Incorporating Representativity Error in Data Assimilation
Waller, J.A.1; Nichols, N.K.1; Dance, S.L.1; Lawless, A.S.1; Eyre, J.R.2
1University of Reading, UNITED KINGDOM; 2Met Office, UNITED KINGDOM

Observations used in combination with model predictions for data assimilation can contain information at smaller scales than the model can resolve. Errors of representativity are the result of small scale observational information being incorrectly represented in the model. A better understanding of these errors would allow them to be incorporated into the observation error statistics to provide more accurate analyses and enable us to make better use of available observations.

The research described here is one of the ESA Data Assimilation Projects and its aims are to investigate the structure and properties of representativity errors and to incorporate and assess the impact of these errors in data assimilation. The work is being developed as part of a NCEO PhD project and a NERC CASE Award with the Met Office.

Initially a technique for diagnosing static representativity error covariances has been implemented in which it is assumed that the observations can be written as the mapping of a high resolution state into observation space and that the model state is a truncation of the high resolution state. We have applied this technique to determine the structure of static representativity errors in a nonlinear advection-diffusion model with multi-scale behaviour and have also applied the method to temperature and humidity data from the Met Office UKV system. The results from these experiments have shown that errors of representativity are correlated and are state and time dependent.

From this work we have concluded that although this diagnostic method can be used to reveal the structure of representativity errors, the results are not readily applicable in data assimilation due to the underlying assumptions. We have now developed and tested a new method for diagnosing and incorporating time-dependent representativity error covariances in an ensemble data assimilation system. We recover the true observation error covariance in cases where the initial estimate of the error covariance is incorrect, and also follow time-varying observation error covariances where the length-scale of the true covariance is changing slowly in time. We find also that including the estimated representativity error in the assimilation improves the analysis.