Green-Ampt Infiltration Parameters

Introduction

There are a number of methods available within TUFLOW to infiltrate water on the 2D surface into the sub-surface. These are Green-Ampt, Horton and Initial Loss/Continuing Loss. The models are used to represent hydrological losses particularly when direct rainfall is applied directly to the 2D surface and runoff is generated. As such, the infiltration module used, and the parameters selected, are important calibration parameters which should be used to calibrate simulated flows to observed flows. This is particularly important for whole of catchment modelling.

Green-Ampt Infiltration

The Green-Ampt approach varies the rate of infiltration over time based on the soil’s hydraulic conductivity, suction, porosity and initial moisture content. The method assumes that as water begins to infiltrate the soil, a line is developed differentiating between the ‘dry’ soil with moisture content θ__i) and the ‘wet’ soil (with moisture content equal to the porosity of the soil η). As the infiltrated water continues to move through the soil profile in a vertical direction, the soil moisture changes instantly from the initial content to a saturated state. This concept is shown in Figure 1.

Figure 1 Green-Ampt Model Concept
Figure courtesy of University of Texas

The basic form of the Green-Ampt equation is expressed as follows:

Where:

t is time

K is the saturated hydraulic conductivity

∆θ is defined as the soil capacity (the difference between the saturated and initial moisture content)

φ is the soil suction head

h₀ is the depth of ponded water

F(t) is the cumulative infiltration calculated from:

United States Department of Agriculture (USDA) soil types have been hardwired into TUFLOW and are presented in Table 1 along with the soil parameters. Alternatively, it is possible to define a customised soil type by specifying user defined values within the tsoilf.

Table 1 USDA Soil types for the Green-Ampt Infiltration Method (from Rawls, W, J, Brakesiek & Miller, N, 1983, ‘Green-Ampt infiltration parameters from soils data’, Journal of Hydraulic Engineering, vol 109, 62-71.)

USDA Soil Type	Suction (mm)	Hydraulic Conductivity (mm/hr)	Porosity (Fraction)
Clay	316.3	0.3	0.385
Silty Clay	292.2	0.5	0.423
Sandy Clay	239	0.6	0.321
Clay Loam	208.8	1	0.309
Silty Clay Loam	273	1	0.432
Sandy Clay Loam	218.5	1.5	0.33
Silt Loam	166.8	3.4	0.486
Loam	88.9	7.6	0.434
Sandy Loam	110.1	10.9	0.412
Loamy Sand	61.3	29.9	0.401
Sand	49.5	117.8	0.417

Table 2 presents summary statistics for the Green-Ampt Parameters types.

Table 2 USDA Summary Statistics for all Soil types for the Green-Ampt Infiltration Method

Stat	Suction (mm)	Hydraulic Conductivity (mm/hr)	Porosity (Fraction)
Min	49.5	0.3	0.31
Max	316.3	117.8	0.49
Mean	184.04	15.86	0.4
SD	94.82	34.92	0.05

In order to help calibration off TUFLOW models to observed data, a sensitivity analysis of the various parameters have been undertaken to show the effect of each parameter in isolation. The comparison has been undertaken on a real-world whole catchment model of the Plynlimon catchment in mid-Wales. The model was run with a real rainfall event from 2015 with a temporal resolution of 30 minutes as shown in Figure 2.

Figure 2: Plynlimon Rainfall

For the purposes of this sensitivity analysis of the parameters a single soil type was used representing the general clay soil types that are present.

Green-Ampt Infiltration: User Parameters

Where the inbuilt USDA soil types are not used, the user can specify their own values for the Suction, Hydraulic Conductivity, Porosity and Initial Soil Moisture. What follows is a description of each parameter and the sensitivity to a low, medium and high value based on the USDA soil type summary values.

Capillary Suction Head

The suction head, represented in millimeters, is the capillary attraction on the soil voids. It is large for fine grain soils such as clays and smaller for sandy soils.
To test the sensitivity of the simulated runoff at a gauged location, a low (49.5mm), mid representing the mean (184.4mm) and high (316.3mm) value of the suction head parameter were used with other parameters representing a clay soil (soil type 1).
The larger the value the capillary suction head value, the more capillary action that is achieved and the amount of infiltration that takes place. This is shown by the increase in cumulative infiltration in the graph below with a greater cumulative infiltration for the increase in the suction head.

