Infiltration → Beven's Method

The input variables used by Beven's "Exponential-K" 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]
L = vertical length scale [meters] (see Notes below, L > 0)
C = storage suction factor [meters] = Δ θ * Δ ψ (see Notes below)
K'0 = effective hydraulic conductivity at z=0 [m / s] (see Notes below)
P = precipitation rate [mm / sec]
M = snowmelt rate [mm / sec]

For a detailed discussion of these variables 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 Beven's Method

fc = (K'0 / J) * (C + F) / [exp(F / J) - 1] = infiltrability [m / sec] (max infiltration rate)
J = L * (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]


Notes on the Equations

  1. 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.

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

  3. If (P + M) > Ks, then after a sufficiently long time F will become large, the exponential term in the denominator will grow much faster than the numerator and fc will decrease asymptotically to 0. This differs from the behavior of the Green-Ampt and Smith-Parlange methods which approach Ks for large times. Perhaps Ks should simply be added to fc to correct this.

  4. 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.

  5. The current implementation is meant for single events only since F is only reset to 0 at the start of each model run.

  6. Like the Green-Ampt and Smith-Parlange methods this method is 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.

  7. This method is based on the idea that the effective value of hydraulic conductivity behind the wetting front, K', decreases exponentially with depth, z, below the soil surface such that K'(z) = K'(0) * exp(-z/L). It is assumed that K'(0) < Ks, which implies that K'(z) < Ks. In the notation of Beven (1984), L = (-1/f) and (f < 0). Beven (1984) gives values for f from regression analysis that range from -12.8 to -1.2.

  8. Another key assumption of this method is that the storage suction factor , C, as defined by Morel-Seytoux and Khanji (1974) can be taken to be a constant. Beven (1984) cites experiments by Childs and Bybordi (1969) for which this was found to hold.


References

Beven, K. (1984) Infiltration into a class of vertically non-uniform soils, Hydrological Sciences, 29(4), 425-435.

Morel-Seytoux, H.J. and Khanji, J. (1974) Derivation of an equation of infiltration, Water Resources Research, 10, 795-800.