Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 255

11.4.5 Singular Vectors

Besides the verification of the numerical correctness of TL and AD versions of the
model and the examination of the validity of TL approximation, singular vectors
can be used to find out whether the new schemes do not lead to a growth of spurious
unstable modes. Such modes would indicate the existence of strong non-linearities
and threshold processes in the model and would have a negative impact on the
usefulness of the linearized model.

11.5 ECMWF's Linearized Physics Package

11.5.1 Description

The set of ECMWF physical parameterizations used in the linearized model (called
simplified or linearized parameterizations) comprises six different schemes: radia-
tion, vertical diffusion, orographic gravity wave drag, moist convection, large-scale
condensation/precipitation and non-orographic gravity wave activity, sequentially
called in this order. The current linearized physics package is therefore quite
sophisticated and is believed to be the most comprehensive one used in operational
global data assimilation. Each physical parametrization scheme of this package is
described below starting with dry processes.

11.5.1.1 Radiation

The radiation scheme solves the radiative transfer equation in two distinct spectral
regions. The computations for the longwave (LW) radiation are performed over the
spectrum from 0 to 2,820 cm 1 (100 to 3.5 m). The shortwave (SW) part of the

scheme integrates the fluxes over the whole shortwave spectrum between 0.2 and
4.0

m. The scheme used for data assimilation purposes must be computationally
efficient to be called at full spatial resolution to improve the description of cloud-
radiation interactions during the assimilation period ( Janiskova et al. 2002 ).

The Shortwave Radiation Scheme

The linearized code for the SW radiation scheme has been derived from ECMWF's
original non-linear scheme developed by Fouquart and Bonnel ( 1980 ) and revised by
Morcrette ( 1991 ). In this scheme, previously used in the operational forecast model,
the photon-path-distribution method is applied to separate the parametrization of
scattering processes from that of molecular absorption. Upward F sw and downward