real-time remote sensing driven river basin modeling using...
TRANSCRIPT
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Real-time remote sensing driven river basin modeling using radar 1
altimetry 2
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Silvio J. Pereira Cardenal1, Niels D. Riegels1, Philippa A.M. Berry2, Richard G. 4
Smith2, Andrey Yakovlev3, Tobias U. Siegfried4, Peter Bauer-Gottwein1* 5
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1 Department of Environmental Engineering, Technical University of Denmark, 7
Miljøvej, Building 113, 2800 Kgs, Lyngby, Denmark 8
2 Earth and Planetary Remote Sensing Laboratory, De Montfort University, The 9
Gateway, Leicester, LE19BH, UK 10
3 Hydrological Forecasting Department – UzHydromet, Tashkent, Uzbekistan 11
4 The Water Center, The Earth Institute, Columbia University, New York, USA. 12
* Corresponding Author 13
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To be submitted to the Journal of Hydrology 15
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Abstract 17
Remote sensing (RS) data are an alternative to in-situ hydrometeorological data in 18
remote and poorly monitored areas and are increasingly used in hydrological 19
modeling. This study presents a lumped, conceptual, river basin water balance 20
modeling approach based entirely on RS data: precipitation was obtained from the 21
Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis 22
(TMPA), temperature from the European Centre for Medium-Range Weather Forecast 23
(ECMWF) global reanalysis dataset and evapotranspiration was derived from 24
temperature data. The Ensemble Kalman Filter was used to assimilate radar altimetry 25
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(ERS2 and Envisat) measurements of reservoir water surface elevations. The 26
modeling approach is applied to the Syr Darya River Basin, a primarily snowmelt 27
driven basin with large topographical variability and scarce meteorological data that is 28
shared between 4 countries with conflicting water management interests. 29
Assimilation of radar altimetry data improved model results significantly. Without 30
data assimilation, model performance was limited, probably because of the size and 31
complexity of the model domain, simplifications inherent in model design, and the 32
uncertainty of RS data. Data assimilation reduced the mean of the reservoir water 33
surface level residuals from 19.5 to 4.5 meters, and model root mean square error 34
from 16.7 meters to 6.4 meters. 35
By providing an impartial source of information about the hydrological system that 36
can be updated in real time, the modeling approach described here could provide 37
useful hydrological forecast information that could be updated at time scales 38
appropriate for decision-making. The approach has potential to facilitate cooperation 39
in transboundary basins with conflicting management objectives. 40
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Keywords 42
Data assimilation, Radar altimetry, River basin modeling, Syr Darya, Ensemble 43
Kalman Filter 44
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Introduction 46
Hydrological models are constructed for two main purposes: improved hydrological 47
process understanding and practical decision support for water resources 48
management. One of the main tasks in planning and management of water resources 49
is to identify and characterize the properties of the resources in a basin and their 50
interactions (Loucks et al., 2005). The hydrological assessment becomes more 51
challenging when the basin is shared between political units, either at the intra- or 52
interstate level, with conflicting upstream and downstream interests in time and space. 53
Hydrology is a discipline limited by data availability. Many hydrological variables are 54
hard to measure, and those that can be measured are only available for limited 55
intervals in space and time. This situation is improving due to the increasing 56
availability of RS techniques and automatic ground sensors. Hydrological modeling in 57
remote or data-scarce areas must often rely on RS data only. Satellite-based data with 58
high temporal resolution have the potential to fill critical information gaps in such 59
ungauged basins (e.g. Grayson et al., 2002; Lakshmi, 2004) 60
Remote sensing data can be used in hydrological models in two ways (Brunner et al., 61
2007): as input parameters (or forcing data) and as model constraining data during 62
calibration. The most popular remote sensing data sources for hydrological 63
applications are multispectral imagery for the determination of actual 64
evapotranspiration (e.g. Bastiaanssen et al., 1998; Jiang et al., 2001; Stisen et al., 65
2008b), active microwave sensors for the mapping of the soil moisture distribution 66
(e.g. Parajka et al., 2006), total water storage change estimates from GRACE (e.g. 67
Hinderer et al., 2006; Winsemius et al., 2006), and river and lake level variations from 68
radar altimetry (e.g. Birkett, 2000; Alsdorf et al., 2001) and interferometric SAR (e.g. 69
Alsdorf et al., 2001; Wdowinski et al., 2004). Several previous studies have used 70
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remote sensing data in the context of river basin water balance modeling (e.g. Campo 71
et al., 2006). Andersen et al. (2002) built a distributed hydrological model of the 72
Senegal River Basin using precipitation derived from METEOSAT data and leaf area 73
index (LAI) estimated from the normalized difference vegetation index (NDVI) from 74
NOAA AVHRR data. Stisen et al. (2008a) developed a distributed hydrological 75
model of the same catchment using potential evapotranspiration (PET) estimated from 76
global radiation, precipitation from satellite-derived cold cloud duration, and LAI 77
calculated from NDVI. Boegh et al. (2004) used RS-data to derive PET and LAI as 78
input to a distributed agro-hydrological model. Francois et al. (2003) used Synthetic 79
Aperture Radar (SAR) estimates of soil moisture in a lumped rainfall-runoff model. 80
Distributed, physically based hydrological models represent the hydrological 81
processes at a specific resolution in space and time. However, such models require 82
accurate spatially resolved input data, computational loads for large systems are high 83
and sometimes prohibitive, and for some hydrological processes (such as overland 84
flow, actual evapotranspiration and infiltration), parameterization and/or effective 85
parameter values can be scale dependent (Bloschl et al., 1995; Sivapalan, 2003). For 86
all these reasons, lumped hydrological modeling remains an attractive and widely 87
used method for river basin water balance simulations (Reed et al., 2004; Carpenter et 88
al., 2006). 89
