Evaluating snow data assimilation methods for use in distributed models

1. Evaluating snow data assimilation methods for use in distributed models Jan Magnusson1, David Gustafsson2, Tobias Jonas1 1 WSL - Institute for Snow and Avalanche Research SLF 2 SMHI - Swedish Meteorological and Hydrological Institute

2. Background Snow melt related floods in Switzerland (example from October 2011)

3. Background For reliable model predictions we need to accurately estimate initial conditions! However, large snow cover variability makes such estimations difficult …

4. Background Snow depth (m) … because station recordings do often not reflect the average conditions needed in model applications due to high natural variability (example from Egli et al., 2012)

5. Research – Motivation & Study site • Predict average snow amounts and melt rates as accurately as possible • Use all relevant information to estimates these quantities • High uncertainty in many of our available data sources • How can we make appropriate use of point snow depth observations • in distributed snow cover modeling? Model domain Combine model results & snow observations INPUT DATA: TA + PREC (METEOSWISS) DISTRIBUTED SNOW MODEL SNOW DEPTH OBSERVATIONS SIMULATION RESULTS x – Snow depth; o – Snow water equivalent

6. Research – Motivation & Study site • Point snow depth observations have several good properties • Access to many snow depth observations (easy and cheap) • Continuous and works in most weather conditions • … but are often not representative for areal averages and errors can vary with time depending on for example wind direction during individual storms

7. Computing snow water equivalents (1) Compute snow water equivalents from snow depth records using a model simulating snow densities; (2) Change in SWEHSgives snowfall amounts and melt rates Height of snow (Snow depth) Snow water equivalent Solid precipitation Meltrates

8. Sequential assimilation methods Basic filter behaviour Weighting between simulation and observation depending on ingoing uncertainties Filter option 1: Optimal interpolation Specify model and observation error statistics a priori Filter option 2: Ensemble Kalman filter Evolving model error statistics using an ensemble of simulation results Filter assumptions required for optimality Normally distributed errors, linear model, infinite number of ensembles, unbiased … INPUT DATA MODEL FORECAST FILTER OBSERVATION ANALYSIS

9. Experiment - Assimilating states Correcting model states using estimated snow water equivalents INPUT DATA: TA + PREC SNOW MODEL FORECAST ENKF SWEHS Introduce spatially correlated error statistics so that the filter algorithm propagates information from observation sites (crosses on the map) to validation points (circles on the map) lacking assimilation data ANALYSIS

10. Experiment - Assimilating fluxes 1st step: Correcting accumulation component of snow model INPUT DATA: TA + PREC PRECIPITATION MODEL FORECAST OI PSOLIDHS ANALYSIS

11. Experiment - Assimilating fluxes 1st step: Correcting accumulation component of snow model 2nd step: Correcting ablation component of snow model INPUT DATA: TA + PREC INPUT DATA: TA + PSOLID PRECIPITATION MODEL SNOW MODEL FORECAST FORECAST OI PSOLIDHS ENKF MELTHS ANALYSIS ANALYSIS

12. Results - Control simulation Run temperature-index snow model driven by interpolated air temperature and total precipitation Test against independent snow water equivalent observations captured every second week over three years starting 2006 (circles on the map)

13. Results – Mapping approach Project snow water equivalents computed from snow depth observations to validation points using an interpolation scheme optimized for snow data and our validation data set

14. Results - Assimilating states Update snow model results by assimilating the snow water equivalents inferred from the snow depth records (ensemble Kalman filter) (Filter including spatially correlated error information)

15. Results – Assimilating fluxes Update the temperature-index model results by assimilating solid precipitation amounts (optimal interpolation) and melt rates (ensemble Kalman filter)

16. Fractional simulated snow covered area The model approximately reproduces snow covered fraction without and with data assimilation Snow covered fraction often not sensitive to variations in snow water equivalent

17. Example of assimilating snowfall amounts Statistical interpolation (optimal interpolation) for updating snowfall estimates • Snowfall for 2006-12-08 • Large errors in background field can persist throughout simulation period • Statistical interpolation easy and quick method to improve simulations • Snowfall spatially variable and observations uncertain

18. Example of assimilating melt rates Ensemble Kalman filter for updating forecasted snowmelt • Melt rates for 2008-05-05: • Temperature-index model sometimes incapable of capturing melt for short periods • Information propagates from stations to neighborhood (spatial error correlations) • Melting spatially homogeneous (elevation bands)

19. Difference between filter and control

20. Difference between methods 2009-03-15

21. Final remarks Data assimilation schemes: • improve simulation results • can give more realistic results than simpler methods (interpolation) • partly compensate for non-stationary parameters and station availability Although: • discrepancy between true error distributions and filter assumptions is currently limiting realistic uncertainty estimations