Data Assimilation Meetings at Reading

Date Meeting type Speakers
25 March 2015
Agric 1L14
Internal speaker Adam El-Said (Univeristy of Reading)
Conditioning of the weak-constraint 4DVAR problem
Data assimilation merges observations with a dynamical model to find the optimal state estimate of a system given a set of observations. It is cyclic in that it is applied at fixed time intervals and the beginning of each cycle incorporates a forecast from the previous cycle known as the background or apriori estimate. Variational data assimilation aims to minimise a non-linear, least-squares objective function that is constrained by the flow of the (perfect) dynamical model, better known as 4DVAR. Relaxing the perfect model assumption gives rise to weak-constraint 4DVAR, which has two formulations of interest. Gradient-based iterative solvers are used to solve the 4DVAR problem operationally, so we focus on these techniques for the weak-constraint 4DVAR problem. We gain insight into the sensitivities of the problems to initial data, as well as the accuracy and convergence characteristics by studying the condition number of the Hessian of both formulations. We present new theoretical bounds on the condition number of the Hessians of both these formulations. The sensitivities obtained from the theoretical bounds are demonstrated using the linear advection equation. By analysing the bounds and demonstrating the found sensitivities on the linear advection model, we show that these sensitivities also extend to a nonlinear chaotic model such as the Lorenz-95 model.

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