Connectivity as an emergent property of geomorphic systems State of Science Connectivity as an emergent property of geomorphic systems Ellen Wohl,1* Gary Brierley,2 Daniel Cadol,3 Tom J. Coulthard,4 Tim Covino,5 Kirstie A. Fryirs,6 Gordon Grant,7 Robert G. Hilton,8 Stuart N. Lane,9 Francis J. Magilligan,10 Kimberly M. Meitzen,11 Paola Passalacqua,12 Ronald E. Poeppl,13 Sara L. Rathburn14 and Leonard S. Sklar15 1 Colorado State University, Geosciences, Fort Collins, Colorado USA 2 University of Auckland, School of Environment, 10 Symonds Street, Auckland, New Zealand 3 New Mexico Institute of Mining and Technology, Earth and Environmental Science, 801 Leroy Pl, Socorro, New Mexico USA 4 University of Hull, Geography, Cottingham Road, Hull HU6 7RX, UK 5 Colorado State University, Ecosystem Science and Sustainability, Campus Delivery 1499, Fort Colins, Colorado USA 6 Macquarie University, Department of Environmental Sciences, Herring Road, North Ryde, New South Wales Australia 7 USDA Forest Service, Pacific Northwest Research Station, 3200 SW Jefferson Way, Corvallis, Oregon USA 8 Durham University, Geography, Science Laboratories, South Road, Durham DH1 3LE, UK 9 Université de Lausanne, Institute of Earth Surface Dynamics, Géopolis, Quartier Mouline, Lausanne, Vaud Switzerland 10 Dartmouth College, Geography, 6017 Fairchild, Hanover, New Hampshire USA 11 Texas State University, Geography, 601 University Drive, San Marcos, Texas USA 12 The University of Texas at Austin, Department of Civil, Architectural, and Environmental Engineering, 301 E. Dean Keeton St, STOP C1700 Austin, Texas USA 13 Department of Geography and Regional Research, University of Vienna, Universitaetsstrasse 7, Vienna, Austria 14 Geosciences, Colorado State University, 1482 Campus Delivery, Fort Collins, Colorado USA 15 Concordia University, Geography, Planning, and Environment, Henry F. Hall Building, Montreal, Quebec Canada, H3G 1M8 Received 8 September 2017; Revised 16 May 2018; Accepted 23 May 2018 *Correspondence to: Ellen Wohl, Colorado State University, Geosciences, Fort Collins, Colorado, USA. E-mail: ellen.wohl@colostate.edu ABSTRACT: Connectivity describes the efficiency of material transfer between geomorphic system components such as hillslopes and rivers or longitudinal segments within a river network. Representations of geomorphic systems as networks should recognize that the compartments, links, and nodes exhibit connectivity at differing scales. The historical underpinnings of connectivity in geomor- phology involve management of geomorphic systems and observations linking surface processes to landform dynamics. Current work in geomorphic connectivity emphasizes hydrological, sediment, or landscape connectivity. Signatures of connectivity can be detected using diverse indicators that vary from contemporary processes to stratigraphic records or a spatial metric such as sediment yield that encompasses geomorphic processes operating over diverse time and space scales. One approach to measuring connectivity is to determine the fundamental temporal and spatial scales for the phenomenon of interest and to make measurements at a sufficiently large multiple of the fundamental scales to capture reliably a representative sample. Another approach seeks to char- acterize how connectivity varies with scale, by applying the same metric over a wide range of scales or using statistical measures that characterize the frequency distributions of connectivity across scales. Identifying and measuring connectivity is useful in basic and applied geomorphic research and we explore the implications of connectivity for river management. Common themes and ideas that merit further research include; increased understanding of the importance of capturing landscape heterogeneity and connectivity patterns; the potential to use graph and network theory metrics in analyzing connectivity; the need to understand which metrics best represent the physical system and its connectivity pathways, and to apply these metrics to the validation of numerical models; and the need to recognize the importance of low levels of connectivity in some situations. We emphasize the value in evaluating bound- aries between components of geomorphic systems as transition zones and examining the fluxes across them to understand landscape functioning. © 2018 John Wiley & Sons, Ltd. Introduction Connectivity has become a widely used conceptual framework within geomorphology. Our primary objectives in this paper are to: (i) facilitate careful consideration of how to