a paradigm shift in hydrology: storage thresholds across scales influence catchment runoff...

A Paradigm Shift in Hydrology: Storage ThresholdsAcross Scales Influence Catchment Runoff Generation

Christopher Spence*Environment Canada, Canada

Abstract

A paradigm shift is occurring in the science surrounding runoff generation processes. Results ofrecent field investigations in landscapes and during periods previously unobservable are shapingnew ideas on how runoff is generated and transferred from the hillslope to the catchment outlet.The previous paradigm saw runoff generation and contributing area variability as a continuum.The new paradigm is based not on continual storage satisfaction and runoff generation but thresh-old-mediated, connectivity-controlled processes dictated by heterogeneity in the catchment. Thisreview focuses on the body of literature summarizing research on storage, storage thresholds andrunoff generation, particularly over the last several years during which this paradigm shift hasoccurred. Storage thresholds that control the release of water exist at scales as small as the soilmatrix and as large as the catchment. Hysteresis in storage–runoff relationships at all scales manifestbecause of these thresholds. Because storage thresholds at a range of scales have now been recog-nized as important, connectivity has become an important concept crucial to understanding howwater is transferred through a catchment. This new paradigm requires basins to be instrumentedwithin the context of a water budget investigation, with measurements taken within key catch-ment units, in order to be successful. New model approaches that incorporate connectivity arerequired to address the findings of field hydrologists. These steps are crucial if our communitywishes to adopt the holisitic view of the catchment necessary to answer the questions posed to usby the society.

Introduction

The amount of storage in a catchment has long been recognized as important for runoffgeneration. When investigating storage–runoff relationships, hydrologists of all typesremain strongly influenced by ideas like the partial area concept of Betson (1964) and thevariable source area concept of Hewlett and Hibbert (1967). Both concepts view runoffgeneration as a function of the volume or rate of inputs relative to the ability of landscapecomponents to receive them. Hewlett and Hibbert (1967) eminently stated one way inwhich storage influences runoff response. They observed:

The yielding proportion of the watershed shrinks and expands depending on the rain-fall amount and the antecedent wetness of the soil. When subsurface flow of water fromupslope exceeds the capacity of the soil profile to transmit it, the water will come to thesurface and the channel length will grow. (Hewlett and Hibbert 1967)

This statement has shaped hydrological research for 40 years, and was on the vanguardof a massive effort to understand and model runoff generation. Following Hewlett andHibbert (1967) were seminal field studies that demonstrated the spatial and temporaldynamics of variable source areas (e.g. Dunne and Black 1970) and modelling studiesthat related these areas to topography (e.g. Beven and Kirkby 1979). Runoff from a

Geography Compass 4/7 (2010): 819–833, 10.1111/j.1749-8198.2010.00341.x

ª 2010 Her Majesty the Queen in Right of CanadaJournal Compilation ª 2010 Blackwell Publishing Ltd

catchment was envisioned as a function of continual shrinking and expanding saturatedhillslope source areas around the stream channel. Difficulty in applying models based onthese ideas in some environments has lead hydrologists to conduct field studies over thelast 10–15 years (e.g. Allan and Roulet 1994; Branfireun and Roulet 1998; Quintonet al. 2003; Spence and Woo 2003; Tromp van Meerveld and McDonnell 2006).Results have revealed that there are nuances about the spatial distribution of storage andstorage thresholds. Changes to areas contributing to runoff are not continuous or contig-uous, contributing areas are not necessarily centred around the stream, and the streamnetwork is not always synonymous with the topographic drainage network. Furthermore,a key recent paper by Zehe et al. (2005) provided model results that showed that it isnot the mere quantity of water stored in a catchment that is influential. A change instorage can have a disproportionate effect on runoff response depending on how closeparts of the basin are to meeting saturation thresholds. They demonstrated that a changein the spatial pattern in which storage capacity is met changes the spatial pattern ofcontributing areas. This results in temporal differences in concentration of flow and inturn a change in the hydrograph shape, all with the same rainfall input and averageantecedent conditions.

