Dynamic river basins and hypsometric analyses: implications to land management and prioritization in Bohol, Central Philippines

ABSTRACT The study presented a method of characterizing landform dynamics that integrates a divide stability metric and hypsometric analysis. Chi (χ) - a proxy for steady-state river channel elevation - indicated a drainage divide stability. Simultaneously, the hypsometric analysis provided information on a basin's geologic development stage and erosion proneness. The study used a 30 m SRTM digital elevation data, the DivideTool/TopoToolbox of MATLAB, and the SWAT model. The tool computed χ values following the stream network, enabled the selection of divide sections, extracted channel head's χ values, determined divide stability by predicting migration direction for unstable divides, and produced histograms of χ values for each divide section. Equal χ values at the channel heads of opposing river networks indicated a stable divide. In contrast, a difference in χ values suggested an unstable divide and a potential to migrate from low χ values towards the divide's high χ values side. The study proposed the mean χ difference (χmd) metric to indicate the degree of divide mobility. Meanwhile, the SWAT model defined the basins and subbasins and set the hypsometric analysis parameters. Each subbasin's hypsometric integral (HI) was used to create a continuous surface of HI values. The combination of χmd and HI analysis revealed nine subbasins with highly mobile divides and high erosional areas, identifying them as high-priority conservation zones. River basin characterization can utilize the new approach to target areas for location-specific land and water conservation measures and other developmental goals.


