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Land surface assimilation
March 2001
By Jean-François Mahfouf and Pedro Viterbo
European Centre for Medium-Range Weather
Forecasts
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2 Design of land surface parametrizations
2.1 General features
The aim of land surface schemes is to compute temperature and specific humidity at the lower boundary of atmospheric models. These two variables are required in the estimation of heat, water and momentum exchanges between the continental surfaces and the lower atmosphere.
The surface temperature
is
derived as the solution of the surface energy balance written as:
|
(1) |
where Rn is the net radiation flux converted in latent heat flux
, sensible
heat flux 
and
ground heat flux 
.
The ground heat flux G depends upon deep soil temperatures and soil thermal properties.
The surface specific humidity can be written formally as :
|
(2) |
where
represents the value of specific humidity
at the lowest model layer. The quantities 
and 
(described with more details in the
next paragraph) depend upon soil moisture 
which is obtained
by solving the surface water budget :
|
(3) |
where P is the precipitation flux, E the total evaporation flux and R the surface runoff.
This brief description shows that a land surface scheme must manage at least two prognostic equations for the temperature and soil moisture in the soil. Heat and water transfers are governed by the following diffusion laws :
|
(4) |
|
(5) |
The diffusivity D and conductivity K coefficients are non-linear functions of soil moisture content. The diffusion equations are generally discretized over 2 to 4 layers in order to deal with time scales ranging from days to months.
2.2 Surface fluxes
The link between soil and atmospheric variables is provided through the expression of the surface fluxes, usually based on Monin-Obukhov theory; the crucial variable here is the evaporation flux because its magnitude depends explicitly upon surface properties. Recent land surface schemes represent differently the grid box fractions covered by: a) bare soil, with evaporation controlled by soil moisture in a shallow top soil layer; b) vegetation, with transpiration controlled by soil moisture in the root zone affecting the magnitude of stomatal resistance; c) snow or interception reservoir, evaporating at the potential (maximum) rate. These two last components require the existence of model prognostic equations for snow mass and interception reservoirs.
Evaporation from bare soil can be written as (see Mahfouf and Noilhan 1991 for a review) :
|
(6) |
The efficiency of the turbulent transfers is accounted for through the aerodynamic resistance
, while
the control by the surface soil moisture 
is represented by the surface relative humidity 
[
and 
in Equation
(2)]. A typical variation
of 
is presented on the left panel of Fig.
1 . Evaporation takes place at the potential rate above a threshold
value (field capacity) 
(defined from soil texture) up to
the saturation 
.Transpiration from vegetation canopy writes similarly:
|
(7) |
The analogy with Equation (2) leads to
and 
. Water transfers from the root zone to the atmosphere
depend both on biological and physical controls. Plants limit their water
losses in unfavorable environmental conditions determined by soil moisture
in the root zone, atmospheric water vapour deficit, solar radiation, air
temperature and carbon-dioxide concentration. A typical dependency of the
canopy resistance 
with soil moisture is shown on the right
panel of Fig. 1 . Below
a threshold value often defined as the permanent wilting point 
, it is assumed that plants are unable to pump
water from the root zone to the stomatal cells, corresponding to a rapid
decrease of transpiration (increase in 
). As for bare soils, it if often assumed that above the
field capacity the plant transpiration is not controlled by soil moisture.
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12.06.2002 |
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