Influence of hysteresis on groundwater wave dynamics in an unconfined aquifer with a sloping boundary

Abstract

In this paper, the influence of hysteresis on water table dynamics in an unconfined aquifer was examined using a numerical model to solve Richards’ unsaturated flow equation. The model was subject to simple harmonic forcing across a sloping boundary with a seepage face boundary condition. Time series from both hysteretic and non-hysteretic models were subject to harmonic analysis to extract the amplitude and phase profiles for comparison with existing sand flume data (Cartwright et al., 2004). The results from both model types show good agreement with the data indicating no influence of hysteresis at the oscillation period examined (T = 348 s). The models were then used to perform a parametric study to examine the relationship between oscillation period and hysteresis effects with periods ranging from 3 min to 180 min. At short oscillation periods, (T ≈ 180 s) the effects of hysteresis were negligible with both models providing similar results. As the oscillation period increased, the hysteretic model showed less amplitude damping than the non-hysteretic model. For periods greater than T = 60 min, the phase lag in the non-hysteretic model is greater than for the hysteretic one. For periods less than T = 60 min this trend is reversed and the hysteretic model produced a greater phase lag than the non-hysteretic model. These findings suggest that consideration of hysteresis dynamics in Richards’ equation models has no influence on water table wave dispersion for short period forcing such as waves (T ≈ 10 s) whereas for long period forcing such as tides (T ≈ 12.25 h) or storm surges (T ≈ days) hysteresis dynamics should be taken into account.