Infiltration from a Trickle Source: I. Mathematical Models

Brandt, A.; Bresler, Eshel; Diner, N.; Ben-Asher, I.; Heller, J.P.; Goldberg, Daniel W.

doi:10.2136/sssaj1971.03615995003500050018x

Cited by 138 publications

(70 citation statements)

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“…Among these issues, we can list the presence of steep wetting fronts; the elliptic form of Richards' equation in saturated domains; the non-mass-conserving of algorithms solving for ; and the fact that -based algorithms cannot be applied to situations where parts of the domain are saturated [Milly, 1985[Milly, , 1988Hills et al, 1989;Kirkland et al, 1992]. Different finite difference algorithms were developed that deal with these issues [Klute, 1952;Hanks and Bowers, 1962;Rubin, 1968;Brandt et al, 1971;Neuman, 1972;Vauclin et al, 1979]. Mass conservation was significantly improved by Celia et al [1990].…”

Section: Numerical Solutions Of the Infiltration Equationmentioning

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: Numerical Solutions Of the Infiltration Equationmentioning

confidence: 99%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

222

115

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“…Brandt, et al (1971) e Bresler et al (1971 desenvolveram soluções matemáticas para analisar o movimento multidimensional transitório a partir de uma fonte pontual. Os primeiros autores basearam-se em num modelo de fluxo em 2 dimensões envolvendo as coordenadas cartesianas x e z. Já Bresler et al (1971) basearam-se num modelo de fluxo vertical e radial descrito pelas coordenadas cilíndricas z e r, sendo que somente para o caso onde a taxa de infiltração foi grande é que foram encontradas significativas discrepâncias entre os dados teóricos e os medidos no laboratório. Tanto a teoria, assim como os dados experimentais, indicam que para as condições estudadas, um incremento na taxa de descarga resulta num incremento do molhamento horizontal em detrimento do molhamento vertical.…”

Section: Fluxo E Distribuição De áGua Sob Irrigação Por Gotejamentounclassified

“…Modelos de infiltração e redistribuição para fontes pontiformes foram apresentados por Brandt et al (1971), Warrick (1974), Ben-Asher et al (1978) e Warrick (1986, entre outros. Mmolawa (2000b) relatou que a dinâmica de água e solutos no solo, em ausência de culturas, pode ser representada adequadamente por soluções analíticas do fluxo transitório a partir de fontes puntiformes.…”

Section: Introductionunclassified

Modelagem da dinâmica da água e do potássio na irrigação por gotejamento superficial.

Rivera¹

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“…Numerical methods also have been developed to simulate this phenomenon (Brandt et al, 1971;Taghavi et al, 1984;Healy, 1987). For instance, HYDRUS 2D is a model based on finite-element numerical solutions of the flow equations (Simunek et al, 2006) allowing simulations of threedimensional axially symmetric water flow, solute transport and root water and nutrient uptake.…”

Section: Introductionmentioning

confidence: 99%

Estimating soil wetting patterns for drip irrigation using genetic programming

Samadianfard

Sadraddini

Nazemi

et al. 2012

Span. j. agric. res.

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Drip irrigation is considered as one of the most efficient irrigation systems. Knowledge of the soil wetted perimeter arising from infiltration of water from drippers is important in the design and management of efficient irrigation systems. To this aim, numerical models can represent a powerful tool to analyze the evolution of the wetting pattern during irrigation, in order to explore drip irrigation management strategies, to set up the duration of irrigation, and finally to optimize water use efficiency. This paper examines the potential of genetic programming (GP) in simulating wetting patterns of drip irrigation. First by considering 12 different soil textures of USDA-SCS soil texture triangle, different emitter discharge and duration of irrigation, soil wetting patterns have been simulated by using HYDRUS 2D software. Then using the calculated values of depth and radius of wetting pattern as target outputs, two different GP models have been considered. Finally, the capability of GP for simulating wetting patterns was analyzed using some values of data set that were not used in training. Results showed that the GP method had good agreement with results of HYDRUS 2D software in the case of considering full set of operators with R 2 of 0.99 and 0.99 and root mean squared error of 2.88 and 4.94 in estimation of radius and depth of wetting patterns, respectively. Also, field experimental results in a sandy loam soil with emitter discharge of 4 L h -1 showed reasonable agreement with GP results. As a conclusion, the results of the study demonstrate the usefulness of the GP method for estimating wetting patterns of drip irrigation.Additional key words: genetic programming; HYDRUS 2D; infiltration; numerical models; soil texture triangle. ResumenEstimación mediante programación genética de los patrones del suelo humectantes para el riego por goteo El riego por goteo está considerado como uno de los sistemas de riego más eficientes. El conocimiento del períme-tro del bulbo mojado durante la fase de infiltración del agua es importante para el proyecto y manejo de sistemas de riego por goteo eficientes. Los modelos numéricos son una herramienta útil para analizar la evolución del bulbo mojado durante el riego a fin de explorar estrategias de manejo del riego por goteo que determinen el tiempo de riego y optimicen la eficiencia del uso del agua. En este trabajo se examinó el potencial de la programación de algoritmos genéticos (GP) para la simulación de la forma de bulbos mojados en riego por goteo. En primer lugar se ha simulado, con el programa de métodos numéricos HYDRUS 2D, el bulbo mojado en 12 texturas de suelo y diferentes caudales de goteros y tiempos de riego. A partir de las estimaciones de la profundidad y radio mojado como variables objetivo, se han considerado dos modelos GP diferentes. Por último, se ha analizado la capacidad de GP para simular la forma del bulbo mojado a partir de valores que no se utilizaron durante el proceso de entrenamiento. Los resultados obtenidos con GP, considerando el co...

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Infiltration from a Trickle Source: I. Mathematical Models

Cited by 138 publications

References 0 publications

Infiltration into soils: Conceptual approaches and solutions

Infiltration into soils: Conceptual approaches and solutions

Modelagem da dinâmica da água e do potássio na irrigação por gotejamento superficial.

Estimating soil wetting patterns for drip irrigation using genetic programming

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