Water

Editorial

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Open AccessEditorial

Commemorating Dr. Gudmundur “Bo” Bodvarsson (1951–2006), a Leader of the Deep Unsaturated Flow and Transport Investigations

by Chin-Fu Tsang, Marcelo Lippmann, Patrick Dobson, Yvonne Tsang, Boris Faybishenko, Sally Benson, Jens Birkholzer, Stefan Finsterle, Daniel Hawkes, Susan Hubbard, Timothy Kneafsey, Hui-Hai Liu, Curtis M. Oldenburg, Karsten Pruess, Eric Sonnenthal, Maryann Villavert, Joseph Wang, Yu-Shu Wu and Robert W. Zimmerman

Water 2018, 10(1), 18; https://doi.org/10.3390/w10010018 - 30 Dec 2017

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Abstract

The Special Issue “Water and Solute Transport in Vadose Zone” in the journal Water is dedicated to the memory of Dr. Gudmundur “Bo” Bodvarsson, the former director of the Earth Sciences Division of Lawrence Berkeley National Laboratory (http://eesa.lbl.gov/profiles/gudmundur-bo-sbodvarsson/).[...] Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

Research

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12 pages, 3269 KiB

Open AccessArticle

A Simplified Infiltration Model for Predicting Cumulative Infiltration during Vertical Line Source Irrigation

by Yanwei Fan, Ning Huang, Jiaguo Gong, Xiaoxia Shao, Jie Zhang and Tong Zhao

Water 2018, 10(1), 89; https://doi.org/10.3390/w10010089 - 20 Jan 2018

Cited by 20 | Viewed by 5409

Abstract

Vertical line source irrigation is a water-saving irrigation method for enhancing direct water and nutrient delivery to the root zone, reducing soil evaporation and improving water and nutrient use efficiency. To identify its influencing factors, we performed computer simulations using the HYDRUS-2D software. [...] Read more.

Vertical line source irrigation is a water-saving irrigation method for enhancing direct water and nutrient delivery to the root zone, reducing soil evaporation and improving water and nutrient use efficiency. To identify its influencing factors, we performed computer simulations using the HYDRUS-2D software. The results indicate that for a given soil, the line source seepage area, but not the initial soil water content and buried depth, has a significant effect on the cumulative infiltration. We thus proposed a simplified method, taking into account the seepage area for predicting the cumulative infiltration based on the Philip model. Finally, we evaluated the accuracy of the simplified method using experimental data and found the cumulative infiltrations predicted by the simplified method were in very good agreement with the observed values, showing a low mean average error of 0.028–0.480 L, a root mean square error of 0.043–0.908 L, a percentage bias of 0.321–0.900 and a large Nash-Sutcliffe coefficient close to 1.0 (NSE ≥ 0.995). The results indicate that this simplified infiltration model, for which the only emitter parameter required is the seepage area, could provide a valuable and practical tool for irrigation design. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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23 pages, 9591 KiB

Open AccessArticle

Inverse Modeling of Soil Hydraulic Parameters Based on a Hybrid of Vector-Evaluated Genetic Algorithm and Particle Swarm Optimization

by Yi-Bo Li, Ye Liu, Wei-Bo Nie and Xiao-Yi Ma

Water 2018, 10(1), 84; https://doi.org/10.3390/w10010084 - 18 Jan 2018

Cited by 22 | Viewed by 4850

Abstract

The accurate estimation of soil hydraulic parameters (θ_s, α, n, and K_s) of the van Genuchten–Mualem model has attracted considerable attention. In this study, we proposed a new two-step inversion method, which first estimated the hydraulic [...] Read more.

