Variational data assimilation with two-dimensional shallow water equations and three-dimensional Florida State University global spectral models

This thesis investigates the feasibility of the 4-D variational data assimilation (VDA) applied to realistic situations and improves existing large-scale unconstrained minimization algorithms. It first develops the second order adjoint (SOA) theory and applies it to a shallow-water equations (SWE) model on a limited-area domain to calculate the condition numbers of the Hessian. Then the Hessian/vector product obtained by the SOA approach is applied to one of the most efficient minimization algorithms, namely the truncated-Newton (TN) algorithm. The newly obtained algorithm is applied here to a limited-area SWE model with model generated data where the initial conditions serve as control variables.;Next, the thesis applies the VDA to an adiabatic version of the Florida State University Global Spectral Model (FSUGSM). The impact of observations distributed over the assimilation period is investigated. The efficiency of the 4-D VDA is demonstrated with different sets of observations.;In all of the previous experiments, it is assumed that the model is perfect, and so is the data. The solution of the problem will have a perfect fit to the data. This is of course unrealistic.;The nudging data assimilation (NDA) technique consists in achieving a compromise between the model and observations by relaxing the model state towards the observations during the assimilation period by adding a non-physical diffusion-type term to the model equations. Variational nudging data assimilation (VNDA) combines the VDA and NDA schemes in the most efficient way to determine optimally the best conditions and optimal nudging coefficients simultaneously. The humidity and other different parameterized physical processes are not included in the adjoint model integration. Thus the calculation of the gradients by the adjoint model is approximate since the forecast model is used in its full-physics (diabatic) operational form.