Topological controls on catchment‐scale sediment dynamics

The episodic transfer of sediment from source to sink is a fundamental process in fluvial systems that influences river morphology, aquatic and riparian ecosystems, and risk from a variety of associated natural hazards. The hierarchical structure of river networks has been identified as a key control on spatiotemporal patterns of sediment routing at the catchment scale, but very few studies have systematically explored this relationship. In this paper, we investigate the role that drainage network topology plays in modulating sediment flux and morphodynamic activity. We simulate the geomorphological responses of four topologically distinct catchments from New Zealand's South Island to sequences of flood events using a landscape evolution model. Spatiotemporal variation in different types of geomorphological activity is assessed via a link‐based framework, and potential interrelationships between within‐network changes and discharge and sediment yield at the catchment outlets are explored to provide insights into relative levels of network connectivity. We also investigate the occurrence of geomorphic ‘hotspots’ in relation to network topology, and their impact on the downstream transfer of sediment in different network ‘types’. Dissected networks were found to exhibit much greater spatiotemporal variability in geomorphological activity compared to narrow, elongated networks where change was concentrated in mainstem reaches. The frequency and significance of geomorphological hotspots are shown to vary between network types, with strong contrasts evident between dissected networks with steep topography and elongated networks with more gentle gradients. Dissected networks exhibited mostly non‐linear relationships between within‐network geomorphological activity and outlet discharge and sediment yield. However, moderate to strong linear relationships between these variables were observed in mainstem‐dominated networks, indicating much greater levels of connectivity across a range of flow conditions. We discuss the implications of these findings on the transformation of environmental signals through fluvial systems with different topological structures, and the differential responses of catchments to disturbance events.

fluvial systems and a lack of efficient analytical tools have impeded a comprehensive understanding of catchment-scale sediment flux. This complexity is largely driven by the highly non-linear relationship that exists between sediment flux and water flow (Coulthard & Van De Wiel, 2007), in which the same volume of water flowing through a given reach can alternately generate erosion, deposition, or no response at all. This lack of understanding is exacerbated at the catchment scale, which has traditionally been neglected in favour of reach and local scales that are more straightforward to study.
Research into the downstream transfer of sediment has historically focused on the localized transport of grains and the movement of individual sediment pulses through a reach (e.g. James, 2010;Lisle et al., 2001;Sklar et al., 2009), particularly the relative significance of dispersion and translation processes (e.g. Knighton, 1989;Lisle et al., 2001;Meade, 1985). Other studies have explored the impact of intersecting tributaries or 'tributary-trunk' dynamics (e.g. Knighton, 1980;Rice, 1998), focusing on the impact of tributaries on the downstream trunk channel with regard to grain size characteristics and downstream fining (e.g. Church & Kellerhals, 1978;Dawson, 1988;Knighton, 1980;Rice & Church, 1998). Relatively few studies have attempted to develop these concepts at the catchment scale, with some exceptions exploring the catchment-scale distribution of significant confluences (Benda, 2008;Benda et al., 2004a;Rice, 2017) and the influence of network structure in modulating sediment waves (Benda et al., 2004b;Gran & Czuba, 2017;Sklar et al., 2006Sklar et al., , 2009. More recently, studies have explored the role of geomorphic 'hotspots' as key nodes in the river network predisposed to changes in storage and geomorphic change (Czuba & Foufoula-Georgiou, 2014Walley et al., 2018). Network topology emerges from this literature as a key element in organizing catchmentscale sediment flux, but only the work of Walley et al. (2018) systematically compares how different network structures impact patterns of sediment routing, highlighting the role of regional characteristics in governing both network configuration and sediment flux.
Analysing catchment-scale sediment transfer thus necessitates consideration of the underlying network topology, and the associated regional-scale processes. Over much longer timescales, the same processes which control regional sediment transfer also determine the topology of river networks at the catchment scale, such as the tectonic and climatic settings that establish topology during initial mountain building, and continue to evolve networks over time (Castelltort et al., 2012;Hovius et al., 1998;Viaplana-Muzas et al., 2015). This relationship between topology and regional processes is thus key to understanding catchment-scale sediment flux; however, the complex relationships and the spatial and temporal scales over which these processes occur make them difficult to understand or quantify. Previous approaches to catchment-scale analysis have employed the network structure as a tool to organize system complexity, most notably in the form of stream-ordering frameworks (e.g. Horton, 1945;Shreve, 1967;Strahler, 1957) and their associated derivatives (e.g. Benda et al., 2004b;Heasley et al., 2019;Tokunaga, 1978;Zanardo et al., 2013). Walley et al. (2020) employ these metrics to classify 59 catchments in the South Island of New Zealand into five 'types', identifying a clear relationship between network topology and regional setting.
