Linking principles of soil formation and flow regimes

Journal of Hydrology 393 (2010) 3–19

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Journal of Hydrology

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Linking principles of soil formation and flow regimes

Henry LinDept. of Crop and Soil Sciences, The Pennsylvania State Univ., University Park, PA 16802, United States

a r t i c l e i n f o

Keywords:Preferential flowPedogenesisSoil architectureNon-equilibrium thermodynamicsConstructal theoryNetwork theory

0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.02.013

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s u m m a r y

Preferential flow (PF) is a fundamentally important soil hydrologic process that controls a variety of soilphysical, chemical, and biological functions. However, the lack of theory in this field and the existence ofconceptual and technological bottlenecks continue to hinder the advancement of PF modeling and pre-diction. This paper explores three theoretical perspectives on the relationships between pedogenesisand flow regimes in field soils. First, we examine non-equilibrium thermodynamics as applied to opendissipative field soils with continuous energy inputs and mass exchanges with the surrounding environ-ment. The dual-partitioning of pedogenesis (dissipating and organizing processes) is consistent with thetheory of dissipative structure, which explains the genesis and evolution of soil architecture (struc-ture + matrix) and organized heterogeneity found in various soils. Such organized heterogeneity leadsto widespread potential for PF occurrence. Second, we investigate constructal theory to explain the ten-dency for dual-flow regimes in soils – one with high resistivity (Darcy flow) and the other with low resis-tivity (PF) – together, they form PF configuration that provides the least global flow resistance. Thistheory is applied to explain some general characteristics of weathering processes and related flow regimechanges, which are supported by limited chronologic data from the literature on subsoil’s saturatedhydraulic conductivity decrease after a soil reaches a certain age. Third, the theory of evolving networkssheds light on a variety of PF networks observed in field soils, which increase the effectiveness of energyand mass transfer in the subsurface. This is because networks are a part of the organization resulting fromthe minimum energy dissipation principle and far-from-equilibrium thermodynamics. All the three the-ories discussed support the notion that the potential for PF occurrence in field soils is likely universal.However, controversies and challenges associated with these theories require further efforts to rigorouslytest their applicability in natural soils and to formulate explicit quantitative relationships between PFoccurrence and its controls. The principle of soil formation and evolution provides a useful guide to thisendeavor.

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Introduction

Preferential flow (PF) (also called non-uniform flow, non-equi-librium flow, or bypass flow) is a generic term used here to referto the process whereby water (and materials carried by water)moves by preferred pathways in an accelerated speed through afraction of a porous medium, thus bypassing a portion of the matrix(see illustrations in Figs. 1 and 2). Currently, there is no a unifiedclassification of diverse PFs observed in field soils, so Table 1 lists15 commonly reported non-uniform flow of water in various soils,including vertical or lateral flow, saturated or unsaturated flow, andflow at the surface or in the subsurface. Mechanism-wise, vastmajority of PFs are heterogeneity-related (Figs. 1 and 2), althoughinstability in flow could also be generated in homogeneous medium(e.g., leading to gravity-driven fingering). Common PFs includemacropore flow, finger flow, funnel flow, and hydrophobicity-in-

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duced flow that are more frequently reported in the soil science lit-erature (often at the pore and pedon scales), and pipe flow, returnflow, throughflow, depression-focused flow, and flow at the soil–bedrock interface that are more commonly reported in the hydrol-ogy literature (often at the hillslope or catchment scales).

Numerous studies over the past four decades or so have dem-onstrated that PF can occur in practically all natural soils andlandscapes (e.g., Whipkey, 1965; van Genuchten and Wierenga,1976; Bouma et al., 1977; Kirby, 1978; Beven and Germann,1982; Gish and Shirmohammadi, 1991; Flury et al., 1994; Linet al., 1997; Bosch et al., 2000; Uhlenbrook, 2006; Jarvis, 2007;Li et al., 2009). As Clothier et al. (2008) summarized well, PFcan occur spatially at the pore scale of spatial order 10�3 m, atthe core scale (10�1 m), in pedons (100 m), down hillslopes(101–103 m), through catchments (104–105 m), and across largeregions of P106m. Time-wise, PFs can operate during fluid flowsat the temporal order of 100–101 s, during hydrological events100–102 h, throughout seasonal changes 100 year, and across in-ter-annual variations of 101 years.

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Fig. 1. Illustration of strong connection between heterogeneity and preferential flow in natural soils. Two contrasting soil columns visualized under X-ray show manyearthworm borrows and root channels in an agricultural soil derived from limestone (left) and large amount of rock fragments in a forest soil derived from shale (right).

Fig. 2. Illustration of landscape-scale preferential flow. The hillslope diagram is modified from Atkinson (1978). The catchment-wide soil moisture deficit map is taken fromGrayson and Blöschl (2000). The mole hole drain photo was taken from a watershed in South Africa (courtesy of Cornie van Huyssteen, Univ. of Free State, South Africa).

4 H. Lin / Journal of Hydrology 393 (2010) 3–19

Table 1Main features of 15 types of preferential flow of water occurred in soils. These listed types of preferential flow are not necessarily mutually exclusive, and it is not uncommon tosee several types of preferential flow to co-exist in a soil profile.

Type ofpreferentialflow

Location offlowoccurrence

Flowdirection

Flowsituation(soilsaturation)

Main features and mechanisms Common occurrence conditions Examplecase studies

Overland flow Soilsurface

Lateral Saturated orunsaturated

Runoff on soil surface caused by sealing,crusting, hydrophobicity, infiltration excess, orsaturation excess

In arid and semi-arid regions where rainfallintensity is high and soil infiltration isreduced because of surface sealing orpavement; in humid or semi-humid regionswhere surface has been compacted, crusted,nearly-saturated, or a subsurface restrictinglayer exists; more commonly seem in slopinglandscapes, riparian zones, and valleybottoms

Horton(1940) andHewlett andHibbert(1967)

Return flow Soilsurface

Lateral Saturated orunsaturated

Re-surfaced runoff after water infiltrates soil onan upslope portion of a hillslope and exfiltratesat the surface after flowing laterally throughsubsurface

Mostly seem in toeslope of steep hillslopes orareas close to stream channels

Whipkey(1965) andDunne et al.(1975)

Depression-focused flow

Soilsurface

Vertical Saturated Water accumulation at local topography lows Commonly seem in areas with undulatingtopography, especially after largeprecipitation or significant snowmelt

Mosley(1979)

Stemflow-induced flow

Soilsurface

Verticalor lateral

Unsaturated Water flow through plant stems or tree trunksthat reaches the litter or mineral soil surface,often with water quality changed

Commonly seem in areas covered by tress orother vegetations after significantprecipitation events

Levia andFrost (2003)and Li et al.(2009)

Throughfall-induced flow

Soilsurface

Verticalor lateral

Unsaturated Water passing through plant canopy withoutinterception and directly reaches soil surface(no water quality changed) or through plantinterception and then reaches soil surface asdrips from leaves or braches (usually withwater quality changed)

Commonly seem in areas cover with plants,especially after trees and crops develop theirfull canopy

Burch et al.(1989), Leviaand Frost(2003)

Macropore flow Soilsurface orsubsurface

Verticalor lateral

Saturated orunsaturated

Gravity-dominated flow through variousmacropores (generally >0.075 mm in diameter),either surface-connected or not, such as rootchannels, worm holes, animal borrows, fissures,pore space between soil aggregates or betweenliving roots or rock fragments with surroundingsoil matrix

Occurs commonly in diverse soils with plantgrowth and borrowing animal activities, aswell as in structured soils or soils with cracksor fissures (such as that in shrink–swell claysoils)

McDonnell(1990), Linet al. (1996)

Hydrophobicity-induced flow

Soilsurface orsubsurface

Verticalor lateral

Unsaturated Soil hydrophobicity induced differentialinfiltration or localized surface runoff

Commonly seem in forest floors andgrasslands during dry seasons or after fire

Burch et al.(1989),Ritsemaet al. (1993)

Heterogeneity-induced flow

Soilsurface orsubsurface

Verticalor lateral


Non-uniform flow related to soil heterogeneitycaused by factors other than those identified inother preferential flow types, such as pockets oforganic or loose soils, wavy soil horizonboundary, localized subsoil hydrophobicity,rock fragments, and microbial activities etc.

Occurs where heterogeneity exists in a soilprofile given right flow condition

Flühler et al.(1996) andLin and Zhou(2008)

Pipe flow Subsurface Mostlylateral

Mostlysaturated

Special type of concentrated macropore flowwith large and more continuous pores (calledpipes, often >1 cm in diameter), which arecreated by large decayed tree roots, largeanimal borrows, chemical dissolutions, orinternal erosion.

Occurs mostly in forested headwatercatchments or grasslands with borrowinganimal activities

Uchida et al.(2002, 2005)

Film flow(rivulet flow)

Subsurface Verticalor lateral

Unsaturated Special case of macropore flow where waterflows down the wall of macropores in thin film(instead of filling up the entire macroporespace)

Occurs where macropores or small fissures(mesopores) are wetted up underunsaturated condition

Germannet al. (2007)

Mat flow (littleflow)

Subsurface Lateral Saturated orunsaturated

Flow through the interface between O and Ahorizons (i.e., at the base of forest little layer orwithin)

Occurs in forest floors, especially duringsnowmelts or large storms or when soil isfrozen or very wet

McDonnellet al. (1991)

Finger flow(unstableflow)

Subsurface Vertical Unsaturated Infiltrating front becomes unstable and breaksinto narrow, quickly moving ‘‘fingers” of flowbecause of two mobile phases, at fine-over-coarse layers, water repellency, or airentrapment

Occurs mostly in coarse sandy soils Ritsemaet al. (1993)

Funnel flow Subsurface Lateralandvertical


Sloping layer of lower permeability lensesdivert unsaturated flow over the layers andconcentrate the flow as it funnels between orthrough the layers

Occurs in soils with clay or other types oflenses in sandy soils

Kung (1990)

(continued on next page)

H. Lin / Journal of Hydrology 393 (2010) 3–19 5

Table 1 (continued)

Type ofpreferentialflow

Location offlowoccurrence

Flowdirection

Flowsituation(soilsaturation)

Main features and mechanisms Common occurrence conditions Examplecase studies

Throughflow(subsurfacestormflow)

Subsurface Lateral Saturated orunsaturated

Water-restricting layer causes lateral watermovement downslope, often with perchedwater table

Occurs in soils with water-restrictingsubsurface horizons or features (such asfragipan, duripan, glacic layer, permafrost,ortstein, petrocalcic, petrogypsic, placic, andother soil horizons with clay accumulationleading to aquitard or aquiclude), mostcommonly seem in upland terrains, especiallyin humid environment and steep terrain withconductive soils or soils with water-restricting layer underneath

Whipkey(1965) andDunne et al.(1975)

Soil–bedrockinterfaceflow

Subsurface Lateral Saturated Flow at soil–bedrock interfaces Nearly impermeable bedrocks or stratified ordense geological materials (C or R horizons)with a hydrologically-restrictive layer,leading to perched water table and lateralwater movement

Freer et al.(2002),Graham et al.(2010)


From a systems viewpoint, the notion that PF appears universalis supported by numerous published results, which can be brieflysummarized below:

a. Input variability: Sources of water entering soils, hillslopes,and watersheds are seldom uniform because of widespreadheterogeneity in rainfall distribution, weather condition,vegetation cover, stem flow, throughfall, topography, surfaceroughness, land use change, human alternations, and soilinfiltrability.

b. Process diversity: Different mechanisms have been identifiedthat can lead to various PFs, including flows induced by: (1)macropores or fractures, (2) interfacial layers (especiallyrestrictive layers within or underneath soil profiles), (3)instability of wetting front, (4) water repellency, (5) topogra-phy variation, (6) biological activities, and (7) land use/man-agement disturbance.

c. Output non-uniformity: Variability in soil moisture distribu-tion, ground water table fluctuation, early arrival and long-tail of solute breakthrough curve, spatially variable evapo-transpiration, and flow variability revealed by imagesobtained through diverse methods at different scales (e.g.,computed tomography, nuclear magnetic resonance, dye-tracing, and watershed monitoring) all have demonstratedubiquitous heterogeneous outputs in natural soils.

