation of LAF (y-axis), climate variability expressed as the coefficient of variation of catchment storage (x-axis left), and storage sensitivity of streamflow ²S (α, β,Q LAF ) (x-axis right).
8.4
Discussion
This study uses a very simplified representation of water balance components to generate understanding of the processes that control LAF in the United States. The first simplification is that potential evaporation is obtained from long term averaged pan evaporation data, thereby ignoring the role of inter-annual variability of E p . Although time varying potential evaporation estimates can be used instead, their changes to the results are expected to be minimal; E p is only used in the seasonality analysis, whereby the comparison of the mean timing of the LAF and hypothesized mechanisms is not directly affected by ignoring inter-annual variability of E p . Since our aim is to provide a “scientific validation" [33], rather than providing precise predictive models of future conditions, the first order comparison of our analysis is expected to be robust to the E p estimation method. E p is not used in other parts of the analysis. The bucket model to represent soil water storage dynamics is a very simplified representation of catchment functioning. However, similar to the potential evaporation estimate, the uncalibrated model was the only one that could reasonably well explain the seasonality conditions of the catchments, thereby indicating the dominant role of this process for the timing of low flow conditions. Further sophistication of the model can improve the correspondence of simulated and observed seasonality of LAF, but this would not affect the first order comparison we make. More 118
8.5. CONCLUSION
complex and highly parameterized models thereby also do not easily allow identifying the first order role of the main processes. In other parts of the analysis the bucket model is not used. We also ignored any direct human influence to the water system. MOPEX catchments are characterized by limited human influence. Changes from natural land cover, as observed in many of the catchments [324], can influence the nature of low flow conditions. Our results show the dominant controls on the catchment’s low flow conditions, given the conditions they are currently in. Human influence such as sewage return flows, and reservoir operation can affect the low flow conditions of catchments. Because there is no direct information on these aspects we did not include these effects in our study. Obtaining the water balance components with simplified hydrograph recession characteristics relies on the assumption that during hydrograph recession streamflow is driven by water storage in the catchment [156], and that this can be represented by the non-linear relationship of Brutseart and Nieber [44]. Limits of hydrograph recession analyses continue to be discussed [66, 253, 285, 292], which for obtaining storage changes and evaporation rates can also be improved. On the other hand our method does not require complex numerical models, does not use potential evaporation, and does depend on not-validated representations of evaporation either. Measurements of water storage do not have the spatial and temporal resolution that water balance estimates of this study can directly be validated. Neither are evaporation measurements at the correct temporal and spatial scale available. The evaporation estimated using the hydrograph recession characteristics are in over 90% of the cases within the limits of potential evaporation (not shown here), which improves confidence that our evaporation estimates are reasonable. The simplified model of catchment sensitivity can also be subject to improvement of hydrograph recession analysis. Yet, the provided estimates, without being perfect, already show how strongly the filtering role of the landscape controls the occurring flow regime.
8.5
Conclusion
In this study we exposed information on the timing, magnitude and associated causes of 10-day moving average lowest annual flow (LAF) conditions of 420 catchments in the United States. First, using low flow seasonality, data shows that for most catchments and for most years, LAF occur at the end of summer and beginning of fall. The seasonality of LAF is generally poorly explained by meteorological conditions (precipitation, temperature, potential evaporation) alone, because for most catchments reasonable reproduction of LAF seasonality can only be obtained when evaporation dominated subsurface storage depletion is considered. The depletion of storage over periods of high evaporative demand postpones LAF by several weeks to months, compared to ignoring this storage component. Second, by doing hydrology backward, we obtained storage 119
CHAPTER 8. LOW FLOW PATTERNS AND MECHANISMS
changes and evaporation rates during the period prior to LAF. In line with the seasonality analysis, data indicates that during this period evaporation is the dominating flux of the water balance, inducing storage changes that cause low flow conditions. Evaporation thereby almost always exceeds precipitation and is often an order of magnitude higher than streamflow rates. Third, we separated the role of climate variability and catchment functioning on for the inter-annual variability of the magnitude of low flow conditions. We thereby highlight how the sensitivity of the LAF magnitude to storage changes (how the landscape functions), rather than climate variability (as expressed by storage variability), controls the inter-annual variability of the LAF magnitude. Together, these three analyses expose the seasonality characteristics, the contribution of water balance components, and the variability in the magnitude of US low flow conditions. Although regional difference exist, our analysis suggests that evaporation-dominated subsurface storage depletion is generally the primary cause for the occurrence of annual low flow conditions, whereby drainage properties of the catchment strongly control the associated magnitude of events.
