HydroWidth: A small‐scale approach to calculate river width and its variability

Digital map processing techniques have enabled new computational methods to extract geographic features from scanned map sources. These are mainly historical maps and are rich in spatiotemporal information which can be derived by descriptive metrics. River channel width is such a typical ecological metric used to calculate properties such as water discharge rates and, generally, often applied in hydrological and ecological monitoring. Measures of river channel width in previous ecological work have successfully measured width based on in situ measurements or remote sensing efforts, but poorly captured the variability in river width due to simplifications of the river network or due to sparse availability of in situ measurements. As river width can greatly vary and change over space and time, capturing its variability with modern geospatial processing techniques is a key interest in interdisciplinary fields studying spatiotemporal changes of riverine properties. This article proposes HydroWidth, a small‐scale approach to measure river width continuously along a channel, capable of capturing the variability in width in simple as well as complex river structures without the use of river masks. The small‐scale approach is compared to two conventional vector‐based discrete river width measurement techniques to test the robustness of the methods in terms of measuring river width and its variability. Furthermore, this article evaluates the adaptability of HydroWidth by performing three experiments measuring river width variability at rivers of different structure, length, and complexity. The methods are applied on rivers of historical map sources, allowing a novel perspective of applying algorithms measuring river width on non‐airborne data sources. Lastly, the computational performance results of the conventional and HydroWidth methods at each experimental site are presented and discussed.

scanned map sources. These are mainly historical maps and are rich in spatiotemporal information which can be derived by descriptive metrics. River channel width is such a typical ecological metric used to calculate properties such as water discharge rates and, generally, often applied in hydrological and ecological monitoring. Measures of river channel width in previous ecological work have successfully measured width based on in situ measurements or remote sensing efforts, but poorly captured the variability in river width due to simplifications of the river network or due to sparse availability of in situ measurements. As river width can greatly vary and change over space and time, capturing its variability with modern geospatial processing techniques is a key interest in interdisciplinary fields studying spatiotemporal changes of riverine properties. This article proposes HydroWidth, a small-scale approach to measure river width continuously along a channel, capable of capturing the variability in width in simple as well as complex river structures without the use of river masks.
The small-scale approach is compared to two conventional vector-based discrete river width measurement techniques to test the robustness of the methods in terms of measuring river width and its variability. Furthermore, this article

| INTRODUC TI ON
Digital map processing (DMP) techniques enable new computational methods for the extraction and recognition of geographic features from historical map sources, such as archived images of maps (Chiang et al., 2014). These sources hold geographic information of several decades that are of interest for studies of spatiotemporal changes or ecological monitoring of features, such as rivers. The information embedded in the geospatial data can be derived into descriptive ecological metrics by various geospatial processing techniques in geographic information system (GIS) environments. Such metrics refer to the geometry and topology of the extracted vector features. In the context of this article, methods are investigated to derive the river channel width metric under consideration of uncertainty.
The river channel width, for simplification hereafter referred to as river width, is a hydromorphological shape metric that can be defined as the cross-sectional distance between the water edges of a river, orthogonal to the river channel (Pavelsky & Smith, 2008). Different from the channel system width, which measures as the sum of width of all adjacent channels (Bufe et al., 2019), the river width defined here measures the width of the water surface of a single wetted channel, not including gravel banks or other components within the riverbed. The variability in river width is an important ecological property to study as it is an indicator for the lateral connectivity of the river (Woolsey et al., 2007) as well as for the diversity of riverine environments (J.  and certain river morpho-dynamics (Monegaglia, 2018). Furthermore, river width is one of the key variables needed to calculate river discharge, along with river depth and velocity, and is thus a key shape property for many hydrological studies (Leopold & Maddock, 1953).
Although deemed important for various ecological applications, measures of river widths often lack in data quantity or quality. Conventional methods to measure river width include the use of transects (Ridolfi et al., 2014;Thelen et al., 2006) or segments (Leathwick et al., 2005), where transects are a cross-sectional measurement of the river width at a specific location and segments are an average of the measured river width over a predefined section of the river. The transect method may show width measurements of high quality when the width is based on gauging stations or other in situ (i.e., on site) measurements (Mengen et al., 2020); however, transect measurements based on in situ observations often lack in measurement quantity and coverage, in part due to the global decrease in gauging stations and the cost associated with in situ measurements (Mengen et al., 2020;J. Yang et al., 2020). In general, sparse river width measurements are unable to capture the variations of a river channel and how the river width varies over space and time (J. . The segment method poses similar problems as averaging values eliminates small variations in width and, depending on the application, the spacing and delineation of segments greatly influence the results (Mengen et al., 2020). Clearly, measuring river width is a process that lends itself to geodata-based workflows, substituting costly in situ measurements. Estimating the river width over larger segments of rivers is common practice as it can be done from satellite or aerial imagery evaluates the adaptability of HydroWidth by performing three experiments measuring river width variability at rivers of different structure, length, and complexity. The methods are applied on rivers of historical map sources, allowing a novel perspective of applying algorithms measuring river width on non-airborne data sources. Lastly, the computational performance results of the conventional and HydroWidth methods at each experimental site are presented and discussed.
in ungauged basins (J. . This method should, however, be used with caution as river width derived from satellite images by various extraction and generalization algorithms tend to simplify the river system (Pavelsky & Smith, 2008). These simplifications, such as applying a channel mask to simplify branching river sections, lead to river width measurements that are not always perpendicular to the true river channel, effecting measurement quality. Despite the drawbacks, the conventional methods of transects and segments are used across various disciplines (Fleckenstein et al., 2006;Leathwick et al., 2005;Pavelsky & Smith, 2008).
In this article, we present a small-scale method to measure river width, capable of capturing the variability of river width in simple as well as complex river structures in channels as narrow as ~5 m. The presented approach is an adaptation of the methods described in Yamazaki et al. (2014), modified in several key steps and utilized on historical map sources. The small-scale approach, keyed hereafter as HydroWidth, renders quantitative and highly detailed results as no channel mask algorithms are necessary and river width is measured continuously along the river channel, without the use of transects. This article further presents an analysis of the HydroWidth method compared to the transect and segment methods. A set of computational experiments demonstrate the smallscale approach and investigate what method is most robust and adaptive to measure river width variability. In the context of this article, robust refers to the reliability of the results and the applicability of the method to various river types. In addition, adaptive refers to the flexibility and transferability of the method at various scales. For the analysis, three typical river types were chosen and extracted in vector form from historical maps of the 1880s.
The chosen types include a braided, a human-modified (i.e., modified), and a meandering river type, all of different levels in river channel complexity and overall river length. As channelized rivers do not show much variability in width, the modified river channel serves as a compromised type, showing strong human influence on the channel, which is common for many rivers, yet with some sections of branching or complexity due to waterway intersections, giving it some variability in width.
The contributions of this article are threefold: • A small-scale adaptation of the algorithm used in Yamazaki et al. (2014) to measure river channel width and its variability from historical map sources.
• A quantitative analysis of the methods performance when applied to three different river types extracted from historical maps.
• A comparison of the small-scale method with two established approaches for validation, also for the three river types.

