Spatial heterogeneity as a component of river geomorphic complexity

Abstract

One component of geomorphic complexity results from spatial heterogeneity in river corridors. The characteristics of this form of complexity have important implications for habitat and biodiversity, attenuation of downstream fluxes, resistance and resilience of river ecosystems, river processes, ability to characterize patterns and changes through time, and river management and restoration. Numerous measures of complexity have been applied to heterogeneity from spatial scales of bed grain size distribution to entire river networks. Studies explicitly incorporating geomorphic complexity have increased substantially since 2000, but there is no single, widely used metric of complexity. Despite increasingly explicit scientific appreciation of the importance of complexity in river corridors, public attitudes toward rivers continue to emphasize an attractive appearance, which commonly equates to a physically simple and homogeneous river corridor.

Keywords

River complexity resistance resilience diversity spatial heterogeneity

I What is complexity?

Thoreau’s advice to “simplify, simplify” notwithstanding, complexity is inherent in rivers and our ability to characterize complexity reflects our understanding of processes and forms in river corridors – defined here as channels and floodplains. Complexity is used in different contexts within physical geography. One context involves complex behavior or complexity as a property of a system. Complexity in this context refers to the simultaneous presence of simple and complicated behaviors or the presence of nonlinear dynamics, self-organization, and emergent properties (e.g., Phillips, 2014; Werner and McNamara, 2007; Table 1). A second context for complexity involves spatial heterogeneity. This paper focuses on geomorphic complexity in the context of spatial heterogeneity, although spatial heterogeneity and complex behavior are commonly interrelated (e.g., Cadenasso et al., 2006; Murray and Fonstad, 2007; Peipoch et al., 2015; Phillips, 2007). Spatial heterogeneity in the following discussion subsumes concepts such as evenness, diversity, and physical complexity.

Table 1.

Examples of definitions of complexity.

Definitions	References
1) Three-part definition of biocomplexity 1) Structure of a system of interest spatially explicit structure: heterogeneity described as patch richness (the number of patch types present), patch frequency (the number of each patch type), patch configuration (patch arrangement in space relative to each other), patch change (which patches change and how they change), shifting mosaic (patch changes are spatially explicit and quantified) historical contingency: refers to relationships that extend beyond direct, contemporary ones organizational connectivity	Cadenasso et al. (2006)
2) Complex behavior nonlinear behavior (existence of thresholds) self-organization (appearance of pattern or structure in a system) emergent properties (formation of a structured output in response to multiple, simple interactions within a system)
3) Highly connected explanation or model
Geomorphic complexity of behavior nonlinear dynamic systems that display complex, seemingly unpredictable behavior, including events that occur without external forcing (chaotic behavior), patterns that emerge spontaneously (self-organization), and asynchronous and contrasting responses within a system (complex response)	Favis-Mortlock (2013); McDowell (2013); Rhoads (2013)
Diversity of environmental systems diversity is a property of a sampling unit containing a set of events or objects (O) of any kind, of which C(O) is a partition, measurable by numbers, that combines the number of classes (S) of C(O) and the average dissimilarity between the S classes diversity can be characterized with respect to richness and evenness (how much the quantity used for weighting the S classes is uniformly distributed among the classes)	Feoli et al. (2013)

Spatial heterogeneity can also be used in different ways and is dependent on the scale of interest (Adler et al., 2001; Li and Reynolds, 1995). Ecologists commonly describe spatial heterogeneity in terms of patches, which are discrete areas that differ in structure, composition, or function (Cadenasso et al., 2006). Spatial heterogeneity of patches can then be described with respect to number of different types of patches, number of each type of patch, spatial configuration of patches, and so forth (Table 1). Recognition of patches gave rise to hierarchical patch dynamics, which conceptualizes an ecosystem as a dynamic mosaic of physically and biologically defined patches (Thorp et al., 2008; Wu and Loucks, 1995). Although there is no directly analogous conceptual model in geomorphology, some of the primary elements of hierarchical patch dynamics, including continuous transient dynamics rather than equilibrium, correspond to concepts in geomorphology (e.g., Tooth, 2000).

As in ecology, spatial heterogeneity in river geomorphology varies with spatial scale and timespan of interest. Spatial heterogeneity of a sinuous river could be characterized with respect to grain diameters on a point bar at a moment in time, individual meander bend migration over decades, meander geometry over river reaches kilometers in length and through centuries, and so forth. Consequently, spatial heterogeneity can be quantified using metrics that emphasize spatial diversity within river characteristics such as cross-sectional or planform geometry at a given time, spatial statistics that identify pattern at varying scales, and metrics that include a temporal component that reflects variations in heterogeneity through time (e.g., Girard et al., 2010). Although complexity can vary with time following disturbance (e.g., Klaar et al., 2009), the remainder of this paper focuses on river geomorphic complexity through space rather than through time.

II Why does complexity matter?

As reviewed in this section, geomorphologists and ecologists have focused on geomorphic complexity in river corridors (channels and floodplains) for at least six reasons. First, complexity in the form of habitat diversity can correlate with biodiversity. Second, complexity influences attenuation of downstream fluxes of diverse materials – water, solutes, mineral sediment, and particulate organic matter. Third, complexity is closely connected to the resistance and resilience of river systems to natural and human-induced disturbances. Fourth, complexity both reflects and influences processes in rivers. Fifth, spatial heterogeneity influences our ability to characterize patterns and to detect changes through time and across space. Finally, because of the assumed or demonstrated correlations between complexity and biodiversity, attenuation, resilience, and process, complexity is increasingly a focus of river management, including restoration.

1 Habitat and biodiversity

River geomorphic complexity in the form of spatial heterogeneity of channel substrate, cross-sectional geometry, planform, or other characteristics does not necessarily correspond to habitat complexity, which reflects niche diversity (the variety of habitats in which an organism can live) (Peipoch et al., 2015). Although a common assumption is that geomorphic complexity links to habitat complexity and ecological function as expressed in biodiversity and bioproductivity, this is not always the case if other influences such as introduced species or limited connectivity constrain biodiversity (Lepori et al., 2005; Palmer et al., 2010). Several studies, however, have found that greater habitat diversity correlates with greater biodiversity and bioproductivity (e.g., Bellmore and Baxter, 2014; Greene and Knox, 2014; Luck et al., 2010; Scott et al., 2003; Wyżga et al., 2012). This correlation underlies the shifting habitat mosaic concept of Stanford et al. (2005), which describes how large floods create and destroy habitats, so that the assemblage of habitat types remains relatively stable and diverse, even though the spatial patterning of floodplain habitats changes through time.

