Mathematical approach to the performance evaluation of three dimensional variational data assimilation

We analyse and discuss the performance of a decomposition approach introduced for solving large scale Variational Data Assimilation (DD-VAR DA) problems. Our performance analysis uses a set of matrices (decomposition and execution)[9], built to highlight the dependency relationship among component parts of a computational problem and/or among operators of the algorithm that solves the problem [10?], that are the fundamental characteristics of an algorithm. We will show how performance metrics depend on the complexity of the algorithm and on parameters characterizing the structure of the two matrices, like their number of rows and columns. We use a new definition of speed up, involving the scale-up factor which measure the performance gain in terms of time complexity reduction, to describe the non-linear behavior of the performance gain.