The accurate estimation of soil hydraulic parameters (θ_s, α, n, and K_s) of the van Genuchten–Mualem model has attracted considerable attention. In this study, we proposed a new two-step inversion method, which first estimated the hydraulic parameter θ_s using objective function by the final water content, and subsequently estimated the soil hydraulic parameters α, n, and K_s, using a vector-evaluated genetic algorithm and particle swarm optimization (VEGA-PSO) method based on objective functions by cumulative infiltration and infiltration rate. The parameters were inversely estimated for four types of soils (sand, loam, silt, and clay) under an in silico experiment simulating the tension disc infiltration at three initial water content levels. The results indicated that the method is excellent and robust. Because the objective function had multilocal minima in a tiny range near the true values, inverse estimation of the hydraulic parameters was difficult; however, the estimated soil water retention curves and hydraulic conductivity curves were nearly identical to the true curves. In addition, the proposed method was able to estimate the hydraulic parameters accurately despite substantial measurement errors in initial water content, final water content, and cumulative infiltration, proving that the method was feasible and practical for field application. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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1001 KiB

Open AccessArticle

Effects on Infiltration and Evaporation When Adding Rapeseed-Oil Residue or Wheat Straw to a Loam Soil

by Xuguang Xing, Yibo Li and Xiaoyi Ma

Water 2017, 9(9), 700; https://doi.org/10.3390/w9090700 - 14 Sep 2017

Cited by 24 | Viewed by 4685

Abstract

The application of additives (e.g., wheat straw (WS) or rapeseed-oil residue (RR)) to soils is a common agronomic practice, used for improving soil water retention. Through a laboratory investigation, this study examined the effects of RR and WS on infiltration, evaporation, water distribution, [...] Read more.

The application of additives (e.g., wheat straw (WS) or rapeseed-oil residue (RR)) to soils is a common agronomic practice, used for improving soil water retention. Through a laboratory investigation, this study examined the effects of RR and WS on infiltration, evaporation, water distribution, and water retention. The results indicated that the migration rate of the wetting front, as well as the accumulative infiltration and evaporation, decreased with the amount of applied additives. RR was more effective than WS for infiltration and evaporation suppression. Furthermore, in the Kostiakov model, the value of a decreased with an increasing amount of additive, becoming smaller than the corresponding control treatment (CK) value; by contrast, the value of n decreased with increasing amount of applied additive, remaining larger than the CK value. In the Rose model, the values of A for the soils mixed with additives were smaller than those of the CK, and decreased with increasing amount of additive. Moreover, compared with the CK, the maximum water content for the RR-applied soils increased by 17.84% after infiltration and by 47.66% after evaporation. In addition, the water retention coefficients (calculated as the soil moisture after evaporation divided by that after infiltration) for soils mixed with RR were the highest, indicating that RR is more effective than WS for improving the water retention of the soil layer. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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231 KiB

Open AccessFeature PaperArticle

Incorporating the Vadose Zone into the Budyko Framework

by Garrison Sposito

Water 2017, 9(9), 698; https://doi.org/10.3390/w9090698 - 13 Sep 2017

Cited by 9 | Viewed by 3577

Abstract

The Budyko framework provides a quantitative description of long-term average annual evapotranspiration at catchment scales in terms of macro-climatic variables. This framework, however, makes no reference to the vadose zone because it neglects changes in ubsurface storage in the catchment water balance. Recent [...] Read more.

The Budyko framework provides a quantitative description of long-term average annual evapotranspiration at catchment scales in terms of macro-climatic variables. This framework, however, makes no reference to the vadose zone because it neglects changes in ubsurface storage in the catchment water balance. Recent studies have shown clearly that vadose-zone water storage cannot be neglected at sub-catchment or sub-annual space and time scales, resulting in numerous model attempts to extend the original Budyko framework to incorporate the full water balance equation. Here we apply the approach taken in a companion paper on the original Budyko framework to show that it can be generalized rigorously to include changes in vadose-zone water storage in a manner that is both parsimonious in hypotheses and broad in scope. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

3298 KiB

Open AccessArticle

Influencing Factors and Simplified Model of Film Hole Irrigation

by Yi-Bo Li, Yan-Wei Fan, Ye Liu and Xiao-Yi Ma

Water 2017, 9(7), 543; https://doi.org/10.3390/w9070543 - 20 Jul 2017

Cited by 28 | Viewed by 5504

Abstract

Film hole irrigation is an advanced low-cost and high-efficiency irrigation method, which can improve water conservation and water use efficiency. Given its various advantages and potential applications, we conducted a laboratory study to investigate the effects of soil texture, bulk density, initial soil [...] Read more.

