Abstract
In this study, the relationship between rainfall and groundwater recharge (GR) was established and evaluated with cost benefit. Rainfall data in Kano, Nigeria between 1905 and 2018 was analysed statistically and was used to fix the unknown constants of the modified numerical formula (NF) using Microsoft Excel Solver. The NF was used to estimate GR from the rainfall. Accuracy of the NF was evaluated statistically (relative error; the degree of accuracy, numerical reliability, Model of Selection Criterion (MSC) and Akaike Information Criterion (AIC)) and compared with standard formulae in use using field GR Uttar Pradesh (UP) as the reference GR. A basic cost benefit of GR was conducted using standard method. The study showed that non parameter test of the rainfall data revealed that Mann- Whitney (U), Wilcoxon (W) and standardized index were 1532, 3878 and – 0.185 respectively. Sen’s slope estimator of the rainfall data was 54.59 mm Yr-1. GR estimated using the modified numerical formula was similar to GR using UP, Chaturvedi, Kumar and Seethapathi , Rao Islam, Amritsar and BhaHacharjee, but different in magnitude of GR. NF provided the lowest relative error of 0.006 %, the highest MSC of 15.94; the degree of accuracy of 99. 99 % and the lowest AIC of -486.64 with BhaHacharjee formula having highest relative error of 244.16%, the lowest MSC of -4.88; the degree of accuracy of -144.16 % and the highest AIC of 1881.0. The current average cost benefit of groundwater recharge in Kano was found to be 1034.28US $ (₦377,512.4) m-2Yr-1. It is concluded that the modified numerical formula GR with minimum error and it is good tool in water resources management.

Key words: Groundwater recharge, soil-moisture, numerical solution, Microsoft Excel Solver, Kano.