The resulting network classifications are used in this study to investigate the role that drainage network topology plays in modulating the spatiotemporal pattern of sediment transfer from source to sink. While quantitative frameworks exist which utilize digital elevation models (DEMs) and remote sensing-derived indices to characterize catchment-scale sediment connectivity and landform evolution (e.g. Bracken et al., 2015;Brierley et al., 2006;Heckmann et al., 2018), a numerical modelling approach was deployed here to enable a greater degree of experimental control and exploration of effects over large spatiotemporal scales. The CAESAR-Lisflood model was identified as a fit-for-purpose catchment-scale application, which simulates sediment transfer and morphodynamic adjustment in a computationally efficient manner, with a good degree of process replication. The model is also capable of large-scale simulations over hundreds to thousands of years and hundreds of square kilometres (Coulthard et al., 2013), and given the difficulty of validating catchment-scale models with real-world data, CAESAR-Lisflood was additionally chosen as a well-known landscape evolution model (LEM) that is established in the literature (Coulthard & Skinner, 2016;Coulthard et al., 2013;Hancock et al., 2015Hancock et al., , 2017Liu & Coulthard, 2017;Xie et al., 2018). We thus use CAESAR-Lisflood in this paper to examine the distribution and modulation of sediment movement through topologically distinct networks and establish whether there are key differences in the emergent sediment pathways. Potential inter-relationships between geomorphological activity within the different networks and discharge and sediment yield at their outlets are explored to provide further insight to network connectivity. We also investigate the occurrence of geomorphic 'hotspots' in relation to network topology, and their impact on the downstream transfer of sediment in different network 'types'.

| TOPOLOGICALLY DISTINCT NETWORK STRUCTURES
The network classifications identified by Walley et al. (2020) were used to select topologically representative catchments in which modelled spatiotemporal patterns of sediment connectivity could be compared. The five network 'types' are distinguished by catchment topography and network structure (Figure 1), in which Types A, B, D, and E exhibit values along the extremities of each axis. These groupings are characterized by distinct topological properties (Table 1), while the catchments in Type C reflect a mixture of topologies with elements from the other types. It was assumed that the greatest contrast in sediment routing patterns would occur between the outermost network 'types', and Type C was consequently removed from further analysis. The representative networks from the remaining 'types' identified by Walley et al. (2020) were evaluated for this study, but the data necessary to parameterize the CAESAR-Lisflood model was only available in the Type A catchment. The networks from the Types B, D, and E clusters were thus replaced with those that fell closest to the centre of the cluster for which the necessary data was obtainable.
The four identified study catchments were evaluated in the same manner as by Walley et al. (2020), to establish the internal characteristics of the catchment topography and network structure. The Type A network was identified by Walley et al. (2020) as the Motueka River, which exhibits a dissected network structure, with wide headwaters narrowing towards the outlet (Figures 2a and e). The catchment is relatively large and contains symmetrical gentle to moderate slopes (Figures 3a and e) which steepen towards the western boundary. This network is similar in structure to the South Ashburton River, which represents the Type B catchments, and also contains a branching, dissected network topology (Figures 2a and b). The South Ashburton catchment is smaller than the Motueka and does not extend upstream into the Southern Alps, so the topography exhibits gentle slopes and very wide valley floors (Figures 2j and 3f). Both catchments are relatively rounded in shape and neither exhibit a prominent mainstem, suggesting that patterns of sediment routing are likely to be dominated by geomorphic hotspots at key confluences (Benda et al., 2004b;Rice, 2017;Walley et al., 2018).
