Topological structures of river networks and their regional‐scale controls: A multivariate classification approach

Landscape evolution is governed by the interplay of uplift, climate, erosion, and the discontinuous pattern of sediment transfer from the proximal source of erosion to distal sedimentary sinks. The transfer of sediment through the catchment system is often referred to as a cascade, the pattern of which is modulated by the interaction of key network characteristics such as the distribution of transport capacity and resultant zones of sediment storage. An understanding of how sediment production is modulated through river networks with different topological structures at the associated timescales has remained elusive but presents significant implications for the knowledge of river response to disturbance events, and floodplain asset management.


Introduction
The processes that control the flux and storage of sediment have been widely researched at a variety of spatial and temporal scales, however an understanding of how these processes operate across entire drainage networks remains elusive. Previous research has focused on the transfer of individual grains, the movement of sediment pulses through a reach (e.g. Lisle et al., 2001;James, 2010), and the impact of intersecting tributaries (e.g. Knighton, 1980;Rice, 1998), with relatively few aiming to develop our understanding at the catchment scale. Understanding the discontinuous pattern of sediment routing through river networks is key to estimating spatial and temporal responses to significant disturbance events (Benda and Dunne, 1997b;Lisle et al., 2001). Extreme disturbance events can result in landslide dams (e.g. Costa and Schuster, 1988;Hewitt, 2002;Korup, 2012;Kaiser et al., 2017), significant aggradation leading to channel avulsion (Miller and Benda, 2000;e.g. Clague et al., 2003;Korup, 2005), habitat degradation and loss of geo-ecological heterogeneity of the valley floor (Nakamura et al., 2000;e.g. Geertsema et al., 2006;James, 2010), and sediment contamination and reductions in water quality (Lin et al., 2008;e.g. Geertsema et al., 2009). The propagation of effects downstream presents a secondary risk of bank erosion and flooding, often causing damage to local infrastructure in low-lying areas (Davies and Scott, 1997; e.g. Anthony and Julian, 1999;Geertsema et al., 2006). As such, it is vital to address the role that river systems play in controlling the episodic behaviour of sediment transfer, and thus the impact of individual and coincident sediment pulses.
At the catchment scale, network configuration becomes a significant control on the modulation of sediment flux in river systems (Benda and Dunne, 1997a,b;Benda et al., 2004a,b;Benda, 2008;Ferguson and Hoey, 2008). This is particularly evident at confluence zones, in which the morphology reflects the relative flow and sediment inputs from the converging tributaries, as well as the episodic nature of sediment supply (Knighton, 1980;Benda and Dunne, 1997a;Rice, 1998;Benda, 2008). Each reach in a network converges with another of variable scale, forcing an interaction between regimes with different characteristics and magnitudes. Zones of significant sediment convergence and aggradation are interspersed with reaches of efficient routing to produce a pattern of discontinuous downstream transport, a pattern controlled by the configuration of effective and ineffective tributaries (Rice, 1998). Recent research in this area has centred on geomorphic 'hotspots' as key nodes in the river network predisposed to changes in storage and geomorphic change Foufoula-Georgiou, 2014, 2015;Walley et al., 2018).
Over much longer timescales, the same processes which control regional sediment transfer also determine the topology of river networks at the catchment scale. Tectonic and climatic settings establish topology during initial mountain building, and continue to evolve networks over time (Hovius et al., 1998;Castelltort et al., 2012). Complex relationships exist between regional setting, topology, and sediment regimes, and the spatial and temporal scales over which these processes occur make them difficult to understand or quantify. The purpose of this study is to better understand the variation in topology across a range of river networks, and how this relates to regional setting/processes. Networks are classified into topological 'types' within the South Island of New Zealand, identifying and defining the range of topology across the region. The resulting classes represent a 'snapshot' of regional topology, allowing insights into the relationship between regional setting and network configuration, and establishing representative catchments for future regional-scale studies.

Regional Setting
The South Island of New Zealand is a highly dynamic landscape, in which active tectonics, weak lithology, high rates of rainfall, and alpine processes at altitude combine to produce some of the highest rates of sediment production in the world (Milliman and Meade, 1983). The Southern Alps dominate the landscape, running the length of the island and rising to over 3000m a.s.l. at multiple locations ( Figure 1a) (Tippett and Kamp, 1995;Cook et al., 2014). The ridgeline is referred to as the 'Main Divide', separating Westland from the Canterbury Plains, and experiences rapid tectonic uplift (8-10mm year À1 ) Kamp, 1993, 1995;Chamberlain et al., 1999) and extremely high precipitation (14myear À1 ) (Henderson and Thompson, 1999). The Southern Alps have a history of extensive glaciation, leading to the development of large, overwidened parabolic valleys and widespread alluvial megafans in the piedmont plains, exemplified by the Canterbury Plains. The dramatic topography of the South Island generates substantial diversity in the region's fluvial environments, particularly between the east and west coasts.
