A note on the time compression approximation

Liu, M.-C.; Parlange, J.‐Y.; Sivapalan, Murugesu; Brutsaert, Wilfried

doi:10.1029/98wr02741

Cited by 21 publications

(16 citation statements)

References 15 publications

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“…The The problem is first solved numerically to obtain I(t) by linearizing the right-hand side of (3) using the transform u = • D dO and then applying the method of lines [Schiesser, 1991] with a finite volume discretization on a fine variable spatial grid and a stiff ordinary differential equation integrator. In particular, for a -0, numerical and exact analytical results [Liu et al, 1998] are identical for the number of significant figures given in Table la. Tables lb, lc …”

Section: Time Compression Analysismentioning

confidence: 57%

“…An earlier paper [Liu et al, 1998] showed that the time compression approximation (TCA) predicts the cumulative infiltration with remarkable accuracy for linear soils. As pointed out by Salvucci and Entekkabi [1994], knowledge of the cumulative infiltration is most important in practice, whereas others, like infiltration rates after ponding, are less important.…”

Section: Introductionmentioning

confidence: 99%

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A note on the error analysis of time compression approximations

Parlange¹,

Hogarth²,

Ross³

et al. 2000

Water Resources Research

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Abstract. The accuracy of the time compression analysis (TCA) is analyzed by comparison with a numerical solution. Both the standard TCA and a new modified TCA are considered for a power law diffusivity and constant surface flux. As expected, the error of the approximations decreases with increasing power, and the error of the modified TCA is about half the error of the standard TCA. In a second part, the errors of the two TCAs are measured using a simple analytical solution instead of a numerical solution. It is shown that the conclusions remain the same for the analytical and numerical solutions. The advantage of using the analytical solution is to obtain simple analytical expressions, showing the influence of parameters. This is done to estimate the maximum error of both TCAs. A practical estimate of the errors can be obtained from equations which only require knowledge of the soil water diffusivity. It appears that for real soils the errors of the TCA are always <1% and thus are a very reliable tool for practical problems. Although not studied systematically, it also appears that gravity effects reduce the errors of the TCA so that the error obtained in the absence of gravity provides a conservative estimate when gravity is present. IntroductionAn earlier paper [Liu et al., 1998] showed that the time compression approximation (TCA) predicts the cumulative infiltration with remarkable accuracy for linear soils. As pointed out by Salvucci and Entekkabi [1994], knowledge of the cumulative infiltration is most important in practice, whereas others, like infiltration rates after ponding, are less important.In the following we first extend the analysis of Liu et al. [1998], which applies to unrealistic soils, to one with a realistic soil water' diffusivity obeying a power law. For the linear soil, exact analytical solutions are available. For a power law diffusivity it is necessary to use numerical tools and/or analytical approximations.As usually done, when TCA is used, the possibly complex dependence of the rainfall rate on time is replaced, until pond- Time Compression AnalysisWe consider the case of infiltration into a soil initially at uniform water content with constant (average) rainfall F/until pending. (Again, the additional problems associated with the time dependence of rainfall are ignored here.) We take a realistic representation of the soil water diffusivity D = D sO%where 0 is the reduced water content (water content measured relative to its initial value divided by its saturated value). The 2401

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Section: Time Compression Analysismentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

A note on the error analysis of time compression approximations

Parlange¹,

Hogarth²,

Ross³

et al. 2000

Water Resources Research

Self Cite

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“…[39] Modification of the TCA that does not assume that the average flux before ponding is the flux at ponding but rather uses a priori information on t p or I(t p ) was proposed by Liu et al [1998], Parlange et al [2000], and Hogarth et al [2011]. This modification reduced by half the error in the cumulative infiltration estimates resulting from the original TCA.…”

Section: Postponding Infiltration: Tcamentioning

confidence: 99%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

189

100

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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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“…Liu et al (1998) provide a nice description of the exact solution for one dimensional linearized infiltration. As an approximate correction for the difference between the exact infiltration solution and the Philip solution, according to the time-compression approximation (TCA) (also termed the Infiltrability-Depth Approximation, see Smith, 2002, for detailed discussion), cumulative infiltration may be used as a surrogate for time (Sherman, 1943;Liu et al, 1998). Accordingly, one assumes that at time t p the cumulative infiltration under the constant flux is equal to the cumulative infiltration under the Philip curve up to time t e .…”

Section: Infiltrationmentioning

confidence: 99%

Simplified stochastic soil-moisture models: a look at infiltration

Rigby

Porporato

2006

Hydrol. Earth Syst. Sci.

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Abstract. A simplified, vertically-averaged model of soil moisture interpreted at the daily time scale and forced by a stochastic process of instantaneous rainfall events is compared with a vertically-averaged model which uses a nonoverlapping rectangular pulse rainfall model and a more physically based description of infiltration. The models are compared with respect to the importance of short time-scale (intra-storm) variable infiltration in determining the probabilistic structure of soil-moisture dynamics at the daily timescale. Differences in approach to infiltration modelling show only minor effects on the probabilistic structure of soilmoisture dynamics as simulated in the two models. The partitioning of losses during a single rainfall event are examined closely and the conditions under which surface-controlled runoff is significant, as a proportion of total losses, are delineated.

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A note on the time compression approximation

Cited by 21 publications

References 15 publications

A note on the error analysis of time compression approximations

A note on the error analysis of time compression approximations

Infiltration into soils: Conceptual approaches and solutions

Simplified stochastic soil-moisture models: a look at infiltration

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