Film hole irrigation is an advanced low-cost and high-efficiency irrigation method, which can improve water conservation and water use efficiency. Given its various advantages and potential applications, we conducted a laboratory study to investigate the effects of soil texture, bulk density, initial soil moisture, irrigation depth, opening ratio (ρ), film hole diameter (D), and spacing on cumulative infiltration using SWMS-2D. We then proposed a simplified model based on the Kostiakov model for infiltration estimation. Error analyses indicated SWMS-2D to be suitable for infiltration simulation of film hole irrigation. Additional SWMS-2D-based investigations indicated that, for a certain soil, initial soil moisture and irrigation depth had the weakest effects on cumulative infiltration, whereas ρ and D had the strongest effects on cumulative infiltration. A simplified model with ρ and D was further established, and its use was then expanded to different soils. Verification based on seven soil types indicated that the established simplified double-factor model effectively estimates cumulative infiltration for film hole irrigation, with a small mean average error of 0.141–2.299 mm, a root mean square error of 0.177–2.722 mm, a percent bias of −2.131–1.479%, and a large Nash–Sutcliffe coefficient that is close to 1.0. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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4431 KiB

Open AccessArticle

HYDRUS Simulation of Sustainable Brackish Water Irrigation in a Winter Wheat-Summer Maize Rotation System in the North China Plain

by Kangkang He, Yonghui Yang, Yanmin Yang, Suying Chen, Qiuli Hu, Xiaojing Liu and Feng Gao

Water 2017, 9(7), 536; https://doi.org/10.3390/w9070536 - 18 Jul 2017

Cited by 38 | Viewed by 6988

Abstract

Freshwater resources in the North China Plain (NCP) are near depletion due to the unceasing overexploitation of deep groundwater, by far the most significant source of freshwater in the region. To deal with the deepening freshwater crisis, brackish water (rich but largely unused [...] Read more.

Freshwater resources in the North China Plain (NCP) are near depletion due to the unceasing overexploitation of deep groundwater, by far the most significant source of freshwater in the region. To deal with the deepening freshwater crisis, brackish water (rich but largely unused water in agriculture) is increasingly being used in irrigation in the region. However, inappropriate irrigation with brackish water could lead to soil salinization and cropland degradation. To evaluate such negative impacts, the HYDRUS-1D model was used to simulate soil salt transport and accumulation under 15 years of irrigation with brackish water. The irrigation scenarios included brackish water irrigation during the wintering and jointing stages of winter wheat and then freshwater irrigation just before the sowing of summer maize. Freshwater irrigation was done to leach out soil salts, which is particularly vital in dry years. For the littoral region of the plain, HYDRUS-ID was used to simulate the irrigated cropping system stated above for a total period of 15 years. The results showed that it was feasible to use brackish water twice in one year, provided freshwater irrigation was performed before sowing summer maize. Freshwater irrigation, in conjunction with precipitation, leached out soil salts from the 100 cm root-zone depth. The maximum salt accumulation was in the 160–220 cm soil layer, which ensured that root-zone soil was free of restrictive salinity for crop growth. Precipitation was a critical determinant of the rate and depth leaching of soil salt. Heavy rainfall (>100 mm) caused significant leaching of soluble salts in the 0–200 cm soil profile. Salt concentration under brackish water irrigation had no significant effect on the variations in the trend of soil salt transport in the soil profile. The variations of soil salinity were mainly affected by hydrological year type, for which the buried depth of soil salt was higher in wet years than in dry years. The study suggested that 15 years of irrigation with brackish water is a reliable and feasible mode of crop production in coastal regions with a thick soil column above the water table. The scheme proposed in this study allowed the use of brackish water in irrigation without undue salinization of the crop soil layer, an intuitive way of resolving the deepening water crisis in the NCP study area and beyond. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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3124 KiB

Open AccessArticle

Flood Effect on Groundwater Recharge on a Typical Silt Loam Soil

by Guohua Zhang, Gary Feng, Xinhu Li, Congbao Xie and Xiaoyu Pi

Water 2017, 9(7), 523; https://doi.org/10.3390/w9070523 - 14 Jul 2017

Cited by 27 | Viewed by 11090

Abstract

Floods are of great concern as the global climate changes, and investigations of flood water infiltration and groundwater recharge are important for water resource management worldwide, especially under conditions of global climate changes. However, information on the relationship between the flood water and [...] Read more.

