Scaling soil moisture for hydrological models - Hydrologie.org

Scales in Hydrology and Water Management/

Echelles en hydrologie

et gestion de l'eau

77

(IAHS Publ. 287, 2004)

Scaling soil moisture for hydrological models

1

ALAIN PIETRONIRO , ERIC D. SOL LIS & N. KOUWEN 1 National Water Research Saskatoon, Saskatchewan al.pictroniro@,ec.gc.ca 2 Department

Institute, National Hydrology S7N 3EIS, Canada

of Civil Engineering,

University

of Waterloo,

Research

Centre,

Waterloo,

2

11 Innovation

Ontario

N2L 3G1,

Blvd.,

Canada

Abstract Surface soil moisture status is probably the most ubiquitous of all hydrological state variables. It is also often the most important since it is the dominant control for understanding runoff. Remote sensing techniques show promise in assisting hydrologists in describing and measuring surface soil moisture and much effort has gone into this problem. Yet, the reality is that even if we could estimate soil moisture at any scale, there would be no clear advantage from the numerical modelling point of view to do so. This paper describes work dedicated towards understanding of soil moisture variability and the feasibility of using remotely sensed derived estimates in a meaningful way for hydrological modelling applications. The results are quite ambiguous as to the ideal scale to represent soil moisture for hydrological applications. K e y w o r d s h y d r o l o g i c a l m o d e l l i n g ; r e m o t e s e n s i n g ; s c a l e ; soil m o i s t u r e ; v a r i a b i l i t y

Invariance d'échelle de l'humidité du sol pour les modèles hydrologiques Résumé L'état de l'humidité du sol superficiel est sans doute la plus répandue des variables hydrologiques d'état. C'est souvent aussi la plus importante puisqu'elle la variable dominante du contrôle des écoulement. Les techniques de télédétection ont donné l'espoir qu'elles pourraient aider les hydrologues à représenter et à mesurer l'humidité du sol superficiel et beaucoup d'efforts ont été consacrés à cette tâche. Cependant, la réalité est que même si nous arrivions à estimer l'humidité du sol à toute échelle, il n'y aurait pas d'avantage évident à le faire du point de vue numérique. Cet article présente un travail consacré à la compréhension de la variabilité de l'humidité du sol et la faisabilité d'utiliser des estimations dérivées de la télédétection de façon satisfaisante pour la modélisation hydrologique. Ces résultats sont tout à fait indifférents à l'échelle idéale pour représenter l'humidité du sol pour les applications hydrologiques. M o t s clefs h u m i d i t é d u s o l ; t é l é d é t e c t i o n ; v a r i a b i l i t é ; é c h e l l e ; m o d é l i s a t i o n h y d r o l o g i q u c

INTRODUCTION Extensive work has been done over the last few years in both soil moisture monitoring using remote sensing and the application of remote sensing to hydrological runoff modelling. Recent publications by Schultz & Engman (2000), Beven & Fisher (1996) and others, have noted that that there have been few studies that have incorporated remote sensing soil-moisture information into rainfall-runoff studies. The reasons for this are varied. Much of it is related to the robustness of soil moisture estimates derived from satellite platforms, but it is also due to the fact that the spatial and temporal time scales for which the data are available are often not suitable for hydrological application.

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A lain Pietroniro et ai.

There is a growing tendency in the modelling community to put much more faith in remote sensing technologies than perhaps is deserved. In many cases there also appears to be a misunderstanding of the effects of scale and the appropriate use of the term "soil moisture" as it relates to the true status in the field. This paper examines the meaning of the term soil moisture from the perspective of the field hydrologist and modeller and attempts to provide some insights into the ubiquitous terminology. An examination of field experiments in a relatively idealized case and the sensitivity of soil moisture in a conceptual hydrological model application are discussed. Background information on established methods of soil moisture monitoring and their limitations is presented and an introduction to the application of remotely sensed soil moisture estimates in hydrological models is provided.

MEASURING SOIL MOISTURE Estimating the amount of water stored in a soil profile is essential in most water management projects. Implementation of appropriate techniques for water manage ment and conservation practices requires quantitative assessment of the soil water status. This is particularly true in agricultural water management projects and operational hydrological modelling such as flood forecasting. In many cases, particularly watershed-scale monitoring or modelling, soil moisture is inferred from more easily obtainable hydrological variables such as rainfall, runoff and temperature. Conventional in situ measurements of soil moisture are costly and provide information at only a few selected points. In most hydrological models, the soil moisture component is an intermediary component within the water balance equation and is not assessed using measured soil moisture data. Engman (1990) states: "In these models, soil moisture is a system state that must be initiated and then, time wise, recomputed by increasing it when precipitation is added or decreased by drainage and évapotranspiration. In general, existing models' representation of soil moisture is simply a step to make the model work and not a physical representation of soil moisture." In order to obtain spatial and temporal estimates of soil moisture at a small scale or at the basin scale, traditional and non-traditional approaches to this mapping must be used. Traditionally, ground data are used to assess the accuracy of any remote sensing algorithm and are a fundamental component of data analysis (Foody, 1991). The method used for soil moisture estimation of the grab samples is usually based on oven drying techniques and automatic soil moisture extraction using time-domain reflectometry (TDR) probes. Curtis & Trudgill (1974) note that there are a wide variety of techniques that exist for soil moisture determination, with the oven drying technique the most common. In all cases if the wet weight, dry weight, volume of the sample and weight of the container are known, then bulk density, gravimetric and volumetric soil moisture for each sample can be estimated. Bulk density is defined as the mass of a unit volume of dry soil (Brady, 1974). Bulk density (g cm" ) is calculated as: 3


