Geoscience Reference
In-Depth Information
Chapter 4
Observation Influence Diagnostic of a Data
Assimilation System
Carla Cardinali
Abstract The influence matrix is used in ordinary least-squares applications for
monitoring statistical multiple-regression analyses. Concepts related to the influence
matrix provide diagnostics on the influence of individual data on the analysis,
the analysis change that would occur by leaving one observation out, and the
effective information content (degrees of freedom for signal) in any sub-set of
the analysed data. In this paper, the corresponding concepts are derived in the
context of linear statistical data assimilation in Numerical Weather Prediction. An
approximate method to compute the diagonal elements of the influence matrix
(the self-sensitivities) has been developed for a large-dimension variational data
assimilation system (the 4D-Var system of the European Centre for Medium-Range
Weather Forecasts). Results show that, in the ECMWF operational system, 18 % of
the global influence is due to the assimilated observations, and the complementary
82 % is the influence of the prior (background) information, a short-range forecast
containing information from earlier assimilated observations. About 20 % of the
observational information is currently provided by surface-based observing systems,
and 80 % by satellite systems.
A toy-model is developed to illustrate how the observation influence depends
on the data assimilation covariance matrices. In particular, the role of high-
correlated observation error and high-correlated background error with respect to
uncorrelated ones is presented. Low-influence data points usually occur in data-rich
areas, while high-influence data points are in data-sparse areas or in dynamically
active regions. Background error correlations also play an important role: high
correlation diminishes the observation influence and amplifies the importance of the
surrounding real and pseudo observations (prior information in observation space).
To increase the observation influence in presence of high correlated background
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