The idea that storage thresholds impact runoff response is not new, but thoughts aresubstantially changing. Research of runoff generation across a range of scales is supportinga shift to a new paradigm that views runoff generation not as the function of continualstorage accumulation or depletion but as a threshold-mediated, connectivity-controlledprocess dictated by storage heterogeneity in soils, hillslopes and catchments. It is the liter-ature that has lead to the paradigm shift that is the focus of this review. The nature of thisfocus means that much attention will be on situations where storage effects are most pro-nounced, but attempts have been made throughout the manuscript to show the readerthere are a few general themes that make this new paradigm applicable across a range ofscales and landscapes.

Storage and storage thresholds across spatial scales

UNSATURATED SOIL MATRIX

For water to be stored in soil, surface tension must retain water against the force ofgravity. Smaller void radii can support longer columns of water. If the water tabledrops, voids now in the unsaturated zone need to empty until a suitably smaller con-trolling radius can be found. As water drains from the soil, a larger number of voidsbecome empty, leaving a more circuitous route for the remaining water (Knapp 1978),resulting in asymptotic drainage. Furthermore, void heterogeneity dictates that saturationis not a complete reversal of drainage. The capillary pressure needed to drain pores iscontrolled by the minimum radii, and the capillary pressure to fill empty pores is con-trolled by the maximum radii. The result is the non-linearity and hysteresis betweenthe pressure head, water content and soil hydraulic conductivity (Rawls et al. 1992)common to analytically described moisture characteristic curves (e.g. Brooks and Carey1964; van Genuchten 1980). The hysteresis is more often than not disregarded in manypractical, and academic, applications because of its complicating nature. However, itsimportance has been noted by the likes of Torres et al. (1998) and Quinton et al.(2008) who demonstrated the impact of soil column scale hysteresis on hillslope runoffresponse.

820 Paradigm shift in hydrology

ª 2010 Her Majesty the Queen in Right of Canada Geography Compass 4/7 (2010): 819–833, 10.1111/j.1749-8198.2010.00341.xJournal Compilation ª 2010 Blackwell Publishing Ltd

MACROPORES

There remains no concensus on the definition of a macropore. Macropores can be classi-fied by size or origin or both (Beven and Germann 1982). In this review, macropores aredefined to include all pores that are large enough to conduct water a significant distancedownslope at rates higher than the surrounding soil matrix. This definition incorporatesthe role that an increased pore diameter has on velocities and the applicability of Darcy’sLaw (Freeze and Cherry 1979). It also recognizes the importance of macropore connec-tivity in promoting pipeflow (Beven and Germann 1982; Bouma 1981; Jones 1971). Justas capillary pressure and gravity thresholds dictate hydraulic conductivity in the unsatu-rated soil matrix, the frequency at which macropores conduct pipeflow is governed bymacropore storage thresholds and the ability of the soil matrix to receive and conductwater. The rate of transfer from the soil matrix, rainfall or snowmelt along the macroporeneeds to equal or exceed infiltration losses from the macropore to the soil matrix in orderto fill the macropore and initiate and sustain pipeflow. Unless there is a source of upslopewater from exposed bedrock (Peters et al. 1995) or another macropore (Carey and Woo2001), this may require the water table to be above the elevation of the macropore(McCaig 1983; Roberge and Plamandon 1987). It may require the soil matrix infiltrationcapacity or hydraulic conductivity to be exceeded. When the rate at which water isapplied to the macropore is higher than the surrounding soil matrix hydraulic conductiv-ity, the soil matrix relinquishes control on the initiation of pipeflow and rainfall intensitybecomes important (McDonnell 1990). Pipeflow occurs only when one type of thesethresholds are exceeded.

In documenting differences in lag times between the initiation of rainfall and pipeflowduring the same storm, Jones (1987) implied that different macropores have differentthresholds of response. The differences in macropore response are due to two controls.The first is the nature of the area supplying water to the macropore (i.e. the possibletopographic catchment area contributing to the macropore and ⁄or the location of themacropore relative to source water). The second is the nature of the macropore network(i.e. the number, size and connectivity of macropores) (McDonnell 1990). For example,macropores with perennial pipeflow are obviously well connected and have better accessto groundwater stores than macropores with ephemeral flow. As the former are alreadysaturated and do not require filling by the soil matrix or upslope water, they react morequickly to rainfall events. For those macropores that are not perennial, the not uncom-mon requirement for the water table to be above the elevation of the macropore meansthe moisture state of the surrounding soil matrix and its moisture characteristic curvesdictate how, when and where the soil and macropore network become saturated inresponse to a given input of water.

