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DY: Fachverband Dynamik und Statistische Physik

DY 39: Data Analysis and Stochastic Modeling II (jointly with UP)

DY 39.4: Talk

Thursday, March 17, 2011, 17:45–18:00, ZEU 255

Continuous Time Data Assimilation And Ensemble Generation — •Jochen Bröcker¹ and Ivan G. Szendro² — ¹Max Planck Institut für Physik komplexer Systeme, Dresden, Germany — ²Institut für Theoretische Physik, Universität zu Köln, Germany

Variational data assimilation in continuous time is revisited. Adopting techniques from the theory of optimal nonlinear control, we obtain a continuous time generalisation of what is known as weakly constrained four dimensional variational assimilation (WC–4D–VAR) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two point boundary value problem. For imperfect models, the trade off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. A minimum out of sample error is proposed as a criterion to settle this trade of, i.e. to select an optimal weighting between dynamical and observational error. Even if the model is perfect though, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularise the problem. Finally, we investigate the problem of generating ensemble forecasts by exploiting information obtained from the said boundary value problem.