All PFs are fundamentally important as they influence runoff,erosion, water quality, nutrient cycling, biogeochemical processes,ecological functions, biological activities, gas emission, and con-taminant fate in the environment. The value of PFs to ecosystemservices has been estimated to be some $304 billion per year glob-ally (Clothier et al., 2008). Despite such importance and the longrecognition of PF in soils (as early as 1850 by Thomas Way, asnoted by Stamm, 1997), the universality of PF occurrence in soilsremains elusive. This is in part due to the lack of a systematic the-oretical underpinning for understanding various PF occurrences,plus the classical perception that PF is the exception rather thanthe rule (we call this the conceptual bottleneck). Another reason isthe difficulty in observing or monitoring PF in situ and in mappingPF-related soil architecture across scales – especially nondestruc-tively and with high enough spatial–temporal resolutions (we callthis the technological bottleneck). These two bottlenecks result inthe neglect or inadequate treatment in modeling and predictingPF in the real world. As Beven (2006) noted, ‘‘Nearly all hydrologic,water quality, and sediment transport models use the same small-

scale laboratory homogeneous domain theory to represent integratedfluxes at the much larger scales of hillslope and catchment.. . . This isthe root of many discrepancies between model predictions and thereality.” Such a view is now widely shared across scientific commu-nities (e.g., Sidle et al., 2001; Lin et al., 2006; Uhlenbrook, 2006;Kirchner, 2006; McDonnell et al., 2007; CUAHSI, 2007). Amongthe challenged assumptions in standard models for flow and trans-port in real-world porous media is unknown boundary condition(Beven, 2006) or flow configuration (Bejan, 2007).

Traditionally, hydrologic processes have been conceptualizedwithin the continuum domain (e.g., Darcy’s Law). Classical hydrol-ogy has applied findings from fluid mechanics, together with nec-essary constitutive relations to develop sets of governing equations(much in the same way as the study of atmospheric and oceaniccirculation and the distribution of stresses in solids). However, het-erogeneities in porous geomedia, hierarchical structures of soils,widespread fractures in geological materials, land surfaceroughness, surface water flow channel geometry, vegetative covervariability, diverse biological activities in the subsurface, and wide-ranging human impacts all make the land surface and subsurfacedeviate significantly from the continuum assumption (i.e., contin-uous matter, space, pathway, and connectivity). It is now recog-nized that the solid Earth is not like a continuous fluid; rather, itposes hierarchical heterogeneities with discrete flow networksembedded in the mosaics of land surface and subsurface (Forman,1995; Rodriguez-Iturbe and Rinaldo, 1997; CUAHSI, 2007). Thus, anew conceptualization is needed for developing a next generationof hydrologic models that can explicitly consider dynamic flowpathways, patterns, and flow configuration evolution.

The classical continuum concept assumes that fluid in a porousmedium is distributed throughout – and completely fills – thespace it occupies. This concept allows the approximation of phys-ical quantities (such as velocity, density, pressure, and tempera-ture) at infinitesimally small points, by ignoring the fact thatmatter is not continuous and is commonly heterogeneous (espe-cially in natural systems, as opposed to engineered systems). Dif-ferential equations (such as the Richards equation) can then beused in solving problems in continuum mechanics. Some of thesedifferential equations are specific to materials being investigated,while others capture fundamental physical laws, such as the con-servation of mass (the continuity equation), the conservation ofmomentum (the equations of motion and equilibrium), and theconservation of energy (the first law of thermodynamics). In real-ity, however, pore space in natural soils is highly irregular andcomplex across scales, and water filling these pore space is rarely


uniform and seldom completely fills the space – as has been re-vealed by numerous studies using diverse methods across scales(e.g., Beven and Germann, 1982; Jardine et al., 1989; Kung, 1990;Jarvis et al., 1991; Roth et al., 1991; Ritsema et al., 1993; Fluryet al., 1994; Lin et al., 1996; Noguchi et al., 1999; Jarvis, 2007;Lin and Zhou, 2008) (see illustrations in Figs. 1 and 2).

Another challenge for studying PF in the field has been techno-logical constraints, as adequate in situ determination of opaquesubsurface has been difficult, especially nondestructive mappingor imaging of soil architecture and related flow dynamics. Mostfield investigations of PF conducted in the past have been destruc-tive and one-time result, and provided records after events – suchas dye-tracing followed by soil excavation (e.g., Flury et al., 1994;Lin et al., 1996; Noguchi et al., 1999). Although monitoring at cer-tain depths in a soil profile, trenching at the base of a hillslope, orgauging at an outlet of a catchment provide continuous time-seriesdata, these spatially-aggregated results provide almost no informa-tion about where and how PF might have occurred along the waybefore reaching the monitoring location (e.g., Grayson and Blöschl,2000; Tromp-van Meerveld and McDonnell, 2006a,b; Lin and Zhou,2008). Hence, highly transient phenomena (such as quick pulses ofmacropore flow over a short distance, or a transient perched watertable that triggers lateral flow) could have been missed.

Non-invasive techniques, such as geophysical tools and remotesensing, are becoming more popular and are expected to be contin-uously improved. Their current use, however, is limited by theirgenerally coarse spatial and temporal resolution and the fact thatthey do not measure properties of interest directly. Considerableuncertainties exist in the inversion algorithms used with geophys-ical or remote sensing data for inferring soil hydrologic properties(e.g., Rubin and Hubbard, 2005; Jackson and Le Vine, 1996). In re-cent years, with increasing use of nondestructive microscopicimaging techniques in the laboratory (such as X-ray computingtomography and nuclear magnetic resonance) and growing arraysof sensor networks for in situ point-based monitoring in real-time(such as soil moisture and temperature monitoring networks), newopportunities arise for better documenting and understanding PFoccurrence and its timing and frequency under natural conditions(e.g., Lin and Zhou, 2008). Nonetheless, there is still a large gap be-tween laboratory measurements and field observations and be-tween point-based monitoring and landscape-scale processes.Therefore, better sensors and tools and improved techniques formore effective and efficient in situ determination of pore structureand flow dynamics in the subsurface across space and time are ur-gently needed. Only through such technological breakthroughs canwe possibly embody the effects of network-like pore space and itsrelation to complex fluid dynamics into a new theory of flowthrough structured and heterogeneous field soils (Beven and Ger-mann, 1982; McDonnell et al., 2007).

In a new vision for watershed hydrology, McDonnell et al.(2007) raised a number of fundamental questions: ‘‘Why heteroge-neity exists? Why there is preferential, network-like flow at allscales? Why are hydrological connections at the hillslope and wa-tershed scales so threshold-like when the soil, climate, vegetation,and water appear so tightly coupled?” In addressing flow configu-ration generation and evolution in nature, Bejan (2007) challengedthe hydrology community by stating that ‘‘hydrology research isproving every day that science has hit a wall.” In light of these con-cerns and the need to develop a unified PF theory, the objective ofthis paper is to take a first step in exploring three theoretical per-spectives regarding PF occurrence and its links to soil formationand evolution. We first investigate non-equilibrium thermody-namics and related dual-partitioning of pedogenesis to explainthe simultaneous formation of soil structure and soil matrix inthe field. Next, we discuss constructal theory to understand thetendency for dual-flow regimes in soils and apply the theory to

characterize some general features in soil profile development.Thirdly, modern network theory is reviewed to shed light on pos-sible new path for understanding and modeling hydrologic connec-tivity and threshold-like behavior that are linked to PF networksobserved in soils.

Non-equilibrium thermodynamics and dual-partitioning ofpedogenesis

Real-world systems are not isolated from their environmentand therefore are continuously exchanging energy and matter withtheir surroundings (including being driven by external energysources as well as dissipating internal energy to the surroundings).It is such energy and mass flow across various gradients andboundaries (and associated transformations) that have driven theevolution and functioning of soils and ecosystems. Non-equilib-rium thermodynamics (also called open systems thermodynamics,far-from-equilibrium thermodynamics, or irreversible thermody-namics) can be used to enhance the understanding of how soil sys-tems interact with their surroundings and their evolution overtime.

While there are different branches of thermodynamics (see, forexample, Muschik, 2008), non-equilibrium thermodynamics ismost relevant to natural systems and has been used in a large vari-ety of biological, chemical, and mechanical engineering applica-tions (e.g., Prigogine, 1967; de Groot and Mazur, 1963; Demireland Sandler, 2004; Tiezzi, 2006; Jørgensen et al., 2007). Demireland Sandler (2004) reviewed the advantages and disadvantagesof non-equilibrium thermodynamics, and concluded that ‘‘develop-ments in the thermodynamic optimality of processes, dissipative struc-tures, coupled transport and rate processes, and biological systemssuggest that in some circumstances non-equilibrium thermodynamicscan be quite useful.” Therefore, despite some unsolved problemsand controversies (U. Müller-Herold, personal communication), itis in the spirit of exploration that non-equilibrium thermodynam-ics (especially Prigogine’s theory) is discussed in this paper.

Thermodynamic entropy as a measure of soil system’s order–disorderand an arrow of soil evolutionary time

The second law of thermodynamics states that the entropy (S)of an isolated system not in equilibrium will tend to increase overtime, approaching a maximum at equilibrium. Although thermody-namic entropy as originally introduced by Clausius (1865) hadnothing to do with order or disorder, it was interpreted as a mea-sure of a system’s disorder or randomness from statistical mechan-ics viewpoint by Boltzmann (1896): the higher the S, the greaterthe mixture or homogeneity. In other words, an isolated system’sinternal differences in pressure, density, temperature, or chemicalpotential will diminish over time, moving towards no difference atequilibrium (called ‘‘thermal death” by Rudolf Clausius). Interest-ingly, S is a unique physical quantity that tends to a maximum inthe universe (Clausius, 1865). Thus S seems to imply a particulardirection for time, so it is also called an arrow of time (Tiezzi,2006; Jørgensen et al., 2007).

Prigogine (1967) distinguishes two terms in the total change ofentropy, dS, in an open system: the first, diS, is the S produced in-side the system; the second, deS, is the transfer of S across the sys-tem boundaries. According to the second law of thermodynamics,the first term is always positive:

dS ¼ diSþ deS;diS P 0: ð1Þ

It is in this formulation that the distinction between reversibleand irreversible processes is essential (Prigogine, 1967). Onlyirreversible processes (such as convection, diffusion, and certainchemical reactions) contribute to S production, leading to


one-sidedness of time. This irreversibility results from a certainheat energy dissipation due to intermolecular friction and collisions– energy that cannot be recovered if the process is reversed. From athermodynamics perspective, all complex natural processes areessentially irreversible (Prigogine, 1980; Demirel and Sandler,2004; Jørgensen et al., 2007), including pedogenesis and PF thatare the focus of this paper. Often, a threshold behavior is involvedin the time evolution of complex systems and their responses toexternal forcing, which is called phase transition in statistical phys-ics (Strogatz, 2005).

In an open dissipative system like field soils, while diS is alwayspositive, deS can be positive or negative depending on S exchangebetween the soil system and its environment (Smeck et al.,1983). A dissipative system is a thermodynamically open systemthat is operating far-from-equilibrium in an environment withwhich it exchanges energy and matter (Prigogine, 1967). A dissipa-tive system is characterized by the spontaneous appearance ofsymmetry breaking (leading to anisotropy) and the formation of com-plex structures (leading to heterogeneity) (Fig. 3) (Prigogine, 1980).Heterogeneity here differs from randomness: the former is associ-ated with order while the later is linked to disorder. As shown inTable 1 and Figs. 1 and 2, heterogeneity is the key to the occurrenceof various PFs in field soils.