In this study, we use RS-data exclusively as inputs to a lumped conceptual 90
hydrological model. Precipitation is obtained from the Tropical Rainfall Measuring 91
Mission (TRMM) Multisatellite Precipitation Analysis (TMPA; Huffman et al., 92
2007); daily temperature is obtained from the European Centre for Medium-Range 93
Weather Forecast (ECMWF) global reanalysis dataset (Molteni et al., 1996); and 94
potential evapotranspiration is derived from temperature using Hargreaves equation 95
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(Allen et al., 1998). The water level in a cascade of reservoirs is simulated in the 96
model, and satellite radar altimetry data (Berry et al., 2005) are used to update the 97
state of the reservoirs using data assimilation techniques. 98
Research in data assimilation (DA) has led to the development of a set of statistical 99
methods to infer the most likely state of a system using all sources of information 100
available. These methods were first used for oceanography and meteorology 101
applications, but have been used in hydrology since the 1990’s (McLaughlin, 1995; 102
Evensen, 2003). Previous studies using data assimilation techniques on hydrological 103
modeling included land surface models (e.g. Reichle et al., 2002), surface water 104
models (e.g. Madsen et al., 2005) and groundwater models (e.g. Franssen et al., 2008). 105
DA has proved to be a very valuable tool for hydrological modeling because it can 106
improve operational forecasts and also allow the model to adapt to changes after 107
calibration. In our case study, satellite altimetry measurements over four reservoirs are 108
assimilated into a hydrological model, reducing the deviation of model predictions 109
from the “true” state of the system. Several DA techniques are available, including the 110
Particle Filter (Arulampalam et al., 2002) and the Reduced Rank Square Root Filter 111
(Verlaan et al., 1997); The Ensemble Kalman Filter (Evensen, 2003) is used here 112
because it has a simple conceptual formulation, it is easy to implement and is 113
computationally feasible. 114
We present a river basin modeling approach to the Syr Darya River Basin (SDRB) 115
that can be used for real time modeling. In this basin, the four riparian nations face a 116
complicated trans-boundary water resources management problem. Real-time 117
hydrological modeling can support the decision makers in adaptive management as 118
forecasts of, for instance, water availability can be updated continuously as new data 119
become available. 120
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Methods and Data 121
Case study 122
The Syr Darya River is located in the Central Asian republics of Kyrgyzstan, 123
Uzbekistan, Tajikistan, and Kazakhstan and, along with the Amu Darya River, is one 124
of two principal tributaries to the Aral Sea (Figure 1). About 22 million people in the 125
region depend on irrigated agriculture for their livelihoods, and 20% to 40% of GDP 126
in the riparian countries is derived from agriculture, most of which is irrigated 127
(Bucknall et al., 2003). Much of the region has an arid climate, with strongly seasonal 128
precipitation and temperature patterns. The extensive development of irrigation in the 129
basin is associated with a number of environmental problems including desiccation of 130
the Aral Sea, which has lost up to 90% of its pre-1960 volume and has received 131
international attention as an environmental disaster area (Micklin, 2007). 132
The Syr Darya River originates in the Tien Shan Mountains of Kyrgyzstan and is 133
formed by the confluence of the Naryn and Karadarya rivers near the border of 134
Kyrgyzstan and Uzbekistan. The population of the basin is approximately 20 million, 135
with an area of about 400,000 km2. Annual precipitation averages about 320 mm and 136
ranges from 500-1500 mm in the mountain zones to 100-200 mm in desert regions 137
near the Aral Sea. The bulk of runoff comes from melting snow and glaciers in the 138
mountains of Kyrgyzstan. Because of the combined effects of snowmelt and glacial 139
runoff, about 80% of runoff in the basin occurs between March and September. The 140
onset of the snowmelt period shifts from early spring to early summer with increasing 141
elevation, distributing snowmelt runoff over a period of several months. In the 142
summer months, glacial ablation peaks and prolongs the period of peak runoff. 143
Annual runoff averages about 39 km3/year, and approximately 90% of the river’s 144
mean annual flow is regulated by reservoirs (Savoskul et al., 2003). 145
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The Syr Darya River was extensively developed for irrigation and hydropower during 146
Soviet times, particularly after 1960, with the primary goal of producing cotton. Total 147
irrigated area in the Aral Sea basin increased from 5 million hectares in 1965 to 7.9 148
million hectares in 2000 (Micklin, 2007). About 1.7 million hectares are currently 149
irrigated directly from the Syr Darya River (Siegfried et al., 2007). Cotton is an 150
important source of foreign exchange in Uzbekistan, and continued production 151
through irrigated agriculture is a priority for the government (World Bank, 2004). 152
A significant change to the natural hydrological pattern of the basin occurred with the 153
construction of the Toktogul Reservoir in 1974. Because the timing of the March-154
September natural runoff peak coincides with the irrigation season, substantial 155
reservoir storage is not required to regulate seasonal runoff. However, the aggressive 156
expansion of irrigation during Soviet times created a need for multi-year storage to 157
store excess flows in wet years to supplement dry year flows. Toktogul Reservoir was 158
constructed on the Naryn River (the principal tributary to the Syr Darya) to serve this 159
purpose. The reservoir is the largest storage facility in the Aral Sea basin and has a 160
total capacity of 19.5 km3 (14 km3 active storage). The construction of the reservoir 161
was accompanied by the building of four smaller downstream reservoirs and power 162
plants to maximize electricity generation from reservoir releases. The five facilities, 163
commonly called the Naryn Cascade, have a combined generation capacity of 2870 164
MW (World Bank, 2004). 165
Toktogul Reservoir and the Naryn Cascade are at the heart of a dispute over 166
management of the Syr Darya River that has existed since the downfall of the Soviet 167
Union in 1991. In the Soviet system, the reservoir was operated to benefit irrigated 168
agriculture and power was produced incidentally as flows were released to meet 169
downstream demands. In 1992, the Central Asian riparian states agreed to continue 170