HILLSLOPES

The discussion above described how subsurface flow, by either matrix flow or pipeflow,has inherent storage thresholds that must be necessarily breached to initiate the transfer ofrunoff downslope. Once an entire soil column becomes saturated, hydraulic conductivityacross that section of the hillslope increases exponentially and a different suite of processesbecomes important. This suite of processes that transmits water from saturated hillslopesincludes Hortonian flow, subsurface flow, saturation overland flow and fill-and-spill run-off. There have been numerous excellent reviews, summaries and commentaries (e.g.Anderson and Burt 1990; Beven 2007) discussing the relative importance of each in

Paradigm shift in hydrology 821


different landscapes to which the reader is directed for a general overview. The focus ofthis discussion will continue to be on the role of storage and storage thresholds on thepresence of these hillslope processes.

Each runoff generation process is dictated by its own inherent thresholds. The spatialdistribution of Hortonian runoff is controlled by where infiltration capacity is exceeded(Betson 1964). Saturation overland flow is generated at the topographic surface when therate at which water is supplied to the soil column is higher than the hydraulic conductiv-ity (Hewlett and Hibbert 1967), which tends to be at a maximum near the soil surface(e.g. Quinton and Marsh 1999). In one of the original contributions discussing saturationoverland flow, Dunne and Black (1970) noted that 1 in 25 year storms were needed togenerate saturation overland flow from New England hillslopes. The correct combinationof soil thickness, soil type, slope, possible contributing area and local hydrometeorologyare necessary. Dunne and Black’s (1970) classic comparison of convex and concave slopesand Devito et al.’s (1996) contribution highlighting the importance of soil thickness andcontributing area show the importance of soil and topography on where saturation over-land flow can occur. Central to the fill-and-spill concept of runoff generation (Spenceand Woo 2003) is that storage is spatially variable and key stores across the hillslope needto be satisfied before water is transmitted by this process (Tromp van Meerveld and Mc-Donnell 2006). Fill-and-spill runoff requires a certain combination of hillslope topologyand topography that would permit a mechanism by which water can coalesce in upslopelocations. All these mechanisms result in dynamic contributing areas on hillslopes overspace and time. Some of the best examples of dynamic contributing areas on hillslopesproduced by a variety of mechanisms are shown in Dunne (1978), Tromp van Meerveldand McDonnell (2006) and McNamara et al. (2005).

Different runoff mechanisms have been documented on the same hillslopes underdifferent wetness conditions (Montgomery and Dietrich 1995). The potential exists forany process to occur on any hillslope, but it is the interplay between inputs and storagethresholds on each hillslope that defines when and how frequent each process’ thresholdswill be crossed. Figure 1 illustrates a hypothetical hillslope on which unsaturated flow,pipeflow, saturated matrix flow, saturation overland flow, direct precipitation on saturatedareas, and Hortonian flow all occur. Increasing rainfall thresholds and different efficienciesare assumed for each process, and a uniform increase in saturated area with saturationoverland flow. Smaller events only produce saturated matrix flow, as thresholds initiatingother processes have not been exceeded. The ‘zone of higher contribution’ that has beendocumented by Jones (1987) in the field for pipeflow is apparent in Figure 1. There isanother storage threshold associated with pipeflow upon which the relative influence ofpipeflow declines, if not the volume. This is when macropores are full, but not overflow-ing, such that neither the soil matrix nor macropores can conduct all the water enteringthe hillslope. This triggers saturation excess overland flow. Only the largest eventsproduce Hortonian flow, but as this process results in ponding at the surface, a portion ofthe runoff must come from direct precipitation on saturated areas. This may be compli-cated on more heterogeneous hillslopes where the physiography of the hillslope is alsoimportant. Allan and Roulet (1994) noted the simultaneous presence of both saturationoverland and Hortonian overland flow on Canadian Shield hillslopes. The relative contri-bution of each depended on when thresholds were breached in landscapes patches withdifferent storage thresholds.

