Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 247

are explained. The implications of the linear constraint for any parametrization
schemes, such as simplification and regularization are described in Sect. 11.3 .The
methodology for the development of linearized simplified parameterizations is
provided in Sect. 11.4 . To fully appreciate the achieved level of sophistication of
the linearized physical parametrization schemes used at ECMWF, which can still be
integrated even over 48 h on the global scale without producing spurious noise, each
of them is described in Sect. 11.5 . The impact of different physical processes on the
tangent-linear approximation, adjoint sensitivity, as well as the performance in data
assimilation are demonstrated in Sect. 11.6 . Finally, conclusions and perspectives
are given in Sect. 11.7 .

11.2 The Need for Physics in Variational Data Assimilation

Two main reasons can justify the need for linearized physical parameterizations in
variational data assimilation.
The first one lies in the necessity to compute model-observation departures at
a given time, so that the variational cost function can be minimized. For instance,
if satellite microwave brightness temperatures are to be assimilated, one must be
able to translate the model control variables (typically temperature, humidity, wind
and surface pressure) into some equivalent simulated brightness temperatures. In
this example, this can be achieved by applying moist physics parameterizations to
simulate cloud and precipitation fields first, and then a radiative transfer model to
obtain the desired microwave brightness temperatures, as seen by the model. The
goal of data assimilation is to define the atmospheric state such that the mismatch
between the model and observations (or cost function, ) is minimum. To minimize

the cost function for obtaining the optimal increments in each model state vector
component, its gradient with respect to model variables needs to be assessed. In
the chosen example of microwave brightness temperatures, this would be achieved
by applying the adjoint of the radiative transfer model followed by the adjoint of
the moist physical parameterizations to the gradient of

J

in observation space. The
adjoint of a given operator is simply the transpose of its Jacobian matrix with respect
to its input variables.
Secondly, in the particular context of 4D-Var data assimilation, the model state
needs to be compared to each available observation at the time the latter was
performed. It is therefore necessary to evolve the model state from the beginning
of the 4D-Var assimilation window (time 0) to the time of the observation (time

J

i ).

This is achieved by integrating the full non-linear (NL) forecast model, M , from

time 0 to , which measures

the total distance between the model and all observations available throughout the
assimilation window, requires the computation of its gradient, r x .t 0 / J

i . Again, the minimization of the 4D-Var cost function, J

with respect
to the model state at the beginning of the 4D-Var assimilation window, x .t 0 / .

To achieve this, the gradient of the observation term, J o , of the cost function in

observation space can be first computed through simple differentiation as