Background covariance of diagnostic variables describing low-altitude refractivity based on ensembles

In Refractivity Data Fusion (RDF), the Cartesian representation of refractivity calculated from the Numerical Weather Prediction (NWP) output is mapped into a set of 2-dimensional diagnostic variables which are surfaces over the NWP domain. The diagnostic parameters (e.g. duct base height, duct strength, duct thickness, evaporation duct height) include those generated by electromagnetic (EM) inverse problem solutions (e.g. refractivity-from-clutter or “RFC”). RDF produces an analysis of refractivity in the diagnostic space which is then mapped back into Cartesian coordinates for consumption in EM propagation assessment tools used by the Navy to gauge operational sensor performance. A companion presentation describes RDF in more detail.

Performance of RDF's objective analysis requires characterization of background error. The whole set of diagnostic variables used in RDF are not currently used in traditional variational data assimilation. Since the mapping from the space of the NWP output as defined on a Cartesian grid into the space of the diagnostic variables is non-linear, determination of the background error in the diagnostic space cannot be achieved via scaling (i.e., as realized by matrix multiplication).

The Wallops 2000 data set is being used to develop RDF. This data set includes radar clutter data, EM propagation loss measurements and a variety of in situ meteorological observations. We investigate the use of mesoscale NWP ensembles as a means to estimate a background covariance matrix (B) for the Wallops domain. An ensemble Kalman filter (EnKF) extension to the Naval Data Assimilation System (NAVDAS) is used to generate a 32-member ensemble that spans a 168 hour period beginning 28 April to 4 May 2000. Automated routines diagnose the above mentioned parameters from vertical profiles of refractivity calculated from the ensemble members.

To provide a means for examining the fidelity of values based upon the ensembles, we use an ad hoc estimation of the zero-lag (in the horizontal) error correlations for the diagnostic variables. For example, errors such as upward displacement (i.e., layers in the model appear to be upwardly displaced with respect to the observations), with otherwise unchanged air masses above and below the interfacial layer, should result in strong correlations in errors for parameters associated with height.

An elliptical Gaussian spatial correlation coefficient form is assumed. The ensembles are then used to calculate the zero-lag covariance values and those of the spatial correlation coefficients. For the most part, the values of the zero-lag correlation coefficients are close in magnitude and sign to our heuristic estimates. The spatial correlation function has more rapid decorrelation in the direction normal to the coastline (and the Gulf-stream) than in the direction parallel to it. This is likely due to the change in sea surface temperature across the eastern edge of the gulfstream. Ducting may appear in some ensemble members and not in others, or multiple ducts may be present, which complicates the ability to develop a generalized algorithm.