2 Attenuation of downstream fluxes

Geomorphic complexity spanning a range of spatial scales – from small sand ripples or minor bank embayments through channel-spanning logjams to secondary channels and floodplain wetlands – can attenuate downstream fluxes over time scales ranging from minutes for solutes trapped in a small eddy to millennia for sediment stored on a large floodplain. Complexity within a channel can promote flow separation that reduces velocity and transport capacity and increases transient surface storage (Gooseff et al., 2007). Complexity can also cause flow obstructions, backwaters, in-channel sedimentation (Brummer et al., 2006), enhanced hyporheic exchange (Boano et al., 2014), and increased overbank flow and sedimentation (Jeffries et al., 2003). Studies examining correlations between complexity and attenuation of fluxes include those focused on peak and base flows (Westbrook et al., 2006; Woo and Waddington, 1990), stream metabolism and nutrient spiraling (Craig et al., 2008; Ensign and Doyle, 2006), trapping and retention of organic matter (Compson et al., 2009; Sheldon and Thoms, 2006; Small et al., 2008), and sediment storage (Pollock et al., 2007; Wohl and Scott, 2016, in press). A specific example of a positive feedback between complexity and flux attenuation comes from logjams that, by obstructing flow, enhance bank erosion and overbank flow. This leads to channel avulsion and the formation of multi-thread channel planforms, further increasing complexity and attenuation of downstream fluxes (e.g., Collins et al., 2012; O’Connor et al., 2003). Analogously, complexity in the form of riparian vegetation enhances hydraulic roughness, facilitating sediment deposition that creates planform complexity and additional attenuation of downstream fluxes of water, sediment, and organic matter (Corenblit et al., 2009).

Connectivity is another aspect of the attenuation of downstream fluxes. Connectivity can be used to describe lateral, vertical, and longitudinal fluxes within a river corridor (e.g., Ward, 1989). Geomorphic complexity can either increase or decrease different forms of connectivity. Complexity in the form of logjams, for example, decreases longitudinal connectivity of water, solutes, sediment, and organic matter (Beckman and Wohl, 2014), but increases vertical connectivity between the channel and hyporheic zone (Sawyer et al., 2011) and lateral connectivity between the channel and floodplain (Jeffries et al., 2003).

3 Resistance and resilience

Ecologists define resistance as the ability of a system to resist changes in form and process caused by external factors (Webster et al., 1975); a resistant system experiences little change. Geomorphologists have expanded on this to distinguish structural resistance as a result of location sensitivity, or position of each element relative to the point of change (e.g., distance to base level), and transmission resistance, which is the capacity of the system to transmit inputs of matter or energy (Brunsden, 2001). Ecologists define resilience as the persistence of an ecosystem and its ability to return to pre-disturbance conditions following disturbance (Holling, 1973; Webster et al., 1975); a resilient system recovers quickly from disturbance and is persistent rather than transient. Resilience is more commonly referred to in fluvial geomorphology as either (i) response time (Bull, 1991) or the transient form ratio, which describes the transience or persistence of a landform relative to the recurrence interval of the flow that created the landform (Brunsden and Thornes, 1979), or (ii) sensitivity, defined as the severity of a response to a disturbance, relative to the magnitude of the disturbance force (Fryirs, 2016; Reid and Brierley, 2015). In the context of river corridors, resistance, resilience, sensitivity, and related concepts essentially seek to characterize system response to disturbance such as floods or human-induced changes in water and sediment yield and channel geometry.

An example of how complexity can influence resistance and resilience comes from beaver meadows, which are spatially heterogeneous, wet-valley bottoms where numerous beaver dams create obstructions that increase the depth, extent, and duration of overbank flow and maintain high riparian water tables (Westbrook et al., 2006, 2011). Beaver meadows can increase open water area and base flow during dry periods (Hood and Bayley, 2008), thus increasing resistance and resilience to drought. Personal observations in the Colorado Front Range indicate that the complexity of beaver meadows also facilitates resistance to wildfires and to extreme floods.

4 River processes

Geomorphic complexity in the form of spatial heterogeneity can reflect river processes and influence river processes. Complexity of channels and floodplains reflects the history of hydraulic force and sediment movement through time. Choné and Biron (2016), for example, found a strong link between channel mobility and habitat diversity. Examples of complexity influencing river processes include diversity of grain size and bed elevation that increase hydraulic resistance, with consequent effects on hydraulic force and sediment movement (e.g., Yochum et al., 2012); and the piece complexity (branching) of large wood, which influences its mobility within a river and thus the effects of the wood on hydraulics and aquatic habitat (Vaz et al., 2013).

Analyses of changes in channel pattern downstream, across a network, or through time provide a useful illustration of how complexity can influence ability to detect pattern and change. Numerous papers are devoted to characterizing planform geometry of sinuous rivers along which individual meander bend geometry varies, reflecting the difficulty of choosing appropriate metrics to characterize this planform (e.g., Hooke, 2013). In the vertical dimension, uncertainty associated with registration error of aerial imagery increases as terrain relief (one form of complexity) increases (Lea and Legleiter, 2016).

5 River management and restoration

Measures of geomorphic complexity have been used in several studies to compare rivers with different levels of anthropogenic alteration and particularly to compare restored river segments to altered, unrestored river segments and reference segments (e.g., Gooseff et al., 2007; Laub et al., 2012; Legleiter, 2014b; Polvi et al., 2014). A critical consideration here is that context matters: different river segments have differing forms and magnitudes of complexity, so that assessments of complexity in restored rivers must use appropriate reference segments (e.g., Fryirs and Brierley, 2009).

Complexity has been used to assess the effects of specific management actions, such as introducing engineered logjams, on channel form and functions such as sediment storage (Brooks et al., 2004), or the effects of specific human disturbances, such as excess sediment (Bartley and Rutherfurd, 2005). River restoration can also be explicitly designed to increase geomorphic complexity (Wohl et al., 2015), although it remains challenging to determine what types (e.g., bedform versus planform) and what magnitudes (e.g., for bed grain size, maximum grain size versus sorting) of complexity are needed to restore desired river functions (e.g., Lepori et al., 2005). Just as restoration of habitat complexity may not be sufficient to restore biodiversity if other factors constrain biotic communities, so restoration of geomorphic complexity may not create the desired effect if watershed-scale processes such as flow or sediment regimes do not sustain the restored complexity (Roni et al., 2015).