Dunne and Black (1970) observed that small portions of a hillslope (7.5%) can producedisproportionate amounts of runoff (50%). This field study confirmed that some parts of ahillslope can have higher efficiencies than others. Jones (1987) conceptualized that



pipeflow and saturated matrix flow each have different contributing areas, but these areasmay not necessarily be mutually exclusive. Pipeflow contributing areas sometimes containa saturated soil matrix that provides some water downslope. Runoff generation processesmay not be mutually exclusive but juggle predominance because of differences inefficiencies, which may be expressed through recession coefficients (Montgomery andDietrich 1995). It is also expressed in hydraulic conductivities. Dunne and Black (1970)note that once saturation overland flow occurs, the overland flow has velocities 500 times

Fig. 1. Variation in the volume and fraction occupied by different runoff generation processes with increasing eventsize on a hypothetical hillslope.



faster than the fastest subsurface stormflow, which is still continuing. The contributingarea has not changed with the introduction of saturation overland flow, but the propor-tion of water in contributing areas with a higher efficiency increases. Tromp van Meer-veld and McDonnell (2006) demonstrated how the initiation of fill-and-spill runoffincreased transmission velocities from the hillslope by an order of magnitude. The opera-tion of saturation overland flow also increases the amount of area eligible for the highlyefficient runoff process of direct precipitation on saturated areas.

As with macropores and a saturated soil matrix, field studies of hillslope runoff in adiversity of landscapes imply hydrologic connectivity, defined as saturated conditions adja-cent to one another along a flowpath to the outlet, is a necessary condition for the trans-mission of widespread lateral surface flow. In their investigation of a peatland in theCanadian Shield, Branfireun and Roulet (1998) showed that significant runoff from thehillslope only occurred once water tables in key locations reached threshold levels. Thisphenomenon is highly non-linear to the point where hillslope storage and stream dis-charge can be hysteretic (Branfireun and Roulet 1998) in that water tables can be higherduring the rising limb for the same level of runoff during recession. McNamara et al.(2005) showed that mid slope capacities must be filled in order for upslope subsurfaceflows to connect to downslope positions, expanding the contributing area. The occur-rence of hillslope runoff processes are not static, do not follow steady state principles andare threshold-mediated (McGlynn and McDonnell 2003). Assuming otherwise has notimproved our understanding of how different landscape units interact over time to pro-duce a catchment runoff signal.

CATCHMENTS

The upscaling of hillslope runoff response to the catchment has perplexed many a hydro-logist. This is an important conceptual and practical problem to be solved because almostall water resource management problems occur at the catchment scale. It is often acceptedthat as catchment size increases, complex local patterns become attenuated. In reality, it isnot always so easy. Most catchment scale studies have involved some degree of modellingbecause of the logistical difficulties of instrumenting large areas. Assumptions had to bemade on the nature of how hillslope processes upscale to the catchment, which may haveprovided us with fortuitous answers to our questions.

There has been no study that has definitively shown how small scale storage thresholdsinfluence catchment scale runoff response, but there have been several that have demon-strated the impact of hillslope scale features. Hewlett and Hibbert (1967) and especiallyDunne and Black (1970) illustrated how different storage thresholds associated with differ-ent topographic slopes (i.e. straight, concave or convex) dictate catchment runoffresponse. In a period when the interaction between basin geomorphology and hydrologywas of great interest, Boyd et al. (1979) and Rodriguez-Iturbe and Valdes (1979) bothtook a phenomenological and probabilistic approach to the storm hydrograph concepts ofNash (1957), Dooge (1959) and Wooding (1965) and the idea that topography dictatesrunoff response to develop the concepts commonly referred to as the geomorphic instan-taneous unit hydrograph (GIUH). The GIUH methodology includes the assumption thateach stream reach in a catchment is comparable to an independent reservoir reacting toeffective rainfall. In addition, the efficiency with which each reach transmits runoff exhib-its a statistical function that is tied to basin form which is expressed through the Hortonlaws of stream order, length and area (Horton 1945). Robinson et al. (1995) built uponthe GIUH by permitting efficiency to change with the extent of the stream network.



This was an important step as field studies since have demonstrated that spatially variablewater stores across hillslopes (Tromp van Meerveld and McDonnell 2006) and catchments(Bowling et al. 2003; Spence 2006) are crucial to the lateral transfer of water in higherefficiency contributing areas increases.

