Horton Infiltration

Horton Infiltration

Parameters in the Horton Equation 3-6 are

f_∞         = minimum or ultimate value of f_p (infiltration capacity), in./hr [mm/hr],

f_o         = maximum or initial value of f_p, in./hr [mm/hr], and

α          = decay coefficient, hr^-1.

 
The equation may be derived theoretically (Eagleson, 1970) but is almost always applied by curve-fitting to infiltrometer data.  A regeneration parameter, R, is also required to compute a regeneration rate coefficient, a_d = R a (Equation 3-20). 

            Although the Horton infiltration equation is probably the best-known of the several infiltration equations available, there is little to help the user select values of parame­ters f_o and α for a particular application.  (Fortunately, some guidance can be found for the value of f_c.)  Since the ac­tual values of f_o and α (and often f_c) depend on the soil, vege­tation, and initial moisture content, ideally these parameters should be estimated using re­sults from field infiltrometer tests for a number of sites of the watershed and for a number of ante­cedent wetness conditions.  An example of Horton parameters for Georgia soils is given in Table 3-8 (Rawls et al., 1976).  Horton’s (1940) estimates are shown in Table 3-9.  Skaggs and Khaleel (1982) provide Horton-type decay curves on the basis of theoretical estimates. 

Table 3-8. Horton parameters for selected Georgia soils (Rawls et al., 1976).

Table 3-9. Horton equation parameters provided by Horton (1940).

            If it is not possible to use field data to find estimates of f_o, f_∞, and α for each subcatchment, the following guidelines should be helpful. The NRCS, formerly the Soil Conservation Service or SCS, has classified most soils into Hydrologic Soil Groups, A, B, C, and D, dependening on their limiting infiltra­tion capacities, f_c.  (Well drained, sandy soils are “A”; poorly drained, clayey soils are “D.”)  A listing of the groupings for more than 4000 soil types can be found in the SCS Hydrology Handbook (1972, pp. 7.6-7.26); a simi­lar listing is also given in Chow’s Handbook of Applied Hydrology (Ogrosky and Mockus, 1964, pp. 21.12-21.25), but the former reference also gives alterna­tive groupings for some soil types depending on the degree of drainage of the subsoil.  NRCS soil classification data are also available on CD-ROMs from vendors such as Earth Info (Boulder, CO).  The soil type itself may be found in the U.S. from county NRCS Soil Survey maps.

            The best source of information about a particular soil type is a publica­tion entitled “Soil Survey Interpretations” available from a local NRCS office in the U.S.  Information on the soil profile, the soil proper­ties, its suit­ability for a variety of uses, its erosion and crop yield potential, and other data are included on the sheet for undisturbed soil samples.  A copy of the listing for Conestoga silt loam is shown in Figure 3-37.  Parameter f_∞is essentially equal to the saturated hydraulic conductivity, K_s, which is called “permeability” on the soil survey interpretation sheet.  For Conestoga Silt Loam, a range of 0.63-2.0 in./hr (16-51 mm/hr) is shown.  Similar data are presented in aggregate for most counties in the United States in the Soil Survey for that county, again, obtainable from local NRCS offices or from a local Soil and Water Conservation District. 

            Alternatively, values for f_∞ according to Musgrave (1955) are given in Table 3-10.  To help select a value within the range given for each soil group, the user should consider the texture of the layer of least hydraulic conduc­tivity in the profile.  Depending on whether that layer is sand, loam, or clay, the f_c value should be chosen near the top, middle, and bottom of the range respectively.  For example, the data sheet for Cones­toga silt loam iden­tifies it as being in Hydrologic Soil  Group B, which puts the estimate of f_c into the range of 0.15-0.30 in./hr (3.8-7.6 mm/hr), much lower than the K_s value dis­cussed above.  Examina­tion of the texture of the layers in the soil profile indicates that they are silty in nature, sug­gesting that the estimate of the f_∞ value should be in the low end of the range, say 0.15-0.20 in./hr (3.8-5.1 mm/hr).  A sensitivity test on the f_∞ value will indicate the importance of this parameter to the overall result.

Table 3-10.  Values of f_∞ for Hydrologic Soil Groups (Musgrave, 1955).  (Hydrologic Soil Group is defined in Table 3-15 and discussed in Section 3.8.8.5.)

 
            Caution should be used in applying values from Table 3-10 to sandy soils (group A) since reported K_s values are often much higher.  For instance, sandy soils in Florida have K_s values from 7 to 18 in./hr (180-450 mm/hr) (Carlisle et al., 1981).  Unless the water table rises to the surface, ultimate infil­tration capacity will be very high, and rainfall rates will almost always be less than f_∞, leading to little or no overland flow from such soils.

