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

Input

Layer 1

Output

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)

[math]\displaystyle{ f_{c}= K_{s} + \gamma \ast \left ( K_{s} - K_{i}\right) / [ exp \left ( \gamma \ast F / J \right) - 1 ] }[/math]

(1)

[math]\displaystyle{ J= G \ast \left ( \theta_{s} - \theta_{i}\right) }[/math]

(2)

• Infiltration rate at surface (K_s < (P + M))

[math]\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. }[/math]

(3)

• Cumulative infiltration depth (from 0 to t)

[math]\displaystyle{ F= \int v_{0}\left ( t \right) dt }[/math]

(4)

Nomenclature

Symbol	Description	Unit
Ks	saturated hydraulic conductivity	m / s
Ki	initial hydraulic conductivity (typically much less than Ks)	m / s
θs	soil water content at ψ = 0 (typically set to the porosity, ψ)	-
θi	initial soil water content	-
G	capillary length scale	m
P	precipitation rate	mm / sec
M	snowmelt rate	mm / sec
γ	Smith-Pariange method parameter (between 0 and 1, near 0.8)
fc	infiltrability or max infiltration rate	mm / sec
F	cumulative infiltration depth	m
J		-
v0	infiltration rate at surface	mm / sec
t	time	s

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.

t_p = time of ponding [minutes] = the time when the soil becomes saturated at the surface, after which v₀=f_c or v₀=0 (after surface inputs stop). If (P + M) < K_s, then ponding cannot occur.

The equation for v₀ implies that v₀ = 0 whenever (P + M) = 0, since f_c > 0.

If (P + M) > K_s, then after a sufficiently long time F will become large, the term with the exponential in the denominator will approach zero and f_c will decrease asymptotically to K_s.

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 f_c can be simplified to: f_c = [K_s * exp(F / J) - K_i] / [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:

• Upload file: https://csdms.colorado.edu/wiki/Special:Upload
• Create link to the file on your page: [[Image:<file name>]].

See also: Help:Images or Help:Movies

Developer(s)

Scott Peckham

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.

Links

Related Help Pages

• Model help:TopoFlow-Infiltration-Green-Ampt
• Model help:TopoFlow-Infiltration-Richards 1D
• Model help:TopoFlow-Saturated_Zone-Darcy_Layers
• Model help:TopoFlow-Soil Properties Page

Model Metadata

• Model:TopoFlow-Infiltration-Smith-Parlange
• Model:TopoFlow