define and measure connectivity and disconnectivity across diverse spatial and temporal scales; (ii) explore the implications of connectivity, including the situations in which connectivity provides a useful EARTH SURFACE PROCESSES AND LANDFORMS Earth Surf. Process. Landforms 44, 4–26 (2019) © 2018 John Wiley & Sons, Ltd. Published online 9 July 2018 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/esp.4434 http://orcid.org/0000-0001-7435-5013 http://orcid.org/0000-0002-4408-8548 http://orcid.org/0000-0002-6077-6076 http://orcid.org/0000-0001-5047-4288 http://crossmark.crossref.org/dialog/?doi=10.1002%2Fesp.4434&domain=pdf&date_stamp=2018-07-09 framework or new insight, potential signatures of connectivity in geomorphic systems, and how connectivity can be used in resource management; and (iii) highlight gaps in current under- standing of connectivity and potential pathways for future research. We first introduce some basic characteristics of con- nectivity as viewed in a geomorphic context, then review both the historical underpinnings of and recent work on connectivity in geomorphology. We then discuss the challenges of identifying and measuring connectivity, use river basins to illustrate the management implications of connectivity, and conclude with a summary of key questions and challenges to understanding and using connectivity in a geomorphic context. Connectivity in a geomorphic context As the scientific study of surface processes and landforms, and as a discipline that has largely developed from geology and physical geography, geomorphology has come to focus upon the fluxes of fluids (air, water) and sediment and the landforms resulting from, and influencing, those fluxes. The term geomorphic systems rec- ognizes couplings among seemingly discrete components of Earth’s surface and near-surface environments, such as water and sediment fluxes from hillslopes that govern the configuration of river channels or fluxes of eolian dust that influence rates of soil formation in geographically distant locations (Martignier et al., 2013). Attention to fluxes of material through landscapes dates to the founding of geomorphology as a discipline (Gilbert, 1880). The term connectivity has become widely used to de- scribe these fluxes within the past two decades. Several definitions of connectivity have been proposed (Table I). We define connectivity as the efficiency of transfer of materials between system components. Definition of system components varies between disciplines, such as between geo- morphology and ecology, and in relation to the material under consideration (e.g. water versus sediment). Geomorphic sys- tems can be represented as networks with compartments, links, and nodes. Using a drainage basin as an example, hillslopes and valley bottoms are compartments, channel segments are links, and channel junctions are nodes. Connectivity has value as a conceptual framing for investigat- ing the spatial and temporal variability of fluxes because it directs attention to: (i) interactions among geomorphic system compo- nents that may appear to be isolated in time and space, such as how relative base level fall triggers river incision and subsequent hillslope adjustments over timespans of 103–104 years (Burbank et al., 1996); (ii) the response of diverse geomorphic systems to varying inputs, such as how water and sediment fluxes from indi- vidual drainage basins respond to extreme storms as a function of characteristics such as basin size, river network structure, and the temporal sequence of extreme storms (Cenderelli and Wohl, 2003); (iii) the specific features of geomorphic systems that gov- ern connectivity, such as the landforms that limit sediment fluxes within a drainage basin (Fryirs et al., 2007a); and (iv) how human alterations of geomorphic systems influence system behavior, such as how flow regulation and associated changes in water and sediment connectivity alter river geometry and biotic com- munities. Connectivity also has value as a common framing shared among disciplines (Tetzlaff et al., 2007; Werner and Mc- Namara, 2007; Larsen et al., 2012; Puttock et al., 2013; Hauer et al., 2016). Connectivity is not an either/or attribute, but rather a contin- uum. Consequently, representations of geomorphic systems as networks must recognize that the compartments, links, and nodes exhibit connectivity at differing spatial and temporal scales and include diffuse and concentrated fluxes, and vari- able rates of flux (Passalacqua, 2017). Connectivity is typically limited to some degree