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Estimating the Time Dependence of Air Temperature Using Daily Maxima and Minima: A Comparison of Three Methods

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  • 1 U.S. Dept. of Agriculture, Agriculture Research Service, St. Paul, Minnesota
  • | 2 U.S. Dept. of Agriculture, Agriculture Research Service, Morris, Minnesota
  • | 3 University of Minnesota, St. Paul, Minnesota
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Abstract

Many models in a variety of disciplines require air temperature throughout the day as an input, yet often the only data available are daily extrema. Several methods for estimating the diurnal change in temperature from daily extrema have been reported. This paper compares the performance of three such algorithms (a sine wave, a sine-exponential, and a linear model) at all times of the year. Each was used to generate four years of hourly temperatures using as input the daily highs and lows recorded by the National Weather Service at the Minneapolis-St. Paul International Airport for the years 1970, 1971, 1973 and 1974. The output from the models was compared with the actual hourly values recorded at the same site. Residual sums and standard errors computed for all three models, both as functions of day and month of the year, showed that all three were more accurate in summer than in winter.

Differences in the overall standard errors of estimate among the three models were small relative to the standard errors themselves. The sinusoidal model was the most accurate of three in predicting midday summer temperatures, suggesting that it would be the best choice for photosynthesis or transpiration models. There was little difference in overall residual sums, indicating equal suitability for use in models driven by accumulated heat units.

Abstract

Many models in a variety of disciplines require air temperature throughout the day as an input, yet often the only data available are daily extrema. Several methods for estimating the diurnal change in temperature from daily extrema have been reported. This paper compares the performance of three such algorithms (a sine wave, a sine-exponential, and a linear model) at all times of the year. Each was used to generate four years of hourly temperatures using as input the daily highs and lows recorded by the National Weather Service at the Minneapolis-St. Paul International Airport for the years 1970, 1971, 1973 and 1974. The output from the models was compared with the actual hourly values recorded at the same site. Residual sums and standard errors computed for all three models, both as functions of day and month of the year, showed that all three were more accurate in summer than in winter.

Differences in the overall standard errors of estimate among the three models were small relative to the standard errors themselves. The sinusoidal model was the most accurate of three in predicting midday summer temperatures, suggesting that it would be the best choice for photosynthesis or transpiration models. There was little difference in overall residual sums, indicating equal suitability for use in models driven by accumulated heat units.

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