Alfred T. C. Chang Memorial Symposium NASA Goddard Space Flight Center Assimilating remotely sensed snow observations into a macroscale hydrologic model Konstantinos M. Andreadis1, Marketa McGuire2, and Dennis P. Lettenmaier1 1. Department of Civil and Environmental Engineering, Box 352700, University of Washington, Seattle, WA 98195 2. Golder Associates, Redmond WA Alfred T. C. Chang Memorial Symposium NASA Goddard Space Flight Center 5 3 Hydrologic Model MODIS SCE and AMSR-E SWE Assimilation Results ABSTRACT Accurate forecasting of snow properties is important for effective water resources management, especially in mountainous areas like the western United States. Current model-based approaches to hydrologic forecasting are hindered by model biases and input data uncertainties. Remote sensing offers an opportunity for observing snow properties, like areal extent and water equivalent, over larger areas. Data assimilation provides the framework for optimally merging information from remotely sensed observations and hydrologic model predictions. Direct insertion and an ensemble Kalman filter (enKF) were used to assimilate remotely sensed snow observations into the Variable Infiltration Capacity (VIC) macroscale hydrologic model over the Snake River basin. A preliminary assessment that utilized the MODIS snow covered extent (SCE) product, and the snow water equivalent (SWE) product from the Advanced Microwave Scanning Radiometer (AMSR-E, flown on board the NASA Aqua satellite) into the VIC model was conducted for the winter of 2004. The effect of assimilation of the SCE product on observed reservoir inflows, and (to a more limited extent) reservoir storage volume forecasts were evaluated. While assimilation of the MODIS SCE data resulted in some forecast improvements, especially for relatively short lead forecasts in spring, the results were less encouraging for the AMSR SWE product (for which comparisons were made with surface SWE observations from the SNOTEL station network rather than river discharge). The lack of improvement in model predictions appears to reflect biases in the AMSR-E SWE product that result from saturation of the SWE estimates for deep mountain snowpacks. Figure 2. VIC model schematic. VIC SWE VIC-enKF SWE MODIS SCE Figure 6. Snapshots of simulated SWE without assimilation (VIC), with assimilation of MODIS SCE data (VIC-enKF), and observed SCE (MODIS) for two dates in winter of 2001. The hydrologic model used in this study is the Variable Infiltration Capacity (VIC) model (Liang et al. 1994). Essentially the model solves a water and energy balance over a grid mesh. VIC accounts for subgrid variability in topography and land cover by representing each grid cell as a number of subgrid tiles of a certain land cover type and elevation zone (Figure 2). SCE is represented indirectly, by assuming that a tile is fully covered if any snow is present. Thus, SCE is just the area-weighted sum of all snow-covered tiles. Two additional experiments were conducted, to assess the performance of a more sophisticated data assimilation system in the prediction of SWE. The first one involved the assimilation of MODIS SCE data into VIC, using the enKF and a snow depletion curve (SDC) model as the observation operator H. The simulation period was 2000-2003, and the study area was the same as for the direct insertion experiment. The enKF successfully updated model-predicted SCE, and also updated SWE in a consistent fashion with the MODIS observations (Figure 6). Filter predicted SWE values were validated against surface observations from the SNOTEL station network (66 available stations). To account for scale differences between areal estimates and point measurements, SWE values from both SNOTEL and VIC were expressed as percentiles of their respective climatology (20 year dataset). The enKF improved the RMSE between VIC and SNOTEL at about half of the stations, but performed worse for the rest of the stations. An interesting feature, was that the overall performance of the enKF was better during snowmelt and worse during accumulation (Figure 7). This is happening because of simplifications in the assumptions about the error and SDC models, and the non continuity (0 to 1) of SCE, i.e. when both model-predicted and observation values show full coverage the assimilation has no effect, and some ensemble members produce erroneous SWE estimates. The second experimental option involved the assimilation of AMSR-E SWE data for the winter of 2004. A cut-off SWE value of 240 mm was used to Snowpack dynamics are modeled using a two-layer energy and mass balance model (Figure 3). The upper layer solves the energy balance between the snowpack and the atmosphere, while the lower layer acts as storage of excess snow and simulates deeper snowpacks. Other processes accounted for include snow densification and interception (Cherkauer and Lettenmaier, 2003). Figure 3. VIC snow model component. 