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Soviet water allocation policies and established the Interstate Commission for Water 171
Coordination (ICWC) to oversee the allocation process. However, the new system 172
immediately came under strain as the competing interests of the newly independent 173
states emerged. Toktogul Reservoir came under the control of Kyrgyzstan, which is 174
less dependent on irrigated agriculture and lacks fossil fuel resources for energy 175
generation. Kyrgyzstan had been supplied with fossil fuels under the Soviet system 176
but found itself in the position of having to purchase energy supplies on world 177
markets after 1991. Kyrgyzstan turned to hydropower for its own energy needs, which 178
peak in winter because of heating demands, placing the country’s operational 179
objectives in direct opposition to those of its downstream neighbors; Kyrgyzstan 180
would prefer to store summer peak flows for winter power generation, while the 181
downstream countries would like winter releases minimized to conserve water for the 182
summer season (Biddison, 2002; World Bank, 2004; Siegfried et al., 2007). Increased 183
winter releases also cause flooding, as many of the downstream irrigation works are 184
not built to handle high flows and ice in the river bed reduces winter flow capacity 185
(Biddison, 2002). 186
Under these new conditions, the Soviet allocation pattern proved to be infeasible, and 187
the riparian countries entered into a series of annual agreements in which downstream 188
countries agreed to purchase hydropower from Kyrgyzstan during the summer 189
irrigation period in order to ensure summer releases. These agreements were 190
essentially barter transactions in which the downstream states agreed to compensate 191
Kyrgyzstan for summer releases by delivering electricity, oil, coal, and gas during the 192
winter months. In practice, the downstream countries did not always deliver the 193
agreed amounts of energy, forcing Kyrgyzstan to make additional winter releases. In 194
addition, the ad hoc nature of the annual agreements meant that multi-year storage 195
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considerations, which were the original purpose of Toktogul Reservoir, were not 196
given adequate consideration in the allocation process. As a result of increased year-197
round pressure and a lack of long-term planning, Toktogul storage declined to a 198
previously unsurpassed low of 7.5 km3 1998 (World Bank, 2004). 199
Kyrgyzstan, Uzbekistan, and Kazakhstan attempted to reform the ad hoc system that 200
developed after 1991 by entering into a framework agreement in 1998. The new 201
agreement recognized the need to provide compensation for lost generating capacity 202
and expressed an intention to move away from a barter system towards cash 203
transactions for water and power. The agreement also recognized the need for multi-204
year regulation of the river (World Bank, 2004). Although considered an 205
improvement over the ad hoc arrangements that existed previously, the 1998 206
agreement has not resolved the upstream-downstream conflict and today it appears 207
that the agreement has essentially been abandoned and the riparian countries have 208
reverted to an ad hoc allocation system (Abdukayumov, 2008). On a visit to the 209
region in May 2008, the authors observed that storage in Toktogul had dropped to 210
about 6.5 km3, only slightly above dead storage (5.5 km3). The riparian states appear 211
to be pursuing national solutions, with Kyrgyzstan attempting to build new 212
hydropower facilities upstream of Toktogul Reservoir and Uzbekistan and Kazakhstan 213
seeking to construct new storage facilities to capture winter releases. These facilities 214
are expensive and inefficient, and considerable resources could be saved by basin-215
wide cooperation (Biddison, 2002). 216
In these circumstances of mutual distrust between the up- and downstream countries, 217
remote sensing and data assimilation hold great promise for increasing transparency, 218
reducing forecast uncertainty, and increasing the speed at which forecasts can be 219
developed and updated. Because remotely-sensed data products are available to all, 220
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their increased use in the region has the potential to reduce distrust by providing a 221
common base of information. The increasing availability of these products in real-222
time also has the potential to accelerate the forecasting process so that water 223
allocation plans can be agreed upon earlier in the irrigation season. Statistical methods 224
like the Ensemble Kalman Filter offer a way to fine-tune forecasts as new data 225
become available, giving the countries more flexibility to respond to changing 226
conditions at the seasonal scale. 227
River Basin water balance modeling 228
The river basin model is implemented using the commercial software package DHI 229
Mike Basin (DHI, 2009). The model consists of a rainfall-runoff component, a river 230
network component that includes the reservoirs and an irrigation component that 231
simulates the major irrigation water users in the basin. The simulation is run in 1 day 232
timesteps from January 1st, 2000 to December 31st, 2007. 233
Rainfall-runoff model 234
The runoff processes in the catchment were simulated through a lumped conceptual 235
hydrological model. The NAM (Nedbør – Afstrømningsmodel, Danish for rainfall-236
runoff model) is a modeling system consisting of mass balance equations that account 237
for the water content in four different storages representing processes occurring in the 238
land phase of the hydrological cycle: snow storage, surface storage, lower soil zone 239
storage and groundwater storage (DHI, 2000). The minimum data requirements of the 240
modeling system are precipitation, potential evapotranspiration and observed 241
discharge. Daily mean temperature is also required if snowmelt contributes to runoff. 242
A comparison of data requirements and performance of NAM with other hydrological 243
models is provided by Refsgaard et al. (1996). The four storage are typically 244
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described using a set of 17 parameters, about 10 of which are commonly used for 245
model calibration. 246
Due to the limited amount of observed in-situ river discharge data, it was impossible 247
to achieve a unique and stable calibration based on 10 free model parameters. Instead 248
a more robust version of NAM was developed using only two free calibration 249
parameters: one describing soil moisture storage and the other groundwater response 250
times. The structure of this simplified version of NAM is shown in Figure 2. Table 1 251