The landscape of New Zealand is intrinsically linked to deformation along the Australia-Pacific plate boundary ( Figure 1a). The westward subduction of the Pacific plate beneath the Australian plate off the east coast of the North Island, and the eastward subduction of the Australian plate beneath the Pacific plate off the south coast of the South Island, are linked by an oblique compressional zone of active continent-continent convergence (Tippett and Kamp, 1993;Davey et al., 1998;Chamberlain et al., 1999;Sutherland et al., 2000;Craw et al., 2013;Duvall et al., 2019). This section of the plate boundary, the Alpine Fault, runs the length of the South Island and has resulted in the uplift of the Southern Alps (Figure 1b). At the northern end of the Alpine Fault, where plate collision transitions into subduction, the Marlborough Fault System (MFS) is characterized by a set of predominantly strike-slip faults splaying north-eastward (Figure 1a), which have also caused the uplift of linear mountain ranges (Craw et al., 2013;Duvall et al., 2019).
The Alpine Fault also divides the basement geology of the island into the Western and Eastern Provinces ( Figure 1b). The Western Province comprises quartz-rich metamorphic and intrusive igneous rocks of Paleozoic-Mesozoic age (Buller-Takaka Terrane), intruded by Median Batholith granites in the Devonian and Early Cretaceous (Davey et al., 1998;Mortimer, 2004;Cox and Barrel, 2007;Shulmeister et al., 2009). The Eastern Province comprises successive terranes of largely low-grade metasediments from the Permian-Jurassic period (Figure 1b), which are being upthrust along the Alpine Fault (Davey et al., 1998;Shulmeister et al., 2009). Rapid uplift of marine sediments close to the fault has formed a band of highly metamorphosed schists (Grapes and Watanabe, 1992;Shulmeister et al., 2009), the grade decreasing eastward to relatively unaltered greywacke within 15km of the fault (Davey Y. WALLEY ET AL. et al., 1998;Shulmeister et al., 2009). A 460km offset of the terranes along the Alpine Fault (Figure 1b), and the rapid uplift of the Southern Alps mountain range, reflects the highly active nature of the boundary (Tippett and Kamp, 1995;Chamberlain et al., 1999;Sutherland et al., 2000). Numerous branching faults cross the entirety of the South Island (Figure 1a), and tectonics have consequently played a significant part in the shaping of the landscape Kamp, 1993, 1995;Sutherland et al., 2000).
The dominant topography of the Southern Alps plays a significant role in the pattern of regional climates across the South Island. The mountain range is oriented near-perpendicular to the prevailing westerly winds coming off the Tasman Sea, forcing strong orographic rainfall and a subsequent extensive rain shadow (Figure 2a) (Griffiths and McSaveney, 1983;Chamberlain et al., 1999;Sturman and Wanner, 2001;Craw et al., 2013). The forcing of rapidly rising air over the Alps causes an average of 12m of rainfall a year on the west coast, compared to less than 1myear À1 on the east coast (Griffiths and McSaveney, 1983;Craw et al., 2013). The rain shadow is particularly pronounced in inland Central Otago, as easterly and southerly weather systems can increase rainfall along the eastern coastline (Craw et al., 2013). The rainfall gradient can be exacerbated by the El Niño Southern Oscillation (ENSO), particularly in winter months (Golledge et al., 2012).
