Assimilation of radar altimetry to a routing model of the Brahmaputra River



[1] While satellite-based remote sensing has provided hydrologists with valuable new data sets, integration of such data sets in operational modeling systems is usually not straightforward due to spatial or temporal resolution issues or because remote sensing does not directly measure the hydrological quantities of interest. This is the case for satellite-based radar altimetry. River-level variations can be tracked using radar altimetry at a temporal resolution between 10 and 35 days, depending on the satellite, but hydrologists are typically interested in river flows rather than levels and require predictions at daily or even subdaily temporal resolutions. One way to exploit satellite radar altimetry is therefore to combine the data with hydrological models in a data assimilation framework. In this study, radar altimetry data from six ENVISAT virtual stations were assimilated to a routing model of the main reach of the Brahmaputra River driven by the outputs of a calibrated rainfall runoff model. The extended Kalman filter was used to update the routed water volumes for the years 2008–2010. Model performance was improved with the Nash-Sutcliffe model efficiency for daily discharge increasing from 0.78 to 0.84. The method uses very little in situ data and is easily implemented as an add-on to hydrological models, and it therefore has the potential for large-scale application to improve hydrological predictions in many river basins.

1. Introduction

[2] Global monitoring of the hydrological cycle has greatly improved with the vast amount of data made available by satellite-based remote sensing. For surface water monitoring in particular, radar altimetry has proven to be a valuable tool. While originally designed for ocean monitoring, satellite-based radar altimetry data has been shown to successfully track inland water levels over lakes [e.g., Morris and Gill, 1994; Birkett, 1995], wetlands [e.g., Birkett, 1998], and rivers [e.g., Koblinsky et al., 1993; Birkett, 1998; Campos et al., 2001; Frappart et al., 2006]. For river basins that are poorly monitored or where access to in situ data is restricted or subject to delays in transmission, the ability to monitor river levels from satellites is extremely valuable due to its global coverage and the fact that the data can potentially be obtained in near real time.

[3] However, the direct use of radar altimetry data over rivers by hydrologists and water managers is hindered by the fact that discharge rather than water level is typically the variable of interest and by the low spatial (80 km interorbit spacing at the equator for ENVISAT) and temporal resolution (between 10 and 35 days return period) of the altimetry data set. In order to overcome these limitations, many studies have focused on combining radar altimetry with in situ data or models.

[4] To obtain discharge from levels, one approach is to use in situ measured discharge and altimetry measured river levels at a nearby satellite crossing of the river network (called virtual station) to derive rating curves [e.g., Kouraev et al., 2004; Zakharova et al., 2006; Papa et al., 2010]. While good results are obtained using this method, it only allows for the computation of flow values from the data of virtual stations located near in situ gauges where the time coverage of the in situ and altimetric data sets overlap. In order to obtain discharge values at virtual stations not located near in situ gauges, Bjerklie et al. [2003] proposed a method to develop rating curves based on the measurement of hydraulic data from satellite platforms. Getirana et al. [2009] and Getirana and Peters-Lidard [2013] developed rating curves based on altimetric level measurements and modeled discharge from a hydrological model and a routing scheme, respectively, in order to estimate river discharge.

[5] These methods allow for discharge values to be obtained at the time and location of the satellite passes. In order to obtain measurements with a higher temporal resolution than the satellite revisit time, Roux et al. [2008] developed a method to obtain daily time series from altimetry by exploiting neighboring in situ gauging stations, thereby densifying an existing level gauging network. To improve water level predictions at locations other than the satellite pass at different lead times, Biancamaria et al. [2011b] successfully used linear regressions between upstream radar altimetry data over the Brahmaputra and Ganges and downstream gauged levels.