Introduction
Enhancing the sustainable use of land and water resources while protecting their sensitive nature is the primary goal of the integrated river basin management (IRBM) approach.A basin characterization encompassing all of its resources and ecosystems is a crucial phase of this approach involving an inventory of basin components and features.Tools such as geographic information systems (GIS) and remotely sensed data facilitate the extraction of basin properties and other parameters related to geo-hydrological processes that form the essential information necessary for planning and decision-making.A growing number of studies across the globe utilized GIS and spatial datasets to carry out river basin characterization (Pande et al., 2018;Asfaw & Workineh, 2019;Abdeta et al., 2020;Harsha et al., 2020;Sharma & Mahajan, 2020;Obeidat et al., 2021;Benzougagh et al., 2022).
A river basin, the unit of analysis in IRBM, is a hydrologically defined landform comprising drainage divides and stream channel networks.Drainage divides and river networks are dynamic elements of river basins that continue to change in response to tectonic and erosional forcings (Willett et al., 2014), with critical implications on how land resources will be managed and used.Drainage divides play a significant role in shaping drainage basins by setting the boundary between adjacent basins.At the same time, the network of stream channels is the pathways of bedrock erosion, water, nutrient, and sediment transport from uplands to oceans (Willett et al., 2014).Drainage basins are previously assumed to be stationary.However, observations of stream capture (Linkevičiene, 2009;Bloxom & Burbey, 2015;Shugar et al., 2017), long-term erosion studies (Beeson et al., 2017), and numerical modeling (Goren et al., 2014) demonstrate that basin geometry and network topologies continuously approach asymptotic value.Differential erosion rates between adjacent basins drive the geometric adjustments (Goren et al., 2014).Goren et al. (2014) further explain that continuously migrating divides become sources of autogenic sediment flux variations in a landscape, potentially impacting resource management.
In the past and recently, efforts to characterize a river basin have generated geomorphic and topographic indices considered rapid assessment tools and proxies of different surficial processes (Strahler, 1952;Singh, 2009;Forte & Whipple, 2018;Schwanghart et al., 2018).Geomorphic analysis, investigating the linear, relief, and areal aspects of a basin, has been carried out globally to identify and prioritize areas in a basin for urgent attention (Obeidat et al., 2021;Odiji et al., 2021;Benzougagh et al., 2022).The primary input is the present-day surface topography that resembles a complex interaction between tectonics and climate forces on varying lithology occurring over a geologic time setting, and which is the same topography becomes the fundamental basis for basin management strategies (Pande et al., 2018;Harsha et al., 2020;Sharma & Mahajan, 2020).
One of the commonly used methods in river basin characterization is hypsometric analysis.The hypsometric analysis examines the distribution of ground surface area or horizontal cross-sectional area of a landmass to its elevation (Strahler, 1952) from topographic sheets and GIS-based analysis of digital terrain data.A hypsometric analysis produced geomorphic indices, the hypsometric curve, and the hypsometric integral (HI) (Strahler, 1952;Chen et al., 2019).The shape of the hypsometric curve classifies a basin into different stages of geologic development, and, at the same time, HI represents the area under the curve and expresses the volume of a basin that has not been eroded but is not directly related to relative active tectonics (El Hamdouni et al., 2008). El Hamdouni et al. (2008) consider the shapes of the hypsometric curves, whether convex in its upper portion, convex to concave, or convex in the lower portion, and the corresponding HI value.They also classify HI values into high (> 0.5), intermediate (between 0.4-0.5)and low (<0.4).The hypsometric curves with high HI values are convex in shape, intermediate HI values are convex to concave or straight, and low HI values tend to have concave shapes (El Hamdouni et al., 2008).Together with the shape of the hypsometric curve, high HI values are possibly associated with young active tectonics.According to the study, low HI values are related to older landscapes that have been more eroded and less impacted by recent active tectonics.An assumption is that if the shape of the curve in its lower portion is convex, it may relate to uplift along a fault or perhaps uplift associated with recent folding (El Hamdouni et al., 2008).Meanwhile, Singh (2009) carry out a hypsometric analysis to estimate basins' erosion status and prioritize areas for soil and water conservation measures in the Lesser Himalayan region.The study found that higher annual sediment yield comes from the basin with a higher hypsometric value indicating the landmass's youthful nature.
The metric of drainage divide stability as a geomorphic parameter is new for river basin characterization.Expressed as chi (χ), its development as a measure of divide stability anchors the notion of differential rates of river channel erosion on opposite sides of a divide (Willett et al., 2014).When varying across-divide erosion rates exist between opposing river channel heads, the intervening drainage divide is set in motion until it reaches a steady state.The χ is an integral solution to the stream power model proposed by Perron and Royden (2013), expressed as: where A is the upstream drainage area, A o is an arbitrary scaling area, x is the location of a point along the channel, x b is the base level, and m and n are empirical constants.χ values computed along stream channels map the horizontal motion of drainage divides and their dynamic evolution identifying transient erosional signals (Willett et al., 2014).χ maps are appealing and are simple to calculate because they provide a rapid visual assessment of divide stability over large areas (Willett et al., 2014;Forte & Whipple, 2018).χ maps can characterize the variability of a river network's topology and geometry in a river basin as they transmit tectonic and climatic signals throughout the landscape (Willett et al., 2014).
Recent studies on divide stability metrics have established a relationship between predicting landslide events and assessing physical infrastructure hazard vulnerability.Dahlquist et al. (2018) investigated the role of landslide-generating events on the reorganizations of drainage basins and landscape evolution.Their study conducted a topographic analysis using channel metrics to assess drainage divide stability and migration over areas where natural disasters have triggered large landslides.The study found that the resulting area exchange between basins due to landslides was consistent with landforms that advanced towards steady-state conditions as suggested by the channel metrics.Similarly, Schwanghart et al. (2018) used a topographic metric expressing river steepness and the earthquake ground acceleration to predict earthquake damage to hydropower projects in the Himalayan region.Their study identified some areas of the Himalayan river network as unsuitable for hydropower infrastructure due to the high probabilities of earthquaketriggered landslides.
The present study integrates the χ-metric (Perron & Royden, 2013) and the commonly used hypsometric analysis (Strahler, 1952) to characterize a dynamic drainage system.Specifically, the study aims to: a) assess the stability of drainage divides of river basins using the χ-metric and determine the degree of basin disequilibrium by evaluating the mean χ difference (χ md ), b) examine the spatial variation of erosional landforms using hypsometric analysis and c) identify and map highly dynamic drainage divides and erosional subbasins.The methodology developed is applied on the island of Bohol in the Central Philippines.As a rapid assessment tool developed in this study, identifying and prioritizing highly erosional areas with their migrating divides is possible, thus facilitating the resource planning process.The study is limited to demonstrating the use of these tools, while further studies are needed to validate the results.