The Last Glacial Maximum (LGM) in New Zealand occurred approximately 28000-18000years BP (Alloway et al., 2007;Golledge et al., 2012), and was characterized by cooling of >6°C, a fall of typically 25% in annual precipitation (Golledge et al., 2012). The Southern Alps during this period were covered in an elongate ice field, extending to sea level at points along the west coast (Golledge et al., 2012). Rapid warming during the Late Glacial (14000-10000years BP) led to glacial retreat, which continued into the early Holocene, until approximately 6000years BP (Leckie, 2003). A resurgence of small glacial events at around 5000years BP occurred before the modern climate was established by 2500years BP (Salinger and McGlone, 1990). The most recent maximum extension of glaciers in the Southern Alps was in the Little Ice Age (LIA) in the 17th to 19th centuries (Chinn et al., 2005;Dykes and Brook, 2010). This was followed by a warming period between 1910 and 1970, in which glaciers retreated (Dykes and Brook, 2010). Historically, the glaciation of the Southern Alps has exacerbated erosion in the region and resulted in significant volumes of sediment transported downstream (Wilson, 1989;Leckie, 2003;Rowan et al., 2012). The LGM was associated with lower temperatures and precipitation, decreased vegetation cover, and consequent erosion in the headwaters and fluvial aggradation (Leckie, 2003). This was particularly significant on the east coast, as glacial outwash from the major rivers formed wide valley floors, braided river morphology, and megafans, eventually coalescing to form the Canterbury Plains (Leckie, 2003;Rowan et al., 2012).
Patterns of land use are influenced by a number of factors, including geology, topography climate, and access to water, as well as economic and societal pressures (Journeaux et al., 2017). These factors are evident in the bands of land use identifiable in Figure 2b, which correspond to patterns of geology, relief, and rainfall. The steep slopes on the west coast are largely covered by indigenous forest, with pockets of grassland along flat valley floors. Pockets of exotic forest are also evident, indicating forestry activity in the region. The highest altitudes are mostly untouched by human activity, and are covered in permanent snow and ice, and exposed sediments. The Eastern High Country is a mixture of grassland and tussock grassland, typically used for extensive agriculture, compared to the gentle gradients on the east coast, which are largely grassland and cropland, with pockets of exotic forest. Similar regions were identified by Harding and Winterbourn (1997) in a classification of 'ecoregions' based on climate, rainfall, relief, vegetation, soils, and geology. The multivariate comparison identified two primary clusters: native forest and high rainfall on the west coast, and tussock grassland, pasture, and lower rainfall on the east coast. The classification also identifies eastern regions as being impacted more by human modification compared to the west coast.
Regional controls produce distinctly different fluvial environments across the South Island. Particularly pronounced is the ; the orographic rainfall gradient between the west and east coasts is evident, as well as the rainfall shadow in inland South Canterbury/Otago. (b) Land cover classification (Landcare, 2015); the Southern Alps dominate the landscape such that patterns of land use correspond to those of geology, relief, and rainfall. [Colour figure can be viewed at wileyonlinelibrary.com] 2871 TOPOLOGICAL STRUCTURES OF RIVER NETWORKS divide between the west and east coasts, in which the Alpine Fault, and consequently the Southern Alps, force strong contrasts in lithology, topography, and climate. The western flanks of the Southern Alps descend steeply from the main divide, with glacial moraines creating interfluves between catchments and outwash plains extending to the coast (Shulmeister et al., 2009). Rivers on these slopes are steeper, with coarser gravel beds which occupy gorges for much of their extent (Griffiths, 1979). The catchments are shorter, more closely spaced, and oriented sub-perpendicular to the Alpine Fault, compared to the long, generally oblique catchments to the east (Castelltort et al., 2012). Rivers on the eastern slopes of the Southern Alps descend from steep eastern headwaters into highlands of intermontane basins and extensive piedmont plains. A distinct, although lesser, contrast can be defined in the region of South Canterbury and Otago, in which the pronounced rain shadow effects and anthropogenic influence have significantly impacted sedimentary regimes. This region is also underlain by Otago Schist, which is weaker than the surrounding greywacke, generating complex topography and concentrating drainage into the Clutha River catchment (Craw et al., 2012). The transition of subduction to convergence within the MFS ( Figure 1a) has produced another fluvial environment, characterized by long, linear valleys and drainage anomalies, driven by uplift, deformation, and river capture (Duvall et al., 2019). These distinct regional settings produce variations in the hydraulic and sedimentary regimes of each area. In addition, agriculture, forestry, and various forms of mining are key contributors of anthropogenic sediment, the extent of which depends on the methods and controls used (Ryan, 1991). Extensive hydraulic dam networks, particularly in South Canterbury and Otago, are also potential contributors to anthropogenic sedimentary regimes, although many are constructed downstream of lakes and reservoirs, limiting their impact on sediment regimes (Jowett, 1984). Very few studies have been conducted or published on the specific sources or impacts of anthropogenic sediment in New Zealand, and their role in the evolution of existing catchments is therefore not well understood (Ryan, 1991;Harding and Boothroyd, 2004).

