Assimilating Observations with Correlated Errors in an Ensemble Kalman Filter

Abstract:

Ensemble data assimilation systems for large geophysical problems like the atmosphere and ocean
often ignore the possibility of correlated errors between observations at different spatio-temporal
locations. However, most instruments are known to have correlated errors. The correlated
errors can range from simple time-averaged bias to complicated functions of both the state of
the geophysical system and the observation geometry for instruments like satellite radiometers.
One possible solution is to construct a statistical model that predicts the correlated part of
the error for a given instrument and remove the estimated error before assimilation. Here, a
complementary approach is studied in which differences between correlated observations are
assimilated rather than the raw observations. The details of the ways in which observations are
paired for differences can have a significant impact on the quality of the resulting assimilation.
Pairings in which a given observation is used in more than one difference lead to correlated
errors in the resulting difference observations but may retain more information content.
Low-order model results comparing assimilation of raw observations with correlated errors to
assimilations of various types of differences are presented. The potential impact for ensemble
assimilation of remote sensing observations is discussed.
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