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Chapter 4. Subgrid-scale orographic
drag
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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4.3 Specification of subgrid-scale orography
For completeness, the following describes how the subgrid-scale orography fields were computed by Baines and Palmer (1990). The mean topographic height above mean sea level over the gridpoint region (GPR) is denoted by
, and the coordinate 
denotes elevation above this level. Then the topography relative
to this height 
is represented by four parameters, as follows(i) The net variance, or standard deviation,
 , of  in the grid-point region. This is calculated
from the US Navy data-set, or equivalent, as described by
Wallace et al. (1983). The quantity  gives a measure of the amplitude and  approximates the physical envelope of the peaks. |
(ii) A parameter  which characterizes the anisotropy of the topography within the grid-point
region. |
(iii) An angle  , which denotes the angle between the direction of the low-level
wind and that of the principal axis of the topography. |
(iv) A parameter  which represents the mean slope within the grid-point region. |
The parameters
and 
may be defined from the topographic gradient correlation tensor
,
where
, and 
, and where the terms be calculated (from the USN data-set) by using
all relevant pairs of adjacent gridpoints within the grid-point region.
This symmetric tensor may be diagonalized to find the directions of the
principal axes and the degree of anisotropy. If
 ,
|
(4.20) |
the principal axis of
is oriented at an angle 
to the 
-axis, where 
is given by
 .
|
(4.21) |
This gives the direction where the topographic variations, as measured by the mean-square gradient, are largest. The corresponding direction for minimum variation is at right angles to this. Changing coordinates to
which are oriented along the principal axes 
and 
, the new values of 
, 
and 
relative to these axes, denoted 
, 
and 
, are given by
,
where
, 
and 
are given by Eq. (4.20). The anisotropy of the orography
or `aspect ratio'. 
is then defined by the equations
|
(4.22) |
If the low-level wind vector is directed at an angle
to the 
-axis, then the angle 
is given by
 .
|
(4.23) |
The slope parameter,
, is defined as
 ,
|
(4.24) |
i.e. the mean-square gradient along the principal axis.
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05.04.2002 |
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