            When water ponds on the surface, the limiting value of surface infiltration is the saturated hydraulic conductivity, K_s.  Thus,

            f_c∞ ≈ K_s                                                                                    (3-133)

Good, generalized estimates for K_s will be discussed in conjunction with Green-Ampt parameter estimates in the next section and likely are the best source of values for f_∞ in the absence of site-specific data. 

            For any field infiltration test the rate of decrease (or “decay”) of in­fil­tration capacity, α, from the initial value, f_o, depends on the initial moisture content.  Thus the α-value determined for the same soil will vary from test to test.

Figure 4-19.  Soil Conservation Service Soil Survey Interpretation for Conestoga silt loam (found near Lancaster, PA).

           It is postulated here that, if f_o is always specified in relation to a particular soil moisture condition (e.g., dry), and for moisture contents other than this the time scale is changed accordingly (i.e., time “zero” is adjusted to correspond with the constant f_o), then α can be considered a constant for the soil independent of initial moisture content.  Put another way, this means that infiltration curves for the same soil, but different antecedent condi­tions, can be made coincident if they are moved along the time axis.  Butler (1957) makes a similar assumption.

            Values of α found in the literature (Linsley et al., 1975; Overton and Meadows, 1976; Wanielista, 1978; ASCE, 1996) range from 0.67 to 120 hr^-1.  Nevertheless most of the values cited appear to be in the range 3-6 hr^-1 (0.00083-0.00167 sec^-1). [MSOffice1]  The evidence is not clear as to whether there is any relationship between soil texture and the α value although several pub­lished curves seem to indicate a lower value for sandy soils.  If no field data are available, an estimate of 0.00115 sec^-1 (4.14 hr^-1) could be used.  Use of such an estimate implies that, under ponded conditions, the infiltra­tion capacity will fall 98 percent of the way towards its minimum value in the first hour, a not uncommon observation.  Rates of decay of infiltration for several values of α are shown in Table 3-11.

Table 3-11.  Rate of decay of infiltration capacity for different values of α

            The initial infiltration capacity, f_o depends primarily on soil type, initial moisture content, and surface vegetation conditions.  For example, Linsley et al. (1982) present data that show, for a sandy loam soil, a 60 to 70 percent reduction in the f_o value due to wet initial conditions.  They also show that lower f_o values apply for a loam soil than for a sandy loam soil.  As to the effect of vegetation, Jens and McPherson (1964, pp. 20.20-20.38) list data that show that dense grass vegetation nearly doubles the infiltra­tion capacities measured for bare soil surfaces.

            For the assumption to hold that the decay coefficient α is indepen­dent of initial moisture content, f_o must be specified for the dry soil condition.  When SWMM is run in continuous mode, the program automatically calculates the f_o value applic­able for wetter conditions as part of the moisture accounting routine.  How­ever, for any single-event simulation, the user must specify the f_o value for the storm in question, which may be less than the value for dry soil condi­tions.  For this reason, it is often useful to let the program “warm up” by simulating 7 – 14 days prior to the event in question, to let the model establish its own initial conditions.
 

            Published values of f_o vary depending on the soil, moisture, and vegeta­tion conditions for the particular test measurement.  The f_o values listed in Table 3-12 can be used as a rough guide.  Interpolation between the values may be required.

Table 3-12.  Representative values for f_o.

 
            For continuous simulation, infiltration capacity will be regenerated (recovered) during dry weather according to Equation 3-20.  The value of R is probably << 1.0, (implying a “longer” drying curve than wetting curve, Figure 3-7). 

            On well-drained porous soils (e.g., medium to coarse sands), recovery of infiltration capacity is quite rapid and could well be complete in a couple of days.  For heavier soils, the recovery rate is likely to be slower, say 7 to 14 days.  The choice of the value can also be related to the interval between a heavy storm and wilting of vegetation.  The value of α_d is then,

            α_d = 0.02/D                                                                              (3-134)

where

α_d         = R α = recovery curve decay coefficient, day^-1, and

D         = number of days required for the soil to dry out (recover).

 
The factor of 0.02 in Equation 3-134 assumes 98 percent recovery of infil­tra­tion capacity (i.e., e^-0.02 = 0.98).  The value of R may then be calcu­lated from Equation 3-20.  For example, for α = 4.14 day^-1 and drying times of 3, 7 and 14 days, values of R are 1.61 x 10^-3, 6.9 x 10^-4 and 3.45 x 10^-4, respectively.