through time and across space, so that understanding of one extreme of the continuum, disconnectivity, is equally important (Faulkner, 2008). Components or processes that are disconnected are those that either are too remote from each other in space or time, so that a change in one component or process does not lead to change in another, or those in which a threshold must be overcome to allow connectivity: a critical shear stress must be exceeded to allow sediment transport, for example, or a flow magnitude must be exceeded to overtop the channel banks and laterally connect the channel and floodplain. The end member of disconnectivity must be treated with caution because something that is disconnected at a short time scale may be connected at a longer time scale. In general, all mea- sures of connectivity are dependent on time and space scales and are relational in the sense of describing transfers between components of a system (Grant et al., 2017). Figure 1 illustrates the temporal aspect of connectivity in a manner similar to Schumm and Lichty’s (1965) conceptualiza- tion of variables changing between dependent and indepen- dent status over diverse time scales. In this figure, sediment transport is highly connected and continuous over longer time and larger space scales, but disconnected in time and space when considered over periods of years to decades that include substantial periods of lower flow without sediment transport. Analogously, the longitudinal profile may be continuously adjusting to fluctuations in relative base level and thus longitu- dinally connected over cyclic time scales, but segmented by the presence of knickpoints and thus less longitudinally con- nected over graded and steady time scales. Investigations of connectivity and disconnectivity in geomor- phic systems can focus on fluxes of different types of materials, such as water (Bracken et al., 2013; Larsen et al., 2017) or sed- iment (Fryirs et al., 2007a; Bracken et al., 2015; Li et al., 2016). Investigations can emphasize features that enhance or limit connectivity, such as landforms that create physical thresholds which must be exceeded before material can move between compartments (Kondolf et al., 2006; Fryirs et al., 2007a). Alter- natively, investigations can emphasize the magnitude, dura- tion, frequency, strength, timing, or spatial extent of connectivity (Cote et al., 2009; Cavalli et al., 2013). Jaeger and Olden (2012), for example, used electrical resistance sen- sors to quantify the longitudinal extent and duration of stream flow in an ephemeral channel network in Arizona, USA. Framing connectivity in a geomorphic context provides a ba- sis for considering both structural and functional components of the landscape. What has been referred to as structural con- nectivity is dependent on the position and spacing of landscape units and the extent to which they are in contact or distant from one another (Wainwright et al., 2011). Landscape units can vary from entire mountain ranges or drainage basins down to patches of land cover (e.g. forest versus grassland) or individual grass clumps on a hillslope with spatially discontinuous vegeta- tion cover. Structural connectivity influences the thresholds of magnitude and duration necessary to create fluxes between in- dividual landscape units. Floodplain wetlands adjacent to an active channel and at lower elevations may require a lower magnitude flood to achieve surface hydrologic connectivity with the channel than do floodplain wetlands farther from and/or higher than the channel (Galat et al., 1997; Poole et al., 2002). The occurrence of longitudinally continuous flow along intermittent or ephemeral channels in drylands depends partly on the magnitude and duration of precipitation inputs, but also on the structural connectivity governed by valley sur- face and subsurface geometry as this geometry creates alluvial reservoirs that must be saturated before surface flow occurs (Falke et al., 2011; Jaeger and Olden, 2012). 