Data assimilation represents indispensable tool for numerical weather prediction and
meteorological forecast. The objective of atmospheric data assimilation is to combine our
knowledge of the atmosphere, from both observations and the general principles of
dynamics, in order to predict the future state via numerical integration of the equations of
motion and thermodynamics. In particular, variational data assimilation (4D-Var)
represents an optimization problem, based on finding the best fit between the solution of
a model, a set of observations that the model is meant to predict, and our knowledge of
errors implicit in the model and observations. Mathematically, the problem is poorly
conditioned and underdetermined.
At Surrey, we are conducting research into understanding the effects of the conservation
properties of the variational data assimilation problem, which can be formulated as a
Hamiltonian system. As a part of VISDEM project, which stands for Variational
Inference in Stochastic Dynamic (Environmental) Models, we study data assimilation
problems not only for the deterministic systems, but for systems with stochastic forcing
too. Over few past decades stochastic modeling gained a lot of interest due to the nondeterministic nature of real world. The method devised within VISDEM project combines
stochastic inference with variational data assimilation technique allowing Stochastic
differential equations to be approximated by a known Gaussian process.
Fig. Cost functional for three components Lorenz model.