| Home > Research > Ifsdocs > PHYSICS > |
Chapter 3. Turbulent diffusion and
interactions with the surface
IFS documentation Front Page
Chapter 1. Overview
Chapter 2. Radiation
Chapter 3. Turbulent diffusion and interactions with the surface
Chapter 4. Subgrid-scale orographic drag
Chapter 5. Convection
Chapter 6. Clouds and large-scale precipitation
Chapter 7. Land suface parametrization
Chapter 8. Methane oxidation
Chapter 9. Climatological data
REFERENCES
Previous Section
3.5 The skin temperature
The surface energy balance is satisfied independently for the tiles by calculating the skin temperature for each tile. The skin layer represents the vegetation layer, the top layer of the bare soil, or the top layer of the snow pack, has no heat capacity and therefore responds instantaneously to changes in e.g. radiative forcing. In order to calculate the skin temperature, the surface energy balance equation is linearized for each tile leading to an expression for the skin temperature. This procedure is equivalent to the Penmann-Monteith approach which can be derived by eliminating the skin temperature from the surface energy balance equation assuming that the net radiation minus ground heat flux is known (e.g. Brutsaert, 1982). The approach followed here is an extension to the Penmann-Monteith derivation in the sense that it allows for coupling with the underlying soil (or snow, ice). Because of the short time scale associated with the skin layer, the equation for its temperature is solved implicitly together with the vertical diffusion in the boundary layer.
The following general discussion applies to each tile but the parameters are tile dependent as discussed in the land surface part of the documentation (Chapter 7). The surface energy balance equation can be written as:
|
(3.51) |
where
and 
are the net shortwave and longwave radiation fluxes at the surface
and the right hand side represents the ground heat flux through coupling
with the underlying soil, snow or ice with temperature 
. The turbulent sensible and latent heat fluxes
are
|
(3.52) |
|
(3.53) |
|
(3.54) |
In order to solve for the skin temperature implicitly, the surface energy balance is solved together with the vertical diffusion equations. After the downward elimination scan of the tridiagonal system of equations (3.45) a relation is obtained between the lowest model level values and the surface values, i.e. between
and 
, and between 
and 
:
|
(3.55) |
|
(3.56) |
Since the vertical diffusion equation is formulated in terms of the time extrapolated parameters (indicated by a hat, see equation (3.44)), the skin temperature has to be extrapolated as well. Eliminating the lowest model level parameters and linearizing with respect to previous time step skin temperature leads to
|
(3.57) |
|
(3.58) |
Also
needs to be expressed in surface variables. For this purpose
the moisture correction in 
is evaluated from the previous time level:
|
(3.59) |
|
(3.60) |
The net long-wave radiation at the surface is linearized with respect to skin temperature at the previous radiation time step (indicated by superscript
, which can be up to 3 hours earlier):
|
(3.61) |
Substituting
in (3.57) and replacing 
and 
in surface energy balance equation
(3.51) by equations (3.57) and (3.58) leads to an expression for
skin temperature 
at the extrapolated time level.
|
(3.62) |
with
from equation (3.60). Following the downward elimination
scan of the tridiagonal matrices for 
and 
, equation (3.62) is solved for all the tiles,
using the appropriate parameters for each tile (note that also the transfer
coefficients and therefore coefficients 
, 
, 
, 
are tile dependent). The resulting skin temperatures
are used in (3.48) with the corresponding weights
of the tiles as a boundary condition before doing the upward scanning back-substitution.
This procedure is fully implicit for the dominant tile in the sense that atmospheric and skin variables are in equilibrium at the new time level. However, equilibrium for non-dominant tiles is not necessarily achieved. It can happen that the surface fluxes from the dominant tile changes the temperature and moisture substantially at the lowest model. If the fluxes to another tile (with small fraction) happen to be very different, this tile will not see the correct atmospheric state in the computation of the skin temperature. A full implicit coupling would require the solution of a matrix problem involving the skin temperatures of all the tiles simultaneously.
Next Section
Previous Section
 |
05.04.2002 |
 |
© ECMWF |