Topological Classification
Network extraction Catchment boundaries for the entire South Island were extracted from a mosaicked 8m digital elevation model (DEM) originally produced from 1:50000 topographic data (Geographx, 2012). Polygons in the centre of the island were clipped to the piedmont of the Southern Alps to remove lowlands in which clear drainage networks were not identifiable. River networks in catchments with an area larger than 300 km 2 were extracted in MATLAB using the TopoToolbox software (Schwanghart and Kuhn, 2010;Schwanghart and Scherler, 2014) and the method outlined by Tarboton et al. (1991Tarboton et al. ( , 1992. The definition of first-order reaches and hillslope units is problematic, particularly in disturbed landscapes where small channels, rills, and gully systems can extend beyond the confines of the valley network (Montgomery and Dietrich, 1994). This is further exacerbated at a regional scale, in which area-only thresholds produce variable accuracy between different catchments. Figure 3 outlines Tarboton's method for extracting river networks.
The DEM was initially processed by filling sinks and establishing flow direction within the catchment. A Peucker-Douglas skeleton was generated based on the method of Peucker and Douglas (1975), creating a skeleton of the stream network based on grid cells with upward curvature. This skeleton was applied to a contributing area raster as a weighted input, and the resulting raster used to calculate a stream drop analysis based on the work of Broscoe (1959). The stream drop analysis calculates the statistical significance of a number of accumulation threshold values, from which the optimal value was identified as the most statistically significant difference between the drop in elevation of first-order streams compared to those of higher order (Tarboton et al., 1991(Tarboton et al., , 1992. Stream drop thresholds were calculated for each of the 59 catchments, and the optimal values used to extract a link-based vector network from the weighted contributing area raster. A numerical connectivity structure was generated for each network, in which each link is assigned an ID and connected to the IDs of the two upstream links and the link immediately downstream.
Topological metrics A number of methods exist for characterizing the topology of river networks, which typically employ a number of metrics to capture the spatial distribution of links (e.g. Benda et al., 2004b;Zanardo et al., 2013;Heasley et al., 2019). Previous studies have focused on one of these variables (Strahler, 1957;e.g. Shreve, 1967;Zanardo et al., 2013), or encompassed several within conceptual frameworks (e.g. Benda et al., 2004b). More recently, studies have compared a number of quantitative metrics within several catchments, relating the internal structure to patterns of hydrology and FIGURE 3. Method for extracting the stream networks from the DEM. The method is described by Tarboton et al. (1991Tarboton et al. ( , 1992 and primarily involves a Peucker-Douglas skeleton of upwardly curving grid cells, and a stream drop analysis to define network channel heads.
sediment flux (Sklar et al., 2016;Heasley et al., 2019). Classifying the topological structures of the South Island region, however, required the identification of a set of key topological metrics which encompassed the size, shape, and internal branching structures, as well as enabled the calculation of a single representative value for each catchment (Table 1). Four common variables of network topology were initially identified as Strahler order, Shreve magnitude, drainage density, and confluence angle (Strahler, 1957;Shreve, 1967;Benda et al., 2004b). Strahler order in particular is frequently used in reach-and catchment-scale applications as a measure of network magnitude, and drainage density is often calculated to establish the level of landscape dissection (Benda et al., 2004b;Heasley et al., 2019). Values for Strahler order and Shreve magnitude were taken from the outlet, and drainage density was calculated for each network as the total network length divided by catchment area. The values of Shreve magnitude were later removed from the classification, as a Spearman's correlation matrix did not identify the variable as statistically significant. Confluence angles were calculated for each junction in the network following the method outlined by Seybold et al. (2017), and the mean value of all confluences taken as a representative value for each catchment.
The four identified variables establish the magnitude of network structure, but do not account for the spatial arrangement of links or the internal topography of each catchment. A value of network branching was thus calculated using Tokunaga's (1978) methodology, further developed by Tarboton (1996), Cui et al. (1999), Zanardo et al. (2013), Danesh-Yazdi et al. (2017), and Walley et al. (2018). The c value (also referred to as K in other literature) is a measure of change in the average degree channel bifurcation between all Strahler orders, such that links with 'self-similar' branching   upstream (e.g. dendritic patterns) exhibit smaller values than those with long mainstems bounded by small tributaries (e.g. trellis patterns). A full description of this method is outlined in Walley et al. (2018). Two final values were calculated using catchment width and elevation, in order to capture the internal topography. Similar to the method of Heasley et al. (2019), each catchment was divided into 20 bands representing 5% of the total flow distance to the outlet. The number of links (by midpoint) and the mean elevation were calculated in each band, and the ratio between the 16th and 84th percentile calculated as representative values of catchment shape.

