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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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5.8 Momentum transports
Equation set (5.3) includes a treatment of the vertical transport of horizontal momentum by convection. Studies have shown that for deep convection momentum transports are over estimated by the plume models unless the effects of cloud scale horizontal pressure gradients are included (Gregory et al. 1997b). For unorganised convection the effects of the pressure gradients are to adjust the in-cloud winds towards those of the large-scale flow. This can be represented by an enhanced turbulent entrainment rate in the cloud momentum equations. To ensure mass continuity the turbulent detrainment rate is also increased by an equivalent amount. As the air entrained as detrained have differing properties this adjusts the in-cloud wind back towards the large-scale value.
Hence for deep and mid-level convection the turbulent entrainment and detrainment rates used in the updraught momentum equation are
|
(5.46) |
where
is the value of 
in level 
, while 
and 
are given
by equation (5.7).When
(below the mid-level of the cloud) 
, while if
(in the upper part of the cloud) then 
. Gregory (1997)
suggests that the above formulation provides an adequate description of
the effects of cloud scale pressure gradients in cases of deep convection.
For shallow convection and downdraughts it is assumed that the effects of
the pressure gradient term can be neglected and no enhancement of the entrainment
rates in the momentum equations is applied. This formulation limits the
momentum transports to be downgradient. Upgradient transports by highly
organized convective systems (e.g. African squall lines) are not captured
by this method.The definition of the horizontal wind in the updraught and downdraught at cloud base and LFS is not well known. For the updraught the value at cloud base is set to an average of the large-scale winds over the depth of the sub-cloud layer. For the downdraught the initial values at the LFS are set equal to the average values of the winds in the updraught and those of the large-scale flow.
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05.04.2002 |
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