[6] Exploiting the altimetry data in calibration and assimilation frameworks is another option to overcome the limitations of the low temporal resolution. Getirana [2010] showed that radar altimetry from the ENVISAT satellite (35 days repeat cycle) could be used for automatic calibration of a hydrological model of the Branco river basin and found similar results to using in situ discharge data, provided knowledge of the rating curve at the virtual stations' locations. The assimilation of daily in situ flows or water levels to routing models have successfully been implemented [e.g., Refsgaard, 1997; Madsen and Skotner, 2005]. In terms of remotely sensed river levels, Neal et al. [2009] showed that hydrodynamic model predictions could be improved through the assimilation of water levels derived from combining synthetic aperture radar imagery and high-resolution digital elevation models (DEMs). Andreadis et al. [2007] and Biancamaria et al. [2011a] showed that assimilating virtual wide swath altimeter data to hydrodynamic models with known bathymetry could improve modeled river depth and discharge.

[7] The objective of this study is the development of a strategy for the assimilation of radar altimetry in order to improve modeled discharge in a large river basin, where neither rating curves nor ground river bathymetry at the locations of the altimetric measurements are known. The extended Kalman filter (EKF) is used to update the states of a storage routing model of the Brahmaputra River using altimetric level data from six ENVISAT virtual stations located along approximately 700 km of the main river reach for the years 2008–2010.

[8] The Brahmaputra River is located in South Asia and drains a basin of over 580,000 km2. It flows along 2880 km from its source north of the Himalayas in Tibet, first east to the Chinese/Indian border before changing course and flowing west to the Indian/Bangladeshi border from which it turns south before merging with the Ganges and flowing into the Bay of Bengal (Figure 1). The area is subject to flooding and the availability of reliable flow predictions is therefore of utmost importance.

Figure 1.

Base map with location of the subbasin outlets (red numbers) and Envisat virtual stations (black numbers).

[9] Finsen et al. [2013] used synthetic rating curves to obtain discharge from altimetry over the Brahmaputra River basin. A constant gain factor was then used to update the state of a routing model at the time and location of altimetric measurement and updates were carried over to the next time steps using a constant discount factor. The current study furthers the work undertaken by Finsen et al. by using the covariances of the state estimates and measurements at each time step to determine the innovations.

2. Materials and Methods

2.1. Radar Altimetry

[10] The river lake hydrology (RLH) data product from the ENVISAT satellite was used in this study (see Berry et al. [2005] for details on the retrieval algorithms). The data are accessible on the European Space Agency River and Lake Project homepage (

[11] There are six ENVISAT altimetry virtual stations on the main Brahmaputra River (numbered 4–10 in Figure 1, stations 1–3 not being located on the main reach), which were all used for assimilation in this study. Though there is very little available in situ data which overlaps with the altimetric measurements from ENVISAT for validation of the data, the virtual stations show good agreement among themselves and the quality of the altimetric data is expected to be very high and root-mean-square errors relative to in situ expected to be of the order of 20–40 cm based on previous studies over large rivers (e.g., Papa et al. [2010] over the Brahmaputra; Frappart et al. [2006] over the Amazon). Figure 2 shows the good agreement in water level anomalies that can be seen over the few overlapping data points between Bahadurabad gauging station and virtual station number 4, which is located approximately 70 km upstream (see Figure 1).

Figure 2.

Water level variations at virtual station 4 and Bahadurabad gauging station. The mean of the difference on coincident measurement days was used to shift the in situ time series.

2.2. Modeling

[12] The river model used in this study was a Muskingum routing scheme driven by the outputs of a calibrated Budyko type rainfall runoff (RR) model of the Brahmaputra River basin.

[13] For the RR model, the basin was split into 19 subbasins and the outlets were chosen to correspond to the locations of available in situ and altimetric stations (Figure 1). Catchment delineation and drainage network were derived from a digital elevation model (DEM from the shuttle radar topography mission (SRTM) version 4). The model consists of three components: Snow storage, rainfall-runoff, and river routing.

[14] Snow storage and melt were modeled using a simple temperature index method [Hock, 2003]. The snowmelt and direct precipitation were then used to drive the RR model which was set up using a Budyko approach [Zhang et al., 2008] and river routing was carried out using the Muskingum method [e.g., Chow et al., 1988]. The model was calibrated using in situ flows at three gauging stations located at the outlets of subbasins 3, 5, and 17. Calibration parameters were assumed constant within two sections based on geography and on availability of in situ data: the upstream portion of the river located north of the main Himalayan chain (reaches 1–6) and the downstream portion located south of the main Himalayan chain (reaches 7–19). A more detailed description of the RR model used can be found in Finsen et al. [2013]. The outputs of the RR component of the model were then used to drive the routing model in the assimilation scheme.

