Modeling variability of infiltration tests in ephemeral stream beds as a random function for uncertainty quantification

Abstract

Infiltration processes are highly variable in space and time, and therefore, building reliable hydrological models without considering the variability is questionable. In this research, we propose a methodology that can systematically handle the variability in the infiltration process. The methodology is based on the theory of random functions in a dimensionless formalism that allows the derivation of a generalized model from the observed infiltration test data. The Monte Carlo technique is utilized to generate hypothetical infiltration tests that carputer the characteristics of the real tests. The methodology is applied to a case study in ephemeral stream beds located in Al Madinah Al Munawarah Province in Saudi Arabia. The measurements are made by the double-ring infiltrometer. Beta distribution fits the dimensionless cumulative infiltration relatively well at a 1% significant level at all times, and therefore, it can be used to model the uncertainty in hydrological modeling. High variability is observed in infiltration tests at the early time (a platykurtic distribution with high dispersion); however, it decreases at the late time (Leptokurtic distribution with low dispersion) since the infiltration reaches a steady infiltration. Some extreme tests show different behavior from the fourteen tests that cannot be captured by the model and therefore need special treatment.