Calibration of the Ångström–Prescott coefficients (a, b) under different time scales and their impacts in estimating global solar radiation in the Yellow River basin

Abstract The Angstrom–Prescott (A–P) equation relating in its current form the incident top-of-atmosphere solar radiation to the solar radiation received at the surface, is one of the most accurate and widely used sunshine-based methods estimating global solar radiation (Rs). The key in its application is the calibration of the locally specific coefficients. Although the coefficients have been extensively studied and calibrated in many places over the world, their relations with time scale are much less investigated. This paper addressed the variation in these coefficients caused by time scale and how this variation results on the accuracy of Rs predictions. This was done using long-term data at 31 sites from the Yellow River basin in China by parallel calibration at three time scales: daily, monthly mean daily and yearly mean daily. We found that the A–P coefficients obtained using monthly data generally had higher a and lower b and larger variations over those using daily data. At yearly time scale, the sunshine–radiation relationship can no longer be described by the linear A–P formula. The difference in coefficients between daily and monthly calibration was rather large accounting for 71% of the differences in a and 61% in b that in turn were greater than 0.03, corresponding to 81% for a and 49% for b being greater than 10%. Time scale had a larger effect on a than on b, and it caused a maximum variation of 82% in a and 43% in b in the basin, equaling half of the variation caused by geographical location. However, the large effect of time scales on a and b produced no significant impact on the estimation accuracy of Rs because of the conservative response of the sum a + b to time scale. In this sense, the coefficients calibrated at daily scale are interchangeable with those calibrated at monthly scale, indicating the high flexibility of the A–P formula. Nevertheless, calibration made at daily scale has two important advantages over monthly scale in that it requires fewer years’ data to obtain stabilized coefficients, and that it is easily predicted more accurately with common site information. Our findings have two implications. Firstly, they provide an additional guidance on the explanation of the large variability of the coefficients found in the literature for the same geographical location. Secondly, they facilitate the choice of the coefficients in practical applications by proving their interchangeability in the estimation of Rs.