Classification
Principal component analysis (PCA) was used to explore topological relationships between the selected variables and reduce dimensionality. Two significant components were identified from a Spearman's correlation matrix, with eigenvalues greater than 1 and each representing more than 20% of the variance (Figure 4a). The loading values for each of the original parameter values are included in Table 1, and their correlations with the two principal components are displayed in Figure 4b.
The two principal components were used to perform an agglomerative hierarchical clustering analysis (AHC), using the Euclidean dissimilarity distance measure. Results obtained using five different linkage methods (complete, flexible, weighted, unweighted, and Ward's) were compared, and clusters established based on membership consistency (Figure 5a). The groupings were validated using the k-means clustering method as a comparison (Figure 5b), which produced very similar clusters to the AHC method with the exception of cluster D. This disparity was attributed to the relatively small size of cluster D, and the tendency of the k-means method to produce spherical clusters of similar sizes due to the use of Voronoi cells in their calculation. Removing the three observations in cluster D thus furthers the validation of the other classes (Figure 5c), although given that there is no reason to assume topologically comparable networks would occur in similar numbers across a given landscape, these networks were not excluded from further analysis. Kruskal-Wallis with Dunn's multiple comparison tests was thus performed on the AHC clusters, revealing statistically significant differences (p <0.0001). Box-and-whisker plots of factor scores along the two primary components also show significantly distinct groupings, in which clusters with overlapping score ranges in one principal component do not indicate any overlap in the second ( Figure 6).

Topological 'types'
The five clusters of catchments thus identify 'types' of networks based on their topological characteristics. Each class represents a subset of the original parameters (Table 2), as identified by the loading value for each primary component (Figure 4b). The first component (PC1) is linked to Strahler order, network branching (c value), and width ratios, and thus was interpreted to represent variance in network structure. The second component (PC2) is linked to elevation ratios, drainage density, and confluence angles, and was interpreted to represent variance in topography. Catchments in classes A-E therefore exhibit  decreasing size and increasing values of network branching, with a shift from catchment shapes with wide headwaters to those of more consistent widths (Table 2; Figure 4b). Along PC2, drainage density and elevation difference are greatest in classes B and E, while class D includes networks with the largest confluence angles. The greatest contrast in topological 'types' is therefore evident between diagonally opposite classes (i.e. A and E, B and D) (Figure 5a; Table 2). Catchments in class A tend to be larger, with much of the catchment area occurring furthest from the outlet and narrowing with distance. Elevation differences and drainage density are moderate, with relatively large catchment angles. In contrast, class E catchments are much steeper, smaller, and have a consistent width with distance from the outlet. The networks are more structured than for class A, and contain smaller confluence angles. Class B is similar to class A in that the networks are larger and less structured, with a mix of catchments exhibiting wide headwaters and consistent widths. The topology is closer to class E along the secondary component, exhibiting steeper elevation differences, high drainage density, and smaller confluence angles. Finally, class D shares greater similarity with class E along component 1

Internal Network Structure
To identify the type of networks in each class, it is necessary to explore properties not included in the original parameters. The PCA/AHC method necessarily reduces variables of topology to single values, and thus does not account for internal variability within each catchment. The exception to this is the c value, the calculation of which is designed to represent the cumulative magnitude of upstream network branching (Tokunaga, 1978;Walley et al., 2018). Sklar et al. (2016) consider catchments as a collection of point locations, in which each point can be attributed individual values for a variety of variables. Their methods of displaying elevation, travel distance, and slope variables are employed in order to better understand the internal topological variability within each catchment, and within the identified classes. In order to clearly draw comparisons between each of the classes, the objects closest to the centroid of each cluster were identified as representative of network topologies in that group. The catchments are presented in order through Figures 7, 8, and 9, such that panels a-e in each figure correspond to the associated class.