[15] The routing model for the assimilation was formulated in terms of reach storage in order to simplify the relation between the propagated state (storage) and the measurements to be assimilated (water level) in the absence of in situ rating curves. Starting from the equations presented in Chow et al. [1988, pp. 257–258], the storage of the Nth reach at time step j + 1 can be expressed as a function of the previous reach storages and the forcing from the rainfall runoff model:

display math(1)


display math(2)

and C1N and C3N are defined as in Chow et al. [1988]

display math(3)
display math(4)

where reach number 1 is the furthest upstream and reach N is the furthest downstream, math formula is the storage in reach N at time step j (m3), and math formula is the rainfall-runoff model generated inflow to reach N at time step j (m3/s). XN, a weighing factor and KN, the travel time of the flood wave through the reach (days), are assumed constant for each reach N and Δt is the model time step (days) [e.g., Chow et al., 1988, p. 258].

[16] The X values were obtained from the calibration process of the RR model described previously and the K parameter was obtained through the calibration of channel flow velocity and the application of the Muskingum-Cunge method [e.g., Chow et al., 1988, p. 302].

[17] While equation (1) expresses the state transition for the case where all reaches considered are located on the main river stretch as is the case in this study (Figure 1), the contribution of tributaries can easily be implemented to the scheme because of the linearity of the propagation equations: the contributions from different tributaries to the storage of a downstream reach can be routed separately before being summed.

2.3. Measurement Operator

[18] Because radar altimetry does not measure reach storage but water level, a measurement operator expressing the measurement as a function of the state variable was defined.

[19] In the absence of in situ cross-section data, reaches were assumed to have trapezoidal cross sections which are constant along the length of each reach. The dimensions of the trapezoidal cross sections were determined using satellite imagery: river widths and water levels were obtained at low and high flows to determine bank slope and bottom width assumed equal to low-flow width. Reach storage was then expressed as the product of the cross-sectional area by the length of the reach:

display math(5)

where s is the water stored in the reach (m3), d is the water depth (m), w is the width of the river bed (m), L is the reach length (m), and αb is the bank slope (rad).

[20] Solving equation (3) for depth and keeping the positive solution yields:

display math(6)

[21] However, radar altimetry measures water elevation rather than river depth and in the absence of a known river bed elevation or coincident in situ depth measurements, a common reference was set as follows.

[22] The routing model was run and storages converted to depths using equation (6). Measured altimetry elevations were then converted to depths by adding an offset equal to the mean difference between coincident modeled depths and altimetry heights over the calibration period (2005–2007).

display math(7)

where dalti is the depth value from altimetry (m), alti is the altimetric height measurement (m), t are the altimetry measurement acquisition dates, and nt is the number of altimetric measurements. The measurement operator h is then defined as

display math(8)

2.4. Data Assimilation Procedure—The Extended Kalman Filter (EKF)

[23] The Kalman filter is a widely used linear sequential data assimilation technique in which forecasted states are updated as new measurements are acquired taking into account the relative uncertainties of the forecasted state and of the measurement. The basic equations for the propagation of the model state and its covariance matrix in the Kalman filter at the (k + 1)th time step are [see e.g., Jazwinski, 1970]:

display math(9)
display math(10)

where s is the state vector, u is the forcing, w is a sequence of white Gaussian noise with covariance Q, F is the state transition matrix, G is the control input matrix, Г is the noise input matrix, and P is the state covariance matrix. The superscript f indicates a forecasted state or covariance.

[24] Equations (9) and (10) are used to propagate the state and its covariance until a time step m when an observation is acquired. The state and covariance at time step m are then updated with the new measurement using the following:

display math(11)
display math(12)

[25] The a exponent indicates the analysis or updated state, and H is the measurement operator defined as

display math(13)

where y is the measurement, st is the state, and v is a sequence of white Gaussian noise with covariance Rm representing measurement and measurement operator error. The difference math formula is the innovation or measurement residual.