Organizing vs. dissipating processes in pedogenesis

Pedogenesis is an energy-consuming process (Volobuyev, 1964;Runge, 1973; Smeck et al., 1983; Addiscott, 1995; Rasmussen et al.,2005; Lin, 2010a). Smeck et al. (1983) explained that soil systemsexperience outfluxes as well as influxes of energy and matter, butthe net balance must favor energy influxes in order to drive soil-forming processes for soil development to proceed. Soil systemswith aggregates, horizons, and profiles formed over time (from

Fig. 3. Schematic of a soil system open to continuous energy and mass exchange with thebut the soil system’s total entropy can be reduced or increased depending on the magniproduction in the open soil system give rise to two categories of pedogenic processes: (1dissipative processes leading to destruction of soil structure and formation of soil matrixbalance of these two groups of processes leads to various soil architectures in diverse s

parent materials) represent more and more ordered states thantheir precursors (Smeck et al., 1983).

Energy (E) inputs and S production result in two categories ofprocesses during pedogenesis (Fig. 3): (1) organizing processes thatlead to the formation of soil profile and soil structure, which gener-ally involve S reduction, such as aggregation, humus accumulation,horizonation, flocculation, and others and (2) dissipating processesthat lead to destruction of soil structure and the formation of soilmatrix (here soil matrix specifically refers to individual soil parti-cles or molecules), which generally involve S increase, such asaggregate degradation, humus decomposition, erosion, dispersion,and others (Smeck et al., 1983; Addiscott, 1995; Rasmussen et al.,2005; Lin, 2010a). This dual-partitioning of pedogenesis results ina variety of soil architecture (i.e., the entirety of how the soil isstructured, which is equivalent to soil structure + soil matrix). Thisarchitecture is the foundation for PF occurrence in field soils.

Based on the energy balance of an open dissipative system(Fig. 3), the change in internal energy of a soil system (DU) duringpedogenesis equals to the net amount of heat added to the system(Q = Qin � Qout) minus the work done by the system with availableenergy (W), plus energy flux associated with net mass transfer intothe system (m = min �mout):

DU ¼ Q �W þmh; ð2Þ

where h is specific enthalpy (indicating relative heat contents in themass). Equivalently, using the fundamental thermodynamic rela-tion (which also holds for irreversible processes), we have

DU ¼ TDStotal � PDV þ DG; ð3Þ

where T�

and P�

represent the overall averaged temperature andpressure, DStotal is the total change in soil’s S during pedogenesis,DV is soil volume change occurred, and DG is the change in soil’sGibbs (free) energy during pedogenesis. Gibbs energy is defined as

surrounding environment. The mass and energy are conserved during pedogenesis,tude of entropy exchange with the environment. Energy consumption and entropy) ordering processes leading to the formation of soil profile and soil structure and (2)

(soil matrix here specifically refers to individual soil particles or molecules). Theoils around the globe. See text for the explanation of the symbols used.


G = H � TS, where H is enthalpy, T is temperature, and the productTS is the heat that the system absorbs or radiates to the environ-ment. Similar to Prigogine’s (1967) formulation, DStotal may be par-titioned into two parts:

DStotal ¼ DSmatrix þ DSstructure; ð4Þ

where Smatrix is the S related to dissipative processes (including Sgenerated internally in the soil), while Sstructure is the S related toorganizing processes (notably S exported from the soil to the sur-rounding). Smeck et al. (1983) have suggested that DStotal for mostsoils are negative after they grouped soil-forming processes into po-sitive and negative DS: positive DS assigned to processes that resultin disorder of soil (e.g., physical mixing and primary mineral weath-ering) and negative DS assigned to processes that sort soil constit-uents (e.g., aggregation and accumulation of organic matter).

Near-equilibrium, far-from-equilibrium, and models of soildevelopment

Because of the irreversible nature of pedogenesis, Eq. (4) essen-tially dictates that all field soils will evolve towards structured het-erogeneity and thus non-uniform flow. Since Stotal generallydecreases because of organizing processes during pedogenesisand S export to the surrounding, soil development results in thesystem moving away from equilibrium. Non-equilibrium condi-tions may be approximated using assumptions of local equilibriumand local S production (r) (Balzhiser et al., 1977; Demirel and San-dler, 2004). Matter and energy flow across the boundary betweenthe system and the surrounding under certain gradient results in(Bejan, 2006).

r ¼X

JiXi P 0; ð5Þ

where Ji and Xi represent the driving forces and fluxes, respectively,of all possible gradients i. The conjugate force–flux relation JiXi rep-

Fig. 4. Illustration of a possible pedogenic sequence from an Entisol to an Ultisol and tconditions.

resents a generalized framework of the potential work energy andthe system displacement from equilibrium.

Near-equilibrium systems tend towards a unique steady-statecondition bounded by the force–flux relations (Nicolis and Prigo-gine, 1989). Near-equilibrium fluxes exhibit linear relations totheir conjugate forces, as exemplified by the laws of Darcy, Fourier,Fick, and Ohm for water, heat, gas, and electrical transfer processes,respectively. As the forces or gradients become steeper, the linearpostulates become unreliable, and the system transitions throughthreshold and bifurcation phenomena to the non-linear realm offar-from-equilibrium thermodynamics (Nicolis and Prigogine,1989). Open, far-from-equilibrium systems exhibit highly improb-able states characterized by a large degree of temporal and spatialorganization maintained by force–flux driven S production and ex-port. The organization of these systems is thus dependent on theforce–flux relation and the continuous flux of energy, matter, andentropy across the system boundary. Interestingly, far-from-equi-librium systems evolve to a state of organization that most effi-ciently dissipates available E, resulting in a state that maximizesthe flow of energy, matter, and entropy through the system (Nico-lis and Prigogine, 1989; Schneider and Kay, 1994).

Smeck et al. (1983) suggested two models of soil development –steady-state and continuous evolution. They suggested that pedo-genesis is best depicted as a combination of these two models. Inthe continuous evolution model, time is the only independent var-iable of soil formation and all soils are in a state of continuous evo-lution (e.g., Rode, 1961; Chesworth, 1973). The occurrence of somesoil orders within this continuous evolution framework is illus-trated in Fig. 4. For example, it has been suggested that Alfisolsare only an infantile stage of Ultisols (Cline, 1961; Novak et al.,1971). In the steady-state model, constructional processes just bal-ance degradational processes, resulting in all state variables of thesoil system being independent of time. In both soils and livingorganisms, there is a drive towards states of higher order and

he related soil properties changes in a well-drained soil with appropriate climatic


differentiation (i.e., loss of S) during constructional stages (Smecket al., 1983). They only exhibit a net loss of E following degradationof the soil profile (similar to aging or death of a living system).Prigogine (1967) has shown that a system cannot easily leave asteady-state (a state of minimum S production) by spontaneousirreversible processes. If a system deviates from the steady-statedue to changes in external flux, spontaneous internal changes takeplace which return the system to the steady-state that may be at adifferent level. This offers some explanation for the stability of soilsystems at steady-state despite the variation of external fluxessuch as the seasonal variation of solar radiation. An alternativeexplanation for the invariant nature of soil features is the slownesswith which some soil features are altered by pedogenic processes(Smeck et al., 1983). Other soils may develop features that limitfurther change (called self-terminating by Yaalon, 1971). The mostcommon example of this is the formation of an argillic horizonthat, over time, limits water downward percolation because of de-creased permeability in the Bt horizon, which in turn retards fur-ther leaching and illuviation of clays (Fig. 4). Degraded (aged)argillic horizon functioning as an aquitard has been widely recog-nized (e.g., Lin et al., 2008).

Constructal theory and preferential flow configurationgeneration and evolution

Emerging constructal theory is claimed to explain and predictthe occurrence of flow patterns in nature under a principle sum-marized below: ‘‘For a finite-size flow system to persist in time (tosurvive), it must evolve in such a way that it provides easier and eas-ier access to the currents that flow through it” (Bejan, 2000, 2007).

Fig. 5. (A) Illustration of constructal theory applied to elemental area of a river basin: seelow resistivity (fast flow u) proceeds horizontally. Constructal sequence of assembly andpoint flows (A1, A2, . . .), will ultimately lead to a tree-like flow network; (B) and (C) illustrfreedom to change flow configurations over time at fixed global external size (L) or at fi

As explained below, this flow tendency results in at least two flowregimes – one with high resistivity (Darcy flow) that fills thegreater part of the available space and the other with low resistiv-ity that provides fast access through various preferred pathways(such as channels and macropores). Together, the fast flowpathsand slow interstitial space constitute natural PF architecture –the dynamic configuration of which offers the least global flowresistance over time for the overall flow system (Bejan, 2000,2007).

While constructal theory is largely a statement without rigor-ous mathematical formulae at the present time and its applicationto the real world soils and hydrologic systems remains to be seen,this theory offers an interesting perspective regarding the possiblegeneration and evolution of PF in soils. The dual-flow regime antic-ipated by constructal theory is similar to the dual-porosity or dual-domain approach that has long been used to model flow and trans-port in structured soils and geological materials (e.g., van Genuch-ten and Wierenga, 1976; Gerke and van Genuchten, 1993; Šimuneket al., 2003). The dual-flow regime is also consistent with pedo-genic dual-partitioning discussed above.

Flow configuration generation and evolution – new extension ofthermodynamics

Constructal theory was first published in 1996 in the context offacilitating the access to flow between one point and an infinity ofpoints (area or volume, in two- or three-dimensional systems,respectively), with application to traffic (Bejan, 1996), electronicscooling (Bejan, 1997a), and living fluid (Bejan, 1997b,c). In the pastdecade or so, this theory has been used as a physical principle in

page with high resistivity (Darcy flow v) proceeds vertically, and channel flow withoptimization, from the optimized elemental area (A0) to progressively larger area-

ate the three principles derived from constructal theory: global flow performance vs.xed global internal size (V) (modified from Bejan, 2007).


engineering design and as a guide to explain the occurrence of flowpatterns in nature (Bejan, 2000, 2007).

Constructal theory attempts to describe flow configuration gen-eration and evolution before reaching a possible equilibrium(Fig. 5). According to Bejan and Lorente (2004), this represents anew extension of thermodynamics for non-equilibrium flow sys-tems with configurations. Bejan (2000) suggested two physics phe-nomena with time direction: (1) the time arrow of the second lawof thermodynamics, i.e., the time arrow of irreversibility and (2)the time arrow of constructal theory, i.e., the time arrow of howflowing thing acquires its structure and evolves. The constructaltime arrow is claimed by Bejan (2007) to account for how andwhere everything flows before reaching possible equilibrium.

According to constructal theory, there is initially no structure tothermodynamic flow systems. Over time, the flow system gener-ates its structure in a sequential manner (Fig. 5A). The mode oftransport with high resistivity (slow flow) is placed at the smallestscale, filling the smallest elements. Modes of transport with suc-cessively lower resistivity (fast flow) are placed as ‘‘channels” inthe larger constructs, where they are used to connect and facilitatearea-to-point or volume-to-point flows (Bejan, 1997c). The archi-tecture that emerges through such sequential construction is oftena tree-like geometry (Errera and Bejan, 1998). This tree-like net-work embedded in the matrix is constantly morphing, adjusting,and getting more efficient, leading to greater and greater flow ac-cess (Bejan, 2007). Thus, the tree-like PF flow architecture in a por-ous media may be a result of such an evolutionary process. Afterreaching steady-state, the evolution toward greater global flow ac-cess may continue, but the increases in global flow conductancecome with a diminishing return: the global flow performance ofthe changing flow architecture tends toward a plateau, called‘‘equilibrium flow structure” by Bejan and Lorente (2004).

One of the challenges that constructal theory faces is that flowarchitecture in natural systems is not necessarily generated byflow itself; instead, a number of other factors and processes are in-volved in generating various PF pathways in soils and thus dictatethe evolution of flow configuration, such as plant roots, animal bor-rows, mycorrhizal fungi, soil aggregation, hydrophobicity, crack-ing, rock fragments, and land use/land cover changes.

Constructal principles

Conceptually, constructal theory offers a framework to relatenon-equilibrium flow dynamics to flow configuration generationand evolution. Its lack of mathematical formulae, however, hindersits rigorous testing. After reviewing a large body of theoreticalwork, Lorente and Bejan (2005) concluded that ‘‘Future work couldexamine more quantitatively the similarities between the natural andthe [theoretically] deduced architectures. Such work may shed light onthe natural process that generates multiple scales and heterogeneity inflow systems such as hillslope drainage.” Bejan (2007) has arguedthat there is a place for new theory in hydrology, as the ever-increasing complex models and measurements only provide betterdescription of the system, but not the explanation of why and howthings should be. He challenged that the ‘‘boundary conditions”routinely assumed in order to solve flow equations are in fact abig unknown (Bejan, 2007).