79

where DW is the mass of dry soil in grams and Vol is the volume of the sampling device. Because consistent volume measurements are taken at each sampling point at the sites, the volumetric moisture (cm cm" ) can also be calculated directly as: S

3

3

m = ( WW - D W )/( Vol p,„) v

S

(2)

s

where WW is the wet weight of the soil and p„, is the density of water which is assumed to be 1.0 g cm" . Thus m is expressed in cm of water per unit volume of soil. The gravimetric moisture content (m ) is defined as: S

3

3

v

g

nig = (WW -DW )/DW S

S

(3)

S

and is expressed as a ratio or percentage of mass of water per unit dry mass of soil. When only gravimetric samples are taken and bulk density is known, conversion to volumetric moisture is estimated by re-arranging Equation (1) and combining it with (2). This results in an expression for converting between gravimetric and volumetric moisture: m= v

[p, (WWs-DW )/DW \xBD y

s

s

= p mgBD w

(4)

The spatial distribution of soil moisture is much more difficult to characterize and depends on local and regional topographic variations, rainfall and snow distributions as well as local soil properties. Field experiments in the Roseau River basin of southern Manitoba, Canada, were carried out and intensive sampling of soil moisture using TDR and grab samples were obtained and analysed using the methods described above. The fields were bare soil agricultural fields in a prairie region. Changes in elevation within the sampling regions were in the order of centimetres and represent the ideal target for soil moisture and remote sensing studies. The soil types in the larger area varied from sandy soils to clay soil. Examples of two field sites samples are shown below (Figs 1 and 2). The time series plots in each of the figures represent the average field condition changes over a one week period in August. The spatial distribution of soil moisture is shown for one time slice of intensive field sampling at 1-metre intervals and the semi-variogram is shown at the bottom left. In both cases the correlation lengths for a very flat region (clay and sand) are still quite low. Because of the high variability of soil characteristics, water table depth and soil moisture within a given area, it is very difficult to account for varying soil moisture status and the resulting variable infiltration capacities. It is well understood that saturation excess and infiltration excess overland flow are primarily controlled by the surface soil moisture and because of this understanding Beven et al. (1984) and others have tried to model this variation using the well-known soil topographic index. Of course all deterministic hydrology models and land-surface models require knowledge about the distribution of surface moisture. Remote sensing techniques as opposed to point measurements clearly have the advantage of providing an overall picture of a particular region or basin. Depending on the sensor, resolution can vary from 25 m to a number of kilometres, however, the signal received from a remote sensing platform is usually the result of a mixture of land cover, topographic and atmospheric effects. Reasonable knowledge of electromagnetic energy interaction within the biosphere and the atmosphere is required to separate these components. Passive and active microwave remote sensing of soil moisture offer the most promise for hydrological applications because of their cloud penetrating capabilities. In both cases, the soil dielectric property is an indicator of soil moisture content but in the

Alain Pietroniro et al.

3.111^ GGÎI t m

i r*

::

2;*

„-*o

5

:-c

2**

3

6

increments. The average rainfall intensities were set to 2.10 mm h" for a 2-year return period, 3.15 mm h" for a 10-year return period and 4.46 mm h" for a 100-year return period, corresponding to total cumulated rainfalls of 5.04 cm, 7.56 cm and 10.71 cm, respectively, for a 24-h storm duration. Surface runoff will occur when the rainfall intensity is greater than the potential infiltration rate that is estimated at each time step, and is estimated as the difference between the cumulative infiltration and cumulative rainfall. Initial moisture conditions will also influence cumulative Green-Ampt infiltration values. This is depicted in Fig. 3 where cumulative infiltration is plotted as a function of initial moisture conditions and time. This figure shows the influence of initial conditions on the cumulative infiltration for a fixed return period. This clearly shows that wetter soils result in greater surface runoff. Total potential infiltration as a function of initial conditions and soil type are shown in Table 1. Table 2 contains a list of the total actual infiltration values estimated during the 100-year simulated storm. The soils with increasing suction head and conductivity values are influenced more by initial condi tions as is evident from these tables. 1

1

1

Scaling soil moisture for hydrological

models

85

Total Infiltration (cm)

0

4

8

12

16

20

24

Time(hours)

Fig. 3 Cumulative infiltration for 10-year design storm and variable initial conditions.

Table 1 Total potential infiltration (cm).

Sand Loamy sand Sandy loam Loam Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay

Initial volumetric moisture 0.2 0.1 0.15

0.25

0.3

0.35

291.34 79.35 35.12 13.46 26.27 9.43 7.74 8.66 5.77 5.98 4.63

288.04 76.59 32.28 11.92 23.51 7.47 6.35 7.09 4.54 4.84 3.70

286.82 75.55 31.16 11.31 22.44 6.62 5.79 6.45 4.02 4.38 3.32

285.52 74.4 29.91 10.62 21.25 5.53 5.14 5.72 3.39 3.86 2.89

Initial volumetric moisture 0.1 0.2 0.15

0.25

0.3

0.35

7.59 4.82 6.02 4.94 5.85 4.66 4.39 4.60 3.93 4.00 3.54

7.59 6.77 5.72 4.67 5.57 4.23 4.03 4.13 3.4 3.59 3.05

7.59 6.63 5.62 4.63 5.47 4.00 3.78 4.06 3.16 3.27 2.81

7.59 6.48 5.5 4.51 5.37 3.66 3.61 3.79 2.83 3.12 2.49

290.28 78.48 34.24 12.99 25.41 8.84 7.31 8.18 5.40 5.63 4.34

289.19 77.57 33.29 12.48 24.49 8.20 6.85 7.66 4.99 5.26 4.03

Table 2 Total actual infiltration (cm) for 10-year design storm.

