A Mathematical Model for the Generation of Hourly Temperatures

Abstract

A stochastic model for hourly temperatures for Big Spring, Tex., has been developed. The governing parameters were deduced from an 11-year developmental sample, and give hourly temperatures as a function of harmonics representing annual and diurnal variations, and a first-order Markov chain process. The latter incorporates adjustments for the seasonal variation of the serial (hour-to-hour) correlation coefficient, and for the seasonal and diurnal variations of the variability and non-normality of frequency distributions of hourly temperatures. Each of the characteristics is given explicitly as a function of hour of the year. Two 10-year samples were generated and compared to the developmental sample. Criteria were established to determine how well the model duplicates nature. The variability of mean monthly temperature and the frequency of occurrence of low diurnal ranges are underestimated. However, the model gives good estimates of the duration of temperatures below 32°F, and above 65° and 90°F, and of the frequency distribution of monthly 3, 6, 12, 24, 72 and 144 h maximum and minimum temperatures. The general applicability of the model and its utility are discussed. The model could be used to determine the effects of climatic trends, e.g., a gradual cooling, on the average length of the growing season, the mean number of heating/cooling degree days, and other temperature-related parameters.