Snow Assimilation with the NSIPP Catchment-based Land Surface Model using the Extended Kalman filter

Land surface model: the NASA NSIPP catchment-based Land Surface Model (Koster et al. 2000) that has a three-layer snow model component.

Snow model: three-layer snow model (Fig. 1) that incorporates detailed physics including evaporation/sublimation/condensation, radiation, precipitation as rain or snow, mechanical compression, melt water flow through, etc (Lynch-Stieglitz, 1994; Stieglitz et al., 2001).

Snow state variables: snow water equivalent (W), depth (D) and heat content (H). To ensure a smooth transition from bare-soil to snow-cover conditions, a minimum snow water equivalent of
13 mm is assumed. When fresh snow falls on bare soil, the fractional coverage grows until the entire catchment is covered with snow. At this point, the model begins to grow the snow pack.

Forcing: bias-corrected ECMWF forcing data for the past 20 years over North America (Berg et al., 2001).

Assimilation of snow water equivalent (SWE) into the CLSM

Assimilation procedure

There are four steps to assimilate SWE observation at a given time step:

(1) Forecasting step: the SWE states evolve nonlinearly according to model dynamics; its covariances are propagated linearly with time.

(2) Updating step: the SWE of each layer is updated using the Kalman filter equations.

(3) Analysis step: Snow depth and heat content are calculated using SWE, snow density and snow temperature. When the model predicts no snow and the updated SWE being non-zero, snow density is 150 km/g³ and the air temperature at 2 m is assigned to snow temperature. Otherwise, snow density and temperature predicted by model are used.

(4) Repartition step: At this step, the total snow depth is evaluated and the thickness of each layer is reassigned to ensure a layer 1 thickness of 5 cm. The SWE and heat content are calculated accordingly.

Assimilation results

Conclusions

An identical twin experiment starting from poor initial condition on 1/1/87, shows that the assimilation scheme is able to recover the “true” SWE effectively. This is to be expected because the observation used is the total snow water equivalent.

Snow depth is overestimated initially due to a poor estimate of the snow density by the model. It steadily converges towards the truth by the end of February 1987 (Fig. 7).

Snow temperature is well estimated in both the assimilation and forecast simulations .

Points to ponder…

Disappearing layers and states.

Arbitrary redistribution of mass between layers.

Lack of information in SWE on density and temperature.

Lack of information in snow cover on mass, density and temperature.

Forcing error/bias causes unrealistic snowmelt or accumulation.

Future directions…

Test another assimilation scheme which only updates total SWE (not SWE in each layer), but involve model dynamics in the estimation of state transition matrix (here it becomes a scalar). The SWE, snow depth, and heat content are derived from the geometrical relationship between snow layers, and utilizing estimated density and temperature from model.

Perform a numerical study on bias correction with respect to surface snow temperature and/or air temperature. Investigate the utility of assimilating novel snow observation products, such as snow melt signature and fractional snow cover.

Assimilate real data. Specifically, SWE measured by passive microwave measurement from satellites in the North America, specifically those measurements taken over the past 20 years from SSMR and SSM/I. This study may be expanded over the whole globe.



	Land surface model: the NASA NSIPP catchment-based Land Surface Model (Koster et al. 2000) that has a three-layer snow model component.

	Snow model: three-layer snow model (Fig. 1) that incorporates detailed physics including evaporation/sublimation/condensation, radiation, precipitation as rain or snow, mechanical compression, melt water flow through, etc (Lynch-Stieglitz, 1994; Stieglitz et al., 2001).

	Snow state variables: snow water equivalent (W), depth (D) and heat content (H). To ensure a smooth transition from bare-soil to snow-cover conditions, a minimum snow water equivalent of 13 mm is assumed. When fresh snow falls on bare soil, the fractional coverage grows until the entire catchment is covered with snow. At this point, the model begins to grow the snow pack.

	Forcing: bias-corrected ECMWF forcing data for the past 20 years over North America (Berg et al., 2001).


	There are four steps to assimilate SWE observation at a given time step:
	(1) Forecasting step: the SWE states evolve nonlinearly according to model dynamics; its covariances are propagated linearly with time.
	(2) Updating step: the SWE of each layer is updated using the Kalman filter equations.
	(3) Analysis step: Snow depth and heat content are calculated using SWE, snow density and snow temperature. When the model predicts no snow and the updated SWE being non-zero, snow density is 150 km/g³ and the air temperature at 2 m is assigned to snow temperature. Otherwise, snow density and temperature predicted by model are used.
	(4) Repartition step: At this step, the total snow depth is evaluated and the thickness of each layer is reassigned to ensure a layer 1 thickness of 5 cm. The SWE and heat content are calculated accordingly.


	An identical twin experiment starting from poor initial condition on 1/1/87, shows that the assimilation scheme is able to recover the “true” SWE effectively. This is to be expected because the observation used is the total snow water equivalent.
	Snow depth is overestimated initially due to a poor estimate of the snow density by the model. It steadily converges towards the truth by the end of February 1987 (Fig. 7).
	Snow temperature is well estimated in both the assimilation and forecast simulations .


	Disappearing layers and states.
	Arbitrary redistribution of mass between layers.
	Lack of information in SWE on density and temperature.
	Lack of information in snow cover on mass, density and temperature.
	Forcing error/bias causes unrealistic snowmelt or accumulation.


	Test another assimilation scheme which only updates total SWE (not SWE in each layer), but involve model dynamics in the estimation of state transition matrix (here it becomes a scalar). The SWE, snow depth, and heat content are derived from the geometrical relationship between snow layers, and utilizing estimated density and temperature from model.
	Perform a numerical study on bias correction with respect to surface snow temperature and/or air temperature. Investigate the utility of assimilating novel snow observation products, such as snow melt signature and fractional snow cover.
	Assimilate real data. Specifically, SWE measured by passive microwave measurement from satellites in the North America, specifically those measurements taken over the past 20 years from SSMR and SSM/I. This study may be expanded over the whole globe.