lists the parameters chosen to enforce this model structure. Because of its simplicity, 252
the modeling approach is robust and appropriate given the general scarcity of 253
observation data in the SDRB. 254
Precipitation falls as snow if the temperature is below 0 degrees Celsius. Each single 255
catchment is divided into 10 separate elevations zones of equal area and the 256
precipitation discrimination is done for each individual elevation zone using 257
temperature lapse rates based on Tsarev et al. (1994). Snow melt is modeled using a 258
simple degree-day approach: 259
260
Equation 1 261
where SMpot is the potential snowmelt (mm day-1), T is the temperature in degrees 262
Celsius, SS is the snow storage (mm day-1), and M is a seasonally variable degree day 263
factor (mm day-1 deg-1) based on a parameterization proposed by Shenzis (1985) for 264
the Central Asian Mountains. Snowmelt parameters are shown in 265
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266
Table 2. Snow melt is calculated for each elevation zone separately. Snow melt and 267
precipitation enter the soil storage. Water in the soil storage is depleted by 268
evapotranspiration. Actual evapotranspiration is calculated as a function of potential 269
evapotranspiration and soil wetness: 270
271
Equation 2 272
where ETref is the reference ET calculated using Hargreave’s equation (mm day-1), L 273
is the soil storage (mm) and Lmax is the maximum soil storage (mm). Lmax is a 274
calibration parameter. Percolation from the soil storage to the groundwater storage is 275
calculated using the following parameterization: 276
277
278
Equation 3 279
where P is the precipitation in mm day-1. Baseflow from the groundwater reservoir to 280
the river is calculated using a linear reservoir approach: 281
282
Equation 4 283
where GS is the groundwater storage in mm and CKBF is the response time of the 284
groundwater (days). This is the second calibration parameter. Rainfall-runoff 285
processes are thus simulated in a very simple approach with two calibration 286
parameters only: Lmax and CKBF. 287
An automatic calibration module is available for NAM (Madsen, 2000). The module 288
is based on the Shuffled Complex Evolution (SCE) algorithm, and it allows the 289
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optimization of multiple objectives: (1) overall water balance; (2) overall RMSE, (3) 290
peak flow RMSE and (4) low flow RMSE. The catchments were classified into 291
calibration, validation, prediction and inactive catchments, based on the discharge 292
data provided by the Operational Hydrological Forecasting Department 293
(UzHydromet) in Tashkent, Uzbekistan. Catchments with continuous discharge 294
records of 8 years or more were used for calibration, while those with 3-7 years of 295
discontinuous data were used for validation. Prediction catchments are defined as 296
those where no discharge data are available, but topography and land cover suggest 297
considerable runoff. Areas were no runoff is expected were considered inactive. In 298
total there were 32 prediction catchments (excluding those used for calibration and 299
validation) and 60 inactive catchments. 300
The input data of calibration catchments were duplicated and only the second half of 301
the duplicated record was used for calibration, while the first half was used to drive a 302
model warm-up period. The two parameters Lmax and CKBF were adjusted through the 303
automatic calibration module, minimizing overall root mean squared error. The 304
maximum number of iterations was set to 1000, which was never exceeded. It was 305
noted that while CKBF was relatively stable, the results for Lmax were either very 306
high (median of 3510 mm) or very low (median of 32 mm); the latter was generally 307
associated with a significantly negative water balance. The validation procedure 308
showed that low Lmax values performed substantially better in windward-facing 309
catchments, whereas high Lmax values resulted in a better fit in leeward-facing 310
catchments. This could be due to underestimation of orographic precipitation by the 311
TMPA product. However, there were too few precipitation stations to substantiate 312
this. The median Lmax values were used in prediction catchments (Table 6, in 313
Results). 314
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315
River network and water allocation model 316
The Mike Basin river network consists of nodes and reaches. The catchments dewater 317
into the river network at catchment nodes. The water transfer from one node to the 318
next is instantaneous, i.e. at every node a simple water balance equation is solved. The 319
only nodes that can store water temporally are the reservoir nodes. Irrigation sites are 320
introduced into the model as water demand nodes. Figure 1 shows the Mike Basin 321
river network layout. 322
Information on the reservoirs was obtained from the Scientific Information Council of 323
the Interstate Commission for Water Coordination in Central Asia (ICWC, 2009). The 324
reservoirs in the Syr Darya River Basin are implemented as rule curve reservoirs. The 325
reservoir water balance is calculated from inflow, outflow and losses. The level-area-326
volume curve is used to convert volume to water level. This information was provided 327
by UzHydromet. Once the water level reaches the flood control level, all additional 328
water is instantaneously routed downstream. Observed release time series are 329
available from the ICWC (2009). The observed releases were prescribed as minimum 330
downstream release time series for the various reservoirs. In a real-time application 331
mode of the model, these releases would be replaced by planned/projected releases. 332
The irrigation areas in the Syr Darya River Basin are lumped into 6 major demand 333
sites, following Raskin et al., 1992. These are High Naryn, Fergana, Mid Syr, Chakir, 334
Artur and Low Syr. Irrigation areas and crop distributions were taken from Raskin et 335
al. (1992). Irrigation water demand was calculated using the FAO-56 methodology 336
(Allen, 2000). Growing season time periods were estimated based on FAO-56. During 337
the growing season, the soil water balance is calculated on a daily time step from 338
precipitation, crop evapotranspiration and irrigation for each demand site. 339
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Precipitation is taken from the TMPA product (see below), crop evapotranspiration is 340
calculated using the FAO dual crop coefficient approach and reference ET and 341
irrigation is calculated using the standard FAO-56 irrigation model. This model 342
assumes that irrigation is triggered if the soil water content decreases below 50% of 343
the readily available water. Soil water contents at field capacity and wilting point 344
