One dimensional vertical infiltration

Talsma, T; Parlange, J.‐Y.

doi:10.1071/sr9720143

Cited by 101 publications

(76 citation statements)

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“…Because the solution in equation (10) is basically a perturbation series around the solution for sorption, it fails to behave properly for large values of t, when the role of gravity is preponderant. In the case of ponded infiltration, (A 1 þ K s ) should tend to K s for large values of t. However, Philip [1969] and Talsma and Parlange [1972] …”

Section: Empirical Expressionsmentioning

confidence: 99%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

222

115

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[1] Infiltration is a key process in aspects of hydrology, agricultural and civil engineering, irrigation design, and soil and water conservation. It is complex, depending on soil and rainfall properties and initial and boundary conditions within the flow domain. During the last century, a great deal of effort has been invested to understand the physics of infiltration and to develop quantitative predictors of infiltration dynamics. Jean-Yves Parlange and Wilfried Brutsaert have made seminal contributions, especially in the area of infiltration theory and related analytical solutions to the flow equations. This review retraces the landmark discoveries and the evolution of the conceptual approaches and the mathematical solutions applied to the problem of infiltration into porous media, highlighting the pivotal contributions of Parlange and Brutsaert. A historical retrospective of physical models of infiltration is followed by the presentation of mathematical methods leading to analytical solutions of the flow equations. This review then addresses the time compression approximation developed to estimate infiltration at the transition between preponding and postponding conditions. Finally, the effects of special conditions, such as the presence of air and heterogeneity in soil properties, on infiltration are considered.

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Section: Empirical Expressionsmentioning

confidence: 99%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

222

115

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“…Finally, we have already mentioned that for a ¼ 0 346 and 1, i.e., the limiting cases, the branches of the Lam-347 bert W-function are related to I, see (4) and (10). Thus, 348 for 0 < a < 1, I provides an interpolation between W À 0 349 and W À1 which can be used to define a generalised W 350 function, W g , by W g ðxÞ ¼ ð2a À 1ÞI½À1 À lnðÀxÞ þ ½1 þ lnðÀxÞa À 1; ð25Þ 352 352 valid for À expðÀ1Þ 6 x < 0: Approximating I using (17) 353 provides a convenient estimate of W g , which is accurate, 354 except for a very close to 1, when one or more iterations 355 should be used, particularly as x !…”

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

confidence: 99%

“…Here, we find that 333 using (23) to estimate I À t for a ¼ 1, when the one-di-334 mensional intercept exists, gives a maximum relative 335 error of 0.03%, which can be compared with the 0.02% 336 error of (23). Even worse would be to estimate I À t À 1 337 for a ¼ 1, i.e., W À 0 , see (10), since as t ! 1, I !…”

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

confidence: 99%

“…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 the volumetric moisture content), a 56 relationship that was first proposed in [11]. These lim-57 iting cases are both easily derived from Richards' 58 equation [8].…”

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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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“…The other limit (Parlange, 1980) is given by the model of Talsma and Parlange (1972). Both the Green-Ampt and Talsma-Parlange models rely on two soil properties, these being the sorptivity, S, and the saturated hydraulic conductivity, Ks.…”

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confidence: 99%