| REL ATED WORK
In this section, we recall the two conventional, or well established, shape metrics for measuring river width and what advancements have been made thus far to measure river width and its variability.

| The conventional methods: Transects
Ecology as a key area of applied GIS research has produced a plethora of shape measures, such as transect (crosssectional measurements) or segment measures (averages over predefined section lengths or areas) in hydraulic, geographic and hydrologic based studies (Khallaghi & Pontius, 2021;Ridolfi et al., 2014;Woolsey et al., 2007).
The transect method can be described as the measurement of a river property such as its width taken as a crosssectional measurement on site, derived from remotely sensed imagery, or from other topographic sources such as maps or digital elevation models. As described in Glenn et al. (2016), transects are measured as straight lines perpendicular to the centerline of the river, or similarly described in Pavelsky and Smith (2008) as orthogonals to the centerline pixels. Following these definitions, the transect method described in this study measures the crosssectional width along a channel transect (CT) orthogonal to the centerline of the river channel (see CT in Figure 1).
Although numerous studies exist utilizing transect measurements to study water discharge rates, parameterize hydraulic models, or to track geomorphologic changes (Bartley et al., 2008;Mengen et al., 2020;Ridolfi et al., 2014), guidelines on transect spacing, location, or frequency are lacking within the literature. Generally, the transect spacing and location are determined by the purpose and intention of the study (Glenn et al., 2016). Some guidelines on location and spacing of cross-sections exist, such as the guidelines defined by Samuels (1990), which are based on a combination of common sense, mathematical equations and practical experience (Md Ali et al., 2015). While the guidelines are helpful, they are intended for 1D hydraulic models and aim to provide accurate reproduction of the backwater effects and representation of physical waves (Md Ali et al., 2015;Samuels, 1990). Nonetheless, the equations developed by Samuels have performed well as guidelines to determine good transect spacing, as shown in Md Ali et al. (2015) who explored the impact of cross-section spacing in 1D hydraulic models based partially on Samuels equations and the modeler's own judgment.
As transect location and spacing may have significant impact on the properties investigated, some studies explicitly test these properties and their influence in sensitivity studies (Glenn et al., 2016;Md Ali et al., 2015).
A study by Cook and Merwade (2009), investigating different effects such as geometric configurations on flood inundation maps, found that the flood extent increases as the number of cross-sections increases. Here, the initial distance between transects were approximately at 120 m for a 6.4 km river and at 1.2 km for a 62 km river. The transect spacings were then doubled, tripled, halved, or otherwise fractioned to test the effect of spacing on the resulting inundation maps (Cook & Merwade, 2009). Another study by Glenn et al. (2016), investigating the effect of transect location, spacing, and interpolation methods for accuracy of interpolated bathymetry, found that transect spacing is the primary factor influencing bathymetry accuracy.
Overall, transect spacing and location are poorly defined in the literature, yet transect spacing has shown to have significant impact on results. To account for this, different transect spacings should be considered when implementing the transect method. In addition, the literature shows that cross-sectional measurements, or transects, are utilized across various disciplines, despite the lack of guidelines on transect spacing. Due to its wellestablished usage to measure river width, this conventional method can be implemented as a comparative method to HydroWidth.

