Infiltration Under Ponded Conditions

Haverkamp, R.; Parlange, J.‐Y.; Starr, J. L.; Schmitz, Gerd; Fuentes, Carlos

doi:10.1097/00010694-199005000-00006

Cited by 112 publications

(49 citation statements)

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“…If, however, greater preci-299 sion is required, (14) can be used for iterative processes. 300 We observe that, since any value of k can be used in 301 the approximation (17)- (21), other simple, yet poten-302 tially useful approximations can be deduced.…”

Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

“…For ex-303 ample, the case of k ¼ 2 has the virtue of simplifying the 304 approximation considerably. Taking this value, and it-305 erating using (14) for the case of a ¼ 1 gives the ap-306 proximation:…”

Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

“…Thus, the present expression, largely obtained 340 from the short time behaviour of I, is excellent to obtain 341 I, and still quite good for I À t, but some care should be 342 taken in its use. Even in such cases, however, the itera-343 tion (14) could be applied to improve predictions, as we 344 have already indicated in Fig. 3.…”

Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

“…280 Even though the relative error shown in Fig. 3 would 281 be satisfactory for most applications, this error can be 282 further reduced by iteration using (14). This error is also 283 plotted in Fig.…”

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Explicit infiltration equations and the Lambert W-function

Parlange

Barry

Haverkamp

2002

Advances in Water Resources

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10The Green and Ampt infiltration formula, as well as the Talsma and Parlange formula, are two-parameter equations that are 11 both expressible in terms of Lambert W-functions. These representations are used to derive explicit, simple and accurate approx-12 imations for each case. The two infiltration formulas are limiting cases that can be deduced from an existing three-parameter in-13 filtration equation, the third parameter allowing for interpolation between the limiting cases. Besides the limiting cases, there is 14 another case for which the three-parameter infiltration equation yields an exact solution. The three-parameter equation can be 15 solved by fixed-point iteration, a scheme which can be exploited to obtain a sequence of increasingly complex explicit infiltration 16 equations. For routine use, a simple, explicit approximation to the three-parameter infiltration equation is derived. This approxi-17 mation eliminates the need to iterate for most practical circumstances. 20Due to the many circumstances where infiltration 21 into porous media plays a role, theoretical equations for 22 predicting quantities such as infiltration flux and cu-23 mulative infiltration are in widespread use. A subset of 24 these circumstances involves one-dimensional vertical 25 infiltration, a branch of vadose-zone hydrology that has 26 a rich history stretching back to the early part of last 27 century. For a given soil type, the formulas aim to es-28 timate IðtÞ, the cumulative infiltration, I, that enters the 29 soil as a function of time, t. The archetype problem to 30 which infiltration laws apply is infiltration into an ini-31 tially dry, homogeneous soil where the surface of the soil 32 is saturated, but not ponded. It is this situation that is 33 considered below. 34In practice, it is useful to have infiltration laws that 35 are both physically based and easy to implement. The 36 latter feature is inherent in explicit expressions for IðtÞ, 37 whereas the former is a feature of laws that are based on 38 standard soil properties such as the soil-water diffusivity, 39 D, and hydraulic conductivity, K. Physically based in-40 filtration laws for one-dimensional infiltration typically 41 use the sorptivity, S, and particular values of the hy-42 draulic conductivity, e.g., the hydraulic conductivity at 43 saturation, K s , or at the surface moisture content. The 44 sorptivity, we recall, is derived from D and the boundary 45 and initial conditions that pertain [1][2][3][4]. 46 As demonstrated elsewhere [5][6][7][8], infiltration laws 47 have two ''limiting'' behaviors. We remark that they are 48 limits in that they appear to cover the possible range of 49 infiltration behaviour; they are not formal mathematical 50 limits. One limit is represented by the Green and Ampt 51 formula [9], which relies on a soil having a rapidly 52 varying diffusivity and a near-constant hydraulic con-53 ductivity. The other is represented by Talsma and Par-54 lange [10] result relying on proportionality between D 55 and dK=dh (h being...

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Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

Section: U N C O R R E C T E D P R O O Fmentioning

confidence: 99%

mentioning

confidence: 96%

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Explicit infiltration equations and the Lambert W-function

Parlange

Barry

Haverkamp

2002

Advances in Water Resources

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“…(18) is the same as in other studies (Haverkamp et al, 1990;Morelsey and Khanji, 1974;Philip, 1958;Stewart et al, 2013;White and Sully, 1987) in which the first term in the second bracket on the right side of the equation was replaced by a variable representing the achievement of "capillary potential." From Eq.…”

Section: Methods Based On Constant Pressure Head Absorption (Mcpa)mentioning

confidence: 99%

An improved method for determining Brooks–Corey model parameters from horizontal absorption

Zhang

Lai

et al. 2016

Geoderma

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Low-cost, simple, rapid and accurate approaches for measuring soil hydraulic properties are of great importance in the application of hydrologic models of the vadose zone. A recently proposed method of constant-saturation absorption (MCSA) for determining Brooks-Corey (BC) model parameters is promising. However, this method has not been tested using experimental data. In this paper, measured soil-water diffusivity or soil-water retention curves (SWRCs) of 20 soil samples were used to test the reliability of MCSA. The results indicate that MCSA consistently estimated soil-water diffusivities by the Bruce and Klute method, but it substantially overestimated air-entry suctions (h d ) and thereby soil suction. A new method (MCPA) is proposed herein to overcome the problems associated with MCSA. Using the improved method, estimated SWRCs are consistent with observation. With the estimated soil hydraulic parameters, HYDRUS-1D generated very accurate simulations of the cumulative absorption curves. Compared with direct or other indirect methods, MCPA is a more accurate, low-cost, and simple method, and it is especially useful for rapid determination of SWRC for soil-water movement simulations. However, if unsaturated soil-water diffusivity is of greater concern, our results also indicate that MCSA more accurately predicts this quantity and thus should be preferred.

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Falling head ponded infiltration in the nonlinear limit

Triadis

2014

Water Resources Research

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The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green-Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low-conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green-Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding.

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Infiltration Under Ponded Conditions

Cited by 112 publications

References 0 publications

Explicit infiltration equations and the Lambert W-function

Explicit infiltration equations and the Lambert W-function

An improved method for determining Brooks–Corey model parameters from horizontal absorption

Falling head ponded infiltration in the nonlinear limit

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