Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 263

Entrainment and Detrainment

Entrainment rate in the updraught ( u ) is split into turbulent and organized com-

ponents, which are both modulated by humidity conditions in the environment.
Detrainment in the updraught (

ı u ) is assumed to occur inside the convective cloud
only where the updraught vertical gradient of kinetic energy and buoyancy are
negative, that is usually in the upper part of the convective cloud.
Entrainment in downdraughts ( d ) is assumed to occur only between the level

of free sinking and the top of the 60 hPa atmospheric layer just above the surface.
Inside this layer, it is set to a constant value. Detrainment (

ı d ) is defined such as to
ensure a downward linear decrease of downdraught mass flux to zero at the surface.

Precipitation Processes

The formation of precipitation from the cloud water contained in the updraught is
parameterized according to Sundqvist et al. ( 1989 ) and a simple representation of
precipitation evaporation is included. Precipitation formed from cloud liquid water
at temperatures below the freezing point is assumed to freeze instantly, which affects
the dry static energy tendency.

Closure Assumptions

One needs to formulate so-called closure assumptions to relate the convective
updraught mass-flux at cloud base,

bas u , to quantities that are explicitly resolved
by the model. For deep convection, the closure is based on the balance between the
convective available potential energy in the subgrid-scale updraught and the total
heat release in the resolved larger-scale environment. The cloud base mass flux is
expressed as the ratio of the latter two quantities, modulated with an adjustment
timescale. This timescale depends on the updraught vertical velocity averaged over
its depth and on spectral truncation. For shallow convection, the closure assumption
links the moist energy excess at cloud base to the moist energy convergence inside
the sub-cloud layer. The ratio of these two quantities yields the cloud base mass flux
for shallow convection.

M

Regularization

Various regularizations need to be applied in the TL and AD code of the convection
scheme to avoid spurious instabilities. These include reducing or setting to zero the
perturbations of some terms that directly depend on the updraught vertical velocity
as well as reducing updraught buoyancy and cloud base mass flux perturbations.