| The conventional methods: Segments
The segment method differs from the transect method in that the width is computed as the average over a predefined segment where the segment may include only the river channels or also islands and gravel deposits F I G U R E 1 The conventional methods: Illustration of calculating width by the use of channel transects (CTs) or based on effective width (EW) and the required components for EW (W b , A w , and A t ). Example shown is of 100 m spacings between transects and 100 m segments.
(non-wetted area) within the segment. Similar to the transect method, the guidelines on how long the segments should be depend on the purpose of the study (X. . Variations of utilizing segments are well implemented in satellite and aerial imagery-based approaches, such as approaches utilizing the algorithm RivWidth (described in Section 2.3) to calculate river width (Frasson et al., 2019;Mengen et al., 2020) or to validate river width (Andreadis et al., 2013). In some applications, river width and other properties are averaged over reachscale segments to calculate, for example, flow rate (Mengen et al., 2020) or river discharge rates (Feng et al., 2021).
Applications at various segment scales are also found beyond the scope of calculating geometric configurations, such as to predict fish distributions over certain river segments (Leathwick et al., 2005) or to characterize underwater acoustic signals at segment scale (Tonolla et al., 2011).
In Yamazaki et al. (2014), two river width measurements are compared, described as the effective width and bank to bank width of a river. The effective width considers the wetted and non-wetted area within a specified river segment and can be described as follows: where EW is the effective width, W b is the bank to bank width of a transect, A w is the wetted area within the segment extent, and A t is the total area within the segment extent, including islands and gravel deposits (Yamazaki et al., 2014). Based on the definition of effective width above, the segment method implemented in this study measures the effective width of segments along a river at various spacings ( Figure 1). Similarly to the transect method, the implemented segment method measuring the effective width over a specific segment distance is a well-established method to measure a form of river width. Thus, this method can be implemented as another comparative method to HydroWidth.

| Remote-sensing-based methods to calculate river width
While the conventional, initially in situ oriented, methods show widespread application in the past, river width measurements and variability to calculate, for instance, water discharge rates have shifted their focus to remote rather than on site measurements. It is not surprising then that in situ measurements are increasingly replaced by geodata-driven ecological studies, making use of remote sensing methods. The software tool RivWidth, introduced by Pavelsky and Smith (2008), is an alternative method to in situ measurements which utilizes the conventional method of transects and remotely sensed imagery to estimate river width, most notably used to estimate river discharge. The RivWidth tool is a raster data-based algorithm using channel and river masks as inputs to calculate a series of transects orthogonal to the river centerline (i.e., the line equidistant to the shoreline on either side of the river channel) at each centerline pixel (Pavelsky & Smith, 2008). While the RivWidth tool successfully calculates width values, its application is limited. The RivWidth tool calculates river width by use of orthogonal lines on a simplified centerline derived from the channel mask input, which is not always truly orthogonal in complex river channels. In addition, the tool is limited to satellite and raster-based data and the quality of river width depends greatly on the quality and resolution of the channel mask given as input (Pavelsky & Smith, 2008).
In terms of making use of remote sensing methods, the Global Width Database for Large Rivers (GWD-LR) was developed by Yamazaki et al. (2014) for application at global and continental-scale river modeling. The GWD-LR measures effective width and bank-to-bank river width for large-scale rivers of widths >183 m between 60S and 60N (Yamazaki et al., 2014). Although the GWD-LR uses a channel mask, calculates bank-to-bank width, and is applicable only to large rivers, the methods presented in Yamazaki et al. (2014) show potential for further use in developing methods of small-scale river channel width measurements. Thus, the methods presented in this article show several adaptations of the method presented by Yamazaki et al. (2014) and are described in Section 3.
A few years after the GWD-LR, the Global River Widths from Landsat (GWRL) database was developed with a global coverage of rivers and streams wider than 30 m (Allen & Pavelsky, 2018). The GWRL is a large-scale measurement of width at mean annual discharge and, according to Allen and Pavelsky (2018), most accurate and complete at rivers wider than 90 m. While the GWRL is not applicable for small-scale river width measurements (<30 m), its global coverage is a great advancement in the field and has found widespread application.
RivWidthCloud, an improvement of RivWidth, was introduced in 2020 as an automated Google Earth engine algorithm also measuring river width from remotely sensed imagery. RivWidthCloud does not require cloud-free images as input and extracts river centerlines and widths from remotely sensed images with minimal user input (X. . Different from RivWidth, the RivWidthCloud algorithm allows for multiple centerlines in a river. However, RivWidthCloud relies on the GWRL to calculate the connecting centerlines of the river and still uses a channel mask with artificially reduced topological complexity (X. . Thus, due to the river masks required by RivWidth and RivWidthCloud, they are not applicable to measure river channel width and its variability in small-scale and complex river structures, such as in braided rivers with multithread channels. RivaMap, introduced by Isikdogan et al. (2017), is an automated river analysis approach based on remotely sensed imagery that does not require a river mask. The RivaMap engine uses water-enhanced cloud-free composite images as input and applies a singularity index to extract curvilinear features (e.g., rivers, but also roads if not enhanced). As described in Isikdogan et al. (2017), the singularity index is sensitive to the intensity of the input data which may cause islands to be mistaken as rivers, specifically in complex river structures. In addition, the RivaMap engine is tailored to large-scale application, for instance to develop the width data set for North American rivers from Landsat images at a spatial resolution of 30 m/pixel (Isikdogan et al., 2017).
The literature shows various applications of the conventional methods as well as alternative approaches based on remotely sensed data implemented to measure river width. While the remotely sensed approaches produce quantitative data, the simplifications of the shape of the river reduce the potential application of the methods to study small-scale river width variability. In addition, these approaches mostly focus on large-scale rivers where the raster resolution has low granularity (such as 30 m/pixel), making it hard to measure small variabilities in river width.

