Evaluation and calibration of three models for daily cycle of air temperature

Abstract Three simple empirical models for daily cycle of air temperature were parameterized and evaluated using one- to three-hourly temperature data from one to nine years at five locations in North Carolina. All three models calculate temperatures continuously from daily maximum and minimum temperatures. These models are the sine—exponential model and two versions of sinusoidal models. The sine—exponential model uses a truncated sine function for the day time and an exponential function in the night. The sinusoidal model has a cosine function for the period between times of minimum and maximum temperatures and another cosine function between times of maximum temperature and minimum temperature of the next day. A modified sinusoidal model uses a truncated sine function instead of cosine function for the interval between the times of minimum and maximum temperatures. The models were fitted to temperature data for each location and year by a nonlinear least-squares procedure. They were then evaluated for accuracy and stability in terms of the mean-square error and the variation in parameter estimates over year and location. The sine—exponential model gave the smallest mean-square error for the data tested and the sinusoidal model gave the largest. The least square estimates of parameters for the sine—exponential model had less variation among years than among locations. However, a set of averaged parameters can be used for all locations tested and all years without substantially increasing the error over the best fit model.