Time Series Analysis of Daily Solar Radiation and Air Temperature Measurements for Use in Computing Potential Evapotranspiration

Abstract

ABSTRACT THE bivariate relationships between daily maximum, minimum, or average air temperatures and solar radiation were examined using time series analysis techniques. The data utilized in the analysis consisted of 1096 daily observations of the four variables taken near Arvin in the San Joaquin Valley, California, for the years 1959-1961. Spectral analysis procedures were used to determine the relationships between the deterministic frequency components of each temperature series and the corresponding components of the solar radiation series. The annual cycle (frequency = 2TT/365 radians/day) and the semi-annual cycle (frequency = 4n/365 radians/day) were found to contribute the most to the variance of all four series. At these two frequencies, the coherence between each temperature series and the solar radiation series was = 1.00. After removing these deterministic cyclic components, Box-Jenkins transfer function modelling techniques were utilized to derive the relationships between the residuals of each temperature series and the solar radiation series. The transfer functions developed were utilized, in conjunction with the results of the spectral analysis, to yield relations for estimating the solar radiation series from each temperature series. The residual variance of the estimates obtained using these relations were compared to those derived by the linear regression equations of the solar radiation on each temperature variable. The residual variance of the estimates were 4819.5, 5752.0, and 5700.2 respectively, when using the transfer function relations with the maximum, minimum, and average tempreature as input. These values were substantially lower than the corresponding values of 14,252.7, 19,995.9, and 15,155.3 obtained by using the linear regression equations. Potential evapotranspiration was calculated by the Jensen-Haise equation using the estimated daily solar radiation values. The results were compared with field measured evapotranspiration at the same location.