1 Background Snow plays a key role in the hydrologic cycle over large areas of the mid latitudes, through its effects on water storage and surface albedo. In the western United States snowmelt accounts for about 75% of the annual runoff. Consequently, accurate estimation and monitoring of snow properties, such as snow coverage and water equivalent, have important implications for water resources management. Surface measurements are too sparse, in both time and space, for observation of snow properties over large areas. For this reason, large scale observation strategies rely heavily on remote sensing. Operational maps of both snow cover extent (SCE) and snow water equivalent (SWE) have been produced from various satellite instruments. SCE is usually mapped using visible wavelength sensors such as the AVHRR, while SWE can be observed from the passive microwave brightness temperature of the snowpack. However, both types of sensors have limitations; visible wavelength sensors require cloud-free conditions and also lack any information about snow water storage. On the other hand, retrieval of snow parameters from passive microwave sensors is hindered by snow metamorphism, and presence of wet snow, among others. Additional information about snow properties can be obtained from land surface hydrology models that are forced with meteorologic variables, and represent the effects of topography and land cover on snow accumulation/ablation. Nonetheless, this information is imperfect because of uncertainties in forcing data, and model biases. Ideally, a system that optimally combines snow information from both remote sensing and modeling predictions and at the same time accounts for the limitations of each should provide estimates that are superior to those derived from either models or remote sensing alone. This method is commonly known as data assimilation. Figure 7. Time series of the spatial average of the SWE percentile differences between VIC/enKF simulations and SNOTEL station data. 4 MODIS SCE Direct Insertion Results Retrospective streamflow forecasts were produced from the VIC model in the Snake River basin, utilizing MODIS SCE imagery to update model snow cover. The updating occurred for all days (prior to the forecast data) when MODIS images were available and the cloud cover fraction was less than 50%. Direct insertion was used as the updating procedure for SCE, while an arbitrary addition of 5 mm of SWE was necessary for the cases of VIC-MODIS disagreements. In addition to the retrospective analysis, near-real time forecasts were produced for four dates in winter 2004, using MODIS SCE updating. account for the snowpack saturation effect on its microwave emission. A normally distributed error with zero mean and 20% standard deviation was assumed for this study. The same procedure with the MODIS assimilation was used for validation of the simulated SWE values. The assimilation actually improved the percentile RMSE for 32 (out of 66 available) SNOTEL stations. although the average RMSEs for both simulations were comparable. Further insight can be obtained by looking at the time series at a specific station (Figure 8). The RMSEs were 0.145 and 0.236 for VIC and the enKF respectively. We can see in the figure, that AMSR-E SWE estimates have a large error when compared to SNOTEL. In addition, simplifications about the observation error, hinder the enKF performance at a large extent. An interesting aspect of the impact of assimilating the AMSR-E SWE data can be seen in Figure 9, which shows the percentile RMSE between the two simulations and SNOTEL as a function of the peak station SWE. While the enKF shows a slight improvement for shallow snowpacks, it produces a higher RMSE for deeper snowpacks. AMSR-E tends to underestimate SWE for these, and when the predicted value is larger than 240 mm (that is, no updates are happening), SWE is simulated based on model physics only and the “initial” value at the last update. Nonetheless, this has been a preliminary assessment of the value of AMSR-E assimilation, and we believe that further research, with a focus on better modeling of the AMSR-E errors, is required. Figure 4. Mean absolute error of streamflow