Shallow Unconfined Flow on a Sloping Base Redux.

Area of Science:

• Hydrogeology
• Groundwater Modeling
• Mathematical Hydrology

Background:

• Unconfined aquifer analysis often involves complex models to account for sloping bases.
• Existing implicit solutions provide limited insight into the significance of base slope.
• The intuitive understanding of slope impact may be insufficient for accurate modeling.

Purpose of the Study:

• To explicitly solve the unconfined aquifer sloping base problem.
• To determine when complex models are justified based on sloping base impact.
• To offer a more insightful characterization of sloping base effects than existing methods.

Main Methods:

• Utilized recent mathematical advancements, specifically the Lambert W function.
• Developed an explicit analytical solution for the sloping base problem.
• Compared the explicit solution's insights against traditional implicit solutions (Dupuit, Polubarinov-Kochina, Harr, Child).

Main Results:

• The impact of a sloping base is not solely dependent on the slope's magnitude.
• An explicit solution reveals that the ratio of saturated thickness to change in base elevation is the key characterizing factor.
• This ratio provides superior insight compared to implicit solutions.

Conclusions:

• The simplified characterization using saturated thickness and base elevation change is crucial for determining the necessity of complex unconfined aquifer models.
• The explicit solution offers a more robust understanding of sloping base hydraulics.
• This research provides a new criterion for model selection in hydrogeology.