III Measures of complexity

Despite the attention given to geomorphic complexity in river corridors, there is no single broadly applicable, widely accepted geomorphic complexity metric. Instead, there are a plethora of measures that have been employed in different studies during the past twenty years to assess various spatial scales and forms of complexity (Table 2). Quantifications of complexity range from the mathematically relatively simple approaches such as classification of units and count or percent data (e.g., Klaar et al., 2009), through clustering analysis (e.g., Hugue et al., 2014; Nelson et al., 2014), spatial statistics based on moving window averages and variograms or correlograms to test for spatial dependence (e.g., Legleiter, 2014a), to using fractal dimensions (Zhang et al., 2015) to analyze either linear or two-dimensional data for characteristic signals that relate to features such as grain size or bedforms (e.g., Singh et al., 2012; Timm and Wissmar, 2013). Basic categories include measures that characterize the diversity of features (e.g., number of separate functional surfaces), those that characterize the numerical range within a feature (e.g., standard deviation of channel width), and those that describe the arrangement of features in space (e.g., variogram). Of these, measures that characterize numerical range within a feature appear to be the most widely used in studies of river spatial heterogeneity (Table 2).

Table 2.

Examples of metrics used to characterize geomorphic complexity in the form of spatial heterogeneity and diversity within river corridors (after Bartley and Rutherfurd, 2005, Table 1; Laub et al., 2012, Table 2; Polvi et al., 2014, Table 2).

