Journal of Water and Climate Evaluation of climate change impacts on extreme rainfall events characteristics using a synoptic weather typing based daily precipitation downscaling model --Manuscript Draft-Manuscript Number:
JWC-D-16-00107R1
Full Title:
Evaluation of climate change impacts on extreme rainfall events characteristics using a synoptic weather typing based daily precipitation downscaling model
Article Type:
Research Paper
Corresponding Author:
sara nazif IRAN (ISLAMIC REPUBLIC OF)
Corresponding Author Secondary Information: Corresponding Author's Institution: Corresponding Author's Secondary Institution: First Author:
Hamed Tavakolifar, PhD candidate
First Author Secondary Information: Order of Authors:
Hamed Tavakolifar, PhD candidate Ebrahim Shahghasemi sara nazif
Order of Authors Secondary Information: Abstract:
Climate change affects all phenomena in the hydrologic cycle, especially extreme events. GCMs are used for investigate its impacts. Due to their low resolutions, downscaling methods are developed. In this study, a novel downscaling method called synoptic statistical downscaling model is proposed for daily rainfall downscaling with an emphasis on extreme events characteristics preservation. In this method, first, synoptic weather typing process is done to detect the circulation types using the SOM method. For each CT, two regression models are developed for rainfall occurrence and amount downscaling. To improve the models performance in preservation of the extreme rainfall characteristics the weighted mean square error method is used for model's development. The proposed model is applied to a region located in central Iran. The results show that the developed model can downscale all percentiles of rainfall events with an acceptable performance and there is no assumption about the similarity of future rainfall data with the historical observations. The outputs of CCSM4 for two representative concentration pathways of RCP4.5 and RCP8.5 are used to investigate the climate change impacts in the study region. The results show 40% and 30% increase in the number of extreme rainfall events under RCP4.5 and RCP8.5, respectively.
Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation
Manuscript
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Click here to download Manuscript first revision .docx
1
Evaluation of climate change impacts on extreme rainfall events characteristics
2
using a synoptic weather typing based daily precipitation downscaling model
3 4
Hamed Tavakolifar
5
Ph.D. candidate, School of Civil Engineering, College of Engineering, University of
6
Tehran, Tehran, Iran, Email:
[email protected]
7 8
Ebrahim Shahghasemi
9
Assistant Professor, School of Civil Engineering, College of Engineering, University of
10
Tehran, Tehran, Iran, Email:
[email protected]
11 12
Sara Nazif
13
Assistant Professor, School of Civil Engineering, College of Engineering, University of
14
Tehran, Tehran, Iran, Email:
[email protected]
15 16
Abstract
17
Climate change has impacted all phenomena in the hydrologic cycle, especially extreme
18
events. GCMs (general circulation models) are used for investigate climate change
19
impacts but due to their low resolutions, downscaling methods are developed to provide
20
data with resolutions high enough for regional studies from GCMs outputs. The
21
performance of downscaling methods is commonly acceptable in preserving average
22
characteristics, but they do not preserve the extreme events characteristics especially
23
amount and its distribution. In this study, a novel downscaling method called synoptic
24
statistical downscaling model (SSDM) is proposed for daily precipitation downscaling
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
25
with an emphasis on extreme events characteristics preservation. In the proposed method,
26
first, synoptic weather typing process is done to detect the circulation types (CTs) using
27
the Self-organizing Maps (SOM) method based on the 500-hPa geopotential heights data.
28
For each CT, two regression models are developed for rainfall occurrence and amount
29
downscaling. To improve the models performance in preservation of the extreme rainfall
30
characteristics beside the mean events statistics, the weighted mean square error (WMSE)
31
method is used for model’s development. The proposed model is applied to a region
32
located in central Iran. The results show that the developed model can downscale all
33
percentiles of precipitation events with an acceptable performance and there is no
34
assumption about the similarity of future rainfall data with the historical observations.
35
The outputs of CCSM4 GCM for two representative concentration pathways (RCP) of
36
RCP4.5 and RCP 8.5 are used to investigate the climate change impacts in the study
37
region. The results show 40% and 30% increase in the number of extreme rainfall events
38
under RCP4.5 and RCP 8.5, respectively.
39 40
Keywords: Downscaling, Synoptic weather typing, SOM, Extreme events, Circulation
41
type, Synoptic statistical downscaling model
42 43
1
Introduction
44
The investigation of local rainfall events characteristics, especially extreme ones, is a key
45
issue in hydrologic research in different fields such as urban drainage system management
46
and flood control strategies. Due to climate change impacts, the intensity and frequency
47
of extreme rainfall events are increasing. Based on the 5th report of Intergovernmental
48
Panel on Climate Change (IPCC, 2014), the frequency and intensity of heavy
2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
49
precipitation events have increased in the Northern Hemisphere. General circulation
50
models (GCMs) are the primary available tools for investigating the response of the
51
hydro-climate system to climate change impacts (IPCC 2014).
52
In Figure 1, the spatial and temporal scale of various weather phenomena, the time and
53
space domains of available GCMs outputs and the time and space domains required in
54
some hydrological investigations are compared. As shown in this figure, the coarse
55
gridding of GCMs outputs cannot capture all types of mesoscale phenomena which have
56
important influences on temporal and spatial patterns of local rainfall in small regions
57
which are considered in flood risk or urban drainage management. For example, in terms
58
of spatial scale, storms in urban basins (usually less than 500 km2) are the mesoscale
59
phenomenon (Willems et al. 2012) and in terms of temporal scale, daily rainfall is the
60
largest time scale applicable in urban flood management. Because of the spatial and
61
temporal scale mismatch between the outputs of GCMs and the scale at which
62
hydrological investigations about climate change impacts are commonly carried out,
63
downscaling methods are applied (Wilby et al. 1998).
64
Two main approaches in downscaling are dynamical (numerical) downscaling and
65
statistical (empirical) downscaling (Benestad et al. 2008). In dynamical downscaling,
66
limited-area regional climate models (RCM) are applied and the GCMs outputs are used
67
as their initial conditions (Feser et al., 2011). In the statistical downscaling (SD) methods,
68
statistical or empirical models are used to relate the GCMs outputs and local rainfall
69
(Wilby and Dawson 2013). Different methods, techniques and approaches are proposed
70
in the SD context including stochastic weather generators (WG) (Baigorria and Jones
71
2010; Richardson 1981; Semenov 2008; Semenov and Barrow 1997; Wilks 2010),
72
transfer function (TF) approaches (Chau and Wu 2010; Chen et al. 2010; Dibike et al.
3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
73
2008; Hessami et al. 2008; Karamouz et al. 2013b; a; Najafi et al. 2011; Pasini 2009;
74
Tavakol-Davani et al. 2013; Tomassetti et al. 2009; Wilby et al. 2002; Willems and Vrac
75
2011) and weather typing (WT) approaches (Arnbjerg-Nielsen 2008; Cheng et al. 2010,
76
2011; D’onofrio et al. 2010; Hewitson and Crane 2006; Vrac and Naveau 2007).
77
Previous studies have commonly focused on reproducing the mean behavior of the daily
78
rainfall. However, some studies devoted to downscale daily precipitation with an
79
emphasis on the extreme events (Benestad 2009; Cheng et al. 2011; Hundecha and
80
Bárdossy 2008). It is difficult to preserve the characteristics of extreme daily rainfalls
81
during the downscaling process due to local phenomena that affect extreme daily rainfall
82
amounts, the considerable number of dry days and a non-Gaussian statistical distribution
83
on wet days (Benestad 2009). In many downscaling approaches, there is a tendency to
84
underestimate the extreme precipitation events (Arnbjerg-Nielsen 2008; D’onofrio et al.
85
2010; Fealy and Sweeney 2007).
86
To overcome this shortage, some methods are proposed such as bias correction and
87
change factor methods. Sarr et al. (2015) compared the performance of the delta-change
88
method with a quantile–quantile transformation (QQ) method in downscaling the amount
89
of daily extreme rainfall events with 5 to 100 years return period in 6 stations in Senegal.
90
The results showed that these methods in some cases over estimate and in some stations
91
underestimate the extreme rainfall events amount. A comparison between different types
92
of these methods can be found in Sunyer et al. (2015), Tryhorn and DeGaetano (2011)
93
and Wang et al. (2015). According to their reviews, considering merely a limited number
94
of extreme events in the bias correction method and inability to reproduce timing
95
characteristics (chronology) of daily rainfall such as the length of dry/wet spells are some
96
limitations of these approaches.
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
97
Another approach to overcome the limitations of ordinary SD models for downscaling
98
daily precipitation is combining WT methods with SD models. The main idea in
99
developing this approach is that the precipitation occurrence in different periods of time
100
with a particular synoptic scale weather pattern follows a similar scheme (Willems et al.
101
2012).
102
Cheng et al. (2010) applied a synoptic WT using principal component analysis (PCA) and
103
the logit and nonlinear regression procedures as the within-weather-type daily rainfall
104
simulation models. Although, the results show that the proposed method has a good
105
potential to simulate daily rainfall occurrence and amount, it does not display a stable
106
performance in all ranges of rainfall amounts. Hertig and Jacobeit (2013) also used the
107
PCA (Principal Component Analysis) on 700-hPa geopotential heights to determine
108
circulation patterns (CP) in the synoptic scale and the Poisson regression model for daily
109
precipitation simulation. Their model overestimated the precipitation below the 90%
110
percentile and underestimated precipitations above this threshold.
111
Using k-means clustering technique to determine synoptic CPs, D’onofrio et al. (2010)
112
simulated daily rainfalls according to daily precipitation probability density function (pdf)
113
in each CP. Their approach was fairly straight and simple, but the results were
114
overestimated for extreme values and wet/dry sequences. In addition, they assumed
115
stationarity in precipitation pdf in future climate conditions. Similarly, Haberlandt et al.
