[M-GI26] Data assimilation: A fundamental approach in geosciences

[MGI26-03] Including cross correlations between the forecast and observation errors in the ensemble Kalman filter

*Shun Ohishi¹, Yuki Kobayashi², Takemasa Miyoshi¹ (1.RIKEN Center for Computational Science, 2.Kyoto University)

Keywords:Data assimilation, Ensemble Kalman filter, Cross correlation

The Kalman filter is an unbiased minimum variance estimator under an assumption of no cross correlations between the forecast and observation errors. However, some data assimilation systems use observations like satellite retrievals and sea surface temperature analysis data which may not be independent of forecasts, even though the forecasts may come from an independent system. These observations may contain errors correlated with the forecast errors. This study investigates the impact of including cross correlations between the observation and forecast errors in the ensemble Kalman filter by perfect-model twin experiments using the Lorenz-96 model. The observation errors are generated by including the forecast errors, i.e., a mixture of random numbers and the forecast errors in the observation space. We derived the ensemble transform Kalman filter (ETKF) with the cross correlations (ETKFCC) and performed experiments to compare the ETKFCC and the standard ETKF without the cross correlations.
The results show that positive (negative) cross correlations result in lower (higher) analysis accuracy because the forecasts and observations tend to be located on the same (opposite) side relative to the true values for the positive (negative) correlation. The sensitivity experiments demonstrate that the ETKFCC is more accurate than the standard ETKF for both positive and negative correlations.