5GEOMORPHIC CONNECTIVITY © 2018 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, Vol. 44, 4–26 (2019) Table I. Definitions and quantitative metrics of connectivity (after Wohl, 2017, Tables I and II) A) Definition Reference Connectivity in the context of landscape dynamics describes the transmission of matter and energy among system components (Harvey, 1987, 1997, 2001, 2002; Godfrey et al., 2008) Hydrological connectivity as the exchange of matter, energy, and biota between different elements of the riverine landscape via the aqueous medium Amoros and Roux, 1988 Hydrological connectivity can be defined as the physical linkage of water and sediment through the fluvial system. Hooke, 2003; Lesschen et al., 2009 Hydrologic connectivity refers to the water-mediated transfer of matter, energy, and/or organisms within or between elements of the hydrologic cycle Pringle, 2003 River hydrologic connectivity refers to the water-mediated fluxes of material, energy, and organisms within and among components, e.g. the channel, floodplain, alluvial aquifer, etc. of the ecosystem Kondolf et al., 2006 Static/structural connectivity: static elements of hydrological connectivity are spatial patterns, such as hydrological runoff units, that can be categorized, classified, and estimated; spatial patterns in the landscape (Turnbull et al., 2008) Bracken and Croke, 2007 Dynamic/functional connectivity: describes both the longer term landscape developments, such as changes following abandonment of agriculture, and short-term variation in antecedent conditions and rainfall inputs to systems that result in nonlinearities in hillslope and catchment response to rainfall; how spatial patterns interact with catchment processes to produce water transfer in catchments (Turnbull et al., 2008) Bracken and Croke, 2007 Process connectivity: the evolutionary dynamics of how systems operate; also defined as flow of information among a system’s drivers, where information is a reduction of the uncertainty in a variable’s state Bracken and Croke, 2007; Passalacqua, 2017; Ruddell and Kumar, 2009 Three stages of landscape connectivity: coupled linkage when there is free transmission between landscape units; partial coupling when a discontinuity between units results in pulses of sediment movement; partly connected stage when there is a decrease of transmission due to impediments, but some material can pass the impediment during an effective event; buffers hinder lateral connectivity, barriers hinder longitudinal connectivity, and blankets hinder vertical connectivity Fryirs et al., 2007a; Jain and Tandon, 2010 Initiation of a shallow groundwater table across hillslope, riparian, and stream zones Jencso and McGlynn, 2011 Hydrologic connectivity describes connection, via the subsurface flow system, between the riparian zone and the upland zone, which occurs when the water table at the upland–riparian zone interface is above the confining layer (Also presents 10 other definitions from the literature, categorized with respect to water cycle or landscape features at the watershed scale, and landscape features, spatial patterns, and flow processes at the hillslope scale) Bracken et al., 2013 Sediment connectivity: the degree of linkage that controls sediment fluxes throughout landscapes and in particular between sediment sources and downstream areas Cavalli et al., 2013 Sediment connectivity is the water-mediated transfer of sediment between two different compartments of the catchment sediment cascade; catchment disconnectivity can be expressed as the degree to which any limiting factor constrains the efficiency of sediment transfer relationships Fryirs, 2013 Connectivity defined as the transfer of matter between two different landscape compartments Wester et al., 2014 Connectivity describes the integrated transfer of sediment across all possible sources to all potential sinks in a system over the continuum of detachment, transport, and deposition, which is controlled by how the sediment moves between all geomorphic zones; on hillslopes, between hillslopes and channels, and within channels. Bracken et al., 2015 Describe two fluxes as connected if they are in close spatial proximity along the river network; refer to connectivity as the state of two or more fluxes being connected; dynamic connectivity refers to how the connectivity of fluxes changes in time Czuba and Foufoula-Georgiou, 2015 Defines five layers of hydrologic connectivity as hillslope, hyporheic, stream-groundwater, riparian/ floodplain, and longitudinal within channels Covino, 2017 B Description Metric Reference Primarily hydrologic metrics Integral connectivity scale lengths (ICSL) Average distance over which wet locations are connected using either Euclidean distances or topographically defined hydrologic distances; 1 of 15 indices of hillslope hydrologic connectivity in Bracken et al. (2013: Table IV) Western et al., 2001 Attenuated imperviousness (I) I ¼ ∑j AjWjð ÞAc � � Weighted impervious area as a percentage of catchment area; Aj is the area of the jth impervious surface; Wj is the weighting applied