| Medial axis transform to calculate centerlines
A well-implemented method that preserves the shape of features in terms of the extent and connectivity of the original shape is the medial axis transform (MAT), also termed skeletonization of an object or feature (Ogniewicz, 1994). The MAT reduces the shape of an object to a one-dimensional graph-like structure, the medial axis, which has at least two points on the objects boundary that are at equidistant to a point on the medial axis (Lee, 1982;Ogniewicz, 1994). There are several ways the MAT can be calculated. The traditional method, first introduced by Harry Blum (1967), utilizes points on the shapes boundary and finds the corresponding maximally inscribed circles (Widyaningrum et al., 2020). However, numerous definitions of MAT with various implementations and different methods are found in the literature, such as utilizing Voronoi diagrams and Delaunay triangulation (Lewandowicz & Flisek, 2020;McAllister & Snoeyink, 2000;Ogniewicz, 1994).
The MAT is a well-adapted method to skeletonize simple shapes, often used to construct centerlines of rivers (Lewandowicz & Flisek, 2020;McAllister & Snoeyink, 2000); however, the MAT seems to have drawbacks when calculating a centerline for complex shapes, such as for braided or branching rivers with islands. In McAllister and Snoeyink (2000), where MAT was utilized to calculate a centerline of simple and complex polygons, only few implementations of MAT for polygons were robust and most implementations poorly handled lines with multiple endpoints. In addition, the authors found that lakes and river areas with sandbars or islands resulted in a medial axis with a complex branching structure which disregarded islands (McAllister & Snoeyink, 2000).
The complex branching structure would require extensive additional pruning of the skeleton branches, as done in Ogniewicz (1994), to allow for river width measurements to be taken on the centerline created by the MAT method, especially in complex river structures. The traditional method of calculating the MAT is also utilized in Esri's own tool to calculate the centerline of a polygon "Polygon to centerline" (Lewandowicz & Flisek, 2020). As described in Lewandowicz and Flisek (2020), the centerline calculated with the tool creates distributary channels within an elongated polygon feature which need to be eliminated manually.
In general, the MAT method constructs a skeleton considered on the center axis of a shape; however, the center axis constructed splits at the ends of a structure and results in multiple branches as the shape gains complexity.
As spurious branches should be avoided for width measurements, the MAT-based centerline is not applicable for HydroWidth. The method presented in this article determines a centerline sensitive to side channels and regions where branching occurs.

| PROP OS ED ME THOD: HydroW idth
The small-scale approach presented makes use of standard raster and terrain analysis methods in a different context. To calculate river width and its variability, HydroWidth can be broadly divided into three main steps: deriving (1) the Euclidean distance of the shoreline, (2) the profile curvature surface of the Euclidean raster, and (3) a detailed centerline to extract the width measurements. Similar to Yamazaki et al. (2014) are the calculation of shoreline distances and determination of centerline pixels, different are the input data to the algorithm, the gradient transform used, and the small-scale approach on individual river channels (significantly smaller than 183 m).
Prior to a more thorough explanation of the three main steps, we will present the required data inputs.

| HydroWidth data input
The HydroWidth script requires one input: the full river in vector form. No simplifications of the river, such as river masks which do not allow gaps within the river's extent, are required. Complex river types showing various river branches within a riverbed can be an input as well as simple river types with a single river channel. In addition, no flow direction maps or drainage area maps are required as for similar algorithms (Yamazaki et al., 2014). The first step of HydroWidth is to convert the river into the river shoreline which is used to calculate the Euclidean distance. For the purpose of this study, the river inputs are in vector form, extracted from historical maps by deeplearning algorithms (see Wu et al., 2022).