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9
S TORAGE SENSITIVITY OF STREAMFLOW
This chapter is published a "Research Letter" in Geophysical Research Letters (ISSN: 1944-8007). This publication has been slightly modified to ensure consistency throughout this thesis. This chapter benefited from the constructive comments of D. Rupp and of two anonymous reviewers. Citation: Berghuijs, W. R., A. Hartmann, and R. A. Woods (2016), Streamflow sensitivity to water storage changes across Europe, Geophysical Research Letters, 43, 1980-1987, doi:10.1002/2016GL067927.
Abstract Terrestrial water storage is the primary source of river flow. We introduce storage sensitivity of streamflow (²S ), which for a given flow rate indicates the relative change in streamflow per change in catchment water storage. ²S can be directly derived from streamflow observations. Analysis of 725 catchments in Europe reveals that ²S is high in e.g. parts of Spain, England, Germany and Denmark, whereas flow regimes in parts of the Alps are more resilient (that is, less sensitive) to storage changes. A regional comparison of ²S with observations indicates that ²S is significantly correlated with variability of low (R 2 = 0.41), median (R 2 = 0.27), and high flow conditions (R 2 = 0.35). Streamflow sensitivity provides new guidance for a changing hydrosphere where groundwater abstraction and climatic changes are altering water storage and flow regimes.
9.1
Introduction
Climate change and direct anthropogenic impacts on the water cycle are altering river flow regimes, thereby affecting water resources and natural hazards [203, 280]. The magnitude of 121
CHAPTER 9. STORAGE SENSITIVITY OF STREAMFLOW
hydrologic change depends both on the change in forcing (e.g. climate conditions and groundwater use) and the catchment’s sensitivity to these changes. Exposing this sensitivity helps characterize the hydrologic functioning and can support water management strategies and climate change impact assessments [39, 237].
A widely used hydrologic sensitivity measure is climate elasticity of streamflow, which expresses a catchment’s annual or seasonal streamflow change per change of climatic condition (e.g. rainfall, temperature, potential evaporation, snow fraction) [26, 213, 256, 262, 311]. Climate elasticity is useful as it exposes where river flow is most sensitive to change, without the use of highly parameterized models, and independent of the uncertainty of future climatic conditions.
For instantaneous streamflow the development of a similar parsimonious expression for streamflow as a function of precipitation rates (or other climate conditions) is hindered by the temporal disparity between meteorological conditions and consequent streamflow response; similar sized rainfall events can lead to orders of magnitude difference in runoff coefficients, depending on antecedent wetness conditions [305]. Although precipitation intensity controlled runoff-generating processes can be observed during periods of rainfall [69], for many catchments subsurface water storage is for the majority of time the main driver of streamflow response [188, 245, 279]. There are regional differences in the estimated volume and timescale of the subsurface contributions to streamflow [16]. Both climatic changes and variations, and human groundwater abstractions are affecting groundwater storage around the globe[60, 97, 101, 243, 289], but a theory that exposes the sensitivity of flow to storage changes across diverse landscapes and spatial scales is currently not exploited.