Network maps (Figures 7a-e) and width functions (Figures 7f-j) exhibit the Strahler magnitudes and planform structure for each of the central objects. Notably, classes A and B contain catchments with more rounded shapes, compared to the elongate shapes in classes D and E, which corresponds to the trends in the width functions. For example, the distribution for the Arahura River (Figure 7j) is symmetrical with a low peak, reflecting the rectangular shape of the catchment. In contrast, most of the area in the Motueka River (Figure 7f) occurs in the upper half of the catchment, reflecting the narrowing towards the outlet. These differences in planform structure reflect the distribution of catchments along PC1 (Figure 4b), and thus correspond to c values for each catchment, which are much larger in classes D and E. Network maps also display a shift in scale corresponding to the Strahler value, as catchments in classes A and B tend to be larger than those in classes D and E. Note that for each variable, catchments in class C tend to reflect a mixture of characteristics of the other classes. Figure 7 also includes hypsometry functions, generated in the same manner as the width functions. In contrast to the network structure variables, elevation varies along PC2 (Figure 4b), thus classes B and E exhibit very similar trends in which most of the catchment area occurs at low elevations. Catchment area in classes A and D subsequently occurs at low to mid-elevations in relatively normal distributions. To further explore patterns of topography, bivariate frequency distributions of elevation and travel distance for every point in each catchment (point area = 50km 2 ) were generated in the manner of Sklar et al. (2016) (Figures 8a-j). Values of point density were additionally mapped onto the original catchment grid to explore the spatial distribution of high-density areas (Figures 8k-o). The areas of highest density in classes B and E occur along the valley floor in areas of minimal elevation change, corresponding to the trends observed in the hypsometry functions. Of note, however, is that these flat areas in class B tend to occur towards the centre of the catchment, while they are closer to the outlets in class E. In contrast, class A catchments exhibit the highest point density along tendrils which curve away from the valley floor, indicating that elevation increases at a similar rate with distance from the outlet in multiple parts of the catchment. As can be observed in the map of the Motueka catchment (Figure 8k), these patterns indicate a topographic symmetry of the valley floor upstream of certain outlets, in which elevation increases with travel distance at a similar rate along the upstream links.
The topographic patterns observed in the bivariate frequency distributions are reinforced by the spatial distributions of mean slope, calculated as the ratio of elevation and travel distance at every point in each catchment (Figures 9f-j). Common values appear as linear trends through the distributions of travel distance and elevation (Figures 9a-e) and as contours when mapped onto the original catchment grid (Figures 9k-o) (Sklar et al., 2016). Classes B and E both include catchments with very steep (e.g. Arahura River) and very gentle (e.g. Tokomairiro River) gradients. The former trend occurs in catchments located on the west coast of the South Island, where the topography of the Southern Alps forces very steep changes in elevation over relatively short distances. The histograms reflect the greater range in slopes occurring at lower frequencies (Figure 9j), which also tend to include a high-frequency bar at a very low slope value. In contrast, the catchments with more gentle gradients tend to produce left-skewed histograms, many of which have only a few very high-frequency bars at low slopes (Figure 9g). These catchments tend to be found on the east and south coasts of the South Island, where they occupy a much larger land area than those on the west coast or do not extend to the main divide of the Southern Alps. Classes A and C include catchments with low to moderate elevation change, occurring over greater distances than classes B and E. Histograms are more normally distributed, with moderate frequency peaks (Figure 9f). A few distributions extend into greater slopes; these tend to occur where relatively high elevations occur towards the catchment outlet (Figure 9h). Note that no trend was identifiable in class D for mean slope, given the small size of the group. Contour maps (Figures 9k-o) reflect the trends in topography observed in the bivariate frequency distributions (Figure 8). Classes B and E include areas of very flat topography, occurring  (Figure 9l). Class A exhibits steady elevation-distance relationship in multiple links (Figure 9k). These maps additionally highlight the network structure trends, in which catchments in classes A and B contain dissected networks, while those in classes D and E exhibit prominent central mainstems.

Evaluation
The relationship between each class and the principal components is summarized in Figure 10. Class A contains large, wide catchments with dissected network structures, situated on low to moderate slopes in which elevation tends to increase constantly with distance from the outlet. Class B also contains catchments with dissected network structures, however they are more elongate than those in class A, including a mixture of sizes and very steep and gently sloped gradients. These catchments tend to include areas of very flat topography towards the middle reaches. Class C depicts no clear trend, instead the networks reflect a mixture of topologies, with elements from the other classes. Catchments in class D exhibit significant structural influence, with smaller, elongate shapes on moderately steep slopes, and clear mainstem-dominated networks. Class E catchments are similar to class D but occur across steeply sloping gradients and tend to have large flat areas of topography at the outlet.
