Data assimilation in the presence of forecast bias

Statistical analysis methods are generally derived under the assumption that forecast errors are strictly random and zero in the mean If the short term forecast used as the background eld in the statistical analysis equation is in fact biased so will the resulting analysis be biased The only way to properly account for bias in a statistical analysis is to do so explicitly by estimating the forecast bias and then correcting the forecast prior to analysis We present a rigorous method for estimating forecast bias by means of data assimilation based on an unbiased subset of the observing system The result is a sequential bias estimation and correction algorithm whose implementation involves existing components of operational statistical analysis systems The algorithm is designed to perform on line in the context of suboptimal data as similation methods which are based on approximate information about forecast and observation error covariances The added computational cost of incorporat ing the algorithm into an operational system roughly amounts to one additional solution of the statistical analysis equation for a limited number of observa tions O line forecast bias estimates based on previously produced assimilated data sets can be produced as well using an existing analysis system We show that our sequential bias estimation algorithm ts into a broader theoretical framework provided by the separate bias estimation approach of estimation theory In this framework the bias parameters are de ned rather generally and can be used to describe systematic model errors and observational bias as well We illustrate the application of on line forecast bias estimation and correction in a simulated data assimilation experiment with a one dimensional forced dissipative shallow water model A climate error is introduced into the forecast model via topographic forcing while random errors are generated by stochastic forcing In this simple experiment our algorithm is well able to estimate and correct the forecast bias caused by this systematic error and the climate error in the assimilated data set is virtually eliminated as a result