forecasts, averaged over 2000-2003. Open symbols are for 2004 near real-time two-week forecasts. In general, inclusion of the MODIS data resulted in forecast error reduction (or no change in forecasts) in 63% of the seasonal forecasts (71% of the two-week forecasts), while mean absolute error increased in only 37% of the seasonal forecasts (29% of the two-week forecasts). .Figure 4 shows the mean absolute error of two-week lead-time streamflow forecasts, averaged over 2000-2003, and the respective real-time values, using unadjusted and MODIS adjusted initial conditions. Forecasts of runoff volume from the forecast date through July, indicate smaller improvements in streamflow prediction using MODIS for seasonal forecasts, than the two-week forecasts. 2 Data Assimilation Techniques There are several data assimilation techniques, from simple (e.g. direct insertion) to more complex (e.g. variational methods). Direct insertion, which requires that the state variable is directly observable, basically consists of substituting the model-predicted value of the state variable with the value that was observed at that time. The implication is the assumption of “perfect” observations, that is they do not contain any errors. A more sophisticated technique involves the use of the Kalman filter (KF), which (in its simplest form) solves the optimal estimation problem. The KF accounts for errors in both model and observations, by explicitly propagating the model error covariance information in time (Gelb, 1974). This proves to be very expensive computationally for large-scale applications. Evensen (1994) developed a Monte Carlo approach to the KF, the ensemble Kalman filter (enKF). This avoids the propagation of the error information, by implicitly calculating the required error covariances from an ensemble of model states (Figure 1). The algorithm starts with the propagation of each model ensemble member to the timestep that an observation becomes available (forecast step). The ensemble is generated at each timestep by treating model parameters as a stochastic variables (e.g. forcing data). At the observation time (analysis step), the calculated error covariance matrix is used to compute the Kalman gain, that weighs the magnitude of the effect of the observations, and the model-predicted state is updated to . H is the observation operator, which relates the state variables to the observations. This allows for assimilation of indirectly observed variables, e.g. assimilation of SCE to update model-predicted SWE. Each ensemble member i is updated separately and the filter estimate is usually taken as the mean of the ensemble values. Figure 5. Mean absolute error of streamflow forecasts volume from forecast date through July, averaged over 2000-2003, using unadjusted and MODIS adjusted initial conditions. Figure 5 shows the mean absolute errors of streamflow forecast volume. Performance improvements were more apparent in forecasts produced for May. Accumulation of snow after the forecast date could be the cause of poor results in the early season forecasts. In general, MODIS updated initial conditions appear to have a greater impact on shorter lead time forecasts at forecast dates within the snow ablation period. Finally, regarding reservoir storage, for reservoirs where the reservoir model performed well in retrospective simulations, storage forecast errors were reduced (or unchanged) in 74% of the seasonal forecasts as a result of MODIS updates. At each timestep Forecast Step : If an observation is available Analysis Step : Forecast Step Analysis Step Forecast Step Figure 8. SWE percentile time series for Jackson Peak station (2121 m elevation). Figure 9. VIC and enKF SWE percentile RMSE as a function of peak SNOTEL SWE for the winter of 2004. REFERENCES Cherkauer, K.A., and D.P. Lettenmaier, Simulation of spatial variability in snow and frozen soil, J. Geophys. Res., 108 (D22), 8858, doi:10.1029/2003JD003575, 2003. Evensen, G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99 (C5), 10 143-10162, 1994. Gelb, A., Ed., Applied optimal estimation. The MIT Press, 1974. Liang, X., Lettenmaier, D.P., E.F. Wood, and S.J. Burges,. “A simple hydrologically based model of land surface water and energy fluxes for general circulation models.” J. Geophys. Res., 99(D7), 14,415-14,428, 1994. McGuire M., and D.P. Lettenmaier, Use of satellite data for streamflow and reservoir storage forecasts in the Snake River Basin, ID, ASCE Journal of Water Res. Management (in review), 2004. Time Figure 1. Schematic representation of the ensemble Kalman filter.