The Waiau Toa/Clarence River represents the Type D catchments and is the largest of the four study networks. In contrast to the Motueka and South Ashburton catchments, the Waiau Toa/Clarence River has an elongate shape and relatively consistent width ( Figures 2c and g), resulting in a prominent mainstem and increasing network symmetry in the headwaters (Figure 3g). The Waiau Toa/Clarence network is additionally characterized by drainage anomalies, including river bends of more than 90 , tributaries joining the network oriented in an upstream direction, and parts of the river which flow laterally across mountain ranges (Duvall et al., 2020).
These anomalies reflect the highly active tectonic landscape and indicate a history of river capture across the region. The Waihao River, which represents the Type E catchments, contains two elongate subcatchments which exhibit the same narrow, mainstem-dominated structure as the Waiau Toa/Clarence network (Figure 2d). It does not exhibit the same tectonic influence, however, and has a gentler topography similar to the South Ashburton catchment. The patterns of sediment routing are likely to be strongly influenced by the mainstem channels in these catchments, and exhibit geomorphic hotspots at the head of the mainstem reaches (Benda et al., 2004b;Rice, 2017;Walley et al., 2018).

| THE CAESAR-LISFLOOD MODEL
To explore patterns of sediment flux at the catchment scale, the four identified topologically dissimilar networks were simulated using the CAESAR-Lisflood LEM (Coulthard et al., 2000(Coulthard et al., , 2002(Coulthard et al., , 2005(Coulthard et al., , 2013. CAESAR-Lisflood simulates landscape evolution by moving water over a DEM, and uses fluvial and slope processes to calculate erosion and deposition in each cell for each timestep (Coulthard et al., 2013).
In catchment-scale simulations, a 'real-time' rainfall input is used to calculate runoff, which is routed using the LISFLOOD-FP 2D inertial flow model and used to calculate flow depth and velocity in each grid cell. These are in turn used to calculate fluvial erosion and deposition in up to nine grain size fractions, with a method of storing subsurface sediment in layers allowing for vertical grain size variability. Slope processes additionally allow for the erosion of sediment into the fluvial system via soil creep and mass movements, the latter triggered when a critical slope threshold is exceeded. A catchmentscale simulation in CAESAR-Lisflood thus requires a DEM of the study catchment and a time series of hourly rainfall rates as the two primary inputs, which must be set up to maximize output detail, while also allowing for realistic model run times. The resolution of the DEM determines the number of calculations required for each timestep and must be considered alongside the length of the rainfall input, as shorter simulations can be carried out at higher resolutions.
It is also necessary to identify the m value that controls the peak and duration of simulated hydrographs (Beven, 1997;Beven & Kirkby, 1979), which can be calibrated against hydrological gauge data.

| Parameterization and validation
The surface DEM is one of the key components of the CAESAR-Lisflood model, and the balance between catchment size and grid resolution is a key consideration for parameterization. Rescaling each DEM to an appropriate cell size has significant implications for the simulations, as a linear increase in resolution results in an exponential increase in the number of grid cells and a greater than exponential increase in simulation time. High resolutions can also cause steeper slopes between cells and thus greater potential for erosion and deposition. Finding an appropriate resolution depends on the size of the study catchment, as CAESAR-Lisflood is best suited to applications with resolutions below 100 m and less than 500 000 cells. Surface data for the study catchments was therefore taken from a mosaicked 8 m DEM (Geographx, 2012) and resampled to the smallest resolution, which produced a DEM containing less than 250 000 cells, or 500 000 cells where the smaller value was not possible (Table 2). An appropriate slope failure threshold was identified by running sensitivity tests in CAESAR-Lisflood for one simulation day, to identify the lowest value which would not produce widespread hillslope failure within the first few iterations. Bedrock DEMs were produced by subtracting 1 m from the entire surface, acting to prevent excessive and unrealistic incision occurring in steeper channel sections during simulations (Hancock et al., 2011). In the absence of spatial data on bedrock depth, an erodible layer of constant thickness was specified to ensure a significant reservoir of material was available for erosion and transport through the networks. size distributions were not available in the necessary spatial or temporal resolutions in any of the study catchments. The model was therefore run using a single representative grain size fraction in order to isolate the catchment-scale sediment pathways in each catchment, and compare these patterns directly between their topologically distinct structures. Given the relatively steep, active nature of rivers in the South Island of New Zealand, sediment smaller than 2 mm was assumed to be fully transported in suspension and was subsequently excluded from this analysis. Gravel bedload was assumed to be the dominant grain size in active transport. Representative values were taken from the midpoint of common diameter ranges for fine, medium, and coarse gravel, and test simulations identified the fine gravel value of 5 mm to transport sufficient volumes within realistic simulation times.
