Observation Influence Diagnostic of a Data Assimilation System - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 104

Moreover, diagnostics may reveal other patterns e.g. that the estimates are based
primarily on a specific sub-set of the data rather than on the majority of the data.
In the context of 4D-Var there are many components that together determine
the influence given to any one particular observation. First there is the specified
observation error covariance R , which is usually well known and obtained simply
from tabulated values. Second, there is the background error covariance B ,which
is specified in terms of transformed variables that are most suitable to describe a
large proportion of the actual background error covariance. The implied covariance
in terms of the observable quantities is not immediately available for inspection,
but it determines the analysis weight given to the data. Third, the dynamics and
the physics of the forecast model propagate the covariance in time, and modify it
according to local error growth in the prediction. The influence is further modulated
by data density. Examples for surface pressure and aircraft wind observations
have been shown indicating that low influence data points occur in data-rich areas
while high influence data points are in data-sparse regions or in dynamically active
areas. Background error correlations also play an important role. In fact, very high
correlations drastically lessen the observation influence (it is halved in the idealized
example presented in Sect. 4.3.3 ) in favour of background influence and amplify
the influence of the surrounding observations. The observation influence pattern of
AMSU-A channel 8 suggests some affectation of the correlation expresses by the B
covariance matrix.
The global observation influence per assimilation cycle has been found to be
18 %, and consequently the background influence is 82 %. Thus, on average the
observation influence is low compared to the influence of the background (the prior).
However, it must be taken into account that the background contains observation
information from the previous analysis cycles. The theoretical information content
(the degrees of freedom for signal) for each of the main observation types was also
calculated. It was found that AMSU-A radiance data provide the most information
to the analysis, followed by IASI, AIRS, Aircraft, GPS-RO and TEMP. In total,
about 20 % of the observational information is currently provided by surface-based
observing systems, and 80 % by satellite systems. It must be stressed that this
ranking is not an indication of relative importance of the observing systems for
forecast accuracy. Nevertheless, recent studies on the 24-h observation impact on the
forecast with the adjoint methodology have shown similar data ranking ( Langland
and Baker 2004 ; Zhu and Gelaro 2008 ; Cardinali 2009 ; Cardinali and Prates 2011 ).
If the influence matrix were computed without approximation then all the
self-sensitivities would have been bounded in the interval zero to one. With the
approximate method used, out-of-bound self-sensitivities occur if the Hessian
representation based on an eigen-vector expansion is truncated, especially when few
eigen-vectors are used. However, it has been shown that this problem affects only a
small percentage of the self-sensitivities computed, and in particular those that are
closer to one.
Self-sensitivities provide an objective diagnostic on the performance of the
assimilation system. They could be used in observation quality control to pro-
tect against distortion by anomalous data; this aspect has been explored by