Here we introduce storage sensitivity of streamflow (²S ), which is a measure of the sensitivity of streamflow to changes in catchment scale water storage. We use hydrograph recession analysis [44, 288] which allows us to express a catchment’s storage driven streamflow response to water storage change [156]. For 725 mostly non-regulated catchments across Europe we (i) calculate hydrograph recession characteristics, (ii) expose how hydrograph recession characteristics lead to differences in ²S between catchments, and (iii) expose the regional patterns in ²S whereby we identify for which catchments the flow regimes are more sensitive to water storage changes. Both meteorological forcing and how the landscape filters this meteorological forcing determine regional differences in flow regimes [23, 39]. To assess to what degree a catchment’s storage sensitivity of streamflow influences regional differences in flow regimes, we (iv) compare ²S with the slope of different parts of the Flow Duration Curve (FDC) [317]. 122
9.2. DATA
9.2
Data
We use daily streamflow values covering a maximum time period of 1863-2008 from 725 catchments; most of the records are part of the UNESCO’s European Water Archive (EWA), which includes data provided by the European subnetwork (EURO-FRIEND, http://ne-friend.bafg.de) of the international research project FRIEND (Flow Regime from International Experiment and Network Data), which is maintained by the Global Runoff Data Centre (GRDC; http://grdc.bafg.de). French and Spanish discharge time series were accessed via the French water agency (Eaufrance, http://hydro.eaufrance.fr/), and the Spanish Centre for Civil Engineering Studies and Experimentation (CEDEX, ceh-flumen64.cedex.es). Catchments range in size from 5 to 6133 km2 (median = 237 km2 ), in mean elevation from 12 to 2659 mASL (median = 662 mASL), in precipitation from 398 to 2603 mm/a (median = 853 mm/a), and in mean annual temperature from -2 to 16 o C (median = 8 o C). A few of the 725 catchments show large gaps in their observed time series (up to 77% missing data) but 90% of them have 2 (57/725 catchments) ²S increases (goes to infinity from
zero) as discharge decreases. The α values scale the slope of the storage discharge relationship; a 125
CHAPTER 9. STORAGE SENSITIVITY OF STREAMFLOW
larger α value indicates a steeper slope of the storage discharge relationship, for a given value of β. However, because of α’s dependency on β (see units), a direct comparison of α-values without
considering the associated β values is not meaningful. Since each α value combines information on the magnitude of Q as well as the value of β, no physical interpretation can be placed on the spatial patterns of α.
Figure 9.2: Storage sensitivity of streamflow (²S ) for different three different flow values: Q = 0.1 (mm/d) (left), Q = 0.5 (mm/d) (center), and Q = 1.0 (mm/d) (right). The catchments’ α (mm1−β dayβ−2 ) and β (-) values are indicated by black markers. (NB: it is only meaningful to compare α values between catchments when their β values are the same).
Based on Equation 9.5 we can calculate the sensitivity of streamflow to storage changes, ²S (α, β,Q), where α and β are assigned the values of the catchment displayed in Figure 9.1, and Q
can be set at any value of interest. As exemplified for three different flow values that occur in the vast majority of catchments (Q = 0.1 mm/d, Q = 0.5 mm/d, Q = 1.0 mm/d), the storage sensitivity of streamflow varies strongly across catchments (Figure 9.2); ²S shows orders of magnitude difference in the streamflow response to a given storage change, depending on α and β values and the flow rate. This highlights differences in storage-discharge relationships of catchments, but the sensitivity of the flow regimes to storage changes also depends on the flow values that occur. ²S is calculated for low flow (Q 85 ), median flow (Q 50 ), and high flow (Q 15 ) conditions of the individual catchments (Figure 9.3). The sensitivities vary per part of the flow regime and per catchment. ²S is on average higher for the low flow values (median ²S = 0.062) than for median flow values
(median ²S = 0.038) and high flow values (median ²S = 0.023). In some cases Q15 exceeds the maximum observed streamflow of the hydrograph recessions, but this is only the case for a limited number of catchments (79/725). For all parts of the flow regime, ²S is generally highest in many catchments in Spain, in parts of England and Germany, and the Danish island of Zealand, whereas catchments in the southern parts of the Alps are most resilient to water storage changes. The slopes of flow duration curves are empirically related to storage sensitivity across 126
9.5. DISCUSSION
Figure 9.3: The storage sensitivity of streamflow (²S ) for low flow (Q 85 ), median (Q 50 ), and high flow (Q 15 ) conditions.
catchments for three streamflow regimes: low, median, and high flow (Figure 9.4). The degree of correlation in log-log space between ²S and slopes of the flow duration curve for low (R 2 = 0.40, p < 0.001), median (R 2 = 0.27, p < 0.001), and high (R 2 = 0.35, p < 0.001) flow values suggests that the sensitivity of streamflow to storage changes partly controls the historical variability of the flow regime.