The final element of parameterizing the CAESAR-Lisflood model is the hourly rainfall input, which is converted into discharge and routed through the channel network. One of the primary parameters in the hydrological model is therefore the m value, the parameter which controls the magnitude and duration of the hydrograph for each rainfall event (Beven, 1997). This value can be calibrated from the master recession curve (MRC) of a hydrological gauge dataset from the catchment of interest (Lamb & Beven, 1997). Discharge time series were thus obtained from automatic gauging stations in each study catchment, and rainfall time series acquired from the closest rainfall gauge. A continuous time series of discharge and rainfall was then generated by matching the dates from these datasets, and the m value calculated using the method of Lamb and Beven (1997).
Appropriate recession curves were first manually identified from the discharge record as those with minimal recharge from rainfall events, and of at least 4 days duration ( Figure 4a). Each curve was then shifted along an arbitrary timeline relative to the other recession curves until a good alignment was found (Figure 4b), and the parameters of the MRC were calculated by visually calibrating the smoothed line of best fit (Figure 4c). A value for m was then estimated from the gradient of the relationship between discharge per unit area and relative storage deficit (Table 3), in which the latter was calculated by cumulatively summing discharge per unit time with the deficit at peak discharge assumed to be zero (Lamb & Beven, 1997).  the channel network into a linear network format ( Figure 6). The river network was thus defined as a set of hierarchically connected 'links', which each represent a segment of the network between two tributary junctions, or between a tributary junction and a source/outlet.
The active channel network first had to be defined within the raster grid, which was achieved by generating a buffer around each linear network shapefile with a width three times the grid cell size. This tively, compared to those in the Type A network. These patterns suggest that sediment moves more readily through the Type B catchment and may therefore be more sensitive to disturbance events, with the identified hotspots possibly having a lesser impact on the overall pattern of sediment connectivity.
In contrast to the Type A and B catchments, the Type D river is large, elongate, and contains a network oriented around a central mainstem. The spatial pattern of dynamic reaches occurs predominantly through this mainstem channel, but also extends upstream of location 2 into the headwater tributaries (Figure 7c). This confluence is both a significant point of convergence in the network and a drainage anomaly in which the tributaries converge at an angle greater than 90 , and subsequently exhibits a value of absolute change significantly higher than anywhere else in the catchment. The map of relative change indicates that hotspot 2 is a highly aggradational set of links ( Figure 7g), and it is therefore likely that this site intercepts sediment from the upstream network and modulates its delivery downstream.
The downstream pattern of relative change then suggests that transport through the mainstem channel is intermittent, with alternating aggradational and erosional links. This pattern is particularly emphasized at hotspot 2, which indicates a zone of aggradation immediately upstream of a gorge. The Type E network has a similarly mainstem-dominant structure but is split between two key subcatchments which converge at location 1 (Figure 7d). This confluence thus represents a significant point of convergence in the network and consequently exhibits dynamic behaviour like those in the other catchment types. The western subcatchment upstream of hotspot 1 appears to be more dynamic than the eastern network, with high values of absolute change concentrated through the central mainstem up to hotspot 4. The pattern of relative change through this reach suggests a somewhat intermittent pattern of transport (Figure 7h), similar to behaviour in the Type D mainstem. Location 3 is the most dynamic link in the network, however, which occurs just upstream of hotspot 4, separated by a highly confined reach. This location accumulates sediment transported from the small subnetwork upstream, likely in response to the controlling influence of the downstream link, and thus exhibits similarities to hotspots 3 and 6 in the Type A network.

| Temporal patterns of sediment flux
The simulation results were divided into annual timesteps to explore how the observed spatial patterns of absolute and relative change Given this more consistent spatial pattern in the Type D catchment, a relationship between the distribution of dynamic links and the volume of total absolute change is difficult to determine at the larger volumes (e.g. Animation D.2, timesteps 13, 5, 4, and 26). Figure 8 indicates that the spatial pattern is more consistent over a large range of absolute shift in spatial pattern in timesteps of little total absolute change. With decreasing volumes, the dynamic behaviour moves upstream (e.g. Animation D.2, timesteps 11 and 18) and becomes consistently aggradational regardless of the sequential order of the timesteps (e.g. Animation D.2, timesteps 22 and 24), and these patterns likely reflect the shift from fluvial transport to hillslope processes.
