Forecast Skill of Targeted Observations: A Singular-Vector-Based Diagnostic

Abstract

Targeted dropsonde data have been assimilated using the operational ECMWF four-dimensional variational data assimilation (4DVAR) system for 10 cases of the North Pacific Experiment (NORPEX) campaign, and their impact on analyses and corresponding forecasts has been investigated. The 10 fastest-growing ?analysis? singular vectors (SVs) have been used to define a subspace of the phase space where initial conditions are expected to be modified by the assimilation of targeted observing. A linear combination of this vector basis is the pseudoinverse, that is, the smallest perturbation with the largest impact on the forecast error. The dropsonde-induced analysis difference has been decomposed into three initial perturbations, two belonging to the subspace spanned by the leading 10 SVs and one to its complement. Differences and similarities of the three analysis components have been examined, and their impact on the forecast error compared with the impact of the pseudoinverse. Results show that, on average, the dropsonde-induced analysis difference component in the subspace spanned by the leading 10 SVs and the dropsonde-induced analysis difference component along the pseudoinverse directions are very small (6% and 15%, respectively, in terms of total energy norm). In the only case where dropsonde data were exactly released in the area identified by the SVs, the different components of the dropsonde-induced analysis difference and the pseudoinverse had consistent impacts on the forecast error. It is concluded that the poor agreement between the dropsonde location and the SV maxima is the main reason for the relatively small impact of the NORPEX targeting observations on the forecast error.