Detecting Dependence in the Sensitive Parameter Space of a Model Using Statistical Inference and Large Forecast Ensembles

J. G. McLay Naval Research Laboratory, Monterey, California

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M. Liu Naval Research Laboratory, Monterey, California

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Abstract

This study looks for evidence of correlation among model physical parameters in the sensitive parameter space defined by those randomly sampled physical parameter vectors that induce the most notable response in some forecast metric. These “sensitive parameter vectors” are identified through an ensemble methodology. The correlation analysis is facilitated by two established techniques from statistical inference theory. The random parameter vectors are found to induce a considerable range of forecast responses in terms of five metrics, such as bias and variance. The metrics enable measurement not only of the biggest forecast response but also of the most beneficial forecast response (e.g., in terms of reduction of forecast error). For most metrics, multiple parameter pairs exhibit significantly more correlation than would be expected from random sampling processes. The correlations frequently involve parameters from two different physical routines. These inference results are independently supported by a Monte Carlo simulation. The results suggest that correlations among parameters must be taken into account in order to gain the most response from a model when carrying out parameter variation experiments. Also, they reinforce the idea that parameter estimation efforts need to be expanded so that they simultaneously estimate the joint distribution of parameters across multiple physical routines.

Corresponding author address: J. G. McLay, Naval Research Laboratory, Stop 2, 7 Grace Hopper Ave., Monterey, CA 93943. E-mail: justin.mclay@nrlmry.navy.mil

Abstract

This study looks for evidence of correlation among model physical parameters in the sensitive parameter space defined by those randomly sampled physical parameter vectors that induce the most notable response in some forecast metric. These “sensitive parameter vectors” are identified through an ensemble methodology. The correlation analysis is facilitated by two established techniques from statistical inference theory. The random parameter vectors are found to induce a considerable range of forecast responses in terms of five metrics, such as bias and variance. The metrics enable measurement not only of the biggest forecast response but also of the most beneficial forecast response (e.g., in terms of reduction of forecast error). For most metrics, multiple parameter pairs exhibit significantly more correlation than would be expected from random sampling processes. The correlations frequently involve parameters from two different physical routines. These inference results are independently supported by a Monte Carlo simulation. The results suggest that correlations among parameters must be taken into account in order to gain the most response from a model when carrying out parameter variation experiments. Also, they reinforce the idea that parameter estimation efforts need to be expanded so that they simultaneously estimate the joint distribution of parameters across multiple physical routines.

Corresponding author address: J. G. McLay, Naval Research Laboratory, Stop 2, 7 Grace Hopper Ave., Monterey, CA 93943. E-mail: justin.mclay@nrlmry.navy.mil
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