A new formulation of WRFDA analysis control variables

Background error covariance matrix B plays a crucial role in data assimilation. It ensures a balance preserving transfer of observational information to the unobserved parts of a computational domain. Storage and manipulation require reduction of the number of its non-null entries. In general, reduction is ensured via an appropriate diagonalization procedure resulting in a necessity of storing exclusively matrix diagonal terms, alongside the diagonalizing transformation, so that full form of the matrix could be restored whenever required. This transformation has usually some physical foundations and reflects balance expected to be found in nature. Frequently, however, it is identified by means of statistical analysis performed on a time series of model outputs (NMC method). Consequently, definition of control variables for variational data assimilation is based on splitting model variables into balanced and unbalanced contributions. A balanced field represents a fraction of the full field, which can be explained by the means of other control variables. A correlation scheme allowing identification of the balanced fields exists in WRFDA but it does not account for any link between moisture and other control variables. Consequently, incorporating moisture observations in data assimilation procedure modifies exclusively moisture field. Conversely, observations other than humidity do not impact moisture field. To remedy this flaw we report here an attempt of introducing a correlation between moisture and the remaining control variables