Abstract
It is well known that the ensemble-based variants of the Kalman filter may be thought of as producing a state estimate that is consistent with linear regression. Here, it is shown how quadratic polynomial regression can be performed within a serial data assimilation framework. The addition of quadratic polynomial regression to the Data Assimilation Research Testbed (DART) is also discussed and its performance is illustrated using a hierarchy of models from simple scalar systems to a GCM.
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