Full 4DVAR posterior error convarinace diagonal matrix

[arango]

Implemented two new options to compute the initial (POSTERIOR_ERROR_I) and final (POSTERIOR_ERROR_F) assimilation time-window posterior error covariance matrix for the W4DPSAS and W4DVAR algorithms. This represents the diagonal elements of the full error analysis covariance matrix. These should be compared to the background error variances (squared standard deviations) for each variable which are specified in the STDnameI, STDnameI, STDnameB, STDnameF input NetCDF files. The analysis error covariance are written to a new NetCDF ERRname which is specified in s4dvar.in. Currently, the analysis error is only possible for a single outer loop, Nouter=1.

The options POSTERIOR_ERROR_I and POSTERIOR_ERROR_F must be run separately and never together. If the POSTERIOR_EOFS option is defined with either of these options, the EOFS of the analysis error covariance matrix at either time are also computed along with the trace estimate. They are saved in the HSSname output NetCDF file.

Warning: The Lib/ARPACK/BLAS and Lib/ARPACK/LAPACK directories were updated to include new files for matrix inversion. Users need to recompile the serial and parallel ARPACK libraries (libarpack.a and libparpack.a).

Many thanks to Andy Moore for his help in developing and testing these new options. We are almost done with all the 4DVAR developments! Very good news indeed...