Estimation of background error correlation functions

The aim of this work is to find optimal error correlation functions that enable 2DVAR to arrive at an analysis that contains as much as possible small-scale information. It is expected that such an improved analysis has little effect on the 2DVAR selection process (step 2), because the ASCAT ambiguities are well defined and limited in number. However, rotating pencil beam scatterometers like SeaWinds and OSCAT have unfavourable measurement geometry at nadir. It has been shown for SeaWinds that the wind product can be improved by using 2DVAR in combination with MSS [Vogelzang et al., 2009]. Under such conditions a more detailed analysis may result in improved ambiguity skill.
For obtaining the background error correlations two methods exist at the moment. The first one is synthetic and employs model predictions at different prediction times to estimate the background error correlations using a procedure similar to Kalman filtering. This method is implemented in a number of NWP models, including that of ECMWF. The second method exploits the fact that the background error correlation equals the correlated differences between observations and background (O-B) when the observation errors are uncorrelated. Hollingsworth and Lönnberg [1986] binned the spatial correlations of radiosonde measurements, extrapolated it to to remove the contribution of the observation error variance, and fitted a Bessel series expansion through the binned values.
In this work an alternative for the second method is given using the fact that scatterometer winds are available on a dense and regular grid. This allows direct solution of the differential equations that relate the autocorrelation of the background errors to the error correlation functions.