Accounting for Missing Data in Sparse Wavelet Representation of Observation Error Correlations

One of the problems in numerical weather prediction is the determination of the initial state of the system. Indeed, the true state of the atmosphere and ocean, at a given moment and in all points of space, are not accessible. In order to retrieve an optimal initial condition one uses the so called data assimilation methods that combine information from observations, model equations and their respective error statistics.Since the late 70s, in numerical weather prediction, a dominant source of information comes from many satellites. Errors associated to such data are highly correlated in space, which can be detrimental if this is not properly accounted for. However their density in space allows for the efficient use of multi-scale transformation, which in turn permit a cheap but good approximation of said error statistics representation. The drawback of such approach is that the angling of missing data may not be trivial, the aim of this paper is to propose possible solutions to overcome this problem