[26] For cases where the model or measurement operators are nonlinear, the extended Kalman filter (EKF) in which the nonlinear model or measurement operators are replaced by their first-order Taylor approximations can be used. The linearized operators are then directly applied in equations (9)-(13).

[27] In the present study, the model operator is linear (see section 3.2) but the measurement operator, h is nonlinear (see section 3.3). The linearized measurement operator H is therefore defined as

display math(14)

where the sf is the forecasted reach storage from equation (9) and all other terms are as defined in section 3.3.

2.5. Error Modeling

[28] Model error stems from many different sources such as, for example uncertain inputs, in particular precipitation forcing for hydrological models, uncertain calibration data sets, uncertain model parameters, or model structure. It is, however, usually not possible to distinguish between these different error sources and simplifications in the error representation need to be made. In this study, the forcing from the RR model was assumed to be the dominant source of model error. As the magnitude of the error on RR model outputs is typically proportional to the magnitude of the modeled flow, the expected error was implemented as a multiplicative error term applied to the forcing.

[29] No measurements of the runoff produced within the different catchments are available in order to determine the magnitude of the forcing error. The normalized model residuals at the Bahadurabad gauging station were therefore used in order to obtain an estimate of the total forcing error. The error was then assumed to stem from all subbasins in equal proportions.

display math(15)

where wk is the normalized residual (-), Qinsituk is the in situ measured flow at Bahadurabad at time step k, and Qmodelk is the modeled flow at Bahadurabad at time step k. Two time steps are included in the error estimation because the forcing term in equation (1) appears as the sum of the runoff from the previous and current time steps.

[30] Analysis of the residuals showed a high temporal correlation, which was taken into account in order for the filter to perform well. The autocorrelation of errors was assumed to be represented by a first-order autoregressive (AR1) model:

display math(16)

where a is the AR1 parameter and ɛ is a sequence of white Gaussian noise with covariance Q′. The a parameter was determined using the Burg method [Kay, 1988]. The Kalman filter equations can be applied by augmenting the state vector with the correlated noise term by setting [e.g., Jazwinski, 1970]

display math

where all matrices and vectors are as defined in section 3.4 and I is the identity matrix. Equation (9) can then be rewritten as

display math(17)

and the equations from section 3.4 can be applied replacing s, F, G, and Г by S, F′, G′, and Г′.

[31] The RR forcing error is also expected to be spatially correlated due to correlated meteorological inputs and model structure among other factors and the error correlation was assumed equal to that of the forcing itself. The correlation matrix of the RR forcing was therefore computed and, assuming homoscedasticity, Q from equation (16) set as

display math(18)

where C is the spatial correlation of the RR forcing and σ(ɛ)2 is the variance of the white noise input to the AR1 model.

[32] Finally, the measurement error covariance was determined. Measurement errors were assumed uncorrelated in space and time. As for the other error terms, no data were available to determine the magnitude of the error. Previous studies have documented errors between approximately 20 and 80 cm for altimetry levels from ENVISAT over various rivers [see e.g., Frappart et al., 2006; Birkinshaw et al., 2010; Papa et al., 2010; Michailovsky et al., 2012]. The value of 70 cm was chosen initially in this study because of the added uncertainty from the measurement operator and will be discussed in the results.

2.6. Evaluation Criteria

[33] The criteria by which the performance of the model with assimilation versus the run without assimilation was assessed were chosen to represent the fit as well as the reliability and sharpness of the model.

[34] The following measures were used: Nash-Sutcliffe efficiency (NSE), root-mean-square error (RMSE), reliability (or coverage, i.e., the percentage of observations that fall within the predicted nominal confidence interval), sharpness (i.e., the width of the confidence bounds), and Interval Skill Score (ISS) which is defined as follows [Gneiting and Raftery, 2007]:

display math(19)

where i are the time steps and

display math(20)

where u and l are the upper and lower confidence bounds for the estimate, x is the observed value, and α is the significance level. The interval skill score takes into account both sharpness and reliability by rewarding narrow confidence intervals and penalizing observations located outside of the nominal confidence intervals. This allows for models to be compared in the case where a tradeoff needs to be made between sharpness and reliability, with the better model having the lower ISS value. In this study, the significance level α was chosen to be of 0.05.