Sand Loamy sand Sandy loam Loam Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay

7.59 7.03 5.93 4.89 5.76 4.54 4.3 4.37 3.61 3.81 3.37

7.59 6.9 5.83 4.75 5.67 4.40 4.17 4.37 3.63 3.76 3.19

86


Examining the changes in soil type and moisture content, the sensitivity of soil type to initial conditions can be estimated as:

where F is the cumulative infiltration, type is the soil type and 0 is the initial moisture condition. The sensitivity value measured between the sand and clay soil, at 0.1 and 0.35 volumetric moisture for total 24-h potential infiltration is approximately 162. This signifies that the difference in total 24-h cumulative infiltration is 162 times higher across the soil textures and prescribed moisture. Obviously, soil texture is extremely important in total infiltration calculations and initial conditions will not exert as great an influence on overall cumulative infiltration. The infiltration rate for the sandy soil parameters is constant for all initial moisture conditions. This is because in all simulation cases, the rainfall rate does not exceed the infiltration rate of the soil, allowing all the rainfall to infiltrate. In the case of the actual infiltration estimates made for the 24-h simulated storms, initial moisture conditions were more important than for the potential infiltration case. The sensitivity factor for a 10-year return period storm for sand to clay at 0.1 to 0.35 initial moisture is calculated as 4.8 to 1. This is again due to the fact that all rainfall infiltrates into the sandy soil and the limiting factor is the rainfall amount rather than the soil capacity. For the loamy sand and clay soil, using the same moisture conditions as above, the sensitivity factor is 2.4, 3.8 and 4.9 for the 2, 10 and 100-year return intervals, respectively. In these cases, not all the rainfall infiltrated and initial conditions played an important part in determining total cumulative infiltration. As noted above, the Green-Ampt equation can be solved for a unique set of parameters and a fixed initial soil moisture condition for given rainfall inputs and applies to a point location. Areal estimates of Green-Ampt infiltration require an assumption about the distribution of soil moisture, conductivity and suction head for a uniform rainfall field. For example, if an initial distribution of soil wetness is assumed, with all other parameters fixed, then the resulting distribution is not easily derived. The same situation exists for all other model parameters. Studies examining the effects of the spatial distribution of infiltration parameters on the infiltration process have been conducted using a variety of infiltration models (De Roo et al, 1992; Smith & Hebbert, 1979; Russo & Boton, 1992; Loague & Gander, 1990). Results obtained using the Green-Ampt equation for sensitivity were not found in the literature. Russo & Bouton (1992) showed that initial moisture and saturated moisture data for samples taken from a 20 m long by 1.7 m wide by 2.5 m deep experimental plot were normally distributed. Saturated conductivity was shown to be log normally distributed. This is not surprising since soil moisture is bounded at both the saturation and wilting-point moisture contents. Examining the effects of saturated conductivity, suction head and saturated moisture distributions on Green-Ampt infiltration is beyond the scope of this work. However, since the focus is initial moisture conditions, it is important to determine how initial moisture distributions will affect Green-Ampt infiltration. For this research, a normal distribution of initial soil moisture conditions was used to simulate GreenAmpt infiltration and the resulting distribution of total infiltration was examined. This


models

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was accomplished through a simple Monte Carlo simulation, allowing for normally distributed initial moisture values within a given standard deviation. The normal deviates were generated using the method outlined by Press et al. (1988) and simulations were performed for steady rain conditions and for the 2-year and 100-year storms described earlier. The first sets of results are for a constant rainfall rate of 10 mm h" using a silty-loam and clay loam soil and simulating 1000 initial conditions. The Green-Ampt parameters were taken from Chow et al. (1988) and initial conditions were set at 0.1, 0.2, 0.3 and 0.4 volumetric moisture with a standard deviation of 0.05 and 0.1. Examples of the distributions obtained are shown in Table 3 and an example of the time evolution of infiltration is plotted in Fig. 4. The table highlights the differences in cumulative Green-Ampt infiltration for different initial conditions, two different soils and two standard deviations. In all cases, the mean cumulative infiltrations are almost identical using either standard deviation. Clearly for constant rainfall, the mean initial moisture value will determine the overall infiltration, provided the initial moisture distribution is normal. In all cases, the difference among the 24-h cumulative Green-Ampt infiltration and the point value are minimal. The largest difference is for the silty-clay loam with an initial volumetric moisture content of 0.40, and the difference represents less than 2% of the total infiltrated volume. The next sets of results shown in Table 4 are for variable rainfall conditions and demonstrate a trend similar to that obtained in the constant rainfall case. The largest difference between the two initial distributions is at the 0.4 % volumetric moisture level for the silty clay loam soil and represents less than 1% of the infiltrated volume. These results demonstrate that the mean soil moisture value for a fixed set of GreenAmpt parameters provides a reasonable estimate of cumulative infiltration for both constant and variable rainfall cases. This has important implications when deriving soil moisture algorithms for distributed models. 1

Table 3 Differences between point and distributed cumulative infiltration using Monte Carlo simulations to estimate distributed infiltration for a constant rainfall of 1 cm h" for 24 h. 1