At the same time as the GIUH methodology was being introduced, Beven and Kirkby(1979) and O’Loughlin (1981) presented predictive methodologies able to account forthe different observed thresholds of saturation overland flow that occur in differentgeomorphological and soil conditions. This approach assumed locations where saturationdeficits could be exceeded and saturation overland flow generated could be basedprimarily on topography; from (Beven and Kirkby 1979):

lna

tan b

� �>

ST

m� S

mþ k ð1Þ

where a is contour length, b is local slope angle, ST local maximum storage, m is a con-stant related to recession and S and k are functions representing the amount of availablestorage. These topographic-index models have been widely applied, more often than notsuccessfully (Kirkby 1997), but as with anything that becomes ubiquitous and popular(e.g. Disney), they have been exposed to their share of criticism. In recent years, two keyfindings have come to light that imply limits to the applicability of Eq. 1. The first is rec-ognition that just as with macropores and an unsaturated soil matrix, runoff efficiency isnot spatially uniform (e.g. McNamara et al. 2005). The second is the recognition that abroader definition is needed of where saturation deficits are generally exceeded in acatchment. Field studies in more heterogeneous catchments have suggested that topogra-phy is but one influence on where saturation thresholds are exceeded (e.g. Allan andRoulet 1994). Wet climates can encourage topographically controlled connectivity, butin dry regions topography may not always act as a surrogate when there are other primaryinfluences on soil moisture distribution (Grayson et al. 1997). Typology of sub-catchmentunits within a heterogeneous landscape controls storage thresholds and potential evapo-transpiration losses. Topology, or relative location of these landscape units, dictates theavailability of water directed to any specific location in the catchment, controlling storagestates (Spence and Woo 2006). In recognizing the importance of topology and typologyin addition to topography, Buttle (2006) proposed that the first order controls on catch-ment runoff generation follow a T3 (typology, topology and topography) classification.The reaction to Buttle’s proposal has been mixed, but it has generated much needed dis-cussion questioning the dominance of topography as a predictor for runoff generation.

Topography is now recognized as only one possible control of storage thresholds acrosscatchments. The focus is now shifting away from using a surrogate for storage (i.e. topog-raphy) to storage itself as the predictor for runoff response. Both Spence (2007) andKirchner (2009) demonstrated that much can be learned about runoff response by simplyplacing catchments within a theoretical construct where discharge is a function of storage.A new paradigm is emerging that recognizes it is the different attributes of the storageacross the catchment; where it is; when it occurs and how it becomes accessible, that areproving important to catchment runoff response. Furthermore, as the discussions earlieron the nature of storage at smaller scales imply, satisfaction of storage across a catchmentdoes not occur as a continuum, but following a series of discontinuous thresholds. Often,upscaling these thresholds to the catchment scale and superimposing the different runoffprocesses in Figure 1 together produces a non-linear relationship between inputs and run-off. However, these thresholds can be so high in places, that runoff can be completely



intercepted, stored, evapotranspired and prevented from reaching the basin outlet (Mielkoand Woo 2006; Stichling and Blackwell 1957). The most profound effect at the catch-ment scale of this hillslope scale threshold behaviour is a diverse contributing area. Rouletand Woo (1988), Quinton et al. (2003), Laudon et al. (2007) and Spence (2006) allshowed how the distribution of storage thresholds at the hillslope scale dictate the organi-zation of the stream network, contributing areas overtime and runoff response at thecatchment outlet. In very different catchments, both McGlynn et al. (2004) and Spenceand Woo (2006) documented how noting the location and topology of key landscapeunits within a catchment provides insight into where each of the classical runoff mecha-nisms occur, and the relative importance of each on catchment runoff response. It isimportant to note how different are the research catchments of McGlynn et al. (2004)and Spence and Woo (2006) in order to demonstrate the wide applicability of their find-ings. McGlynn et al. worked at the wet steep Maimai catchment in New Zealand.Spence and Woo worked on gentle Canadian Shield terrain in a boreal climate withone-tenth the rainfall.