116
(2015) developed a stochastic rainfall downscaling model of which the parameters were
117
conditioned based on CPs. They investigated the non-stationarity of the relationship
118
between rainfall and CPs and concluded that the modification of the parameters of the
119
stochastic rainfall downscaling model for its future application is necessary.
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
120
Despite the improvements in SD precipitation downscaling methods in previous studies,
121
preserving all statistical characteristics of the observed local daily rainfall by the
122
downscaling model is still a challenge. The previous studies cannot simulate the daily
123
precipitation pdf for all ranges of rainfall amount without the assumption of the constant
124
precipitation pdf for current and future climate conditions.
125
As estimation of extreme rainfall events is a vital issue in urban areas in planning for
126
flood events and due to climate change impacts on characteristics of extreme rainfall
127
events. It is needed to consider climate change impacts in extreme rainfalls evaluation.
128
On the other side, the common methods used for evaluation of climate change impacts on
129
rainfall events, does not provide satisfactory results for extreme rainfall events
130
investigation. Therefore, the main aim of this study is to develop a downscaling model
131
which can preserve the distribution frequency or percentile values of the observed daily
132
precipitation for all ranges of rainfall with an emphasis on extreme events. The proposed
133
method that is called synoptic-statistic downscaling model (SSDM) is based on a
134
combination of synoptic WT of upper-level atmosphere conditions which affect the local
135
atmosphere states, and SD models for simulating daily rainfall in each weather type. The
136
performance of SD models is improved by applying some modifications in common
137
methods including skewness reduction and weighted least squares (WLS). These changes
138
have made SSDM capable of overcoming some of the reported challenges and
139
disadvantages in literature including reproducing extreme events frequencies, and
140
inherent non-Gaussian statistical distribution of daily rainfall. In the proposed method,
141
stability in relationships between predictors and local rainfall in each weather type as well
142
as the adequacy of recognized WTs for future events are assumed. There is no assumption
143
about the stationarity of the daily rainfall pdf in future conditions, and changes in the
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
144
frequency distribution of predictors (because of climate change) can result in daily rainfall
145
pdf changes. The proposed method is applied to an area located at the north of Tehran,
146
the capital of Iran, as the study area. The historical floods of this city have resulted in
147
considerable damages to people and properties in the past. Therefore, the investigation of
148
climate change impacts on precipitation regime of this region with an emphasis on
149
extreme events is of high importance.
150
In the next section, the proposed method in this study for rainfall downscaling, SSDM, is
151
described. Then, the case study and data used in the study are introduced. Next, SSDM’s
152
development for the study area is described and the results of its application are discussed.
153
Afterwards, climate change impacts on rainfall characteristics are investigated for the
154
study area by applying SSDM on outputs of a GCM. Finally, a summary and conclusion
155
are given.
156 157
2
Method
158
2.1
159
There are different types of precipitation (cyclone-related, frontal or convective). Most of
160
the precipitation types are synoptic scale phenomena. In the proposed SSDM approach,
161
the effects of synoptic scale phenomena on the mesoscale rainfall are considered using
162
the synoptic weather typing method. Regarding the multi-scale nature of the atmospheric
163
processes that affect the rainfall formation, different sets of climatic variables contribute
164
to the prediction of rainfall in different weather types (D’onofrio et al. 2010). In SSDM,
165
days are classified according to the circulation type (CT) which occurs in each day. SSDM
166
algorithm includes two main phases. Figure 2 shows these two phases and their main
SSDM Algorithm
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
167
steps and components as well as how they are related to each other. The detailed
168
description of SSDM algorithm is given in the following parts.
169
2.1.1 Phase I: Synoptic-Scale Classification Model
170
Synoptic climatology was defined by Yarnal (1993) as the study of the linkage between
171
the atmospheric circulation and an environmental response. A successful classification of
172
atmospheric conditions is an essential step in the investigation of this linkage. Therefore,
173
the first phase in SSDM algorithm is clustering the large-scale atmospheric CTs that
174
mainly influence the local surface weather conditions.
175
Self-Organizing Maps (SOM)
176
In this study, the SOM technique is used for synoptic based classification of CTs for their
177
successful application in climatological fields in the last decade (Hewitson and Crane
178
2002; Sheridan and Lee 2011). SOM was first presented in details by Kohonen (1995).
179
Inspired by the neural networks, the SOM methodology utilizes an array or lattice of a
180
low-dimensional (typically two-dimensional) matrix of neurons or nodes, which are
181
trained to produce a discretized representation or map of the input space. Each node
182
(considered a cluster) is defined by a reference vector of weighting coefficients, which
183
has the same dimension as the input data vector. At first, nodes are randomly distributed
184
in data space.
185
There are some standard SOM configurations used for its development including sheet,
186
cylinder and toroid. The structure used here for SOM development is a sheet shape
187
(matrix) of nodes with a rectangular lattice neighborhood structure. Since in the synoptic
188
scale studies the two dimensional variations of climatic variables is investigated, the sheet
189
shape is used similar to previous studies such as Hewitson and Crane (2002) and Sheridan
190
and Lee (2011). The cylinder and toroid map shapes of SOM are used when three-
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
191
dimensional analysis of data is considered. About the neighborhood condition in SOM
192
map development two cases of hexagonal and rectangular are available which both of
193
them are considered in this study and due to better performance of the rectangular
194
neighborhood it is adopted in this study. In addition to SOM strcuture, the appropriate
195
number of nodes in SOM structure should also be determined. Commonly, a subjective
196
method is used for this purpose (Sheridan and Lee 2011). In many cases, different
197
numbers of nodes are considered, and then by evaluation of the developed models’
198
performance, the best number of nodes that results in the best model performance, is
199
determined.
200
In training procedure, each input vector is presented to the SOM and the best matching
201
unit (BMU) is determined. BMU is the node that has the least Euclidean distance from
202
the input vector. Then the weighting coefficients of BMU and its neighboring nodes are
203
modified in a way that the distance from the input vector is minimized. The weighting
204
coefficients modifications are controlled by some factors such as learning rate.
205
Neighborhood adjustment is utilized to preserve the topological properties of the input
206
space. The training can be sequential (introducing input data one by one to the SOM) or
207
batch training (introducing all input data simultaneously to the SOM). The training
208
process has two stages of rough training (with large neighborhood radius and high
209
learning rate) and fine-tuning (with small radius and low learning rate). The termination
210
criteria for the training process can be the achievement of the minimum value of SOM
211
error measurement called average quantization error (Kohonen and Honkela 2007) or
212
reaching a predefined number of training epochs. A practical public domain software
213
package for implementing SOMs along with extensive references and documentations are
9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
214
provided by Helsinki University of Technology’s Laboratory of Computer and
215
Information Science that is available at http://www.cis.hut.fi/projects/somtoolbox/.
216
Relating CTs and daily precipitation
217
In order to analyze the relationship between the daily precipitation and the driving large-
218
scale atmospheric CTs, a performance index (PI) (Zhang et al. 1997) beside the
219
interpretation of the composite maps (Yarnal et al. 2001) is utilized. Using this PI will
220
help to quantify this relationship and makes easier to determine CTs which result in wet
221
and dry days which is necessary in this study. PI will help to provide the same
222
interpretation for CTs in different cases which is a very important in reproducing the study
223
result. PI compares the mean daily precipitation for ith CT with the climatological daily
224
mean precipitation as follows: 𝑃𝐼(𝑖) =
𝑅𝑖 ⁄𝑛𝑖 𝑅 ⁄𝑛
(1)
225
where 𝑛𝑖 is the number of days included in ith CT, 𝑅𝑖 is the total amount of precipitation
226
in ith CT and 𝑅 is the total amount of precipitation received in the study region in the
227
considered period of 𝑛 days. PI values close to one show that the given CT leads to
228
precipitation amounts around the climatological mean. PI values close to zero mean that
229
the corresponding CT does not considerably contribute to precipitation, or the CT is un-
230
conducive to rainfall formation while PI values greater than one mean that the given CT
231
is conducive to considerable precipitation.
232
2.1.2 Phase II: Local Scale Statistical Model
233
At the second phase of the SSDM algorithm, two statistical models are developed for
234
each CT. The first model, called rainfall occurrence model (ROM), determines that a day
235
is wet or dry and the second model called rainfall amount model (RAM) estimates the
236
amount of precipitation for wet days. Both models are regression-based. A combination 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
237
of subjective and automatic methods is used for the selection of the independent variables
238
in both regression models. In order to improve the ability of regression models to
239
reproduce extreme rainfall events’ characteristics, transformation functions (TF) and
240
WLS are used respectively for reduction of daily precipitation skewness and estimation
241
models’ parameters.
242
Variable Selection
243
For developing a statistical rainfall simulation model, appropriate features of the
244
atmosphere are chosen as the predictors. There are numerous features of the atmosphere
245
that can be used for this purpose. The potential variables are initially screened based on
246
the physical process of rain formation and suggestions available in the literature for the
247
study region. This initial screening is followed by an automatic variable selection
248
procedure that determines the best set of variables to be used in the statistical models. In
249
this study, the stepwise linear regression is used for this purpose.
