Proceedings - C-SRNWP Project

COSMO: Overview and Strategy on Data Assimilation for
LM
1. Current Status
Christoph Schraff
DWD, Kaiserlei Str. 29-35, D-63067 Offenbach, Germany
christoph.schraff@dwd.de
The data assimilation for LM is performed by a scheme based on nudging towards direct
observations. It is currently the only scheme implemented in LM and used to compute initial
conditions directly on the model grid. In this technique, a relaxation term is introduced into
the model equations, and the tendency for the prognostic variable ψ(x,t) is given by
∂
ψ ( x,
t)
= F(
ψ , x,
t)
+ Gψ
⋅
∂t
∑
k(
obs )
[ ψ −ψ
( x , )]
W k
⋅ t
(F denotes the model dynamics and physical parameterisations, ψ k the value of the k th
observation influencing the grid point x at time t, x k the observation location, G ψ the constant
nudging coefficient and W k an observation-dependent weight.) Currently, such a relaxation
term is added to the original model equation only for the horizontal wind components,
temperature and specific water vapour content at all model levels and for pressure at the
lowest model level. In the equations above, the observation increments are expressed in terms
of model variables. This can be generalised (at least approximately) to variables that can be
mapped to a single model variable. Thus, observation increments of relative humidity are used
to adjust the model’s specific humidity. The increments from all upper-air observations are
spread laterally along purely horizontal surfaces since spreading along the terrain-following
model levels as usually applied in nudging-type schemes has disadvantages near steep
orography particularly in cases with low stratus (Schraff, 1997). In contrast, surface-level
increments are spread along the model levels to limit the area of influence to close to the
ground. The wind correlations are split into a longitudinal and transverse part, and this allows
for specifying the degree of non-divergence of the wind analysis increment field (Lorenc et
al., 1991). Both the correlation scales for all variables and the degree of non-divergence are
time-dependent and increase with height and with distance to the observation time.
In a plain nudging scheme, balancing between the different model variables occurs implicitly
due to the direct inclusion of the model dynamics and physics in the assimilation process. The
balancing thus induced considers all scales and is flow-dependent, however it is (more or less)
incomplete. To enhance the balancing in the LM scheme, the analysis increment fields from
the plain nudging are partly balanced explicitly in three extra steps before being added to the
model fields. First, a hydrostatic upper-air temperature correction balances the (near-)surface
pressure analysis increments. Approximating statistical background errors for the mesoscale,
it is nearly constant within the lowest 1500 m (therefore hardly modifies the stability within
the boundary layer) and decreases rapidly further above such that the mass field above 400
hPa is not directly modified by the surface pressure nudging. This significantly reduces the
vertical extent of the mass field disturbance, results in a better wind adjustment, and greatly
improves the assimilation of pressure data. Secondly, a geostrophic wind correction partly
balances the mass field increments from the surface pressure nudging. Finally, upper-air
pressure increments balance the total analysis increments hydrostatically in the nonhydrostatic
k
k
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