Polynomial Regression and Serial Ensemble Kalman Filtering

Dan Hodyss* and William F. Campbell, Jeffrey L. Anderson, Nancy Collins
Naval Research Laboratory, Monterey, California
National Center for Atmospheric Research, Boulder, Colorado

It is well-known that the ensemble Kalman filter (EnKF) may be thought of as producing a state estimate that is consistent with linear regression. Here, we will show how polynomial regression of any order can be performed using an EnKF framework. We will prove the remarkable property that an Nth order polynomial regression simply requires N^2 EnKF routine calls. For example, quadratic (N = 2) polynomial regression requires 4 EnKF assimilation routine calls. Clearly this makes an EnKF that performs quadratic polynomial regression 4 times more expensive, but it also shows that configuring an already constructed EnKF to perform polynomial regression is relatively simple. We then will go on to discuss how we added quadratic polynomial regression to the Data Assimilation Research Testbed (DART), and we will illustrate its performance using a hierarchy of models from simple scalar systems to a GCM.

*email: daniel.hodyss@nrlmry.navy.mil
*Preference: Oral