Measuring floodplain spatial patterns using continuous surface metrics at multiple scales

    Measuring floodplain spatial patterns using continuous surface metrics at multiple scales Murray W. Scown, Martin C. Thoms, Nathan R. De Jager PII: DOI: Reference:

S0169-555X(15)30010-6 doi: 10.1016/j.geomorph.2015.05.026 GEOMOR 5232

To appear in:

Geomorphology

Received date: Revised date: Accepted date:

2 December 2014 22 May 2015 23 May 2015

Please cite this article as: Scown, Murray W., Thoms, Martin C., De Jager, Nathan R., Measuring floodplain spatial patterns using continuous surface metrics at multiple scales, Geomorphology (2015), doi: 10.1016/j.geomorph.2015.05.026

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ACCEPTED MANUSCRIPT Measuring floodplain spatial patterns using continuous surface

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Murray W. Scowna,*, Martin C. Thomsa and Nathan R. De Jagerb

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metrics at multiple scales

Riverine Landscapes Research Laboratory, University of New England, Armidale, NSW 2350,

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Australia

United States Geological Survey, Upper Midwest Environmental Sciences Center, La Crosse, WI

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54603, USA

Murray Scown

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Ph. +1 (513) 569 7775

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*Corresponding author:

[email protected]

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Mailing address: U.S. Environmental Protection Agency, MS-587, 26 W. Martin Luther King Dr., Cincinnati, OH 45268

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ACCEPTED MANUSCRIPT Abstract Interactions between fluvial processes and floodplain ecosystems occur upon a floodplain

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surface that is often physically complex. Spatial patterns in floodplain topography have only

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recently been quantified over multiple scales, and discrepancies exist in how floodplain surfaces

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are perceived to be spatially organised. We measured spatial patterns in floodplain topography for pool 9 of the Upper Mississippi River, USA, using moving window analyses of eight surface metrics applied to a 1 × 1 m2 DEM over multiple scales. The metrics used were Range, SD,

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Skewness, Kurtosis, CV, SDCURV, Rugosity, and Vol:Area, and window sizes ranged from 10 to 1000 m in radius. Surface metric values were highly variable across the floodplain and revealed a high

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degree of spatial organisation in floodplain topography. Moran’s I correlograms fit to the landscape of each metric at each window size revealed that patchiness existed at nearly all

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window sizes, but the strength and scale of patchiness changed within window size, suggesting

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that multiple scales of patchiness and patch structure exist in the topography of this floodplain.

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Scale thresholds in the spatial patterns were observed, particularly between the 50 and 100 m window sizes for all surface metrics and between the 500 and 750 m window sizes for most metrics. These threshold scales are ∼ 15–20% and 150% of the main channel width (1–2% and

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10–15% of the floodplain width), respectively. These thresholds may be related to structuring processes operating across distinct scale ranges. By coupling surface metrics, multi-scale analyses, and correlograms, quantifying floodplain topographic complexity is possible in ways that should assist in clarifying how floodplain ecosystems are structured. Keywords: floodplain; spatial pattern; surface metrics; scale

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ACCEPTED MANUSCRIPT 1. Introduction Floodplain topography interacts with the flow regime of rivers to influence spatial patterns

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of inundation, sedimentation, biogeochemical conditions, vegetation, and surface water–

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groundwater exchanges (Everson and Boucher, 1998; Thoms, 2003; Stanford et al., 2005;

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Alsdorf et al., 2007; Hamilton et al., 2007). Floodplains are areas of low relief within the riverine landscape, but their surface topography is often highly complex (Jones et al., 2008; Rayburg et al., 2009; Scown et al., in press), which is thought to contribute to their elevated biodiversity

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and productivity (Everson and Boucher, 1998; Ward et al., 2002b; Hamilton et al., 2007). ‘Complexity’ has been defined in terms of the number and diversity of parts or components,

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localised interactions and feedbacks among those parts or components, and the degree of spatial organisation—all of which contribute to the nonlinear character of complex systems

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(Simon, 1962; Levin, 1998; Phillips, 1999).

The topographic complexity of floodplains can be described, in part, by the heterogeneity

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and variability in elevation, slope, aspect, and curvature throughout the floodplain (Hoechstetter et al., 2008; Tarolli, 2014), as well as the spatial assemblage of morphological units created by these surface properties (Hamilton et al., 2007). However, topographic

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complexity is frequently poorly defined and quantified in floodplain research. Quantitative approaches to measuring the surface properties that contribute to topographic complexity in floodplains are required in order to evaluate floodplain complexity and its influence on geomorphological, hydraulic, and ecological processes. Many approaches are available to quantify topography and topographic complexity. These have been applied, inter alia, to the analysis of landslides, hillslope processes, stream networks, river channel morphology, volcanoes, sea floors, coral reefs, and intertidal zones (Florinsky, 1998b; Pike, 2000; Walker et al., 2009; Brown et al., 2014; Legleiter, 2014a). Many utilise highresolution digital elevation models (DEMs), particularly from remote sensing, to characterise topography based on relief, slope, aspect, and curvature (Evans, 1972; Zevenbergen and Thorne, 3

ACCEPTED MANUSCRIPT 1987; Nogami, 1995; Florinsky, 1998a) or to classify topography into discrete landforms or morphological units (Iwahashi and Pike, 2007; Jones et al., 2007; Tarolli et al., 2012; Jasiewicz and Stepinski, 2013; Wyrick et al., 2014). Commonly, metrics that characterise surface patterns

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at each cell in the DEM, or within a delineated area, are employed to capture the overall surface topography. However, these metrics do not provide information on actual surface complexity

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(Wood, 1996; Scown et al., in press). Alternately, an extensive suite of surface metrics and geostatistical tools can be used in order to quantify the spatial variability, structure, and

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autocorrelation of topographic surfaces (see Table 1), although little attempt has yet been made to apply such approaches to floodplains (Scown et al., in press). Surface metrics are quantitative

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measures of continuous variables (McGarigal et al., 2009; Cushman et al., 2010). Environmental applications of surface metrics have occurred in mountainous regions (Nogami, 1995; Riley et

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al., 1999; Dorner et al., 2002; McGarigal et al., 2009; Iwahashi et al., 2012) or on the sea floor

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(McCormick, 1994; Brock et al., 2004; Wilson et al., 2007; Wedding et al., 2008; Walker et al., 2009; Zawada and Brock, 2009; Zawada et al., 2010; Friedman et al., 2012), with only limited

2014b).

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applications in riverine settings (Everson and Boucher, 1998; Aberle et al., 2010; Legleiter,

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Spatial phenomena are influenced by scale (Turner et al., 1989). Understanding how scale influences the use of surface metrics to capture topography is important for a number of practical and theoretical reasons. First, comparisons between studies must be made at similar scales for any results to be meaningful and not an artefact of different scales of investigation (Turner et al., 1989; Levin, 1992). Second, measurement scales of any physical component of an ecosystem must be relevant to the scales of the organism or process of interest (Turner et al., 1990; Wilson et al., 2007). Third, correlations between, and redundancies of, metrics may be inconsistent across scales (Evans, 1972). Finally, the scaling behaviour of metrics can be used to infer domains of dominant structuring processes and scale thresholds between these domains (Woodcock and Strahler, 1987; Turner et al., 1990; Holling, 1992) or to identify scales at which significant human interference has altered the structure of an ecosystem (Zurlini et al., 2007; De 4

ACCEPTED MANUSCRIPT Jager and Rohweder, 2012). The organisation of spatial pattern is important when measuring floodplain topography.

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Variables can be distributed continuously, in patches, a combination of both or randomly

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throughout space (Gustafson, 1998), and this has important implications for sampling and for

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understanding ecosystem patterns and processes. First, the location of measurements can greatly influence results obtained when measuring any spatial phenomena (Southwell and Thoms, 2006; Legleiter, 2014a; Scown et al., in press); and if a good geographic distribution of

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samples is not taken, results can be unrepresentative of the entire area and misleading. This issue applies to raw elevation data, which has implications for uncertainty in DEMs (Rayburg et

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al., 2009; Wheaton et al., 2010; Carley et al., 2012), as well as to derived data (such as surface metrics), which has implications for the conclusions drawn about topography across entire

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floodplains when only small areas are actually measured (Scown et al., in press). Second,

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changes in the spatial correlation of surface characteristics with distance can be useful in identifying structural patterns in the surface (Legendre and Fortin, 1989; Bar Massada and

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Radeloff, 2010). For example, patchiness in surface topography is observed when nearby samples of a particular metric are more highly correlated than more distant samples (Turner et

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al., 1989), and the characteristic length scale of patches and their spatial organisation can be inferred from distances at which data switch from being correlated to uncorrelated, or vice versa (Sokal, 1979; Woodcock and Strahler, 1987). Here we distinguish patchiness in topography, which relates to the spatial organisation of surface metric values, from patchiness in elevation, which relates to the spatial organisation of the raw elevation data. Application of spatial correlation analyses to surface metrics computed at multiple scales allows for the detection of patchy spatial patterns and patch structure in floodplain topography at multiple scales. Spatial patterns in floodplains have largely been viewed from two contrasting perspectives or paradigms: the gradient or ecotone paradigm and the patch mosaic paradigm (Scown et al., in

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ACCEPTED MANUSCRIPT press), both of which reflect varying degrees of ‘complexity’. The gradient paradigm provides a relatively simple perspective of spatial patterns in floodplains, with variability being explained by distance from the channel and spatial organisation being continuous and predictable from

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proximal to distal parts of the floodplain (e.g., Junk et al., 1989). Conversely, the patch mosaic paradigm suggests a high degree of distinct organisation, with nonlinear and abrupt changes in

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space throughout floodplains (e.g., Stanford et al., 2005), but reflects only organisation at the particular scale at which patches are delineated (McGarigal et al., 2009). Discrepancies in how

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floodplains are considered to be structured may lie in the scale or location of observation. Over small areas, or at coarse resolutions, spatial patterns in floodplains may appear as gradients, for

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example; whereas at other spatial extents and resolutions patches may be clear (Southwell and Thoms, 2006). The question of how floodplain topography is spatially organised—or at a higher

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level how complex floodplain topography is—may therefore depend on the scales and locations

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at which it is measured (Scown et al., 2015; Scown et al., in press). This paper examines how spatial patterns in topography emerge in the Upper Mississippi

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River floodplain when measured from a LiDAR-derived DEM using surface metrics, and what the influence of sampling scale (window size) is on the surface metrics and patterns. In

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particular, we ask four questions: How is floodplain surface topography spatially organised in this study area? Is the topography of the floodplain organised along a spatial gradient, in distinct patches, randomly, or as some combination of those? 