Patterns of topology in the South Island are determined by a complex interplay of tectonic, climatic, and erosional evolution, potentially dating back to before the initial uplift of the Southern Alps (Castelltort and Simpson, 2006;Willett et al., 2014;Viaplana-Muzas et al., 2015). Studies have suggested that drainage networks in mountain ranges are established during initial collision and uplift (Hovius et al., 1998;Castelltort and Simpson, 2006;Viaplana-Muzas et al., 2015), but the influence of regional setting on subsequent evolution is relatively unknown. Rather than analysing the relationship of a single network with its regional controls, the identification of topological 'types' enables an analysis of how elements of regional setting are distributed across groups of networks with similar characteristics. South Island datasets of estimated uplift, average annual rainfall, and suspended sediment yield were thus used to represent regional setting, and box-and-whisker plots were generated from the mean values from each catchment (Figure 11).
Active mountain regions like the Southern Alps exhibit ongoing tectonic movement, driving reorganization of established river networks through river capture, catastrophic landsliding, and passive deformation (Hovius et al., 1998;Castelltort et al., 2012). Uplift processes thus strongly influence the patterns of drainage networks in the region, as evidenced by Figure 11a. Classes A to E exhibit ranges of uplift rates and stepped increases in mean value, which is similar in classes A and B, C and D, and much greater in class E. This pattern is driven by the multitude of small class E catchments along the west coast of the South Island (Figure 12a), which are intersected by the underlying Alpine Fault (Figure 12b). The high rates of uplift in class E (Figure 11a) thus suggest a correlation between tectonics and topological network structure ( Figure 10), with mainstem-dominated networks more strongly influenced by tectonic activity.
The Alpine Fault is an oblique-dextral fault in which the Pacific plate in the east is ramping up against the western Australian plate (Davey et al., 1998;Sutherland et al., 2000;Duvall et al., 2019). The western flanks of the Southern Alps are consequently much narrower than those to the east, limiting the available space for headwater extension and network growth, and giving rise to multiple small networks of classes B and E spanning from the Main Divide to the coast (Figure 11a). The size of these catchments, and the offset of the Alpine Fault from the Main Divide, cause entire networks to be in close proximity to the rapid uplift along the alpine fault, driving dynamic reorganization in response to tectonic strain through river capture and catastrophic landsliding (Castelltort et al., 2012). It is also likely that the multitude of faults across the South Island may impose network orientation along weak structures Castelltort et al., 2012;Kirby, 2012), which is evident in the MFS (Figure 1a), which contains a number of mainstem-dominated networks aligned with underlying faults (Duvall et al., 2019).
Uplift along the Alpine Fault additionally gives rise to the Southern Alps, which transect the prevailing westerly winds and generate a strong orographic rainfall gradient across the South Island (Figure 2a). This rainfall gradient is reflected in the distribution of rainfall across the topological classes (Figure 11b), in which class E catchments on the west coast are significantly wetter than those in other classes. The distribution of rainfall is similar to that of specific suspended sediment yield (Figure 11c), reflecting the correlation between sediment transport and discharge. Both graphs indicate higher values in class E, driven by the prevalence of small, steep west coast catchments, underlain by weak geology crushed by the active tectonics.
In contrast, the other classes exhibit relatively low mean values of rainfall and specific suspended sediment yield, reflecting the relatively dry environments across the rest of the South Island (Figure 2a). Class A exhibits a relatively narrow range of low rainfall values, which reflects the prevalence of these catchments on the eastern and northern coasts of the South Island (Figure 12a). Combined with the relatively weak geology and availability of space due to the position of the Alpine Fault, these networks have likely grown through river capture and mass movement, evidenced by their relatively large sizes and wide headwater networks. This is particularly evident in the Clutha River, the largest catchment which occupies the area underlain by Otago Schist (Figure 1b). It is possible that the size of the catchment has been exacerbated by the exceptionally weak geology and pronounced rain shadow. There is therefore no apparent connection between climate and rainfall as established by Seybold et al. (2017), who indicated that smaller confluence angles occur in more arid environments and increase with humidity. In contrast, the catchments in classes B and E contain the smallest confluence angles (Table 2) but exhibit distinctly different ranges of annual rainfall (Figure 11b). Catchments in the same topological class are expected to exhibit common trends in patterns of sediment connectivity. The spatial arrangement of links within river networks concentrates the routing of sediment and water into parts of the catchment, often at particular confluences (Czuba and Foufoula-Georgiou, 2015;Walley et al., 2018;Heasley et al., 2019). These 'hotspots' give rise to particularly dynamic tributary junctions, and there is some evidence to suggest that their location can be defined through network topology (Benda et al., 2004a;Czuba and Foufoula-Georgiou, 2015;Czuba et al., 2017;Walley et al., 2018). Highly dynamic tributary junctions can be expected to occur in all network types but will likely have varying impacts on the catchment-scale patterns of sediment flux. In catchments with wide headwater networks and large confluence angles such as those in class A, hotspots are likely to occur where large sub-networks converge, and may have a primary role in modulating patterns of sediment routing through these networks (Czuba and FIGURE 11. Box-and-whisker plots of regional controls on network topology, for which mean values were calculated for each catchment. Regional controls include (a) estimated uplift (interpolated from approximate contours of uplift rates; Williams, 1991), (b) average annual rainfall (NIWA, 2015), and (c) suspended sediment yield (Hicks et al., 2019).