The spatial pattern of absolute change in the Type E catchment is less dynamic than the Type A or B networks, but also indicates less consistency over time than the Type D river (Animation E.1). The locations of key reaches appear to correspond with those highlighted in the previous maps of the full simulation results (Figure 7), and the western subcatchment remains more consistent than the east throughout the simulation. Hotspot 3 consistently acts as an aggradational sink, likely influencing the predominantly erosional behaviour of the downstream reaches, while hotspot 2 exhibits intermittent transport through a collection of reaches. As in the Type D network, hotspot 1 lies at the junction of two key subnetworks and acts as a

| Outlet relationships
The relationship between the spatial pattern of dynamic links and the magnitude of network-scale change can be further explored through the processes of sediment and flow discharge at the outlet. These are likely to be the primary drivers of total absolute change, and the strength of the relationships provides insight into the network's connectivity. The CAESAR-Lisflood model does not record flow or sediment discharge throughout the catchment, so Spearman's correlation matrices were generated from the annual values at the outlet. Table 4 displays the correlation coefficients in which insignificant relationships (p > 0.05) are greyed out. Full correlation matrices for each catchment are provided in the supplementary material.
The Type A catchment exhibits a strong, positive relationship between the total absolute change and sediment discharge at the outlet, but no significant relationships between the other variables. This pattern suggests that the volume of sediment reaching the outlet is proportional to the volume of sediment moving within the network, and thus the volume of absolute change in each timestep is largely driven by processes of sediment transport. These variables are not related to flow discharge, however, which indicates that the sediment transport and absolute change processes are disconnected from flow magnitude. These relationships thus indicate a disconnected catchment, in which sediment stores within the network prevent sediment transport in proportion to flow discharge.
In contrast to the Type A catchment, the Type B network does not display significant relationships between total absolute change and either of the other variables, but contains a significant, moderate relationship between sediment and flow discharge (Table 4). This pattern suggests that the network contains relatively few perturbations which modulate the sediment signal, and that geomorphic change occurs across a range of flow conditions that are not always conveyed to the outlet. These relationships thus indicate that the Type B network is more connected than the Type A, as high flows transport larger volumes of sediment more consistently, but the relatively weak relationship and non-linear correlation with total absolute change indicate the catchment is still largely disconnected. As in the Type A catchment, sediment is likely being trapped by internal stores and thus not transported to the outlet, although Figures 9b and 10b suggest this transfer occurs much more efficiently during peak flows.
The Type D catchment exhibits significant, moderate relationships between all three variables, with a slightly stronger correlation between total absolute change and sediment discharge at the outlet (Table 4). As in the Type A network, this suggests that the volume of sediment reaching the outlet is relatively proportional to the volume of sediment moving in the network, and that the volume of absolute change in each timestep is driven by sediment transport processes.
Unlike the Type A catchment, however, both total absolute change and sediment discharge exhibit moderate correlations with flow discharge, indicating greater connectivity within the catchment overall.
The moderate relationship between flow and sediment discharge displays variable sediment volumes within both high-and low-flow discharges, suggesting some disconnectivity within the network. As previously observed, this is likely to be the modulating influence of the hotspot at location 2 at the head of the mainstem reach, which acts as a bottleneck preventing ready sediment transport downstream and impeding stronger relationships between flow discharge and the other variables.
The Type E catchment exhibits significant, strong relationships across all three variables, indicating that sediment transfer is more connected than any of the other catchments (Table 4). High-flow conditions drive high sediment discharge and geomorphic change across the network, and these values decrease steadily with flow magnitude.
As in the Type B catchment, the Type E network exhibits skewed distributions of total absolute change and sediment discharge, indicating a low-energy river which often operates in baseflow conditions. This has not impacted the strength of the relationships as much as in the Type B network, however, despite being particularly pronounced in the two distinct groupings within the sediment discharge data. These groups appear to be associated with high-and low-flow conditions with no values occurring in between, suggesting that some disconnectivity likely occurs under very low-flow conditions.  (Coulthard & Van De Wiel, 2007). This same study identified catchment morphology as the most significant driver of non-linearity in fluvial systems due to the varying potential for internal sediment storage (Coulthard & Van De Wiel, 2007); Walley et al. (2018) identified a greater potential for storage in a dissected river network compared to a mainstem-dominant structure, resulting from an increased number of confluences at which similar-sized tributaries converged.