Complexity dimension	Complexity metric	Equation	References
Hydraulics	Froude number variance: spatial variability in Froude number for multiple cross sections under the same discharge	$F = \frac{v}{\sqrt{g d}}$	Danehy et al. (1998)
Hydraulics	Stage-dependent spatial variability modeled using a gamma probability density function: Shear stress Velocity Depth and velocity		Paola (1996); Lamouroux et al. (1995); Stewardson and McMahon (2002)
Size distribution of bed sediment	Heterogeneity: spread in sediment distribution above median grain size spread in lower portion of sediment distribution	$\frac{D_{84}}{D_{50}}$ $\frac{D_{10}}{D_{60}}$	Laub et al. (2012); Schwoerbel (1961)
	Sorting: standard deviation of distribution	$\frac{D_{84} - D_{16}}{2}$	Bartley and Rutherfurd (2005)
	Fredle index: porosity of bed sediments	$\frac{\sqrt{D_{16} D_{84}}}{\sqrt{\frac{D_{75}}{D_{25}}}}$	Lotspeich and Everest (1981)
	Gradation coefficient: spread in sediment distribution	$\frac{(\frac{D_{84}}{D_{50}} + \frac{D_{50}}{D_{16}})}{2}$	Bunte and Abt (2001)
	Sediment coefficient of variation: cv of sediment distribution using geometric standard deviation and median	$\frac{\sqrt{\frac{D_{84}}{D_{16}}}}{D_{50}}$	Baker (2009)
	Kurtosis: measure of peakedness of distribution	$\frac{D_{90} - D_{10}}{1.9 (D_{75} - D_{15})}$	Briggs (1977)
	Phi skewness: measure of asymmetry of sediment distribution	$\| \frac{D_{84} - D_{50}}{D_{84} - D_{16}} - \frac{D_{50} - D_{10}}{D_{90} - D_{10}} \|$	Bartley and Rutherfurd (2005)
Longitudinal profile	Thalweg R-square: goodness of fit of linear regression to longitudinal thalweg profile	R² value from linear regression of longitudinal profile	Polvi et al. (2014)
	Thalweg SSE: sum of errors between measured and predicted elevation values	Sum of squared errors of linear regression	Polvi et al. (2014)
	Thalweg MSE: mean of errors between measured and predicted elevation values	Mean squared error of linear regression	Polvi et al. (2014)
	Longitudinal standard deviation: standard deviation of thalweg elevations relative to highest point in profile after detrending profile	$\sqrt{1 / N \sum_{i = 1}^{n} {(z_{i} - z_{m i n})}^{2}}$	Bartley and Rutherfurd (2005)
	Longitudinal roughness: proportionally weighted deviations from predicted elevation	$\sum_{i = 1}^{n} \| z_{o b s, i} - z_{p r e d, i} \| I_{p}$	Gooseff et al. (2007); Baker et al. (2012)
	Average thalweg concavity: proportionally weighted concavities between successive points along thalweg profile	$\sum_{i = 1}^{n} (\| \frac{d^{2} z_{i}}{d x_{i}^{2}} \| I_{p})$	Anderson et al. (2005); Laub et al. (2012)
	Average water surface concavity: proportionally weighted concavities at successive points along the water-surface profile	$\sum_{i = 1}^{n} (\| \frac{d^{2} z_{w, i}}{d x_{i}^{2}} \| I_{p})$	Anderson et al. (2005)
	Thalweg sinuosity: ratio of cumulative lateral distance along profile to straight line distance	$L_{t h} / L_{s}$	Polvi et al. (2014)
	CV of maximum cross section depths: standard deviation of maximum cross section depths scaled by mean maximum cross section velocity	$\frac{s_{z}}{\bar{z}}$	Laub et al. (2012)
	Fractal mean of longitudinal profile: crookedness of thalweg elevation profile		Bartley and Rutherfurd (2005)
	Standard deviation of thalweg residuals from the line of best fit		Brooks et al. (2006)
	Standard deviation of 3D residuals of change compared with baseline survey of channel bed		Brooks et al. (2006)
	Fourier transform of bed elevations along longitudinal profile: transform used to extract bedform heights and lengths, which were then used to calculate mean, standard deviation, and CV of bedform dimensions		Singh et al. (2012)
	Pool volume per length of channel or valley	$\frac{P_{v o l}}{L}$	Livers and Wohl (2016)
Cross sectional	Chain and tape: ratio of topographic distance to straight line distance of cross section	$\frac{L_{t}}{L_{s}}$	Bartley and Rutherfurd (2005)
	Depth CV: coefficient of variation of bankfull depths at a cross section	$\frac{S_{d_{b f}}}{d_{b f}}$	Laub et al. (2012)
	Fractal dimension of the wetted width profile		Laub et al. (2012)
	CV of maximum cross section velocity: standard deviation of maximum cross section velocity scaled by mean maximum cross section velocity	$\frac{s_{v}}{\bar{v}}$	Laub et al. (2012)
Planform	Width standard deviation	S_w	Polvi et al. (2014)
	Width CV: coefficient of variation of widths	$\frac{S_{w}}{\bar{w}}$	Laub et al. (2012)
	Width residual: sum of proportionally weighted deviations in width scaled by mean width	$\frac{\sum_{i = 1}^{p} (\| w_{i} - \bar{w} \| I_{p})}{w}$	Baker et al. (2012); Laub et al. (2012)
	Average width-profile concavity: proportionally weighted concavities at successive points along the width profile	$(\frac{1}{n}) (\sum_{i = 1}^{n} \| \frac{d^{2} w}{d x_{i}^{2}} \|)$	Anderson et al. (2005); Laub et al. (2012)
	Bank length ratio: ratio of total bank length to reach length	$\frac{L_{t}}{L_{r}}$	Polvi et al. (2014)
	Multithread index: average number of channels along 20 evenly spaced transects along the reach	$\bar{x_{c h}}$	Polvi and Wohl (2012)
	Planform sinuosity: ratio of downstream channel length to straight line distance	$\frac{L}{L_{s}}$	Gooseff et al. (2007)
	Ratio of total channel length in a multithread planform such as anabranching, to valley length	$\frac{L_{c h}}{L_{v}}$	Livers and Wohl (2016)
	Ratio of channel area to valley area	$\frac{A_{c h}}{A_{v}}$	Livers and Wohl (2016)
	Channel complexity: sum of areal extents of active bar and secondary water features over consistent lengths of valley	$Σ (A_{b a r} + A_{w}) / L$	Curtis et al. (2015)
	Planform complexity: number of separate functional surfaces per unit of channel length	$\frac{x_{s u r f a c e s}}{L}$	Graf (2006)
	Fractal dimension (D) defined by slope of line (2/D) obtained by regressing log perimeter on log channel area		Timm and Wissmar (2013)
	Ratio of channel width to valley-bottom width: use average values for multiple transects perpendicular to downstream trend within a river segment; add channel widths if multiple channels present	$\frac{w_{c h}}{w_{v}}$	Livers and Wohl (2016)
	Habitat index: standardized sum of 3 habitat-related features (oxbow, bar, logjam) per channel length	$\frac{Σ (A_{b a r} + A_{w} + A_{L W})}{L}$	Choné and Biron (2016)
	Braiding index: average number of separate channels in a cross section of the river, or total length of channels within a unit length of the river	$\bar{x_{c h}}$ or $\frac{{ΣL}_{c h}}{L}$	Ashmore (2013)
Instream LW	Total wood volume	$V_{L W}$	Polvi et al. (2014)
	Total wood pieces	$x_{L W}$	Polvi et al. (2014)
	Wood load per area: m³ wood/ha of channel surface	$V / A$	Harmon et al. (1986)
	Wood load per length: m³ wood/100 m of channel length	$V / L$	Berg et al. (1998)
	Wood pieces per length: no. of pieces/100 m of channel or valley length	$x_{L W} / L$	Bilby and Ward (1989)
	Wood obstructions per length: no. of bridge or ramp pieces per length of channel or valley	$\frac{x_{b r, r a}}{L}$	Livers and Wohl (2016)
	Ratio of average height/downstream spacing of channel-spanning logjams	$\frac{H_{L W}}{L}$	Livers and Wohl (2016)
	Surface area of wood per length of shoreline	$A / L$	Kramer and Wohl (2015)
Floodplain	Surface elevation: relief, standard deviation, skewness, coefficient of variation, standard deviation of curvature using LiDAR-derived DEMs, rugosity (ratio of surface area to planar area)		Scown et al. (2015a, 2015b)
Valley geometry	Border index: defined using a minimum bounding rectangle (Mbr) that encloses a valley polygon, the length and width of the Mbr, and the perimeter of the valley	$\frac{P m}{(M b r L + M b r W) X 2}$	Huang et al. (2014)
	Number of branches: number of sub-valleys	$x_{s u b v a l l e y s}$	Huang et al. (2014)
	Rugosity: ratio of surface area to planar area	$\frac{SA}{PA}$	Huang et al. (2014)
River network	Fractal dimension		Zhang et al. (2015)
	Node count: number of fork, junction, outlet, end, and start nodes in a distributary network	$x_{n o d e s}$	Millard et al. (2010)
	Complexity index: based on overall relief, terrain roughness (slope variability), and stream order, with different partial indices standardized to a value between 0 and 1 and complexity index as average of these values		Cavalli and Marchi (2008); Baartman et al. (2013)
Composite	Reach-level complexity: for each of five features (% secondary channel area, % pool habitat, number of pools, variance of residual pool depth, pool diversity), individual reach values and mean & standard deviation calculated across all reaches; overall mean is subtracted from reach value and divided by standard deviation for each feature, then five values are summed		Anlauf et al. (2011)
Composite	Variogram: a spatial statistic that expresses difference as a function of distance		Legleiter (2014)
Generic	Parametric measures of diversity that are less sensitive to richness and more to dominance (the opposite of evenness), such as alpha diversity D(O) for objects (O) in relation to probability p_i to find something related to the ith class with sensitivity parameter α; and nonparametric measures; several examples of each, largely drawn from ecological literature, are given in Feoli et al. (2013)	$D (O) = \frac{l n Σ_{i} p_{i}^{α}}{1 - α}$	Feoli et al. (2013)

Different measures of geomorphic complexity in rivers are categorized in Table 2 as relating primarily to one of ten distinct aspects of spatial heterogeneity. The lack of consistently used measures likely reflects at least two factors. First, individual studies have different objectives. An investigation of salmonid habitat, for example, is likely to focus on substrate and hydraulic heterogeneity, whereas a study of flood frequency may emphasize heterogeneity of drainage density and topology at the scale of the entire river network. Second, investigators do not necessarily know a priori what types of complexity exert the greatest influence on a particular process or response variable. Studies of connectivity distinguish structural connectivity – the extent to which landscape units are contiguous or physically linked to one another – from functional connectivity, which describes the way in which interactions between multiple structural characteristics of the system in question affect geomorphic, ecologic and hydrologic processes (Wainwright et al., 2011). Analogously, structural and functional complexity can be differentiated. Structural complexity is all forms of spatial heterogeneity within a particular river corridor without reference to any functional effects, whereas functional complexity is spatial heterogeneity that can be shown to affect either a specific process, such as enhanced hyporheic exchange, or a specific response variable, such as biodiversity (Li and Reynolds, 1995; Livers and Wohl, 2016). In an example of a study focused on functional complexity, Schwartz and Herricks (2008) designated mesohabitat units such as pool front and pool rear based on the biological resource needs of different fish species. They then documented differences between fish assemblages and density among distinct units, suggesting that their designated units represented functional complexity.