were uniformly set to 0.15 and 0.05 respectively. A total loss fraction of 0.3 was 345
generally assumed for all demand sites. 346
347
Data Assimilation 348
The Ensemble Kalman Filter (EnKF) has become a popular data assimilation 349
technique within several fields because of its ease of implementation and its 350
computational feasibility (Evensen, 2003). 351
In the EnKF, the covariance matrix used in a traditional Kalman Filter is replaced by 352
an ensemble of model states. The mean of the ensemble is assumed to be the “truth” 353
and the model error (or covariance) is represented by the sample variance of the 354
ensemble members. The ensemble members are then updated according to model and 355
observation errors, as it would be done in a traditional Kalman Filter. Let Xf be the 356
model forecast ns × ne matrix containing all model states for every ensemble member, 357
where ns is the number of state variables and ne is the number of ensemble members. 358
359
Equation 5 360
where xf1… xf
ne are the forecast vectors containing all state variables for each 361
ensemble member. The model error covariance Pf is 362
363
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364
Equation 6 365
where the overbar denotes an average over the ensemble. The model states of every 366
member are then updated through the traditional update equation 367
368
, 369
Equation 7 370
where xa is the vector of updated model states for the ith ensemble member, H is an 371
no × ns operator (no is the number of observations) that transforms the states into 372
observation space and y is a no × 1 vector that contains the observations for every 373
state variable. The Kalman gain K is denoted by 374
375
376
Equation 8 377
where R is the no × no error covariance matrix of the observations. The observations 378
yi (in Eq. 7) must be treated as random variables having a distribution with mean y 379
and a covariance R (Evensen, 2003). A normally distributed, uncorrelated distribution 380
is assumed. 381
Because Mike Basin does not have a DA module, the assimilation algorithm described 382
in Verlaan (2003) was adapted to run a set of Mike Basin models automatically and to 383
assimilate water level measurements over several reservoirs. Since the only input to 384
the Mike Basin water allocation model is runoff and irrigation, the ensemble of 385
models was produced by stochastically perturbing the area of irrigation districts and 386
the runoff timeseries of active catchments. The average standard deviation of the 387
runoff residuals from the validation process ( 388
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Table 6, in Results) was used as the standard deviation for the runoff perturbations; 389
while an uncertainty factor of ± 0.2 was assigned to the irrigation area. This was 390
implemented as: 391
392
Equation 9 393
where Qi is the specific runoff for the ith ensemble member, Q0 is the estimated 394
specific runoff for every catchment and σQ is the runoff uncertainty and has zero mean 395
and a standard deviation equal to the runoff standard error. An uncertainty factor of ± 396
0.2 was assigned to the irrigation area. Since this uncertainty could not be estimated, it 397
was used as filter tuning parameter, as described below. The irrigation uncertainty 398
was implemented as follows: 399
400
Equation 10 401
where IWDi is the irrigation water demand for the ith ensemble member, IWD0 is the 402
water demand estimated from Raskin et al. (1992), and σIWD is the uncertainty about 403
the current area of the irrigation districts. This approach was chosen for IWD because 404
it prevents the fictitious generation of water demand during non-growing periods, 405
when IWD0 is zero. 406
The DA scheme was practically implemented in Mike Basin by running one model 407
time step ne times and storing the evolution of the state variables for every ensemble 408
member. The appropriate ensemble size, runoff and IWD perturbation levels were 409
chosen by running a series of experiments (Table 3). 410
Input, Forcing and Calibration/Validation datasets 411
All input, forcing and calibration/validation datasets were obtained from remote 412
sensing data sources. 413
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Table 4 provides an overview of the various data sources used in this study. 414
Catchment delineation 415
The digital elevation model (DEM) of the area was obtained from the Shuttle Radar 416
Topography Mission (SRTM). The mission is described by Rabus et al. (2003), and 417
an assessment of its results is provided by Rodriguez et al. (2006). The data with a 3 418
arc second (90 meter) resolution was resampled to 1 km spatial resolution. The 1 km 419
DEM was used to delineate the river network and the catchments. 420
Rainfall 421
The Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation 422
Analysis (TMPA; Huffman et al., 2007) has been used as the data source for 423
precipitation in the Syr Darya basin. The 3B42 research product was found suitable 424
because of its temporal and spatial resolution (3 hours and 0.25°, respectively) and the 425
incorporation of surface observation data. The TMPA rainfall estimates have been 426
validated in diverse regions, e.g. USA (Villarini et al., 2007), Argentina (Su et al., 427
2008) and Brazil (Collischonn et al., 2008). 428
The 3-hourly data were accumulated over one day periods and area-averaged over the 429
different catchments. The precipitation product was not altitude-corrected because it 430
has already been adjusted to match observations of a global gauge network. The 431
global bias of the 3B42 product relative to the available station data was calculated as 432
minus 20%. This bias was corrected by multiplying the 3B42 precipitation by a factor 433
of 1.25. 434
Mean temperature 435
Snowmelt modeling requires daily mean temperature inputs. Therefore, the decadal 436
(10-day) ground observations provided by the RCHT could not be used. An ECMWF 437
operational dataset that includes 2-meter temperature was used (ECMWF, 2009). The 438
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data is available in near real time and has a temporal resolution of 6 hours (0000, 439
0600, 1200 and 1800 UTC) and a spatial resolution of 0.5° up to 2006, and 0.25° 440
thereafter. The temperature fields were averaged over daily periods, with the time for 441
this procedure corrected by the median longitude of the Syr Darya basin (70° E), i.e. 442
UTC + 0600. The pixel-wise daily mean temperature was then area-averaged over the 443
catchments. The mean catchment elevation was used as the reference elevation when 444
extrapolating the temperature to the different elevation zones in the catchment. 445
Reference evapotranspiration 446