9.5
Discussion
Streamflow sensitivity to water storage changes have been used before as part of an analysis of two catchments in Wales [156], but that study did not explicitly focus on streamflow sensitivity per se, nor as a diagnostic of vulnerability. The relative changes in the flow per unit of water storage change provides a parsimonious hydrological model, with parameters directly derivable from streamflow observations, that quantifies the sensitivity of instantaneous storage-driven flow values to water storage changes. Other modeling approaches often need additional data and longer time-series to calibrate the model [189]. Predictions of low flow conditions are often based on multi-model assessments [e.g. 236] that have large uncertainty in parameters related to subsurface runoff generation [138, 141] and do not provide efficient guidance in understanding regional landscape differences. Storage discharge relationships form the basis of the derived streamflow sensitivity. Yet, a single α and β are not a perfect characterization of the drainage properties of a catchment; the power law coefficient, α, and the exponent β can vary with the chosen methodology [66, 253, 285, 292], spatial variation of rainfall and groundwater discharge [34], and the quality of data [253, 285]. Questions still remain about whether the α parameter is a meaningful way to summarize recession behavior. Further refinements of hydrograph recession analysis will continue to be the topic 127
CHAPTER 9. STORAGE SENSITIVITY OF STREAMFLOW
Figure 9.4: Scatterplot of the storage sensitivity to streamflow (²S ) for low flow (²S (Q 85 )), median (²S (Q 50 )), and high flow (²S (Q 15 )) conditions, and associated slopes of the flow duration curves for low (S FDC (Q 75 ,Q 95 )), median (S FDC (Q 40 ,Q 60 )), and high (S FDC (Q 5 ,Q 25 )) flow conditions.
of future studies, whereby refined methods can be implemented in calculations of storage sensitivity. The example provided is already informative by exposing for the first time strong regional differences in storage sensitivity of streamflow across Europe. The method can be immediately implemented in other catchments where streamflow observations are available. The data used in this study is from near-natural catchments across Europe. However, streamflow sensitivity to water storage changes characterizes the catchment’s hydrologic functioning given its current land use and anthropogenic conditions, and in theory could be applied to systems with strong human influence, provided that discharge is still controlled by storage. The imperfect fit between ²S and slopes of the FDC indicates that other factors, such as regional differences in climatic variability [23, 109], non-storage related runoff-generating mechanisms [69], and human influences [146, 233], are also important for the nature of the catchment’s flow regime. However, independent of its uncertainties and unaccounted factors, ²S still explains a significant part of the flow variability between places indicating that the storage discharge relationships of the catchments partly determine the nature of flow regimes. This suggests that how a catchment filters water storage is an important factor in regional differences of flow regimes. Unexplained variability will be caused by regional climate differences, overland flow, snowmelt, and uncertainties associated with the used sensitivity characterization. Predicting streamflow sensitivity to storage changes by landscape (catchment area, mean elevation, mean slope, lithology) or climate descriptors (annual precipitation, mean temperature) remains a difficult task. Only precipitation (r = −0.25, p < 0.001) and temperature (r = 0.29, p < 0.001) provide significant correlation (see Appendix D). Catchment aridity gives a similar correlation as catchment precipitation, and thus the inclusion of potential evaporation does not (appear to) improve the link with sensitivity values. Missing information on for example the aquifers’ volume, residence time, 128
9.6. CONCLUSIONS
and spatial organization may help to further explain regional differences in streamflow sensitivity. Projections of future changes to the flow regime are available [e.g. 5, 115, 236, 263], but are strongly affected by uncertainties in precipitation predictions, model representation and water abstractions [29]. Independent of the uncertainties in future climate and water use conditions, streamflow sensitivity to water storage changes helps identifying which regions are most resilient or vulnerable to climatic shifts and other water storage affecting factors. The sensitivity of flow regimes thereby shows orders of magnitude differences within Europe (Figure 9.3). The regional differences of streamflow sensitivity to water storage changes have not been reported before in scientific literature and provide guidance to those places that are most sensitive to water storage changes, independent of their cause. As the landscape and hydrologic features that control sensitivity are not exposed by our method, more in-depth site research should expose the causes of sensitivity values, thereby providing additional information often critical for local decision-making.