250
Stepwise regression develops a multivariate regression model in which the choice of
251
predictive variables is carried out by an automatic procedure. At each iteration, some
252
predictors that improve the explanatory power of the model are added to the subset of
253
predictive variables of the model. At the same time, variables whose elimination does not
254
considerably affect the model’s performance are removed from the subset of predictive
255
variables of the model. The null hypothesis states that the statistical relationship between
256
a considered variable and the rainfall is arbitrary. For a variable that is not currently
257
included in the model, if there is sufficient evidence to reject the null hypothesis, the
258
variable would be added to the model. Conversely, for a variable that is included in the
259
model, if there is insufficient evidence to reject the null hypothesis, the variable would be
260
removed from the model. The null hypothesis is checked through an F-statistic and by
11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
261
computing the corresponding p-value. The p-value shows the statistical significance level
262
of the model and indirectly can be used to control the number of predictive variables in
263
the regression model. Smaller p-values result in higher level of statistical significance and
264
fewer variables in the model. In this study, the p-values for ROMs and RAMs are set to
265
0.001 and 0.05 respectively. The procedure of determination of predictive variables
266
through the stepwise regression is stopped when no more predictors can be justifiably
267
entered or removed from the stepwise model (Ryan 1997).
268
Skewness Reduction
269
In linear regression modeling, there is an assumption that variables follow the normal
270
distribution. Non-normally distributed variables (e.g. highly skewed or kurtotic variables)
271
can distort relationships and significance tests. In such cases, the simple linear regression
272
on the original data could provide misleading results, or may not be the best test available
273
(Draper and Smith 1998). Daily precipitation is a highly skewed variable, especially in
274
arid and semi-arid areas. Therefore, for skewness reduction of daily precipitation, in each
275
submodel (ROM and RAM), a TF is applied on daily rainfall. The considered TF for
276
ROM submodel is the Box-Cox transformation after checking different common transfer
277
functions. This TF is selected after checking different types of TFs. This TF is applied on
278
daily rainfall values as shown in Equation 2. TF of RAM is Box-Cox transformation
279
applied on the square root of daily precipitation as given in Equation 3 (Box and Cox
280
1964; Li 2005). Different power transformations can be considered in TF of RAM but in
281
this study, the best results were obtained using square root transformation.
282
a. TF of ROM submodel (𝜆) 𝑦𝑖
(𝑦𝑖 + 1)𝜆 − 1 = { 𝜆 ln(𝑦𝑖 + 1)
𝑖𝑓 𝜆 ≠ 0
(2)
𝑖𝑓 𝜆 = 0
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
283
b. TF of RAM submodel (𝜆) 𝑦𝑖
(𝑦𝑖 0.5 )𝜆 − 1 = { 𝜆 ln(𝑦𝑖 0.5 )
𝑖𝑓 𝜆 ≠ 0
(3)
𝑖𝑓 𝜆 = 0 (𝜆)
284
where 𝑦𝑖 is daily precipitation amount, 𝑦𝑖
285
is the Box-Cox transformation parameter. The TF of ROM is applied on all days but TF
286
of RAM is just applied on wet days.
287
is transformed daily precipitation data and 𝜆
Model Parameters Estimation
288
Ordinary least squares (OLS) is a standard method for estimating the unknown parameters
289
in a linear regression model, with the goal of minimizing the differences between the
290
observed and simulated values. The sum squared error (SSE) or mean squared error
291
(MSE) that are usually used as objective functions in OLS are calculated as follows (Ryan
292
1997): 𝑛
𝑆𝑆𝐸 = ∑(𝑦𝑖 − 𝑓(𝑥 ⃗⃗⃗𝑖 , 𝛽 ))2
(4)
𝑖=1 𝑛
1 𝑀𝑆𝐸 = ∑(𝑦𝑖 − 𝑓(𝑥 ⃗⃗⃗𝑖 , 𝛽 ))2 𝑛
(5)
𝑖=1
293
where 𝑦𝑖 is the observed value, 𝑓 is the developed linear regression model, 𝑥 is the
294
predictor variables vector, 𝛽 is the linear model parameters and 𝑛 is the number of
295
observations.
296
The observed daily precipitation histograms are commonly strongly skewed. The mean
297
and the median of the precipitation data are different because the data are not normally
298
distributed. As the majority of daily precipitation data are concentrated around the mean
299
value, the effect of extreme rainfall amounts is underestimated in the estimation of MSE.
300
As a result, the variance of the model errors is not independent of its value. Inconstant
13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
301
error variance is often termed “heteroscedasticity” (Carroll and Ruppert 1988; Draper and
302
Smith 1998). But, one of the assumptions of the regression model is that the error variance
303
is the same everywhere. In heteroscedasticity case, OLS measures are inefficient because
304
they give equal weight to all observations regardless of the fact that those with large
305
residuals contain less information about the regression.
306
One approach to overcoming this issue is using the weighted least squares (WLS) for
307
estimating model parameters. In WLS, the weighted sum of square errors (WSSE) is
308
calculated as follows: 𝑛
𝑊𝑆𝑆𝐸 = ∑ 𝑤𝑖 (𝑦𝑖 − 𝑓(𝑥 ⃗⃗⃗𝑖 , 𝛽 ))2
(6)
𝑖=1
309
where 𝑤𝑖 is the weight of an observation. In the current study, weights are estimated based
310
on data variance in each percentile. The variance of daily rainfall amount data in each
311
percentile is calculated as follows: 𝑛𝑝
𝛿𝑝
2
1 = ∑(𝑦𝑗 − 𝑦̅)2 𝑛𝑝
(7)
𝑗=1
312
where 𝛿𝑝 2 is the variance of the observed precipitation in the pth percentile, 𝑛𝑝 is the
313
number of observations in the pth percentile and 𝑦̅ is the mean daily rainfall amount. Then,
314
𝑤𝑝 for each percentile is estimated as follows: 𝑤𝑝 =
𝛿𝑝 2
(8)
2 ∑100 𝑛=1 𝛿𝑛
315
where 𝑤𝑝 is the initial weight of the pth percentile. This weight is used for all rainfall
316
amounts between pth and (p+1)th percentiles. For more accuracy and flexibility of the
317
model in reproducing extreme rainfall events values, the initial weights are modified
318
during the model training process as follows:
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
319
a: for high percentiles (above 98 percent) and low percentiles (below 50 percent) the
320
initial weights are increased;
321
b: for middle percentiles (between 50 and 98 percent) the initial weights are decreased;
322
The amount of change in initial weights in each of the above-mentioned categories is
323
determined by trial and error to provide a better model performance.
324 325
Regression Models
The mathematical formulations of ROM and RAM are as follows: 1 ⃗⃗⃗⃗𝑜 , ⃗⃗⃗⃗ 𝑅𝑂𝑀𝑘 (𝑥 𝛽𝑘 ) = { 0
−1 ⃗⃗⃗⃗𝑜 , ⃗⃗⃗⃗ 𝑖𝑓 (𝐹𝑘 (𝑥 𝛽 𝑘 ))(𝜆 ) ≥ 𝑅 𝑡 𝑘
(9)
𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑘 𝑎 ⃗⃗⃗⃗𝑎 , ⃗⃗⃗⃗ 𝑅𝐴𝑀𝑘 (𝑥 𝛼 𝑘 ) = 𝛼0𝑘 + 𝛼1𝑘 𝑥1𝑎 + 𝛼2𝑘 𝑥2𝑎 + ⋯ + 𝛼𝑚 𝑥𝑚
(10)
326
where ⃗⃗⃗⃗ 𝑥 𝑜 and ⃗⃗⃗⃗ 𝑥 𝑎 are the vectors of the selected predictive variables for ROM and RAM
327
submodels respectively, resulting from stepwise regression procedure, ⃗⃗⃗⃗ 𝛽 𝑘 and ⃗⃗⃗⃗ 𝛼 𝑘 are the
328
coefficient vectors in linear models of ROM and RAM for the kth CT, and 𝑅 𝑡 𝑘 is the
329
rainfall event threshold that distinguishes between wet and dry days. If the output value
330
of the regression model developed for ROM model for a day is greater than or equal to
331
𝑅 𝑡 𝑘 , that day is considered a wet day and vice versa. The value of this threshold is a
332
parameter in the model that should be determined in a way to better fit the distribution of
333
the observed daily precipitation values. 𝜆−1 represents the reverse transformation
334
function. For each CT, ROM and RAM submodels (𝑅𝑂𝑀𝑘 and 𝑅𝑂𝑀𝑘 ) are developed.
335
The final statistical model (𝑅𝑘 ) is the product of ROM and RAM as follows: (𝜆−1 )
⃗⃗⃗⃗𝑎 , ⃗⃗⃗⃗ ⃗⃗⃗⃗𝑎 , ⃗⃗⃗⃗ 𝑅𝑘 (𝑥 𝑥 𝑜 ) = 𝑅𝐴𝑀 (𝑥 𝛼𝑘)
⃗⃗⃗⃗𝑜 , ⃗⃗⃗⃗ × 𝑅𝑂𝑀 (𝑥 𝛽𝑘 )
(11)
336
⃗⃗⃗⃗𝑎 , ⃗⃗⃗⃗ where 𝑅𝑘 (𝑥 𝑥 𝑜 ) is the transfer function which downscales the large scale (mesocale)
337
atmospheric variables to local precipitation.
338
3
Case study 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
339
The SSDM is applied for downscaling daily precipitation in an area located in the north
340
of Tehran. The location of the study area is shown in Figure 3. The data used for SSDM
341
development in the study area are described in the following.
342
3.1
343
Data
Observed Daily Precipitation
344
In this study, the observed daily precipitation dataset provided by the APHRODITE
345
project for the Middle East is utilized (Yatagai et al. 2012). Its state-of-the-art gridded
346
daily precipitation datasets, with high-resolution grids over Asia, are based on
347
interpolations of data collected from the rain-gauge observation networks. The data
348
release for the APHRO_V1101_ME for the period of 1970 to 2006 (13514 days) is used.
