💧🌱 Infiltration Models 🌱💧 - https://www.epa.gov/water-research/infiltration-models

 💧🌱 Infiltration Models 🌱💧

Dive into the world of infiltration models presented on our platform! These models were crafted using the sophisticated Mathcad Plus 6.0. 🖥️ Please note: Mathcad is a trademark of Mathsoft, Inc. The use of this or any commercial product doesn't imply any endorsement or recommendation by EPA. Ensure you've configured your browser to recognize and launch the MathCad application. Alternatively, you can save the worksheet for later by right-clicking and choosing “Save Link As” or “Save Target As.”

🌧️ Understanding Water Infiltration 🌍

When rain or irrigation showers the land, water starts its journey, seeping through the soil via infiltration. If the water supply rate exceeds the soil's infiltration capacity, the excess water either pools on the surface or turns into runoff. The term "infiltrability" refers to the soil's maximum absorption rate. This rate indirectly determines how much water will flow over the surface and how much will permeate the soil. The water's journey within the soil is beautifully illustrated in Figure 1.

🌱 Zones of Water Infiltration 🌱 In our ideal soil profile, there are five distinct zones:

1. Saturated Zone - A realm where water fills every pore.
2. Transition Zone – Where water content decreases rapidly with depth.
3. Transmission Zone – Characterized by a gradual change in water content.
4. Wetting Zone – A zone where water content decreases sharply from transmission zone levels.
5. Wetting Front – The boundary separating wet and dry soil.

Water's movement within the soil is governed by various factors like rain duration, soil properties, vegetation, and surface texture.

🌐 Dive Into the Models 🌐

1. SCS Model 🌊 An empirically crafted model, the SCS approach visualizes the infiltration process. It balances physical representation and mathematical function to mimic observed infiltration features. Explore more with the SCS MathCad Code 📥.

2. Philip's Two-Term Model 🌦️ Developed by Philips in 1957, this model is a truncated power series solution, essential for the early stages of infiltration. Delve deeper with the Philip's Two-Term MathCad Code 📥.

3. Layered Green Ampt Model 🌿 Modified to compute water infiltration in diverse soils, this model is indispensable for layered terrains. Discover more with the Layered Green Ampt MathCad Code 📥.

4. Explicit Green Ampt Model 💦 A fundamental model that describes water's journey into the soil. It’s a favorite due to its simplicity and efficiency. Dive in with the Explicit Green Ampt MathCad Code 📥.

5. Constant Flux Green Ampt Model 🌧️ This model requires two formulations: one for when the water application rate is less than soil's capacity, and another for when it exceeds. Explore with the Constant Flux Green Ampt MathCad Code 📥.

6. Infiltration/Exfiltration Model 🌾 This model, crafted by Eagleson in 1978, highlights the dynamic balance between infiltration and exfiltration. Get started with the Infiltration/Exfiltration MathCad Code 📥.

💡 For an in-depth exploration, check out our comprehensive report: Estimation of Infiltration Rate in the Vadose Zone.

Infiltration Models

SCS Model

The SCS model is an empirically developed approach to the water infiltration process (Jury, et al. 1991). It has been developed by first finding a mathematical function whose shape as a function of time matches the observed features of the infiltration rate. This function is then provided a physical explanation of the process. In semi-empirical models, most physical processes are represented by commonly accepted and simplistic conceptual methods rather than by equations derived from fundamentally physical principles. The commonly used semi-empirical infiltration model in the fields of soil physics and hydrology is the SCS model. A scenario was chosen to simulate water infiltration into a soil for conditions with rainfall and surface runoff by using the SCS model. Input parameters and simulation results are discussed in Estimation of Infiltration Rate in the Vadose Zone: Compilation of Simple Mathematical Models, Volume II.  

Philip's Two-Term Model

The Philip's Two-Term model (PHILIP2T) is a truncated power series solution developed by Philips (1957). During the initial stages of infiltration (when t is very small), the first term of the model/equation dominates the process. In this stage, the vertical infiltration proceeds at almost the same rate as absorption or horizontal infiltration. In this stage of infiltration, the gravity component, represented by the second term of the model/equation, is negligible. As infiltration continues, the second term becomes progressively more important until it dominates the infiltration process. Philips (1957) suggested the use of the two-term model in applied hydrology when t is not too large. A scenario was chosen to simulate the water infiltration into a sandy soil by using the PHILIP2T model. Input parameters and simulation results are discussed in Estimation of Infiltration Rate in the Vadose Zone: Compilation of Simple Mathematical Models, Volume II.  

Layered Green Ampt Model

The Green Ampt model has been modified in this application to calculate water infiltration into non-uniform soils by several researchers (Bouwer 1969, Fok 1970, Moore 1981, Ahuja and Ross 1983). The implementation for layered systems (GALAYER) used for this project was developed by Flerchinger, et al. (1989). Specifically, the model could be used for the determination of water infiltration over time in vertically heterogeneous soils. Two simulation scenarios were selected for inclusion in the applications worksheet. The first scenario was to estimate water infiltration into a soil with two layers (sand over a loam). The second scenario was designed to estimate the water infiltration into a soil with three layers (sand over loam, over clay). Comparisons and results are presented and discussed in Estimation of Infiltration Rate in the Vadose Zone: 

Explicit Green Ampt Model

The initial Green Ampt model was the first physically based model/equation describing the infiltration of water into soil. It has been the subject of considerable development in soil physics and hydrology, owing to its simplicity and satisfactory performance for a great variety of water infiltration problems. This model yields cumulative infiltration and the infiltration rate as an implicit function of time (i.e., given a value of time (t), values of the cumulative infiltration (I) and the infiltration rate (q) can be directly obtained. Thus, the model functions are q(t) and I(t), rather than of t(q) and t(I).) The Explicit Green-Ampt model as defined and used for this project's application was developed by Salvucci and Entekhabi (1994). The application provides a straightforward and accurate estimation of infiltration for any given time. This formulation supposedly yields an error of less than 2 percent at all times when compared to the exact values resulting from the Implicit Green Ampt model.  

Constant Flux Green Ampt Model

For the constant flux Green-Ampt model, two formulations are required: one for the condition that the application rate (r) is less than the saturated hydraulic conductivity (Ks), and one for the condition that the application rate is greater than the saturated hydraulic conductivity. When r<Ks, the infiltration rate (q) is always equal to the surface application rate (r) and the surface never becomes saturated. When r>Ks , the surface becomes saturated at the time of the initial application (t0). 

Infiltration/Exfiltration Model

The vertical movement of water in the soil profile from the surface to water table is a dynamic condition. It can be conceptualized as being composed of basically two predominant processes: infiltration and exfiltration. Exfiltration can be envisioned as the processes dominating during drying periods; water released during this period can be thought of as being released through evaporation to the atmosphere. The model (INFEXF) selected for this project is a formulation of the Philips model developed by Eagleson (1978) to account for water infiltration during the wetting season and exfiltration during the drying season. Infiltration and exfiltration as described in this application assumes the soil medium to be effectively semi-infinite and the internal soil water content at the beginning of each storm event and inter-storm period is assumed to be uniform at its long-term and space-time average. The exfiltration equation is modified for the presence of natural vegetation through the approximate introduction of a distributed sink representing the moisture extraction by plant roots. Two scenarios are presented in the accompanying worksheet applications: water infiltration during the rainy season and water exfiltration during the drying season.