Bejan (2000, 2007) suggested three principles to explain howflow configuration evolves over time. To understand these princi-ples, some global properties of a flow system with configurationneed to be defined, as follows:

(a) Global external size, e.g., the length scale of the body bathedby the flow (L).

(b) Global internal size, e.g., the total volume of conductive chan-nels in the flow system (V).

(c) Global measure of performance, e.g., global flow resistance ofthe flow network (R) (or its reciprocal, global flow conduc-tance K).

(d) Freedom to morph, i.e., the degree of freedom for changingthe flow configuration over time t, which is often repre-sented by time itself.

(e) Configuration of the flow system, which may be quantified byvarious flow network parameters, including the so-calledsvelteness (Sv) defined by Lorente and Bejan (2005) as

Sv ¼ external length scaleinternal length scale

¼ L

V1=3 : ð6Þ

This dimensionless ratio describes the proportion of channel open-ing in a flow system.

The three constructal principles are summarized below, accord-ing to Bejan (2007):

(1) Principle I, called survival by increasing flow performance:This applies to flow configuration changes under finite-sizeconstraints. That is, if flow configurations are free to change,in time they will move at constant L and constant V (i.e.,plane I in Fig. 5B) in the direction of progressively smallerR. Thus, the time evolution of non-equilibrium flow struc-tures toward equilibrium will have an edge of the cloud ofpossible flow configurations (with the same L) that followsthe shape of curve R(V) in Fig. 5B. This curve has a negativeslope:

@R@V

� �L< 0: ð7Þ

This indicates that the flow resistance decreases as flowchannels evolve and expand over time.

(2) Principle II, called survival by increasing svelteness: Thismeans that flow architectures with the same R and L evolvetoward compactness (i.e., plane II in Fig. 5B), meaning thatsmaller volumes are dedicated to internal channels whilelarger volumes are reserved for the working ‘‘tissue” (theinterstices). This is survival based on the optimal use ofavailable space, so

@R@Sv

� �L> 0; ð8Þ

i.e., a positive slope of the curve R(Sv) in Fig. 5B. This is math-ematically equivalent to the 1st principle, but has an oppositeevolutionary direction (Fig. 5B).

(3) Principle III, called survival by increasing flow territory: This
suggests that flow configurations with the same R and V willmorph toward new ones that cover progressively larger ter-ritories (i.e., plane III in Fig. 5C), that is, the flow resistanceincreases in time as the distance traveled increases. This isrepresented by a curve, R(L) in Fig. 5C, with a positive slope:
@R@L

� �V> 0: ð9Þ

Mathematically, this is similar to the 2nd principle and sharesthe same evolutionary direction (Fig. 5C). However, the 2nd princi-ple is under the constraint of constant L, while the 3rd principle isunder the constraint of constant V. Bejan (2007) pointed out thatthere is a limit to the spreading of a flow structure as set by theconstructal configuration (e.g., R and V).

Soil development and its hydraulic properties change over time

Based on the above three constructal principles, we explorehere a new but preliminary explanation of soil developmental


sequence and related flow path generation and evolution. We viewflow channel openings during weathering as a result of eitherphysical breakdown of rocks or chemical/biological actions (suchas dissolution and root penetration). We distinguish a weatheringzone behind the weathering front that is below the solum in a soilprofile (Fig. 4). In situ weathering from a rock into a soil may beapproximated as proceeding in a layer-by-layer manner (such alayer may be very thin or with certain thickness depending onthe type of rock and climate), as illustrated in Fig. 4. Using the con-structal principles, we may expect the following sequence to occuras weathering proceeds:

(1) At first, as time increases, more pore space would gradu-ally become available for flow within the weatheringzone (i.e., V increases under constant L, which followsthe constructal principle I). This results in a reduced Rin the weathering zone (i.e., an increase in saproritepermeability).

(2) Once the above process reaches a limit (e.g., set by a max-imum V in the material being weathered), then the weath-ering would expand into new parent material underneath(i.e., L increases under constant V, which follows the con-structal principle III). When flow invades into new parentmaterial, the above 1st step would start over again in thenew weathering zone. Note that, although the weatheringinto new parent material may likely be a more gradual pro-cess, it nevertheless may be modeled or approximated in astep-wise fashion (i.e., layer-by-layer, as illustrated inFig. 4).

(3) As the overall weathering profile thickness reaches a possi-ble limit (e.g., set by environmental constraints, such as cli-mate), then the weathering profile would start to increase itssvelteness (i.e., Sv increases under constant L and V, whichfollows the constructal principle II). This would lead to theformation of a possible compacted layer inside the soil pro-file (e.g., a degraded argillic horizon or a fragipan) (Fig. 4).Because of the heterogeneous nature of the soil profile, suchcompactness would likely occur in a location where thematerials would most easily be compacted (e.g., due to tex-ture, or cementing agent, or soil moisture condition). Thislocation often appears in approximately the mid-portion ofa soil profile, likely because of clay illuviation and eluviation.This explanation is consistent with the formation of argillichorizon or fragipan (or other water restricting soil layers)in approximately mid-portion of many soil profiles (Linet al., 2008).

Translating the above general understanding of soil profiledevelopmental sequence into soil properties change over time,we may expect the following general trend (assuming no othercomplicating factors; Fig. 4): soil thickness would increase asweathering increases, but soil saturated hydraulic conductivity(Ksat) would first increase and then decrease in the subsoil (approx-imately the mid-portion of a soil profile). Furthermore, as moreorganization and structural heterogeneity develop through pedo-genesis, more PF paths would likely to appear (either verticallyor laterally or both).

Limited chronologic data of soil hydrologic properties are avail-able from the literature, which are summarized below. They seemto support (at least partially) the general pedogenic trend de-scribed above. Apparently it is desirable to have additional studiesto more fully test this.

Lohse and Dietrich (2005) compared a 300-year old Andisoland a 4.1-million year old Oxisol, both derived from basalt and lo-cated at a soil substrate age gradient across the Hawaiian Islands.

The young Andisol was shallow, coarse-textured, drained freely,and had a high Ksat throughout the soil profile; whereas the oldOxisol was deep and highly weathered, with a near-surfaceplinthite horizon overlying numerous clay-rich subsurface hori-zons and thus required significantly more suction to drain. TheOxisol’s subsoil Ksat was two to three orders of magnitude lowerthan that of the Andisol’s subsoil Ksat (average subsoil Ksat forthe Oxisol and the Andisol was 0.08 and 10 cm/h, respectively).However, the Oxisol’s surface Ksat remained about three timeshigher than that of the Andisol’s (average surface Ksat for the Oxi-sol and the Andisol was 36 and 10 cm/h, respectively). Elsenbeeret al. (1999) and Godsey and Elsenbeer (2002) also reported sim-ilar soil Ksat change over time between Oxisols and less weatheredUltisols derived from the same sedimentary rock in Brazil: Ksat ofthe Oxisols subsoil dropped below that of the Ultisols, but Ksat inthe surface remained higher in the Oxisols. Godsey et al. (2004)reported a similar trend between andesite-derived Oxisols andsiltstone-derived young Cambisols in Panama, although theirmagnitude of the difference was smaller. In these three examplesfrom tropical areas, the Oxisols were older and more weatheredthan the other soil orders considered. Thus, the Oxisols had obvi-ous thicker solum but showed reduced Ksat in roughly mid-por-tion of the soil profiles as compared to the youngercounterparts. These results suggest that as soil developmentreaches a certain age, subsurface Ksat values would start to de-cline, hence impeding rates of vertical flow but at the same timeincreasing subsurface lateral PF (Fig. 4).

In arid environments, Young et al. (2004) examined surfacesoil hydraulic properties along a soil chronosequence at theMojave National Preserve, CA. The surface covered by mixed plu-tonic parent material ranged in age from 50 to 100,000 years.They showed that soil hydraulic properties covary with time inarid desert pavement environment and that Ksat declined in valueby 100-fold as the desert pavements formed in the surface overtime. Shafer et al. (2007) also showed a 5-fold decrease in Ksat

in inter-canopy surface areas from the youngest (30 years old)to the oldest sites (125,000 years old) in the northern MojaveDesert, but no relationship between Ksat and soil age was foundin under-canopy sites. Shafer et al. (2004) reported that age didnot affect surface Ksat of bioturbated soils underneath canopies,because water could infiltrate deeper into the soil in localizedareas around shrubs. Meadows et al. (2008) showed that whileaverage Ksat of younger (�10 ka) soil peds were significantlygreater than that of older (�10–100 ka) soil peds in the surfaceAv horizons associated with desert pavements, the steady-stateinfiltration rate was equal for all soil surfaces of different ages.This result indicates that the soil development over time led toa more structured soil surface with greater potential for flow be-tween peds (i.e., an increase in interpedal PF) but with a lowerKsat of soil peds themselves (i.e., a reduction in matrix flowthrough peds) (Meadows et al., 2008). In other words, PF has in-creased as soil age increased. Nimmo et al. (2009) also reportedthat while infiltration and downward flow rates were greater inyounger soils, spatial heterogeneity of soil properties and lateralPF generally increased with pedogenic age in the Mojave Na-tional Preserve area.

Since Ksat varies considerably with many local variables, suchas soil horizon, inter- or intra-canopy, biological disturbance, soilsample size, as well as measurement method used and the timeof measurement, a more systematic hydrologic assessment ofsoils with different ages is needed to more rigorously test thepedogenic trend discussed above in relation to soil hydrologicchanges, which can provide further test of the applicability ofconstructal theory to pedogenesis and flow regime changes insoils.

Fig. 6. Illustrations of various natural networks found in above- and belowground (A: image from NASA; B: adopted from http://en.wikipedia.org/wiki/Leaf; C: adopted fromPaik and Kumar, 2008; D: adopted from http://www.iwmi.cgiar.org/drw/imggallery/88_DrySoil.jpg; E: courtesy of B. Clothier: F: adopted from http://www.flickr.com/photos/aaronescobar/2569091622/in/set-72157602046046491; G: adopted from http://www.uoguelph.ca/~gbarron/; H: adopted from http://www.millstreamgardens.co.nz/blog/wp-content/uploads/2008/07/blog22-7-027.jpg).


Network theory and preferential flow networks in soils

Networks are observed everywhere in nature (Fig. 6) and insociety – from trees, streams, blood vessels, to highways, Internet,and social networks – all are interconnected conduits for matter,energy, or information transfer. Many networks are formed to in-crease the efficiency or effectiveness of these transfers.

Considerable work has been published on biological networks(e.g., Harris-Warrick et al., 1992; Képès, 2007), ecological networks(e.g., Forman, 1995; Bascompte, 2007), river networks (e.g., Rodri-guez-Iturbe and Rinaldo, 1997; Rinaldo et al., 2006), social net-works (e.g., Barabási and Albert, 1999; Newman et al., 2006), andinfrastructure networks (e.g., Albert and Barabási, 2002; Dorogovt-sev and Mendes, 2002). Understanding the fundamental character-istics of these naturally-formed or man-made networks could shedlight on the understanding of complex but generally hidden flownetworks in soils.

Classical and new network theory

Classical network theory is an area of applied mathematics anda part of graph theory that deals with graphs as a representation ofsymmetric or asymmetric relations between discrete objects (Biggset al., 1986). A ‘‘graph” in this context refers to a collection of ver-tices (or called nodes) and edges (or called links) that connect pairsof vertices, which abstracts away all the details of original contextexcept for its connectivity. Thus, a network is nothing more than aset of discrete nodes, and a set of links (representing interactions)that connect the nodes together. The nodes and their links can beanything – such as individuals (nodes) and their social interactions

(links), web pages (nodes) and WWW (links), species (nodes) andfood webs (links), or individual soil pores (nodes) and their con-nectivity (links).

