Studying the properties of variational data assimilation methods by applying a set of test-examples

The variational data assimilation methods can successfully be used in different fields of science and engineering. An attempt to utilize available sets of observations in the efforts to improve (i) the models used to study different phenomena and/or (ii) the model results is systematically carried out when data assimilation methods are used. The main idea, on which the variational data assimilation methods are based, is pretty general. A functional is formed by using a weighted inner product of differences of model results and measurements. The value of this functional is to be minimized. Forward and backward computations are carried out by using the model under consideration and its adjoint equations (both the model and its adjoint are defined by systems of differential equations). The major difficulty is caused by the huge increase of both the computational load (normally by a factor more than 100) and the storage needed. This is why it might be appropriate to apply some splitting procedure in the efforts to reduce the computational work. Five test-examples have been created. Different numerical aspects of the data assimilation methods and the interplay between the major computational parts of any data assimilation method (numerical algorithms for solving differential equations, splitting procedures and optimization algorithms) have been studied by using these tests. The presentation will include results from testing carried out in the study.