Model errors and operational data assimilation

It has been said that the greatest potential benefit of data assimilation lies in the model improvements that can result from it. The process of continuously confronting model output with observations should help to quantify model errors, to identify their causes, and ultimately to improve components of the model. Systematic errors in atmospheric general circulation models are considerable, as manifested by a persistent drift of model forecasts with respect to observations. As a result, various aspects of the model climates are biased in known ways. The rather modest progress that has been made since the 1980's in alleviating these problems can hardly be attributed to advances in data assimilation techniques. Current operational data assimilation systems either represent model errors by extremely simple (stationary, white, and additive) noise processes, or neglect them altogether. In particular, the estimation methods that have been implemented in these systems all assume that models (as well as observations) are unbiased. It is easy to understand that, as a result, assimilated data products inherit elements of the systematic errors of the underlying model. A particularly unhappy consequence for historical reanalysis data sets is that they contain spurious climate trends, induced by the interaction of model errors with changes in the observing system. During the development of the field of data assimilation a great deal of emphasis has been placed on modeling the random components of model error (as represented by error covariances). This in spite of the fact that model developers and users alike prefer to describe model performance in terms of systematic errors. Much more information is actually available about the latter than about random components of model error, and it therefore seems surprising that this is not reflected in the data assimilation techniques that are used in practice. If one can formulate a model for a deterministic component of the model error, then it is possible in principle to derive an estimation procedure for the unknown parameters of such a model. For example, a substantial component of the aggregate model error in atmospheric models is spatially large-scale and varies slowly with time. This component can be readily estimated from available observations in the context of a data assimilation system. One can then attempt to correct the model bias during the assimilation, and in this way reduce the bias in the assimilated data products, as well as the drift in subsequent forecasts. This procedure can be implemented cheaply and yields valuable information about model errors in real-time, consisting of evolving estimates of the bias in each of the model's dependent variables at any location. The next step would be to model, estimate, and correct other known aspects of model error, such as the mean diurnal bias in the lower troposphere. We will illustrate these remarks with some concrete examples, including results obtained with the global atmospheric data assimilation system which is currently operational at NASA's Data Assimilation Office.