Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 261

components are then given by the divergence of those fluxes obtained through
summation of the total momentum flux (i.e. integrated over all phase speed bins)
in each azimuth i projected onto the east and north directions, respectively:

D g @. F E /
@p

@ u

@t

(11.25)

D g @. F N /
@p

@ v

@t

(11.26)

where g is the gravitational acceleration and p is pressure.

Regularization

In order to eliminate the spurious noise in TL computations caused by the
introduction of this scheme, it was necessary to implement some regularizations.
These include rewriting buoyancy frequency (

N

) computations in the NL scheme
in height coordinates instead of pressure coordinates (as used in the original code)
and setting increments for momentum flux in the last three spectral elements (high
phase speed) of the launch spectrum to zero.

11.5.1.5 Moist Convection

The original version of the simplified mass-flux convection scheme currently used
in the minimization of 4D-Var is described in Lopez and Moreau ( 2005 ). Through
time, the original scheme has been updated so as to gradually converge towards
the full convection scheme used in high-resolution 10-day forecasts ( Bechtold et al.
2008 ). The transport of tracers by convection is also implemented.
The physical tendencies produced by convection on any conservative variable

(dry static energy, wind components, specific humidity, cloud liquid water) can be
written in mass-flux form following Betts ( 1997 )

@
@t

D 1 .M u C M d / @

@ z C D u . u / C D d . d /

(11.27)

The first term on the right hand side represents the compensating subsidence induced
by cumulus convection on the environment through the mass flux, . The other

terms account for the detrainment of cloud properties in the environment with a
detrainment rate,

M

refer to the updraughts and downdraughts
properties, respectively. Evaporation of cloud water and precipitation should also be
added in ( 11.27 ) for dry static energy,

D . Subscripts u and d

s D c p T C g z , and specific humidity.