to Aj; Ac is catchment area Walsh and Kunapo, 2009 River Connectivity Index (RCI) DCIP ¼ ∑ n i¼1 v2i V2 �100 The size of disconnected river fragments between dams in relation to the total size of the original river network, based on Cote et al. (2009) DCI; size can be described in terms of volume (example at left), length, or other variables Grill et al., 2014 (Continues) 6 E. WOHL ET AL. © 2018 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, Vol. 44, 4–26 (2019) The assemblage and spatial pattern of landforms (i.e. type, size, and adjacency) produces the structural, physical template from which to examine the extent to which interactions be- tween landforms at different spatial and temporal scales occur. For example, Jain and Tandon (2010) and Hooke (2003) de- scribe connectivity patterns in terms of whether landforms are connected, partially connected or discrete. Fryirs et al. (2007a) describe the position of landforms that act as blockages within the landscape. As water flows over landforms, elements that influence structural connectivity may be modified as the landscape evolves by weathering and erosion processes. The time scale of this evolution can be rapid, such as during large mass wasting events (Korup et al., 2004), progressive over sea- sons and decades (Lane et al., 2017), or acting over long-term time scales >103 years (Prasicek et al., 2015). Because we define connectivity as the efficiency of material transfer, we suggest that the structural configuration of geomor- phic systems, although strongly influencing connectivity, be described as system configuration rather than structural con- nectivity. This leaves connectivity as referring specifically to what has been called functional connectivity. Functional connectivity operates within this structural tem- plate. In geomorphic terms functional connectivity refers to the processes associated with the sources and fluxes of water, sedi- ment, and solutes through a landscape and the transfer of those materials between multiple, contiguous structural components or between components of a system that are physically isolated except for relatively brief periods of connectivity (Jain and Tandon, 2010; Wainwright et al., 2011). In analyses of functional connectivity, the strength of connectivity or linkage between Table 1. (Continued) B Description Metric Reference Primarily sediment metrics Sediment delivery ratio (SDR) SDR ¼ net erosiontotal erosion Measure of sediment connectivity Brierley et al., 2006 Connectivity Index (IC) IC ¼ log10 DupDdn � � Dup ¼ WS ffiffiffiffi A p Ddn ¼ ∑ i di WiSi W ¼ 1 � RIRIMAX � � Roughness Index (RI) RI ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ 25 i¼1 xi � xmð Þ2 25 vuuut Dup and Ddn are the upslope and downslope components of connectivity, respectively, with connectivity increasing as IC increases; W is the average weighting factor of the upslope contributing area, S is the average slope gradient of the upslope contributing area, and A is the upslope contributing area; di is the length of the flow path along the ith cell according to the steepest downslope direction, Wi and Si are the weighting factor and the slope gradient of the ith cell, respectively; RIMAX is the maximum value of RI in the study area; 25 is the number of processing cells within a 5 X 5 moving window, xi is the value of one specific cell of the residual topography within the moving window, and xm is the mean of the 25 cell values Cavalli et al., 2013 Complexity index based on overall relief Dhmax Dhmax = Emax - Emin and slope variability SV SV = Smax – Smin Where Emax and Emin are the maximum and minimum elevations, respectively, in the catchment; Smax and Smin are the maximum and minimum, respectively, % slope within the area of analysis (moving window) Baartman et al., 2013 Cluster Persistence Index (CPI) CPIi ¼ ∫ over all times t M ið Þ j tð Þdt Defines clusters within a river network where mass (sediment) coalesces into a connected extent of the network; the superscript (i) denotes all clusters M ið Þ j that occupy link i at time t Czuba and Foufoula- Georgiou, 2015 Metrics for diverse fluxes C tð Þ ¼ ∑ m tð Þ i¼1 ∑ ni tð Þ j¼1 pij tð ÞSij tð Þ Patch connectivity, along with line, vertex, and network connectivity, can be used to characterize landscape connectivity; patch connectivity is the average movement efficiency between patches; C is patch connectivity, pij (t) is the area proportion of the jth patch in the ith land cover type to the total area under investigation at time t; S is movement efficiency; 0