349
The network grid of APHRODITE dataset, around Tehran’s urban area and the
350
considered grid in the north of Tehran are shown in Figure 3.
351
Days with equal or more than 1 mm precipitation are considered wet days. This threshold
352
is determined regarding the rainfall recording errors and by checking different values for
353
it. The long-term average of annual rainfall in the study area is about 383 mm and just
354
24% of days are rainy. The histogram of daily rainfall amounts is shown in Figure 4. It
355
can be seen that it is strongly skewed. The average daily rainfall amount is 4.4 mm.
356
According to the national urban drainage systems regulations, the drainage systems are
357
designed based on maximum daily rainfalls with 2 years return period. Therefore, in this
358
study the 2-year maximum daily rainfall amount that is determined based on annual
359
maximum daily rainfall time series, is used as the threshold of extreme rainfall events
360
which stands at 20 mm/day for the study area.
361
Large-Scale Atmosphere Variables
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
362
Large scale atmosphere variables on a 2.5° × 2.5° grid network over Iran and around
363
Tehran’s urban region from 1970 to 2006, obtained from the National Centers for
364
Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR)
365
reanalysis archive (Kalnay et al. 1996; Kistler et al. 2001), were utilized in this study as
366
the observed large-scale atmosphere variables to develop the SSDM model. Data grids in
367
synoptic domain (from 42.5° to 60° longitudes and from 25° to 40° latitudes including 70
368
grids) and mesoscale domain (from 50° to 52.5° longitudes and 35° to 37.5° latitudes
369
including 4 grids around the study area) were respectively utilized for synoptic scale
370
pattern classification and rainfall SD models development. This domain is determined
371
based on the previous studies in the study area such as Alijani (2002) and Raziei et al.
372
(2012 and 2013). These spatial domains are shown in Figure 3. NCEP Reanalysis data
373
provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, are available at
374
http://www.esrl.noaa.gov/psd/.
375
GCM outputs and scenarios
376
Climate change scenarios simulation results of Community Climate System Model,
377
version 4 (CCSM4) GCM under 2 different representative concentration pathways
378
(RCPs) namely RCP4.5 and RCP8.5 in a near future period (from 2006 to 2050) were
379
utilized for evaluation of climate change impacts on daily precipitation in the study area
380
as an experimental analysis. CCSM4 developed at the National Center for Atmospheric
381
Research (NCAR), is one of the climate models included in both the Coupled Model
382
Intercomparison Project’s fifth phase (CMIP5) and the Intergovernmental Panel on
383
Climate Change (IPCC) Fifth Assessment Report (AR5) (Flato et al. 2013). The CCSM4
384
exchanges state information and fluxes between four main components of atmosphere,
385
land, ocean, and sea ice. The CCSM4 was introduced to the climate science community
17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
386
in April 2010 (Gent et al. 2011). Historical experiment from 1970 to 2005 was also
387
utilized for the evaluation of CCSM4 model performance in representation of the
388
observed daily rainfall pattern in the study area. CCSM4 and NCEP reanalysis data are
389
used for the same grids.
390 391
3.2
392
3.2.1 Phase I) Synoptic Scale Pattern Classification
393
Developing SSDM Model
Synoptic Pressure Patterns
394
Upper-air pressure patterns provide insights into the atmospheric conditions that are more
395
conducive (or more un-conducive) to rainfall formation (Lutgens and Tarbuck 2013;
396
Yarnal 1993). Previous studies have shown that changes in moisture delivery to the
397
majority of Iran are domestically controlled by interrelated, synoptic-scale atmospheric
398
pressure patterns (Alijani 2002; Alijani and Harman 1985). Alijani and Harman (1985)
399
concluded that the uplift mechanisms account for more than 70 percent of rainfall events
400
in Iran based on a subjective analysis of daily surface and 500-hPa atmospheric pressure
401
patterns.
402
Raziei et al. (2013) investigated the relationship between daily large-scale atmospheric
403
CTs and wintertime daily precipitation over Iran during the period 1965–2000. In their
404
previous studies, they identified the dominant daily atmospheric CTs in the Middle East
405
and studied their relationship with the occurrence of meteorological dry/wet spells during
406
winter in western Iran (Raziei et al. 2012). They classified daily large-scale weather
407
conditions during the period 1965–2000 into 12 CTs by applying PCA to the 500-hPa
408
geopotential height fields. Results showed that just some limited number of identified
409
CTs affect the precipitation occurrence over the majority of the country while the
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
410
remaining CTs commonly provide regional or negligible contributions to precipitation.
411
Therefore, in this study, patterns of 500-hPa geopotential height were used to determine
412
the synoptic scale atmospheric conditions. For this purpose, the daily average 500-hPa
413
geopotential heights on the synoptic domain scale over Iran (as mentioned in section 3.1)
414
from 1970 to 2007 (13514 cases/days) were considered.
415
SOM Implementation
416
The software that is used in this study for SOM implementation is the public domain
417
software developed in MATLAB environment by Helsinki University of Technology’s
418
Laboratory of Computer and Information Science and is named "The SOM Toolbox"
419
(Vesanto et al. 2000). Here, the topology of SOMs is developed based on the sheet shaped
420
structures with a rectangular lattice neighborhood and the Euclidean distance is taken as
421
distance measure in training and clustering steps. Each case (the daily pattern of 500-hPa
422
geopotential height) is a vector of size 70 (number of grids in the study area). To eliminate
423
the effect of data variability in days with the same pressure pattern, the data for each grid
424
point were normalized as follows: 𝑔ℎ500𝑛𝑜𝑟𝑚 = 𝑖,𝑡
(𝑔ℎ500𝑖,𝑡 − 𝑔ℎ500𝑚𝑒𝑎𝑛 ) 𝑡 𝑣𝑎𝑟 𝑔ℎ500𝑡
(12)
425
where 𝑔ℎ500𝑛𝑜𝑟𝑚 and 𝑔ℎ500𝑖,𝑡 are the normalized and original values of 500-hPa 𝑖,𝑡
426
geopotential height in point i and day t, respectively, and 𝑔ℎ500𝑚𝑒𝑎𝑛 and 𝑔ℎ500𝑣𝑎𝑟 are 𝑡 𝑡
427
respectively the mean and variance values of 500-hPa geopotential heights of all grids in
428
day t.
429
In this study two dimensional SOMs with different sizes, varying from 3×3 to 6×6
430
(different numbers of nodes between 9 and 36) were considered. As mentioned before, PI
431
values far from one, show that the developed CTs better distinguish between wet and dry
19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
432
days. Therefore, the stratification index (SI) is used to evaluate SOM models performance
433
based on the average distance of PIs from one. 𝑛
1 𝑆𝐼 = ∑(𝑃𝐼𝑖 − 1)2 𝑛
(13)
𝑖=1
434
where 𝑛 is the number of nodes in the SOM and 𝑃𝐼𝑖 is the PI of the ith node of the SOM.
435
A higher value of SI means more discrete stratification of daily precipitation. In Table 1,
436
the values of SI for developed SOMs with different sizes are given. According to these
437
results, SOMs with sizes of 4×4, 5×5, 5×6 and, 6×6 have higher SI values and therefore,
438
provide a better performance.
439
By increasing the number of SOM nodes, based on SI, the distinction of wet days from
440
dry days is improved, but choosing the SOM with a bigger size means that more statistical
441
models should be developed in the second phase of SSDM algorithm. Hence in this study
442
the 4×4 SOM size is chosen for classification of synoptic scale pressure patterns.
443
Detected CTs and their relationship with local daily precipitation
444
Figure 5 shows the 16 CTs which were determined in this study by applying SOM
445
method. Each CT map is drawn by averaging the 500-hPa geopotential height values of
446
all days that belong to that CT. To investigate the contribution of CTs to daily
447
precipitation in the study area, some statistical and subjective evaluations were done.
448
The frequency and the chance of rain occurrence in each CT are presented in Figure 6.
449
By moving from right to left in CTs array, a very strong shift from higher to lower
450
pressure pattern and a simultaneous increase in the chance of precipitation occurrence can
451
be seen. Although the conditions become wetter by moving up in CTs array, there is not
452
a clear behavior in pressure patterns. The CTs in the first column (from the right hand
453
side) are associated with high-pressure systems’ (an anticyclone) occurrence over Iran
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
454
with almost zero chance of precipitation. By receding high-pressure systems from the
455
study region or expansion of the mid-latitude westerlies over Iran, the CTs in column 2
456
and 3 are formed and the chance of precipitation is increased. The CTs in the left side of
457
CT array represent the low-pressure systems. These results indicate that days are
458
distributed fairly over the CTs, with relative minima in central part that is related to
459
transitional patterns from high-pressure to low-pressure systems.
460
In Table 2, the frequency of wet days, the proportion of total rainfall amount and
461
frequency of extreme events within 16 CTs are presented and in Table 3 the PI values
462
associated with each CT are given. Based on these results, about 75% of rainy days
463
happen just in 25% of the CTs (4 CTs) including CT(1,4), CT(2,4), CT(1,3) and CT(3,4).
464
These CTs are the most conducive situations to the rainfall formation in the study area.
465
About 85% of the total rainfall amount falls under these four CTs in the study area.
466
Additionally, extreme rainfall events are just observed in these CTs where about 80% of
467
extremes happen in CT (1,4). The PI values of these CTs are also higher than those of
468
other CTs. These results are in good agreement with Raziei et al. (2013) that concluded
469
that a number of identified CTs affect the precipitation occurrence over the majority of
470
Iran.
