Evolution of Analysis Error and Adjoint-Based Sensitivities: Implications for Adaptive Observations

Abstract

The structure and evolution of analysis error and adjoint-based sensitivities [potential enstrophy initial singular vectors (SVs) and gradient sensitivities of the forecast error to initial conditions] are compared following a cyclone development in a three-dimensional quasigeostrophic channel model. The results show that the projection of the evolved SV onto the forecast error increases during the evolution. Based on the similarities of the evolved SV to the forecast error, use of the evolved SV is suggested as an adaptive observation strategy. The use of the evolved SV strategy for adaptive observations is evaluated by performing observation system simulation experiments using a three-dimensional variational data assimilation scheme under the perfect model assumption. Adaptive strategies using the actual forecast error, gradient sensitivity, and initial SV are also tested. The observation system simulation experiments are implemented for five simulated synoptic cases with two different observation spacings and three different configurations of adaptive observation location densities (sparse, dense, and mixed), and the impact of the adaptive strategies is compared with that of the nonadaptive, fixed observations. The impact of adaptive strategies varies with the observation density. For a small number of observations, several of the adaptive strategies tested reduce forecast error more than the nonadaptive strategy. For a large number of observations, it is more difficult to reduce forecast errors using adaptive observations. The evolved SV strategy performs as well as or better than the adjoint-based strategies for both observation densities. The impact of using the evolved SVs rather than the adjoint-based sensitivities for adaptive observation purposes is larger in the situation of a large number of observation stations for which the forecast error reduction by adjointbased adaptive strategies is difficult.