Green and Ampt Infiltration¶

1. Overview¶

Infiltration is a complex process; however, the numerical solution of the Richards equation is expensive. MIKE SHE includes two additional UZ models that require surface infiltration to be calculated: the 2-layer Water Balance (2LWB) method and the Gravity Flow (GF) method. In both of these methods, infiltration is calculated based on the infiltration capacity of the soil and ponding occurs if the rainfall rate exceeds the infiltration capacity. This method neglects the very important water adsorption processes that occur in dry soils, which means that the amount of infiltration is underestimated in dry soils and when the water table is relatively deep.

The Green and Ampt (GA) method is widely used, physics based approximation to the Richards solution for calculating infiltration. As an infiltration model, the GA method can be used to calculate the infiltration in both the 2LWB and the GF UZ methods.

The GA method results in a high infiltration rate to dry soils. This is followed by ponding on the ground surface as the upper zone becomes saturated.

This is followed by a slowly decreasing infiltration rate that is ultimately limited by the saturated hydraulic conductivity.

The Green and Ampt method assumes:

an infinite thickness of soil
no water table, capillary fringe, or lower soil boundary
uniform soil characteristics with depth
uniform water content with depth at t=0
insignificant depth of ponded water

The necessary input parameters are:

saturated hydraulic conductivity
initial water content
saturated water content
rainfall rate, w
effective soil suction ahead of wetting front

The GA method generates three key outputs:

f(t), the infiltration rate at time t
F(t), the total infiltration at time t
the time until ponding after the start of the time step The GA method distinguishes between two main cases:

Case 1: Rainfall rate less than the saturated hydraulic conductivity¶

In this case, no ponding occurs and the infiltration rate equals the rainfall rate and the total infiltration equals the rainfall rate times the time step length.

Thus, f(t) = w

F(t) = w t

Case 2: Rainfall rate greater than saturated hydraulic conductivity.¶

Initially, rainfall will be absorbed into the soil and ponding will occur when the top of the unsaturated zone becomes saturated. However, the initial infiltration rate will be greater than the saturated hydraulic conductivity because the soil will adsorb water ahead of the wetting front. Thus, ponding will occur after the start of the timestep. Prior to the start of ponding Case 1 applies. After ponding starts, the infiltration rate starts to decrease, and the infiltration time is a function of the total amount of infiltration. This must be solved implicitly to find the amount of infiltration corresponding to the time step.

Since the GA method assumes that the infiltration occurs as a sharp front plug flow, the depth of infiltration can be easily calculated by dividing the original deficit by the amount of infiltration.

Actually, there are a couple of special cases in addition to the two main cases.

Case 3: Initial ponding¶

The GA method assumes that there is no ponding on the ground surface. In fact, the infiltration rate depends on the degree of ponding but the ponding level is generally neglected. This is a reasonable assumption since the ponding due to rainfall is generally negligible. However, in MIKE SHE there is often ponding at the beginning of the time step due to flooding. In this case, the we can assume that the top of the soil is saturated and the infiltration rate will equal Ks.

Case 4: Rainfall + Ponded storage depleted during the time step¶

In some cases, there may be a small amount of initial ponded storage in the cell. This should be infiltrated as per Case 3, but once this has been depleted, ponded storage infiltration will cease if the rainfall rate is less than Ks. If the rainfall rate is greater than this, then water will continue to pond and infiltrate at the rate equal to Ks. However, if the rainfall rate is less than Ks, then the infiltration rate should continue at the rainfall rate.

Case 5: Insufficient UZ storage¶

The total amount of infiltration cannot exceed the amount of available UZ storage, so there must be a check to see that this amount is not exceeded. Excess must be added to OL.

2. Implementation of Green and Ampt in the 2LWB method¶

The implementation in MIKE SHE's 2LWB method is relatively straightforward. Since the GA method is only an infiltration model, the current infiltration method for the 2LWB method can nearly be substituted. In the current method, the amount of infiltration in the time step is the same as Case 1 with a maximum equal to Ks.