471
On the other hand, less than 4% of wet days and 2% of rainfall amount occur in 6 CTs
472
which are the CTs in the first column (from right) and the two last ones in the second
473
column in CTs array. Because the number of rainy days and rainfall amount in these CTs
474
are negligible, they can be considered un-conducive situations to rainfall formation in the
475
study area. Also, PI values of this group of CTs are smaller than those of other CTs. The
476
rest of CTs have PI values less than 1 which means that they lead to precipitation amounts
21
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
477
less than the climatological mean value. However, precipitation occasionally occurs in
478
the study area under these CTs.
479
Figure 7 shows the composite map of vorticity at 500-hPa level and relative humidity of
480
700-hPa level corresponding to each CT. In most rainfall-conducive CTs, the tendency to
481
expand the upper-level atmosphere layers that results in uplift motions in the study area
482
is detectable from positive vorticity that expands around the study area. Positive vorticity
483
and high relative humidity (above 60%) of mid-level atmosphere result in uplift motions
484
of wet air mass that can result in rainfall formation in the study area. On the other side, in
485
most rainfall-un-conducive CTs, where a very high-pressure zone is observed over the
486
study area, negative vorticity and low level of humidity in the study area result in dry
487
weather conditions. In other CTs, one of the main components of rain formation (humidity
488
or uplift motion) is not enough, but sometimes local instabilities can result in rainfall
489
occurrence in the study area. It can be concluded that the classification of CTs in the study
490
area could successfully relate the synoptic-scale atmospheric circulation and the local
491
precipitation.
492
3.2.2 Phase II) Local Scale Statistical Downscaling Models for Daily Precipitation
493
After detecting CTs, days were categorized based on CTs and then statistical models were
494
developed for each category to simulate daily rainfall. For each model, the first step is
495
determining the predictors. The set of predictors considered for both statistical models of
496
ROM and RAM development are listed in Table 4. These variables are used at a spatial
497
mesoscale domain (4 neighbor grids around the study area as shown in Figure 3) and at
498
the three levels of atmosphere including near surface, mid-level (700-hPa geopotential
499
height) and high-level (500-hPa geopotential height). Three kinds of variables are
500
considered in this set to represent different conditions of the rain occurrence and are used
22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
501
in ROMs development. Dew point is the indicator of the moisture content of the air.
502
Vorticity is the indicator of the tendency of upward motion of the atmosphere, and dew
503
point depression is the indicator of the level of saturation. In RAMs development, the air
504
temperature, geopotential height, and relative humidity as well as the sea level pressure
505
are considered in addition to the variables included in the ROM.
506
Using the stepwise regression procedure, the predictor variables in ROMs and RAMs
507
were chosen. The TFs (Box-Cox and square root), were also applied on the observed
508
rainfall data for skewness reduction purpose. 80% of daily data were randomly selected
509
for calibration of the models and the remaining data were used for models’ validation.
510
Both ROMs and RAMs are linear models and WLS was used to determine RAMs
511
coefficients as described in section 2.2.2. The selected variables in each model are given
512
in Table 5. Even though some un-conducive CTs include a limited number of wet days,
513
developing SD models for them with appropriate performance is impossible because of
514
limited data. Therefore, all days corresponding to these CTs, are considered dry days and
515
are not included in Table 5.
516
3.3
517
The comparison between some statistical characteristics of the downscaled and observed
518
daily rainfall values for calibration and validation datasets as well as the total dataset are
519
presented in Table 6. The differences between mean and standard deviation of the
520
observed and simulated rainfall amounts are less than 5% and 13%, respectively, in both
521
calibration and validation datasets. Although the difference between skewness of the
522
observed and simulated rainfall amounts in calibration dataset is small (3.3%), in the
523
validation dataset it is considerable (about 40%). Based on this table, the differences
524
between modeled and simulated percentages of wet days, mean daily rainfall and standard
Daily rainfall simulation results
23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
525
deviation of wet days' rainfall amount, considering both calibration and validation period,
526
are less than 10% which show a good agreement between the observed and modeled
527
rainfall amounts. However, it should be mentioned that in simulation of the maximum
528
rainfall value and skewness of wet days' rainfall amount in the validation period, the
529
model is not very successful.
530
For a better comparison of model performance in calibration and validation datasets, the
531
Q-Q plots of the modeled and observed daily rainfalls are presented for both datasets in
532
Figure 8. As can be seen, the model performance in calibration is very good (the all points
533
lie quite close to the line) but as it is expected, in the validation dataset, the model
534
performance is not as good as the calibration dataset. In the validation data set, rainfalls
535
above 8 mm are underestimated. The maximum difference between the modeled and
536
observed daily rainfall values in the validation data set is smaller than 13%.
537
To evaluate the model performance in extreme events representation, the time series of
538
the simulated and observed annual maximum daily rainfalls are compared as given in
539
Figure 9. The two-sample Kolmogorov-Smirnov (KS) test which is a nonparametric
540
hypothesis test, is used to evaluate the similarity between the empirical CDF (cumulative
541
distribution function) of these two time series. The results of this test confirm that both
542
time series have the same distribution at 95% significant level.
543
The observed and modeled distributions of wet days are also compared in Figure 10.
544
Based on this figure, the percentile plots and CDFs of the observed and simulated wet
545
days match with each other and this shows the successful performance of the model. This
546
also approved by Q-Q plots. The model’s performance in monthly time scale is also given
547
in Figure 11. Wilcoxon signed-rank test and Levene's test (Karamouz et al. 2011) are
548
used, respectively, to test the equality of the mean and variance of observed and simulated
24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
549
monthly rainfall values as well as the number of wet days. Based on Wilcoxon signed-
550
rank test, mean monthly rainfall values of the simulated and observed series are equal at
551
95% significance level. However, the maximum differences between simulated and
552
observed mean monthly rainfall values are observed in the months of March and January.
553
The equality of the simulated and observed monthly mean of wet days is only rejected in
554
July. Based on Levene's test, the equality of the variance of the simulated monthly rainfall
555
with the observed values is approved at 95% significance level except in months of May,
556
July and August. The same result is obtained for monthly variance of the number of wet
557
days. This can be due to the limited number of wet days in these months.
558 559
4
560
The developed SSDM model for downscaling daily rainfall was used to evaluate the
561
probable climate change impacts on the rainfall characteristics in the near future horizon
562
(2006-2050) in the study area. For this purpose, the CCSM4 GCM model outputs for the
563
historical, RCP4.5 and RCP8.5 experiments were used.
564
The acceptability of the chosen GCM performance in the simulation of the synoptic and
565
mesoscale climate characteristics of the study area was evaluated through comparing the
566
simulations of CCSM4 in the historical period of 1970 to 2005 with NCEP records. This
567
evaluation was done in two aspects:
568
Climate change impacts evaluation in the study area
569 570 571
The differences between rainfall occurrence frequencies of CTs in CCSM4 results and NCEP records, especially for most rainy CTs.
Comparison of the Q-Q plots of the predictors developed based on the CCSM4 outputs and NCEP records in the study area.
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
572
The 500-hPa geopotential height patterns of CCSM4 simulations for the historical period
573
and NCEP records in the synoptic scale were classified by applying the developed SOM.
574
The frequencies of daily patterns in each CT are given in Table 7 for both NCEP and
575
CCSM4. The differences between frequencies of CTs in CCSM4 simulations and NCEP
576
records are very low, especially in rainy CTs. The Q-Q plots are also used to illustrate the
577
capability of CCSM4 in reproducing NCEP records of predictors in the study area. For
578
example, Figure 12 shows the Q-Q plots of the vorticity and dew point depression values
579
in mesoscale grids for both CCSM4 outputs and NCEP records. These results confirm the
580
ability of CCSM4 for reproducing predictors in the study area at an acceptable level of
581
accuracy. The percentiles of the downscaled daily rainfall series by applying developed
582
SSDM on CCSM4 outputs (for the historical experiment) and NCEP records are
583
compared in Figure 13. The agreement between them in all percentiles is remarkable. The
584
maximum difference is observed in the last percentile which is less than 1.5%.
585
By applying the developed SSDM model to CCSM4 outputs for RCP4.5 and RCP8.5
586
experiments in the future period (2006 to 2050), the possible climate change impacts were
587
investigated. The CTs occurrence frequencies are given in Table 8. The results show that
588
the CTs occurrence frequencies do not change considerably under climate change
589
impacts. There are small alterations in different cases, but there is no consistent scheme.
590
In Figure 14, the distribution of the simulated daily rainfall for historical, RCP4.5 and
591
RCP8.5 experiment results are compared. The results show that there is an upward trend
592
in high frequency daily rainfall amounts (above 80%) in both future climate pathways,
593
but in low frequency amounts, there is not any significant change. To better detect
594
changes in future daily rainfall characteristics in the study area, the Q-Q plots of the
595
simulated wet day amounts in historical and two future RCPs are illustrated in Figure 15.
26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
596
Based on this figure, as a result of climate change, the intensity of extreme events is
597
increasing in both RCPs and this increase is slightly more in RCP4.5.
598
The characteristics of wet days under climate change impacts are compared in Table 8.
599
Based on this table, it seems that the percentages of wet days are decreasing under climate
600
change impacts, but the average rainfall values are increasing. Furthermore, the increase
601
in the variance of daily rainfall shows the increasing possibility of extreme rainfall values.
602
The number of extreme rainfall events in a year is also increasing under climate change
603
impacts.