Study area and the flow of analysis
Figure 1 shows the geographic location of the study area.The Philippine Archipelago, made up of more than 7100 islands, is located about a hundred kilometers off the Asian continent between the Pacific and the South China Sea and is confined between the Sundaland-Eurasian plate on the west and the Philippine Sea plate on the east.The Central Visayas group of islands, including Bohol, comprises numerous Cretaceous oceanic lithospheres formed and deposited in different geologic locations and diverse ways (Dimalanta et al., 2006).These islands emerge from the sea in about Mid-Tertiary (Salomon, 2012).
Bohol Island has about 411,276 ha land area, where around 66% of the land is devoted to agriculture-related activities.The island's drainage morphology consists of two major basins dissecting the central part: the Loboc and the Wahig-Inabanga River Basins.The former discharges on the southwestern side while the latter drains to the island's northern side.Both basins are of high economic importance where the Loboc River Basin hosts the famed Loboc River while the Wahig-Inabanga River Basin supports agricultural activities.Using the PAGASA-Tagbilaran Station climate data (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), the mean annual rainfall is about 1653 mm: April is the driest month, and December is the wettest month with 78 and 185 mm of precipitation, respectively.The temperature ranges from 24 o C to 32 o C, while the average relative humidity is 83%.On average, 20 typhoons visit the country annually, where around three of these pass the island.Bohol is a tectonically active island, and the most recent and destructive one was the Mw7.2 on October 10, 2013.Kobayashi (2014) mapped the ground displacement associated with this earthquake.
The digital elevation dataset used in the subsequent analysis is a Shuttle Radar Topography Mission (SRTM) data downloaded from https://earthexplorer.usgs.gov.The elevation data, officially published in September 2014, is void-filled data with a resolution of 1 arc-second (∼30 m).The study area consists of four tiles.Preprocessing includes tile mosaicking, projecting to WGS UTM 1984 Zone 51N, and extracting the study area.Figure 2 shows the analysis flow, as described in the following subsections.

Drainage divide stability with χ metric
The study applies the χ metric, a proxy for steady-state river channel elevation, to examine drainage divide stability and predict the direction of divide migration for unstable divides.It uses the DivideTools (Forte & Whipple, 2018), a series of Matlab-based tools for analyzing drainage divide stability built on top of TopoToolbox (Schwanghart & Scherler, 2014), to compute the χ metric values following the river networks.Forte and Whipple (2018) provide a detailed description of the tool.The χ analysis starts with the DivideStability function, which calculates drainage divide stability metrics and produces a river network shapefile with fields for the metrics.The study is particularly interested only in the χmetric as a topographic proxy for assessing drainage boundaries' equilibrium.Inputs to run the function are a DEM, a flow direction grid, and a few parameter values: the minimum accumulation area is 50 pixels (equivalent to 45000 m 2 ), the default theta_ref value is 0.45, and the minimum elevation is 1 m.Stream initiation depends on the minimum accumulation area.The theta_ref or the reference concavity is a constant for calculating χ and the 'min_elevation' parameter sets the minimum elevation for the base level.The function also produces a structure that stores the metric values at the channel heads for use in the companion code 'AcrossDivide'.
The AcrossDivide function evaluates in detail the stability of a selected divide.The procedure consists of manually selecting a divide by clicking on the areas of adjacent basins.The process highlights the channel heads, extracts the χ values in tabular form, and creates across divide plots of χ values.The study uses the standard deviation of the mean to determine the divide stability.A divide is stable when the 'mean of one side of the divide is within one standard deviation of the mean of the other side'; otherwise, a divide is unstable (Forte & Whipple, 2018).Histograms display the degree of separation or overlap of χ values and label the drainage divide movement's predicted direction.The direction of potential movement is from the side where channel heads have lower χ values towards the side where channel heads have higher χ values.For unstable divides, the study proposes a measure called the mean χ difference, χ md , which represents the degree of potential divide mobility following the equation: where, x mean is the mean χ values, while subscripts 1 and 2 refer to the opposite sides of a divide section.Based on the range of x md values, the study classified them into three degrees of mobility: low (x md <135), moderate (135≥ x md ≤255) and high (x md >255).
The study selects an unstable divide, extracts opposing rivers' elevation and χ values, maps their pathways, and plots their χ and elevation profiles in a GIS platform to show the reorganizing river networks' patterns.The river networks that share an unstable divide are described in Willett et al. (2014) as constantly adjusting their drainage areas either by divide migration or river capture.They are called the aggressive and the victim streams: the aggressive streams have lower channel head χ values than the victim streams (Willett et al., 2014).