Soil Type

Initial conditions Mean Standard deviation

Loam Loam Loam Loam Loam Loam Loam Loam Silty clay Silty clay Silty clay Silty clay Silty clay Silty clay Silty clay Silty clay

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4

loam loam loam loam loam loam loam loam

0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.1

Total 24 hour infiltration Point simulation Distributed simulation Infiltration (cm) Mean infiltration (cm) 13.16 12.27 11.19 9.75 13.16 12.27 11.19 9.75 8.54 7.58 6.41 4.81 8.54 7.58 6.41 4.81

13.17 12.27 11.18 9.72 13.15 12.23 11.10 9.82 8.55 7.58 6.40 4.71 8.53 7.53 6.27 4.73


88

Occurrences 1200 i Mean = 0 . 3 0 St. D. - 0.05

• 24 hours • 18 hours • 12 hours El 6 hours • 1 hour

600 400 200 0 •

In JUr

3.81

5.13

6.45

2.93

7.77

Cumulative infiltration (cm)

4.07

5.21

6.36

Cumulative Infiltration (cm)

Fig. 4 Green-Ampt infiltration distribution for silty-clay-loam soil and constant rainfall.

Table 4 Green Ampt cumulative infiltration for variable rainfall condition. Time (h) Sandy clay 1 18 24 Sandy clay 1 18 24 Sandy clay 1 18 24 Sandy clay 1 18 24

Volumetric moisture 0.4 0.3 0.2

Time (h) 0.1

loam 2-year storm (SD = 0.05) 0.06 0.06 0.06 0.06 2.26 2.63 2.87 2.95 2.68 3.05 3.29 3.46 loam 2-year storm (SD = 0.1) 0.06 0.06 0.06 0.06 2.23 2.59 2.85 3.03 2.65 3.01 3.27 3.45 loam 100-year storm (SD = 0.05) 0.12 0.12 0.12 0.12 3.07 3.89 4.35 4.57 3.88 4.77 5.25 5.47 loam 100-year storm (SD = 0.1) 0.12 0.12 0.12 0.12 3.84 3.78 4.28 4.56 3.83 4.64 5.18 5.46

Loam 1 18 24 Loam 1 18 24 Loam 1 18 24 Loam 1 18 24

soil

soil

soil

soil

Volumetric moisture 0.4 0.3 0.2 2-year storm (SD = 0.05) 0.06 0.06 0.06 2.77 2.96 3.13 3.19 3.38 3.55 2-year storm (SD = 0.1) 0.06 0.06 0.06 2.79 2.96 3.13 3.21 3.38 3.55 100-year storm (SD = 0.05) 0.12 0.12 0.12 4.6 4.88 5.14 5.5 5.78 6.04 100-year storm (SD = 0.1) 0.12 0.12 0.12 4.63 4.88 5.15 5.53 5.78 6.05

0.1 0.06 3.28 3.7 0.06 3.28 3.70 0.12 5.42 6.32 0.12 5.37 6.27

SOIL MOISTURE REPRESENTATION IN HYDROLOGICAL MODELS The study of storm runoff generation forms the basis from which deterministic hydrological models are derived. Historically, runoff was often simulated by a black box approach, where the transformation of rainfall to runoff did not involve the detailed hydrological processes which actually generate the runoff (Chow et al, 1988). The first and most common of these approaches is the unit hydrograph developed by Sherman (1932). The development of the unit hydrograph method coincided with the development of the Richards equation for unsaturated flow, as well as Horton's work on infiltration and the production of runoff. Using computers and computer modelling in hydrology allowed the internal process inherent in the black box approach to be divided into a number of conceptual or empirical processes; however, the system states such as soil moisture are still estimated states within the black box processes (Engman, 1986). It appears that over the last few decades, research has been implemented to help


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formulate a better understanding of the streamflow generation process with much of the attention centred on infiltration and consequently the determination of effective rainfall. Given the diverse nature of the infiltration process, this is by no means a simple task. As stated by Wood et al. (1990) "Ideally, a prediction of the effective rainfall should be based on a proper understanding of the processes involved, but study of these processes has revealed patterns of real complexity." It would appear that runoff generation stems from a number of mechanisms, involving both surface and subsurface flow routes. Kirkby (1978) discussed stream runoff generation mech anisms, where methods other than the Hortonian, infiltration limiting mode are examined and these are summarized by Wood et al. (1990). In general, overland flow may be generated through the infiltration excess of rainfall on lower permeability soils or through rainfall on contributing saturated areas. Therefore, one notion in current modelling practice is the partial area hydrology concept. This is based on dividing a watershed into contributing areas which do and do not produce runoff during a storm event. These contributing areas are primarily dependent on topographic and soil properties (Wood et al, 1990). There are two basic problems associated with identifying these contributing areas (van de Griend & Engman, 1985). The first problem is the dependence on topographical, pedagogical and geomorphological variation within an area or sub-basin. Obviously, these factors will have tremendous influence on the soil moisture and saturation characteristics of a given area. The second stems from the temporal variation of these contributing areas. In this case, soil moisture and saturation characteristics will depend on season, rainfall and climate conditions. Hydrological models need to deal with the spatial patterns of antecedent moisture conditions, soil hydraulic characteristics and rainfall intensities, knowing that these patterns will be highly variable in both space and time. In order to deal with spatial variability in hydrological models (particularly soil moisture and soil properties), various methods of basin segmentation have been proposed and implemented in hydrological models. A technique proposed by Wood et al. (1988) requires discretization of the basin into Representative Elemental Areas (REA). The REA is defined as an areal element within a basin where the hydrological properties of this area are definable but are not significantly different at a smaller scale. This technique has been implemented within the SHE model which was classified by Wood et al. (1990) as a completely physically-based distributed model which uses a finite difference approach to solve the combinations of partial differential equations which describe surface and subsurface flow. The approach stems from earlier work carried out by Freeze & Harlan (1969) with simplifications for modelling at the basin scale. The computational complexity of the model made calibration and validation difficult. Another method of discretization is the Hydrologie Response Unit (HRU) approach. In this case a basin is subdivided into areas which represent hydrologically homogeneous characteristics such as land cover, slope and aspect. Kite & Kouwen (1992) note that these computational elements may be based on a grid system, as in the Hydrotel system, or on a sub-basin system, as in the USGS-PRMS (Leavesley & Stanard, 1990) model. In both cases, the HRU will generate a distinct hydrological response but its location within the basin is only important for routing considerations (Donald, 1992). This differs from the REA approach where the element's location will influence hydrological response.

