Comparing Two Approaches for Assessing Observation Impact

Langland and Baker introduced an approach to assess the impact of observations on the forecasts. In that approach, a state-space aspect of the forecast is defined and a procedure is derived ultimately relating changes in the aspect with changes in the observing system. Some features of the state-space approach are to be noted: the typical choice of forecast aspect is rather subjective and leads to incomplete assessment of the observing system, it requires availability of a verification state that is in practice correlated with the forecast, and it involves the adjoint operator of the entire data assimilation system and is thus constrained by the validity of this operator. This article revisits the topic of observation impacts from the perspective of estimation theory. An observation-space metric is used to allow inferring observation impact on the forecasts without the limitations just mentioned. Using differences of observation-minus-forecast residuals obtained from consecutive forecasts leads to the following advantages: (i) it suggests a rather natural choice of forecast aspect that directly links to the data assimilation procedure, (ii) it avoids introducing undesirable correlations in the forecast aspect since verification is done against the observations, and (iii) it does not involve linearization and use of adjoints. The observation-space approach has the additional advantage of being nearly cost free and very simple to implement. In its simplest form it reduces to evaluating the statistics of observationminus-background and observation-minus-analysis residuals with traditional methods. Illustrations comparing the approaches are given using the NASA Goddard Earth Observing System.