Harmonic analysis of solar irradiation and rainfall data in the context of various climatic indicators in Saudi Arabia

Harmonic techniques are used for computing solar irradiation for 14 stations in Saudi Arabia in order to map amplitudes (AMPs), percentages of variances (PVs), and phase angles (Φ) for six harmonics of solar irradiation. The annual cycle of solar irradiation is considered the main cycle prevailing over the semi-annual and seasonal cycles with first harmonic PVs of 96, 97, and 93% for north, east, and central regions, respectively. In the southwest region, at stations Abha and Albaha, there are some contributions of semi-annual cycle which reduce the PVs of the first harmonic to 60 and 55% at Abha and Albah, respectively. The low percentages at southwest stations are due to the wet summer monsoon. On the other hand, rainfall records at five stations are used in harmonic analysis in order to find the interrelationships between the two elements. It is found that the greater the amplitude of solar irradiations is the offset by the lack of rainfall and vice versa. Weak correlations between rainfall and solar irradiation in the majority of cities in all regions which are represented by Riyadh (− 0.23) for the central region, Tabuk (0.24) for the northern region, and Jazan (− 0.08) for southwest region, while there are three stations that are unique in exhibiting medium correlations among the stations of their regions; these are Taif (− 0.42), Abha (− 0.44), and Hail (− 0.56). These differences arise from, first the synoptic climatology, such as in Hail (weather system with respect to time and location), second the elevations of the station such as Abah and Taif. Finally, climatic rainfall indices are calculated to enrich the discussion on the interrelationships between rainfall and solar irradiation. The study shows that the stations of low amplitudes of solar irradiation are offset by an increase of both number of days where daily precipitation ≥ 20 mm (R20mm), and the annual sum of daily precipitation > 95th percentile (R95p) and vice versa, low amplitudes of solar irradiation with decreasing the number of consecutive dry day (CDD).