Kostas M. Andreadis1, Dennis P. Lettenmaier1 Assimilating MODIS Snow Areal Extent Data Using an Ensemble Kalman Filter Kostas M. Andreadis1, Dennis P. Lettenmaier1 1UW Land Surface Hydrology Research Group Civil and Environmental Engineering, University of Washington

Introduction Importance of snow to hydrologic cycle has long been recognized Prediction of snow properties from hydrologic models and observations (in situ or remotely sensed) Both of these sources present shortcomings Data assimilation is the framework that allows the optimal combination of different information sources

Ensemble Kalman Filter (EnKF) System model : state vector : hydrologic model : observations Forecast Step Initial estimates for Analysis Step

Variable Infiltration Capacity model Macroscale hydrologic model Subgrid variability (topography, vegetation and soil moisture) Water and energy balance over grid cells Two layer energy- and mass-balance model for snow Simulates accumulation, ablation, snowmelt, refreezing and canopy interception

Experiment setup Upper Snake river basin Snow exerts large control over runoff Extensive calibration of VIC already exists for this area Fractional snow covered area observations MODIS product MOD10A1 @ 500 m resolution Typical monthly errors of snow cover maps range from 5% to 18% Synthetic observation experiment Real observation experiment

EnKF Implementation State vector Snow cover at each elevation band and vegetation type Ensemble generation Perturbation of precipitation and temperature forcing data Ensemble size of 25 members Precipitation error → Lognormal random field with 25% relative error Temperature error → Gaussian random fields perturbing both mean and range of daily temperature Local analysis Updates are made independently from grid cell to grid cell Cloud cover threshold of 50% Observation error → Gaussian random number with 10% s.d Consistency scheme Snow cover is zero → Snow properties are reset Snow cover is non-zero → 5 mm of SWE are added and density is calculated from air temperature as new snow density

Synthetic Experiments VIC simulation using “correct” forcing data → True state VIC simulation using an ensemble of perturbed forcing data without assimilation → Prior estimate True fields are perturbed to provide the synthetic observations to be assimilated To emulate cloud cover days when precipitation was over 5 mm were not used in the assimilation

Results – Synthetic experiments Snow cover area fraction 19 Nov 25 Feb 31 Mar True state No Assimilation SCA spatial plots (truth-prior-assimilated) EnKF SCA fraction < 20% SCA fraction > 20%

Results – Synthetic experiments Snow Water Equivalent differences from true state (in mm) 19 Nov 25 Feb 31 Mar True State No Assimilation SCA spatial plots (truth-prior-assimilated) Assimilation estimate

Results – Synthetic experiments Time series of SWE departures from true state Time series of SWE for 3 different grid cells

Real Observations Same enKF implementation as for synthetic experiments Use of real MODIS fractional snow cover product during 10/2002 – 7/2003 Comparison with simpler assimilation scheme that uses SNOTEL station anomalies to adjust SWE

Results – Real observations 7 Jan 03 13 Mar 03 9 Apr 03 MODIS No Assimilation SWE time series incorporating SNOTEL point data (spatial averages) EnKF SCA fraction < 20% SCA fraction > 20% Cloud cover

Results – Real observations 7 Jan 03 13 Mar 03 9 Apr 03 No Assimilation EnKF SWE time series incorporating SNOTEL point data (spatial averages) SWE difference

SWE anomaly based assimilation approach This is the method currently used at the U.S. West- wide Seasonal Streamflow Forecasting Project 1 Snow water equivalent estimate updated every 15 days SNOTEL stations are assigned a weight value for every VIC grid cell based on elevation difference and distance Weights are variable throughout the simulation period and are calculated based on pre-defined influence radii A weight is also assigned to the simulated value The weighted station anomalies are applied to the simulated long-term means, and then combined with the current simulated value 1 http://www.hydro.washington.edu/Lettenmaier/Projects/fcst/index.htm

Comparison results Comparison of SWE estimates (in mm) for Feb 1 2003 SNOTEL EnKF No Assimilation Assimilation

Conclusions EnKF is an efficient and computationally attractive solution Snow cover maps showed improvement Difficult to significantly improve SWE Lack of density or depth information in SCA observations Define an appropriate observation operator in order to include SWE as a state variable Add comments about Gaussianity, SCA binary variable and problems in general

Questions?