Infiltration → Green-Ampt Method
The input variables used by the simple Green-Ampt method for modeling
infiltration are defined as follows:
Ks |
= saturated hydraulic conductivity [m / s] |
Ki |
= initial hydraulic conductivity [m / s]
(typically much less than Ks) |
θs |
= soil water content at ψ=0 [unitless]
(typically set to the porosity, φ) |
θi |
= initial soil water content [unitless] |
G |
= capillary length scale [meters] |
|
= integral over all ψ of K(ψ) / Ks |
|
= (almost always between ψB and 2*ψB) |
P |
= precipitation rate [mm / sec] |
M |
= snowmelt rate [mm / sec] |
For a detailed discussion of these variables and infiltration
theory, see the References below.
For each variable, you may choose from the droplist of data
types. For the "Scalar" data type, enter a numeric value with
the units indicated in the dialog. For the other data types,
enter a filename. Values in files must also use the indicated
units.
Single grids and grid sequences are assumed to be stored as
RTG and
RTS files, respectively.
Time series are assumed to be stored as text files, with one value
per line. For a time series or grid sequence, the time between
values must coincide with the timestep provided.
Choosing an entry from the droplist labeled "Closest standard soil type"
will change the values in the dialog to tabulated values for the selected
soil type. However, these values were determined from plot-scale measurements
and are unlikely to be appropriate for large grid cells. For large grid
cells, some type of upscaling is typically required.
Equations Used by the Green-Ampt Method
fc |
= Ki + [(Ks - Ki) * (F + J) / F] |
= infiltrability [m / sec] (max infiltration rate) |
|
= Ks + (J / F) * (Ks - Ki) |
= infiltrability [m / sec] (max infiltration rate) |
J |
= G * (θs - θi) |
= a quantity used in previous equation [meters] |
v0 |
= min[(P + M), fc] |
= infiltration rate at surface [mm / sec]
(Ks < (P + M)) |
|
= (P + M) |
= infiltration rate at surface [mm / sec]
(Ks > (P + M)) |
F |
= ∫ v0(t) dt, (from times 0 to t) |
= cumulative infiltration depth [meters] (vs. I' in Smith (2002) |
Notes on the Equations
- tp = time of ponding [minutes] = the time when the soil
becomes saturated at the surface, after which v0=fc
or v0=0 (after surface inputs stop). If (P + M) < Ks,
then ponding cannot occur.
- The equation for v0 implies that v0 = 0 whenever
(P + M) = 0, since fc > 0.
- If (P + M) > Ks, then after a sufficiently long time
F will become large, (F+J)/F will approach a value of 1 and fc
will decrease asymptotically to Ks.
- The definition of F implies that dF/dt = v0. Here, F is
the quantity that Smith (2002) refers to as I', but that doesn't display
well in HTML.
- The current implementation is meant for single events only
since F is only reset to 0 at the start of each model run.
- In the case where (P + M) is uniform in time, it is possible to compute
the surface soil moisture using a relationship of the form, K = K(θ).
This type of relationship, found empirically, is called a soil
characteristic function and is also used in conjunction with the
1D Richards' equation method of infiltration.
See Smith (2002, pp. 81-85) for details.
- The Green-Ampt and Smith-Parlange methods for modeling infiltration are
based on the infiltrability-depth approximation or IDA, which uses
the cumulative infiltrated depth as a "replacement" for time. For details, see
Smith (2002, pp. 71-73). These methods are not well-suited to modeling
redistribution between events or drying of surface layers by evaporation.
They are best used for single events.
- If there is standing water of depth, d, at the surface, then G can/should
be replaced by (G + d) in the equation for J. This isn't done in the current
version, since channels typically only occupy a small fraction of a grid cell
and water depth on hillslopes is typically very small.
- This model can be viewed as a special case of the
Smith-Parlange 3-parameter
model in which γ=0. See the Notes on the help page for that model.
References
Smith, R.E. (2002) Infiltration Theory for Hydrologic
Applications, Water Resources Monograph 15, AGU.
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