1. 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

2. 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

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

4. 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

5. 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 500 m resolution
Typical monthly errors of snow cover maps range from 5% to 18%
Synthetic observation experiment
Real observation experiment

6. 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

7. 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

8. 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%

9. 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

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

11. 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

12. 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

13. 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

14. 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

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

16. 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

17. Questions?