Wadis are arid region drainage basins, mostly in the Quaternary depositions of different facies and grain size distributions depending on the paleogeologic environmental processes. Random and heterogeneous setup of the subsurface geological layer composition gives rather independent, haphazard and different aquifer numerical properties even along short distances. The aquifer storativity and transmissivity estimations from a set of wells provide spatial variability feature that can be captured by probability and statistical methodologies leading to risk assessment. Three methodologies are employed for the uncertainty assessments in this paper. The heterogeneity can be treated either through deterministic formulations by a set of assumptions or by statistical and probabilistic approaches giving way to risk assessments. They are the classical deterministic approach, statistical procedure that takes into consideration arithmetic average, standard deviation and correlation coefficient of hydrogeological variables and finally the probabilistic method with risk attachments. The first approach depends on the constant aquifer parameters or their arithmetic averages only. The second procedure considers the deviations (perturbations) from the arithmetic average and then various statistical parameters enter into the calculations. Finally, the last method considers the probability distribution function (pdf) of each hydrologic variable and their composition through specific groundwater storage capacity equation with risk levels at 10 % 25 %, 50 %, 75 %, 90 % and 95 %. The application of the methodology is presented for wadi Fatimah that lies in the central western part of the Kingdom of Saudi Arabia.