The existence of smaller scale thresholds that control catchment runoff manifests in theform of non-linear response functions to changes in storage, which may be distinct toindividual catchments, or types of catchments. McGlynn et al. (2004) and Spence et al.(2009) have demonstrated that these functions are hysteretic, and are comparable topatterns between storage and outflow documented at the smaller scales discussed earlier;including soil columns (Brooks and Carey 1964), hillslopes (Dunne 1978) and streamchannels (Chow et al. 1988) (Figure 2). Spence et al. (2009) were able to relate portionsof these hysteretic curves to different catchment functions. There are a host of problems

Fig. 2. Examples from the literature demonstrating hysteresis between storage and water flux at a range of scalesincluding a soil matrix (a), hillslope (b) stream channel (c) and catchment (d). Adapted from van Genuchten (1980),Branfireun and Roulet (1998), Chow et al. (1988) and Spence et al. (2009).



and issues with deriving and applying storage–discharge curves at the catchment scale.Nonetheless, recognizing their existence is useful as they permit a numerical representa-tion of the physical relationship between storage in dynamic contributing areas andstreamflow response at the catchment outlet. Compilation of curves from a diversity ofcatchments may aid in catchment classification (McDonnell and Woods 2004). Theappearance of connectivity and hysteresis functions at the catchment scale because of traitsand processes occurring at smaller scales is what Sivapalan (2005) has termed emergentbehaviour. Analysis of the signatures of this emergent behaviour (i.e. degree of connectiv-ity and magnitude and direction of hysteresis) in catchment storage-discharge curveswould permit basins to be classed not only by their streamflow response (e.g. Church1974), but also incorporate hydrological function and could infer the first order controlsresponsible for catchment behaviour (Buttle 2006).

What does this mean for how we should investigate catchment streamflow response?

IMPLICATIONS FOR FIELD METHODS

Hydrologists have sometimes derided themselves for not having an overarching scientificfoundation. This may be because so many of the historical roots of the field are in waterengineering and management. One applicable concept across a multitude of spatial andtemporal time scales is the water budget, which generally can be expressed as:

DS ¼ I �O ð2Þ

where DS is change in storage, I is inputs and O is outputs. The subdivision of I and Ointo specific fluxes on the right hand side of the equation changes among catchments andtime. For instance, snowmelt has to be included when investigating cold catchments. Ifstudies take place over a short time period, certain slow processes such as deep percola-tion may be ignored. The energy budget, which drives the entire hydrological system, isclosely associated with the water budget through an evapotranspiration ⁄ latent heat term,E, if included as part of O in Eq. 2:

Rn ¼ H þ E þG ð3Þ

where Rn is net radiation, H is sensible heat and G is heat storage.Not enough catchment field studies report water budget estimates, as too many focus

only on precipitation ⁄ snowmelt and runoff. Although most hillslope studies have plethorawells, piezometers, soil moisture probes and tensiometers, only some calculate storage orcumulative change in storage. Although having a direct measurement of antecedent mois-ture at their fingertips, many still use individual wells or antecedent precipitation as anindex. Storm and water year precipitation ⁄ runoff ratios are often less than 50%. Wheredoes the majority of the water go? Strangely, evapotranspiration is often an afterthought,or assumed to be non-existent or inconsequential. The benefit of nested instrumentedwatersheds in improving understanding of streamflow production has been well estab-lished (Pomeroy et al. 2005; Prowse et al. 2007; Sivapalan et al. 2003). A case can also bemade for instrumenting these hillslopes and watersheds for full water budget evaluation.Doing so provides insight on water fluxes, and how they draw upon basin storage, that ispossible no other way. Some may argue that basin heterogeneity and measurement errorare too high to calculate a reliable catchment water budget. Hydrologists should alwaysbe suspicious when their water budget calculations come too close to balancing.



However, evidence shows that individual fluxes are often large enough that the errorbounds do not prevent fair conclusions to be made. It is important to attempt water bud-get evaluations as part of this new paradigm. A better understanding will be gained ofwhere and how storage thresholds are being breached across the catchments if attemptsare made to measure all fluxes.

