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Chapter 5. Convection
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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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5.6 Cloud microphysics
5.6.1 Freezing in convective updraughts
We assume that condensate in the convective updraughts freezes in the temperature range
maintaining a mixed phase within that range
according to (6.6) (see Chapter
6 `Clouds and large-scale precipitation' ).5.6.2 Generation of precipitation
The conversion from cloud water/ice to rain/snow is treated in a consistent way with that in the large-scale precipitation scheme by using a formulation following Sundqvist (1978)
|
(5.30) |
where
and 
. 
is the updraught vertical velocity and
is limited to a maximum value of 10 m s-1 in Eq.
(5.30). The value of the autoconversion coefficient has been increased
from values used in previous cycles of the convection scheme by a factor
of 1.5Sundqvist (1988) takes account of the Bergeron-Findeisen process for temperatures below
through a temperature dependent modification
of 
and 
;
|
(5.31) |
where
|
(5.32) |
,and 
.Eq. (5.30) is integrated analytically in the vertical.
5.6.3 Fallout of precipitation
The fallout of rain water/snow is parametrized as (e.g. Kuo and Raymond, 1980)
|
(5.33) |
where
is the model layer depth. The terminal velocity 
is parametrized as (Liu and Orville, 1969)
|
(5.34) |
where
is given in units of 
. Since the
fall speed of ice particles is smaller than that of water droplets, only
half the value of 
calculated
with Eq. (5.28)is used for ice.
In estimating the fallout of precipitation in the mixed phase region of
the cloud a weighted mean of the fall speed for ice and water precipitation
is used. Eq. (5.33) is integrated analytically
in the vertical5.6.4 Evaporation of rain
The evaporation of convective rain is parametrized following a proposal of Kessler (1969), where the evaporation is assumed to be proportional to the saturation deficit
and to be dependent
on the density of rain 
(
)
|
(5.35) |
where
is a constant being zero for 
.As the density of rain
is not given by the model it is convenient
to express it in terms of the rain intensity 
(
) as
|
(5.36) |
where
is the mean fall speed of rain drops which again is parametrized
following Kessler (1969).
|
(5.37) |
(Note that this is different from the formulation used in the estimation of the fallout of precipitation).
Thus we have
|
(5.38) |
Since the convective rain takes place only over a fraction
of the grid area, the evaporation rate at level 
becomes
|
(5.39) |
where the constants have the following values (Kessler, 1969)
In view of the uncertainty of the fractional area of precipitating clouds a constant value of
is assumed.The evaporation rate is calculated implicitly in the model by means of
|
(5.40) |
which follows from
|
(5.41) |
and
|
(5.42) |
5.6.5 Melting and freezing of precipitation
Melting of snow falling across the freezing level (
) is parametrized
by a simple relaxation towards 
;
|
(5.43) |
where
is the amount of snow (kg m2 s) melting and 
is a relaxation time scale which decreases with increasing temperature,
|
(5.44) |
The parametrization may produce melting over a deeper layer than observed (Mason 1971) but this has been intentionally introduced to account implicitly for the effects of vertical mixing which may develop in response to the production of negative buoyancy.
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05.04.2002 |
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