| Euclidean distance
Euclidean distance gives the straight-line distance from each cell in a raster to the closest source. The shoreline of the selected river is determined as the source and converted internally to a raster with a predefined cell size of 0.5 m. To incorporate only cells within the river, the Euclidean distance is calculated at 0.5 m/pixel from either shoreline bank toward the center of the river. For local maximum distance measurements between the shorelines, the center of the river then holds the highest values as it is the furthest distance from each shoreline (details on local maximum in Section 3.3). As the pixels with the highest distance values are at the midway point (i.e., the center) between the shoreline distances, the Euclidean distance values are doubled for each center cell to render the river width at that cell between the shorelines. Figure 2a illustrates the use of Euclidean distance on a section of the braided river type. The orange highlighted oval in Figure 2 draws attention to complex situations when multiple branches come together. As shown, the distance values in these complex regions are not extracted for width measurement as they do not represent the highest values (i.e., the center of the river).

| Curvature and centerline
The following steps include the derivation of a centerline to extract the maximum width measurements at the correct locations. To do so, the profile curvature surface of the Euclidean distance raster is calculated. The profile curvature is measured parallel to the direction of maximum slope and creates a surface raster of the input representing convex (−), concave (+), or linear (0) curvature between the initial pixel and its neighbors, a property which in terrain analysis affects the acceleration or deceleration of flow across a surface (Kimerling et al., 2016). Thus, the resulting profile curvature surface presents positive values when the value between two neighboring pixels is upwardly concave, negative values when upwardly convex, and zero values when the pixel shows a linear surface between that cell and its neighboring cells (Kimerling et al., 2016). As the Euclidean distance raster is mostly linear, the profile curvature surface shows mostly values around zero (Figure 2b) with small concavity or convexity.
Within the center of the Euclidean distance raster, the maximum values form a peak, or ridge, as the values at each cell next to the maximum center cell decreases. This makes the center unique as all other Euclidean distance cells continuously increase or decrease compared to their neighbors. Here, the profile curvature raster renders strong negative values as the surface is upwardly convex and flow would decelerate over this surface. Different than in the Euclidean distance raster, the curvature surface detects strong negative (or peak) values in the center of small as well as large channels. If only a distance raster was applied, the center values showing maximum distance to the shoreline within a small channel and a very large channel would be significantly different. As channel-specific width is measured, this use of curvature is important to determine center pixels in both large channels with large width measurements and small channels with small width measurements that exist within the same section of the multithread river. To determine the centerline of the river, the second condition for centerline determination described in Yamazaki et al. (2014) can be applied. As the profile curvature surface provides a gradient transformation of the Euclidean raster, different from the distance raster used in Yamazaki et al. (2014), the condition is adapted to determine the most negative gradient values of the curvature surface between the considered pixel and its eight neighboring pixels that are smaller than the threshold gradient (set to −80 in this study). This adaptation of the curvature surface allows for a more sensitive determination of the centerline for complex braided rivers.
The resulting cells represent the centerline of the river. Lastly, the Euclidean distance values calculated are extracted at each centerline pixel to render the river width at each centerline cell. As shown in Figure 2c, the output of HydroWidth are quasi-continuous river width measurements along the centerline of the river. The HydroWidth output includes river width measurements for small river branches or channels as well as discontinued channels, capturing the detailed variability in river width. Note, although termed centerline and hence implying continuity, HydroWidth actually produces a linear set of raster pixels that are interrupted where no clear center can be defined.

| E XPERIMENTS: COMPARING CONVENTIONAL ME THODS TO HydroW idth
We conducted three experiments to test the small-scale approach compared to the transect and segment methods. The three experiments consist of different river types illustrating the expected complexities of vector features from DMP analysis in ecology, each of varying river length and structural complexity.
Overall, this section first describes the data and selected river types and then continues with the experimental setup of the selected river types as well as site-specific methodological steps taken for the conventional methods. The experimental results and comparison of the methodological approaches are presented in Section 5.

| Data
The data used in this study consist of rivers extracted from scanned historical topographic maps by several For the analysis, three map sheets with different river types were selected that feature river sections with varying lengths and river width complexity. The three river types selected are a braided, a modified, and a meandering river type within the Swiss plateau (see Figure 3). The map sheets in Figure

| Braided river type
Shown in Figure 3a is a section of the Aare River, a large river flowing entirely within Switzerland and a tributary of the Rhine River. The river section depicted is of a Siegfried map sheet (TA 138) from 1876, with a river length (measured from the centerline) of approximately 40.5 km over a map sheet river extent (measured as straight-line distance) of 6.5 km. Braided rivers adopt a multithread channel pattern, as shown in Figure 3a, where some channels are linked to the main channel by more confined single-thread sections (Zanoni et al., 2008). The individual channel threads can vary greatly in width, making the braided river type a complex shape to measure river width variability. Figure 3b shows branches off the Thur River, a lowland river situated in the northeast of Switzerland. The historical map depicted is a Siegfried map sheet (TA 057) from 1880. The modified river type investigated has a river length of approximately 42 km over a map sheet river extent of 24 km. The strongly human modified river channel shows sections of the river that have been channelized (i.e., straightened). As channelized rivers do not show much variability in width, the modified river serves as a medium between a human-modified river type and a river type with some variability in channel width. This modified river type shows strong human influence on the river yet with some sections of branching or complexity due to waterway intersections. As many rivers experience strong human influence, this "modified" category was included for width measurement.

