Assimilating Satellite Observations with a Local Ensemble Kalman Filter

Title of dissertation: ASSIMILATING SATELLITE OBSERVATIONS WITH A LOCAL ENSEMBLE KALMAN FILTER Elana Judith Fertig Doctor of Philosophy, 2007 Dissertation directed by: Professor Brian R. Hunt Department of Mathematics Numerical weather prediction relies on data assimilation to estimate the current state of the atmosphere. Generally speaking, data assimilation methods combine information from observations and from a prior forecast state, taking into account their respective uncertainties. Ensemble-based data assimilation schemes estimate the forecast uncertainty with the sample covariance from an ensemble of forecasts. While these schemes have been shown to successfully assimilate conventional observations of model state variables, they have only recently begun to assimilate satellite observations. This dissertation explores some of the complications that arise when ensemble-based schemes assimilate satellite observations. Although ensemble data assimilation schemes often assume that observations are taken at the time of assimilation, satellite observations are available almost continuously between consecutive assimilation times. In Chapter 2, we formulate a “four-dimensional” extension to ensemble-based schemes that is analogous to the operationally used scheme 4D-VAR. Using perfect model experiments with the Lorenz-96 model, we find that the four-dimensional ensemble scheme can perform comparably to 4D-VAR. Many ensemble data assimilation schemes utilize spatial localization so that a small ensemble can capture the unstable degrees of freedom in the model state. These local ensemble-based schemes typically allow the analysis at a given location to depend only on observations near that location. Meanwhile, the location of satellite observations cannot be pinpointed in the same manner as conventional observations. In Chapter 3, we propose a technique to update the state at a given location by assimilating satellite radiance observations that are strongly correlated to the model state there. For satellite retrievals, we propose incorporating the observation error covariance matrix and selecting the retrievals that have errors correlated to observations near the location to be updated. Our selection techniques improve the analysis obtained when assimilating simulated satellite observations with a seven-layer primitive equation model, the SPEEDY model. Finally, satellite radiance observations are subject to state-dependent, systematic errors due to errors in the radiative transfer model used as the observation operator. In Chapter 4 we propose applying state-space augmentation to ensemble based assimilation schemes to estimate satellite radiance biases during the data assimilation procedure. Our approach successfully corrects such systematic errors in simulated biased satellite observations with the SPEEDY model. ASSIMILATING SATELLITE OBSERVATIONS WITH A LOCAL ENSEMBLE KALMAN FILTER