Testing Distributed Parameter Hypotheses for the Detection of Climate Change

Haroon S. Kheshgi Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, New Jersey

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Benjamin S. White Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, New Jersey

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Abstract

A general statistical methodology, based on testing alternative distributed parameter hypotheses, is proposed as a method for deciding whether or not anthropogenic influences are causing climate change. This methodology provides a framework for including known uncertainties in the definition of the hypotheses by allowing model parameters to be specified by probability distributions and thereby allowing the definition of more realistic hypotheses. The method can be used to derive the unique statistical test that minimizes errors in test conclusions. The method is applied to illustrative detection problems by first defining alternative hypotheses for global mean temperature; second, deriving the most powerful test and calculating its statistics; third, applying the test to observed temperature records; and finally, illustrating the test statistics and results on a receiver or relative operating characteristic curve showing the relation between false positive and false negative test errors. It is demonstrated, with an illustrative example, that proper accounting for the uncertainty in all the parameters can produce very different statistical conclusions than the conclusions that would be obtained by simply fixing some parameters at nominal values.

Corresponding author address: Dr. Haroon S. Kheshgi, ExxonMobil Research and Engineering Co., Route 22E, Annandale, NJ 08801. Email: hskhesh@erenj.com

Abstract

A general statistical methodology, based on testing alternative distributed parameter hypotheses, is proposed as a method for deciding whether or not anthropogenic influences are causing climate change. This methodology provides a framework for including known uncertainties in the definition of the hypotheses by allowing model parameters to be specified by probability distributions and thereby allowing the definition of more realistic hypotheses. The method can be used to derive the unique statistical test that minimizes errors in test conclusions. The method is applied to illustrative detection problems by first defining alternative hypotheses for global mean temperature; second, deriving the most powerful test and calculating its statistics; third, applying the test to observed temperature records; and finally, illustrating the test statistics and results on a receiver or relative operating characteristic curve showing the relation between false positive and false negative test errors. It is demonstrated, with an illustrative example, that proper accounting for the uncertainty in all the parameters can produce very different statistical conclusions than the conclusions that would be obtained by simply fixing some parameters at nominal values.

Corresponding author address: Dr. Haroon S. Kheshgi, ExxonMobil Research and Engineering Co., Route 22E, Annandale, NJ 08801. Email: hskhesh@erenj.com

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