Figure 3: Sensitivity of cumulative infiltration in the Plynlimon Gwy catchment to the Capillary Suction Head parameter in the Green-Ampt infiltration model.

As a consequence of this, there is a less runoff generated as shown in Figure 4. As can be seen, the model is not particularly sensitive to the suction head parameter and this fits with observations made within the literature from other similar studies.

Figure 4: Sensitivity of simulated flow at the Cefn-Brwn gauge location in the Plynlimon Gwy catchment to the Suction head parameter in the Green-Ampt infiltration model.

It can also be seen that the higher the suction head value that the longer it takes the hydrograph to start rising, with the high suction head scenario less responsive to the rainfall.

Saturated Hydraulic Conductivity

The saturated hydraulic conductivity, measured in mm per hour, represents the ease that water can travel through the soil whilst it is saturated. The saturated hydraulic conductivity is the equivalent of the limiting infiltration rate in the Horton infiltration model. The hydraulic conductivity is high for sandy soils but low for compact clays. Again, the sensitivity was conducted by varying the value for clays, which itself is relatively by low, with three scenarios, low (0.3mm/hr), mid representing the mean (15.86mm/hr) and high (117.8mm/hr). The results shown in figure 5, show that the parameter is very sensitive to the changes in the hydraulic conductivity with the mid and high values providing significant infiltration such that no runoff is generated and the flow is zero at the downstream gauge. The importance of hydraulic conductivity in the calculation of infiltration with the Green-Ampt equation has been well documented. As expected, the higher the hydraulic conductivity, then the more infiltration that occurs and the less runoff that is generated.

Figure 5: Sensitivity of simulated flow at the Cefn-Brwn gauge location in the Plynlimon Gwy catchment to the Saturated Hydraulic Conductivity parameter in the Green-Ampt infiltration model when using a clay soil type.

Figure 6: Sensitivity of cumulative infiltration in the Plynlimon Gwy catchment to the Saturated Hydraulic Conductivity parameter in the Green-Ampt infiltration model.

Porosity

The porosity value represents the volume of dry voids per volume of soil and provides the maximum moisture deficit that is available, the difference between the moisture content at saturation and at the start of the simulation.
Sandy soils tend to have lower porosities than clay soils, but drain to lower moisture contents between rainfall events because water is not held as strongly in the soil pores. Therefore, values of porosity tend to be higher for sandy soils when compared to clay soils.
As shown in figure 7, the higher the porosity value, then the less runoff that is generated due to increased infiltration although the model is not particular sensitive to the porosity value.

Figure 7: Sensitivity of simulated flow at the Cefn-Brwn gauge location in the Plynlimon Gwy catchment to the porosity parameter in the Green-Ampt infiltration model.

Figure 8: Sensitivity of cumulative infiltration in the Plynlimon Gwy catchment to the porosity parameter in the Green-Ampt infiltration model.

In built USDA soil type

The model was also run with the default in-build USDA soil types. Figure 9 shows the outputs. As expected the higher the soil type, then typically the more the infiltration and the lower the produced runoff. Soils 8-11, which represent sandy soils do not show any runoff in this example as the rainfall applied directly to the mesh is all infiltrated.


Figure 9: Sensitivity of simulated flow at the Cefn-Brwn gauge location in the Plynlimon Gwy catchment to the USDA soil type parameter in the Green-Ampt infiltration model.

Summary

The Green-Ampt infiltration model is one of the available infiltration models within TUFLOW. There is a wide range of literature on Green-Ampt applications and some suggested parameter values for particular soil types, albeit mostly soil types from the US. The 3 main Green-Ampt parameters have been tested to show the sensitivity of model outputs to the values as well as the variation in initial moisture. The results show that the model is relatively insensitive to the porosity value and suction head parameter. However, the outputs do show significant variations in runoff volume due to variations in both hydraulic conductivity. As part of any calibration exercise it is suggested that it is the hydraulic conductivity, in conjunction with the initial moisture content, which would be the parameters that are most focused on. The hydraulic conductivity appears to affect the runoff volume throughout the event whereas the initial soil moisture has a limited impact at the beginning of the event before soils become saturated and results converge.