| Meandering river type
Another common river type is a meandering river, a single river channel of regular sinuous curves winding through a valley. The width variability here is rather simple, but studies of meandering river types are common, for instance due to their importance in sediment bar dynamics (Monegaglia, 2018). Thus, the conventional and small-scale approach to measure width is also tested for a meandering river type, this will allow for a comparison of the method robustness. Figure 3c depicts a section of the Reuss river near the town of Baumgarten, Switzerland. With a river length of approximately 17.5 km over a map sheet river extent of 7.5 km, the Reuss river section depicted is from a Siegfried map sheet of 1882 (TA 157).

| Braided river experiment
The braided river posed the most complex geometrical shape tested as the width varies significantly between the many channels. The rivers represented in this study continue over bordering map sheets. For the braided river type, the main river channel continues over further map sheets while some channels end within the chosen map sheet. To account for the fact that the rivers may not end at the map sheet border and to omit the methods potential assumption of such, the map sheet borders are not considered in the analysis. Furthermore, the width of river branches and channels which end within the selected map sheet are included in the analysis as no river mask or other simplifications are applied.

| Additional work of the conventional methods
In terms of preparatory work of the conventional methods, some additional work was required for the transect method to create mostly orthogonal transects along the braided river. As the complex river type has multiple centerlines, the transects along the centerlines would at random result in non-orthogonal lines in areas where multiple centerlines exist due to a split or merge of the river channels. To enhance the results of the transect method for better comparison to HydroWidth, the preparatory work included creating a mask of the main channel and handling farreaching channels and branches as separate entities (Figures 4a,b). As shown in Figure 4a, a total of two side channels and three branches of the main channel were delineated in addition to the main channel mask for the transect method.
The approach of applying a channel mask is a common practice within the literature to reduce the complexity of the generated centerline (Mengen et al., 2020;Pavelsky & Smith, 2008). The centerline of the main channel mask and of the separate entities then rendered more accurate transects of the complex river as a whole (Figure 4b), instead of simply generating transects across the entire river channel system based on one centerline.
The segment method, measuring effective width, did not follow the same manual work as done for the transect method. To keep the segment method as described in Yamazaki et al. (2014), a river mask was generated for the entire main channel riverbed, including the main branches ( Figure 5). For the braided river type, the only entities separated from the mask were the far-reaching side channels. Figure 5 illustrates the river mask and bank to bank transects used to calculate the effective width of the braided river. As described in Section 2.2, the effective width is calculated as the bank to bank transect width multiplied by the ratio of the wetted area of the segment extent over the total area of the segment extent. The segment extents are measured in the same increments as the transect method, at 50, 100, 200, and 300 m.

| Modified and meandering river experiments
The modified and meandering river types illustrate rather simple geometrical shapes, where the modified river section shows some complexity at waterway intersections and the meandering river shows some variability due to its sinuous behavior. For the analysis, the map sheet boundaries were excluded here as well, as the river types continue over multiple map sheets.
In terms of preparatory work for application of the conventional methods, the modified and meandering river type did not require much additional work. Similar to the braided river, the approximate river width had to be known to estimate the length of the transects. Described in Section 2.1, the transect spacing is assumed to have the most significant impact on the results which is why four different spacings were selected and tested. However, to investigate whether the transect location is truly less significant than the spacing, an additional analysis was performed testing the transect location of the 200 m transect spacings, described in Appendix A.

| RE SULTS
Overall, the results show that the HydroWidth method presented significantly larger sample sizes and was able to capture variability in width for all three river types (Figures 6a-c). As shown in Table 1, the largest differences in mean, median, and maximum width measurements were observed in the braided river type, a more complex river system experiencing large variability in width. For simpler geometrical shapes such as the meandering and modified river type, the HydroWidth and conventional methods showed similar results, with some significant differences between the effective width and HydroWidth results. and steep peaks indicate that most observations of that method are condensed to a small spread of river width. As shown in Figure 6a, the sampling size of the braided river type was significantly higher for HydroWidth with a sample count of 15,840 compared to the sample count of the segment or transect methods, which rendered a sample count of 398 and 723 for the 50 m spacings of the segment or transect method, respectively. In addition, the spread of river width observations for HydroWidth shows many observations continuously over the full range of width measurements, compared to observations from the traditional methods. The HydroWidth method found the mean river width to be 64.2 m and the median to be 38 m for the braided river (Table 1). The segment method of 50 m spacing found the mean and median river width to be 95 and 17 m, respectively, an overestimate of 30 m for the mean and an underestimate of 21 m for the median river width compared to HydroWidth. In general, the river width median found with HydroWidth is significantly higher (between 15 and 21 m) compared to the conventional methods.