How does floodplain surface topography and its spatial organisation change across different scales of investigation?

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Are there correlations among surface metrics, and how are these affected by sampling scale?

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Are there scale thresholds in floodplain surface topography? Are there any sampling scales at which the spatial patterns observed or the information provided by surface

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ACCEPTED MANUSCRIPT metrics dramatically change? In answering these questions we aim to determine how sampling scale can affect

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investigations of floodplain spatial patterns using surface metrics and how floodplain

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topography is spatially organised in this study area. Our aim is also to contribute to the

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development of a quantitative approach for future investigations of floodplain topographic

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complexity.

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2. Methods 2.1. Study location

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This study was conducted on the floodplain of the Upper Mississippi River (UMR) in mid-

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west USA. The UMR is divided into a series of ‘pools’, which are lengths of the river between two locks and dams. This study was conducted in pool 9, which lies between the states of Minnesota,

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Iowa, and Wisconsin (Fig. 1). The river valley floor in Pool 9 is approximately 50 river kilometres in length and generally between five and six kilometres wide (Fig. 1). The floodplain,

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river channels, and impounded water of pool 9 occupy over 210 km2. 2.2. Digital elevation model The DEM used in this study was a 1 × 1 m2 gridded bare earth DEM of the floodplain in the upper half of Pool 9 (Fig. 1). This DEM was derived from airborne laser scanning (LiDAR) that was obtained in 2007, when river flow conditions were low, by the U.S. Army Corps of Engineers’ Upper Mississippi River Restoration-Environmental Management Program (UMRREMP). From the LiDAR spot heights, the U.S. Geological Survey’s Upper Midwest Environmental Sciences Center (UMESC) created the Tier 2 DEM used in this study that has undergone rigorous quality assurance testing (UMESC, 2013). The processed DEM available online (UMESC, 2015) was used for this study. LiDAR typically provides spot heights with a horizontal accuracy within

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ACCEPTED MANUSCRIPT 1 m and a vertical accuracy within 15–30 cm, although they can be much better. This accuracy range was considered acceptable for analysis of the entire floodplain (> 100 km2); however, cognisance of the effects of LiDAR accuracy on derived floodplain topographic metrics is

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important, particularly across different vegetation types (Charlton et al., 2003). These effects can create uncertainty in the DEM and in the derived metrics (Gonga-Saholiariliva et al., 2011).

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The floodplain examined in this study has densely vegetated areas of reed canary grass (Phalaris arundinacea L.), which has been found to cause overestimation of the surface elevation

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and increased surface variability in LiDAR-derived DEMs. The effects of vegetation on surface metrics in this floodplain are investigated in a partner study (Scown et al., in prep.).

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The DEM was clipped to remove any areas of open water, agriculture or development, as well as a 50-m buffer within the outer edge of the floodplain to eliminate any possible effects of

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significant man-made structures, valley sides, and errors in the LiDAR data associated with

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water. These areas constituted only a small proportion of the study area. The water extent shown in Fig. 1 is approximately the extent of this river channel that has become permanently

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wetted since the construction of dams and weirs for navigation. Thus, the topography shown represents the extent of the present day floodplain (i.e., the periodically inundated alluvial

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landform adjacent to the channel; sensu Nanson and Croke, 1992). Some elevated, developed areas are observable in Fig. 1; however, these were removed from the analysis during the geoprocessing described above. The DEM was detrended relative to the 30-year mean low water level; that is, the average annual low water surface elevation in the main channel (in masl) for a period of 30 years from 1982 to 2012. This level was available for each river mile from USGS hydrological data. The level at each river mile was extrapolated across the floodplain to river mile contours placed perpendicular to the valley centreline. A plane DEM was then interpolated between the river mile contours and subtracted from the DEM to remove the downstream slope. This approach was chosen over reach-based regression detrending because it provided a quantitative measure

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ACCEPTED MANUSCRIPT of downstream slope (based on the channel water surface) for the entire floodplain at each river mile without the need to determine and delineate reaches, which potentially adds bias. A clear trend in water surface elevation was observed downstream in the main channel; thus, we

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assumed that variability in valley floor slope at scales smaller than 1 river mile was minimal. The detrended DEM (

) used as the base data set for this study contained a height

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value above the 30-year mean low water level plane for every 1 × 1 m2 cell (i.e., the zero elevation datum was the low water level and every cell in the detrended floodplain DEM had a

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2.3. Surface metric selection and calculation

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positive elevation above the water surface).

Eight surface metrics reflecting various components of topographic complexity in floodplains were measured across multiple scales using moving windows. These metrics were Range, SD,

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Skewness, Kurtosis, CV, SDCURV, Rugosity, and Vol:Area (Table 1). These eight surface metrics

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represent attributes of topography that are important for floodplain ecological and geomorphic

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patterns and processes; for example, because of their influence on spatial variation in flood frequency, soil saturation, vegetation patterns, erosion and deposition, hydraulic conditions, and channelisation (Buchholz, 1981; Hughes, 1990; Pollock et al., 1998; Lane et al., 2003;

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Nicholas and Mitchell, 2003; Hamilton et al., 2007). Some metrics, such as the fractal dimension of topography, were not used in this study because of software limitations in measuring these metrics locally using moving windows. The eight surface metrics were measured from the

grid and its derivatives

(Table 2). These metrics were calculated in ArcGIS 10.0 (ESRI, 2010) using a number of Focal Statistics routines and algebraic equations in Raster Calculator. The DEM Surface Tools add-in (Jenness, 2012) was used to derive two additional grids from

that were used in the

calculation of SDCURV and Rugosity. These were the grids of total curvature and surface area ratio, respectively (Jenness, 2012). The automated Focal Statistics routines are denoted in Table 2 as , where

indicates which routine and

indicates the input 9

ACCEPTED MANUSCRIPT raster grid. The DEM Surface Tools routines are denoted in Table 2 as

.

Each surface metric was calculated for every cell in the input grid based on a neighbourhood

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around that cell using a moving window analysis. The values of the central (focal) cell and all

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other cells within that neighbourhood were used in the metric calculation. NoData values were

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ignored for all metrics except Vol:Area, for which they were set at zero (i.e., the low water surface lever) for areas containing water, or ignored for other areas that were removed from the DEM during geoprocessing. The neighbourhood type was always a circle, with radius

=

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10, 20, 30, 40, 50, 100, 150, 200, 250, 300, 400, 500, 750, and 1000 m to account for multiple scales of measurement. These neighbourhood sizes were chosen to extend over two orders of

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magnitude at relatively regular log-intervals. The purpose of choosing these neighbourhood sizes in a regular manner was to determine any effects of measurement scale on the surface

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metrics and subsequently their spatial organisation. Our intention was not to first determine the

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scale(s) at which the floodplain surface is organised (e.g., Brown and Pasternack, 2014;

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Legleiter, 2014a) and sample within those scales, which may be of interest for future research. Each cell in the output raster grid contained the metric value measured for that particular neighbourhood centred over that particular cell. Because of the precision of floating point raster

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grid types in ArcGIS, all cells where

and

were removed from the

calculation of Skewness and Kurtosis, respectively, as these values form the denominator in each equation and cannot equal zero. Because of the scarcity of

values in some areas of the floodplain, some

neighbourhoods contained only a very small proportion of data. This created the risk of spurious metric results because of small sample sizes in these areas. Therefore, whenever the neighbourhood around a focal cell did not contain at least 60% data, this cell was removed from the output grid. This percentage was chosen based on a visual inspection of the number and spatial distribution of cells retained in the output grids when minimum limits from 10 to 90% data, in increments of 10%, were applied. Sixty percent was deemed appropriate to minimise 10

ACCEPTED MANUSCRIPT spurious metric values while ensuring at least half of the original cells were retained in the output grid for all neighbourhood sizes and that these cells had a broad spatial distribution.

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2.4. Analysis of surface metric distributions across scales

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To determine the influence of window size on the distribution of surface metric values, 500

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sample cells were randomly selected throughout the study area and the value of each surface metric measured within each window size was extracted from these cells in ArcGIS 10.0. Four

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cells were found to have highly spurious values at some measurement scales and were removed from the sample. This produced a matrix of 496 random cells, each with 8 surface metrics .

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measured at 14 window sizes

The values extracted at each window size were then pooled within each metric and range to remove any influence of measurement units between the different metrics.