The application of isotopes and other hydrochemical approaches to catchment studieshas provided remarkable insight into runoff generation processes. Chemistry providesevidence of the dynamics of source areas that hydrometric approaches cannot. A key lim-itation of water chemistry methodologies is that they do not permit the determination bywhich processes the water gets to the stream. This has to be inferred (McGlynn andMcDonnell 2003). In turn, it becomes difficult to make conclusions about which storagethresholds are being crossed and how efficient are different parts of the catchment. Theuse of a multi-tracer approach (e.g. isotopes with silica or chloride) may alleviate thisproblem. Further to this point, the author wishes to reiterate the opinion of Buttle andPeters (1997) who demonstrated why hydrochemical approaches should always be used inconjunction with hydrometric methods. This helps narrow the different possibilitieshydrologists have to contend with when results from one method are inconclusive as towhich source areas, pathways and runoff processes are predominant at a given time.

McGlynn et al. (2004) suggested that rather than investigate specific runoff mecha-nisms, a more appropriate course of action for understanding watersheds may be to focuson key catchment units that collect and convey water. It may be possible to combine therecommendations of McGlynn et al. (2004) and findings of Spence et al. (2009) andderive storage–streamflow curves for research catchments and their key component parts.This could provide a qualitative and quantitative means to develop upscaling relationshipsuseful for predicting streamflow. Furthermore, complementary full water budget measure-ments within these key catchment units would provide insight on how catchments andtheir parts behave and function.

IMPLICATIONS FOR MODELLING AND PREDICTION

Troch et al. (2008) recently commented that hydrology is moving towards a more holis-tic view that recognizes the importance of landscape heterogeneity. Crucial to a successfulmigration to this new paradigm is recognition of the role of storage and its thresholdsacross heterogenous landscapes. A common approach to modelling storage thresholdsunder the old paradigm is epitomized by Sugawara (1967) in which stores on the land-scape are conceptualized by tanks of different capacities. What has not been fully recog-nized in such models is the importance of topology and connectivity. This is relativelyeasy in distributed models as key linkages can be explicitly represented. It is alsosurmountable at the hillslope scale or smaller where we are confident in the location ofimportant intermittent linkages where, again, they can be explicitly represented in mod-els. For example, Reaney et al. (2006) developed the Connectivity of Runoff Model(CRUM) which explicitly accounts for surface depressional storage; parameterized usingsurface roughness and slope. Lehmann et al. (2007) applied an explicit model of an instru-mented hillslope at Panola, Georgia, based upon the principles of percolation theory thatperformed very well.

Semi-distributed models require more elegant approaches where sub-grid connectivityneeds to be parameterized. Many lateral transfer schemes in semi-distributed models usedat the sub-grid scale are rudimentary. For example, the Canadian Land Surface Scheme(CLASS), uses a simple additive approach that does not permit any interaction among



sub-grid landscape units. Topography-based models represent connectivity based on slopeand antecedent wetness. Deriving the probability of saturation overland flow across acatchment using Eq. 1 is a fair approach as in many landscapes, the saturated areas are indownslope locations aligned with drainage networks (Buttle et al. 2004). However, asnoted earlier, we are discovering that in many landscapes, saturation overland flow occursin areas unrelated to topography. New sub-grid parameterization schemes will need toaccount for the dynamic distributions of unit topology, morphology and storage tran-sience, as these dictate the spectrum of landscape unit function. This is particularly impor-tant if demands are placed on modellers to properly reproduce sediment, carbon ornutrient fluxes in addition to water.

Meerkerk et al. (2009) are correct; hydrologists need to follow the lead of landscapeecologists who have an accepted universal definition of connectivity. This is requiredbefore we can provide consistent quantitative measures of connectivity. Ecologists haveaccepted a definition that recognizes that as long as habitat is contiguous, it provides con-nection (Li and Reynolds 1993). Contiguous habitat is not necessarily quality habitat thatwill provide a connected pathway for all individuals of a species, but field observationsshow that this is generally acceptable. Western et al. (2001) defined hydrological connec-tivity in a similar manner as this landscape ecology definition; where locations of similarmoisture state are adjacent, they are connected. Physically, this does not imply hydrologi-cal connectivity, in that a drop of water can actually move between adjacent locations.Usually slope dictates unidirectional connectivity, and drainage divides sever hydrologicalconnectivity. Bracken and Croke (2007) propose a good definition adapted from fluvialgeomorphology; connectivity occurs when there is the potential for a specific particle tomove through the system and it is transferred from one zone or location to another.They also propose a means by which to measure it by looking at the relative values ofapplied water and ability to transfer downslope.