604
5
605
In this study, SSDM is proposed for daily rainfall downscaling that can preserve the
606
statistical characteristics of the observed local daily rainfalls especially extreme rainfall
607
events that are used in different hydrological investigations such as flood management
608
issues. SSDM is an SD model conditioned on synoptic scale CTs. The model includes
609
two parts. The first part is clustering synoptic weather patterns into CTs and then
610
investigating the relationships between identified CTs and local daily rainfall events. The
611
SOM is trained to cluster synoptic patterns into CTs and then it is used to classify each
612
day's synoptic pattern to determined CTs. The second part of SSDM includes developing
613
occurrence and amount regression SD models in each CT to simulate local daily rainfall.
614
The developed model is based on two main assumptions. The first one is that the
615
regression equations developed between predictors and rainfall will be valid in the future.
616
The second assumption is that the considered CTs would cover all the future events.
617
Further investigations would be necessary for the evaluation of validity of these
618
assumptions under climate change impacts.
Summary and Conclusion
27
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
619
The model is applied to the northern part of Tehran as the study area. In the first step, 16
620
CTs were determined using SOM model developed based on 500-hPa geopotential height.
621
The investigation of the relationship between determined CTs and local daily rainfall
622
demonstrates that detected CTs can explain the main atmospheric features that result in
623
dry and wet conditions in the study area. In the second step, two models for rainfall
624
occurrence and amount simulation are developed. The models' parameters are estimated
625
using WLS and skewness reduction techniques to better cover the extreme events in the
626
model development. Applying these methods for estimating regression models’
627
coefficients has improved the ability of developed models in reproducing local rainfall
628
amounts. Beside this improvement, still the model performance in simulation of some
629
ranges of rainfall amount is not satisfactory. This could be because of local phenomena
630
that affect the rainfall variability and are not considered in the developed models. Further
631
investigations on comparison of the developed model in this study with the other models
632
and the methods that could overcome this methods weaknesses can be considered in
633
future studies.
634
Then experiment outputs of CCSM4 GCM model under AR5 climate change scenarios
635
(RCP4.5 and RCP8.5) were used to investigate climate change impacts in the study area.
636
The results show that under climate change impacts the number of extreme rainfall events
637
is increasing. It must be emphasized that since in this study only one GCM and one run
638
of climate change scenarios were used, the obtained results are experimental. More
639
investigations through considering different climate change scenarios and different
640
GCMs are needed for a more reliable judgment about climate change impacts on rainfall
641
regimes in the study area.
642
28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
643
6
Acknowledgment
644
We acknowledge the World Climate Research Program's Working Group on Coupled
645
Modeling, which is responsible for CMIP, and we thank the National Center for
646
Atmospheric Research (NCAR) for producing their model outputs (CCSM4) and making
647
them available for us. For CMIP, the U.S. Department of Energy's Program for Climate
648
Model Diagnosis and Intercomparison provided coordinating support and led the
649
development of software infrastructure in partnership with the Global Organization for
650
Earth System Science Portals.
651 652 653
7
References
654
Alijani, B. (2002). “Variations of 500 hPa flow patterns over Iran and surrounding areas
655
and their relationship with the climate of Iran.” Theoretical and Applied
656
Climatology, 72(1–2), 41–54.
657 658 659
Alijani, B., and Harman, J. R. (1985). “Synoptic Climatology of Precipitation in Iran.” Annals of the Association of American Geographers, 75(3), 404–416. Arnbjerg-Nielsen, K. (2008). “Quantification of climate change impacts on extreme
660
precipitation used for design of sewer systems.” 11th International Conference on
661
Urban Drainage, Edinburgh, Scotland, UK, 1–10.
662
Baigorria, G. A., and Jones, J. W. (2010). “GiST: A Stochastic Model for Generating
663
Spatially and Temporally Correlated Daily Rainfall Data.” Journal of Climate,
664
23(22), 5990–6008.
665
Benestad, R. E. (2009). “Downscaling precipitation extremes.” Theoretical and Applied 29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
666 667
Climatology, 100(1–2), 1–21. Benestad, R. E., Hanssen-Bauer, I., and Chen, D. (2008). Empirical-Statistical
668
Downscaling. Empirical-Statistical Downscaling, World Scientific Publishing
669
Company.
670 671 672 673 674 675 676
Box, G. E. P., and Cox, D. R. (1964). “An analysis of transformations.” Journal of the Royal Statistical Society. Series B, 26, 211–252. Carroll, R. J., and Ruppert, D. (1988). Transformation and Weighting in Regression. Springer-Science+Business Media, B.Y. Chau, K. W., and Wu, C. L. (2010). “A hybrid model coupled with singular spectrum analysis for daily rainfall prediction.” Journal of Hydroinformatics, 12(4), 458. Chen, S.-T., Yu, P.-S., and Tang, Y.-H. (2010). “Statistical downscaling of daily
677
precipitation using support vector machines and multivariate analysis.” Journal of
678
Hydrology, 385(1–4), 13–22.
679
Cheng, C. S., Li, G., Li, Q., and Auld, H. (2010). “A Synoptic Weather Typing
680
Approach to Simulate Daily Rainfall and Extremes in Ontario, Canada: Potential
681
for Climate Change Projections.” Journal of Applied Meteorology and
682
Climatology, 49(5), 845–866.
683
Cheng, C. S., Li, G., Li, Q., and Auld, H. (2011). “A Synoptic Weather-Typing
684
Approach to Project Future Daily Rainfall and Extremes at Local Scale in Ontario,
685
Canada.” Journal of Climate, 24(14), 3667–3685.
686 687
D’onofrio, A., Boulanger, J.-P., and Segura, E. C. (2010). “CHAC: a weather pattern classification system for regional climate downscaling of daily precipitation.”
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
688 689
Climatic Change, 98(3–4), 405–427. Dibike, Y. B., Gachon, P., St-Hilaire, A., Ouarda, T. B. M. J., and Nguyen, V. T.-V. V.
690
(2008). “Uncertainty analysis of statistically downscaled temperature and
691
precipitation regimes in Northern Canada.” Theoretical and Applied Climatology,
692
OURANOS Consortium on Regional Climatology and Adaptation to Climate
693
Change, Montreal, QC, Canada, 91(1–4), 149–170.
694 695 696
Draper, N. R., and Smith, H. (1998). Applied Regression Analysis, 3rd Edition. Wiley Series in Probability and Statistics. Fealy, R., and Sweeney, J. (2007). “Statistical downscaling of precipitation for a
697
selection of sites in Ireland employing a generalised linear modelling approach.”
698
International Journal of Climatology, 27(15), 2083–2094.
699
Feser, F., Rockel, B., von Storch, H., Winterfeldt, J., and Zahn, M. (2011). “Regional
700
Climate Models Add Value to Global Model Data: A Review and Selected
701
Examples.” Bulletin of the American Meteorological Society, American
702
Meteorological Society, 92(9), 1181–1192.
703
Gent, P. R., Danabasoglu, G., Donner, L. J., Holland, M. M., Hunke, E. C., Jayne, S. R.,
704
Lawrence, D. M., Neale, R. B., Rasch, P. J., Vertenstein, M., Worley, P. H., Yang,
705
Z. L., and Zhang, M. (2011). “The community climate system model version 4.”
706
Journal of Climate, 24, 4973–4991.
707
Haberlandt, U., Belli, A., and Bárdossy, A. (2015). “Statistical downscaling of
708
precipitation using a stochastic rainfall model conditioned on circulation patterns -
709
an evaluation of assumptions.” International Journal of Climatology, John Wiley
710
and Sons Ltd, 35(3), 417–432.
31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
711
Hertig, E., and Jacobeit, J. (2013). “A novel approach to statistical downscaling
712
considering nonstationarities: application to daily precipitation in the
713
Mediterranean area.” Journal of Geophysical Research: Atmospheres, 118(2),
714
520–533.
715
Hessami, M., Gachon, P., Ouarda, T. B. M. J. M. J., and St-Hilaire, A. (2008).
716
“Automated regression-based statistical downscaling tool.” Environmental
717
Modelling & Software, 23(6), 813–834.
718
Hewitson, B. C., and Crane, R. G. (2006). “Consensus between GCM climate change
719
projections with empirical downscaling: precipitation downscaling over South
720
Africa.” International Journal of Climatology, 26(10), 1315–1337.
721 722 723
Hewitson, B., and Crane, R. (2002). “Self-organizing maps: applications to synoptic climatology.” Climate Research, 22, 13–26. Hundecha, Y., and Bárdossy, A. (2008). “Statistical downscaling of extremes of daily
724
precipitation and temperature and construction of their future scenarios.”
725
International Journal of Climatology, 28(5), 589–610.
726 727
IPCC. (2014). Climate Change 2013 - The Physical Science Basis. (Intergovernmental Panel on Climate Change, ed.), Cambridge University Press, Cambridge.
728
Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M.,
729
Saha, S., White, G., Woollen, J., Zhu, Y., Leetmaa, A., Reynolds, R., Chelliah, M.,
730
Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K. C., Ropelewski, C., Wang, J.,
731
Jenne, R., and Joseph, D. (1996). “The NCEP/NCAR 40-Year Reanalysis Project.”
732
Bulletin of the American Meteorological Society, American Meteorological
733
Society, 77(3), 437–471.
32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
734
Karamouz, M., Goharian, E., and Nazif, S. (2013a). “Reliability Assessment of the
735
Water Supply Systems under Uncertain Future Extreme Climate Conditions.”
736
Earth Interactions, 17(20), 1–27.
737
Karamouz, M., Nazif, S., and Zahmatkesh, Z. (2013b). “Self-Organizing Gaussian-
738
Based Downscaling of Climate Data for Simulation of Urban Drainage Systems.”
739
Journal of Irrigation and Drainage Engineering, 139(2), 98–112.