The median

and variance

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standardised

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of each range standardised surface metric were then

calculated for each window size. The values of

were then plotted

and least squares linear regression performed on each of the log-log

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against

and

relationships in SPSS v22. The choice of linear regression on log-log data was based on the

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common investigation of power scaling in complex landscapes, which can be used to indicate the complexity of spatial structure as well as scales in structuring processes (e.g., Holling, 1992; De Jager and Rohweder, 2012). 2.5. Analysis of spatial organisation of surface metrics across scales To quantify the spatial organisation of surface metric values across scales, Moran’s I was calculated locally for each surface metric measured at each window size from the 496 random sample cells using the ncf package in R. Calculation of Moran’s I locally, as opposed to globally, involves calculating Moran’s I within discrete lag distance bins. A range of lag distance bins from 100 to 10,000 m were used at equal intervals of 100 m. This provides a quantitative measure of spatial autocorrelation across specific distances throughout the floodplain, rather than a single 11

ACCEPTED MANUSCRIPT value for the entire floodplain. Moran’s I is an index of spatial autocorrelation in a variable in which a value of 1 indicates perfect spatial correlation (i.e., every cell in the output grid is most highly correlated with its immediate neighbours) while a value of -1 indicates perfect spatial

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dispersion (i.e., every cell is least correlated with its immediate neighbours; e.g., a chess board). A value of zero indicates a random spatial distribution in the variable (i.e., no spatial structure

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in the distribution of the variable exists; e.g., cells may or may not be correlated with their neighbours). The minimum number of pairs of sample cells used to calculate Moran’s I across

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the range of lag distance bins was 80.

Each Moran’s I was then plotted against lag distance to create a spatial correlogram, and

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exponential isotropic models were fitted to the

correlograms using SigmaPlot v12. The

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(1)

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exponential isotropic model is defined as:

where is Moran’s I for lag distance ,

is Moran’s I at

(i.e., the nugget),

maximum spatial dispersion in the population of surface metric values, and

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parameter so that the effective range

is the distance at which

is the

is the range is within 5% of the

asymptote (Robertson, 2008). The parameters of the exponential isotropic model are quantitative indicators of the spatial organisation of surface metric values, in much the same was as variogram parameters are (Rossi et al., 1992; Legleiter, 2014a). The nugget

indicates the strength of ‘patchiness’ of the

surface metric, where high values reflect a more patchy distribution of metric values and low values indicate a more random spatial organisation. The range

indicates the distance at

which spatially distributed metric values become uncorrelated; that is, the characteristic length scale of patches. The nugget, range, and explained variance (r2) of the models which best fit each of the

correlograms were plotted against window size for each surface metric to 12

ACCEPTED MANUSCRIPT determine how their spatial organisation changed across scales. 2.6. Analysis of surface metric correlations across scales

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To assess the correlation and clustering of surface metrics across scales, an approach similar

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to that of McGarigal et al. (2009) was adopted. Correlations were investigated at three levels: (i)

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all metrics measured at all window sizes; (ii) all metrics within each window size; and (iii) all window sizes within each metric. Spearman’s rank correlation coefficient ( ) was used to

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account for nonlinear but monotonic relationships (McGarigal et al., 2009) and pairwise scatter plots were examined to ensure the validity of the results. Each correlation matrix was then .

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expressed as a distance matrix with distances between elements equal to

A multivariate hierarchical cluster analysis was then performed on each of the three distance

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matrices using Ward’s minimum-variance clustering approach to minimise within-group

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variance while maximising between-group variance (McGarigal et al., 2000). Clustering was performed using the stats package in R. The optimum number of groups

was determined by

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the first inflection point on the scree plot of level of association against number of groups (McGarigal et al., 2000). The significance of the cluster solution was then determined using

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PERmutational Multivariate ANalysis Of VAriance (PERMANOVA) (Anderson, 2001) in Primer v6 to ensure all pairwise comparisons between groups were significant. Where pairwise comparisons between the

groups were not significant at p = 0.05, the

solution of the

cluster analysis was taken and PERMANOVA repeated until all pairwise comparisons were significant. This ensured that all groups that emerged from the cluster solution were significantly different from all other groups.

3. Results 3.1. Distribution of surface metric values across scales

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ACCEPTED MANUSCRIPT The distributions of surface metric values were influenced by window size (Fig. 2); however, the influence was not consistent across metrics. A power function was capable of explaining change in the median range standardised metric value

with increasing window size for all (as

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metrics (r2 > 0.7) except Kurtosis (r2 = 0.317) (Table 3). The influence of window size on

indicated by the absolute slope of the log-log line) was highest for Range, followed by SD and CV

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(Table 3). These three metrics had a slope an order of magnitude higher than Kurtosis, Rugosity, and Skewness (Table 3), indicating that they are more sensitive to changes in sampling scale. with increasing window size occurred for Vol:Area

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Relatively moderate rates of change in

and SDCURV compared to the other six metrics, indicating that they are less sensitive to changes

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in sampling scale. The values of Range, SD, and CV (all measured in meters) are large relative to the expected accuracy of LiDAR-derived elevation data, particularly at the larger window sizes,

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suggesting that these are real trends and not artefacts of DEM uncertainty.

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The variance of range standardised metric value

also increased significantly with

window size for Range and SD (Table 4), while decreasing significantly for CV, SDCURV, Rugosity,

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and Vol:Area (Table 4). A power function explained the relationship between window size and well (r2 > 0.7) for five of the eight metrics (Table 4). The exceptions to this were Skewness,

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Kurtosis, and CV. On average across all metrics, the effect of window size on the slope of the line) was almost twice that of

(as indicated by

(Tables 3 and 4), indicating that the variability

of surface metric values is more scale-dependent than the median. Again, Range had the highest absolute slope, followed by Rugosity, SDCURV, and SD. A relatively low slope occurred for Vol:Area compared to the other metrics. 3.2. Spatial organisation of metric values across scales Surface metric values were highly variable across the floodplain, and their spatial organisation varied with metric and window size. Distinct areas of different physical character across the floodplain surface were evident from the surface metric maps (Fig. 3). Areas of increased topographic variability were evident along the main and side channels, particularly at 14

ACCEPTED MANUSCRIPT large window sizes. Areas of increased topographic complexity were also highlighted by CV and Vol:Area in the backwaters to the western part of the frames in Fig. 3. Those metrics sensitive to extremes (Range, SD, Skewness, and Kurtosis) showed some areas of abrupt change in metric

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value from low to high, particularly around the main channel at large window sizes (Fig. 3). Other metrics appeared to change more gradually throughout the floodplain. Most of these

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features and patterns were not easily observed from the original DEM.

All eight surface metrics exhibited a highly patchy spatial organisation when measured at

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most window sizes, particularly those of 100 m or more in radius. This was reflected by the Moran’s I correlogram model nugget approaching or exceeding one for most metrics and

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window sizes (Fig. 4). The exceptions to this were Skewness at 10 m and Kurtosis and Vol:Area at 10 and 20 m, for which an exponential isotropic model did not explain the relationship between

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Moran’s I and lag distance well (r2 < 0.3). However, model fit generally improved with

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increasing spatial scale, and the parameters of the models often varied with metric and window

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size (Fig. 4).

On average over all window sizes, the nugget (left axis of Fig. 4) was highest for Kurtosis, followed by Skewness, CV, SD, Rugosity, Vol:Area, Range, and SDCURV. This represents a decline in

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the average strength of patchiness from Kurtosis through to SDCURV. The average model range (right axis of Fig. 4) was highest for CV, followed by SD, Range, Rugosity, Vol:Area, SDCURV, Skewness, and Kurtosis. This represents a decrease in the scale of patch structure from CV through to Kurtosis. Relatively abrupt increases in the model nugget were observed between the 50- and 150-m window sizes for Range, SD, SDCURV, Rugosity, and Vol:Area (Fig. 4), indicating that the strength of ‘patchiness’ in these metrics increases significantly around this sampling scale. Above the 150m window size, the nugget was relatively consistent for these metrics. A decline in the model range for Range and SD between the 50- and 100-m window sizes also occurred (Figs. 4A and B). This indicates that the characteristic length scale of Range and SD patches drops rapidly 15

ACCEPTED MANUSCRIPT around this sampling scale, but the strength of these patches increases. Skewness and Kurtosis were the ‘patchiest’ metrics, both having much higher nuggets than the other metrics at most window sizes above 30 m (Figs. 4C and D). However, changes in the nugget with increasing

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window size were not predictable for these two metrics. The model nugget of CV increased consistently with window size, indicating that the strength of patchiness in this metric increases

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with sampling scale. The scales at which the greatest changes in model parameters across the eight metrics occurred were between the 50- and 150-m window sizes and between the 750-

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and 1000-m window sizes. The exceptions to this were the nuggets for Skewness and Kurtosis, which exhibited a sharp peak at the 200- and 150-m window sizes, respectively (Figs. 4C and D).

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The range parameter was consistently above 1000 m for all metrics and window sizes with the exception of Skewness and Kurtosis (Fig. 4). This indicates that correlation in the surface

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topography of this floodplain extends over 1000 m and, in some cases, up to 5000 m. These high

artefact of sampling scale.

