Model Representation Error Estimation

Jim Richman


The difference between observations and a model simulation can be decomposed into instrument error, model forecast error and representation error. A major challenge for data assimilation is the accurate characterization of these errors. We have developed a technique which identifies the information content of a model. We use a long simulation to formulate a basis for a reduced state space of the model as determined by our metric for the information content. The projection of a sequence of model-data misfits into the reduced model state space can be used to estimate the model forecast errors. The estimate, so obtained, is analogous to the estimate obtained by ensemble methods. The remainder of the misfits, which have no projection on the model state space, can be assigned to the model representation error and instrument error. We separate representation error from instrument error through the further assumption that instrument error is white in time and uncorrelated in space. We test our construction using a coarse resolution ocean general circulation model and satellite observations of sea surface height and temperature. Our construction of the representation error differs from the recent re-mapping technique presented by Oke and Sakov (2008) by explicitly including error of unrepresented physics of the model. We generate a Monte-Carlo realization from our representation error maps, which, when combined with optimal interpolation analysis increments, has a probability density function indistinguishable from the probability density function of the actual model-data misfits. A preliminary application of the approach to a 16 year free run of the ocean component of the NCEP Climate Forecast System will be presented.