740
Kistler, R., Collins, W., Saha, S., White, G., Woollen, J., Kalnay, E., Chelliah, M.,
741
Ebisuzaki, W., Kanamitsu, M., Kousky, V., van den Dool, H., Jenne, R., and
742
Fiorino, M. (2001). “The NCEP–NCAR 50–Year Reanalysis: Monthly Means CD–
743
ROM and Documentation.” Bulletin of the American Meteorological Society,
744
American Meteorological Society, 82(2), 247–267.
745
Kohonen, T. (1995). “Self-Organizing Maps.” Springer-Verlag, Heidelberg.
746
Kohonen, T., and Honkela, T. (2007). “Kohonen network.” Scholarpedia, 2(1), 1568.
747
Li, F. (2005). “Box-Cox Transformations: An Overview (slide presentation).”
748 749 750
Department of Statistics, University of Connecticut. Lutgens, F. K., and Tarbuck, E. J. (2013). The Atmosphere, An Introduction to Meteorology. Pearson.
751
Mearns, L. (1995). “Analysis of daily variability of precipitation in a nested regional
752
climate model: comparison with observations and doubled CO2 results.” Global
753
and Planetary Change, 10(1–4), 55–78.
754 755
Najafi, M. R., Moradkhani, H., and Wherry, S. A. (2011). “Statistical Downscaling of Precipitation Using Machine Learning with Optimal Predictor Selection.” Journal
33
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
756 757
of Hydrologic Engineering, American Society of Civil Engineers, 16(8), 650–664. Pasini, A. (2009). “Neural Network Modeling in Climate Change Studies.” Artificial
758
Intelligence Methods in the Environmental Sciences, S. E. Haupt, A. Pasini, and C.
759
Marzban, eds., Springer Netherlands, Dordrecht, 424.
760
Raziei, T., Bordi, I., Santos, J. a., and Mofidi, A. (2013). “Atmospheric circulation types
761
and winter daily precipitation in Iran.” International Journal of Climatology, 33(9),
762
2232–2246.
763
Raziei, T., Mofidi, A., Santos, J. a., and Bordi, I. (2012). “Spatial patterns and regimes
764
of daily precipitation in Iran in relation to large-scale atmospheric circulation.”
765
International Journal of Climatology, 32(8), 1226–1237.
766 767
Richardson, C. W. (1981). “Stochastic simulation of daily precipitation, temperature, and solar radiation.” Water Resources Research, 17(1), 182–190.
768
Ryan, T. P. (1997). Modern Regression Methods. Wiley, New York.
769
Sarr, M. A., Seidou, O., Tramblay, Y., and El Adlouni, S. (2015). “Comparison of
770
downscaling methods for mean and extreme precipitation in Senegal.” Journal of
771
Hydrology: Regional Studies, 4, 369–385.
772 773 774
Semenov, M. A. (2008). “Simulation of extreme weather events by a stochastic weather generator.” Climate Research, 35(3), 203–212. Semenov, M. A., and Barrow, E. M. (1997). “Use of A Stochastic Weather Generator In
775
The Development Of Climate Change Scenarios.” Climatic Change, Kluwer
776
Academic Publishers, 35(4), 397–414.
777
Sheridan, S. C., and Lee, C. C. (2011). “The self-organizing map in synoptic
34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
778
climatological research.” Progress in Physical Geography, 35(1), 109–119.
779
Sunyer, M. A., Hundecha, Y., Lawrence, D., Madsen, H., Willems, P., Martinkova, M.,
780
Vormoor, K., Bürger, G., Hanel, M., Kriaučiūnienė, J., Loukas, A., Osuch, M., and
781
Yücel, I. (2015). “Inter-comparison of statistical downscaling methods for
782
projection of extreme precipitation in Europe.” Hydrology and Earth System
783
Sciences, Copernicus GmbH, 19(4), 1827–1847.
784
Tavakol-Davani, H., Nasseri, M., and Zahraie, B. (2013). “Improved statistical
785
downscaling of daily precipitation using SDSM platform and data-mining
786
methods.” International Journal of Climatology, 33(11), 2561–2578.
787
Tomassetti, B., Verdecchia, M., and Giorgi, F. (2009). “NN5: A neural network based
788
approach for the downscaling of precipitation fields – Model description and
789
preliminary results.” Journal of Hydrology, 367(1–2), 14–26.
790
Tryhorn, L., and DeGaetano, A. (2011). “A comparison of techniques for downscaling
791
extreme precipitation over the Northeastern United States.” International Journal
792
of Climatology, 31(13), 1975–1989.
793
Vesanto, J., Himberg, J., Alhoniemi, E., and Parhankangas, J. (2000). “Self-organizing
794
map in Matlab: the SOM Toolbox.” Laboratory of Computer and Information
795
Science, Helsinki University of Technology, Helsinki, Finland.
796 797 798
Vrac, M., and Naveau, P. (2007). “Stochastic downscaling of precipitation: From dry events to heavy rainfalls.” Water Resources Research, 43(7), n/a--n/a. Wang, L., Ranasinghe, R., Maskey, S., van Gelder, P. H. A. J. M., and Vrijling, J. K.
799
(2015). “Comparison of empirical statistical methods for downscaling daily climate
800
projections from CMIP5 GCMs: a case study of the Huai River Basin, China.” 35
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
801
International Journal of Climatology, John Wiley and Sons Ltd, n/a-n/a.
802
Wilby, R. L., and Dawson, C. W. (2013). “The Statistical DownScaling Model: insights
803
from one decade of application.” International Journal of Climatology, 33(7),
804
1707–1719.
805
Wilby, R. L., Dawson, C. W., and Barrow, E. M. (2002). “sdsm — a decision support
806
tool for the assessment of regional climate change impacts.” Environmental
807
Modelling & Software, 17(2), 145–157.
808
Wilby, R. L., Wigley, T. M. L., Conway, D., Jones, P. D., Hewitson, B. C., Main, J.,
809
and Wilks, D. S. (1998). “Statistical downscaling of general circulation model
810
output: A comparison of methods.” Water Resources Research, 34(11), 2995–
811
3008.
812
Wilks, D. S. (2010). “Use of stochastic weathergenerators for precipitation
813
downscaling.” Wiley Interdisciplinary Reviews: Climate Change, John Wiley &
814
Sons, Inc., 1(6), 898–907.
815
Willems, P., Arnbjerg-Nielsen, K., Olsson, J., and Nguyen, V. T. V. (2012). “Climate
816
change impact assessment on urban rainfall extremes and urban drainage: Methods
817
and shortcomings.” Atmospheric Research, Elsevier B.V., 103, 106–118.
818
Willems, P., and Vrac, M. (2011). “Statistical precipitation downscaling for small-scale
819
hydrological impact investigations of climate change.” Journal of Hydrology,
820
402(3–4), 193–205.
821 822
Yarnal, B. (1993). Synoptic climatology in environmental analysis: a primer. Belhaven Press.
36
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
823
Yarnal, B., Comrie, A. C., Frakes, B., and Brown, D. P. (2001). “Developments and
824
prospects in synoptic climatology.” International Journal of Climatology, 21(15),
825
1923–1950.
826
Yatagai, A., Kamiguchi, K., Arakawa, O., Hamada, A., Yasutomi, N., and Kitoh, A.
827
(2012). “Aphrodite constructing a long-term daily gridded precipitation dataset for
828
Asia based on a dense network of rain gauges.” Bulletin of the American
829
Meteorological Society, 93, 1401–1415.
830
Zhang, X., Wang, X. L., and Corte-Real, J. (1997). “On the relationships between daily
831
circulation patterns and precipitation in Portugal.” Journal of Geophysical
832
Research, 102, 13495.