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values of the range parameter were independent of window size, indicating that they are not an

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3.3. Clustering of all metrics at all scales

Eight groups emerged from the multivariate cluster analysis of all metrics measured at all

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window sizes, based on the first major inflection point on the scree plot. These groups were all significantly different from each other (PERMANOVA: F = 34.502; d.f. = 7, 104; p = 0.001; no. permutations = 999) with all pairwise comparisons between groups having p ≤ 0.002. In terms of group membership (Fig. 5), Range and SD were highly correlated and always clustered together (Spearman’s ρ ranged from 0.691 to 0.946 over all scales). These metrics describe the magnitude and variability of relief. Rugosity and SDCURV were also highly correlated (Spearman’s ρ ranged from 0.852 to 0.916 over all scales) and indicate vertical and horizontal variability in the surface. These four metrics were also contained in one group at window sizes from 10- to 50-m. A single group contained CV across all scales, and Vol:Area was also in this group for window sizes from 100 to 1000 m. Skewness was clustered with Vol:Area at window 16

ACCEPTED MANUSCRIPT sizes from 10 to 50 m and with Kurtosis at the 750- and 1000-m window sizes. Kurtosis did not cluster with any other metric across the 10- to 500-m window sizes (maximum absolute ρ =

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0.354 against any other metric across these scales).

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In terms of group changes across scales; CV did not change group; Range, SD, Skewness,

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SDCURV, Rugosity, and Vol:Area each changed group once; and Kurtosis changed group twice (Fig. 5). Seven of these eight group changes occurred between the 50- and 100-m window sizes (Fig. 5). These results indicate that surface metrics that characterise vertical as well as horizontal

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variability in the surface, as well as the nature of that variability (e.g., incised, elevated, abrupt, gentle slope), begin to contribute unique information about spatial pattern as the scale of

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3.4. Clustering of metrics within scales

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analysis increases. At fine scales, most metrics provide redundant information.

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Two significantly different groups of surface metrics emerged from the multivariate cluster analyses within each window size for 13 of the 14 window sizes (Fig. 6). The exception was the

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500-m window size, within which three groups of metrics emerged. The assemblage of metrics within the groups varied with window size. Again, Range and SD always grouped together, as

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did SDCURV and Rugosity. Additionally, Skewness and Vol:Area always clustered together at this level of investigation. The most variable of the metrics in terms of which group they occurred in within each window size were CV and Kurtosis (Fig. 6). Both of these metrics changed group four times between the 10- and 100-m window sizes. At window sizes of 100-m radius and above, the two groups of metrics did not change with window size except for at 500 m. 3.5. Clustering of scales within metrics Three or four significantly different groups of window sizes emerged from the multivariate cluster analyses within each metric, depending upon the metric (Fig. 7). Four distinct scale groups occurred for SD, Skewness, CV, and Vol:Area; while three occurred for Range, Kurtosis, SDCURV, and Rugosity. Within all metrics, window sizes of 50-m radius or less never clustered

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ACCEPTED MANUSCRIPT with those of 100-m radius or more. This showed a distinct separation of window size groups between 50- and 100-m radius, regardless of the metric (Fig. 7). Another distinct separation between window sizes occurred from 500 to 750 m within all metrics except Range and

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Vol:Area. Range, CV, and Vol:Area all had another separation between the 300- and 400-m

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window sizes. Other breaks in window size groups were inconsistent among metrics (Fig. 7).

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4. Discussion

Surface metrics provide a useful approach to measuring topography (or any spatially

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continuous variable) across large extents, multiple scales, and all locations within floodplains. The results of this study have implications for measuring floodplain topography using surface

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metrics, for understanding the spatial structure of floodplain surfaces, and for future

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investigations of floodplain topographic complexity using an approach such as this.

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4.1. Measuring floodplain topography using surface metrics The eight surface metrics measured in this study were scale-dependent, in terms of their

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global median value and their variance. The global median metric value increased with window size for all metrics except Vol:Area (Fig. 2). Higher values of Range, SD, Skewness, Kurtosis, CV, SDCURV, and Rugosity indicate increased topographic variability; whereas values of Vol:Area are likely to decrease as the surface becomes more dissected. Thus, as larger areas of the floodplain are included in the measurement of surface metrics, increased topographic variability is observed, on average, in all metrics. This is expected, as a greater range of physical habitats with variable topographic character are likely to be encountered as larger areas of the floodplain are observed. This emphasizes the importance of considering scale in any approach to measuring floodplain topography using surface metrics. In particular, different patterns are likely to be observed at different measurement scales for all of these surface metrics. Therefore, comparisons between studies must be made at the same scales (Turner et al., 1989; Levin, 18

ACCEPTED MANUSCRIPT 1992), and the scale of measurement must be relevant to the scales of the organism or process of interest (Wiens, 1989; Wiens and Milne, 1989; Turner et al., 1990; Wu, 2004). The variance in metric value was also influenced by window size; however, the influence was less consistent

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across metrics than it was for the median metric value. Variance increased with window size for Range and SD, suggesting that these surface attributes become more variable with distance, at

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least over the scales observed in this study. Variance decreased for SDCURV, Rugosity, and Vol:Area, suggesting that these surface attributes become more uniform in space as larger areas

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of the floodplain are observed. A decrease in variance manifests as a smoothing of the surface metric maps (Fig. 3) with increasing window size and may reflect increased amounts of noise

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when these metrics are measured at small scales.

Redundancies in the eight surface metrics measured in this study were evident. A number of

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metrics were highly correlated over all scales. In particular, Range and SD were always highly

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correlated, as were SDCURV and Rugosity. Skewness and Vol:Area were also highly correlated at small window sizes. This suggests that measuring all of these surface metrics is unnecessary

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when investigating floodplain topography, at least in this floodplain. High redundancies of landscape metrics have also been reported by Riitters et al. (1995) and McGarigal et al. (2009).

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However, no single metric can reflect all of the physical complexity important in an ecosystem (Dorner et al., 2002; Frost et al., 2005; Tokeshi and Arakaki, 2012). Therefore, selecting a suite of surface metrics appropriate for the questions being asked is important. Considerations should include what the metrics actually measure in terms of floodplain topography (Table 1), their ecological significance, ease of calculation, sensitivity to extreme or erroneous data values, and redundancy of complicated metrics. Caution when comparing studies that use different metrics is also important (Frost et al., 2005). Correlations in metrics across scales also suggest that, although observations made at different scales may not be absolutely the same, they are correlated within some scale ranges. Therefore, measures of floodplain topography may be undertaken at a single scale and inferred, relatively, across other scales within certain ranges. The finding that different surface metrics are highly correlated in this floodplain is also of 19

ACCEPTED MANUSCRIPT interest for understanding dominant structuring processes of floodplain surfaces, as it may indicate that the same processes determine different attributes of topography. Whether these correlations exist in floodplains from different geographic settings would be worthy of further

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study—for example, to determine whether topography is structured in a consistent manner across floodplains. Departure from the metric correlations found here may indicate

therefore, be useful in identifying such alterations.

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anthropogenic alteration of floodplain topography or its structuring processes and may,

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Scale thresholds in the correlations of surface metric values were observed in this floodplain. The most significant of which occurred between the 50- and 100-m and the 500- and 750-m

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window sizes. This suggests that measurements made above or below these scales should not be inferred beyond them in this floodplain. These threshold scales are ∼ 15–20% and 150% of

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the main channel width (1–2% and 10–15% of the floodplain width), respectively. Other scale

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breaks were observed but were inconsistent across metrics. Therefore, careful consideration of the results of this study is advised as a guide for designing studies aimed at measuring

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floodplain topography using surface metrics. Thresholds in surface metric correlations may also have geomorphological significance. These distinct breaks represent the scale(s) at which most

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restructuring of metric correlations occurred. This has two main implications. First, measurements made at scales of the 50-m window size or less may not correlate well with those measured at the 100-m window size or greater. This means that processes structuring topography locally at small scales (50-m radius or less) may not be the same as those operating at larger scales (100-m radius or more). This contrasts the finding that processes structuring topography globally (i.e., the floodplain average, as indicated by power scaling of metric medians) appear to be consistent across scales. This may be related to the shifting mosaic, steady state that has been hypothesised in floodplains in which local conditions are highly dynamic but the overall composition of conditions remains constant (Stanford et al., 2005). Second, correlations between metrics below the 50-m window size may not be the same as correlations above the 100-m window size. This means that common processes may be 20

ACCEPTED MANUSCRIPT structuring different properties of topography, and hence different metrics, at small scales but not at large scales or vice versa. This was also supported by the inconsistencies of group membership when metrics were clustered within each window size and also by the clustering of

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window sizes within each metric.

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Considering the results of this study, we suggest that a good subset of the 8 metrics and 14 window sizes measured here might be SD, Skewness, CV, and SDCURV at 50-, 200-, and 1000-m window sizes. However, in floodplains that are geomorphologically different from that of the

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Upper Mississippi River, different correlations and scale thresholds may occur, so the results of

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this study should be used with caution.