The majority of the references cited in Table 2 were published after 2000. Given the rapid proliferation of studies attempting to quantify geomorphic complexity and the diverse objectives and spatial and temporal scales considered in these studies, the large number of complexity metrics is not surprising. Although there may be characteristic sources and magnitudes of complexity within distinct types of river corridors (e.g., meandering channel within a forested floodplain versus sand-bed braided channel with minimal woody vegetation), there is unlikely to be a single metric that adequately captures all forms of functional complexity within a river corridor.

IV Where next?

At least three issues represent major challenges to understanding geomorphic complexity in river corridors. The first is understanding sources and forms of complexity in diverse geomorphic process domains. Distinguishing structural and functional complexity, or finding a signal within the noise of diverse scales of spatial heterogeneity in river corridors remains a research challenge. Finally, enhancing public appreciation for complexity in river corridors is a critical component of applying river science.

1 Sources and forms of complexity

Sources of complexity refer to the processes that create and maintain spatial heterogeneity. Where instream wood is an important component of spatial heterogeneity within a channel, for example, the processes of tree growth and mortality, recruitment of wood to the channel, and the transport/storage of wood within the river corridor all influence this spatial heterogeneity. Forms of complexity refer to the categories of spatial heterogeneity listed in Table 1 – hydraulics, bed substrate, channel geometry, and so forth – and to the magnitude and spatial frequency of heterogeneity.

Conceptual understanding of river corridors suggests that there should be characteristic forms and magnitudes of complexity in distinct process domains (Montgomery, 1999) or river styles (Brierley and Fryirs, 2005) (Figure 1). Process domains and river styles are both conceptual frameworks that describe spatially identifiable areas or river segments within a drainage network that are characterized by distinct valley geometry, disturbance regime, and suites of geomorphic processes. Complexity in a steep, narrow bedrock canyon is likely to be associated with heterogeneity of the longitudinal profile and channel width, for example, whereas complexity in a low-gradient river with a broad floodplain may come primarily from a multithread channel planform and patches of distinct floodplain vegetation. Studies associating geomorphic process domains with particular sources and forms of complexity and with distinct biotic communities come mostly from mountainous environments (e.g., Bellmore and Baxter, 2014; Harris, 1988; Polvi et al., 2011), but this approach is amenable to diverse river systems (Fryirs, 2015; Fryirs and Brierley, 2009).

Figure 1.

Conceptualization of how inputs interact with valley context to create distinct forms of geomorphic complexity. Inset photos illustrate different process domains and associated complexity.

Closely related to understanding sources of complexity in a particular river environment is identifying first, what aspects of complexity to measure (Blue and Brierley, 2015) and second, what could be described as desirable forms of complexity. Both of these identifications reflect scientific and social context, as exemplified by the Platte River. Figure 2 illustrates a portion of the Platte River near Kearney, Nebraska in 1938 and 1969. In 1938, the channel was a broad, shallow, braided river with high annual and interannual variability of flow and minimal riparian vegetation. Construction of a dam upstream substantially reduced flow variability, which facilitated the establishment of woody riparian vegetation and transformed the channel to an anastomosing planform by 1969. Each of these alternative forms of this river segment has substantial spatial heterogeneity within the river corridor, but the forms of complexity present in 1938 sustained native, endemic Great Plains fishes that are now threatened or endangered partly because of loss of habitat associated with changes in the form of river complexity. In a social context in which sustaining endangered species receives high priority, the complexity present in 1938 is more desirable than the complexity present in 1969.

Figure 2.

The Platte River near Kearney, Nebraska.

2 Structural and functional complexity

Identifying desirable forms of complexity relates to distinguishing structural versus functional complexity. Every form of spatial heterogeneity in a river corridor is likely to create an associated function. Heterogeneity of bed grain size, for example, can influence hyporheic exchange, nutrient retention, interstitial habitat, hydraulic roughness, sediment mobility and channel response to fluctuating flows, and other processes. Bed grain size is typically highly heterogeneous in steep channels, yet the complexity associated with this heterogeneity may not be as effective at trapping and retaining particulate organic matter as other forms of geomorphic complexity such as backwater pools at logjams (Livers and Wohl, 2016). The assumption underlying the concept of functional complexity is that identifying distinct sources and forms of complexity can be important in managing rivers when river complexity is constrained by human influences. Many lower gradient alluvial rivers historically had extensive floodplains with wetlands and secondary channels that have now been drained for agriculture (e.g., Wallick et al., 2007). Although existing land use may prevent restoration of the original complexity of the entire floodplain, restoring or maintaining other sources of functional complexity with respect to nitrate retention (e.g., riparian forest buffer zones, instream large wood), for example, can substantially improve water quality.

3 Public perceptions of complexity

A striking gap exists between the appreciation of geomorphic complexity by river scientists, on the one hand, and, on the other hand, the engineering mandate to simplify rivers in order to increase conveyance, along with the public perception that “messy” rivers (e.g., rivers with instream wood (Chin et al., 2008), braided rivers (Kondolf, 2006), or river corridors with floodplain wetlands (Wohl, 2013)) need to be “cleaned up” (McCormick et al., 2015). Episodes of geomorphic change, such as floods or large sediment inputs from hillslope failures, are commonly followed by strenuous efforts to clean up rivers and to put channels back in “their place.” This divergence of perception strongly influences reach-scale river restoration efforts, which can involve simplifying natural and functional river corridors that are perceived as unsightly or unhealthy (Kondolf, 2006).

I think that rivers need the type of public educational campaign that transformed the nineteenth-century image of jungles as dark, dangerous places to the twenty-first-century image of tropical rainforests containing enormous biodiversity and providing critically important ecosystem services. Freshwater organisms are among the most endangered groups of species on Earth (Ricciardi and Rasmussen, 1999). Shifting public attitudes toward rivers from an idealized expectation of a single channel meandering slightly through an open woodland to an appreciation of the enormous diversity and geomorphic complexity of river ecosystems would substantially enhance river management and restoration.

Footnotes

Acknowledgements

I thank Natalie Kramer Anderson, Bridget Livers Gonzalez, DeAnna Laurel, Katherine Lininger, and Dan Scott for helpful comments on an earlier draft of this paper. The paper was substantially improved by comments from two anonymous reviewers.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Adler

Raff

Lauenroth

(2001) The effect of grazing on the spatial heterogeneity of vegetation. Oecologia 128: 465–479.