Input data for reference ET calculation based on the Penman-Monteith equation were 447
not available. Reference ET was therefore computed from the temperature data using 448
Hargreaves equation (Allen et al., 1998): 449
450
, 451
Equation 11 452
where Tmean is defined as the average of Tmax and Tmean (not the average of all available 453
temperature measurements) and Ra is the extraterrestrial radiation (converted to mm 454
day-1 through the latent heat of vaporization) for the corresponding Julian day and 455
latitude. Hargreaves et al. (2003) present a comprehensive evaluation of the 456
performance of Equation 11. A temperature averaging period above 5 days is 457
recommended; although some water resource studies (e.g. the IWMI World Climate 458
Atlas) use 10-day temperature averages (Hargreaves et al., 2003). The PET fields 459
were calculated over 10-day periods and then area-averaged over the different 460
catchments. 461
20
Radar Altimetry 462
Satellite radar altimetry was initially used in order to study the marine geoid and 463
ocean dynamics (Rapley, 1990). However, over the past two decades different 464
research groups have derived inland water heights from space-based radar altimetry 465
(e.g. Cazenave et al., 1997; Berry et al., 2005; Cretaux et al., 2006). In this study, 466
altimetry data re-tracked by the Earth and Planetary Remote Sensing Laboratory 467
(EAPRS) over four large reservoirs was assimilated into the MIKE BASIN model in 468
order to update the water level of the reservoirs. The data used is derived from the 469
ERS and ENVISAT satellites, which cover 82° N to 82° S and have repeat cycles of 470
35 days. The altimetry data retracked by the EAPRS lab provide a large number of 471
inland water bodies. In total, 39 ERS2 targets and 37 ENVISAT targets were 472
identified over rivers and lakes in the basin; but only those over the Toktogul, 473
Chardara, Kayrakkum and Charvak Reservoirs (Figure 1) were assimilated into the 474
model. Frappart et al. (2006) reports an accuracy of 0.25-0.53 m for the Radar 475
Altimeter 2 (on board of ENVISAT) over lake targets in the Amazon basin. 476
Results 477
Validation of Remote Sensing Dataset versus Ground Observations 478
Precipitation and Temperature 479
The tendency of the TMPA product to underestimate precipitation has been 480
successfully corrected, although there is still a mismatch between the observed and 481
the RS-based precipitation data (Figure 4). 482
Figure 5 compares the temporal variability of observed precipitation and temperature 483
with corresponding RS-based products on three selected stations (shown in Figure 1). 484
While RS temperature fits well with observed dekadal data, the (corrected) monthly 485
RS-precipitation estimates largely underpredict rainfall. 486
21
Radar altimetry 487
Radar altimetry targets were obtained over four of the main reservoirs in the area. For 488
these reservoirs, the altimetry data were found to have an average actual precision of 489
0.86 m (Table 5), below the accuracy of 0.25-0.53 reported in Frappart et al. (2006) 490
for ENVISAT over lake targets. 491
River Basin Water Balance Modeling Results 492
The modeling approach captures the dominance of snowmelt in the hydrological 493
cycle: precipitation is accumulated during the winter and released throughout the 494
melting season (Figure 6). However, the calibration-validation process shows that 495
model results are uncertain and tend to underestimate runoff ( 496
Table 6). This is not surprising considering the size and complexity of the model 497
domain and the uncertainty associated with remotely-sensed data. Model uncertainty 498
can be significantly reduced through the assimilation of radar altimetry measurements 499
of reservoir water surface elevations. 500
Data assimilation results 501
Figure 8 compares the reservoir levels predicted by the assimilation scheme and the 502
corresponding no-assimilation setup. When altimetry measurements were available, 503
their assimilation considerably improved the results of the model (Table 8). However, 504
when all ensemble models incorrectly simulate an empty or full reservoir (e.g. 505
Kayrakkum in September/2000 or Toktogul in July/2005) the model does not react to 506
the assimilation of altimetry measurements, because the current model error 507
covariance P for that particular state variable becomes zero. 508
The accuracy of the EnKF estimates improve proportionally to the square root of the 509
ensemble size N (Evensen, 2007), although in practical applications this is limited by 510
the number of ensemble members that are computationally feasible to run. A series of 511
22
experiments were run in order to determine tuning parameters that would optimize 512
model performance ( 513
Table 3). 514
An ensemble size of 50 was chosen because it significantly reduced the mean and the 515
standard deviation of the residuals in relation to running the model with only 5 516
ensemble members. An ensemble size of 100 (not plotted) did not show any 517
improvement. A runoff perturbation of 20 L km-2 s-2 and an irrigation area uncertainty 518
of 40% yielded the best results for all four reservoirs (Figure 10). 519
The data assimilation approach described here could benefit the annual water 520
allocation process in the Syr Darya basin by providing an efficient and transparent 521
technology for updating hydrological forecasts in real time. In the current 522
management setup, the riparian states are supposed to agree on an allocation plan at 523
the beginning of April; however, agreement is often delayed until well into the 524
growing season, creating significant uncertainties for irrigation planning and 525
increasing tensions on both sides of the conflict. An obstacle to co-operation is the 526
deteriorated state of the hydro-meteorological monitoring network that existed in 527
Soviet times (Schar et al., 2004). In addition, national hydro-meteorological agencies 528
now responsible for data collection are reluctant to share data and the annual process 529
of data collection and forecasting can also be delayed by poor communications 530
infrastructure (Biddison, 2002). A model driven by remotely sensed data that could be 531
updated in real-time would minimize forecast uncertainties and delays, potentially 532
accelerating the annual allocation process. Although the approach described here uses 533
historical remotely sensed data, it could easily be adapted to forecasted data. 534
Figure 12A shows how the model prediction deviates from the “true” state of the 535
system when no altimetry data is available. Figure 12B shows the average forecast 536
23
error when predicting water levels at Toktogul 1-5 months in advance and 537
assimilating altimetry data until the previous 1-4 months. Predictions one and two 538