4.2. The spatial organisation of topography in the Upper Mississippi River floodplain

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Many physical and ecological attributes of floodplains are frequently viewed as being patchy

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(e.g., Ward et al., 1999; Thoms et al., 2005), and consequently they are delineated as patches with some minimum resolution of analysis. This can result in the loss of information concerned

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with within-patch variability (McGarigal et al., 2009; Scown et al., in press). Our results suggest that patchiness can emerge from spatially continuous topographic data at particular scales, and

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this assists with the identification of spatial scales at which floodplain geomorphological pattern and process may interact. Feedbacks between hydrology and geomorphology underpin the emergence of patchy spatial patterns in floodplains. Interactions between topography and vegetation, for example, are known to occur in floodplains (Nanson and Beach, 1977; Hughes, 1997; Richards et al., 2002), and these have been shown to influence the structure of floodplain topography. Patchiness in topographic change processes also has been reported in previous studies and related to positive and negative feedbacks (e.g., Fuller et al., 2003; Wheaton et al., 2010). Further investigation into the significance of topographic patchiness in large river floodplains such as the Mississippi, and the degree to which feedbacks cause patchiness in structure and change, would be useful. Hierarchical patch structure and dynamics have been observed in many geomorphological 21

ACCEPTED MANUSCRIPT and ecological studies (Holling, 1992; Levin, 1992; Milne et al., 1992; Wu and Loucks, 1995). The scales over which a power function characterises a spatial pattern is thought to reflect constant structuring processes over those scales, as well as hierarchical patch structure (Turner et al.,

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1990; Holling, 1992). Power functions were observed in the scaling of most metric medians and variances in this study (Table 3). Although other functions are also likely to be valid in

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explaining the effects of scale on surface metrics, power functions were chosen because of their ability to describe multiple scales of organisation simultaneously. Power functions have

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previously been observed in aquatic habitat richness and forest cover in the Upper Mississippi River floodplain (De Jager and Rohweder, 2011, 2012) as well as in topography in many fluvial

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environments, indicating fractal-like patterns caused by natural hydrogeomorphic processes (Chase, 1992; Wörman et al., 2007). The good fit of power functions observed in this study

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underscore the emergence of multiple scales of patchiness and patch structure found in spatial

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correlograms and suggest that most attributes of the topography of this study floodplain dominate over the entire range of scales investigated here.

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Scale thresholds observed in surface metric correlations and spatial correlograms were not present in the power scaling of global metric medians. This suggests that distinct scales and

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locations at which spatial organisation and structuring processes change may exist locally within the floodplain; whereas attributes of topography of the entire floodplain, as indicated by the surface metrics global medians, are consistent across scales. Thus, the shifting mosaic steady state hypothesis of floodplain structure and dynamics (Stanford et al., 2005) may be relevant in this floodplain. This hypothesis emphasizes continual local restructuring of landscape patches or components while the overall assemblage of structural components throughout the floodplain is maintained. Departures from power scaling might indicate scales at which significant human interference has altered the overall structure of the floodplain (Zurlini et al., 2007; De Jager and Rohweder, 2012); that is, the steady state has been affected. Scale breaks in power functions applied to aquatic habitat richness have been reported in the Upper Mississippi River and related to loss of aquatic habitat in some areas (De Jager and Rohweder, 2012). The 22

ACCEPTED MANUSCRIPT absence of such scale breaks in the power functions of surface metric medians in this study likely indicate that the floodplain topography of the portion of pool 9 that we studied remains relatively intact, or unaffected by large-scale anthropogenic interferences. A notable exception

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to this would be large piles of dredge spoil on the banks of the main channel that were visible in

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some areas and influenced local metric values.

The spatial organisation of topography, along with variability, are important contributors to topographic complexity (sensu Simon, 1962; Phillips, 1999). The topography of the floodplain

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examined here was highly variable and highly organised in space. Thus, the topography of this floodplain is spatially complex rather than exhibiting simple gradient patterns over any scale

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larger than a few meters. However, correlation in surface metrics commonly extended over 1000 m and up to 5000 m, indicating that large scale structure in the topography of this

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floodplain exists along with small-scale variability. This suggests that the multiple scales of

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patchiness in topography may be superimposed on large-scale trends. Such properties reflect the structured unpredictability, or mix of order and disorder, that is typical in complex systems

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(Weaver, 1948; Simon, 1962). The combined approach of surface metrics and geostatistical analyses employed in this study enables both variability and spatial organisation in any surface

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to be quantified in order to investigate its complexity. Future research may benefit from incorporating such an approach into an index of floodplain, or other, surface complexity. 4.3. Limitations and future research The effects of changing window size on surface metrics and their spatial organisation have been examined in this study. We did not alter the resolution or grain (sensu Kotliar and Wiens, 1990) of the data as LiDAR is capable of capturing high-resolution data over large areas with relatively high accuracy. Generalising such data by reducing the resolution also reduces the power of this excellent data-capture technology. We also calculated surface metrics using only circular windows and quantified their spatial organisation using omni-directional Moran’s I. This approach does not account for anisotropy in floodplain topography, which may be particularly 23

ACCEPTED MANUSCRIPT important in assessing topographic complexity. Consideration of directionality in topography in the absence of an isotropic surface may also be important (Zawada et al., 2010)—particularly in floodplains because of their longitudinal, lateral, and vertical dynamics (Stanford, 1998; Ward et

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al., 2002a). Anisotropic behaviour in surface metrics could be investigated using moving windows with a wedge, irregular, or weighted kernel in the ArcGIS Focal Statistics routine.

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Directional correlograms and variograms may also prove useful in quantifying the spatial organisation of surface metrics and are possible using various spatial statistics packages

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(Dorner et al., 2002; Legleiter, 2014a). We also chose regularly spaced window sizes as our intention was to determine any effects of scale on surface metrics and floodplain topography.

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Future research could first quantify scales of organisation in the original DEM (i.e., organisation in elevation) then measure attributes of topography using surface metrics at scales based on

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this organisation.

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5. Conclusions

Spatial patterns in the floodplain topography of pool 9 of the Upper Mississippi River are

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generally highly organised across multiple scales. Multiple scales of patchiness and patch structure were observed for the eight surface metrics measured, with distinct reorganisation of topographic patterns occurring between measurement scales of 50- and 150-m radius, and between 750- and 1000-m radius. These threshold scales are approximately 15–20 and 150% of the main channel width (1–2 and 10–15% of the floodplain width), respectively. Spatial correlation in surface topography typically existed over distances of more than 1000 m, and up to 5000 m in some cases. Measurement scale influenced all surface metric values, as well as their spatial organisation. Scale thresholds occurred in the spatial patterns observed, particularly between the 50- and 100-m window sizes and the 500- and 750-m window sizes. Correlations among surface metrics and across some scales also occurred, indicating that similar structuring processes may be influencing different attributes of floodplain surface 24

ACCEPTED MANUSCRIPT topography and may be operating over defined scale ranges. We suggest that by coupling the use of continuous surface metrics measured at multiple scales, with geostatistical analyses to quantify spatial organisation, greater insights into the structure and function of floodplain

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environments is possible. These approaches can also be used to quantify the variability and spatial organisation—two important components of spatial complexity—of floodplain and other

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surfaces in order to determine their spatial complexity.

Acknowledgements

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The authors wish to thank Greg Pasternack, Richard Marston, and two anonymous reviewers, whose comments on earlier versions were invaluable in improving this manuscript. We also

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acknowledge support from the University of New England and the U.S.G.S. Upper Midwest

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Environmental Sciences Center, without which this research would not have been possible. Any use of trade, product, or firm names is for descriptive purposes only and does not imply

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endorsement by the U.S. Government.

References

Aberle, J., Nikora, V., Henning, M., Ettmer, B., Hentschel, B., 2010. Statistical characterization of bed roughness due to bed forms: a field study in the Elbe River at Aken, Germany. Water Resources Research, 46, W03521. Alsdorf, D., Bates, P., Melack, J., Wilson, M., Dunne, T., 2007. Spatial and temporal complexity of the Amazon flood measured from space. Geophysical Research Letters, 34, L08402. Anderson, M. J., 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26, 32-46. Bar Massada, A., Radeloff, V. C., 2010. Two multi-scale contextual approaches for mapping spatial pattern. Landscape Ecology, 25, 711-725. 25

ACCEPTED MANUSCRIPT Brock, J. C., Wright, C. W., Clayton, T. D., Nayegandhi, A., 2004. LIDAR optical rugosity of coral reefs in Biscayne National Park, Florida. Coral Reefs, 23, 48-59.

IP

change in mountain rivers. Journal of Hydrology, 510, 551-564.

T

Brown, R. A., Pasternack, G. B., 2014. Hydrologic and topographic variability modulate channel

Brown, R. A., Pasternack, G. B., Wallander, W. W., 2014. Synthetic river valleys: creating

SC R

prescribed topography for form–process inquiry and river rehabilitation design. Geomorphology, 214, 40-55.

NU

Buchholz, K., 1981. Effects of minor drainages on woody species distributions in a successional floodplain forest. Canadian Journal of Forest Research, 11, 671-676.

MA

Carley, J. K., Pasternack, G. B., Wyrick, J. R., Barker, J. R., Bratovich, P. M., Massa, D. A., Reedy, G. D., Johnson, T. R., 2012. Significant decadal channel change 58-67 years post-dam accounting

D

for uncertainty in topographic change detection between contour maps and point cloud

TE

models. Geomorphology, 179, 71-88.

Charlton, M. E., Large, A. R. G., Fuller, I. C., 2003. Application of airborne LiDAR in river

CE P

environments: the River Coquet, Northumberland, UK. Earth Surface Processes and Landforms, 28, 299-306.

Chase, C. G., 1992. Fluvial landsculpting and the fractal dimension of topography.

AC

Geomorphology, 5, 39-57.

