Watersheds and stream networks viewed longitudinally: Example insights from novel spatial portrayals of watershed characteristics

Longitudinal depictions of watershed structure and characteristics, including topography, stream networks, wetlands, ground water levels, and land use, can provide watershed knowledge and understanding unavailable from standard plan view maps. Three case studies provide examples of knowledge gained by applying longitudinal views of stream networks, watershed hydrologic behavior, and land use distributions. Longitudinal views of mountain stream networks show extreme variability in the slope‐area relationships of low Strahler order streams, large discontinuities in drainage area (large parts of drainage area space are absent in networks), and large variations in network curvature. Longitudinal views of a groundwater‐dominated headwater watershed increase the inference available from limited groundwater observations and clearly reveal how groundwater connections affect the permanence of surface water features and the distribution of vadose zone storage in the landscape. Plotting land uses longitudinally illuminates and allows a quantitative analysis of how land uses are distributed relative to topographic position. Viewing watersheds and stream networks longitudinally can provide new insights into watershed forms and processes and motivate new questions and research.


| INTRODUCTION
Two-dimensional (2D) views of watersheds are inherently limited and cannot capture all important aspects of watershed structure. Watersheds are complex three-dimensional structures whose subsurface boundaries may not match surface boundaries in the horizontal directions (Botter, Bertuzzo, & Rinaldo, 2011;Haitjema & Mitchell-Bruker, 2005;Richey et al., 2015), whose lower flow boundaries and internal hydraulic characteristics are difficult to discern and characterize (Beven, 2006;Hrachowitz & Clark, 2017;Koh et al., 2018;Sayama, McDonnell, Dhakal, & Sullivan, 2011;Staudinger et al., 2019), and whose surficial boundaries themselves depend on DEM scale and accuracy (e.g., Baker, Weller, & Jordan, 2006;Lindsay, Francioni, & Cockburn, 2019). However, as scientific knowledge is generally communicated through graphs, schematics, and photos published in journals and books, visual representations of watershed characteristics are generally constrained to two dimensions, often using contour lines, colors, or line thickness to provide information on characteristics varying in other dimensions. The large majority of two-dimensional watershed representations use a planform map view, plotting watershed characteristics across the horizontal dimensions. Some alternative graphical means for characterizing watersheds include Torgegrams (Zimmerman & ver Hoef, 2017), linked micromaps (Silvanima et al., 2018), and hyperscale graphs (Zettler-Mann & Fonstad, 2020).
These are useful for displaying statistical results in a meaningful way for geospatial correlations but are not as suitable for depicting data.
Representing the multi-dimensionality of watersheds in 2D graphics is difficult, and alternative graphical means of representing watershed structure should continue to be explored.
Here, we propose and provide examples of novel and partly novel longitudinal examinations of watersheds and watershed characteristics. While we often think about watersheds longitudinally, we rarely explicitly plot watershed characteristics that way. We examine three case studies in which viewing a stream network or watershed topography longitudinally illuminates watershed characteristics or behaviors not revealed through plan views, yielding new insights and improving watershed understanding. In the first case study, we plot and examine the entire stream network of a watershed in longitudinal spaces, and in doing so, we test aspects of the classic conceptual geomorphic river continuum concept (RCC) of Schumm and Church (Church, 1992;Schumm, 1977). In the second case study, we plot the elevation and flow distance relative to the outlet of every pixel of a watershed along its topographic drain lines (a.k.a. surficial drain lines), stream threads, and wetland water surfaces, along with observed ranges of groundwater elevations. This view amplifies the power of typically limited groundwater observations, illuminating relationships between groundwater levels and the relative permanence of streams and wetlands.
The third longitudinal view of watershed characteristics portrays land use variation in terms of each pixel's relative elevation and flow distance to the outlet. This information allows analysts to describe watersheds in terms of the relative position of development and quantitatively relate the associated hydrologic and water quality effects of development to watershed position.