9.6
Conclusions
We developed a method to quantify a catchment’s streamflow sensitivity to water storage changes. This storage sensitivity of streamflow can be approximated by an analytical equation that is a function of the flow rate of interest, and Brutsaert and Nieber recession parameters that can be directly derived from hydrograph recession analysis. The stream flow response we obtain by the α and β values derived for 725 catchments across Europe (Figure 9.1) can have several orders of magnitude to a given flow change, depending on α and β values and the flow rate (Figure 9.2). The storage sensitivity to streamflow for low flow (²S (Q 85 )), median (²S (Q 50 )), and high flow (²S (Q 15 )) conditions show strong regional differences in sensitivity to water storage changes (Figure 9.3). Although the regional differences vary between the flow percentiles, some regions stand out as being more sensitive to water storage changes. The sensitivities are generally highest in many catchments in Spain, in parts of England and Germany, and the Danish island of Zealand, indicating these regions are most sensitive to water storage changes. The most resilient regions to water storage changes are the catchments in southern part of the Alps. A comparison of sensitivity values with different parts of the flow duration curve indicates that ²S , without any information on climate variability and non-storage driven runoff, explains some of the differences between catchments in the variability of the low, median and high flow spectrum. The distinction of different sensitivities to water storage changes provides a novel indicator for hydrologic resilience to climatic perturbations and anthropogenic water use, which can be valuable improving water management strategies and decision making in times of global change.
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HAPTER
C
10
C ONCLUSIONS AND OUTLOOK
In this thesis we investigated hydroclimatic patterns to better understand regional hydrologic differences, and expose fundamental differences in how catchments function. This investigation started with seasonal climatic patterns, moved towards seasonal water balances, and subsequently used seasonal hydrologic patterns as a reference to understand long-term (mean annual) and event scale (floods and low flows) hydrologic response. The approach used in all chapters using spatial and temporal hydro-climatic patterns to unravel hydrologic response - has provided new tools to bring order to the diverse way catchments function around the world, and provides new insight into regional hydrologic differences and the importance of various hydrological processes. The long-term overarching goal is to work towards a widely accepted global hydrological classification system that, based on measurable catchment properties, can differentiate how regions hydrologically function across multiple timescales. The full development of such a general classification system for hydrological sciences was too ambitious to cover in this dissertation. Instead I have generated some new puzzle pieces that help organising hydrologic functioning at the catchment scale across multiple temporal scales and locations.
10.1
Short summary of chapters
In the first part we focused on seasonal conditions. Recent hydrologic synthesis efforts suggested that seasonal hydrology is at the core of overall catchment responses, and understanding it will assist in understanding streamflow variability at other time scales. With a hypothesized strong influence of seasonal climate on seasonal hydrology, we first focus on seasonal climate conditions. Climate classifications are vital for ordering past, current and future climatic conditions. Yet, previous approaches only captured specific aspects of this climate signal, and lose all other information available in the observations. In Chapter 2 we examined to what degree 131
CHAPTER 10. CONCLUSIONS AND OUTLOOK
observations of the monthly climate signal of precipitation and temperature can be described by a sinusoidal function with an annual period, and no upper bound to the precipitation seasonality. This test revealed to what degree there is a distinct pattern in the global monthly climate signal, which allowed synthesising most of the monthly precipitation and temperature climatology using indices that are straightforward to interpret physically. This quantitative conceptualisation improved our understanding of global seasonal climatology and can provide a basis for climate similarity schemes among different sciences, including hydrology. In Chapter 3 we showed how seasonal climatological conditions are strongly connected to seasonal hydrologic conditions. We grouped catchments located across the continental U.S. into several clusters with similar seasonal water balance behaviour. We then delineated the boundaries between these clusters on the basis of a similarity framework developed in Chapter 2. The clustering of catchments based on the seasonal water balance has a strong relationship not only with regional patterns of the climate indices but also with regional ecosystem, soil, and vegetation classes. Based on the classification we demonstrated that the seasonal water balance does have a strong imprint on signatures of streamflow variability over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). Further exploring this connection formed the basis for the subsequent chapters.
In the second part we focused on long-term average conditions. Mean precipitation and potential evaporation are commonly studied drivers of mean hydrologic response as aridity (the ratio of potential evaporation to precipitation) explains ∼90% of the spatial differences in mean annual runoff across the globe. However, it was uncertain whether documented changes to mean precipitation and potential evaporation also translate to aridity being the dominant driver of changes in water availability over time, and how this dominance varies across the land surface. In Chapter 4 we showed that key assumptions underpinning the recent assessments of the dominant drivers of streamflow changes are contradicted by observations of many watersheds located in diverse climates and landscapes. In Chapter 5 we generated new global patterns on the importance of aridity to changes in runoff by evaluating its relative sensitivity to change in combination with observed trends. This reveals runoff is most sensitive to changes in aridity across only ∼20% of the land surface, meaning other factors dominate for the remaining 80%.
