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.