Anderson

Wondzell

Gooseff

. (2005), Patterns in stream longitudinal profiles and implications for hyporheic exchange flow at the H.J. Andrews Experimental Forest, Oregon, USA. Hydrological Processes 19: 2931–2949.

Anlauf

Jensen

Burnett

. (2011) Explaining spatial variability in stream habitats using both natural and management-influenced landscape predictors. Aquatic Conservation: Marine and Freshwater Ecosystems 21: 704–714.

Ashmore

(2013) Morphology and dynamics of braided rivers. In: Wohl

(ed) Treatise on Geomorphology. Volume 9. Fluvial Geomorphology. Elsevier, 290–312.

Baartman

JEM

Masselink

Keesstra

. (2013) Linking landscape morphological complexity and sediment connectivity. Earth Surface Processes and Landforms 38: 1457–1471.

Baker

(2009) Land use effects on physical habitat and nitrate uptake in small streams of the central Rocky Mountain region. PhD Dissertation, Colorado State University, Fort Collins, CO.

Baker

Bledsoe

Price

(2012) Stream nitrate uptake and transient storage over a gradient of geomorphic complexity, north-central Colorado, USA. Hydrological Processes 26: 3241–3252.

Bartley

Rutherfurd

(2005) Measuring the reach-scale geomorphic diversity of streams: application to a stream disturbed by a sediment slug. River Research and Applications 21: 39–59.

Beckman

Wohl

(2014) Carbon storage in mountainous headwater streams: the role of old-growth forest and logjams. Water Resources Research 50: 2376–2393.

10.

Bellmore

Baxter

(2014) Effects of geomorphic process domains on river ecosystems: a comparison of floodplain and confined valley segments. River Research and Applications 30: 617–630.

11.

Berg

Carlson

Azuma

(1998) Function and dynamics of woody debris in stream reaches in the central Sierra Nevada, California. Canadian Journal of Fisheries and Aquatic Sciences 55: 1807–1820.

12.

Bilby

Ward

(1989) Changes in characteristics and function of woody debris with increasing size of streams in western Washington. Transactions of the American Fisheries Society 118: 368–378.

13.

Blue

Brierley

(2015) ‘But what do you measure?’ Prospects for a constructive critical physical geography. Area DOI: 10.1111/area.12249.

14.

Boano

Harvey

Marion

. (2014) Hyporheic flow and transport processes: mechanisms, models, and biogeochemical implications. Reviews of Geophysics 52: 603–679.

15.

Briggs

(1977) Sediments: Sources and Methods in Geography. London: Butterworths.

16.

Brierley

Fryirs

(2005) Geomorphology and River Management: Applications of the River Styles Framework. Oxford: Blackwell Publishing.

17.

Brooks

Gehrke

Jansen

. (2004) Experimental reintroduction of woody debris on the Williams River, NSW: geomorphic and ecological responses. River Research and Applications 20: 513–536.

18.

Brooks

Howell

Abbe

. (2006) Confronting hysteresis: wood based river rehabilitation in highly altered riverine landscapes of south-eastern Australia. Geomorphology 79: 395–422.

19.

Brummer

Abbe

Sampson

. (2006) Influence of vertical channel change associated with wood accumulations on delineating channel migration zones, Washington, USA. Geomorphology 80: 295–309.

20.

Brunsden

(2001) A critical assessment of the sensitivity concept in geomorphology. Catena 42: 99–123.

21.

Brunsden

Thornes

(1979) Landscape sensitivity and change. Transactions Institute of British Geographers 4: 463–484.

22.

Bull

(1991) Geomorphic Responses to Climate Change. New York: Oxford University Press.

23.

Bunte

Abt

(2001) Sampling surface and sub-surface particle size distributions in wadable cobble- and gravel-bed streams for analyses in sediment transport, hydraulics and streambed monitoring. Report no. RMRS-GTR-74. Fort Collins, CO: USDA Forest Service.

24.

Cadenasso

Pickett

STA

Grove

(2006) Dimensions of ecosystem complexity: heterogeneity, connectivity, and history. Ecological Complexity 3: 1–12.

25.

Cavalli

Marchi

(2008) Characterisation of the surface morphology of an alpine alluvial fan using airborne LiDAR. Natural Hazards and Earth System Science 8: 323–333.

26.

Chin

Daniels

Urban

. (2008) Perceptions of wood in rivers and challenges for stream restoration in the United States. Environmental Management 41: 893–903.

27.

Choné

Biron

(2016) Assessing the relationship between river mobility and habitat. River Research and Applications 32: 528–539.

28.

Collins

Montgomery

Fetherston

. (2012) The floodplain large-wood cycle hypothesis: a mechanism for the physical and biotic structuring of temperate forested alluvial valleys in the North Pacific coastal ecoregion. Geomorphology 139–140: 460–470.

29.

Compson

Mier

Marks

(2009) Effects of travertine and flow on leaf retention in Fossil Creek, Arizona. Hydrobiologia 630: 187–197.

30.

Corenblit

Steiger

Gurnell

. (2009) Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors. Earth Surface Processes and Landforms 34: 1790–1810.

31.

Craig

Palmer

Richardson

. (2008) Stream restoration strategies for reducing river nitrogen loads. Frontiers in Ecology and the Environment 6: 529–538.

32.

Curtis

Wright

Minear

. (2015) Assessing geomorphic change along the Trinity River downstream from Lewiston Dam, California, 1980–2011. Scientific investigations report 2015-5046. Reston, VA: U.S. Geological Survey.

33.

Danehy

Ringler

Stehman

. (1998) Variability of fish densities in a small catchment. Ecology of Freshwater Fish 7: 36–48.

34.

Ensign

Doyle

(2006) Nutrient spiraling in streams and river networks. Journal of Geophysical Research 111: G04009.

35.

Favis-Mortlock

(2013) Systems and complexity in geomorphology. In: Orme

Sack

(eds) Treatise on Geomorphology. Volume 1. The Foundations of Geomorphology. San Diego, CA: Academic Press, 257–270.

36.

Feoli

Ganis

Ricotta

(2013) Measuring diversity of environmental systems. In: Ibáñez

Bockheim

(eds) Pedodiversity. Boca Raton, FL: CRC Press, 29–58.

37.

Fryirs

(2015) Developing and using geomorphic condition assessments for river rehabilitation planning, implementation and monitoring. Wiley Interdisciplinary Reviews Water 2: 649–667.

38.

Fryirs

(2016) River sensitivity: a lost foundation concept in fluvial geomorphology. Earth Surface Processes and Landforms. Epub ahead of print 1 January 2016. DOI:10.1002/esp.3940.