2.7. Data

2.7.1. Meteorological Forcing Data

[35] Precipitation from the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT real-time product was used to drive the RR model [Huffman et al., 2007]. This data set is available from October 2008 onward. To complete the forcing time series, the TRMM 3B42 and 3B42RT products were compared over the years 2008–2011. The 3B42RT rates were found to be approximately 25% higher than the 3B42 rates over the Brahmaputra River Basin. Data from the 3B42 product from 2000 to September 2008 were therefore multiplied by 1.25 to obtain the precipitation forcing for pre-October 2008 and the 3B42RT product was used for post-October 2008 period.

[36] The temperature data used was from the European Centre for Medium range Weather Forecast (ECMWF) Operational Surface Analysis Data Set [Molteni et al., 1996].

2.7.2. Reach Data

[37] Reach length, river bed width, and bank slope were determined from remote sensing imagery.

[38] Reach length was measured from the Digital Elevation Model (DEM) derived drainage network. The DEM used in this study was from the Shuttle Radar Topography Mission (SRTM) and was resampled to 30 arc sec.

[39] At all virtual stations considered, the Brahmaputra River is braided. The river was however represented by an equivalent single river channel (see section 3.3). The width and bank slope of this equivalent river channel were determined by measuring low and high-flow widths from Landsat imagery. The Landsat scenes used were from the years 2003–2005 and the difference between low and high-flow widths were found to be between 2.50 and 7.37 km at the different locations. The mean exceedance probability on the flow duration curve corresponding to the measured low-flow widths was of 83% and of 16% for the high-flow widths.

[40] High and low altimetry values (alti, in meters) were then taken from the same location and bank slope was determined using the assumption of a trapezoidal cross section as

display math(21)

[41] River bed width was approximated as equal to low-flow width.

2.7.3. In Situ Data

[42] Daily in situ discharge data are publicly available at only three locations in the basin: at Nuxia and Nugesha in Tibet and at Bahadurabad in Bangladesh (Figure 1). Recent data for these stations are only available for the flooding season (approximately June–October).

[43] A more complete historical data set which covers the period between 1956 and 2000 is available at the Bahadurabad station and flow during the dry months, between December and April, shows very low inter annual variation. Daily historical mean values were therefore computed for 100 days of the low-flow period starting on the 1st of December and this historically averaged data set was used in order to evaluate the performance of the model in low-flow periods.

[44] The historical data at Bahadurabad was downloaded from and the recent data is published at: Data at Bahadurabad for the years 1995–2003 was obtained from the Institute of Water Modeling in Dhaka, Bangladesh. For the Nuxia and Nugesha stations, the data are available at

[45] The calibration of the RR model was carried out using this data over the years 2005–2007. Evaluation of the assimilation performance was only carried out at Bahadurabad as the available altimetry stations were all located downstream of Nuxia and Nugesha. Because of the absence of current low-flow data at Bahadurabad, the model evaluation criteria for the assimilation of altimetry will be presented both for high-flow periods only and for the entire in situ time series including the historically averaged low flows.

3. Results

3.1. Assimilation Results

[46] The routing model of the Brahmaputra was run without assimilation and analysis of the residuals at Bahadurabad over the calibration period (2005–2007) yielded the following parameters for the AR1 error model:

display math

[47] Using these parameters, the confidence intervals for the run without assimilation slightly exceeded the 95% nominal coverage for the high-flow period during the calibration period (Table 1).

Table 1. Assimilation Results
 Validation PeriodCalibration Period (Base Run)
Base RunAssimilation Run% Change
Coverage (%)All91.9676.30 93.15
High flows85.1467.14 96.07
High flows0.1160.375  
RMSE (m3/s)All10,0458510−15.3 
High flows14,07011,827−15.9 
Sharpness (m3/s)All22,72514,129−37.8 
ISS (m3/s)All42·× 10355·× 10329.6 
High flows79·× 10310·× 10427.0 

[48] Water levels from the six available ENVISAT virtual stations were assimilated to the routing model of the Brahmaputra using the EKF and model results with and without assimilation compared to in situ flows at Bahadurabad over the 3 years of the validation period (2008–2010).

