Tangent linear approximation based observation data impact estimation in 4D‐Var

In variational data assimilation systems (variational DASs), the effect of each assimilated observation dataset on an analysis field is one of the main factors in determining analysis and succeeding forecast accuracy. We call the effects ‘observation impacts’. However, the estimation of the observation impacts is difficult because variational DASs do not construct the Kalman gain that fully determines them. Therefore, all known methods for the estimation have some shortcomings. We construct a new method for the observation impact estimation. The method estimates the observation impacts as a partial analysis increment vector (PIV) that is generated by each observation dataset. For real calculation of the PIVs, we introduce partial departure vectors. The method enables us to see how the Kalman gain transforms information of observations into analysis increments. The method can also estimate the observation impacts on a forecast field while the tangent linear approximation of a forecast model is valid. Comparisons of formulations of three types of the known methods with the new method clarify the origins of nonlinear interactions between observation impacts in the known methods. We perform a preliminary experiment of one analysis cycle on the global variational DAS of the Japan Meteorological Agency to demonstrate the validity and performance of the method. Observation data are divided into satellite radiance and other conventional data, and the latter are further divided into rawinsondes, satellite winds, and the others. The experimental results are as follows: (i) the method can identify the observation impacts of each observation dataset on an analysis and a forecast field in the operational variational DAS, (ii) there are negative correlations between an integrated background error vector and dominant PIVs, and (iii) the nonlinear interactions between observation impacts in the known methods can be estimated quantitatively. The method is useful for observational data impact estimation in variational DASs.