Floods are of great concern as the global climate changes, and investigations of flood water infiltration and groundwater recharge are important for water resource management worldwide, especially under conditions of global climate changes. However, information on the relationship between the flood water and groundwater recharge is limited. The objective of this study was to determine the relationship between the flood water depth and the height of groundwater rise using lysimeters and numerical modeling in the floodplain of the Tarim River in northwestern China. The experimental results suggested that the rise in height of the groundwater table was closely related to the flood water ponding depth, and the groundwater depth decreased quickly after flooding due to the high infiltration rate of water originating at the Tarim River. The water table falling velocity was significantly less than the water table rising velocity. If the initial groundwater table was deeper, the variation in the water table rise depth was smaller and the water table falling velocity was slower. The numerical simulation results showed good agreement with the observed data, with a determination coefficient (R²) of 0.87 and a root mean square error (RMSE) of 63.91 cm. A good relationship (R² = 0.789) between the initial groundwater table depth (H₀), initial soil water content (W₀), flood water depth (h), and height of the water table rise (H) was established. Considering that natural and artificial flood frequencies are related to flood time interval (dt), a relationship (R² = 0.892) was developed between them. These results can enhance the understanding of flood recharge characteristics in the floodplains of inland rivers. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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3558 KiB

Open AccessArticle

An Investigation into the Effects of Temperature Gradient on the Soil Water–Salt Transfer with Evaporation

by Rong Ren, Juanjuan Ma, Qiyun Cheng, Lijian Zheng, Xianghong Guo and Xihuan Sun

Water 2017, 9(7), 456; https://doi.org/10.3390/w9070456 - 24 Jun 2017

Cited by 13 | Viewed by 5690

Abstract

Temperature gradients exist in the field under brackish water irrigation conditions, especially in northern semi–arid areas of China. Although there are many investigators dedicated to studying the mechanism of brackish water irrigation and the effect of brackish water irrigation on crops, there are [...] Read more.

Temperature gradients exist in the field under brackish water irrigation conditions, especially in northern semi–arid areas of China. Although there are many investigators dedicated to studying the mechanism of brackish water irrigation and the effect of brackish water irrigation on crops, there are fewer investigations of the effects of temperature gradient on the water–salt transport. Based on the combination of a physical experiment and a mathematical model, this study was conducted to: (a) build a physical model and observe the redistribution of soil water–heat–salt transfer; (b) develop a mathematical model focused on the influence of a temperature gradient on soil water and salt redistribution based on the physical model and validate the proposed model using the measured data; and (c) analyze the effects of the temperature gradient on the soil water–salt transport by comparing the proposed model with the traditional water–salt model in which the effects of temperature gradient on the soil water–salt transfer are neglected. Results show that the soil temperature gradient has a definite influence on the soil water–salt migration. Moreover, the effect of temperature gradient on salt migration was greater than that of water movement. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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2518 KiB

Open AccessArticle

Influence of Anionic Surfactant on Saturated Hydraulic Conductivity of Loamy Sand and Sandy Loam Soils

by Zhenyang Peng, Christophe J. G. Darnault, Fuqiang Tian, Philippe C. Baveye and Hongchang Hu

Water 2017, 9(6), 433; https://doi.org/10.3390/w9060433 - 15 Jun 2017

Cited by 17 | Viewed by 5719

Abstract

Surfactants released into the terrestrial environment in large amounts can potentially alter the physical, chemical and biological properties of soils, particularly the saturated hydraulic conductivity (K_s). Unfortunately findings regarding this process are quite limited. In this study, column tests were [...] Read more.