[49] Assimilation results for the run using the error parameters obtained above are presented in Table 1 and Figure 3. Model fit was found to improve through assimilation of the altimetry data, with the Nash-Sutcliffe efficiency coefficient going up from 0.78 to 0.84 for discharge over the years 2008–2010. Considering model performance over the flooding season only, the improvement in NSE with assimilation is starker with the value going from 0.12 to 0.38.

Figure 3.

Base and assimilation runs with 95% confidence intervals.

[50] However, while the confidence intervals were found to be over 35% narrower for the assimilation run (Table 1), this resulted in a large loss in reliability: approximately 15% fewer of the flow observations fell within the confidence bounds compared to the baseline leading to the run without assimilation having a better interval skill score meaning that the loss of coverage was not compensated by the gains in sharpness.

3.2. Modification of the AR1 Coefficient

[51] The large loss of reliability even as the RMSE improved highlights issues in the representation of errors. The AR1 parameter for instance was determined based on the residuals of the discharge at the outlet of subbasin 17. This parameter may therefore have been overestimated as smoothing during routing as well as the integration of the runoff from all upstream subbasins may have increased the autocorrelation of the observed errors. Further analysis showed that runoff autocorrelation in the model was found to be on average 28% lower than river discharge autocorrelation at the outlet of subbasin 17.

[52] The AR1 coefficient was therefore lowered by 28% (from 0.9652 to 0.6921) and the proportional error variance coefficient adjusted by trial and error in order for the nominal coverage for high flows in the calibration period to match that from the baseline run (σ(ɛ) = 0.368). The results are presented in Table 2 and show similar values to the baseline assimilation run in terms of RMSE improvement. The coverage for the assimilation run, while lower than that of the run without assimilation, was however greatly improved with approximately 10% more observations falling within the nominal confidence bounds. This increase in reliability led to an improvement of the interval skill score for the assimilation run with the lower AR1 parameter.

Table 2. Assimilation Results With AR1 Coefficient of 0.6952
 Validation PeriodCalibration Period (Base Run)
Base RunAssimilation Run% Change
Coverage (%)All91.5485.90 93.81
High flows83.7177.14 96.07
High flows0.1160.390  
RMSE (m3/s)All10,0458396−16.4 
High flows14,07011,691−16.9 
Sharpness (m3/s)All21,79317,117−21.5 
ISS (m3/s)All43 × 10342 × 103−4.0 
High flows81 × 10377 × 103−4.8 

[53] The loss of coverage in the assimilation run for the baseline case could also be due to an underestimation of the measurement error that was assumed to have a standard error of 0.7 m. However, inspection of the innovations indicated this was not the case. Innovations were found to match their predicted statistics well with 4% of innovations falling outside of the 95% confidence bounds as predicted by the filter equations (Figure 4).

Figure 4.

Innovations and their predicted 95% confidence intervals for the baseline run.

3.3. Temporal Coverage and Persistence of Assimilation Benefits

[54] While the repeat period of the ENVISAT satellite is of 35 days, the six altimetry stations used allowed for a satellite pass to occur over one of the stations every 3–9 days. The maximum time lag observed between two consecutive altimetry measurements can however be longer if the altimeter loses lock and the maximum delay observed over the validation period was of 15 days. The results presented so far include the entire simulation period, encompassing days coinciding with an altimetry measurement as well as days up to 15 days from the day of assimilation.

[55] Figure 5 shows that the improvement due to assimilation was consistently seen until the 6th day from an altimetry measurement, with the first 4 days after the assimilation showing very good results and the improvements steadily decreasing from days 4 to 7. For our case study, 66% of the simulation days fell within 4 days of an altimetric measurement and 87% within 6 days. The results for RMSE improvement are consistent with what would be expected considering a mean flow velocity of the order of 1 m/s for the Brahmaputra [Jian et al., 2009; Finsen et al., 2013], which would make the travel time between the most upstream virtual station and Bahadurabad of 8.5 days and between the most downstream virtual station and Bahadurabad of 0.8 days.

