An analytical solution for estimating percolation rate by fitting temperature profiles in the vadose zone

Area of Science:

• Geophysics
• Environmental Science
• Hydrogeology

Background:

• Heat transfer in multilayer systems, such as the vadose zone, involves both conduction and convection.
• Accurate estimation of subsurface water movement (percolation) is crucial for hydrological and environmental assessments.
• Existing methods may lack the precision or simplicity required for detailed vadose zone characterization.

Purpose of the Study:

• To present a straightforward analytical solution for one-dimensional steady-state heat transfer through multilayered media.
• To demonstrate the inverse application of this solution for accurately estimating percolation rates in the vadose zone.
• To explore the potential of the solution in characterizing lateral flow phenomena at layer interfaces.

Main Methods:

• Developed an analytical model for heat transfer considering conduction and convection in homogeneous layers with constant thermal diffusivity.
• Assumed perpendicular heat/mass flow and constant mass flow rate across the system boundaries.
• Utilized constant, known temperatures at the system's boundaries for model calibration and validation.

Main Results:

• The analytical solution provides temperature as a function of system parameters, including percolation rate.
• Inverse application with reliable field data allows for high-accuracy determination of percolation rates (e.g., to mm/year).
• The model shows potential for identifying and characterizing lateral water flow along different geological layers.

Conclusions:

• The presented analytical solution offers a simple yet effective tool for analyzing heat transfer in multilayered vadose zones.
• This method provides a robust approach for quantifying subsurface water flow, crucial for hydrological modeling and resource management.
• The solution's utility extends to characterizing complex flow dynamics, including lateral movement, within the subsurface.