All three of these sideview case studies use geographic information systems (GIS) analysis of standard digital elevation model (DEM) and hydrography data to reveal new insights into watershed characteristics and behaviors. The methods are simple and accessible to scientists and practitioners of many disciplines. Each case study is presented in its entirety: methods, results, and implications, followed by a summary of findings.  (Altermatt, 2013;Doretto, Piano, & Larson, 2020;Vannote, Minshall, Cummins, Sedell, & Cushing, 1980). The RCC (Figure 1) is one such approach that explains a substantial amount of longitudinal variability in river characteristics, including slope, average discharge, sediment particle size distributions, and valley alluvial storage (Church, 1992;Schumm, 1977), but large deviations from these trends abound (e.g., Carbonneau, Fonstad, Marcus, & Dugdale, 2012;Fonstad & Marcus, 2010). This theory is commonly portrayed as a conceptual model in which these river properties vary continuously as a function of drainage area (Figure 1, Church, 1992, based on concepts of Schumm, 1977). The stream continuum is a useful concept widely used in textbooks, teaching materials, and government reports, but, as we will show, its inherent simplifications ignore the fact that drainage area does not increase continuously along a stream network and that there is extreme variability in elevation, vegetation, slope, and other characteristics of low-order streams in a channel network. At every channel juncture, there is a jump in the drainage area. Consequently, there is no continuum of channel elevations or channel slopes as drainage area increases, as we will illustrate.
Understanding the variability of stream structure throughout stream networks is fundamental to fluvial geomorphology and stream ecology. While physical and biological river continuum theory helps explain many aspects of longitudinal variability in biological and physical characteristics of streams (Doretto et al., 2020;Vannote et al., 1980), researchers have shown that several landscape factors, such as abrupt changes in geology and topography (stream or valley slope), and geographic shifts in climate and vegetation, affect longitudinal variability in stream power, channel form, and habitat suitability for given taxa (Montgomery, 1999;Pringle et al., 1988;Thorp, Thoms, & Delong, 2006;Townsend, 1989). Channel confluences have been identified as locations of channel and habitat complexity and The physical stream continuum (based on Church, 1992 from concepts of Schumm, 1977) hypothesizing a predictable continuum of channel and valley characteristics as a function of drainage area particularly high dynamism (Benda, Andras, Miller, & Bigelow, 2004;Benda, Veldhuisen, & Black, 2003;Church, 1983;Rice, Greenwood, & Joyce, 2001). When streams of different sizes come together, there are often temporal mismatches between flood peaks and sediment transport. Discontinuities in channel controls have implications for sediment routing and management (Curran & Hession, 2013;Poeppl, Fryirs, Tunnicliffe, & Brierley, 2020;Wohl et al., 2015). Integration of longitudinal approaches with patch-based approaches has been shown to increase model accuracy (Collins, Matter, Buffam, & Flotemersch, 2018;Larsen, Bruno, Vaughan, & Zolezzi, 2019).
Here, we use longitudinal views of complete stream networks in two nearby mountain stream basins differing in basin area and topology to illustrate the variety of forms and connections of low-order streams and to show that river continuum theory hides important channel network complexities, for example the stark discontinuities in relationships between channel elevations and slope as explained by drainage area. Similar longitudinal views of portions of stream networks have been used in knickpoint analyses and to illuminate geologic controls on network profiles (Gallen, 2018;Gallen et al., 2011;Gallen, Wegmann, & Bohnenstieh, 2013;Schwanghart & Scherler, 2020), but such views have focused on select threads and have not portrayed entire stream networks. As far as we can tell, longitudinal mapping of entire stream networks is novel. Longitudinal projections of entire stream networks may improve understanding of variation in water quality (e.g., Johnson et al., 2019;McGuire et al., 2014) and channel geometry (Carbonneau et al., 2012;Zettler-Mann & Fonstad, 2020) and assist with experimental and monitoring design (Larsen et al., 2019).

