Variability of the asymptotic curve number in mountainous undeveloped arid basins based on historical data: Case study in Saudi Arabia

Abstract

In temperate regions, there are relatively enough measurements of rainfall and runoff and therefore estimation of curve number (CN) is made by inverse modelling. There is a lack of studies for CN in arid regions from rainfall-runoff measurements, therefore, a focus is made on analyzing CN in mountainous arid catchments in Saudi Arabia (SA) from measured events. The study is carried out on five basins with 19 sub-basins in the southwestern part of SA. 161 rainfall storms are analyzed. The asymptotic fitting method (AFM) is used to estimate the asymptotic CN (CN∞). The analysis showed that the dominant curve number-precipitation (CN–P) relationship is the standard behavior and CN∞ shows high variability. There is an overall trend of increasing CN∞ with the increasing of the initial abstraction ratio (λ). The correlation coefficient, r, and root mean square error (RMSE, CN units) between the measured and fitted CN are 0.77 (14.8), 0.95 (3.3), and 0.96 (2.4) respectively for λ = 0.01, 0.2 and 0.3 respectively for the case of natural sorting of data pairs. The same trend is noticed for the case of ordered sorting of data pairs with relatively higher r, and lower RMSE (0.797 (9.7), 0.979 (1.9) and 0.985 (1.3), for λ 0.01, 0.2 and 0.3 respectively). For the natural data sorting, the CN∞ varies from 0 to 61. However, for the ordered data sorting, the CN∞ varies from 29 to 83. The CN∞, in the current study, is in the same order of magnitude with similar arid and semi-arid regions, however, CN∞ is lower when compared with temperate regions, which reflects the effect of transmission losses in the wadi system in mountainous basins. Most of the floodwater is lost during the infiltration process though the wadi bed. It seems misleading to use CN∞ to estimate runoff in this region since the asymptotic value of CN (CN∞) has not been reached yet within the range of rainfall data except at λ = 0.01 with the lowest correlation coefficient and highest RMSE.