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Add Scale/Variable/Time-Dependent Localization for EnVar #459
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…EnVar (#460) This PR is to add Scale/Variable/Time-Dependent Localization (SDL/VDL/TDL) for GSI EnVar. #459. I checked that it is possible to run regional SDL and VDL and to obtain reasonable results in single observation tests and RRFS cycle tests on Orion. I haven't run global DA tests and GSI's regression tests. (The regression tests are not probably setup on Orion.) Co-authored-by: Sho Yokota <syokota@Orion-login-1.HPC.MsState.Edu>
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Scale-Dependent Localization (SDL) is developed here. In SDL, ensemble perturbations structuring ensemble B are divided into multiple scales, and different localization scales are applied to the divided ensemble perturbations. It is expected to be able to use the larger localization scale for large-scale ensemble perturbations even with limited ensemble size. To this end, the dimension of arrays of ensemble perturbations and control variables are extended. Recursive filter is used for dividing into multiple scales here. (For horizontal smoothing in the global application, spectral filter is also used.) Variable-Dependent Localization (VDL) and Time-Dependent Localization (TDL) are also implemented together using this extend of control variables.
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