months ahead (April and May) are significantly improved as more recent altimetry 539
measurements are assimilated. However, model predictions three or more months in 540
advance are poor, and the impact of data assimilation much less significant 541
542
543
24
Discussion 543
A modeling approach using only remotely-sensed data has been developed and 544
applied to the Syr Darya River Basin. The ability of the river basin model to predict 545
reservoir water surface levels without data assimilation was moderate at best. The 546
general underprediction of reservoir levels might be due to inaccuracies in the RS 547
input data, to the simplification inherent in model structure (e.g. monthly snowmelt 548
coefficient, lack of individual modeling of glacial accumulation/ablation), or to 549
unmodeled changes in the hydrology of the basin (e.g. variation of irrigation water 550
demand or dominance of snowmelt and glacial ablation compared to snow and glacial 551
accumulation). 552
Limited availability of in-situ discharge data for model calibration required that high 553
resolution RS data to be aggregated over very large areas (sometimes as large as 37 554
000 km2). If more discharge stations were available, smaller subcatchments could be 555
used and the fine resolution of the data products would have been better exploited. 556
Although estimates of river discharge from radar altimetry have been reported, (e.g. 557
Coe et al., 2004; Kouraev et al., 2004; Zakharova et al., 2006) these techniques are 558
still under development, have limitations in mountainous areas and require in-situ 559
stage-discharge data. Distributed hydrological models can incorporate high resolution 560
RS data without averaging over sub-catchments but have higher data and 561
computational requirements. Model results showed that RS data alone cannot 562
substitute for ground observations because of calibration needs and the limited 563
accuracy of RS data. 564
Considering the limitations imposed by the lack of ground observations and the 565
uncertainty of RS data, the assimilation of satellite altimetry of reservoir surface 566
elevations can reduce deviations between predicted and observed water levels. Even 567
25
though the mean accuracy of the altimetry data was 0.86 m, it was sufficient to 568
improve the performance of the model. Without such data, reservoir levels would 569
diverge over time from the “true” state of the system. More frequent and higher 570
precision altimetry data would improve the accuracy of the system’s states. 571
The ensemble Kalman filter is a reasonable method for incorporating satellite 572
altimetry data into the Mike Basin modeling package. An ensemble size of 50 resulted 573
in a good trade-off between model performance and computation time. A mean runoff 574
perturbation of 20 L km-1 s-1 and an irrigation area uncertainty of 40% provided the 575
model enough flexibility to assimilate altimetry measurements. 576
The hydrological system in the SDRB has been analyzed in the past: Raskin et al. 577
(1992) simulated water supply and demand in the basin, Antipova et al. (2002) 578
showed an optimization approach for the water and energy systems in the Naryn-Syr 579
Darya cascade of reservoirs and Cai et al. (2002) presented a framework for 580
sustainability analysis of the water resources in the SDRB. Although the studies have 581
identified benefits from cooperation among the riparian countries, they appear to have 582
had little impact on real-world decision-making. Both national agencies and donors 583
have expressed a desire for concrete tools to improve the water management in the 584
basin (Biddison, 2002), and the approach presented here is an important step in this 585
direction. 586
The combined use of remotely sensed data to drive hydrological models and satellite 587
altimetry data to update model states has considerable potential to provide impartial 588
information about the hydrological system. The application of this approach in a 589
(near) real time mode could help facilitate adaptive management of water resources in 590
the region. Additionally, the annual allocation process carried out by the national 591
26
authorities of the riparian states could benefit from a transparent, freely-available 592
information base. 593
Implementing this modeling approach in real time basis will require using the real 594
time precipitation product (3B42RT) instead of the research product (3B42). The RT 595
product does not incorporate gauge data, but becomes available ca. 6 hours after 596
observation (see Huffman et al., 2007; Huffman, 2008, 2009). The temperature data 597
are available 7 hours after observation, and reservoir release policies could be 598
simulated using trends in historical release data. Considering that the model timestep 599
is 1 full day, the model could be ready to run 7 hours after the end of every day (i.e. 600
0700 UTC). Near RT altimetry data is provided 3 days after observation [Philippa: we 601
need a reference here]. This means that the model could be re-run when 602
measurements of any of the reservoirs become available. 603
Future research work includes an assessment of the structural errors inherent in the 604
rainfall-runoff (RR) model, the error assumptions and their impact on the assimilation 605
scheme. The ensemble of models was generated by perturbing runoff and irrigation 606
forcing in the water allocation model (Mike Basin) instead of perturbing 607
meteorological input data in the RR model because the structural error of the RR 608
model is expected to be much larger than the error of the input data. Furthermore, the 609
model errors were assumed normally distributed and uncorrelated, even though the 610
residuals from the calibration-validation process are temporally correlated. 611
Other future areas of research include the implementation of a dual state-parameter 612
optimization approach (e.g. Moradkhani et al., 2005) in order to improve overall 613
model performance. The issue of averaging RS data over subcatchments could be 614
overcome by using satellite altimetry to estimate river discharge. The performance of 615
the hydrological model could also be improved through an improved representation of 616
27
snowmelt processes, as well as representation of glacial processes. Glacial processes 617
were not modeled due to lack of ground data. However, a representation of glacial 618
processes is particularly important, as long term trends and estimates of future 619
conditions indicate that glacial storage is being lost (Hagg et al., 2007; Niederer et al., 620
2008). Reduced glacial storage could have impacts on the annual runoff pattern in the 621
basin by concentrating runoff in the spring snowmelt season and reducing summer 622