Clarke, K. C., 1986. Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method. Computers & Geosciences, 12, 713-722. Cushman, S. A., Evans, J. S., McGarigal, K., Kiesecker, J. M., 2010. Toward Gleasonian Landscape Ecology: From Communities to Species, From Patches to Pixels. Research Paper RMRS-RP-84. U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO. De Jager, N. R., Rohweder, J. J., 2011. Spatial scaling of core and dominant forest cover in the Upper Mississippi and Illinois River floodplains, USA. Landscape Ecology, 26, 697-708. De Jager, N. R., Rohweder, J. J., 2012. Spatial patterns of aquatic habitat richness in the Upper 26

ACCEPTED MANUSCRIPT Mississippi River floodplain, USA. Ecological Indicators, 13, 275-283. Dorner, B., Lertzman, K., Fall, J., 2002. Landscape pattern in topographically complex landscapes: issues and techniques for analysis. Landscape Ecology, 17, 729-743.

IP

T

Dubuc, B., Zucker, S. W., Tricot, C., Quiniou, J. F., Wehbi, D., 1989. Evaluating the fractal dimension of surfaces. Proceedings of the Royal Society of London, Series A, Mathematical

SC R

and Physical Sciences, 425, 113-127.

ESRI, 2010. ArcGIS Desktop: Release 10.0. Environmental Systems Research Institute, Redlands,

NU

CA.

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In:

MA

Chorley, R. J. (Ed.), Spatial Analysis in Geomorphology. Methuen & Co., London, pp. 17-90. Everson, D. A., Boucher, D. H., 1998. Tree species-richness and topographic complexity along the

D

riparian edge of the Potomac River. Forest Ecology and Management, 109, 305-314.

TE

Florinsky, I. V., 1998a. Accuracy of local topographic variables derived from digital elevation models. International Journal of Geographical Information Science, 12, 47-62.

CE P

Florinsky, I. V., 1998b. Combined analysis of digital terrain models and remotely sensed data in landscape investigations. Progress in Physical Geography, 22, 33-60. Friedman, A., Pizarro, O., Williams, S. B., Johnson-Roberson, M., 2012. Multi-scale measures of

AC

rugosity, slope and aspect from benthic stereo image reconstructions. PLoS One, 7, e50440. Frost, N. J., Burrows, M. T., Johnson, M. P., Hanley, M. E., Hawkins, S. J., 2005. Measuring surface complexity in ecological studies. Limnology and Oceanography: Methods, 3, 203-210. Fuller, I. C., Large, A. R. G., Charlton, M. E., Heritage, G. L., Milan, D. J., 2003. Reach-scale sediment transfers: an evaluation of two morphological budgeting approaches. Earth Surface Processes and Landforms, 28, 889-903. Gadelmawla, E. S., Koura, M. M., Maksoud, T. M. A., Elewa, I. M., Soliman, H. H., 2002. Roughness parameters. Journal of Materials Processing Technology, 123, 133-145. Glenn, N. F., Streutker, D. R., Chadwick, D. J., Thackray, G. D., Dorsch, S. J., 2006. Analysis of LiDAR-derived topographic information for characterizing and differentiating landslide 27

ACCEPTED MANUSCRIPT morphology and activity. Geomorphology, 73, 131-148. Gonga-Saholiariliva, N., Gunnell, Y., Petit, C., Mering, C., 2011. Techniques for quantifying the accuracy of gridded elevation models and for mapping uncertainty in digital terrain analysis.

IP

T

Progress in Physical Geography, 35, 739-764.

Gustafson, E. J., 1998. Quantifying landscape spatial pattern: what is the state of the art?.

SC R

Ecosystems, 1, 143-156.

Hamilton, S. K., Kellndorfer, J., Lehner, B., Tobler, M., 2007. Remote sensing of floodplain

NU

geomorphology as a surrogate for biodiversity in a tropical river system (Madre de Dios, Peru). Geomorphology, 89, 23-38.

MA

Hobson, R. D., 1972. Surface roughness in topography: a quantitative approach. In: Chorley, R. J. (Ed.), Spatial Analysis in Geomorphology. Methuen & Co., London, pp. 221-246.

D

Hoechstetter, S., Walz, U., Dang, L. H., Thinh, N. X., 2008. Effects of topography and surface

TE

roughness in analyses of landscape structure – a proposal to modify the existing set of landscape metrics. Landscape Online, 3, 1-14.

CE P

Holling, C. S., 1992. Cross-scale morphology, geometry, and dynamics of ecosystems. Ecological Monographs, 62, 447-502.

Hughes, F. M. R., 1990. The influence of flooding regimes on forest distribution and composition

AC

in the Tana River floodplain, Kenya. Journal of Applied Ecology, 27, 475-491. Hughes, F. M. R., 1997. Floodplain biogeomorphology. Progress in Physical Geography, 21, 501529. Iwahashi, J., Pike, R. J., 2007. Automated classifications of topography from DEMs by an unsupervised nested-means algorithm and a three-part geometric signature. Geomorphology, 86, 409-440. Iwahashi, J., Kamiya, I., Yamagishi, H., 2012. High-resolution DEMs in the study of rainfall- and earthquake-induced landslides: use of a variable window size method in digital terrain analysis. Geomorphology, 153–154, 29-38. Jasiewicz, J., Stepinski, T. F., 2013. Geomorphons — a pattern recognition approach to 28

ACCEPTED MANUSCRIPT classification and mapping of landforms. Geomorphology, 182, 147-156. Jenness, J. S., 2004. Calculating landscape surface area from digital elevation models. Wildlife

http://www.jennessent.com/arcgis/surface_area.htm

IP

Jenness, J. S., 2012. DEM Surface Tools. Jenness Enterprises, [Online]

T

Society Bulletin, 32, 829-839.

SC R

Jones, A. F., Brewer, P. A., Johnstone, E., Macklin, M. G., 2007. High-resolution interpretative geomorphological mapping of river valley environments using airborne LiDAR data. Earth

NU

Surface Processes and Landforms, 32, 1574-1592.

Jones, K. L., Poole, G. C., O'Daniel, S. J., Mertes, L. A. K., Stanford, J. A., 2008. Surface hydrology of

MA

low-relief landscapes: assessing surface water flow impedance using LIDAR-derived digital elevation models. Remote Sensing of Environment, 112, 4148-4158.

D

Junk, W. J., Bayley, P. B., Sparks, R. E., 1989. The flood pulse concept in river-floodplain systems.

TE

In: Dodge, D. P. (Ed), Proceedings of the International Large River Symposium. Canadian Special Publication of Fisheries and Aquatic Sciences, 106, pp. 110-127.

CE P

Kotliar, N. B., Wiens, J. A., 1990. Multiple scales of patchiness and patch structure: a hierarchical framework for the study of heterogeneity. Oikos, 59, 253-260. Kuffner, I. B., Brock, J. C., Grober-dunsmore, R., Bonito, V. E., Hickey, T. D., Wright, C. W., 2007.

AC

Relationships between reef fish communities and remotely sensed rugosity measurements in Biscayne National Park, Florida, USA. Environmental Biology of Fishes, 78, 71-82. Lane, S. N., 2000. The measurement of river channel morphology using digital photogrammetry. The Photogrammetric Record, 16, 937-961. Lane, S. N., Westaway, R. M., Murray Hicks, D., 2003. Estimation of erosion and deposition volumes in a large, gravel-bed, braided river using synoptic remote sensing. Earth Surface Processes and Landforms, 28, 249-271. Legendre, P., Fortin, M., 1989. Spatial pattern and ecological analysis. Vegetatio, 80, 107-138. Legleiter, C. J., 2014a. A geostatistical framework for quantifying the reach-scale spatial structure of river morphology: 1. Variogram models, related metrics, and relation to channel 29

ACCEPTED MANUSCRIPT form. Geomorphology, 205, 65-84. Legleiter, C. J., 2014b. A geostatistical framework for quantifying the reach-scale spatial structure of river morphology: 2. Application to restored and natural channels.

IP

T

Geomorphology, 205, 85-101.

Levin, S. A., 1992. The problem of pattern and scale in ecology. Ecology, 73, 1943-1943.

SC R

Levin, S. A., 1998. Ecosystems and the biosphere as complex adaptive systems. Ecosystems, 1, 431-436.

NU

Mark, D., Aronson, P., 1984. Scale-dependent fractal dimensions of topographic surfaces: an empirical investigation, with applications in geomorphology and computer mapping.

MA

Mathematical Geology, 16, 671-683.

Mark, D. M., 1975. Geomorphometric parameters: a review and evaluation. Geografiska Annaler.

D

Series A, Physical Geography, 57, 165-177.

TE

McCormick, M. I., 1994. Comparison of field methods for measuring surface topography and

87-96.

CE P

their associations with a tropical reef fish assemblage. Marine Ecology Progress Series, 112,

McGarigal, K., Cushman, S., Stafford, S., 2000. Multivariate Statistics for Wildlife and Ecology Research. Springer-Verlag, New York.

AC

McGarigal, K., Tagil, S., Cushman, S., 2009. Surface metrics: an alternative to patch metrics for the quantification of landscape structure. Landscape Ecology, 24, 433-450. Mertes, L. A. K., Daniel, D. L., Melack, J. M., Nelson, B., Martinelli, L. A., Forsberg, B. R., 1995. Spatial patterns of hydrology, geomorphology, and vegetation on the floodplain of the Amazon River in Brazil from a remote sensing perspective. Geomorphology, 13, 215-232. Milne, B. T., Turner, M. G., Wiens, J. A., Johnson, A. R., 1992. Interactions between the fractal geometry of landscapes and allometric herbivory. Theoretical Population Biology, 41, 337353. Moore, I. D., Grayson, R. B., Ladson, A. R., 1991. Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrological Processes, 5, 3-30. 30

ACCEPTED MANUSCRIPT Musick, H. B., Grover, H. D., 1990. Image textural measures as indices of landscape pattern. In: Turner, M. G., Gardner, R. H. (Eds.), Quantitative Methods in Landscape Ecology: The Analysis and Interpretation of Landscape Heterogeneity. Springer-Verlag, New York, pp. 77-103.