| Methods
Using 10 Â 10 m DEMs and stream networks generated as a part of the development of the NHDPlus High Resolution (HR) database, we created side views of a stream networks in both elevation-drainage area space and elevation-distance to outlet space for Cartoogechaye Creek and a portion of the larger Yadkin River, both in the southern   (Montgomery, 1999). The discontinuity of drainage area as an explanatory variable has many implications. The large jumps in drainage area, flow, and sediment loads and the frequent mismatch of flood peak arrival times (Figures 3 and 4;  It is a tenet of groundwater hydrology that the water table of a surficial aquifer "forms a subdued replica of the topography" of the hills and intersects with perennial stream elevations in the valleys (Freeze & Cherry, 1979 (Figure 7). This is a permeable, low-relief, groundwater-dominated watershed Klaus, McDonnell, Jackson, Du, & Griffiths, 2015). The soils consist of loamy sand topsoils over sandy clay loam argillic horizons underlain by unconsolidated sands and clays. Below the stream elevation occurs a dense clay hydrostratigraphic layer, known locally as the Tan Clay, which acts as the base of the surficial aquifer. This site has been previously instrumented with wells, interflow interception trenches, soil moisture sensors, and flumes Ferreira, Rau, & Aubrey, 2021;Griffiths et al., 2016Griffiths et al., , 2017Griffiths et al., , 2019Jackson et al., 2016;Jackson, Bitew, & Du, 2014;Klaus et al., 2015;Vache, Meles, Griffiths, & Jackson, 2021). Here we plot the distribution of monthly water levels measured in the wells located in the focal watershed.

| Findings and implications
These monthly water level measurements occurred between December 2011 and July 2020. Average annual precipitation is 1,269 mm, and average annual evapotranspiration is 861 mm.
We used a LiDAR-generated 10 Â 10 m DEM to delineate topographic drainage lines in Watershed C. All hydrologic conditioning, flow accumulation and direction, topographic drain line extraction, network distances, and network geometry were completed in MATLAB using the TopoToolbox add-in (Schwanghart & Scherler, 2014) (Figure 7). Topographic drainage lines were routed down to the valley edges, where the landscape becomes flat and lumpy and the water table position is near the surface. The valley is defined in this flat, low-relief landscape as the regions with hydric soils, mostly-permanent wetlands, and within 10 m of the ephemeral stream. Perennial, intermittent, and ephemeral streams were defined from the USGS 7.5-min DLG and from USFS reports (Hiergesell, 1999(Hiergesell, , 2004.

| Findings and implications
Plotting water table positions relative to topography, stream lines, and wetlands in relative elevation and distance-to-outlet space increases the inferential power of limited groundwater observations. Water table variation is low in the valleys just above the start of perennial streamflow and becomes much larger higher in the watershed ( Figure 8). The valleys essentially act as grade controls for the water

| Issue
Landscape position is a fundamental driver of ecological processes.
Alexander von Humboldt created the field of biogeography by observing that landscape position, including elevation, slope, and proximity to streams, strongly controls microclimate, resource availability, and the spatial distribution of plants and animals (von Humboldt, Bonpland, Jackson, & Romanowski, 2008). Landscape position also controls the suitability of land for agriculture and building and thus affects human settlement patterns (Boerner, 2006;LaGro, 2005; Zivkovi c, 2019), particularly at lower rural densities. The interactions of human land uses and biogeographic controls affect ecosystem responses to climate change (Elsen & Tingley, 2015). Here, we look at the distribution of land uses across mountainous rural watersheds as a function of distance from the watershed outlet and relative elevation from the outlet. This view provides insight into the interactions between human land use and the biogeographic controls that affect how ecosystems respond to that land use. A simpler, less complete, version of this graphical methodology was used by Webster et al. (2012), but we have not seen it elsewhere.

| Methods
We look at two rural mountainous watersheds, the South Fork Skee-  (Dewitz & USGS, 2021). A 10 Â 10 m DEM was obtained from the NHDPlus HR database (Blodgett & Johnson, 2022;USGS, 2018). We plot the 30 Â 30 m NLCD rasters in the planform figure, along with land use and watershed/geographic centroids with basic watershed features (elevation contours and NHDPlus HR streams (Figure 9)). We represented as a grid (Razavi & Coulibaly, 2017). The watershed centroid is defined within the longitudinal space rather than the planform.
The watershed centroid is calculated similarly to the geographic centroid but uses relative elevation and flow distance to the outlet instead of X, Y coordinates. For clarity, we have excluded from the maps land uses that contribute <2% to the overall area.

| Findings and implications
By plotting the land uses of all pixels in relative elevation/flow distance to the outlet space, the differences in land use distributions that are suggested in the plan view become distinct and also quantifiable (Figures 9 and 10). Such a plot clearly reveals that agriculture and development in the South Fork Skeenah watershed are concentrated in the valleys, with little to no development above the watershed centroid (Figures 9a and 10a)