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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
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3.1 Introduction
The parametrization scheme described in this chapter represents the turbulent transfer of heat, momentum and moisture between the surface and the lowest model level and the turbulent transport of the same quantities between model levels. The scheme computes the physical tendencies of the four prognostic variables (
, 
, 
and 
) due to the vertical exchange by turbulent
(non-moist) processes. These tendencies are obtained as the difference between
the results of an implicit time-step from 
to 
. All the diagnostic computations (such
as the calculation of the exchange coefficients, etc.) are done at time
. The surface boundary condition is
formulated separately for 8 different tiles: water, ice, wet skin, low vegetation,
exposed snow, high vegetation, snow under vegetation, and bare soil. The
different tiles have their own surface energy balance and their own skin
temperature. In this version of the IFS, the mixture of land and ocean tiles
is still not used, i.e. a grid box is either 100% ocean (water + ice) or
100% land (tile 3 to 8). Details about tiles are given in Chapter 7. The equation for the vertical diffusion of any conservative quantity
is:
|
(3.1) |
The vertical turbulent flux
(positive downwards) is written using a first-order turbulence closure,
where 
is the exchange coefficient. The goal of the vertical diffusion parametrization
is to define the exchange coefficients and then to solve equation (3.1) with the following boundary
conditions:
|
(3.2) |
where
is the pressure at the top of the atmosphere. For heat
and moisture the surface boundary condition is provided tile by tile and
fluxes are averaged over the 
tiles, weighted by their fraction 
. The transfer coefficient 
at the lowest model level depends upon the static stability. The
variable 
represents the value of 
at the surface. For heat and moisture, 8 tiles are used (see
Chapter 9). For wind, a single tile is used with a no slip condition at
the surface. The vertical diffusion process is applied to the two horizontal wind components,
and 
, the specific humidity 
and the dry static energy 
, where
|
(3.3) |
where
and 
, 
, and 
are the specific heats at constant pressure of dry air, water vapour
and moist air, respectively, and 
is the geopotential.The problem is simplified by assuming that
remains constant with respect to time during the turbulent diffusion
process (even if in reality 
variations would modify 
). Exchange coefficients (with the dimension of a pressure thickness)
are then computed for momentum and for heat (sensible plus latent) (the
subscripts `
, `
' and `Q' are used to identify the exchange
coefficient for momentum, heat and humidity), with different formulations
for the stable and the unstable case (depending on the sign of a stability
parameter, either the Obukhov length or the bulk Richardson number in the
surface layer). The implicit linear equations for the fluxes of momentum,
firstly for 
and 
and secondly for 
and 
, are solved by a Gaussian-elimination/back-substitution
method. The surface boundary condition is applied between the downward scanning elimination and the upward scanning back substitution. It involves a no-slip condition for
and 
and the tile-by-tile solution of the
surface energy balance for the boundary condition of 
and 
. The water tile is an exception as it ignores the surface energy
balance and uses the specified SST and the saturation specific humidity
as boundary conditions. Finally, the tendency of the variable temperature is computed, modified by the effects of local dissipation (it is assumed that there is no storage of turbulence kinetic energy) and moisture diffusion on
. The tiled surface fluxes of heat and moisture
are also computed for later use by the surface scheme. Next Section
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05.04.2002 |
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