Analysis of the Data Assimilation Methods from the Mathematical Point of View

Abstract

The Bayes estimation theory is the mathematical background of the data assimilation methods in meteorology. According to the Bayes theorem, the conditional density function of atmospheric state, given observations and background, can be expressed by the conditional density function of atmospheric state, given background, and the conditional density function of observations, given atmospheric state. Assuming joint normal distribution and certain premise for the conditional expectation of atmospheric state, given background, can be obtained the variation cost function applied at the data assimilation methods. We present some discussion of the above premise for conditional expectation, furthermore some examination of the background and observation error covariance matrices at the cost function. These terms are key issues at the data assimilation methods and we think them to be related to the climate statistical parameters.