39.

Fryirs

Brierley

(2009) Naturalness and place in river rehabilitation. Ecology and Society 14: 20.

40.

Girard

Fantin-Cruz

Loverde de Oliveira

. (2010) Small-scale spatial variation of inundation dynamics in a floodplain of the Pantanal (Brazil). Hydrobiologia 638: 223–233.

41.

Gooseff

Hall

Tank

(2007) Relating transient storage to channel complexity in streams of varying land use in Jackson Hole, Wyoming. Water Resources Research 43: W01417.

42.

Graf

(2006) Downstream hydrologic and geomorphic effects of large dams on American rivers. Geomorphology 79: 336–360.

43.

Greene

Knox

(2014) Coupling legacy geomorphic surface facies to riparian vegetation; assessing red cedar invasion along the Missouri River downstream of Gavins Point Dam, South Dakota. Geomorphology 204: 277–286.

44.

Harmon

Franklin

Swanson

. (1986) Ecology of coarse woody debris in temperate ecosystems. Advances in Ecological Research 15: 133–302.

45.

Harris

(1988) Associations between stream valley geomorphology and riparian vegetation as a basis for landscape analysis in the eastern Sierra Nevada, California, USA. Environmental Management 12: 219–228.

46.

Holling

(1973) Resilience and stability of ecological systems. Annual Review of Ecology and Systematics 4: 1–23.

47.

Hood

Bayley

(2008) Beaver (Castor canadensis) mitigate the effects of climate on the area of open water in boreal wetlands in western Canada. Biological Conservation 141: 556–567.

48.

Hooke

(2013) River meandering. In: Wohl

(ed) Treatise on Geomorphology. Volume 9. Fluvial Geomorphology. San Diego, CA: Academic Press, 260–288.

49.

Huang

Nichol

Harris

. (2014) Classification of submarine canyons of the Australian continental margin. Marine Geology 357: 362–383.

50.

Hugue

Lapointe

Eaton

. (2016) Satellite-based remote sensing of running water habitats at large riverscape scales: tools to analyze habitat heterogeneity for river ecosystem management. Geomorphology 253: 353–369.

51.

Jeffries

Darby

Sear

(2003) The influence of vegetation and organic debris on flood-plain sediment dynamics: case study of a low-order stream in the New Forest, England. Geomorphology 51: 61–80.

52.

Klaar

Maddock

Milner

(2009) The development of hydraulic and geomorphic complexity in recently formed streams in Glacier Bay National Park, Alaska. River Research and Applications 25: 1331–1338.

53.

Kondolf

(2006) River restoration and meanders. Ecology and Society 11: 42.

54.

Kramer

Wohl

(2015) Driftcretions: the legacy impacts of driftwood on shoreline morphology. Geophysical Research Letters 42: 5855–5864.

55.

Lamouroux

Souchon

Herouin

(1995) Predicting velocity frequency distributions in stream reaches. Water Resources Research 31: 2367–2375.

56.

Laub

Baker

Bledsoe

. (2012) Range of variability of channel complexity in urban, restored and forested reference streams. Freshwater Biology 57: 1076–1095.

57.

Lea

Legleiter

(2016) Refining measurements of lateral channel movement from image time series by quantifying spatial variations in registration error. Geomorphology 258: 11–20.

58.

Legleiter

(2014a) A geostatistical framework for quantifying the reach-scale morphology: 1. Variogram models, related metrics, spatial structure of river and relation to channel form. Geomorphology 205: 65–84.

59.

Legleiter

(2014b) A geostatistical framework for quantifying the reach-scale morphology: 2. Application to restored and natural channels. Geomorphology 205: 85–101.

60.

Lepori

Palm

Brannas

. (2005) Does restoration of structural heterogeneity in streams enhance fish and macroinvertebrate diversity? Ecological Applications 15: 2060–2071.

61.

Reynolds

(1995) On definition and quantification of heterogeneity. Oikos 73: 280–284.

62.

Livers

Wohl

(2016) Sources and interpretation of channel complexity in forested subalpine streams of the Southern Rocky Mountains. Water Resources Research 52: 3910–3929.

63.

Lotspeich

Everest

(1981) A new method for reporting and interpreting textural composition of spawning gravel. Research note PNW-RN-369. Corvallis, OR: USDA Forest Service.

64.

Luck

Maumenee

Whited

. (2010) Remote sensing analysis of physical complexity of North Pacific Rim rivers to assist wild salmon conservation. Earth Surface Processes and Landforms 35: 1330–1343.

65.

McCormick

Fisher

Brierley

(2015) Quantitative assessment of the relationships among ecological, morphological and aesthetic values in a river rehabilitation initiative. Journal of Environmental Management 153: 60–67.

66.

McDowell

(2013) Geomorphology in the late twentieth century. In: Orme

Sack

(eds) Treatise on Geomorphology. Volume 1. The Foundations of Geomorphology. San Diego, CA: Academic Press, 108–123.

67.

Millard

Hogan

Wilford

. (2010) A method to assess fluvial fan channel networks, with a preliminary application to fans in coastal British Columbia. Geomorphology 115: 286–293.

68.

Montgomery

(1999) Process domains and the river continuum. Journal of the American Water Resources Association 35: 397–410.

69.

Murray

Fonstad

(2007) Preface: complexity (and simplicity) in landscapes. Geomorphology 91: 173–177.

70.

Nelson

Bellugi

Dietrich

(2014) Delineation of river bed-surface patches by clustering high-resolution spatial grain size data. Geomorphology 205: 102–119.

71.

O’Connor

Jones

Haluska

(2003) Flood plain and channel dynamics of the Quinault and Queets Rivers, Washington, USA. Geomorphology 51: 31–59.

72.

Palmer

Menninger

Bernhardt

(2010) River restoration, habitat heterogeneity, and biodiversity: a failure of theory or practice? Freshwater Biology 55: 205–222.

73.

Paola

(1996) Incoherent structure: turbulence as a metaphor for stream braiding. In: Ashworth

Bennett

Best

. (eds) Coherent Flow Structures in Open Channels. Wiley, 705–723.

74.

Peipoch

Brauns

Hauer

. (2015) Ecological simplification: human influences on riverscape complexity. BioScience 65: 1057–1065.

75.

Phillips

(2007) Perfection and complexity in the lower Brazos River. Geomorphology 91: 364–377.

76.

Phillips

(2014) State transitions in geomorphic responses to environmental change. Geomorphology 204: 208–216.

77.