Figure 5.

RMSE improvement as a function of time from the latest altimetry measurement

4. Discussion

[56] In this study, six ENVISAT virtual stations located along approximately 700 km of the Brahmaputra River were used in a data assimilation scheme. Assimilating data from multiple stations allowed for a measurement to be acquired in the system with a minimum interval of 3 days and a maximum interval of 9 days rather than at the 35 day ENVISAT repeat period. Overall, the model fit was improved with the NSE increasing from 0.78 to 0.84 in the baseline assimilation case with the highest RMSE improvements (over 15%) observed in the first 4 days after an altimetry measurement. This indicates that further improvements could potentially be obtained with either a higher number of virtual stations or a higher measurement frequency as these results showed that the low temporal resolution could be compensated by denser spatial coverage.

[57] The approach presented here of using external separate routing model for assimilation and updating only reach storage has the advantage of being simple and easy to implement as an add-on to any type of RR model and at potentially very large or global scales. The model fit could however potentially be further improved through the updating of states in the RR model such as, for example, aquifer or soil storages, which have long response times and would therefore allow for the innovations to have a longer lasting influence on the model output.

[58] As the EKF uses the full covariance matrix between states to perform updates, the covariances of the modeled flow estimates were also obtained through the scheme. However, the sharpness and reliability of the confidence bounds were found to be highly sensitive to the representation of model errors. While this was tested with regard to the value of the AR1 parameter, other assumptions in the error model should also be investigated, for instance the assumption of homoscedasticity and independence of the residuals of the AR1 model. Remaining heteroscedasticity as well as bias introduced by the use of an error model based on relative errors could in particular account for the lower reliability observed during peak flows.

[59] This is a drawback of the method as there are many different ways to specify errors and typically little data available in order to base error specification on actual observations. Additionally, an error model found to work well in one area will not necessarily be transferable due to different RR models, quality of calibration, or forcing data. This is a common issue in Kalman filtering and one approach could be to use adaptive filtering, where the model error covariance is treated as a parameter to be estimated [e.g., Kitanidis and Bras, 1980; Van Geer et al., 1991].

[60] The use of altimetric data in models typically requires either available rating curves or detailed bathymetric data, and one of the major advantages of the approach presented in this paper is that neither of these was used with channel cross sections being approximated using remote sensing data only. In situ flow data was however needed for the calibration of the RR model, which may still be a limitation in some areas, but this could be avoided by using the altimetry data for calibration as shown by Getirana et al. [2013], who successfully calibrated a flow routing scheme using only radar altimetry over the Amazon. The assimilation of altimetric data was shown to improve model performance in spite of the very simple trapezoidal cross-section assumption made and the determination of the cross-section parameters using remote sensing data only. While such a simple model may fail in complex river environments, it is expected to be widely applicable where in situ rating curves are not available. This assumption is supported by the good results obtained in our study area despite the river being braided. Moreover, if more in situ data were available at a specific location, for instance detailed river cross section data, the performance could be further improved by integrating this data into the scheme. For cases where rating curves are available, the scheme could also be modified to route flow rather than storages in order to make use of all available information.

5. Conclusion

[61] In this article, the storages of a routing model driven by the output of a calibrated rainfall runoff model were updated using radar altimetry data from the ENVISAT mission. The assimilation led to improved modeled discharge at the Bahadurabad gauging station where in situ flow data was available. The study has shown the potential for the use of altimetric data in combination with hydrological models for flow modeling in rivers where little in situ data is available as the only in situ data used in the study was calibration data for the rainfall runoff model. This is of great interest in particular for large sparsely monitored remote basins where data is only available with long delays as altimetry data can potentially be available in near real time. Additionally, the simple routing model as an add-on to a rainfall runoff module makes the method easy to implement on a large and potentially global scale.


[62] The authors thank Danida, Danish Ministry of Foreign Affairs for funding the research presented in this paper (project number 09-043DTU).