In the past decade, a burst of interest in complex networks hassparked rapid growth in their theoretical studies and diverse appli-cations, largely due to a drastic increase in the availability of net-work datasets coming from the Internet and electronic databases(Barabási, 2009). The evolution of network theory has gonethrough the following stages:

(1) Random graph theory: (Erd}os and Rényi, 1960) introducesprobabilistic (rather than deterministic) methods to graphtheory, especially the asymptotic probability of graphconnectivity.

(2) Small-world networks: (Watts and Strogatz, 1998) are some-where between completely regular and completely random,with high clustering and small characteristic path lengths,with the distances between most of their vertices beingshort (a feature known as the ‘‘small-world” effect).

(3) Scale-free networks: (Barabási and Albert, 1999) recognize acommon feature of many large networks, i.e., the vertex con-nectivities follow a scale-free power-law distribution, lead-ing to a high degree of self-organization. This feature is aconsequence of two generic mechanisms: (i) networks growcontinuously by the addition of new vertices and (ii) newvertices attach preferentially to sites that are already wellconnected.

Network modeling has shifted from the reproduction of net-work’s structure (topology) to the modeling of its evolution

http://en.wikipedia.org/wiki/Leaf

http://www.iwmi.cgiar.org/drw/imggallery/88_DrySoil.jpg

http://www.flickr.com/photos/aaronescobar/2569091622/in/set-72157602046046491

http://www.flickr.com/photos/aaronescobar/2569091622/in/set-72157602046046491

http://www.uoguelph.ca/~gbarron/

http://www.millstreamgardens.co.nz/blog/wp-content/uploads/2008/07/blog22-7-027.jpg

http://www.millstreamgardens.co.nz/blog/wp-content/uploads/2008/07/blog22-7-027.jpg


(dynamics), leading to the emerging theory of evolving networks(Albert and Barabási, 2002). This is the outcome of the realizationthat most complex networks are the result of a growth process.This is akin to statistical physics approach to complex phenomenathat aims to predict the large-scale emergent properties of a sys-tem by studying the collective dynamics of its constituents. Doro-govtsev and Mendes (2002) argued that the understanding ofnetworks is a topic of non-equilibrium statistical physics.

Another turning point in the modern view of complex networksis preferential attachment (Barabási and Albert, 1999), meaning thatnew edges are not placed at random but tend to connect to verticesthat already have a large degree of connectivity. Barabási and Al-bert (1999) showed that the probability P(k) that a vertex in a com-plex network interacts with k other vertices decays as a power law:

PðkÞ � k�c; ð10Þ

where c is a scaling exponent that varies among networks. This so-called scale-free model suggests that highly connected vertices of-ten dominate the connectivity. However, preferential attachment,aging effects, and growth constraints can lead to crossovers to expo-nential decay (Albert and Barabási, 2002). Thus, the functional formof P(k) may be best described by a combination of power laws andexponentials, with a time factor (t) considered simultaneously:

Pðk; tÞ � k�cðtÞe�k=n; ð11Þ

where e�k/n introduces a cut-off at some characteristic scale (Amaralet al., 2000; Jordano et al., 2003). Intuitively, the value n measuresthe number of links below which power laws describe the systemsand above which the number of links per node drops off steeply(Montoya et al., 2006). The scaling exponent, c, is not unique as itcan be tuned continuously by rewiring rates, initial node attractive-ness, and other factors (Albert and Barabási, 2002), so it is a functionof time as expressed in Eq. (11).

Another feature in the theory of evolving networks is that pro-cesses operating at the local level both constrain and are con-strained by the network structure. A principal objective of thenew network science, according to Newman et al. (2006), is anunderstanding of how structure at the global scale (say, the con-nectivity of the network as a whole) depends on dynamical pro-cesses that operate at the local scale (e.g., rules governing theappearance and connections of new vertices). A distinguishing fea-ture between the new network science and the traditional networktheory is the joint consideration of the structural properties of anetworked system and its behavioral dynamics, as well as theirrelationships. The inseparability of the topology and dynamics ofevolving networks is increasingly recognized – though far frombeing fully understood (Albert and Barabási, 2002). This is concep-tually similar to the inseparability of soil architecture and flowdynamics in soils.

It is clear that real networks are far from being random, but dis-play generic organizing principles shared by rather different sys-tems. The resulting networks with long-tailed distributions havequite different properties than classical random graphs. In particu-lar, they may be extremely resilient to random damage or attack(Albert and Barabási, 2002). This substantial property partly ex-plains their abundance in the real-world (Dorogovtsev and Men-des, 2002).

After reviewing theoretical and observational materials onforms and functions of diverse natural networks from physics tobiology, Rinaldo et al. (2006) concluded that one recurrent self-or-ganized mechanism for the dynamic origin of fractal forms is therobust strive for imperfect optimality embedded in many naturalpatterns, where selective criteria blend chance and necessity to-gether. They argued that nature works through imperfect searchesfor dynamically accessible optimal configurations, and that purely

random or deterministic constructs are unsuitable to properly de-scribe networks. This view is similar to the duality of chance andchoice in the evolution of natural systems (Monod, 1971; Colizzaet al., 2004; Tiezzi, 2006).

Despite the evident success in the past decade, however, exist-ing network models are still far from reality and only address par-ticular phenomena in real networks (Barabási, 2009). For instance,most models view networks as essentially homogeneous, with allvertices being roughly equivalent and lacking large-scale structure,strong grouping, directedness, or hierarchy (Albert and Barabási,2002; Newman et al., 2006). Another limitation is the lack of con-sideration of vertices’ properties and their impacts on networks(Newman et al., 2006).

Flow networks in soils

Networks are abundant in soils (despite the difficulty of seeingthem), such as root branching networks, mycorrhizal mycelial net-works, animal borrowing networks, networks of cracks and fis-sures, and others (Fig. 6). Energy inputs cause flow networks toform in soils, and networks provide a means of minimizing energydissipation (or equivalently, maximizing the efficiency of energytransfer). Like the energy of water flowing over the land surfacethat creates dendritic stream networks, water flowing throughsoils also creates network-like flow paths in the subsurface. Aswater moves through soils, changes in soil texture, structure, or-ganic content, mineral species, biological activities, and other fea-tures will modify the resistance to the flow, causing change in flowpath to allow water to follow the least resistant path, thus resultingin a PF network that has the least global flow resistance. Some evi-dence has suggested that a similarity may exist between river den-dritic structures and subsurface PF networks. For example, Deureret al. (2003) found that the drainage network in a sandy soil undera coniferous forest in north Germany closely resembled the drain-age network of mountainous streams. They also found that thefractional area of the entire profile occupied by the network de-creased exponentially with depth (Fig. 6E). By transporting organicsubstances and soil particles, networks in soils will progressivelychange hydraulic properties along these transport paths. Repeatedaction and reaction in a variety of planes of weakness (such as thespace in between peds) lead to the formation of soil structure andPF flowpaths, which are evidenced by numerous observable soilmorphological features (such as thickened clay films or other coat-ings on ped surfaces in many soils).

Deurer et al. (2003) suggested that networks seem to be a scale-invariant functional structure for water and solute transport fromthe pore-scale up to the catchment scale. Depending on the gov-erning physical processes, these networks may exhibit differenttopologies (Fig. 6). Overall, flow and transport networks in soilsare formed by the forcing of soil formation, mainly climate andorganisms. Cycles of wetting and drying, freezing and thawing,shrinking and swelling, coupled with organic matter accumulationand decomposition, biological activities, and chemical reactionslead to the formation of diverse soil aggregates and pore networksin the subsurface. In particular, plant roots, burrowing animals, andmycorrhizal fungi are active in creating networks in soils. CommonPF networks in soils are highlighted below:

(1) Crack and interpedal networks: It is common that when a claysoil dries up, a network of cracks forms (Fig. 6D). Dependingon the severity of drought, such cracks can be as deep asmore than 1 m (Fig. 1). Shrink–swell clays also produce slic-kensides (narrow fissures) that function as PF conduits evenwhen the soil is wet (Lin et al., 1996). Wetting–drying andfreezing–thawing cycles can generate enormous fissuresand interpedal pore space in soils along various planes of


weakness (see examples in Fig. 1). In addition, chemical dis-solution also creates various cavities, fissures, or tunnels insoils.

(2) Root networks: Plant roots are network-like because rootsgrow in all directions to form three-dimensional branchingsystems that are driven by both the genetics of plants andthe soil environmental conditions (Fig. 6F). Both roots them-selves and the space between roots and their surroundingsoils can function as PF paths (e.g., Lin et al., 1996; Li et al.,2009). Roots may also be linked by shared mycorrhizal net-works that constitute pathways for the transfer of resourcesamong plants (Egerton-Warburton et al., 2007). Roots andfungal hyphae form an extensive network in soils and arecovered with extracellular polysaccharides to which soilmicroaggregates are firmly held (Low and Stuart, 1974; Tis-dall, 1995). The networks of encrusted roots and hyphaehold soil macroaggregates intact, so that they do not collapsein water.

(3) Mycorrhizal mycelial networks: Mycorrhizal mycelia extendsfrom plant roots to produce a distinct ‘‘mycorrhizosphere”and a nutrient-absorbing network (Fig. 6G), which, in grass-land, can reach up to 100 m in length per gram of soil (Leakeet al., 2004). It has been suggested that a major proportionof carbon flux from plants to soils moves rapidly through suchnetworks (Staddon et al., 2003). Some plants even dependexclusively on these networks for carbon (Leake et al.,2004). Mutualistic interactions are particularly vital for ter-restrial ecosystems because more than 80% of land plants relyon mycorrhizal relationships with fungi (Johnson et al., 2005).These networks are the most dynamic and functionallydiverse components of the symbiosis, and recent estimatessuggest that they are empowered by receiving as much as10% or more of the net photosynthate of their host plantsand they often constitute 20–30% of total soil microbial bio-mass (Leake et al., 2004). Taylor et al. (2009) also reported thatarbuscular mycorrhizal fungi coevolved with the earliest landplants and affected weathering indirectly by increasing soilstability and by altering soil hydrology, whereas ectomycor-rhizal fungi can weather minerals by exuding organic chela-tors and acidifying soil solution and thus are strongerweathering agents. For these reasons, representation of thecoevolution of roots and fungi in geochemical cycle modelsis required to further the understanding of biota’s role inEarth’s CO2 and climate history (Taylor et al., 2009).

(4) Animal borrowing networks: A wide variety of animals con-struct and use burrows in different soils, including earth-worms (Fig. 6H), insects (particularly ants and termites),mammals (such as moles, mice, rats, squirrels, chipmunks,gophers, prairie dogs, and groundhogs), amphibians, reptiles,and even some birds. Such burrows can range in complexityfrom a simple tube a few centimeters long to a complex net-work of interconnecting tunnels and chambers severalmeters long up to hundreds or thousands of meters in totallength (such as a well-developed rabbit warren). Many ofthese borrows function effectively as drainage pipes undercertain conditions (e.g., see a mole hole about 1 m belowground draining a large quantity of watershed water in Fig. 2).

(5) Man-made subsurface drainage networks: These include awide variety of systems used for drainage (such as tiledrains, ditches, septic adsorption fields, and stormwaterdrainage tunnels), irrigation (such as furrow, drip, and sub-surface drip irrigation systems), and piping (such as under-ground water pipes and various cables that causealternations to original soil environments, hence creating adifferent resistance to water flow as compared to the sur-rounding original soils). All these anthropogenic impacts

contribute to the increased heterogeneity as well as PF net-works in soils around the globe.

Modeling flow networks in the subsurface and related challenges

Various vertical and lateral PFs in soils (Table 1) constitute sub-surface flow networks that often influence how water percolatesthrough the soil, runs down the hillslope, and moves across thewatershed. The origin, dynamics, and recurrent patterns of self-organization of such flow networks in the subsurface have becomethe subjects of recent research and model development (e.g., Leh-mann et al., 2007; James and Roulet, 2007; Weiler and McDonnell,2007; Michaelides and Chappell, 2009). For instance, during stormswith wet soil conditions, a subsurface network often provides pre-ferred pathways for water to flow down gradient with high veloc-ities. Even individual short PF pathways can be linked via a seriesof nodes in a network, which may be switched on or off and expandor shrink depending on local soil moisture conditions, rainfall in-puts, and landscape positions, thus forming dynamic PF networks(e.g., Sidle et al., 2001; Gish et al., 2005; Lin and Zhou, 2008).