833
37
1 834 Table 1: The SI values for different SOM dimensions size 2 3 4 33 34 35 36 44 5SOM (Self-organizing Maps) size 6 7 Number of nodes 9 12 15 18 16 8 SI (stratification index) 0.493 0.476 0.467 0.471 0.527 9 835 10 11 12 836 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 38 63 64 65
45
46
55
56
66
20 24 25 30 36 0.521 0.513 0.555 0.546 0.583
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
837
Table 2: The distribution of daily rainfall characteristics in CTs Rain characteristics
838
CTs* (circulation types)
1
2
3
1 0.6% 3.0% 9.6% 2 0.6% 2.9% 5.0% Rainfall occurrence percentages 3 0.4% 0.8% 3.4% 4 0.5% 0.8% 2.3% 1 0.4% 1.9% 9.2% 2 0.4% 1.6% 3.6% Proportion to total rainfall amount 3 0.2% 0.4% 2.5% 4 0.2% 0.4% 1.4% 1 0.0% 0.0% 10.8% 2 0.0% 0.0% 0.0% Proportion to number of extreme events 3 0.0% 0.0% 0.0% 4 0.0% 0.0% 0.0% th th * The given value in the i row and the j column corresponds to CT (i,j)
839 840 841
39
4 41.5% 16.9% 8.1% 3.7% 54.2% 15.5% 6.0% 2.0% 78.4% 10.8% 0.0% 0.0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
842
843
Table 3: PI values of the developed CTs CTs* (circulation types) 1 2 3 4 1 0.08 0.42 1.31 3.16 2 0.13 0.40 0.75 1.56 3 0.07 0.19 0.60 0.81 4 0.05 0.15 0.32 0.38 th th * The given value in the i row and the j column corresponds to CT (i,j)
844 845
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
846
Table 4: The variable sets considered in development of statistical models of SSDM Submodel
Variable's name
ROM
Vor
°C
Dew
°C
Dep
s-1
Vor
°C
Dew
°C
Dep
Air Temperature
°C
Ta
Geopotential height
m
hgt
700hp, 500hp
Relative Humidity
%
Rhu
Surface, 700hp, 500hp
Sea Level Pressure
N/m2
Slp
Surface
Dew point Temperature Dew point depression Vorticity
RAM (Rainfall amount model)
Considered levels Surface, 700hp, 500hp Surface, 700hp, 500hp Surface, 700hp, 500hp Surface, 700hp, 500hp Surface, 700hp, 500hp Surface, 700hp, 500hp Surface, 700hp, 500hp
s-1
Vorticity (Rainfall occurrence model)
Unit Variable abbreviation
Dew point Temperature Dew point depression
847 848
41
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
849
Table 5: The selected variables (predictors) in the developed statistical models for each
850
CT
851
Predictors* ROM (Rainfall occurrence model) RAM (Rainfall amount model) (1,2) 700hp-Dep, 500hp-Dep 700hp-Rhu 700hp-Rhu, 500hp-Rhu, (1,3) 700hp-Dep, 500hp-Dep 700hp-Vor, 500hp-Vor 700hp-Dew, 500hp-Ta, 700hp-Dep, 500hp-Dep, 500hp-Rhu, (1,4) 700hp-Vor, 500hp-Vor 700hp-hgt, Surface-Slp, Surface -Ta 500hp-Rhu, (2,2) 700hp-Dep, 500hp-Dep 700hp-Vor, 700hp-hgt (2,3) 500hp-Dep 700hp-Rhu 700hp-Dew, 500hp-Dew, 700hp-Dep, 500hp700hp-Rhu, (2,4) Dep 500hp-Rhu, Surface-Ta (3,2) 500hp-Dep 700hp-Vor (3,3) 500hp-Dep 500hp-Rhu (3,4) 700hp-Dep, 500hp-Dep 700hp-Rhu (4,3) 500hp-Dep 500hp-Ta 500hp-Dep, (4,4) 700hp-Dep, 500hp-Dep 500hp-Rhu, 700hp-Rhu * The predictors' descriptions are given in Table 4. CT (circulation types)
852
42
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
853
Table 6: Comparing SSDM results and the observed rainfalls in calibration and validation
854
periods as well as total data. Statistical characteristics
Percent of wet days (%) Average wet days rainfall amount (mm) Standard deviation of wet days rainfall amount (mm) Skewness of wet days rainfall amount Maximum daily rainfall amount (mm) Wet days coefficient of correlation (R) Root Mean Squared Error (RMSE, mm) 855
Calibration Validation Observed Modeled Observed Modeled 23.6 21.5 24.6 21.3
Total Observed Modeled 23.8 21.5
4.3
4.5
4.7
4.6
4.4
4.5
4.1
3.7
4.6
4
4.2
4
3
3.1
2.6
3.7
2.9
3.2
47.1
46.3
32
45.8
47.1
46.3
0.44
0.44
0.44
2.45
2.73
2.51
856
43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
857
Table 7: CTs occurrence distributions in observed (NCEP) and CCSM4 outputs for the
858
historical and future time periods
Source of considered data
859
CTs * (circulation types)
1
2
3
1 6.7% 5.1% 7.1% 2 3.9% 4.5% 4.9% NCEP (1970-2005) 3 4.0% 2.7% 4.5% 4 7.6% 3.4% 4.9% 1 5.7% 4.8% 6.3% 2 3.1% 3.6% 4.5% CCSM4-historical (1970-2005) 3 3.2% 2.8% 4.1% 4 8.5% 4.9% 5.5% 1 5.0% 5.1% 7.0% 2 3.4% 4.5% 4.7% CCSM4-RCP4.5 (2006-2050) 3 3.3% 3.7% 4.0% 4 8.7% 5.1% 6.0% 5 5.9% 5.0% 7.1% 6 3.6% 4.5% 5.0% CCSM4-RCP8.5 (2006-2050) 7 3.4% 3.6% 4.0% 8 7.9% 5.1% 5.1% * The given value in the ith row and the jth column corresponds to CT (i,j)
860
44
4 16.4% 9.9% 8.1% 6.4% 16.6% 9.6% 8.1% 8.7% 16.0% 8.6% 7.4% 7.6% 15.9% 8.5% 7.3% 8.1%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
861
Table 8: Comparing the statistics of the daily precipitation in the study area for the
862
historical period and future under RCP4.5 and RCP8.5 simulations by CCSM4 Historical (1970-2005) Percent of wet days (%) 23.9 Average wet days rainfall values (mm) 4.2 Standard deviation of wet days rainfall 3.9 values (mm) Skewness of wet days rainfall values 3.6 Maximum daily rainfall value (mm) 53.3 Average number of extreme events in a 1.0 year Statistical characteristics
863
45
RCP4.5 (2006-2050) 21.7 4.5
RCP8.5 (2006-2050) 22.7 4.4
4.6
4.4
4 56.6
3.9 55.1
1.4
1.3
Figure 1
Figure 1- The spatial and temporal scale of weather phenomena, available GCMs outputs and hydrological impact evaluation (Adapted from Nese and Grenci (2011))
Figure 2
Start
Selecting synoptic scale variables
Configuring SOM structure (number of nodes, dimensions, …)
Training SOM for clustering the synoptic scale variables patterns
NCEP reanalyzing database Local precipitation observed data
Selecting mesoscale variables by applying stepwise regression for rainfall occurrence model (ROM) and rainfall amount model (RAM) in each CT
Identifying the Circulation Types (CTs)
Fitting the parameters of the linear regression model between selected variables (predictors) and transformed rainfall based on minimizing weighted root mean squared errors (RMSE) in each CT
Interpretation of the relationship between local precipitation and CTs (statistical and physical relations)
Fitted statistical models for each CT (ROMs & RAMs)
Trained SOM
Synoptic classification (SOM classifier) SOM(SVi) = CTk
Skewness reduction of rainfall values (applying Cox-Box transfer function)
Using related statistical models (ROMk & RAMk)
Ri = ROMk(MVi) × RAMk(MVi)
End
Synoptic scale variables pattern of day i (vector SVi)
Phase I: Synoptic Scale Classification Model
GCM outputs
Mesoscale variables vectors of day i (MVi)
Phase II: Local Scale Statistical Model
Figure 2- The algorithm of SSDM and its main phases and steps
Figure 3
Figure 3- Location of the study area in Iran (red line box), mesoscale domain around the study area (dashed line box, 4 points) and the positions of NCEP data grids in synoptic scale domain (70 points) (Left side) Tehran urban and upland areas, positions of APHRODITE data grids around Tehran and the considered area at the north part of Tehran (shaded box) (Right side)
Figure 4
Figure 4- The histogram of wet day precipitation amount in the study area
Figure 5
Figure 5- Circulation types (CTs) resulted from applying SOM method
Figure 6
Figure 6- The frequency of daily 500-hPa geopotential heights patterns in identified CTs and probability of rainfall occurrences in each CT
Figure 7
Figure 7- Composite maps of the mean daily vorticity at 500-hPa and mean daily relative humidity at 700-hPa
Figure 8
Figure 8- Q-Q plot of modeled and observed wet day rainfall values for calibration and validation datasets
Figure 9
Figure 9- Time series of modeled and observed annual maximum daily precipitation
Figure 10
Percentiles of Wet Days Rainfall Values
Empirical Cumulative Distribution Functionof Wet Days Rainfall Values
50.00
1
40.00
0.8
30.00
0.6
20.00
0.4
10.00
0.2
0
0.00 0
20
(a)
40
Modeled
Daily Precipitation (mm)
Quantile-
60
Percentiles
80
0
100
10
20
Observed
30
40
50
Daily Precipitation (mm)
(b)
Modeled CFD
Quantile Plot of Wet Days Rainfall Values
Observed CFD
Histogram of Wet Days Rainfall Values
50
0.35
F(x)
0.3
40 0.25 30
0.2 0.15
20 0.1 10
0.05 0
0
(c)
0
10
20
30
Quantile (Modeled , mm)
40
50
(d)
0
5
10
15
20
25
30
35
40
45
50
Daily Precipitation (mm)
Modeled
Observed
Figure 10- Statistical performance of SSDM in daily precipitation downscaling of north part of Tehran urban area from 1970 to 2006. (a): The percentile plots of wet day rainfall values of observed and modeled precipitation. (b): Observed and modeled empirical cumulative distribution function (CDF) of wet day rainfall values. (c): Q-Q plot of Observed and modeled precipitation values of wet day. (d): Histogram of observed and modeled precipitation values of wet day
Figure 11
Figure 11- Statistical performance of SSDM in monthly precipitation downscaling of north part of Tehran urban area from 1970 to 2006. (a) mean monthly rainfall. (b) monthly wet days. (c) monthly variance. (d) standard deviation of wet days
Figure 12
Figure 12- Q-Q plot of vorticity (top curves) and dew point depression (down curves) values in 500-hp level at two points of mesoscale domain from NCEP and CCSM4
Figure 13
Figure 13- Q-Q plot of SSDM modeled wet day rainfall values sing NCEP and CCSM4-historical predictors for the period of 1970-2005
Figure 14
Figure 14- Comparing the statistical characteristics of the downscaled daily precipitation of north part of Tehran by applying SSDM and CCSM4 outputs (in three experiments: historical (1970-2005), rcp45 and rcp85 (2006-2050)) as predictors and historical observed data. (a) and (b): The percentile plots of wet day rainfall values. (c) and (d): The empirical cumulative distribution function (CDF) of wet day rainfall values
Figure 15
Figure 15- Q-Q plot of wet day rainfall values: CCSM4-historical predictors (past climate condition) against CCSM4-rcp45 and CCSM4-rcp85 predictors (near future climate condition) for north part of Tehran