IP

T

Nanson, G. C., Beach, H. F., 1977. Forest succession and sedimentation on a meandering-river floodplain, northeast British Columbia, Canada. Journal of Biogeography, 4, 229-251.

SC R

Nanson, G. C., Croke, J. C., 1992. A genetic classification of floodplains. Geomorphology, 4, 459486.

NU

Nicholas, A. P., Mitchell, C. A., 2003. Numerical simulation of overbank processes in topographically complex floodplain environments. Hydrological Processes, 17, 727-746.

MA

Nogami, M., 1995. Geomorphometric measures for digital elevation models. Zeitschrift für Geomorphologie Supplementband 101, 53-67.

D

Phillips, J. D., 1999. Earth Surface Systems: Complexity, Order, and Scale. Blackwell Publishers,

TE

Massachusetts.

Phillips, J. D., 2006. Deterministic chaos and historical geomorphology: a review and look

CE P

forward. Geomorphology, 76, 109-121. Pike, R. J., 2000. Geomorphometry – diversity in quantitative surface analysis. Progress in Physical Geography, 24, 1-20.

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Pollock, M. M., Naiman, R. J., Hanley, T. A., 1998. Plant species richness in riparian wetlands – a test of biodiversity theory. Ecology, 79, 94-105. Rayburg, S., Thoms, M., Neave, M., 2009. A comparison of digital elevation models generated from different data sources. Geomorphology, 106, 261-270. Richards, K., Brasington, J., Hughes, F., 2002. Geomorphic dynamics of floodplains: ecological implications and a potential modelling strategy. Freshwater Biology, 47, 559-579. Riitters, K. H., O'Neill, R. V., Hunsaker, C. T., Wickham, J. D., Yankee, D. H., Timmins, S. P., Jones, K. B., Jackson, B. L., 1995. A factor analysis of landscape pattern and structure metrics. Landscape Ecology, 10, 23-39. Riley, S. J., DeGloria, S. D., Elliot, R., 1999. A terrain ruggedness index that quantifies topographic 31

ACCEPTED MANUSCRIPT heterogeneity. Intermountain Journal of Sciences, 5, 23-27. Robertson, G. P., 2008. GS+: Geostatistics for the Environmental Sciences. Gamma Design Software, Plainwell, MI.

IP

T

Rossi, R. E., Mulla, D. J., Journel, A. G., Eldon, H. F., 1992. Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs, 62, 277-314.

SC R

Salo, J., Kalliola, R., Häkkinen, I., Mäkinen, Y., Puhakka, M., Coley, P. D., 1986. River dynamics and the diversity of Amazon lowland forest. Nature, 322, 254-258.

NU

Scown, M. W., Thoms, M. C., De Jager, N. R., 2015. An index of floodplain surface complexity. Hydrology and Earth System Sciences Discussions, 12, 4507-4540.

MA

Scown, M. W., Thoms, M. C., De Jager, N. R., in press. Measuring spatial pattern in floodplains: a step towards understanding the complexity of floodplain ecosystems. In: Gilvear, D. J.,

D

Greenwood, M., Thoms, M., Wood, P. (Eds.), River Science: Research and Applications for the

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21st Century. John Wiley & Sons, UK.

Scown, M. W., Thoms, M. C., De Jager, N. R., in prep. The effects of survey technique and

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vegetation types on measuring floodplain topography from DEMs. Simon, H. A., 1962. The architecture of complexity. Proceedings of the American Philosophical Society, 106, 467-482.

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Sokal, R. R., 1979. Ecological parameters inferred from spatial correlograms. In:Patil, G. P., Rosenzweig, M. L. (Eds.), Contemporary quantitative ecology and related ecometrics. Statistical Ecology Series, vol. 12. International Co-operative Publishing House, Fairland, MD, pp. 167-196. Southwell, M., Thoms, M., 2006. A gradient or mosaic of patches? The textural character of insetflood plain surfaces along a dryland river system. In: Rowan, J. S., Duck, R. W., Werritty, A. (Eds.), Sediment Dynamics and the Hydromorphology of Fluvial Systems. IAHS Press, Wallingford, UK, pp. 487-495. Stanford, J. A., 1998. Rivers in the landscape: introduction to the special issue on riparian and groundwater ecology. Freshwater Biology, 40, 402-406. 32

ACCEPTED MANUSCRIPT Stanford, J. A., Lorang, M. S., Hauer, F. R., 2005. The shifting habitat mosaic of river ecosystems. Verhandlungen des Internationalen Verein Limnologie, 29, 123-136.

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opportunities and challenges. Geomorphology, 216, 295-312.

T

Tarolli, P., 2014. High-resolution topography for understanding Earth surface processes:

Tarolli, P., Sofia, G., Dalla Fontana, G., 2012. Geomorphic features extraction from high-

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resolution topography: landslide crowns and bank erosion. Natural Hazards, 61, 65-83. Thoms, M. C., 2003. Floodplain–river ecosystems: lateral connections and the implications of

NU

human interference. Geomorphology, 56, 335-349.

Thoms, M. C., Southwell, M., McGinness, H. M., 2005. Floodplain–river ecosystems:

MA

Fragmentation and water resources development. Geomorphology, 71, 126-138. Tokeshi, M., Arakaki, S., 2012. Habitat complexity in aquatic systems: fractals and beyond.

D

Hydrobiologia, 685, 27-47.

TE

Turner, M. G., O'Neill, R. V., Gardner, R. H., Milne, B. T., 1989. Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecology, 3, 153-162.

CE P

Turner, S. J., O'Neill, R. V., Conley, W., Conley, M. R., Humphries, H. C., 1990. Pattern and scale: statistics for landscape ecology. In: Turner, M. G., Gardner, R. H. (Eds.), Quantitative Methods in Landscape Ecology: The Analysis and Interpretation of Landscape Heterogeneity.

AC

Springer-Verlag, New York, pp. 17-49. UMESC, 2013. Light Detection And Ranging (LiDAR) Elevation Data. Upper Midwest Environmental Sciences Center, La Crosse, WI. [Online] http://www.umesc.usgs.gov/mapping/resource_mapping_ltrmp_lidar.html UMESC, 2015. Mississippi River – Pool 9. Digital LiDAR Derivatives. Upper Midwest Environmental Sciences Center, La Crosse, WI. [Online] http://www.umesc.usgs.gov/rivers/upper_mississippi/reach_1/pool_9/p9_gis_data.html#de m Walker, B. K., Jordan, L. K. B., Spieler, R. E., 2009. Relationship of reef fish assemblages and topographic complexity on southeastern Florida coral reef habitats. Journal of Coastal 33

ACCEPTED MANUSCRIPT Research, 25, 39-48. Ward, J. V., Tockner, K., Schiemer, F., 1999. Biodiversity of floodplain river ecosystems: ecotones and connectivity. Regulated Rivers: Research & Management, 15, 125-139.

IP

T

Ward, J. V., Malard, F., Tockner, K., 2002a. Landscape ecology: a framework for integrating pattern and process in river corridors. Landscape Ecology, 17, 35-45.

SC R

Ward, J. V., Tockner, K., Arscott, D. B., Claret, C., 2002b. Riverine landscape diversity. Freshwater Biology, 47, 517-539.

NU

Wedding, L. M., Friedlander, A. M., McGranaghan, M., Yost, R. S., Monaco, M. E., 2008. Using bathymetric lidar to define nearshore benthic habitat complexity: implications for

MA

management of reef fish assemblages in Hawaii. Remote Sensing of Environment, 112, 41594165.

D

Weaver, W., 1948. Science and complexity. American Scientist, 36, 536-546.

TE

Wheaton, J.M., Brasington, J., Darby, S.E., Sear, D., 2010. Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets. Earth Surface

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Processes and Landforms, 35, 136-156. Wiens, J. A., 1989. Spatial scaling in ecology. Functional Ecology, 3, 385-397. Wiens, J. A., Milne, B. T., 1989. Scaling of ‘landscapes’ in landscape ecology, or, landscape ecology

AC

from a beetle's perspective. Landscape Ecology, 3, 87-96. Wilson, M. F. J., O'Connell, B., Brown, C., Guinan, J. C., Grehan, A. J., 2007. Multiscale terrain analysis of multibeam bathymetry data for habitat mapping on the continental slope. Marine Geodesy, 30, 3-35. Wood, J. D., 1996. The Geomorphological Characterisation of Digital Elevation Models. Ph.D. Thesis, University of Leicester, UK. Woodcock, C. E., Strahler, A. H., 1987. The factor of scale in remote sensing. Remote Sensing of Environment, 21, 311-332. Wörman, A., Packman, A. I., Marklund, L., Harvey, J. W., Stone, S. H., 2007. Fractal topography and subsurface water flows from fluvial bedforms to the continental shield. Geophysical Research 34

ACCEPTED MANUSCRIPT Letters, 34, L07402. Wu, J., 2004. Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecology, 19, 125-138.

shift in ecology. The Quarterly Review of Biology, 8, 617-631.

IP

T

Wu, J., Loucks, O. L., 1995. From balance of nature to hierarchical patch dynamics: a paradigm

SC R

Wyrick, J. R., Senter, A. E., Pasternack, G. B., 2014. Revealing the natural complexity of fluvial morphology through 2D hydrodynamic delineation of river landforms. Geomorphology, 210,

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14-22.