Surfactants released into the terrestrial environment in large amounts can potentially alter the physical, chemical and biological properties of soils, particularly the saturated hydraulic conductivity (K_s). Unfortunately findings regarding this process are quite limited. In this study, column tests were used to analyze the effects of Aerosol 22, a widely used anionic surfactant, on K_s of loamy sand and sandy loam soils. Solutions were injected into columns from the bottom with controlled pressure heads. Both the overall K_s of columns and the K_s of 6 layers at distances of 0–1 cm, 1–3 cm, 3–5 cm, 5–7 cm, 7–9 cm, and 9–10 cm from the bottom, were continuously monitored before and after the surfactant injections. Results showed that the overall K_s of all columns decreased after 2–4 pore volumes of the surfactant injections. However, stabilization and even increase at the beginning of the surfactant injection was also observed due to the different K_s variations in different layers. Specifically, a surfactant injection of 2–4 pore volumes continuously decreased the K_s of the 0–1 cm layers which yielded a K_s reduction of two orders of magnitude and dominated the K_s variations of the column. In contrast, an increase in the K_s of the 1–3 cm and 3–5 cm layers was more likely, while K_s variation of the 5–10 cm layers was less likely. We hypothetically attributed the K_s variations to the swelling of clay, the collapse of soil aggregates and subsequent particle displacements from surfactant adsorption, which caused pore clogging in the bottom 0–1 cm layer and higher porosities in the layers above. The adsorption of the surfactant aggregates and crystallization were also possibly thought to cause a pore clogging in the bottom layer thus decrease the surfactant concentration from the inlet, the severity of which affects these layers less at greater distances from the inlet. In view of the uncertainty showed by the experimental results, we also suggest to include more replicate columns in future studies, so as to increase the repeatability of the measurements. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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2791 KiB

Open AccessArticle

Simulating the Fate and Transport of Coal Seam Gas Chemicals in Variably-Saturated Soils Using HYDRUS

by Dirk Mallants, Jirka Šimůnek, Martinus Th. van Genuchten and Diederik Jacques

Water 2017, 9(6), 385; https://doi.org/10.3390/w9060385 - 30 May 2017

Cited by 15 | Viewed by 7091

Abstract

The HYDRUS-1D and HYDRUS (2D/3D) computer software packages are widely used finite element models for simulating the one-, and two- or three-dimensional movement of water, heat, and multiple solutes in variably-saturated media, respectively. While the standard HYDRUS models consider only the fate and [...] Read more.

The HYDRUS-1D and HYDRUS (2D/3D) computer software packages are widely used finite element models for simulating the one-, and two- or three-dimensional movement of water, heat, and multiple solutes in variably-saturated media, respectively. While the standard HYDRUS models consider only the fate and transport of individual solutes or solutes subject to first-order degradation reactions, several specialized HYDRUS add-on modules can simulate far more complex biogeochemical processes. The objective of this paper is to provide a brief overview of the HYDRUS models and their add-on modules, and to demonstrate possible applications of the software to the subsurface fate and transport of chemicals involved in coal seam gas extraction and water management operations. One application uses the standard HYDRUS model to evaluate the natural soil attenuation potential of hydraulic fracturing chemicals and their transformation products in case of an accidental release. By coupling the processes of retardation, first-order degradation and convective-dispersive transport of the biocide bronopol and its degradation products, we demonstrated how natural attenuation reduces initial concentrations by more than a factor of hundred in the top 5 cm of the soil. A second application uses the UnsatChem module to explore the possible use of coal seam gas produced water for sustainable irrigation. Simulations with different irrigation waters (untreated, amended with surface water, and reverse osmosis treated) provided detailed results regarding chemical indicators of soil and plant health, notably SAR, EC and sodium concentrations. A third application uses the HP1 module to analyze trace metal transport involving cation exchange and surface complexation sorption reactions in a soil leached with coal seam gas produced water following some accidental water release scenario. Results show that the main process responsible for trace metal migration in soil is complexation of naturally present trace metals with inorganic ligands such as (bi)carbonate that enter the soil upon infiltration with alkaline produced water. The examples were selected to show how users can tailor the required model complexity to specific needs, such as for rapid screening or risk assessments of various chemicals nder generic soil conditions, or for more detailed site-specific analyses of actual subsurface pollution problems. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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5849 KiB

Open AccessArticle

Effects of Pore-Scale Geometry and Wettability on Two-Phase Relative Permeabilities within Elementary Cells

by Emanuela Bianchi Janetti, Monica Riva and Alberto Guadagnini

Water 2017, 9(4), 252; https://doi.org/10.3390/w9040252 - 5 Apr 2017

Cited by 13 | Viewed by 6122

Abstract

We study the relative role of the complex pore space geometry and wettability of the solid matrix on the quantification of relative permeabilities of elementary cells of porous media. These constitute a key element upon which upscaling frameworks are typically grounded. In our [...] Read more.