| Braided river results
In terms of river width variability, the maximum and minimum river width observations and their sample density are of interest. The HydroWidth method found a maximum river width of 336 m, with 195 observations above a river width of 300 m and 843 observations above a river width of 200 m. The largest river width was F I G U R E 5 Illustration of the components to calculate the effective width for the segment method on the braided river type. The segment extent is determined as the area between transects and is shown at spacings of 100 m.  Figure 7 shows the braided river with river width measurements by the HydroWidth method.

| Modified river results
The sample count of the HydroWidth method was significantly higher with 41,929 observations, compared to the segment method with highest observation counts at 630 and the transect method with highest counts at 631.
The mean and median values for the modified river showed small differences between methods, with a mean of 10.6 m for HydroWidth and 10.8-12.4 m for the segment and transect methods of various spacings (see Table 1).
As shown in Figure 6b, the overall spread of data observations over river width is relatively similar for the methods in the modified river experiment. Larger differences are found in the observed maximum width. The HydroWidth  50 m spacings. In other words, 32 m of river length are wider than or at 50 m in river width and are not reflected in the segment or transect method. Figure 8 shows the river width measurements of the modified river type by the HydroWidth method.

| Meandering river results
The meandering river has a rather simple geometrical shape and showed differences of up to 4 m in mean and median values of river width between the HydroWidth and traditional methods (see Table 1). As shown in F I G U R E 7 River width measurements generated by HydroWidth of the braided river.

| Comparing results
All three experiments showed higher observation counts and larger spread of observations in the HydroWidth method compared to the two traditional methods at various spacing intervals. In Figure 10, the differences in maximum, minimum, and average width found per method are compared to HydroWidth. Here, the largest overall differences are seen in the braided river type, with maximum width differences of 200 m to HydroWidth, differences which are larger than the average river width measured in many cases. The large differences observed between the methods in the braided river, as well as the difference observed in the modified and meandering river, demonstrate that the results in river width and its variability may greatly vary depending on the method and sampling granularity used. As expected, the largest differences between methods are observed in the complex braided river and decrease in difference the simpler the geometrical shape is ( Figure 10). An exception to this is the difference observed in minimum width, where specifically larger spaced segments and transects showed differences to the minimum width observed by HydroWidth. In the meandering river, this difference is in part due to small islands which created small branches with a minimum width of 10 m. For the larger segment and transect spacings, these small variabilities were not captured. The average width measured in the modified and meandering types showed small differences of under 5 m to the average width measured with HydroWidth. As in minimum and maximum width measurements, the average width in the complex braided river type showed larger differences to HydroWidth, up to 30 m in the segment method and up to 10 m in the transect method. Table 2 illustrates the respective runtime of the scripts as well as estimated manual efforts, in minutes, to measure river width in the three experiments. The python scripts were written in ArcGIS notebooks, based on Jupyter notebooks. The braided river had a river length of 40.5 km, the modified river of 42 km and the meandering river of 17.5 km. The various spacings were applied within the respective script; thus, the segment and transect methods are listed without specification on spacing distance. On average, the HydroWidth script required more time F I G U R E 8 River width measurements generated by HydroWidth of the modified river type.

| Runtime
than the transect or segment method. However, the manual work time required for the transect method greatly increased the total processing time of the method. In addition, the total runtime of the scripts are similar for all methods in the complex river type. The script runtime decreases for the conventional methods in the less complex river types.

| D ISCUSS I ON
The experiments tested three different methods to measure river width and its variability at three different sites featuring rivers with various geometrical complexity. The results showed that the HydroWidth method is an adaptable and robust approach to measure river width and its variability in complex as well as simple river types.
The HydroWidth method also required the least amount of preparatory and/or manual work, in fact the only manual work done was to remove the map sheet boundaries for all methods. In contrast, the transect method required some manual work for all river types and rigorous work for the braided river type to increase the accuracy of the results. For the transect method in the braided river type, despite the manual efforts to delineate branches and channels in addition to the main channel mask, some erroneous transects occurred. Due to the simplified centerline and directional changes of the individual channels, transects were generated that were not truly orthogonal to the river and resulted in river width measurements larger than the maximum river width of 336 m. Omitting the preparatory work of the transect method and simply running a script as done with HydroWidth would have resulted in larger processing errors or uncertainties of the transect method due to non-orthogonal transects and F I G U R E 9 River width measurements generated by HydroWidth of the meandering river.
multiple centerlines. Hence, with this manual preprocessing, we have made it harder for HydroWidth in comparative experiments.
The HydroWidth approach is less prone to the problem of multiple centerlines in a single channel, even in braided river systems, due to the use of a curvature transform of a Euclidean distance surface. The profile curvature raster created from the Euclidean distance finds the greatest direction of slope at the center. With the additional threshold applied to the curvature values in HydroWidth, the centerline values of a side branch fall under the threshold when the centerline of the side branch reaches another channel. This sensitivity to channels and branches, however, also means that the centerline generated by HydroWidth is not continuous over the full river. Thus, HydroWidth is best used to generate detailed small-scale river channel width measurements and can perhaps be used as base for other measurements at that location, but not to generate a continuous centerline. Furthermore, the Euclidean distance from the shoreline to the center was taken at a resolution of 0.5 m/pixel and doubled for width measurements at the center. This simple doubling may lead to potential overestimates of 0.5 m in river width measurements.
For the segment method, the river mask used to measure bank to bank width had a significant impact on the measured river width results for the more complex braided river type. Far-reaching channels included in the mask resulted in large bank to bank width measurements which are a major factor in measuring effective width, F I G U R E 1 0 Differences in minimum, maximum, and average width between conventional methods to HydroWidth in three river experiments. C, channel transect; E, effective width.