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Another group of distributed models includes the WATFLOOD (Kouwen et al, 1993) and SLURP (Kite & Kouwen, 1992) simulation models. These distributed models differ from other distributed models in that the spatial variability of different hydrological parameters is not captured using areas of similar hydrological response, as in the HRUs. Instead, Kouwen et al. (1993) introduced the concept of Grouped Response Units (GRU). GRUs are heterogeneous groupings that are sized by meteo rological and routing considerations. A GRU is made up of non-contiguous HRUs usually based on land cover classifications, that have similar hydrological response and that share a common drainage system. Runoff generated from the different groups of HRUs is then summed together and routed to the stream and river system (Kite & Kouwen, 1992). For example, two GRUs with the same percentages of land cover, total rainfall and initial conditions will produce the same amount of runoff regardless of how these land cover classes are distributed within the grid. This stems from the well established concept in urban hydrology where runoff from small areas can be calculated by summing runoff from both pervious and impervious areas (Kouwen, 1988). Kite & Kouwen (1992) showed that a semi-distributed watershed model based on the GRU approach using land cover classifications will give better calibration and validation statistics than the lumped version of the same daily runoff model. Similar results were reported by Tao & Kouwen (1989) for an hourly, time-based flood forecasting model (WATFLOOD). The GRU or ASA approach is in some ways scale independent, since the assumption in practice is that parameterization is landscape dependant, and the location of the GRU within the basin will not change its parameterization.

DISTRIBUTED MODELLING OF THE BIG OTTER CREEK WATERSHED The model used in this research (WATFLOOD) is a deterministic, distributed and unsteady flow model developed at the University of Waterloo, Canada (Kouwen, 1988). WATFLOOD uses the Grouped Response Unit (GRU) approach for runoff generation (Kouwen et al., 1993). The watershed chosen for the sensitivity analysis is Big Otter Creek, Ontario, with the outlet at Port Burwell flowing into Lake Erie. Big Otter Creek is located just north of Lake Erie, between 80°30' and 80°56' west and 42°35' and 43°03' north. This basin is well gauged and has been used extensively by Environment Canada for various hydrological studies (OWRC, 1969) and was an IHD (International Hydrological Decade) basin. The physiography of the basin results from deposition associated with glaciation during the late stages of the Pleistocene epoch (Chapman & Putnam, 1984). The watershed is characterized by end moraines, ground moraines, the Norfolk sand plain and abandoned shorelines. The surficial soils consist of deposits of sand and gravel of glacial streams, beach gravel and stratified sands and silts of glacial lakes. The deposits and land forms are related to the glaciation of the basin and the subsequent recession of these glaciers and their resulting melt waters. The melt waters deposited sand and gravel while ice blocked lakes created shorelines. The thicknesses of the overburden averages 15-20 m in the northern part of the basin and 100 m in the southern sections. The overburden is comprised primarily of glacial till (clay, silt, sand and boulders) and lacustrine sand, silt and clay.


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Digitized contours of the basin were used to derive a Digital Elevation Model (DEM) of the basin. The contours were digitized from 1:25 000 NTS maps with 10 m contour intervals. The DEM was used as one of the criteria in selecting the index fields from which soil moisture estimates were made. The watershed is divided into four subbasins by Water Survey of Canada gauges located throughout the basin. Rainfall data for the basin is averaged from six Environment Canada hourly rainfall gauges located outside the watershed boundary. In the case of the Big Otter Creek drainage basin, the watershed was divided into 4 x 4 km grids for modelling purposes. Physiographic parameters required for simulation within WATFLOOD were easily derived from national topographic maps, with the exception of land cover classes. The required physiographic model parameters are listed in Kouwen (2003). A Landsat-TM Geocoded image was used to derive the land use information for the Big Otter Creek basin and subsequent input into the WATFLOOD model. The data sets used for the application of WATFLOOD to the Big Otter Creek gauges were chosen from historic records of hourly streamflow and significant nonsnowmelt runoff events were chosen. The optimized parameters within the model are: permeability, channel roughness, overland flow roughness, depression storage and upper zone depletion. Of these parameters, only channel roughness is not dependent on land use, but is optimized for each gauged basin within the watershed. Kouwen et al. (1993) showed very good transferability of land cover derived parameters between basins within southern Ontario, therefore only the river roughness values were optimized for the Big Otter Creek simulation.

