METEOROLOGICAL DATA PERSPECTIVE
349
current assimilation systems do not generally consider this correlation in the
modelling of the observation-error covariance, because of a lack of accurate
information on the correlation statistics and the technical difficulty of
implementation. Alternatively, most NWP centres tend to use sub-optimal
schemes for which the observation-error covariance matrix is designed to be
diagonal. At the same time, horizontal thinning of remotely sensed
observations is performed in order to reduce their effective error correlation.
Liu and Rabier (2002) have used a simple one-dimensional context to
evaluate the optimal resolution of the observations leading to the best
analysis. The framework is a 1D circle of a length of 8000km, with a gridsize of 100km. Background and observation errors have the same standarddeviation equal to 1 (arbitrary value).The background error correlation
length-scale is taken equal to 200km. The analysis error covariance matrix is
calculated for various observation spacings. Various scenarios were tested:
uncorrelated observation errors and correlated observation errors with a
correlation length of 100km. In the case of correlated observation errors, two
analysis schemes were tested: the optimal one taking into account the proper
observation error covariance matrix and a sub-optimal one neglecting the
observation error correlations (similar to operational practice). Figure 4
shows the analysis error variance resulting from these combinations of
observation density/observation correlation/analysis scheme. The main
results are that, for uncorrelated observation errors, increasing the density
always improves the analysis (dash-dotted line). This is the case even when
the observation density is finer than the background error correlation lengthscale and the analysis mesh. For correlated observation errors, increasing the
observation density beyond a threshold can be harmful in a sub-optimal
scheme for which no correlations are included in the observation error
covariance matrix, as in current systems (dashed line). These results have
been confirmed by a further study in a more realistic 4D context (Liu and
Rabier, 2003) and might explain some of the results found in practical NWP
experience.
It is also found that an optimal thinning of the dataset can extract most of
the information contained in the data, and this approach is the pragmatic one
used in most centres. The “optimal” observation density is usually found by
trial and error. Another ad-hoc approach is to use most of the observations
but to inflate artificially their errors to compensate for their correlations.
More general solutions would of course be preferable. In particular, instead
of performing a thinning of the observations, one might prefer to perform an
averaging of neighbouring observations. The best theoretical framework
might well be to model the correlations in the long term, if feasible.
349
current assimilation systems do not generally consider this correlation in the
modelling of the observation-error covariance, because of a lack of accurate
information on the correlation statistics and the technical difficulty of
implementation. Alternatively, most NWP centres tend to use sub-optimal
schemes for which the observation-error covariance matrix is designed to be
diagonal. At the same time, horizontal thinning of remotely sensed
observations is performed in order to reduce their effective error correlation.
Liu and Rabier (2002) have used a simple one-dimensional context to
evaluate the optimal resolution of the observations leading to the best
analysis. The framework is a 1D circle of a length of 8000km, with a gridsize of 100km. Background and observation errors have the same standarddeviation equal to 1 (arbitrary value).The background error correlation
length-scale is taken equal to 200km. The analysis error covariance matrix is
calculated for various observation spacings. Various scenarios were tested:
uncorrelated observation errors and correlated observation errors with a
correlation length of 100km. In the case of correlated observation errors, two
analysis schemes were tested: the optimal one taking into account the proper
observation error covariance matrix and a sub-optimal one neglecting the
observation error correlations (similar to operational practice). Figure 4
shows the analysis error variance resulting from these combinations of
observation density/observation correlation/analysis scheme. The main
results are that, for uncorrelated observation errors, increasing the density
always improves the analysis (dash-dotted line). This is the case even when
the observation density is finer than the background error correlation lengthscale and the analysis mesh. For correlated observation errors, increasing the
observation density beyond a threshold can be harmful in a sub-optimal
scheme for which no correlations are included in the observation error
covariance matrix, as in current systems (dashed line). These results have
been confirmed by a further study in a more realistic 4D context (Liu and
Rabier, 2003) and might explain some of the results found in practical NWP
experience.
It is also found that an optimal thinning of the dataset can extract most of
the information contained in the data, and this approach is the pragmatic one
used in most centres. The “optimal” observation density is usually found by
trial and error. Another ad-hoc approach is to use most of the observations
but to inflate artificially their errors to compensate for their correlations.
More general solutions would of course be preferable. In particular, instead
of performing a thinning of the observations, one might prefer to perform an
averaging of neighbouring observations. The best theoretical framework
might well be to model the correlations in the long term, if feasible.