TA B L E 2
Runtime of scripts and manual work estimates. resulting in overestimates of up to 200 m in width. In general, the segment (i.e., effective width) method presented very different results to the transect and HydroWidth method, particularly in the complex river type with many islands and gravel deposits within the bank to bank area. The results of the segment method show that the method is perhaps not best practice when measuring small-scale river channel width and specifically when interested in capturing small-scale variability of the width. The segment method would provide best practice results when the bank to bank width of sections of the riverbed is of interest and the wetted width of one location is summed across all channels, perhaps compared to the channel system width described in Bufe et al. (2019).
The results of the conventional methods also varied depending on the spacings applied. Smaller transect spacings of 50 m were able to better capture variability in width than larger transect spacings of 300 m. Overall, we found that the conventional methods are sufficient to use for width variability measurements in modified or meandering river types but fail to capture the variability of width in more complex river types. Variabilities, such as small branches in otherwise simple river systems, are particularly problematic for the conventional methods as these details are lost by averaging over segments or utilizing large transect spacings. Clearly, HydroWidth offers much more detailed information with its quasi-continuous perspective. This high granularity gained regarding especially the variation of river width offers additional insights into the river's ecology. These insights could be applied in studies at reach scale, such as in studies focused on active channel characteristics in complex braided river structures (Tonolla et al., 2020), or at individual floodplain scale where perhaps the wetted parafluvial regions are of interest and current measurements are based on gauging stations (Chanut et al., 2019).
In terms of limitations, the work presented is limited to three experiments performed on vector data. The HydroWidth method requires additional testing with raster-based inputs such as inputs from aerial imagery to be applicable to raster-based inputs. In addition, HydroWidth was limited to a 3 × 3 window (cell size 0.5 × 0.5) in the curvature tool due to the ArcGIS pro version available. Newer versions feature a 15 × 15 window for highresolution data.

| CON CLUS IONS
We have presented a small-scale approach to accurately measure river width variability together with first experimental results of three rivers featuring various river width complexities. We applied three methods to measure width variability at the experimental sites, including different spacings for the conventional, transect and segment, methods. The experiments showed that HydroWidth is a robust and adaptive method to measure river width variability and presents reliable results for all tested river types of different lengths and complexity. HydroWidth is thus flexible and transferable to multiple river types of distinct scale and structure. In addition, the experiments showed that the conventional methods are sufficient to use for simple rivers, such as the meandering and modified river.
The small-scale approach presented was tested on rivers extracted by DMP techniques from historical maps. To expand the application of HydroWidth in future work, it may be applied in measuring river width variability from other inputs, such as remotely sensed or aerial imagery at high granularity, and compared to other river width measuring tools based on satellite or aerial imagery. The small-scale approach is capable of capturing variabilities in river channel width and is thus able to support future spatiotemporal work of river systems from the past to present.

ACK N OWLED G M ENTS
The authors thank the two anonymous reviewers for their helpful comments to improve the article. The authors would also like to thank all project partners for their support and the University of Zurich for open access funding.
Open access funding provided by Universitat Zurich.

SIGNIFICANCE OF TRANSECT POSITION
As briefly stated in Section 4.3 of the article, a supplementary test was conducted to investigate whether the positioning of the transects, or the downstream shifting of the seed position along the river, had an impact on the results. While previous work suggests that transect spacing has a significantly larger impact than the actual positioning of the transects (Glenn et al., 2016), the importance of transect position was tested on the meandering and braided river types to see if this statement holds true for measurements of river width and its variability. The results of the meandering river type showed a mean river width difference of 0.76 and 0.47 m for the offsets of 20 and 70 m, respectively (Table A1). The minimum width differences were approximately 2 m for the offsets compared to the original transect position and the maximum width differences were approximately 12 and 3 m for the offsets of 20 and 70 m, respectively. As shown in Table A1, the results of the braided river type showed a mean river width difference of 0.77 and 4.26 m for the offsets of 75 and 100 m, respectively. For the braided river, the minimum width differed between approximately 4-10 m between the original and the offset values measured.
Based on these results, the conclusion can be drawn that transect position does show smaller differences between river width averages and variability than the differences seen between the transect spacing results (see Sections 5.1-5.4). However, the maximum and minimum river widths measured at the various offsets did show some significant differences in recorded river width. Thus, not only transect spacing but also transect position should be considered when calculating river width and its variability.