Evaluating snow data assimilation methods for use in distributed models

Jan Magnusson1, David Gustafsson2, Tobias Jonas1

1 WSL - Institute for Snow and Avalanche Research SLF2 SMHI - Swedish Meteorological and Hydrological Institute

Background

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

For reliable model predictions we need to accurately estimate initial conditions!

However, large snow cover variability makes such estimations difficult …

Background

… 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)

Background

Snow depth (m)

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?

INPUT DATA:TA + PREC

(METEOSWISS)

DISTRIBUTEDSNOW MODEL

SIMULATIONRESULTS

Model domain

SNOW DEPTHOBSERVATIONS

Combine model results & snow observations

x – Snow depth; o – Snow water equivalent

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

Research – Motivation & Study site

Computing snow water equivalents(1) Compute snow water equivalents from snow depth records using a model simulating snow densities; (2) Change in SWEHS gives snowfall amounts and melt rates

Height of snow(Snow depth)

Solid precipitation

Snow water equivalent

Melt rates

Sequential assimilation methods

INPUT DATA

MODEL

FORECAST

FILTER

ANALYSIS

OBSERVATION

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 …

Experiment - Assimilating states

INPUT DATA: TA + PREC

SNOW MODEL

FORECAST

ANALYSIS

SWEHS

Correcting model states using estimated snow water equivalents

ENKFIntroduce 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

Experiment - Assimilating fluxes

INPUT DATA: TA + PREC

PRECIPITATION MODEL

FORECAST

ANALYSIS

PSOLIDHSOI

1st step: Correcting accumulationcomponent of snow model

Experiment - Assimilating fluxes

INPUT DATA: TA + PREC

PRECIPITATION MODEL

FORECAST

ANALYSIS

PSOLIDHSOI

INPUT DATA: TA + PSOLID

SNOW MODEL

FORECAST

ANALYSIS

MELTHSENKF

1st step: Correcting accumulationcomponent of snow model

2nd step: Correcting ablationcomponent of snow model

Run temperature-index snow model driven by interpolated air temperature and total precipitation

Results - Control simulation

Test against independent snow water equivalent observations captured every second week over three years starting 2006(circles on the map)

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

Results – Mapping approach

Update snow model results by assimilating the snow water equivalents inferred from the snow depth records (ensemble Kalman filter)

Results - Assimilating states

(Filter including spatially correlated error information)

Update the temperature-index model results by assimilating solid precipitation amounts (optimal interpolation) and melt rates (ensemble Kalman filter)

Results – Assimilating fluxes

The model approximately reproduces snow covered fraction without and with data assimilation

Snow covered fraction often not sensitive to variations in snow water equivalent

Fractional simulated snow covered area

Example of assimilating snowfall amountsStatistical 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

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)

Example of assimilating melt rates

Difference between filter and control

Difference between methods

2009-03-15

Final remarksData 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