Data Assimilation, Adaptive Observations and Applications

Abstract

Sensitivity analysis, data assimilation and targeting observation strategies are methods that are applied to various complex mathematical models of fluid dynamics. In this research we investigate new directions to improve on the current strategies used to deploy additional observational resources (targeting strategies) for data assimilation in dynamical systems of fluid mechanics. Targeting strategies aim to determine optimal locations where additional observations will improve the solution of the data assimilation process by identifying regions where state errors in the model have a high potential to grow. Properly accounting for nonlinear error growth is an unresolved issue in targeted observations for numerical weather prediction (NWP). A novel observation-targeting approach based on derivative information from a second order adjoint (SOA) model is proposed to account for the quadratic initial-condition error growth in the model forecasts. Preliminary numerical experiments performed with a two-dimensional shallowwater model indicate that the SOA methodology is effective and may outperform the traditional first-order adjoint approach to targeted observations. Further experiments are required to validate this methodology in realistic NWP models. The impact of model errors on the targeting strategy is also investigated. The motivation being to investigate the validity of the common assumption made to facilitate the practical implementation of 4D-Var, namely that the model representing the dynamical system is perfect. This assumption is not generally valid in real life since representation and numerical errors are present in the models. To asses the impact of model errors in the singular vectors targeting strategy, the derivatives of the singular vectors with respect to the tangent linear model are used. Numerical experiments with a shallow water model show that the derivatives provide a first order approximation to the expected change in the sensitivity fields due to perturbations in the model. Additionally, a parametric sensitivity analysis of a new resolving cloud-aerosol model is presented. This cloud model has smooth dependence on input parameters and data, enabling the computation of derivatives and thus a more amenable sensitivity analysis. The relationship between a key parameter and model output is explored and analyzed.