# Model help:TopoFlow-Infiltration-Smith-Parlange

## TopoFlow-Infiltration-Smith-Parlange

This module is the infiltration process component (Smith-Parlange method) for a D8-based, spatial hydrologic model

## Model introduction

This process component is part of a spatially-distributed hydrologic model called TopoFlow, but it can now be used as a stand-alone model.

## Model parameters

Parameter Description Unit
Component status Enabled/Disabled
Input directory -
Output directory -
Site prefix file prefix for the study site -
Case prefix file prefix for the model scenario -
Number of steps number of time steps -
Number of soil layers -
Time step timestep for infiltration step sec
Parameter Description Unit
K_sat type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
K_sat sat. hydraulic conductivity m / s
K_init type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
K_init init. hydraulic conductivity m / s
theta_sat type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
theta_sat sat. soil water content -
theta_init type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
theta_init init. soil water content -
G type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
G capillary length scale m
gamma type allowed input types (Scale/Grid/Time_series/Grid_sequence) -
gamma Smith-Parlange parameter -
Closet soil_type Closet standard soil_type -
Parameter Description Unit
Save grid timestep time interval between saved grids sec
Save v0 grids toggle option to save grids of infil.rate (at surf) -
Save v0 grids file filename for grid stack of v0 m / s
Save I grids toggle option to save grids of cumul.infil.depth -
Save I grids file filename for grid stack of I m
Save pixels timestep time interval between time series value sec
Save v0 pixels toggle option to save time series of infil.rate (at surf) -
Save v0 pixels file filename for time series of v0 m / s
Save I pixels toggle option to save time series of cumul.infil.depth -
Save I pixels file filename for time series of I m

## Uses ports

• Meteorology
• Snow (Snowmelt)
• Evap (Evaporation)
• Satzone (Subsurface flow in saturated zone)
• Channels (surface water flow in a network of channels)

## Provides ports

• Infil (Infiltration)
• Configure (tabbed dialog GUI to change settings)
• Run (only if used as the Driver)

## Main equations

• Infiltrability (max infiltration rate)
 $\displaystyle{ f_{c}= K_{s} + \gamma \ast \left ( K_{s} - K_{i}\right) / [ exp \left ( \gamma \ast F / J \right) - 1 ] }$ (1)
 $\displaystyle{ J= G \ast \left ( \theta_{s} - \theta_{i}\right) }$ (2)
• Infiltration rate at surface (Ks < (P + M))
 $\displaystyle{ v_{0}= \left\{\begin{matrix} min \left ( \left ( P + M \right), f_{c}\right) & K_{s} \lt \left ( P + M \right ) \\ \left ( P + M \right) & K_{s} \gt \left ( P + M \right ) \end{matrix}\right. }$ (3)
• Cumulative infiltration depth (from 0 to t)
 $\displaystyle{ F= \int v_{0}\left ( t \right) dt }$ (4)

## Notes

Notes on Input Parameters

The Smith-Parlange parameter, γ (gamma), must be between 0 and 1 and typically near 0.8. (see below)

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.

Notes on the Equations

All variables and their units can be seen by expanding the Nomenclature section above.

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, the term with the exponential in the denominator will approach zero 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.

As x approaches zero, a Taylor series shows that exp(x) approaches (1 + x). Using this fact it can be shown that as γ approaches 0, this model approaches the Green-Ampt model. Experimental and numerical results suggest that γ values around 0.8 to 0.85 often give the best fit for normal soils (Smith, 2002, p. 81).

For the case γ = 1, the equation for fc can be simplified to: fc = [Ks * exp(F / J) - Ki] / [exp(F / J) - 1] and this case was analyzed by Smith and Parlange (1978) and Woolhiser et al. (1996).

More information on how soil is modeled in TopoFlow along with published soil property tables can be found on the soil properties page.

## Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

## References

Smith, R.E. (2002) Infiltration Theory for Hydrologic Applications, Water Resources Monograph 15, AGU.

Smith, R.E. and J.-Y. Parlange (1978) A parameter-efficient hydrologic infiltration model, Water Resources Research, 14(3), 533-538.

Woolhiser, D.A., R.E. Smith and J-V. Giraldez (1996) Effects of spatial variability of saturated hydraulic conductivity on Hortonian overland flow, Water Resources Research, 32(3), 671-678.

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