A new method for estimating hourly temperature and degree days

Since biological response to temperature is nonlinear and temperature has a clear daily cycle, it is fundamental to include this systematic temperature variation in the input to agricultural models, such as those describing crop phenology and development based on the accumulation of growing degree days (°D). Although using hourly weather data offers the greatest accuracy for estimating °D, daily maximum (T_x) and minimum (T_n) temperature data are often used to estimate °D by approximating the diurnal temperature trends. This paper presents a new empirical method for estimating hourly mean temperature using the date, latitude, T_x and T_n recorded on the date, and the minimum temperature on the next day (T_p). The temperature model describes the diurnal variation using a sine function from T_n at sunrise until reaching T_x, another sine function from T_x until four hours after sunset, and square root function from then until sunrise the next morning. The model was developed and calibrated using three years of hourly data from five automated weather stations, representing a wide range of climate conditions. The model was tested versus two additional years at each location. The temperature model gave good results with the root mean square error less than 2.0 °C for most years and locations. Degree-day values were calculated using the estimated hourly temperature and using the single-sine and single-triangle methods. The °D estimates calculated with hourly temperature were considerably better than the single-sine and single triangle methods during periods when the threshold temperature was above the daily minimum temperature. The results were similar for all °D calculation methods when the minimum was above the threshold temperature. In all cases, the °D calculation showed a limited accuracy on overcast days.