We study the relative role of the complex pore space geometry and wettability of the solid matrix on the quantification of relative permeabilities of elementary cells of porous media. These constitute a key element upon which upscaling frameworks are typically grounded. In our study we focus on state immiscible two-phase flow taking place at the scale of elementary cells. Pressure-driven two-phase flow following simultaneous co-current injection of water and oil is numerically solved for a suite of regular and stochastically generated two-dimensional explicit elementary cells with fixed porosity and sharing main topological/morphological features. We show that the relative permeabilities of the randomly generated elementary cells are significantly influenced by the formation of preferential percolation paths, called principal pathways, giving rise to a strongly nonuniform distribution of fluid fluxes. These pathways are a result of the spatially variable resistance that the random pore structures exert on the fluid. The overall effect on relative permeabilities of the diverse organization of principal pathways, as driven by a given random realization at the scale of the elementary cell, is significantly larger than that of the wettability of the host rock. In contrast to what can be observed for the random cells analyzed, the relative permeabilities of regular cells display a clear trend with contact angle at the investigated scale. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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266 KiB

Open AccessArticle

Understanding the Budyko Equation

by Garrison Sposito

Water 2017, 9(4), 236; https://doi.org/10.3390/w9040236 - 25 Mar 2017

Cited by 90 | Viewed by 13729

Abstract

The Budyko equation has achieved iconic status in hydrology for its concise and accurate representation of the relationship between annual evapotranspiration and long-term-average water and energy balance at catchment scales. Accelerating anthropogenic land-use and climate change have sparked a renewed interest in predictive [...] Read more.

The Budyko equation has achieved iconic status in hydrology for its concise and accurate representation of the relationship between annual evapotranspiration and long-term-average water and energy balance at catchment scales. Accelerating anthropogenic land-use and climate change have sparked a renewed interest in predictive applications of the Budyko equation to analyze future scenarios important to water resource management. These applications, in turn, have inspired a number of attempts to derive mathematical models of the Budyko equation from a variety of specific assumptions about the original Budyko hypothesis. Here, we show that the Budyko equation and all extant models of it can be derived rigorously from a single mathematical assumption concerning the Budyko hypothesis. The implications of this fact for parametric models of the Budyko equation also are explored. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

1390 KiB

Open AccessArticle

A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

by Allen G. Hunt, Ran Holtzman and Behzad Ghanbarian

Water 2017, 9(2), 104; https://doi.org/10.3390/w9020104 - 9 Feb 2017

Cited by 12 | Viewed by 6851

Abstract

Optimal flow paths obtained from percolation theory provide a powerful tool that can be used to characterize properties associated with flow such as soil hydraulic conductivity, as well as other properties influenced by flow connectivity and topology. A recently proposed scaling theory for [...] Read more.

Optimal flow paths obtained from percolation theory provide a powerful tool that can be used to characterize properties associated with flow such as soil hydraulic conductivity, as well as other properties influenced by flow connectivity and topology. A recently proposed scaling theory for vegetation growth appeals to the tortuosity of optimal paths from percolation theory to define the spatio‐temporal scaling of the root radial extent (or, equivalently, plant height). Root radial extent measures the maximum horizontal distance between a plant shoot and the root tips. We apply here the same scaling relationship to unsteady (horizontal) flow associated with plant transpiration. The pore‐scale travel time is generated from the maximum flow rate under saturated conditions and a typical pore size. At the field‐scale, the characteristic time is interpreted as the growing season duration, and the characteristic length is derived from the measured evapotranspiration in that period. We show that the two scaling results are equivalent, and they are each in accord with observed vegetation growth limits, as well as with actual limiting transpiration values. While the conceptual approach addresses transpiration, most accessed data are for evapotranspiration. The equivalence of the two scaling approaches suggests that, if horizontal flow is the dominant pathway in plant transpiration, horizontal unsteady flow follows the same scaling relationship as root growth. Then, we propose a corresponding scaling relationship to vertical infiltration, a hypothesis which is amenable to testing using infiltration results of Sharma and co‐authors. This alternate treatment of unsteady vertical flow may be an effective alternative to the commonly applied method based on the diffusion of water over a continuum as governed by Richards’ equation. Full article

(This article belongs to the Special Issue Water and Solute Transport in Vadose Zone)

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