Table of contents
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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The code mirrors the basic form of the scheme. Hence there is a routine
defining all the basic input values for the evaluations of drag, wave stress
etc.; a routine to calculate the vertical distribution of wave stress; and
a principal routine which computes the wave stress at the surface and the
total momentum tendencies, including that from the low-level drag.
The orography parametrization is called from CALLPAR as GWDRAG which in
turn calls GWSETUP, and GWPROFIL.
This defines various reference model levels for controlling the vertical
structure of the calculations, and sets up a number of derived atmospheric
variables and geometric calculations required to run the scheme:
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(a) The definition of the Brunt-Väisälä
frequency on half levels |
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(b) The definition of the mean wind components
in the layer  (where  is the standard deviation of the subgridscale orographic height) |
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and similarly for  ; likewise the mean static stability,  , and the mean density,  are calculated. |
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(c) The calculation of necessary geometry pertaining
to geographical orientation of subgridscale orography and wind direction, |
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and  , where  is the orientation of ridges relative to east, and the calculation
of Phillips
(1984) parameters |
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where  is the anisotropy of the subgridscale
orography. |
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(d) The calculation of the vertical wind-profile
in the plane of the gravity wave stress. Defining |
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and similarly for  , where  , |
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then the wind profile is defined level-by-level
as |
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where  and  ; the values of  are also used to compute half level
values  etc. by linear interpolation in pressure. |
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(e) The calculation of basic flow Richardson
Number |
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(f) The calculation of the depth of the layer
treated as `blocked' (i. e. experiencing a direct drag-force due to
the subgrid-scale orography). This is given by the value of  that is the solution to the finite-difference form of the equation |
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where  is a constant defined later. |
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(g) The calculation of the layer in which low-level
wave-breaking occurs (i. e. the layer experiencing gravity wave breaking
(if any) immediately above the `blocked' layer). This is given by
the value of  that is the solution to the finite difference form of the equation |
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the value of  is not allowed to be less than  . |
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(h) The calculation of the assumed vertical profile
of the subgridscale orography needed for the `blocking' computations |
This computes the vertical profile of gravity-wave stress by constructing
a local wave Richardson number which attempts to describe the onset of turbulence
due to the gravity waves becoming convectively unstable or encountering
critical layers. This wave Richardson number can be written in the form
 ,
where  is the Richardson number of the basic
flow. The parameter  in which represents the amplitude of the wave
and  is the wind speed resolved in the direction of  . By requiring that  never falls below a critical value  (currently equal to 0.25), values of wave stress are defined progressively
from the top of the blocked layer upwards.
When low-level breaking occurs the relevant depth is assumed to be related
to the vertical wavelength. Hence a linear (in pressure) decrease of stress
is included over a depth  given by the solution of Eq. (4.32). The linear decrease of stress
is written as
where the asterisk subscript indicates that the value is at the level  .
This is the main routine. After calling GWSETUP, it defines the gravity-wave
stress amplitude in the form,
(where  is a constant defined later and  is the mean slope of the subgrid-scale orography)
and then calls GWPROCIL. The tendencies due to the wave stresses are then
calculated in the form gravity-wave stress amplitude in the form,
where  is a constant defined later and  is the mean slope of the subgrid-scale orography.
where  is the necessary geometric function to generate components,
(similarly for  ).
Next the low-level blocking calculations are carried out for levels below
 . These are done level-by-level as follows. Writing the
low-level deceleration in the form
where  and  and  have been defined earlier, Eq. (4.39) is evaluated in the following
partially implicit manner by writing it in the form
then  and  . Hence
This calculation is done level-by-level.
Finally the tendencies are incremented. This includes local dissipation
heating in the form
where  , and  etc.
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