API and initial soil moisture conditions The moisture conditions within a basin can be monitored by keeping track of the total rainfall falling within the basin. The total decays logarithmically in time for periods of no rainfall. This is known as the Antecedent Precipitation Index (API) method and is expressed mathematically as: A

P

I

,

=

k

(

A

P

I

^

(

1

2

)

where t is the time in days, P is the rainfall amount expressed in mm and A: is a recession constant of 0.84. The current method of assessing soil moisture distribution on a grid basis for the WATFLOOD model is to use a linear relationship between maximum soil moisture capacity that is given as 35% volumetric moisture, and the maximum observed API value for southern Ontario which is approximated at 35 mm. The relationship is assumed to be linear and the corresponding soil moisture estimate is 1/100 of the current API value. This means that an API of 20 mm corresponds to a volumetric soil moisture value of 0.2. Raingauge API values are then distributed throughout the basin on a grid square basis to initialize the model if run in the event mode. When the model is used in a continuous mode, the API is updated hourly.

Model sensitivity to initial moisture conditions In studying the efficiency of model output, several criteria have been developed to assess the simulation capability of the model in question. One numerical criterion

92

A lain Pietroniro et al.

suggested by the WMO (1986) is, S, which is the ratio of the root mean square (RMS) error of estimation to the average of the observed flows. This criterion indicates the size of the estimation error relative to the mean flow and is (Donald, 1992):

1 3

( )

A

where q-, is the observed flow at the z'-th time interval and refers to the estimated value. The model was first run under a number of different uniform initial moisture conditions. In these cases each grid square is assigned the same initial moisture value. These values are 0.1, 0.2, 0.3 and 0.35 and are known as simulations A, B, C and D, respectively. The simulation results are listed in Table 5 highlighting the different simulation errors and peak flows obtained for different initial conditions. The normalized RMS value can change by up to 70% as is the case in the 1979 event. Furthermore API derived initial conditions do not necessarily represent the optimum simulation in term of the S statistic. Peak flows can change by up to 86% when comparing between the driest and wettest conditions. This shows that the model can be very sensitive to basin wide changes in soil moisture. The next step is to examine model sensitivity to distributed soil moisture values between grids within the model. Two scenarios were examined. The first scenario simulates a gradual drying of the basin from north to south with the south end of the basin at 0.1 volumetric moisture and the north end fixed at 0.4 moisture value. Another scenario with the north end of the basin dry and the south end wet is also simulated. As in the constant moisture case, Table 6 highlights results of the simulations and shows differences in peak and normalized RMS values using the two different soil moisture gradient directions within the basin for two events. In both scenarios, the average moisture over the entire basin is the same.

CONCLUSIONS It was shown that the Green-Ampt equation is much more sensitive to model parameters related to soil texture than to initial moisture conditions. However, for a given soil texture, it was shown that the initial moisture conditions can significantly affect total cumulative infiltration. In addition it was demonstrated that for an area with constant Green-Ampt parameters, the distribution of moisture within that area will not significantly affect mean cumulative infiltration, provided the moisture distribution is normally distributed. This is important in the context of the GRU approach since components within a GRU have constant infiltration parameters and this reduces the need to discriminate soil moisture within a grid and estimate the sub-grid soil moisture variability. Knowing the average moisture conditions within a grid is important, as shown in the model simulations; although the hydrological model was sensitive to basin wide changes in soil moisture, it was also sensitive to changes in the distribution of average grid moisture within the basin. On the basis of these observations, the largest scale for soil moisture discrimination would appear to be on a grid basis within


93

models

Table 5 WATFLOOD root mean squared error (S) for gridded initial soil moisture for four constant soil moisture values and north-south basin gradient changes. Storm event Gauge Soil moisture simulations

API

A (RMS) 0.1

B (RMS) 0.2

C (RMS) 0.3

D (RMS) 0.4

79/11/21

Calton Otterville Staffordville Tillsonburg

0.29 0.64 0.46 0.34

0.28 0.65 0.47 0.34

0.27 0.68 0.48 0.33

0.26 0.87 0.57 0.37

0.49 1.43 0.86 0.69

81/08/07


1.51 4.03 1.10 3.65

1.51 4.03 1.09 3.64

1.51 4.03 1.10 3.65

1.50 4.60 1.10 3.66

1.58 4.63 1.32 4.05

81/08/29


Not operational 1.22 1.22 2.00 1.99 0.88 0.88

1.24 2.07 0.91

1.30 2.32 1.06

1.61 3.22 1.69

83/04/29


0.28 0.29 1.24 1.14 0.31 0.29 Not operational

0.28 1.24 0.31

0.39 1.62 0.49

0.78 2.07 0.77

83/05/19


0.64 0.66 0.88 0.92 0.59 0.56 Not operational

0.71 0.98 0.65

0.99 1.26 0.86

1.44 1.97 1.39

83/08/08


3.22 8.3 5.45 5.62

1.88 5.39 3.28 3.58

1.99 5.62 3.45 3.75

2.26 6.23 3.91 4.18

2.82 7.43 4.84 5.02

84/06/16


1.95 1.71 1.98 1.53

2.01 1.78 2.07 1.61

2.11 1.86 2.18 1.69

2.35 2.06 2.45 1.9

2.77 2.37 2.87 2.25

Table 6 Sensitivity of WATFLOOD to changes in gridded soil moisture distribution within the basin. Gauge Storm event Soil moisture simulations

API

RMS Dry North

Dry South

Peak flow (cm) Dry Dry North South

79/11/21


0.29 0.64 0.46 0.34

0.34 1.67 0.54 0.61

0.25 0.7 0.72 0.34

74.7 19.4 10.6 49

54.87 7.78 11.7 25.05

83/04/29


0.28 1.24 0.31

0.57 2.7 0.44

0.46 1.3 0.75

68.1 20.2 10.7 45.5

59.7 10.4 14.6 31.2

the basin. The smallest resolution would be average moisture values on a land cover basis within the GRU grids. We speculate that soil moisture discrimination on a finer

94


scale would not lead to better infiltration estimates, based on the Green-Ampt simulations discussed. The remote sensing needs defined by the requirements of the hydrological model appear at best to be based on the ability to discriminate average moisture values for different GRUs, or to at least discriminate average moisture values within each grid. This is encouraging because the resolution of a remote sensing platform, particularly passive systems, can provide soil moisture estimates at the gridscales commonly used in hydrological and land surface models.