Zawada, D. G., Brock, J. C., 2009. A multiscale analysis of coral reef topographic complexity using

MA

lidar-derived bathymetry. Journal of Coastal Research, 25, S6+. Zawada, D. G., Piniak, G. A., Hearn, C. J., 2010. Topographic complexity and roughness of a

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tropical benthic seascape. Geophysical Research Letters, 37, L14604.

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Zevenbergen, L. W., Thorne, C. R., 1987. Quantitative analysis of land surface topography. Earth Surface Processes and Landforms, 12, 47-56.

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Zhou, G., Lam, N. S. N., 2005. A comparison of fractal dimension estimators based on multiple surface generation algorithms. Computers & Geosciences, 31, 1260-1269. Zurlini, G., Riitters, K. H., Zaccarelli, N., Petrosillo, I., 2007. Patterns of disturbance at multiple

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scales in real and simulated landscapes. Landscape Ecology, 22, 705-721.

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Fig. 1. Regional location and topography of pool 9 of the Upper Mississippi River. Water extent shown is either permanently inundated or land below the 30-year mean low water level. (COLOUR IN PRINT AND WEB)

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Fig. 2. Distributions of surface metric values measured at 14 window sizes from 496 sample cells. (A) Range (m), (B) SD (m), (C) Skewness, (D) Kurtosis, (E) CV (m), (F) SDCURV (Radians/m), (G) Rugosity, (H) Vol:Area.

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Fig. 3. Surface metric values measured across four example window sizes for the upper part of pool 9. (COLOUR IN PRINT AND WEB) 38

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Fig. 4. Exponential isotropic model parameters and r2 for the relationship between Moran’s I and lag distance for each metric measured at each window size. 39

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Fig. 5. Eight group cluster solution showing group members over all scales and threshold between 50-100 m.

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Fig. 7. Scale groups within surface metrics and thresholds between groups.

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ACCEPTED MANUSCRIPT Table 1 Summary of selected surface metrics that have been used to measure topography and topographic complexity Indicates

Brief description

Selected references

Range

Magnitude of relief

Difference between the lowest and highest cells within a given extent.

Nogami (1995), Gadelmawla et al. (2002), Wilson et al. (2007), Walker et al. (2009)

Standard deviation (SD)

Variability about the mean

Standard deviation of surface heights. This metric is less sensitive than range as it accounts for all values not just the highest and lowest.

Coefficient of variation (CV)

Variability relative to the mean

The standard deviation of surface heights divided by the mean. This metric is useful for low-lying areas where standard deviation is relatively low but small elevation changes are ecologically important.

McCormick (1994), Pollock et al. (1998)

Peak and valley characteristics

The skewness of the distribution of surface heights. Positive skewness may indicate that the surface has high peaks or valleys filled in; negative skewness may indicate that peaks are flattened or deep valleys are present (McGarigal et al., 2009). In a geomorphological context, positive skewness may indicate sites of net deposition while negative skewness may indicate sites of net erosion.

Nogami (1995), Gadelmawla et al. (2002), McGarigal et al. (2009), Aberle et al. (2010)

Landscape dominance or evenness

The kurtosis of the distribution of surface heights. High kurtosis may indicate the presence of a dominant height or height range equivalent to the ‘landscape matrix’ upon which peaks and valleys are superimposed; low kurtosis may reflect a more smoothed surface in which heights are more evenly distributed (McGarigal et al., 2009). This metric is similar to Nogami’s (1995) power that measures the degree of concentration of elevations within a given extent.

Nogami (1995), Gadelmawla et al. (2002), McGarigal et al. (2009), Aberle et al. (2010)

Volume area ratio (Vol:Area)

Degree of dissection

The ratio between the volume of land above minimum elevation within a given extent and the volume created by multiplying the extent area with the range of surface heights within that extent. This metric is useful in determining the degree of dissection of a topographic surface as well as erosional and depositional stages of the landscape.

Nogami (1995)

Terrain ruggedness index (TRI)

Surface variability

Index of the absolute height difference between a cell and its eight neighbouring cells. This metric is similar to slope but indicates absolute not directional variability.

Riley et al. (1999), Wilson et al. (2007)

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Evans (1972), Mark (1975), Gadelmawla et al. (2002), Glenn et al. (2006), Hoechstetter et al. (2008), McGarigal et al. (2009), Aberle et al. (2010)

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Kurtosis

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Skewness

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Surface metric

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Table 1 cont. McCormick (1994), Everson and Boucher (1998), McGarigal et al. (2009), Tarolli et al. (2012)

Surface rougness

The ratio between the actual surface area and that of a flat plane occupying the same extent. This indicates surface roughness or convolutedness. Actual surface area is also important in many ecosystems when competition for space is a key structuring process and may be particularly relevant for densely vegetated floodplains such as that of the Amazon (Salo et al., 1986).

Hobson (1972), Nogami (1995), Jenness (2004), Kuffner et al. (2007), Wilson et al. (2007), Wedding et al. (2008), McGarigal et al. (2009), Walker et al. (2009), Friedman et al. (2012)

Texture

Density of pits and peaks

The density of pits and peaks across the surface. This metric is calculated as the number of pits and peaks within a given radius of each cell and first requires the identification of pits and peaks. This metric is similar to Hobson’s (1972) bump frequency distribution that incorporates the number of peaks within an area and their magnitude.

Hobson (1972), Iwahashi and Pike (2007)

Fractal dimension

Geometric complexity of the surface

The fractal dimension of a surface can range between 2 and 3. A surface with a fractal dimension of 2 is a flat plane, while a surface with a fractal dimension approaching 3 is so convoluted that it almost fills the entire volume of its extent. There are numerous techniques for measuring the fractal dimension of a surface, each with varying accuracy (Zhou and Lam, 2005).

Clarke (1986), Dubuc et al. (1989), Moore et al. (1991), Wood (1996), Zhou and Lam (2005), Wilson et al. (2007), Zawada and Brock (2009), Zawada et al. (2010)

Entropy

Diversity and variability in surface heights

The amount of uncertainty associated with predicting the height of a cell selected at random from all cells within the surface. Shannon entropy is likely the most appropriate calculation of entropy for topographical applications; however, other probability-related metrics are also available (Musick and Grover, 1990).

Musick and Grover (1990), Nogami (1995), Wood (1996), Phillips (2006)

Surface variogram

Spatial autocorrelation, spatial lags

The variogram of a topographic surface plots the change in variance of sampled surface heights against distance between sample locations. This metric can be calculated along uni- or omni-directional transects or within an area and is quantified by various parameters of the variogram plot (Legleiter, 2014a). Similar metrics have been referred to as divergence index and variance staircase.

Mark and Aronson (1984), Turner et al. (1990), Mertes et al. (1995), Wood (1996), Lane (2000), Dorner et al. (2002), Phillips (2006), Wilson et al. (2007), Legleiter (2014a)

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Rugosity

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Convolutedness of the surface

The standard deviation of curvature across a surface. This metric may be useful in determining how variable curvature is across a surface and subsequently how convoluted or ‘rough’ that surface is. Surface roughness creates a diverse array of hydraulic and geomorphic conditions in floodplains. Standard deviations of slope and aspect have also been used.

Standard deviation of curvature (SDCURV)

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Table 2 Routines and equations used to calculate the eight surface metrics in ArcGIS 10.0 Metric

Calculation in ArcGIS 10.0

Range

Where:

Where:

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Kurtosis

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is the output grid from standard deviation

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Skewness

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SD

Rugosity

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Where:

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SDCURV

Where: is the output grid from standard deviation

AC

CV

D

is the output grid from standard deviation is the numerator from the Skewness equation

Where:

Where:

Vol:Area is the total number of grid cells within the focal neighbourhood (NoData cells included with value = 0) is range

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Table 3 Log-log linear regression results for F

p

d.f.

r2

Slope

y-intercept

Range

1063.2

0.000

1,12

0.989

0.452

-1.758

SD

1527.5

0.000

1,12

0.992

0.357

-1.577

Skewness

28.2

0.000

1,12

0.702

0.028

-0.384

Kurtosis

5.6

0.036

1,12

0.317*

0.041

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against window radius; * r2 < 0.7

CV

1895.1

0.000

1,12

0.994

0.331

SDCURV

471.8

0.000

1,12

0.975

0.092

Rugosity

89.8

0.000

1,12

0.882

Vol:Area

73.2

0.000

1,12

0.859

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IP

-1.257 -1.347 -0.913 -0.931

-0.135

-0.070

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TE

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0.032

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ACCEPTED MANUSCRIPT Table 4 Log-log linear regression results for significant at p = 0.05, * r2 < 0.7

against window radius; **not

p

d.f.

r2

Slope

y-intercept

Range

157.3

0.000

1,12

0.929

0.736

-3.896

SD

76.8

0.000

1,12

0.865

0.380

Skewness

2.1

0.168**

1,12

0.152*

-0.093

Kurtosis

4.1

0.065**

1,12

0.256*

0.307

CV

5.5

0.037

1,12

0.315*

SDCURV

184.3

0.000

1,12

0.939

Rugosity

1201.7

0.000

1,12

0.990

Vol:Area

39.3

0.000

1,12

0.766

T

F

SC R

IP

-3.011 -2.044 -3.155 -1.806

-0.351

-1.388

-0.601

-1.300

NU

-0.036

-1.712

AC

CE P

TE

D

MA

-0.070

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