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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
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3.8 Diagnostic computations for postprocessing
3.8.1 Diagnostic boundary layer height
Because of its importance for applications (e.g. in air pollution modelling), the boundary layer height is diagnosed and made available for postprocessing. The parametrization of the mixed layer (and entrainment) already uses a model level index as boundary layer height, but in order to get a continuous field, also in neutral and stable situations the parcel lifting method (or bulk Richardson method) proposed by Troen and Mahrt (1986) is used as a diagnostic, independent of the turbulence parametrization. Boundary layer height
is defined as the level where the bulk Richardson number, based on
the difference between quantities at that level and the lowest model level,
reaches the critical value 
. The bulk Richardson is computed from the following set of equations
|
(3.66) |
where index
indicates the lowest model level and 
indicates the boundary layer height i.e the level where 
. The virtual dry static energy from the lowest
level 
is increased with a turbulent part 
and compared to the virtual dry static energy
at boundary layer height 
. The boundary layer height is found by a vertical scan from the
surface upwards. If the boundary layer height is found to be between two
levels a linear interpolation is done to find the exact position. Since
the boundary layer height is needed for 
, the upward scan is done twice. The first one uses 
in the expression for 
; the second scan uses the result of the first scan. 3.8.2 Wind at 10 m level
Wind at the 10 m level is computed for postprocessing because it is the standard level for SYNOP observations. It can be obtained rather easily by vertical interpolation between the lowest model level and the surface, making use of profile functions (3.7) and (3.8). This procedure is appropriate over the ocean or in areas where the surface is smooth and homogeneous. However, the postprocessed field is meant to be comparable to wind from SYNOP observations and for observations over land WMO requires SYNOP stations to be in open terrain in order to be well exposed to wind. So the SYNOP wind observations are not necessarily compatible with the wind that is representative for a large area (i.e. a grid box from the model). Over inhomogeneous terrain, the problem can be particularly serious, because the "aerodynamic roughness length" in the model is adjusted to provide sufficient drag at the surface which is dominated by the rough elements. This approach leads to a low area-averaged wind speed which is not comparable to the "open-terrain" wind speed as observed by WMO stations.
In order to make the postprocessed wind compatible with SYNOP observations, the concept of exposure correction is introduced. The open-terrain wind is obtained by taking the wind information from such a height above the surface that it is less influenced by the underlying terrain. This height is called the blending height
. and for the the interpolation to 10 m an aerodynamic roughness
length is used that is typical for open terrain with grassland. The interpolation procedure is as follows. First the blending height and the interpolation roughness length are set dependent on the model roughness length field:
|
(3.67) |
|
(3.68) |
where
, 
is the horizontal wind speed at the blending height either interpolated
from model levels to 75 m or copied from the lowest model level, and 
is the resulting horizontal windspeed
at 10 m. The wind speed from equation (3.68) is converted to components
making use of the wind direction from the lowest model level. 3.8.3 Temperature and humidity at the 2 m level
Computation of temperature and moisture at the 2 m level is based on interpolation between the lowest model level and the surface making use of the same profile functions as in the parametrization of the surface fluxes. The following expressions are derived from equations (3.9) and (3.10)
|
(3.69) |
|
(3.70) |
with
, 
if 
, and otherwise 
and 
. Temperature 
is derived from 
and 
with equation (3.3). Also the dew point is computed
from 
and surface pressure. The dew point
uses the saturation formulation with respect to water to be consistent with
WMO reporting practise. If the resulting dew point is lower than temperature
, the dew point is set equal to temperature. 3.8.4 Wind gusts
The computation of gusts is intended to be compatible with WMO observing practise for wind extremes. In order to get uniform observations, WMO defines a wind gust as the maximum of the wind averaged over 3 second intervals.
First the horizontal wind speed at the 10 m level is computed from the lowest model level (no exposure correction)
|
(3.71) |
To simulate gusts, the standard deviation of the horizontal wind is estimated on the basis of the similarity relation by Panofsky et al. (1977)
|
(3.72) |
with
. The difference between the gust and 
is proportional to 
, where the multiplier has been determined from universal turbulence
spectra for a 25% exceeding probability of the three-second wind gust (see
Beljaars, 1987). The resulting wind
gust is
|
(3.73) |
From the controlling parameters it is clear that the effects of surface friction (through surface roughness) and stability are captured. However, the approach might be less adequate for gusts in baroclinic situations and gusts due to strong convective events. Parameter
is computed every time step and its maximum since
the last postprocessing time is written out for archiving. Next Section
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05.04.2002 |
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