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Land
surface model: the NASA NSIPP catchment-based Land Surface Model (Koster et
al. 2000) that has a three-layer snow model component. |
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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). |
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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. |
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Forcing:
bias-corrected ECMWF forcing data for the past 20 years over North America (Berg
et al., 2001). |
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There are four steps to assimilate SWE
observation at a given time step: |
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(1) Forecasting step: the SWE states evolve
nonlinearly according to model
dynamics; its covariances are propagated linearly with time. |
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(2) Updating step: the SWE of each layer is
updated using the Kalman filter equations. |
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(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. |
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(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. |
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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. |
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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). |
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Snow
temperature is well estimated in both the assimilation and forecast simulations . |
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Disappearing layers and states. |
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Arbitrary redistribution of mass between layers. |
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Lack of
information in SWE on density and temperature. |
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Lack of
information in snow cover on mass, density and temperature. |
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Forcing
error/bias causes unrealistic snowmelt or accumulation. |
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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. |
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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. |
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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. |
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