TOPOLOGICAL STRUCTURES OF RIVER NETWORKS
Foufoula-Georgiou, 2015; Walley et al., 2018). Similar storage patterns have been observed in networks with wide headwaters (Fryirs and Brierley, 2001;e.g. Benda et al., 2004b;Gran and Czuba, 2017), and at the head of mainstem channels in elongate catchments (e.g. Benda et al., 2004a;Walley et al., 2018). In contrast, routing and storage behaviour in elongate networks exhibits sediment concentrated along valley floors, with rapid transport of sediment from adjacent hillslope tributaries (e.g. Benda et al., 2004a;Farraj and Harvey, 2010;Walley et al., 2018). The structured, steep nature of catchments in classes D and E is therefore likely to reflect this pattern. Catchments in classes A and B may thus exhibit more sediment storage in upstream reaches compared to those in classes D and E, although storage in class B and E catchments is also likely to be controlled by the areas of flat topography.
Catchment-scale models would enable testing of these hypotheses and an exploration of the relationship between topology and sediment connectivity. In particular, the network-based framework model created by Foufoula-Georgiou (2014, 2015) was designed for this purpose, as a system-level model without the pitfalls of reductionist approaches or over-parameterized, physically based models. It is relatively new, however, and model validation using real-world data is difficult given the spatial and temporal scales involved. Benchmarking the model against one known to accurately represent catchment-scale processes would address this issue and allow for an evaluation of both the topology-sediment connectivity relationship and the model itself. The topological classification presented here would thus define the regional topological 'types', as well as allow for a prioritized, representative selection of study catchments.

Conclusions
The regional topology of the South Island of New Zealand presents five distinct catchment 'types' based on six topological metrics. The variables were chosen to encompass the size and shape of catchments as well as the internal distribution of links, and the values for each catchment were calculated to enable the use of PCA and AHC. Each class comprises catchments of significantly different topography and network structure, with the greatest contrast observed between diagonally opposite clusters ( Figure 10). Class A includes large catchments with wide headwaters and confluence angles, and a high degree of valley-floor symmetry extending into the upper reaches of the catchment. Networks in class B are also large, with a mixture of wide headwaters and consistent widths, but the topography tends to be steeper and include large areas of flat relief. Patterns of sediment routing in both classes are likely to be modulated by dynamic hotspots occurring at the confluences of large sub-networks. In contrast, catchments in classes D and E exhibit much greater structural influence on the arrangement of network links, encompassing smaller catchments of consistent widths. Confluence angles are particularly large in class D networks, while those in class E are steeper with greater drainage density. Sediment routing in these networks is therefore likely to be concentrated along the valley floors of mainstem reaches, with rapidly transported inputs from the adjacent hillslope tributaries.
The spatial distribution of classes within the South Island provides insight to the relationship between topology and regional setting, largely dominated by the active tectonics in the region. The offset of the Alpine Fault towards the west coast limits catchment size on the western flanks, and establishes differing patterns of dynamic reorganization and passive deformation on each coast. The pattern of active faulting also has a clear influence on the structure and orientation of networks. The relationship between catchment-scale processes and regional setting is not well understood, despite the clear influence of network configuration on the modulation of sediment flux (Benda and Dunne, 1997a,b;Benda et al., 2004a,b;Benda, 2008;Ferguson and Hoey, 2008). Establishing this relationship has particular implications for the South Island, as there is a high likelihood of widespread landsliding driven by significant tectonic shifts and large storm events. Further research into the patterns of sediment routing through topologically different networks will provide greater clarity on the potential impacts of these events, and the ongoing catchment management in the region.