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Statistical Significance of Long-Range “Optimal Climate Normal” Temperature and Precipitation Forecasts

Daniel S. WilksDepartment of Soil, Crop and Atmospheric Sciences Cornell University, Ithaca, New York

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Abstract

A simple approach to long-range forecasting of monthly or seasonal quantities is as the average of observations over some number of the most recent years. Finding this “optimal climate normal” (OCN) involves examining the relationships between the observed variable and averages of its values over the previous one to 30 years and selecting the averaging period yielding the best results. This procedure involves a multiplicity of comparisons, which will lead to misleadingly positive results for developments data. The statistical significance of these OCNs are assessed here using a resampling procedure, in which time series of U.S. Climate Division data are repeatedly shuffled to produce statistical distributions of forecast performance measures, under the null hypothesis that the OCNs exhibit no predictive skill. Substantial areas in the United States are found for which forecast performance appears to be significantly better than would occur by chance.

Another complication in the assessment of the statistical significance of the OCNs derives from the spatial correlation exhibited by the data. Because of this correlation, instances of Type I errors (false rejections of local null hypotheses) will tend to occur with spatial coherency and accordingly have the potential to be confused with regions for which there may be real predictability. The “field significance” of the collections of local tests is also assessed here by simultaneously and coherently shuffling the time series for the Climate Divisions. Areas exhibiting significant local tests are large enough to conclude that seasonal OCN temperature forecasts exhibit significant skill over parts of the United States for all seasons except SON, OND, and NDJ, and that seasonal OCN precipitation forecasts are significantly skillful only in the fall. Statistical significance is weaker for monthly than for seasonal OCN temperature forecasts, and the monthly OCN precipitation forecasts do not exhibit significant predictive skill.

Abstract

A simple approach to long-range forecasting of monthly or seasonal quantities is as the average of observations over some number of the most recent years. Finding this “optimal climate normal” (OCN) involves examining the relationships between the observed variable and averages of its values over the previous one to 30 years and selecting the averaging period yielding the best results. This procedure involves a multiplicity of comparisons, which will lead to misleadingly positive results for developments data. The statistical significance of these OCNs are assessed here using a resampling procedure, in which time series of U.S. Climate Division data are repeatedly shuffled to produce statistical distributions of forecast performance measures, under the null hypothesis that the OCNs exhibit no predictive skill. Substantial areas in the United States are found for which forecast performance appears to be significantly better than would occur by chance.

Another complication in the assessment of the statistical significance of the OCNs derives from the spatial correlation exhibited by the data. Because of this correlation, instances of Type I errors (false rejections of local null hypotheses) will tend to occur with spatial coherency and accordingly have the potential to be confused with regions for which there may be real predictability. The “field significance” of the collections of local tests is also assessed here by simultaneously and coherently shuffling the time series for the Climate Divisions. Areas exhibiting significant local tests are large enough to conclude that seasonal OCN temperature forecasts exhibit significant skill over parts of the United States for all seasons except SON, OND, and NDJ, and that seasonal OCN precipitation forecasts are significantly skillful only in the fall. Statistical significance is weaker for monthly than for seasonal OCN temperature forecasts, and the monthly OCN precipitation forecasts do not exhibit significant predictive skill.

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