runoff, much of which results from glacial melting. A long-term loss of glacial storage 623
could reduce the resilience of the water resources system because glacial melting 624
compensates for reduced snow melt runoff during hot, dry years. These issues are 625
important for water resources planning at inter-annual and decadal time scales. 626
Conclusions 627
Hydrological models driven by remotely sensed data alone may not be able to provide 628
reasonable simulations of large and complex river basins with scarce calibration data. 629
New remotely sensed data sources such as satellite radar altimetry measurements have 630
potential to improve simulation results by updating model states using data 631
assimilation techniques. 632
Radar altimetry provides the hydrological community with a periodical and impartial 633
source of data. The inclusion of such data into science-based decision support systems 634
has potential to induce cooperation in transboundary river management by providing a 635
basis for the development of operational modeling tools from a transparent and 636
readily-available information base. 637
638
639
28
Acknowledgements 640
The TMPA data were provided by the NASA/Goddard Space Flight Center's 641
Laboratory for Atmospheres and PPS, which develop and compute the TMPA as a 642
contribution to TRMM. The ECMWF temperature data was obtained through the 643
Danish Meteorological Institute; the authors would like to thank Thomas Lorenzen for 644
his support in providing this data. We thank the International Research School of 645
Water Resources (fiva) for supporting T. Siegfried's stay at the Technical University 646
of Denmark. 647
This work is part of the River & Lake Project (Performance Improvement and Data 648
Assimilation into Catchment Models for the Exploitation of River and Lake Products 649
from Altimetry, ESRIN Contract No. 21092/07/I-LG), work package 700. 650
651
652
29
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854 855
34
Figures 855 856
857
Figure 1. Base map of the Syr Darya River Basin (SDRB) 858
859
860
35
860
861
Figure 2: Structure of the rainfall-runoff model 862
863
36
863
Figure 4 Comparison of precipitation datasets: TRMM-3B42 versus RCHT. Monthly averages 864
865
866
37
866
Figure 5. ECMWF average monthly temperature TS versus RCHT at three locations (see Figure 867
1 for locations). 868
869
870
38
870
Figure 6. Rainfall-Runoff modeling results 871
872
873
874
39
874
Figure 8. Reservoir level simulation: data assimilation (black), without data assimilation (red), 875
and observed water levels (blue) for an ensemble size of 50, runoff perturbation of 20 L km-2 s-1 876
and irrigation area perturbation of 40%. The shaded area indicates the 2.5 and 97.5% quantile 877
range of the sample, and the crosses are altimetry measurements. For interpretation of the color 878
reference in this figure, the reader is referred to the electronic version of this article. 879
880
881
882
40
882
Figure 10. Impact of ensemble size, runoff perturbation and irrigation area perturbation. The 883
experiments are described on Table 3. A (), B ( ), C (), D ( ), E (), F ( ) and G (). 884
885
886
887
41
887
Figure 12. (A) Average absolute residuals of reservoir level after assimilation of altimetry data. 888
(B) Average (2000-2007) reservoir level residual in April, May, June and August when data 889
assimilation is interrupted in March, February, January and December (within the same 890
hydrological year). 891
892
893
42
Tables 893
894
Table 1 Parameters used in the rainfall-runoff model (NAM) 895
896
Parametera Description Units Value Umax Maximum water content in surface storage mm 1 CQOF Overland flow runoff coefficient - 0 CKIF Time constant for interflow hours 1e6 CK1,2 Time constants for routing overland flow hours 10 TOF Rootzone threshold value for overland flow - 0.999 TIF Rootzone threshold value for inter flow - 0.999 TG Rootzone threshold value for groundwater recharge - 0 a For a detailed description of these parameters and their interaction the reader is referred to DHI (2000). 897
898
43
898
Table 2. Snowmelt parameters used in the rainfall-runoff model (NAM) 899
900
Lapse rate [deg 100m-1]
Degree day coefficient (M) [mm deg-1 day-1]
wet dry J F M A M J J A S O N D -0.7 -0.5 1.0 1.0 2.2 3.7 5.0 6.0 6.0 6.0 1.0 1.0 1.0 1.0
901
902
44
902
Table 3 Ensemble Kalman Filter tuning parameters 903
Experiment Ensemble size
Runoff uncertainty
Irrigation area unc.
[L km-2 s-1] [%] A 5 5 0,05 B 5 20 0,4 C 50 5 0,05 D 50 5 0,4 E 50 20 0,05 F 50 15 0,2 G 50 20 0,4
904
905
45
905
Table 4 Source and spatio-temporal resolution of the various datasets used in the model 906
Data Type Data Source Resolution Space Time Remotely sensed Precipitation TMPA 3B42 0.25° 3 hrs Temperature ECMWF 0.5°-0.25° 6 hrs PET Func. of Temp 0.5°-0.25° 6 hrs Lake altimetry ERS/ENVISAT 76 targets 35 days DEM SRTM 1000x1000m - Observations Discharge RCHT 18 stations daily Reservoir release ICWC 5 reservoirs monthly Comparison data Precipitation RCHT 16 stations 10 days Temperature RCHT 5 stations 10 days Reservoir levels RCHT 4 reservoirs daily 907
908
909
46
909
Table 5. Altimetry targets over each reservoir. The altimetry error is reported here as the RMSE 910
between the timeseries after the mean of each has been removed. 911
Reservoir Satellite RMSE [m] Chardara ERS 0.63, 0.85 ENVISAT 0.37, 0.48 Toktogul ERS 0.68 ENVISAT 0.89 Charvak ERS 1.81 ENVISAT 1.42 Kayrakkum ERS 0.61
912
913
47
913
Table 6. Results of the rainfall-runoff model calibration. 914
Catchment Station ID
Wind orientationa
Lmax [mm]
CKBF [hr] R2 WBEb
[%] Mean runoff [L km-2 s-1]
Runoff error [L km-2 s-1]
2 16055 W 1600 1201 0.63 -3.3 8.86 5.5 47 16169 W 2090 2575 0.66 -2.6 9.59 3.4 55 16176 W 2280 1445 0.73 -1.7 11.67 5.7 61 16193 W 9220 947 0.7 -0.3 8.24 6.3
145 16198 L 86.8 1552 0.41 -26 10.97 14.2 62 16202 W 5980 984.4 0.62 12.4 11.24 9.5 64 16230 W 4740 664 0.73 -4.1 16.64 11
148 16279 L 23.4 1093 0.71 -27 14.85 12.7
Calibration
147 16290 L 31.7 1102 0.65 -33 19.9 21.1 8 16059 W 3510 1100 0.37 -5.3 9.83 8.05
12 16121 L 32 1100 0.55 6.8 8.5 11.6 14 16127 L 32 1100 0.27 -44 9.52 29.5 15 16134 L 32 1100 0.45 -4.1 9.04 15.3 16 16135 L 32 1100 0.28 -36 8.15 28.9 18 16136 L 32 1100 0.63 -20 8.62 9.9 9 16146 L 32 1100 0.32 -37 12.29 18.4
75 16205 W 3510 1100 0.33 8.3 13.52 8.1
Validation
49 16510 W 3510 1100 -1.7 -3.8 8.25 6.1 a W: winward; L: leeward. 915 b Water balance error 916
917
918
48
918
919
Table 8. Reservoir water level residuals with and without assimilation of radar altimetry data 920
Toktogul Chardara Kayrakkum Charvak Meana
mean(res) 2.72 0.99 -8.20 -6.19 4.5 DA std(res) 2.82 1.16 8.50 13.14 6.4 mean(res) -4.55 0.68 -15.38 -57.72 19.5 No
DA std(res) 14.61 2.59 10.01 39.78 16.7 a: Mean of absolute residuals across all reservoirs. 921