From Model Based Parameterizations to Lookup Tables: An EOF Approach by Leoncini, Pielke Sr. and Gabriel

We have a new research paper that demonstrates an important new way to implement parameterizations within weather and climate models. This paper also illustrates that parameterizations need not be basic physic-based approaches to be as useful when applied to represent the aggregate effect of physical processes. The paper is

 Leoncini, G., R.A. Pielke Sr., and P. Gabriel, 2008: From model based parameterizations to Lookup Tables: An EOF approach. Wea. Forecasting, DOI: 10.1175/2008WAF2007033.1, in press.

Abstract
The goal of this study is to transform the Harrington radiation parameterization into a transfer scheme or lookup table, which provides essentially the same output (heating rate profile and short and longwave fluxes at the surface) at a fraction of the computational cost. The methodology put forth here does not introduce a new parameterization simply derived from the Harrington scheme, but shows that given a generic parameterization it is possible to build an algorithm, largely not based on the physics, that mimics the outcome of the parent parameterization. The core concept is to compute the Empirical Orthogonal Functions of all the input variables of the parent scheme, run the scheme on the EOFs, and express the output of a generic input sounding exploiting the input-output pairs associated to the EOFs. The weights are based on the difference between the input and EOFs water vapor mixing ratios. A detailed overview of the algorithm and the development of a few transfer schemes are also presented. Results show very good agreement (r > 0.91) between the different transfer schemes and the Harrington radiation parameterization with a very significant reduction in computational cost (at least 95%).

Conclusions
In this study a methodology to develop a LUT [Look-Up-Table] or TS [Transfer Scheme] from a parameterization has been presented. It is important to further clarify that this work does not introduce a new parameterization simply derived from a preexisting one, but reduces a parameterization to a TS, whose core concept is to compute the EOFs of the parent scheme input variables, under clear sky conditions, and run it on the EOFs. Then the TS output of a generic input is a weighted average of the EOFs output, where the weights are based on a form of distance between the input and each individual EOF. Several TS have been develop for the Harrington radiation scheme under clear sky conditions, by using different EOFs and their errors have been thoroughly analyzed, as well as their computational speed. The errors with respect to the parent parameterization, at times can be larger than what is commonly accepted as error for a radiation parameterization compared against a line-by-line code, but this kind of analysis has not been published for the HS, as well as for other mesoscale schemes, at least for the clear sky case. Therefore it is not possible to know with certainty the error introduced with the TS and it is suggested that a different weighting strategy is very likely to improve the shortwave flux errors. Furthermore once the best TS has been implemented into RAMS the meteorological fields after a two-day simulation show a good agreement with the parent scheme and a comparison against the meteorological fields obtained by use of the Chen-Cotton scheme indicates that the uncertainties introduced by the TS, as compared with the HS are less significant than the ones due to the second scheme. Finally the calculations necessary for the TS are carried out at a fraction of the original cost.

While this study is limited to the Harrington radiation parameterization, it is reasonable to believe that the same methodology can be extended to a cloudy sky and applied to other parameterizations with similar results as first envisioned in Pielke et al. (2006).

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