SIMULTANEOUS STATE AND PARAMETER ESTIMATION WITH AN ENSEMBLE KALMAN FILTER FOR THERMALLY DRIVEN CIRCULATIONS . PART I : EXPERIMENTS WITH PERFECT PARAMETERS

The effectiveness of the ensemble Kalman filter (EnKF) for a thermally-forced nonlinear two-dimensional sea breeze model is investigated in a perfect-model setting. The model that was developed for this purpose is hydrostatic, non-rotational, and incompressible. Forcing is maintained through an explicit spatially-and diurnally-varied heating function with an added stochastic component. Pure forecast experiments reveal that the model exhibits only modest levels of overall nonlinearity. Strongest nonlinearity coincides with the peak sea breeze phase of the circulation in timing and with the nonlinear sea breeze front spatially. Considerable small-scale error growth occurs at this phase, which is most pronounced for vorticity and vertical motion. Application of data assimilation through an EnKF is observed to successfully remove most of the large-scale phase-difference errors resulting from the climatological initialization method. Even at the first analysis step, domain-averaged error for buoyancy and vorticity is reduced by about 85% and 65%, respectively. Subsequent analyses continue to remove error at an increasingly slower rate and error ultimately saturates within about 24 hours at a level that is determined by observation accuracy. The filter is found to be most sensitive to observation accuracy, observation frequency, and radius of influence while ensemble size has shown significant sensitivity only at smaller numbers of ensemble members. Assimilation of an additional single sounding has also resulted in improved error reduction although the amount of reduction did not seem to be sensitive to the frequency of sounding assimilations.

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