ABSTRACT
When first introduced, data assimilation methods were referred to as “objec-
tive analyses” (see, e.g., ref. [40] and [11]), to contrast them to “subjective
analyses,” in which numerical weather predictions (NWP) forecasts were ad-
justed “by hand” by meteorologists, using their professional expertise. Subse-
quently, methods called “nudging” were introduced based on the simple idea
of Newtonian relaxation. In nudging, the right side of the model’s dynamical
equations is augmented with a term which is proportional to the difference be-
tween the calculated meteorological variable and the observation value. This
term keeps the calculated state vector closer to the observations. Nudging can
be interpreted as a simplified Kalman-Bucy filter with the gain matrix be-
ing prescribed rather than obtained from covariances. The nudging method is
used in simple operational global-scale and meso-scale models for assimilating
small-scale observations when lacking statistical data. The recent advances in
nudging methods are briefly presented in Section 4.1.
