When is the Green-Ampt model a better fit for calculating how water soaks into soil than the Horton model?

The Green-Ampt model is a better fit for calculating how water soaks into soil than the Horton model primarily when a physically-based understanding of the infiltration process, directly related to soil properties, is required. To elaborate, infiltration is the process by which water on the ground surface enters the soil. The Horton model is an empirical model, meaning it is based on observed data and a mathematical curve fit, not on fundamental physical laws. It describes infiltration rate as decaying exponentially from an initial maximum rate to a constant final rate, typically under uniform surface ponding (water standing on the soil surface). Its parameters (initial infiltration rate, final infiltration rate, and a decay constant) are fitted from experimental data and do not directly represent specific soil physical properties.

In contrast, the Green-Ampt model is a physically-based model, derived from Darcy's Law and the principle of mass conservation. It idealizes the infiltration process by assuming a sharp wetting front, which is the distinct boundary between the wetted, saturated soil zone and the drier, unsaturated soil zone below, as water moves downwards. The Green-Ampt model is a better fit under the following conditions:

1. When measurable soil physical properties are known or can be estimated accurately. The Green-Ampt model's parameters are directly related to fundamental soil characteristics: initial water content (the amount of water already in the soil before infiltration begins), saturated hydraulic conductivity (the maximum rate at which water can flow through a fully saturated soil), wetting front suction head (the average capillary suction at the wetting front that pulls water into the dry soil pores), and porosity (the total volume of pore space in the soil). Because these parameters have physical meaning, the model provides a more realistic and transferable prediction of infiltration across different sites and conditions, unlike Horton's empirically derived parameters which may lack such direct physical interpretation.

2. When the initial soil moisture content varies. The Green-Ampt model explicitly incorporates the initial water content. A drier soil has a greater capacity to absorb water and exhibits a stronger capillary pull at the wetting front, leading to a higher initial infiltration rate. By including this parameter, the Green-Ampt model can more accurately predict how antecedent (prior) soil moisture conditions influence the infiltration process, whereas the Horton model's parameters often need to be recalibrated for different initial moisture states.

3. When a distinct wetting front develops and moves through the soil. The Green-Ampt model's core assumption of a sharp wetting front is a good approximation for many soils, especially those that are initially dry and exhibit relatively uniform texture. This physical representation allows the model to explicitly account for the driving forces of infiltration: gravity acting on the water in the wetted zone and the capillary suction at the wetting front pulling water into the dry soil. The Horton model does not explicitly consider these internal soil moisture dynamics or the movement of a wetting front.

4. When a predictive model, rather than just a descriptive fit, is desired. Because its parameters are physically meaningful, the Green-Ampt model is more robust for predicting infiltration under a wider range of scenarios, including changes in rainfall intensity or soil type, provided its fundamental assumptions (like surface ponding and a sharp wetting front) are met. This makes it more suitable for hydrological modeling and forecasting where understanding the underlying physical process is crucial.