REFERENCES Beven, K. J. & Fischer, J. (1996) R e m o t e sensing and scaling in hydrology. In: Scaling up in Hydrology Using Remote Sensing (ed. by J. B . Stewart, E. T. E n g m a n , R. A. Feddes & Y . Kerr), 1-18. John Wiley and S o n s , Chichester, U K . Beven, IC. J., Kirkby, M. J., Schofield, N . & T a g g , A. F. (1984) Testing a physically-based flood forecasting model ( T o p m o d e l ) for three U K c a t c h m e n t s . J. Hydrol. 6 9 , 1 1 9 - 1 4 3 . Brady, N . C. (1974) The Nature

and Properties

of Soils. M a c m i l l a n Publishing C o . Inc., N e w York, U S A .

B o u w e r , H. (1966) Rapid field m e a s u r e m e n t s of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resour. Res. 2 , 7 2 9 - 7 3 8 . B o u w e r , H. (1969) Infiltration of w a t e r into non-uniform soil. J. Irrig. Drain.

Div. ASCE 95, 4 5 1 - 4 6 2 .

Brakensiek, D. L. (1977) Estimating the effective capillary pressure in the Green and A m p t infiltration equation.

Water

Res. 13(3), 6 8 0 - 6 8 2 . "

Resour.

Brakensiek. D. L. & R a w l s , W. J. (1988) Effects of Agriculture and R a n g e l a n d M a n a g e m e n t Systems on Infiltration. In: Modelling Agricultural, Forest and Rangeland Hydrology, A S A E publication no. 0 7 - 8 8 . A m e r i c a n Society of Agricultural Engineers, St. Joseph, M i c h i g a n , U S A . B r o o k s , R. H. & Corey, A. T. (1966) Properties of porous media affecting fluid How../. Irrig. Drain. Div. I R 2 , 6 1 - 8 8 . Burdine, N . T. ( 1 9 5 3 ) Relative p e r m e a b i l i t y calculations from pore-size distribution data. Petroleum Trans. Am. Inst. Mining Engrs 9 8 , 5 1 - 7 7 . C h a p m a n , L. J. & P u t n a m , D. F. (1984) The Physiography of Southern Ontario. O G S Special vol. 2. third edn. University of T o r o n t o Press, C a n a d a . C h o w , V. T., M a i d m e n t , D. R. & M a y s , L. W . (1988) Applied Hydrology. M c G r a w - H i l l , Inc., N e w Y o r k , U S A . Curtis, L. F. & Trudgill, S. (1974) The Measurement of Soil Moisture. British G e o m o r p h o l o g i c a l Research Technical Bulletin 13. G e o Abstracts, N o r w i c h , UK.

Group,

de R o o , A. P. J., Hazelhoff, L. & Heuvclink, G. B . M . (1992) Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model u s i n g M o n t e C a r l o m e t h o d s . Hydrol. Processes 6, 1 2 7 - 1 4 3 . Donald, J. R. (1992) S n o w c o v e r depletion curves and satellite s n o w c o v e r estimates for s n o w m e l t runoff modelling. P h D T h e s i s , University of W a t e r l o o , Waterloo, C a n a d a . E n g m a n , E. T. (1986) Hydrologie research before and after A g R I S T A R S . IEEE 5-11.

Trans.

Geosci.

E n g m a n , E. T. (1990) U s e of m i c r o w a v e r e m o t e l y sensed data in hydrologie modelling. Proc. of Remote

Sensing

in Hydrology,

Remote Workshop

Sens.

GE-14(1),

on

Applications

2 5 9 - 2 7 8 . Saskatoon, S a s k a t c h e w a n , C a n a d a .

F o o d y , G. M. ( 1 9 9 1 ) Soil moisture content ground data for r e m o t e sensing investigations of agricultural regions. Int. J. Remote

Sens. 12(7), 1 4 6 1 - 1 4 6 9 .

Freeze, R. A. & Harlan, R. L. (1969) Blueprints for a physically-based digitally simulated hydrologie response model. J. Hydrol.

9, 237-258.

Kirkby, M. J. (ed.) (1978) Hillslope

Hydrology.

John Wiley, N e w York, U S A .

Kite, G. W. & K o u w e n , N. ( 1992) W a t e r s h e d m o d e l l i n g u s i n g land classifications. Water Resour. Res. 2 8 ( 12), 3 1 9 3 - 3 2 0 0 . K o u w e n , N . ( 1 9 8 8 ) W A T F L O O D : a m i c r o - c o m p u t e r based flood forecasting system based on real-time w e a t h e r radar. Can. Water Resour. J. 13(1), 6 2 - 7 7 . K o u w e n (2003) Watflood Users Manual, http://www.watflood.ca K o u w e n , N . , Soulis, E. D., Pietroniro, A., D o n a l d , J. & Harrington, R. A. (1993) G r o u p e d response units for distributed hydrologie modelling. ACSEJ.

