Why couple ensemble forecasting and data assimilation? A primary goal of ensemble forecasting is predicting the uncertainty of the forecast. Data assimilation, a statistical procedure, requires information about the uncertainty of the forecast in order to determine how much new observations should correct the background (the first guess forecast). Currently, the error statistics used in data assimilation make several restrictive assumptions; for example, the influence of an observation may be felt equally in all directions from an observation, and/or the errors of the forecast are not presumed to be related to the flow of the day, i.e., whether the weather is locally stormy or quiescent.
Properly constructed ensembles of forecasts can provide forecast error statistics will vary from day to day and location to location, resulting in different utilization of similar type observations in different locations. For example, the uncertainty of the forecast may be larger near to a front than in the middle of an air mass, and errors may be correlated more along the front than transverse to it. Error statistics derived from ensemble forecasts may recognize this, providing a stronger fit to the observations near fronts, with corrections to the background stretched out along the front.
We provide a review of data assimilation starting from the first principles of Bayesian statistics. We demonstrate that for ensemble forecasts to be most useful for data assimilation, they should be specially constructed to provide information on short-range forecast errors. We review some of the more suggestive results to date as well as indicate areas requiring more research.