Pollock

Beechie

Jordan

(2007) Geomorphic changes upstream of beaver dams in Bridge Creek, an incised stream channel in the interior Columbia River basin, eastern Oregon. Earth Surface Processes and Landforms 32: 1174–1185.

78.

Polvi

Wohl

(2012) The beaver meadow complex revisited: the role of beavers in post-glacial floodplain development. Earth Surface Processes and Landforms 37: 332–346.

79.

Polvi

Nilsson

Hasselquist

(2014) Potential and actual geomorphic complexity of restored headwater streams in northern Sweden. Geomorphology 210: 98–118.

80.

Polvi

Wohl

Merritt

(2011) Geomorphic and process domain controls on riparian zones in the Colorado Front Range. Geomorphology 125: 504–516.

81.

Reid

Brierley

(2015) Assessing geomorphic sensitivity in relation to river capacity for adjustment. Geomorphology 251: 108–121.

82.

Rhoads

(2013) Process in geomorphology. In: Orme

Sack

(eds) Treatise on Geomorphology. Volume 1. The Foundations of Geomorphology. San Diego, CA: Academic Press, 190–204.

83.

Ricciardi

Rasmussen

(1999) Extinction rates of North American freshwater fauna. Conservation Biology 13: 1220–1222.

84.

Roni

Beechie

Pess

. (2015) Wood placement in river restoration: fact, fiction, and future direction. Canadian Journal of Fisheries and Aquatic Sciences 72: 46–478.

85.

Sawyer

Cardenas

Buttles

(2011) Hyporheic exchange due to channel-spanning logs. Water Resources Research 47: W08502.

86.

Schwartz

Herricks

(2008) Fish use of ecohydraulic-based mesohabitat units in a low-gradient Illinois stream: implications for stream restoration. Aquatic Conservation: Marine and Freshwater Ecosystems 18: 852–866.

87.

Schwoerbel

(1961) Über die Lebendsbedingungen und die Besiedlung des hyporheischen Lebensraumes. Archiv für Hydrobiologie Supplement 2–3: 182–214.

88.

Scott

Skagen

Merigliano

(2003) Relating geomorphic change and grazing to avian communities in riparian forests. Conservation Biology 17: 284–296.

89.

Scown

Thoms

De Jager

(2015a) Floodplain complexity and surface metrics: influences of scale and geomorphology. Geomorphology 245: 102–116.

90.

Scown

Thoms

De Jager

(2015b) Measuring floodplain spatial patterns using continuous surface metrics at multiple scales. Geomorphology 245: 67–101.

91.

Sheldon

Thoms

(2006) In-channel geomorphic complexity: the key to the dynamics of organic matter in large dryland rivers? Geomorphology 77: 270–285.

92.

Singh

Guala

Lanzoni

. (2012) Bedform effect on the reorganization of surface and subsurface grain size distribution in gravel bedded channels. Acta Geophysica 60: 1607–1638.

93.

Small

Doyle

Fuller

. (2008) Hydrologic versus geomorphic limitation on CPOM storage in stream ecosystems. Freshwater Biology 53: 1618–1631.

94.

Stanford

Lorang

Hauer

(2005) The shifting habitat mosaic of river ecosystems. Verhandlungen des Internationalen Verein Limnologie 29: 123–136.

95.

Stewardson

McMahon

(2002) A stochastic model of hydraulic variations within stream channels. Water Resources Research 38: 1007.

96.

Thorp

Thoms

Delong

(2008) The Riverine Ecosystem Synthesis: Toward Conceptual Cohesiveness in River Science. London: Academic Press.

97.

Timm

Wissmar

(2013) Response to disturbance in a highly managed alluvial river: does it conform to La Chatelier’s general law? Geomorphology 182: 116–124.

98.

Tooth

(2000) Process, form and change in dryland rivers: a review of recent research. Earth-Science Reviews 51: 67–107.

99.

Vaz

Merten

Warren

. (2013) Which stream wood becomes functional following wildfires? Ecological Engineering 54: 82–89.

100.

Wainwright

Turnbull

Ibrahim

. (2011) Linking environmental regimes, space and time: interpretations of structural and functional connectivity. Geomorphology 126: 387–404.

101.

Wallick

Grant

Lancaster

. (2007) Patterns and controls on historical channel change in the Willamette River, Oregon, USA. In: Gupta

(ed) Large Rivers: Geomorphology and Management. Chichester, UK: John Wiley and Sons, 491–516.

102.

Ward

(1989) The four-dimensional nature of lotic ecosystems. Journal of the North American Benthological Society 8: 2–8.

103.

Webster

Waide

Pattern

(1975) Nutrient recycling and the stability of ecosystems. In: Howell

. (eds) Mineral Cycling in Southeastern Ecosystems. ERDA (CONF-740513), 1–27.

104.

Werner

McNamara

(2007) Dynamics of coupled human–landscape systems. Geomorphology 91: 393–407.

105.

Westbrook

Cooper

Baker

(2006) Beaver dams and overbank floods influence groundwater-surface water interactions of a Rocky Mountain riparian area. Water Resources Research 42: W06404.

106.

Westbrook

Cooper

Baker

(2011) Beaver assisted river valley formation. River Research and Applications 27: 247–256.

107.

Wohl

(2013) Wide Rivers Crossed: The South Platte and the Illinois of the American Prairie. Boulder, CO: University Press of Colorado.

108.

Wohl

Scott

(2016, in press) Wood and sediment storage and dynamics in river corridors. Earth Surface Processes and Landforms.

109.

Wohl

Lane

Wilcox

(2015) The science and practice of river restoration. Water Resources Research 51: 5974–5997.

110.

Woo

M-K

Waddington

(1990) Effects of beaver dams on subarctic wetland hydrology. Arctic 43: 223–230.

111.

Loucks

(1995) From balance of nature to hierarchical patch dynamics: a paradigm shift in ecology. The Quarterly Review of Biology 70: 439–466.

112.

Wyżga

Oglęcki

Radecki-Pawlik

. (2012) Hydromorphological complexity as a driver of the diversity of benthic invertebrate communities in the Czarny Dunajec River, Polish Carpathians. Hydrobiologia 696: 29–46.

113.

Yochum

Bledsoe

David

GCL

. (2012) Velocity prediction in high-gradient channels. Journal of Hydrology 424–425: 84–98.

114.

Zhang

Guo

Wang

(2015) Correlation between flood frequency and geomorphologic complexity of rivers network: a case study of Hangzhou, China. Journal of Hydrology 527: 113–118.