Water Resour.

Plann. Manage.

119(3), 289-305.

Leavelsey, G. H. & Stannard, L. G. (1990) Application of remotely sensed data in a distributed-parameter watershed model. Proc. Workshop on Applications of Remote Sensing in Hydrolog}', 4 7 - 6 8 . Saskatoon, S a s k a t c h e w a n , C a n a d a . Loague, K. & G a n d e r , G. A. ( 1 9 9 0 ) R-5 revisited. 1. Spatial variability of infiltration on a small rangeland catchment. Water Resour. Res. 2 6 ( 5 ) , 9 5 7 - 9 7 1 . M c C u e n , R. H., R a w l s , W. J. & Brakensiek, D. L. (1981) Statistical analysis of the B r o o k s - C o r e y and the G r e e n - A m p t p a r a m e t e r s across soil texture. Water Resour.

Res. 17(4), 1 0 0 5 - 1 0 1 3 .

M e i n , R. G. & Larson, C. L. (1973) M o d e l i n g infiltration d u r i n g a steady rain. Water Resour.

Res. 9 ( 2 ) , 3 8 4 - 3 9 4 .

95


M e i n , R. G. & Larson, C. L. ( 1 9 7 1 ) Modelling

the Infiltration

Component

of the Rainfall-Runoff

Process.

Bulletin 4 3 .

W a t e r R e s o u r c e s Center, University of M i n n e s o t a , U S A . M u a l l e m , Y. ( 1 9 7 6 ) A n e w model for p r e d i c t i n g the hydraulic conductivity of p o r o u s media. Water Resour.

Res.

12(3).

513-522. M o r e l - S e y t o u x , H. J. & Khanji, J. (1974) Derivation of an equation of infiltration. Water Resour. O W R C ( 1 9 6 9 ) Water

Resources

of the Big Otter

Creek

Drainage

Basin.

Res. 10(4), 7 9 5 - 8 0 0 .

Water R e s o u r c e s R e p o r t 1. O n t a r i o W a t e r

Resources Commission, Toronto, Canada. Pietroniro, A., Soulis, E. D., K o u w e n , N . , R o t u n n o , O. & Mullins, D. W . (1993) Extracting distributed information from C-band w i d e swath S A R imagery. Can. J. Remote

Sens.

1 9 ( 1 ), 7 7 - 8 2 .

Press, W . H., Flannery, B . P., T e u k o l s k y , S. A. & Vetterling, W . T. (1988) Numerical Computing.

Recipes

in C - The Art of

Scientific

C a m b r i d g e U n i v e r s i t y Press, C a m b r i d g e , UK.

R a w l s , W. J. & Brakensiek, D . L. ( 1 9 8 3 a ) A procedure to predict G r e e n - A m p t infiltration p a r a m e t e r s . Advances Infiltration.

in

A S A E publication no. 11-83. A m e r i c a n Society of Agricultural Engineer, St. Joseph, M i c h i g a n , U S A .

R a w l s , W . J, Brakensiek, D. L. & Miller, N . (1983b) G r e e n - A m p t infiltration parameters from soils data. / . Tlvdraul. Div. ASCE 1 0 9 , 6 2 - 7 0 . R u s s o , D. & Bouton, M. (1992) Statistical analysis o f spatial variability in unsaturated flow p a r a m e t e r s . Water Resour. Res. 2 8 ( 7 ) , 1 9 1 1 - 1 9 2 5 . S c h m u g g e , T. J. (1984) M i c r o w a v e sensing of soil moisture. In: Recent Advances in Civil Space Remote Sensing, 2 4 9 - 2 5 7 . SPIE48I. Schultz , G. A. & E n g m a n , E. T. (2000) Remote Sensing in Hydrology and Water Management. Springer-Verlag, Berlin, Germany. S h e r m a n , L. K. (1932) Streamflow from rainfall by the unit-graph method. Engng News Record 1 0 8 , 5 0 1 - 5 0 5 . Smith, R. E. & Hebbert, R. H. B . (1979) A M o n t e C a r l o analysis of the hydrologie effects of spatial variability of infiltration. Water Resour.

Res. 15(2), 4 1 9 - 4 2 9 .

T a o , T & K o u w e n , N . (1989) R e m o t e sensing and fully distributed m o d e l l i n g for flood forecasting. J. Water PIaim. Manage.

ASCE

Resour.

115(6), 809-823.

van de Griend, A. A. & E n g m a n , E. T. (1985) Partial area hydrology and remote sensing. J. Hydrol.

8 1 , 211-251.

van G e n u c h t e n , M. Th. (1980) A closed form equation for predicting the h y d r a u l i c conductivity of unsaturated soils. So/7 Sci. Soc. Am. .1. 44, 8 9 2 - 8 9 8 . W o o d , E. F., Sivapalan, M., B e v e n , IC. & Band, L. (1988) Effects of spatial variability and scale with implications to hydrologie modelling. J. Hydrol.

102, 29^17.

W o o d , E. F., S i v a p a l a n , M . & B e v e n , K. (1990) Similarity and scale in c a t c h m e n t storm r e s p o n s e . Reviews 2 8 ( 1 ) , 1-18. W M O (1986) Intel-comparison G e n e v a , Switzerland.

of Models

for

Snowmelt

Runoff.

Publ. no. 646. World Meteorological

Geophys.

Organization,