1

Real-time remote sensing driven river basin modeling using radar 1

altimetry 2

3

Silvio J. Pereira Cardenal1, Niels D. Riegels1, Philippa A.M. Berry2, Richard G. 4

Smith2, Andrey Yakovlev3, Tobias U. Siegfried4, Peter Bauer-Gottwein1* 5

6

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

14

To be submitted to the Journal of Hydrology 15

16

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

2

(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

41

Keywords 42

Data assimilation, Radar altimetry, River basin modeling, Syr Darya, Ensemble 43

Kalman Filter 44

45

46

3

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

4

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

5

(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

6

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

7

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

8

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

9

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

10

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

11

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

12

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

13

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

15

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

16

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

17

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

18

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

19

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