A Generalized Method for Generating N-fold Joint Distributions from Observations

Some modeling efforts require high-count random realistic distributions of multiple atmospheric parameters (e.g. to support Monte Carlo techniques). Furthermore, to maintain realism such distributions need to preserve the natural dependencies and relationships between variables; thus multiple singly-generated distributions will not suffice. One could also merely sample directly from the underlying observations, but such a method lacks robustness especially if the number of samples desired greatly exceeds the number of observations. This talk will outline and demonstrate a generalized technique for generating such N-fold joint distributions from observations.

The method is based on inverse transform sampling, whereby a flat random distribution between 0 and 1 is used in conjunction with an empirical cumulative distribution function (CDF) to yield a realistic random sampling of the originating distribution. Though the 1-dimensional application is trivial, complicating aspects present themselves with higher dimensions, both in technique and computational cost. The method presented here collapses a given N-dimensional CDF matrix to a single dimension, performs inverse transform sampling, then recursively expands along each chosen value until a full complement is obtained. The method will be illustrated with a boundary layer application requiring 4-fold joint distributions of turbulence, stability, and wind parameters. The fidelity of the produced distributions to the original will be evaluated. Lastly, a discussion of computational resources and opportunities for improvement will also be included.

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This material is based upon work supported by the Federal Aviation Administration under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Federal Aviation Administration.