In the 2LWB method, there is an upper root zone layer (UL) and sometimes a lower layer down to the water table (LL). The calculation algorithm proceeds as follows:

Calculate UZdeficit based on deficit in UL and LL and the normally calculated recharge to SZ
1. If Case 1,
Calculate time to ponding
if time to ponding is greater than the time step, infiltrate all the rainfall in the time step
If time to ponding is less than the time step, infiltrate only the allowed amount.
Recalculate the water contents in the UL and LL, assuming UL is 100% saturated before the LL receives water, and

UL and LL are 100% saturated if there is rainfall in excess of UZ storage.
1. If Case 2,
2. Calculate time to ponding based on the Green and Ampt equation
3. if time to ponding is greater than the time step, infiltrate the maximum rainfall using the Green and Ampt equation
4. if time to ponding is less than the time step, infiltrate only the allowed amount.
5. recalculate the water contents in the UL and LL, assuming UL is 100% saturated before the LL receives water, and UL and LL are 100% saturated if there is rainfall in excess of UZ storage.
6. Add the excess rainfall to OL

Internal infiltration rates

The rate of exchange between the UL and LL, and between the LL and SZ is currently governed by Ks. This should be a function of the water content, defined by the water content of the draining layer. This will significantly reduce the rate of drainage in the layers - especially in the LL if it is thick.

Bypass Flow

The handling of bypass flow directly to SZ is not be affected by the GA implementation.

Overland-groundwater leakage coefficient

If the a leakage coefficient is specified that is lower than the specified Ks then the lower value should be used.

Extra Parameter: Threshold depth for infiltration

This extra parameter is used to prevent infiltration of very small amounts of rain. Instead the water remains on the ground surface and usually evaporates. This parameter is needed because the 2LWB does not remove ET from the soil surface. This parameter is unaffected by the GA method.

3. Implementation in the Gravity Flow method¶

Adding the GA method to the Gravity Flow model is slightly more complicated because the GA method assumes a uniform, infinite soil column.

Many GF models include a fine discretization near the ground surface to capture the infiltration dynamics. However, the GA method is an approximation to these infiltration dynamics and makes the refined grid unnecessary. Using multiple layers within the GA's depth of infiltration would often result in variations of water content with depth, which makes the infiltration calculations difficult.

Multiple UZ layers are handled by reducing the amount of infiltration depending on the actual storage available in the depth of infiltration. In other words, the amount of infiltration and depth based on the average water deficit in the GF layers in the root zone is calculated and then MIKE SHE calculates if the infiltration exceeds the actual available storage in the depth of infiltration. If it does then MIKE SHE only infiltrates the available storage. This is a reasonable physical approximation for the total amount of infiltration, but might under- estimate the rate of infiltration if the upper layers are very dry.

The GF module allows you to have multiple soil types in the same column. Multilayer GA models are technically possible, but this is not implemented in MIKE SHE. If there are multiple soil types within the infiltration depth, a Warning is issued. The infiltration is only calculated based on the soil type in the uppermost UZ layer.

The GA infiltration with the GF method proceeds as follows

Calculate UZdeficit based on entire UZ deficit and an estimate of the current recharge to SZ
1. If Case 1,
Calculate time to ponding
if time to ponding is greater than the time step, infiltrate all the rainfall in the time step
If time to ponding is less than the time step, infiltrate only the allowed amount.
Recalculate the water contents in the layers, assuming, each layer is successively 100% saturated before the layer beneath receives water.
1. If Case 2,
Calculate available storage in the
If time to ponding is greater than the time step,
1. Calculate the maximum rainfall
2. Calculate the maximum depth, and then calculate the maximum actual storage in the layers down to the max depth
3. Infiltrate either (i) or (ii)
4. Update all water contents assuming that each successive layer is 100% saturated.
If time to ponding is less than the time step,
1. infiltrate only the allowed amount
2. Update all water contents assuming that each successive layer is 100% saturated
3. Then add the excess rainfall to OL

Internal infiltration rates

The rate of exchange between the layers is currently governed by Ks ( ). This is unchanged, except that during the GA infiltration, it is ignored.

Bypass Flow

The handling of the bypass flow directly to SZ is not affected by the GA implementation.

Overland-groundwater leakage coefficient

If a leakage coefficient is specified that is lower than the specified Ks then the lower value is used.