Two primary research gaps for modellers need to be addressed. First, we need to dis-cern a better way to parameterize sub-grid or sub-catchment units with appropriate timeconstants relating storage and discharge (perhaps from characteristic curves) so that wecan properly simulate how well they can sustain downslope flow and maintain connec-tions. Second, a key unknown to be addressed is how to better parameterize sub-grid orsub-catchment topology. The transfer functions used in unit hydrograph theory and topo-graphic indices have previously been estimated with assumptions of static stream net-works, effective precipitation, homogenous runoff responses and assumed probabilitydistributions, all of which can be to be severely limiting in some landscapes. By even rec-ognizing connectivity as a viable concept nullifies these assumptions and necessitatesparameterizing topology among disparate sub-catchment units.

Concluding remarks

A paradigm is defined by the questions posed within it, the phenomena of interest, themethodologies employed and the nature with which data is interpreted. A new paradigmin hydrology is emerging (Figure 3) because recent observations of runoff generationcould not be explained readily by existing theories. Field studies have begun to revealthat runoff is not only non-linear but also a hysteretic, threshold-mediated, connectivity-controlled process. The thresholds that control runoff at the catchment scale exist at arange of subordinate scales. Thresholds in the soil matrix produce hysteresis between stor-age and the rate at which soil water can move. Still within the soil, but in macropores,the rate of inputs relative to the ability of the macropore to conduct water determines



when macropores are important for downslope water movement. As such, the thresholdat which macropores become active is intrinsically linked to the hysteretic nature of soilmoisture–conductivity curves. In addition to pipeflow, there is a suite of runoff genera-tion processes that occurs on hillslopes. Each is dictated by its own thresholds. Thephysio-climatic situations on each component of the hillslope determine when and whereany process will tend to occur. Differences in efficiencies with each process cause differ-ent areas to provide disproportionate amounts of runoff. In some landscapes, this willcreate patterns indicative of the variable source area concept. In others, intermittentconnectivity and non-contiguous variable source areas are the norm. Our community islearning that in these landscapes, understanding hillslope runoff patterns requires ideasrespectful of heterogeneity, connectivity, hysteresis and non-steady state conditions. Con-tinual storage satisfaction and runoff generation is the exception, rather than the rule.

The second reason for this paradigm shift is that questions were being posed to thehydrological research community on the hydrological, chemical and ecological behaviourand function of catchments that it could not answer. Answering these questions willrequire more holistic investigative techniques than the previous reductionist ones. Toimprove our understanding of catchment response, nested basins should be instrumentedwithin the context of a water budget investigation, with measurements taken within keycatchment units. New model approaches that incorporate connectivity are required toaddress the findings of field hydrologists and permit constituent and runoff pathways tobe adequately simulated. This is particularly crucial if our community wishes to answerthe questions posed to us by society.

Acknowledgement

The author would like to acknowledge the support of Environment Canada, and severalfunding sources over the years, including the Natural Sciences and Engineering ResearchCouncil and the Canadian Foundation for Climate and Atmospheric Sciences. Some

Fig. 3. Characteristics of the previous (on left) and new (on right) runoff generation paradigms in hydrology.



colleagues and students whom I would like to thank for fruitful discussions about what Ithink is an exciting paradigm shift in hydrology include Ming-ko Woo, Jim Buttle, BrianBranfireun, Sean Carey, Jeff McDonnell, Murugesu Sivapalan, Xiu Juan Guan and RossPhillips, among others.

Short Biography

Christopher Spence holds a B.A. (Hons.) and M.Sc. from the University of Regina,Regina, Canada and a Ph.D. from McMaster University, Hamilton, Canada. He currentlyis a research scientist for Environment Canada in Saskatoon, Canada. He was appointedan adjunct professor in the Department of Geography at the University of Saskatchewanin 2006. His research focuses on hydrometeorological processes in cold regions. He has aparticular interest in the hydrological behaviour and function of complex landscapes suchas the Canadian Shield and Prairie. He has a beautiful wife with whom he has twodaughters (7 and 9 years). He is getting a bit tired of Disney entertainment.

Note

* Corresponding address: C. Spence, Environment Canada, 11 Innovation Boulevard, Saskatoon, SK, Canada S7N3H5. E-mail: [email protected]

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