While there have long been mathematical attempts to modelhydrologic flows through soils, several challenges remain. Perhapsone of the most fundamental among these is the dynamic partition-ing and interaction of flow currents between the more traditionalporous portion of the soil with the PF domain. To address this,one of the attractive approaches is to develop a more integratedmodeling framework that can couple network-based and contin-uum-based approaches. This is because subsurface flow can be de-scribed as complexes of flow networks embedded in land mosaics.Another way forward is to explore direct relationships betweenreal PF networks in soils and the new network theory as expressedin Eqs. (10) and (11). In network modeling, nodes usually play akey role in forming networks as they function effectively as controlpoints. Thus, identifying important nodes in the subsurface wouldbe a key step forward in developing appropriate network modelsfor soil hydrology. However, current technological bottlenecks forfield scale investigations of the opal subsurface constraint suchnode identification. Thus, non-invasive high-resolution imagingof subsurface pore networks and flow dynamics is a technologicalbottleneck for advancing the 21st century hydrology.

Since hydrology often triggers ‘‘hot spots” and ‘‘hot moments” ofbiogeochemical reactions and ecological functions (e.g., Bundt et al.,2001; McClain et al., 2003), improved modeling and prediction of PFwill also have considerable implications for enhanced determina-tion of chemical fluxes and elemental budgets in soils and ecosys-tems. Interpretation of point measurements without knowing PFpaths is now often questioned (e.g., Gottlein and Manderscheid,1998; Netto et al., 1999), because the uncertainty of whether soilsolution is extracted from stagnant or high velocity flow pathsmakes it practically impossible to reliably determine mass fluxrates. Additional complications arise in structured soils for reactivecomponents due to locally variable chemical conditions. In addi-tion, macropore linings and aggregate coatings could restrict lateralmass transfer and reduce sorption and retardation, hence physicaland biochemical non-equilibriums are enhanced. All these suggestthat there is a clear need to identify and model PF networks in realworld soils if we are to improve the modeling and prediction ofinteractive soil physical, chemical, and biological processes, andhence the holistic understanding of the Critical Zone (Lin, 2010b).

Summary and outlook

The lack of PF theory in soils requires concerted efforts from thecommunity to synthesize concepts and advance techniques formeasuring and modeling PF across space and time. The theories

Fig. 7. The three theories discussed in this paper provide interlinked principles forexplaining the occurrence of preferential flow (PF) in soils.


of non-equilibrium thermodynamics, constructal theory, andevolving networks provide interesting perspectives towards amore unified and physics-based understanding and prediction ofPF (Fig. 7), which is closely linked to soil formation and evolution.The three theories discussed in this paper complement each otherin some ways (Table 2). Together, they provide a thought-provok-ing new path for understanding the genesis and evolution of sub-surface heterogeneity, its architecture, and fundamental controlson network-like flow regimes in the belowground world. However,certain controversies and challenges are encountered with each ofthese theories, as summarized in Table 2, thus additional effortsare needed to further test their applicability in natural soil systems.

The irreversible dual-partitioning of pedogenesis, which is sup-ported by Prigogine’s theory of dissipative structure, indicates thatsoils generally evolve towards increased ordering (associated withsoil structure) while maintaining certain level of local randomness(associated with soil matrix). Such a dual-partitioning results inDStotal = DSmatrix + DSstructure, where DSmatrix is the soil thermody-namic entropy change related to dissipative processes and soil ma-trix development, while DSstructure is the entropy change related toorganizing processes and entropy export from the soil to its sur-rounding environment. Moreover, the construal theory suggests anatural tendency for dual-flow regimes to occur in soils, and pro-vides a new perspective on weathering sequences and relatedchanges in soil hydraulic properties over time. The theory of evolv-ing networks further helps the understanding of diverse PF net-works observed in field soils, and suggests that a more integratedmodeling framework (which couples network-based and contin-uum-based approaches, with interfaces between the two domains)

Table 2Summary of the main features of the three theories discussed in this paper.

Theory Non-equilibrium thermodynamics Cons

System � Dissipative open system� Far-from-equilibrium towards

maximizing energy and mass flow

� Finitfreed� Evolv

ier fl

Characteristics � Symmetry breaking and formationof complex structure� Near-equilibrium towards steady-

state

� Tworesis� Thre

unde

Controversies or challenges � Many schools of thermodynamics� Quantification of entropy in natural

systems and its relation to order,life, and time

� Besidotheerati� Lack

mula

Energy dissipation � Most efficient energy dissipation � Mini

Time factor or evolution � Time arrow of irreversibility � Timeacqu

is probably needed for a more comprehensive treatment of subsur-face hydrology.

Advancements in subsurface hydrology hinge on breakthroughsin two bottlenecks discussed in this paper. On the conceptual ortheoretical front, going beyond small-scale physics and embracingthe problem of boundary condition as it relates to flow configura-tion dynamics would permit enhanced partitioning of flow cur-rents between the more traditional porous portion of the soil andthe PF domain. A critical need here is a scaling framework that pro-vides meaningful connection between point-based observationsand area-based patterns, as well as a hierarchical multi-scale mod-eling framework that can guide the development and use of ‘‘gray-box” type of models (that is, something in between a ‘‘black-box”model, which concerns only inputs–outputs, and a ‘‘white-box”model, which describes all microscopic details in between inputsand outputs). In addition, time arrow is essential to both thelong-term evolution of the soil system and the shorter-termchanges in soil functions. On the technological front, the emer-gence of sensor networks and real-time data collection systems,coupled with improved non-invasive geophysical and remote sens-ing tools, could potentially provide increasingly spatially and tem-porally extensive datasets about the subsurface heterogeneity andrelated network-like flow dynamics (e.g., Lin and Zhou, 2008; Rob-inson et al., 2008; Zhang et al., submitted for publication). Beven(2006) clearly pointed out that the most important need to ad-vance hydrology of the 21st century is to provide techniques thatcan measure integrated fluxes and storages at useful scales.

The notion that we do not need to map or fully characterize thecomplex subsurface heterogeneity is debatable. Predicting flowand transport in field soils using input–output relationships with-out an adequate characterization of the ‘‘black-box” in between in-puts and outputs is analogous to diagnosing a patient based onwhat (s)he takes in and excludes out of his/her body without athorough understanding of human body’s complex anatomy andcirculatory systems. Singer (1972) clearly noted, ‘‘. . . in order toachieve a satisfactory understanding of how any biological systemfunctions, the detailed molecular composition and structure of thatsystem must be known.” Revolutionaries in science have oftenrooted in the understanding of fundamental structures of naturalsystems (e.g., DNA for biology, particles for physics, and elementsfor chemistry). The same is true for the study of natural systemssuch as soils, hydrology, and the landscape (e.g., mineral structurefor understanding clay behaviors, molecular structure for revealingwater properties, and landform units for depicting geomorphic

tructal theory Theory of evolving networks

e-size flow system havingom to morphing towards easier and eas-

ow architecture

� System of nodes and links� Interconnected conduits for effective

transfer

flow regimes of high and lowtivitiese constructal principlesr constraints of finite-size

� Growth and evolution, no pure random ordeterministic constructs� Preferential attachment and dominance in

connectivity� Inseparability of topology and dynamics at

local vs. global scales

es flow itself, a number ofr factors are involved in gen-ng flow architecture

of crisp mathematical for-e for testing and prediction

� Existing network models are still far fromreality� Identifying flow networks & key nodes

embedded in subsurface mosaic matrix� Modeling heterogeneous networks

mum global flow resistance � Minimum energy dissipation

arrow of how flowing thingires architecture and evolves

� Evolving networks, with growth con-straints, rewiring rates, aging effects, etc.


processes). Kung (1990) went even further to suggest that untilpedologists and sedimentologists can offer a more detaileddescription of the texture and structure of the vadose zone, simu-lated results of field-scale solute transport by models based on theclassical concept could be completely misleading. He also notedthat although flow pattern in soils could be extremely complex,it is not a random process. Thus, all transport parameters thatare treated as random variables in stochastic models probably willnever be accurately assessed unless the real flow paths can be esti-mated (Kung, 1990).

Note that although the three theories discussed herein suggestthat PF is likely universal in natural soils, further field-based inves-tigations are needed to validate the theoretical predictions. The no-tion that PF may be universal also does not necessarily mean thatPF occurs at all times. While the potential for PF to occur is likelyubiquitous in the natural environment, it does require the rightcombination of soils and environmental conditions for PF potentialto actually occur. Therefore, determining the condition, timing, andfrequency of PF occurrence and its relationships with various con-trols (such as initial moisture, rainfall characteristics, landscapefeature, soil type, and land use) in various regions of the world isan essential step to improve the modeling and prediction of PFacross spatial and temporal scales. This reality check, combinedwith further theoretical studies, would hopefully stimulate moreconcerted efforts from the scientific community to achieve neededbreakthroughs for advancing subsurface hydrology and developinga unified PF theory.

Acknowledgements

I am grateful to Hans-Jörg Vogel of Helmholtz EnvironmentalResearch Center (UFZ) in Germany for bringing Prigogine’s workto my attention during my short sabbatical leave with him in fall2008. Interactions with Adrian Bejan at Duke University helpedmy understanding of his constructal theory. Review commentsprovided by anonymous reviewers (one not so anonymous, UlrichMüller-Herold at ETH) and by Hans-Jörg Vogel, Chris Graham, andthe handling editor Hannes Flühler have helped improve the qual-ity of this paper.

References

Addiscott, T.M., 1995. Entropy and sustainability. European Journal of Soil Science46, 161–168.

Albert, R., Barabási, A.-L., 2002. Statistical mechanics of complex networks. Reviewsof Modern Physics 74, 47–97.

Amaral, L.A.N., Scala, A., Barthélemy, M., Stanley, H.E., 2000. Classes of behavior ofsmall-world networks. Proceedings of the National Academy of Sciences 97,11149–11152.

Atkinson, T.C., 1978. Techniques for measuring subsurface flow on hillslopes. In:Kirkby, M.J. (Ed.), Hillslope Hydrology. John Wiley & Sons, Chichester.

Balzhiser, R.E., Samuels, M.R., Eliassen, J., 1977. Engineering Thermodynamics, vol.668. Prentice-Hall, Englewood Cliffs, NJ.

Barabási, A.-L., 2009. Scale-free networks: a decade and beyond. Science 325, 412–413.

Barabási, A.-L., Albert, R., 1999. Emergence of scaling in random networks. Science286, 509–512.

Bascompte, J., 2007. Networks in ecology. Basic and Applied Ecology 8, 485–490.Beven, K., 2006. Searching for the holy grail of scientific hydrology: Qt ¼ HðS

R

DtAÞas closure. Hydrology and Earth System Sciences 10, 609–618.

Beven, K., Germann, P., 1982. Macropores and water flow in soils. Water ResourcesResearch 18, 1311–1325.

Bejan, A., 1996. Street network theory of organization in nature. Journal ofAdvanced Transportation 30, 85–107.

Bejan, A., 1997a. Constructal-theory network of conducting paths for cooling a heatgenerating volume. International Journal of Heat and Mass Transfer 40, 799–816.

Bejan, A., 1997b. Constructal tree network for fluid flow between a finite-sizevolume and one source or sink. Revue Generale De Thermique 36, 592–604.

Bejan, A., 1997c. Theory of organization in Nature: pulsating physiologicalprocesses. International Journal of Heat and Mass Transfer 40, 2097–2104.

Bejan, A., 2000. Shape and Structure, From Engineering to Nature. CambridgeUniversity Press, Cambridge, UK.

Bejan, A., 2006. Advanced Engineering Thermodynamics. John Wiley & Sons,Hoboken, NJ.

