An Empirical Model of Diurnal Temperature Patterns

Abstract Air temperature is a key driving factor in many crop growth models. Hourly air temperature data required for input are often not available and must be estimated from daily extremes. Several methods to model diurnal patterns exist; all are arbitrary functions of time during the day, chosen to match the daily pattern. Of all possible mathematical shapes, it would be preferable to use the one generated by the data themselves. Thus, our objective was to develop an empirical model to reconstruct the diurnal air temperature curve from measured daily extremes. As usual, temperature was normalized to range from 0 to 1 at the daily extremes. However, we also normalized time, to reduce seasonal variation in the shape of the temperature pattern. Calibration consisted of developing the cumulative distribution function of normalized temperature for a year's data, fitting a beta distribution to the data, and evaluating the 50th percentile, all as a function of time. The resulting vectors of normalized time and air temperature were used to generate diurnal patterns from daily extremes. The model was calibrated with one year's data for each of 14 sites across the USA, and tested for additional years at each site. For the total 32 site‐years, annual mean r 1 ranged from 0.47 to 0.87, with values highest for Arizona sites, intermediate for South Carolina, and lowest for mountainous Idaho sites. Model performance was better than or equal to that of the next‐best model in 16 of 32 site‐years, and also overall. Normalization of both time and temperature produced diurnal air temperature patterns that were sufficiently general to apply with minimal loss of predictive accuracy at widely separate sites in the USA.