Green and Ampt Loss Model

Basic Concepts and Equations
The Green and Ampt loss model is based on a theoretical application of Darcy’s law. The model, first developed in 1911, has the form:
EquationObject157172
Equation 4-41.
Where:
  • f
     = infiltration capacity (in./hr.)
  • K
    s
     = saturated hydraulic conductivity (permeability) (in./hr.)
  • S
    w
     = soil water suction (in.)
  • θ
    s
     = volumetric water content (water volume per unit soil volume) under saturated conditions
  • θ
    i
     = volumetric moisture content under initial conditions
  • F
     = total accumulated infiltration (in.)
The parameters can be related to soil properties.
Assumptions underlying the Green and Ampt model are the following:
  • As rain continues to fall and water infiltrates, the wetting front advances at the same rate throughout the groundwater system, which produces a well-defined wetting front.
  • The volumetric water contents, θ
    s
     and θ
    i
    , remain constant above and below the wetting front as it advances.
  • The soil-water suction immediately below the wetting front remains constant with both time and location as the wetting front advances.
To calculate the infiltration rate at a given time, the cumulative infiltration is calculated using Equation 4-42 and differences computed in successive cumulative values:
EquationObject158173
Equation 4-42.
Where:
  • t
     = time (hr.)
Equation 4-42 cannot be solved explicitly. Instead, solution by numerical methods is required. Once F is solved for, the infiltration rate, f, can be solved using Equation 4-41. These computations are typically performed by hydrologic computer programs equipped with Green-Ampt computational routines. With these programs, the designer is required to specify θ
s
, S
w
, and K
s
.
Estimating Green-Ampt Parameters
To apply the Green and Ampt loss model, the designer must estimate the volumetric moisture content, θ
s
, the wetting front suction head, S
w
, and the saturated hydraulic conductivity, K
s
. Rawls et al. (1993) provide Green-Ampt parameters for several USDA soil textures as shown in Table 4-27. A range is given for volumetric moisture content in parentheses with typical values for each also listed.
Table 4-27: Green-Ampt Parameters
Soil texture class
Volumetric moisture content under saturated conditions θ
s
Volumetric moisture content under initial conditions θ
i
Wetting front suction head S
w
Saturated hydraulic conductivity K
s
Sand
0.437 (0.374-0.500)
0.417 (0.354-0.480)
1.95
9.28
Loamy sand
0.437 (0.363-0.506)
0.401 (0.329-0.473)
2.41
2.35
Sandy loam
0.453 (0.351-0.555)
0.412 (0.283-0.541)
4.33
0.86
Loam
0.463 (0.375-0.551)
0.434 (0.334-0.534)
3.50
0.52
Silt loam
0.501 (0.420-0.582)
0.486 (0.394-0.578)
6.57
0.27
Sandy clay loam
0.398 (0.332-0.464)
0.330 (0.235-0.425)
8.60
0.12
Clay loam
0.464 (0.409-0.519)
0.309 (0.279-0.501)
8.22
0.08
Silty clay loam
0.471 (0.418-0.524)
0.432 (0.347-0.517)
10.75
0.08
Sandy clay
0.430 (0.370-0.490)
0.321 (0.207-0.435)
9.41
0.05
Silty clay
0.479 (0.425-0.533)
0.423 (0.334-0.512)
11.50
0.04
Clay
0.475 (0.427-0.523)
0.385 (0.269-0.501)
12.45
0.02