Bejan, A., 2007. Constructal theory of pattern formation. Hydrology and EarthSystem Sciences 11, 753–768.

Bejan, A., Lorente, S., 2004. The constructal law and the thermodynamics of flowsystems with configuration. International Journal of Heat and Mass Transfer 47,3203–3214.

Biggs, N., Lloyd, E., Wilson, R., 1986. Graph Theory. Oxford University Press.Boltzmann, L., 1896. Lectures on Gas Theory. Dover Publications (March 27, 1995).Bosch, D., King, K., Yoder, R., Parsons, J., Rawls, W., Bergstrom, L., Brown, G., Malone,

R., Ward, A., Shirmohammadi, A., Vellidis, G., 2000. Preferential flow: watermovement and chemical transport in the environment. In: Proceedings of the2nd International Symposium, January 3–5, 2001, Honolulu, Hawaii. ASAE, St.Joseph, Michigan.

Bouma, J., Jongerius, A., Boersma, O., Jager, A., Schoonderbeek, D., 1977. Function ofdifferent types of macropores during saturated flow through 4 swelling soilhorizons. Soil Science Society of America Journal 41, 945–950.

Bundt, M., Widmer, F., Pesaro, M., Zeyer, J., Blaser, P., 2001. Preferential flow paths:biological ‘‘hot spots” in soils. Soil Biology and Biochemistry 33, 729–738.

Burch, G.J., Moore, I.D., Burns, J., 1989. Soil hydrophobic effects on infiltration andcatchment runoff. Hydrological Processes 3, 211–222.

Chesworth, W., 1973. The residua system of chemical weathering: a model for thechemical breakdown of silicate rocks at the surface of the earth. Journal of SoilScience 24, 69–81.

Clausius, R., 1865. Über die Wärmeleitung gasförmiger Körper. Annalen der Physik125, 353–400.

Cline, M.G., 1961. The changing model of soil. Soil Science Society of AmericaProceedings 25, 442–446.

Clothier, B.E., Green, S.R., Deurer, M., 2008. Preferential flow and transport in soil:progress and prognosis. European Journal of Soil Science 59, 2–13.

Colizza, V., Banavar, J.R., Maritan, A., Rinaldo, A., 2004. Network structures fromselection principles. Physical Review Letters 92, 198701. doi:10.1103/PhysRevLett.92.198701.

Consortium of Universities for the Advancement of Hydrologic Science, Inc.(CUAHSI). 2007. Hydrology of a Dynamic Earth – A Decadal Research Plan forHydrologic Science. Washington, DC.

de Groot, S.R., Mazur, P., 1963. Non-equilibrium Thermodynamics. North-Holland,Amsterdam.

Demirel, Y., Sandler, S.I., 2004. Nonequilibrium thermodynamics in engineering andscience. Journal of Physical Chemistry B – Condensed Phase 108, 31–43.

Deurer, M., Green, S.R., Clothier, B.E., Böttcher, J., Duijnisveld, W.H.M., 2003.Drainage networks in soils: a concept to describe bypass-flow pathways.Journal of Hydrology 272, 148–162.

Dorogovtsev, S.N., Mendes, J.F.F., 2002. Evolution of networks. Advances in Physics51, 1079–1187.

Dunne, T., Moore, T.R., Taylor, C.H., 1975. Recognition and prediction of runoff-producing zones in humid regions. Hydrological Sciences Bulletin 20, 305–327.

Egerton-Warburton, L.M., Querejeta, J.I., Allen, M.F., 2007. Common mycorrhizalnetworks provide a potential pathway for the transfer of hydraulically liftedwater between plants. Journal of Experimental Botany 58, 1473–1483.

Elsenbeer, H., Newton, B.E., Dunne, T., deMoraes, J.M., 1999. Soil hydraulicconductivities of latosols under pasture, forest and teak in Rondonia, Brazil.Hydrological Processes 13, 1417–1422.

Erd}os, P., Rényi, A., 1960. On the evolution of random graphs. Bulletin of TheInternational Statistical Institute 38, 343–347.

Errera, M.R., Bejan, A., 1998. Tree networks for flows in composite porous media.Journal of Porous Media 2, 1–17.

Flury, M., Flühler, H., Jury, W.A., Leuenberger, J., 1994. Susceptibility of soils topreferential flow of water: a field study. Water Resources Research 30, 1945–1954.

Flühler, H., Durner, W., Flury, M., 1996. Lateral solute mixing processes – a key forunderstanding field-scale transport of water and solutes. Geoderma 70, 165–183.

Forman, R.T.T., 1995. Land Mosaics. Cambridge.Freer, J., McDonnell, J.J., Beven, K.J., Peters, N.E., Burns, D.A., Hooper, R.P., Aulenbach,

B., Kendall, C., 2002. The role of bedrock topography on subsurface storm flow.Water Resources Research 38 (12), 1269. doi:10.1029/2001WR000872.

Gerke, H.H., van Genuchten, M.Th., 1993. A dual-porosity model for simulating thepreferential movement of water and solutes in structured porous media. WaterResources Research 29, 305–319.

Germann, P., Helbling, A., Vadilonga, T., 2007. Rivulet approach to rates ofpreferential infiltration. Vadose Zone Journal 6, 207–220.

Gish, T.J., Shirmohammadi, A. (Ed.), 1991. Preferential flow. In: Proceedings of theNational Symposium. December 16–17, 1991. American Society of Agri.Engineers, Chicago, IL.

Gish, T.J., Walthall, C.L., Daughtry, C.S.T., Kung, K.-J.S., 2005. Using soil moisture andspatial yield patterns to identify subsurface flow pathways. Journal ofEnvironmental Quality 34, 274–286.

Godsey, S., Elsenbeer, H., 2002. The soil hydrologic response to forest regrowth: acase study from southwestern Amazonia. Hydrological Processes 16, 1519–1522.

Godsey, S., Elsenbeer, H., Stallard, R., 2004. Overland flow generation in twolithologically distinct rainforest catchments. Journal of Hydrology 295, 276–290.

Gottlein, A., Manderscheid, B., 1998. Spatial heterogeneity and temporal dynamicsof soil water tension in a mature Norway spruce stand. Hydrological Processes12, 417–428.

http://dx.doi.org/10.1103/PhysRevLett.92.198701

http://dx.doi.org/10.1103/PhysRevLett.92.198701

http://dx.doi.org/10.1029/2001WR000872


Graham, C.B., Woods, R., McDonnell, J.J., 2010. Hillslope threshold response torainfall: (1) A field based forensic approach. Journal of Hydrology 393, 65–76.doi:10.1016/j.jhydrol.2009.12.015.

Grayson, R., Blöschl, G. (Eds.), 2000. Spatial Pattern in Catchment Hydrology:Observations and Modeling. Cambridge University Press, Cambridge, UK.

Harris-Warrick, R.M., Marder, E., Selverston, A.I., Moulins, M., 1992. DynamicBiological Networks: The Stomatogastric Nervous System. The MIT Press,Cambridge, MA.

Hewlett, J.D., Hibbert, A.R., 1967. Factors affecting the response of small watershedsto precipitation in humid regions. In: Sopper, W.E., Lull, H.W. (Eds.), ForestHydrology. Pergamon Press, Oxford, pp. 275–290.

Horton, R.E., 1940. An approach toward a physical interpretation of infiltrationcapacity. Soil Science Society of America Journal 5, 399–417.

Jackson, T.J., Le Vine, D.E., 1996. Mapping surface soil moisture using an aircraft-based passive microwave instrument: algorithm and example. Journal ofHydrology 184, 85–99.

James, A.L., Roulet, N.T., 2007. Investigating hydrologic connectivity and itsassociation with threshold change in runoff response in a temperate forestedwatershed. Hydrological Processes 21, 3391–3408.

Jardine, P., Wilson, G., Luxmoore, R., McCarthy, J., 1989. Transport of inorganic andnatural organic tracers through an isolated pedon in a forested watershed. SoilScience Society of America Journal 53, 317–323.

Jarvis, N.J., 2007. A review of non-equilibrium water flow and solute transport insoil macropores: principles, controlling factors and consequences for waterquality. European Journal of Soil Science 58, 523–546.

Jarvis, N.J., Bergström, L., Dik, P.E., 1991. Modeling water and solute transport inmacroporous soil. II. Chloride breakthrough under non-steady flow. Journal ofSoil Science 42, 71–81.

Johnson, D., Krsek, M., Wellington, E.M.H., Stott, A.W., 2005. Soil invertebratesdisrupt carbon flow through fungal networks. Science 309, 1047.

Jordano, P., Bascompte, J., Olesen, J.M., 2003. Invariant properties in coevolutionarynetworks of plant–animal interactions. Ecological Letters 6, 69–81.

Jørgensen, S., Fath, B., Bastianoni, S., Marques, J., Muller, F., Nielsen, S., Pattern, B.,Tiezzi, E., Ulanowicz, R., 2007. A New Ecology – Systems Perspective. Elsevier,Amsterdam.

Képès, F. (Ed.), 2007. Biological Networks. Complex Systems and InterdisciplinaryScience, vol. 3. World Scientific Publishing Co., Singapore.

Kirby, M.J., 1978. Hillslope Hydrology. John Wiley & Sons, Chichester, UK.Kirchner, J.W., 2006. Getting the right answers for the right reasons: linking

measurements, analyses, and models to advance the science of hydrology.Water Resources Research 42, W03S04. doi:10.1029/2005WR004362.

Kung, K.-J.S., 1990. Preferential flow in a sandy vadose zone: 1. Field observation.Geoderma 46, 51–58.

Leake, J.R., Johnson, D., Donnelly, D., Muckle, G., Boddy, L., Read, D., 2004. Networksof power and influence: the role of mycorrhizal mycelium in controlling plantcommunities and agroecosystem functioning. Canadian Journal of Botany 82,1016–1045.

Lehmann, P., Hinz, C., McGrath, G., Tromp-van Meerveld, H.J., McDonnell, J.J., 2007.Rainfall threshold for hillslope outflow: an emergent property of flow pathwayconnectivity. Hydrology and Earth System Science 11, 1047–1063.

Li, X.Y., Yang, Z.P., Zhang, X.Y., Lin, H.S., 2009. Connecting ecohydrology andhydropedology in desert shrubs: stemflow as a source of preferential water flowin soils. Hydrology and Earth System Science 13, 1133–1144.

Levia, D.F., Frost, E.E., 2003. A review and evaluation of stemflow literature in thehydrologic and biogeochemical cycles of forested and agricultural ecosystems.Journal of Hydrology 274, 1–29.

Lin, H.S., 2010a. Comments on energy-based pedogenic models by field andMinasny (2008) and Rasmussen (2008). Soil Science Society of America Journal74, 337–339.

Lin, H.S., 2010b. Earth’s Critical Zone and hydropedology: concepts, characteristics,and advances. Hydrology and Earth System Science 14, 25–45.

Lin, H.S., Zhou, X., 2008. Evidence of subsurface preferential flow using soilhydrologic monitoring in the Shale Hills Catchment. European Journal of SoilScience 59, 34–49.

Lin, H.S., McInnes, K.J., Wilding, L.P., Hallmark, C.T., 1996. Effective porosity and flowrate with infiltration at low tensions into a well-structured subsoil.Transactions of the ASAE 39, 131–135.

Lin, H.S., McInnes, K.J., Wilding, L.P., Hallmark, C.T., 1997. Low tension water flow instructured soils. Canadian Journal of Soil Science 77, 649–654.

Lin, H.S., Bouma, J., Pachepsky, Y., Western, A., Thompson, J., van Genuchten, M.Th.,Vogel, H., Lilly, A., 2006. Hydropedology: synergistic integration of pedologyand hydrology. Water Resource Research 42, W05301. doi:10.1029/2005WR004085.

Lin, H.S., Brook, E., McDaniel, P., Boll, J., 2008. Hydropedology and surface/subsurface runoff processes. In: Anderson, M.G. (Ed.), Encyclopedia ofHydrologic Sciences. John Wiley & Sons, Ltd.. doi:10.1002/0470848944.hsa306.

