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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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5.4 Convective types
In using a bulk mass flux scheme, as opposed to a scheme which considers an ensemble of convective clouds (such as that of Arakawa and Schubert, 1974), some determination of convective cloud type must be made so that appropriate choices can be made for the cloud properties. Firstly it must be determined if the profile can support convection from the surface layer. If on carrying out an undilute ascent from the surface layer a cloud base is found where the parcel buoyancy is greater than
K, then either
deep or mid-level convection is initiated. If no such cloud base is found
then higher levels of the model are tested for a buoyant layer, mid-level
convection being initiated from the lowest such level.For convection initiating from the surface, the original version of the convection scheme (Tiedtke 1989) used a comparison of moisture convergence and surface evaporation to determine whether convection was deep or shallow. However this is now done on the basis of the depth of the convective cloud. If the cloud depth exceeds 200 hPa then deep convection is assumed, shallow convection if not.
Once the type of convection has been determined its intensity (controlled by the cloud-base mass flux) is determined as outlined below.
5.4.1 Deep convection
Following Fritsch and Chappell (1980) and Nordeng (1994), the cloud base mass flux for deep convection is estimated from assuming that convection acts to reduce the convective available potential energy (CAPE) towards zero over a specified time scale
;
|
(5.16) |
where
|
(5.17) |
where
and 
describe the vertical variation of the updraught
and downdraught mass flux due to entrainment and detrainment and the subscript
`base' refers to cloud-base quantities. As the downdraught mass flux at
the LFS is linked to the updraught mass flux at cloud base (Eq. (5.11)) then,
|
(5.18) |
Using Eq. (5.18) in Eq. (5.16) results in an expression for the cloud base mass flux. CAPE is estimated from the parcel ascent incorporating the effects of water loading,
|
(5.19) |
In practice the vertical variation of the updraught and downdraught mass fluxes (
and 
above) is estimated from an initial ascent using
an arbitrary value for the updraught mass flux at cloud base followed by
a downdraught calculation. Using these estimates the updraught mass flux
at cloud base is recomputed and downdraught mass fluxes rescaled. A second
updraught ascent is then computed to revise the updraught properties.The adjustment time scale
is rather arbitrary but experience suggests
that to prevent grid-scale saturation it must be set such that
|
(5.20) |
where
is the grid-scale vertical velocity. The magnitude of the grid-scale
vertical velocity roughly doubles when resolution is doubled and so originally
At T63 
is set to
2 hours, and at other resolutions was originally varied linearly with the
spectral truncation (
);
|
(5.21) |
However for resolutions of the deterministic forecasts (TL319) this leads to a value for
of 1400s, close
to the timestep of the model at this resolution (1200s), implying that convection
acts to produce zero CAPE at each time step. It is also shorter than the
time scale associated with the growth of a deep convective cloud, typically
around 1 hour. Thus such a short adjustment timescale may be thought unphysical,
although the association of 
with a physical timescale is a mantter
of debate.As horizontal resolution increases, parts of convective cloud systems may become better resolved (for example the stratiform regions) and be represented through an interaction between the dynamics and cloud scheme of the model. In this scenario an unrestricted decrease of
with resolution may work against a smooth transition
from parametrized to explicit representation of at least part of convection.
Although it is unlikely that this is a significant problem at a resolution
of TL319, a lower limit of 3600s has been applied to the relaxation
timescale given by Eq. (5.21) for horizontal resolutions greater than TL159.The vertical distribution of the updraught mass flux above cloud base is determined by assuming that there is organized entrainment which is directly proportional to the large-scale moisture convergence as
|
(5.22) |
Organized entrainment is only considered in the lower part of the cloud layer where large-scale convergence is encountered, that is, below the level of strongest vertical ascent. The idea to link the cloud mass flux directly to the large-scale moisture convergence has first been advocated as a parametrization by Lindzen (1981) who indicated that it may provide vertical profiles of mass flux and convective heating in good agreement with observations. The assumption (5.22) ensures that the vertical distribution of the convective mass flux follows that of the large-scale ascent which is partly supported by diagnostic studies for tropical convection (e.g. Cheng et al., 1980; Johnson, 1980).
