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On the Estimation of Daily Climatological Temperature Variance

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  • 1 Prescient Weather Ltd., State College, Pennsylvania
  • 2 NOAA/National Centers for Environmental Information, Asheville, North Carolina
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Abstract

The climatological daily variance of temperature is sometimes estimated from observed temperatures within a centered window of dates. This method overestimates the true variance of daily temperature when the rate of seasonal temperature change is large, because the seasonal change within the date window introduces additional variance. The contribution of the seasonal change may be removed by performing the variance calculation using daily temperature anomalies, leading to a bias-free estimate of variance.

The difference between the variance estimation methods is illustrated using both idealized simulations of temperature variability and observed historical temperature data. The simulation results confirm that removing the climatological temperature cycle eliminates bias in the variance estimates. For several U.S. midlatitude locations, the difference in estimated standard deviation of daily mean temperature is on the order of a few percent near the seasonal peaks in climatological temperature change, but the maximum difference is larger in highly continental climates. These differences are shown to be significant when estimating the probability of temperature extremes under the assumption of a Gaussian distribution.

Corresponding author address: Richard P. James, Prescient Weather Ltd., 200 Innovation Blvd., Ste. 229, State College, PA 16803. E-mail: richard.james@prescientweather.com

Abstract

The climatological daily variance of temperature is sometimes estimated from observed temperatures within a centered window of dates. This method overestimates the true variance of daily temperature when the rate of seasonal temperature change is large, because the seasonal change within the date window introduces additional variance. The contribution of the seasonal change may be removed by performing the variance calculation using daily temperature anomalies, leading to a bias-free estimate of variance.

The difference between the variance estimation methods is illustrated using both idealized simulations of temperature variability and observed historical temperature data. The simulation results confirm that removing the climatological temperature cycle eliminates bias in the variance estimates. For several U.S. midlatitude locations, the difference in estimated standard deviation of daily mean temperature is on the order of a few percent near the seasonal peaks in climatological temperature change, but the maximum difference is larger in highly continental climates. These differences are shown to be significant when estimating the probability of temperature extremes under the assumption of a Gaussian distribution.

Corresponding author address: Richard P. James, Prescient Weather Ltd., 200 Innovation Blvd., Ste. 229, State College, PA 16803. E-mail: richard.james@prescientweather.com
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