In the third part we used seasonality to understand event scale hydrological response. First, we focused on flood conditions. In Chapter 6 we exposed the primary drivers of flooding for 420 US catchments, by exploring which flood-generating processes control the seasonality and magnitude of maximum annual flows. The generated continental-scale classification of dominant flood generating processes emphasises the disparity between extreme rainfall and flooding, and can assist predictions of the nature of flooding and flood risk within the continental US. Subsequently we tested if increases in rainfall extremes already lead to increases in floods. Past analyses of trends 132
10.1. SHORT SUMMARY OF CHAPTERS
in observed floods often focus on relatively frequent events, whereas changes in rare floods are only studied for a small number of locations that have exceptionally long observational records. In Chapter 7 we assessed changes in the largest flood events (∼0.033 annual exceedance probability) observed during the period 1980-2009 for 1778 catchments located in Australia, Brazil, Europe and the United States. The occurrence of rare floods shows strong decadal variability and peaked around 1995. During the 30-year period there is an overall increasing trend in the frequency and magnitude of floods. The attribution of the exposed decadal variability and overall increase of extreme floods is key to predicting future flood changes, but is difficult to link to causal factors at this stage.
Subsequently, we focused on low flows, with a particular emphasis on seasonality effects. In Chapter 8 we tested the role of climate and landscape for the timing and magnitude of 10-day moving average lowest annual flow (LAF) conditions of 420 catchments in the United States. First, data indicated that for most catchments and for most years, LAF conditions occur at the end of summer and beginning of fall. The timing is poorly explained by precipitation, snow storage and evaporative demand alone, because for most catchments evaporation dominated subsurface storage depletion postpones LAF by several weeks to months. During the period prior to low flow events evaporation almost always exceeds precipitation and is often an order of magnitude higher than streamflow rates. The sensitivity of the LAF magnitude to storage changes, rather than climate variability, controls the interannual variability of the LAF magnitude. Together this exposes that evaporation dominated subsurface storage depletion is generally the primary cause for the occurrence of annual low flow conditions, whereby drainage properties of the catchment strongly control the associated magnitude of events. This influence of evaporation and landscape should be well represented in hydrologic models and drought indices that inform on low flows.
Because not all spatial hydrological differences can be explained by seasonal hydro-climatic conditions, we concluded with the development of a parsimonious model that describes how catchments release water to river systems. In Chapter 9 we introduced storage sensitivity of streamflow (²S ), which for a given flow rate indicates the relative change in streamflow per change in catchment water storage. ²S can be directly derived from streamflow observations. Analysis of 725 catchments in Europe reveals that ²S is high in e.g. parts of Spain, England, Germany and Denmark, whereas flow regimes in parts of the Alps are more resilient (that is, less sensitive) to storage changes. A comparison of ²S with observations suggests that ²S is a significant control on the regional differences in variability of flow conditions.
Overall, spatial and temporal hydrological patterns helped to expose similarities and differences between catchments, for different processes and different timescales. The seasonal climatic patterns dominate seasonal hydrologic response, and are at the core of overall catchment 133
CHAPTER 10. CONCLUSIONS AND OUTLOOK
response, over a wide range of time scales (daily to decadal) and a wide range of states (low flows to floods). The rest of the unexplained hydrological variabillity can at least partly be explained by regional differences in how catchments filter available water storage into streamflow.