Lohse, K.A., Dietrich, W.E., 2005. Contrasting effects of soil development onhydrological properties and flow paths. Water Resources Research 41,W12419. doi:10.1029/2004WR003403.

Lorente, S., Bejan, A., 2005. Svelteness, freedom to morph, and constructal multi-scale flow structures. International Journal of Thermal Sciences 44, 1123–1130.

Low, A.J., Stuart, P.R., 1974. Micro-structural differences between arable and oldgrassland soils as shown in the scanning electron microscope. Journal of SoilScience 25, 135–137.

McClain, M.E., Boyer, E.W., Dent, C.L., Gergel, S.E., Grimm, N.B., Groffman, P.M., Hart,S.C., Harvey, J.W., Johnston, C.A., Mayorga, E., McDowell, W.H., Pinay, G., 2003.

Biogeochemical hot spots and hot moments at the interface of terrestrial andaquatic ecosystems. Ecosystems 6, 301–312.

McDonnell, J.J., 1990. A rationale for old water discharge through macropores in asteep, humid catchment. Water Resources Research 26, 2821–2832.

McDonnell, J.J., Owens, I.F., Stewart, M.K., 1991. A case-study of shallow flow pathsin a steep zero-order basin. Water Resources Bulletin 27, 679–685.

McDonnell, J.J., Sivapalan, M., Vache, K., Dunn, S., Grant, G., Haggerty, R., Hinz, C.,Hooper, R., Kirchner, J., Roderick, M.L., Selker, J., Weiler, M., 2007. Movingbeyond heterogeneity and process complexity: a new vision for watershedhydrology. Water Resources Research 43, W07301. doi:10.1029/2006WR005467.

Meadows, D.G., Young, M.H., McDonald, E.V., 2008. Influence of relative surface ageon hydraulic properties and infiltration on soils associated with desertpavements. Catena 72, 169–178.

Michaelides, K., Chappell, A., 2009. Connectivity as a concept for characterizinghydrological behavior. Hydrological Processes 23, 517–522.

Monod, J., 1971. Chance and Necessity: An Essay on the Natural Philosophy ofModern Biology. Alfred A. Knopf, New York.

Montoya, J.M., Pimm, S.L., Solé, R.V., 2006. Ecological networks and their fragility.Nature 442, 259–264.

Mosley, M.P., 1979. Streamflow generation in a forested watershed. WaterResources Research 15, 795–806.

Muschik, W., 2008. Survey of some branches of thermodynamics. Journal of Non-Equilibrium Thermodynamics 33, 165–198.

Netto, A.M., Pieritz, R.A., Gaudet, J.P., 1999. Field study on the local variability of soilwater content and solute concentration. Journal of Hydrology 215, 23–37.

Newman, M., Barabasi, A., Watts, D.J. (Eds.), 2006. The Structure and Dynamics ofNetworks. Princeton Univ. Press, Princeton, NJ.

Nicolis, G., Prigogine, I., 1989. Exploring Complexity. W.H. Freeman, New York.Nimmo, J.R., Perkins, K.S., Schmidt, K.M., Miller, D.M., Stock, J.D., Singha, K., 2009.

Hydrologic characterization of desert soils with varying degrees of pedogenesis:1. Field experiments evaluating plant-relevant soil water behavior. Vadose ZoneJournal 8, 480–495.

Noguchi, S., Tsuboyama, Y., Sidle, R.C., Hosoda, I., 1999. Morphological characteristicsof macropores and the distribution of preferential flow pathways in a forestedslope segment. Soil Science Society of America Journal 63, 1413–1423.

Novak, R.J., Motto, H.L., Douglas, L.A., 1971. The effect of time and particle size onmineral alternation in several Quaternary soils in New Jersey and Pennsylvania,USA. In: Yaalon, D.H. (Ed.), Paleopedology. Israel Univ. Press, Jerusalem, pp.211–224.

Paik, K., Kumar, P., 2008. Emergence of self-similar tree network organization.Complexity 13, 30–37.

Prigogine, I., 1967. Introduction to Thermodynamics of Irreversible Processes, 3rded. John Wiley, New York, NY.

Prigogine, I., 1980. From Being to Becoming: Time and Complexity in the PhysicalSciences. W.H. Freeman.

Rasmussen, C., Southard, R.J., Horwath, W.J., 2005. Modeling energy inputs topredict pedogenic environments using regional environmental databases. SoilScience Society of America Journal 69, 1266–1274.

Rinaldo, A., Banavar, J.R., Maritan, A., 2006. Trees, networks, and hydrology. WaterResources Research 42, 06D07-8. doi:10.1029/(2005)WR004108.

Ritsema, C.J., Dekker, L.W., Hendrickx, J.M.H., Hamminga, W., 1993. Preferential flowmechanism in a water repellent sandy soil. Water Resources Research 29,2183–2193.

Robinson, D.A., Binley, A., Crook, N., Day-Lewis, F.D., Ferré, T.P.A., Grauch, V.J.S.,Knight, R., Knoll, M., Lakshmi, V., Miller, R., Nyquist, J., Pellerin, L., Singha, K.,Slater, L., 2008. Advancing process-based watershed hydrological researchusing near-surface geophysics: a vision for, and review of, electrical andmagnetic geophysical methods. Hydrological Processes 22, 3604–3635.

Rode, A.A., 1961. The Soil-forming Process and Soil Evolution. Israel Program Sci.Transl., Jerusalem.

Rodriguez-Iturbe, I., Rinaldo, A., 1997. Fractal River Basins, Chance and Self-organization. Cambridge University Press, Cambridge, United Kingdom.

Roth, K., Jury, W.A., Flühler, H., Attinger, W., 1991. Transport of chloride through anunsaturated field soil. Water Resources Research 27, 2533–2541.

Rubin, Y., Hubbard, S.S. (Eds.), 2005. Hydrogeophysics. Springer.Runge, E.C.A., 1973. Soil development sequences and energy models. Soil Science

115, 183–193.Schneider, E.D., Kay, J.J., 1994. Life as a manifestation of the 2nd law of

thermodynamics. Mathematical and Computer Modelling 19, 25–48.Shafer, D.S., Young, M.H., Zitzer, S.F., Caldwell, T.G., McDonald, E.V., 2007. Impacts of

interrelated biotic and abiotic processes during the past 125,000 years oflandscape evolution in the Northern Mojave Desert, Nevada, USA. Journal ofArid Environments 69, 633–657.

Shafer, D.S., Young, M.H., Zitzer, S.F., McDonald, E.V., Caldwell, T.C., 2004. CoupledEnvironmental Processes and Long-term Performance of Landfill Covers in theMojave Desert. DRI Publ. 45203. DRI, Las Vegas, NV.

Sidle, R., Noguchi, S., Tsuboyama, Y., Laursen, K., 2001. A conceptual model ofpreferential flow systems in forested hillslopes: evidence of self-organization.Hydrological Processes 15, 1675–1692.

Šimunek, J., Jarvis, N.J., van Genuchten, M.Th., Gärdenäs, A., 2003. Review andcomparison of models for describing non-equilibrium and preferential flow andtransport in the vadose zone. Journal of Hydrology 272, 14–35.

Smeck, N.E., Runge, E.C.A., Mackintosh, E.E., 1983. Dynamics and genetic modelingof soil systems. In: Wilding, L.P. et al. (Eds.), Pedogenesis and Soil Taxonomy.Elsevier, New York, pp. 51–81.

http://dx.doi.org/10.1016/j.jhydrol.2009.12.015

http://dx.doi.org/10.1029/2005WR004362

http://dx.doi.org/10.1029/2005WR004085

http://dx.doi.org/10.1029/2005WR004085

http://dx.doi.org/10.1002/0470848944.hsa306

http://dx.doi.org/10.1029/2004WR003403

http://dx.doi.org/10.1029/2006WR005467

http://dx.doi.org/10.1029/2006WR005467

http://dx.doi.org/10.1029/(2005)WR004108


Staddon, P.L., Ramsey, C.B., Ostle, N., Ineson, P., Fitter, A.H., 2003. Rapid turnover ofhyphae of mycorrhizal fungi determined by AMS microanalysis of C-14. Science300, 1138–1140.

Stamm, C. 1997. Rapid Transport of Phosphorus Soils in Drained Grassland. PhDThesis No. 12486 ETH (Swiss Federal Institute of for the Technology of Zurich).

Strogatz, S.H., 2005. Romanesque networks. Nature 433, 365–366.Taylor, L.L., Leake, J.R., Quirk, J., Hardy, K., Banwart, S.A., Beerling, D.J., 2009.

Biological weathering and the long-term carbon cycle: integrating mycorrhizalevolution and function into the current paradigm. Geobiology 7, 171–191.

Tiezzi, E., 2006. Steps Towards A Evolutionary Physics. WIT Press.Tisdall, J.M., 1995. Formation of soil aggregates and accumulation of soil organic

matter. In: Carter, M., Stewart, B. (Eds.), Structure and Organic Matter Storage inAgricultural Soils. Advances in Soil Science. CRC Press, pp. 57–96.

Tromp-van Meerveld, I., McDonnell, J.J., 2006a. Threshold relations in subsurfacestormflow 1: a 147 storm analysis of the Panola hillslope trench. WaterResources Research. doi:10.1029/2004WR003778.

Tromp-van Meerveld, H.J., McDonnell, J.J., 2006b. Threshold relations in subsurfacestormflow 2: the fill and spill hypothesis: an explanation for observed thresholdbehavior in subsurface stormflow. Water Resources Research. doi:10.1029/2004WR003800.

Uchida, T., Kosugi, K., Mizuyama, T., 2002. Effects of pipe flow and bedrockgroundwater on runoff generation in a steep headwater catchment in Ashiu,central Japan. Water Resources Research 38. doi:10.1029/2001WR000261.

Uchida, T., Tromp-van Meerveld, I., McDonnell, J.J., 2005. The role of lateral pipeflow in hillslope runoff response: an intercomparison of non-linear hillsloperesponse. Journal of Hydrology 311, 117–133.

Uhlenbrook, 2006. Catchment hydrology – a science in which all processes arepreferential. HP today. Hydrological Processes 20, 3581–3585.

van Genuchten, M.T., Wierenga, P.J., 1976. Mass transfer studies in sorbing porousmedia. Part 1. Analytical solutions. Soil Science Society of America Journal 40,473–480.

Volobuyev, V.R., 1964. Ecology of soils. Academy of Sciences of the Azerbaidzan SSR.Institute of Soil Science and Agrochemistry. Israel Program for ScientificTranslations, Jerusalem.

Watts, D.J., Strogatz, S.H., 1998. Collective dynamics of ‘‘small-world” networks.Nature (London) 393, 440.

Way, Thomas., 1850. On the power of soils to absorb manure. Journal of the RoyalAgricultural Society of England 11, 313–379.

Weiler, M., McDonnell, J.J., 2007. Conceptualizing lateral preferential flow and flownetworks and simulating the effects on gauged and ungauged hillslopes. WaterResources Research 43, W03403. doi:10.1029/2006WR004867.

Whipkey, R.Z., 1965. Subsurface stormwater from forested slopes. Bulletin of theInternational Association of Hydrological Sciences 10, 74–85.

Yaalon, D.H., 1971. Soil-forming processes in time and space. In: Yaalon, D.H. (Ed.),Paleopedology. Israel Univ. Press, Jerusalem, pp. 29–39.

Young, M.H., McDonald, E.V., Caldwell, T.C., Benner, S.G., Meadows, D.G., 2004.Hydraulic properties of a desert soil chronosequence, Mojave Desert, CA.Vadose Zone Journal 3, 956–963.

Zhang, J., H.S. Lin, Doolittle, J., submitted for publication. Hillslope subsurface flowrevealed by time-lapsed ground penetrating radar and real-time soil moisturemonitoring. Hydrological Processes.

http://dx.doi.org/10.1029/2004WR003778

http://dx.doi.org/10.1029/2004WR003800

http://dx.doi.org/10.1029/2004WR003800

http://dx.doi.org/10.1029/2001WR000261

http://dx.doi.org/10.1029/2006WR004867

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