• DTR;
  • Angstrom equation;
  • DTR plus Angstrom equation;
  • solar radiation;
  • sunshine duration


This paper reports the development of a relationship between incoming shortwave solar radiation and bright sunshine duration. The daily temperature range (DTR) is melt into the existing Angstrom equation to include the advection of atmospheric constituents. The proposed DTR plus Angstrom equations were tested against field investigation. Measurements of solar radiation and sunshine duration from 1997 to 2006 at 20 meteorological stations were used to calibrate and validate the suggested equation. The model parameters required to specify the nature of the relationship between solar radiation and sunshine duration were determined by automatically minimizing the difference between the modeled and measured solar radiation. At the 20 meteorological stations, the root mean square error (RMSE) is improved by 6% for the original Angstrom equation with DTR, while 2% for the modified Angstrom equation with DTR. The average value of the coefficient of determination is 0.889 (0.908) for the original (modified) Angstrom equation whereas 0.901 (0.911) for the original (modified) Angstrom equation with DTR. It is encouraging that the newly suggested equation with DTR generally provides better performance than the existing Angstrom equation that is constructed with brightness sunshine duration only.