A multiple length scale correlation operator for ocean data assimilation

Ocean data assimilation systems can take into account time and space scale variations by representing background error covariance functions with more complex shapes than the classical Gaussian function. In particular, the construction of the correlation functions can be improved to give more flexibility. We describe a correlation operator that features high correlations within a short scale and weak correlations within a larger scale. This multiple length scale correlation operator is defined as a linear combination of Whittle–Matérn functions with different length scales. The main characteristics of the resulting correlation function are described. In particular, a focus is given on features that might be of interest to determine the parameters of the model: the Daley length scale, the normalised spectrum inflexion point and the kurtosis coefficient.

The multiple length scale operator has been implemented in NEMOVAR, a variational ocean data assimilation system. A dual length scale formulation was tested in a one-year reanalysis and compared with a single length scale formulation. The results emphasise the importance of estimating with great care the factors used within the combination. They also demonstrate the potential of the dual length scale formulation, in particular through a decrease of the innovation statistics for salinity profiles. The dual length scale formulation is now operational at the Met Office.