These studies, combined with the disparity in outlet relationships identified using the CAESAR-Lisflood model, suggest that sediment pathways through mainstem-dominant networks are fundamentally different to those in their dissected counterparts, and exhibit greater connectivity over a variety of flow conditions.

| DISCUSSION
The key differences in the spatiotemporal patterns of sediment connectivity between catchments with divergent network structures are summarized in Figure 11, within the framework of the original topo- F I G U R E 1 0 Sediment delivery ratios in each catchment, calculated as the ratio of annual sediment yield at the outlet to annual erosion across the catchment.
F I G U R E 1 1 Conceptual model of the spatiotemporal patterns of sediment connectivity within the topological classification framework.
Type D catchment, which appears to contain the most stable pattern of dynamic links. These patterns were found to correspond to the total absolute change occurring in each annual timestep, and while this relationship was evident in all network types, the pattern of dynamic links adjusted to variation in total absolute change more readily in the dissected catchments. This trend is likely driven by the relationships between total absolute change, flow, and sediment discharge, which were also found to be influenced by network struc-  Georgiou, 2014Georgiou, , 2015 and CASCADE (Schmitt et al., 2016;Tangi et al., 2019)], and may provide better fit-for-purpose solutions.
Rather than attempting to model every aspect of the fluvial system, these models focus on simulating individual processes to limit the necessary computational capabilities without over-simplifying the system.
The topological control of river networks on catchment-scale sediment dynamics has significant implications for our understanding of fluvial systems, river management, and future research opportunities.
Knowledge of the discontinuous transfer of sediment is important for minimizing the impact of a variety of activities, including mineral and gravel mining, channelization and flood protection schemes, and the management of hydropower dams. The role of hotspots in sediment connectivity also has implications for estimating the spatial and temporal responses to disturbance events, and the potential downstream impacts of landslide dams, aggradation and channel avulsion, and habitat degradation. Understanding the spatial and temporal behaviour of hotspots in different network types also has significant implications for our understanding of sedimentary records, and interpretations of paleoenvironmental reconstruction based on stratigraphy. Models of landscape evolution tend to simulate environmental signals as dampened by the transport system or lagged, but it has been suggested that this may be too simplistic (Coulthard & Van De Wiel, 2007;Jerolmack & Paola, 2010). Jerolmack and Paola (2010)  involving sedimentary records, as it suggests that system memory is better preserved in catchments with mainstem-dominant structures, and thus the stratigraphy observed in these networks is more likely to reflect the paleoenvironmental conditions than internal system dynamics. The scale of such networks must also be considered, as particularly large rivers will likely incorporate a variety of internal structures, especially if the catchment area extends into disparate regional environments. Further research is required into these relationships; however, it is clear that the influence of network structure on the spatiotemporal patterns of sediment connectivity is vital for our understanding of fluvial systems at the catchment scale.

| CONCLUSIONS
Drainage network topology plays a clear role in modulating the spatiotemporal pattern of sediment transfer from source to sink. Building on the theoretical understanding of how sediment is transferred through catchment-scale river systems and the analysis of network topology provided by Walley et al. (2020), this study compares patterns of sediment routing across topologically distinct structures, and identifies key differences in the spatiotemporal patterns of sediment transfer.
These patterns indicate that dynamic behaviour is structured differently in each of the network 'types', with particular divergence between the dissected networks (Type A and B) which exhibit dynamic links throughout the network, and the mainstem-dominant structures (Type D and E) which indicate that change is concentrated within the mainstem reach. Key differences were also observed in the occurrence of hotspots across the networks, with the greatest dissimilarity between the patterns observed between the Type B network (which contained several insignificant hotspots) and the Type D structure (in which a single site significantly influenced the overall pattern of connectivity). These distributions likely influence the observed temporal patterns of sediment connectivity, which exhibit similar variation between the most consistent patterns in the Type D network compared to the most inconsistent in the Type B catchment.
Control of network topology on sediment routing and connectiv-