5.4.2 Shallow convection
Here we consider cumulus convection, which predominantly occurs in undisturbed flow, that is in the absence of large-scale convergent flow. Typical examples are trade-wind cumuli under a subsidence inversion, convection occurring in the ridge region of tropical easterly waves and daytime convection over land. This type of convection seems to be effectively controlled by sub-cloud layer turbulence. In fact, most of the diagnostic studies carried out for trade-wind cumuli show that the net upward moisture flux at cloud-base level is nearly equal to the turbulent moisture flux at the surface (Le Mone and Pennell, 1976). In regions of cold air flowing over relatively warm oceans the then relatively high sensible heat flux has been found to be of significant importance. We therefore derive the mass flux at cloud base on a balance assumption for the sub-cloud layer based on the moist static energy budget;
|
(5.23) |
with
|
(5.24) |
The moisture supply to the shallow cumulus is largely through surface evaporation as the contributions from large-scale convergence are either small or even negative, such as in the undisturbed trades where dry air is transported downward to lower levels.
An initial estimate for the updraught base mass flux is obtained using Eq. (5.23). If downdraughts occur (relatively rare for shallow convection due to the low precipitation rates), then a revised estimate is made accounting for the impact of downdraughts upon the sub-cloud layer, the l.h.s. of Eq. (5.23) being replaced by
|
(5.25) |
Again downdraught properties are obtained using the original estimate of the updraught base mass flux and then rescaled by the revised value. For the updraught a second ascent is calculated using the revised value of the base mass flux.
No organized entrainment is applied to shallow convection. As turbulent entrainment and detrainment rates are equal, the mass flux remains constant with height until reducing at cloud top by organized detrainment.
5.4.3 Mid-level convection
Mid-level convection, that is, convective cells which have their roots not in the boundary layer but originates at levels above the boundary layer, often occur at rain bands at warm fronts and in the warm sector of extratropical cyclones (Browning et al. 1973; Houze et al. 1976; Herzegh and Hobbs 1980). These cells are probably formed by the lifting of low level air until it becomes saturated (Wexler and Atlas 1959) and the primary moisture source for the clouds is from low-level large-scale convergence (Houze et al. 1976). Often a low-level temperature inversion exists that inhibits convection from starting freely from the surface; therefore convection seems to be initiated by lifting low-level air dynamically to the level of free convection. This occurs often in connection with mesoscale circulations which might be related to conditionally symmetric instability (Bennets and Hoskins 1979; Bennets and Sharp 1982) or a wave-CISK mechanism (Emanuel 1982).
Although it is not clear how significant the organization of convection in mesoscale rain bands is for the large- scale flow, a parametrization should ideally account for both convective and mesoscale circulations. Such a parametrization, however, is presently not available and we must therefore rely on simplified schemes. Here we use a parametrization which in a simple way considers the finding of the diagnostic studies mentioned above. We assume that convection is activated when there is a large-scale ascent, the environmental air is sufficiently moist, i.e., of relative humidity in excess of 80%, and convectively unstable layer exists above (i.e. at cloud base the buoyancy is greater than
K). The convective mass flux at cloud base is set equal to the vertical mass transport by the large-scale flow at that level:
|
(5.26) |
following the notation of Subsection 5.4.1 above. Again two estimates of the updraught base mass flux are made; first neglecting downdraughts, followed by a revised estimate if downdraughts occur. The closure ensures that the amount of moisture which is vertically advected through cloud base by the large-scale ascent is fully available for generation of convective cells.
In addition to the injection of mass through cloud base, we assume again that cloud air is produced by moisture convergence above cloud base through organised entrainment in the same way as for penetrative convection as given by (5.22).
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05.04.2002 |
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