10.2
Outlook and future work
This thesis leads to several opportunities for follow-up research. The examples we present below are not a complete overview, but provide some of the most obvious follow-up research that further explores issues we have addressed: Improving the description and link of seasonal climatology and hydrology In Chapter 2 we failed to describe the climatology of places with a bi-modal precipitation regime, while the simplicity of the quantification is maintained. Follow-up work can aim at extending the framework, which allows description of these climates too, and thereby would provide further insight into global seasonal climatological patterns. Other extensions to the framework could be including the effects of rainfall variabillity (e.g. interannual variabillity or storminess), or to use the framework for mapping climatic change. Second we have tested and described how seasonal climatological patterns relate to seasonal hydrological patterns, hydrology at other time scales, (and rather qualitatively) to understand how this relates to landscape (soils, vegetation). We have not explored this globally. Once reliable global hydrological data becomes available, using the seasonal climate framework could help to better organize the seasonal hydrological conditions that influence so many things around us. Furthermore the quantitative link between intra-annual climate and vegetation patterns can now be explored with more informative climatic descriptors than what has been done previously. Better understanding snow effects on long-term water availability In Chapter 3 Figure 3.9 we highlighted that snow conditions appear to affect the long-term water balance of a catchment. This pattern is further explored in Appendix E where we show that, contrary to the current paradigm, mean streamflow is likely to reduce for catchments that experience significant reductions in the fraction of precipitation falling as snow. After publication, mutually inconsistent hypotheses have been proposed to explain this behavior [13, 152, 352], but no comprehensive explanations are available to explain the observations. Why does less snow lead to less river flow and more evaporation? Is it caused by changes in snow cover, soil freezing, infiltration processes, timing of plant water uptake or something else? Which processes are important where? Solving this puzzle will have significant follow-on impacts for hydrological models and climate change impacts on water availability, ecosystem functions and other systems impacted by long-term reductions in river flow and evaporation, and their feedbacks to the water cycle. A proposal called CHanges In Precipitation Phase have Effects on River flow - CHIPPER 134
10.2. OUTLOOK AND FUTURE WORK
has been submitted to the Natural Environment Research Council (UK) by Dr. R.A. Woods to further investigate this.
Extending understanding of controls on mean runoff I am currently leading the preparation of a review paper on the Budyko framework, which has played a central role in the Chapters 4 and 5, and closely links to Chapter 3 Figure 3.9. This review will critically evaluate past uses, and provide an outlook on potential future uses of the framework, also in other fields than hydrology alone. In addition the review should help to better organize and understand the factors that control the annual water balance and its changes. Second, in Chapter 5 we currently describe the role of aridity changes for changing water availability, but ideally these can be further separated into changes in precipitation and changes in potential evaporation. This extended version is now in preparation as an article for Water Resources Research.
Combining flood mechanisms with flood change studies The work related to floods has several logical extensions. First the approach presented in Chapter 6 can be applied to other places (and other spatial scales) so we get an overview of global dominant flood generating processes rather than just in the United States. The relatively simple nature of the analysis allows the methods to be applied in other places too. If we want to use regional differences in flood generating mechanisms to improve modelling approaches and further extend our process understanding we may want to extend the analyses with more detailed process representations. Furthermore flood trend analysis can be improved using maps of dominant hydrological processes such as presented in Chapter 6. By investigating the change (in magnitude and/or frequency) of flood peaks, in combination with the change in (in magnitude and/or frequency) of the flood generating mechanisms, we should be able to better attribute observed flood trends. Our analysis in Chapter 6 provides insight into the processes that are responsible for frequently occurring annual flow peaks. This does not necessarily say something about mechanisms causing the biggest flood peak. So before we combine approaches presented in Chapter 6 and 7, we either extend the process representation part to focus on the biggest flood peaks, or we need to focus on trends of more frequently occurring floods.
Working towards a globally accepted classification scheme The longer term goal of working towards a globally accepted classification scheme that helps to order catchments around the world, is challenging, and is constrained by many factors that are beyond the scope of what is presented in this thesis. Yet, we have shown how simple data-based 135
CHAPTER 10. CONCLUSIONS AND OUTLOOK
approaches help to understand and characterise primary differences between catchments. Many of these between-catchment differences have not been unveiled during far more computationally demanding hydrological classifications that lead to mathematically the most distinctive hydrological groups. Yet, simple empirical analysis with a “hydrological perspective" still reveals so many first order differences between places that have not been revealed before using more complex classification approaches. Thus, we should not forget that the journey of working towards a globally accepted classification scheme can benefit a lot from simple data-based approaches. Real progress will be made when we ask the right questions, rather than when we decide to purchase our next supercomputer.
136
APPENDIX
A
S UPPORTING INFORMATION C HAPTER 2
The time-averaged value of P(t) can deviate from P because C r is numerically approximated (see Figure A.1), depending on the δP and s d values
Figure A.1: Range of the time average P(t)/P values that occur for different δP values because the inaccuracy of the correction factor C r .
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APPENDIX A. SUPPORTING INFORMATION CHAPTER 2
Table A.1: A description of the precipitation pattern for regions where X p exceeds 0.3. Region
Description
South-West United States, North-West Mexico
Part of southwestern United States (around Arizona, New Mexico) has a bimodal precipitation regime with a distinct monsoon season during summer time, while total annual precipitation is generally low (P