Hypsometric analysis
Hypsometry produces two indicators of relative erosion rates: the hypsometric curve and the hypsometric integral (HI).The hypsometric analysis evaluates a basin's geologic development stage (Strahler, 1952;Singh, 2009).The hypsometric curve describes the basin area's distribution versus its altitude, while the shape of the curve indicates the degree of dissection and the stage of basin geologic development (Nath et al., 2019).The area under the curve, represented by HI, estimates the landmass volume that remained after erosion.
The hypsometric analysis begins with delineating basins and subbasins using the SWAT Watershed Delineator (https://swat.tamu.edu).A 30-m SRTM DEM is a primary input to run SWAT and create flow direction and flow accumulation rasters.The analysis uses a 300-ha minimum upslope area for stream initiation, enabling the model to delineate smaller catchments along the coastlines and disaggregate large basins into smaller subbasins.SWAT computes topographic values for each subbasin, including minimum, maximum, and mean elevations and the area distribution between one-meter contour intervals.These topographic values are exported to a spreadsheet to calculate, plot, and examine hypsometric curves and HI.The hypsometric curve is a plot of the relative area (a/A) versus the relative altitude (h/H), where a, A, h, and H refers to the area within the two adjacent contour lines, the total area of the basin or subbasin, the contour interval, and the relief of the basin or subbasin, respectively (Strahler, 1952).On the other hand, the HI computations follow Pike and Wilson (1971) as: where Z mean , Z min , and Z max refer to mean, minimum and maximum elevations, respectively.A continuous surface of HI is created by converting the subbasin polygons with the corresponding HI to points and using the kriging interpolation method.A basin and three random

Subbasin dynamics and prioritization
The study examines the dynamics of basin/subbasin through an overlay of the divide stability and the HI maps.The divide stability map highlights a highly mobile divide with χ md > 255, while the HI map identifies highly erosive subbasins having HI = > 0.5.The intersection of the two maps determines highly erosive subbasins with highly mobile divides.These subbasins are considered the top priority areas for land conservation programs.Figure 3A highlights the major basins in the island and their drainage boundaries, emphasizing the χ similarity of a stable divide in Figure 3B and χ differences of an unstable divide in Figure 3C.The map's visual inspection found that drainage divides between the major basins show slight color differences.However, it is noteworthy that at the headwaters of major basins in the southern portion of the island, divide sections shared between major basins and minor basins facing the southern coast show highly contrasting colors indicating high χ anomalies, as highlighted by Figure 3C.

Stability of divides between major basins and at the headwaters
In the current study, histograms of stable and unstable divides are selected, as shown in Figures 3B and 3C.To investigate the χ similarities and differences of the individual divide section quantitatively, Forte and Whipple (2018) use the histogram of χ values at the channel heads of either side of the divide.The histogram in Figure 3B shows the overlapping of χ values of the opposing channel heads.It also shows that the mean χ value of one side of the divide is within one standard deviation of the mean χ value of the other side, a conservative criterion for determining divide stability used by Forte and Whipple (2018).The histogram in Figure 3C shows significant differences in χ values of the opposing channel heads, indicating that the mean χ value of one side of the divide is far from one standard deviation of the mean χ value of the other side.As predicted, this unstable divide migrates from the low χ value side to the high χ value side of the divide or towards the north direction.

Mean chi difference (χ md ) and divide migration
The χ md of a divide is a measure of the χ anomaly between opposing channel heads that share a divide and an indicator of the degree of potential divide mobility: the higher the χ md , the higher the degree of divide migration.Figure 4 highlights the study area's divide sections, the spatial variation, and the migration direction.The mobile divide sections in Figure 4A are classified based on χ md described in Section 2.2.Divides with high χ md are located at the major basins' headwaters adjoining minor basins that drain towards the island's southern coast.These divides extend in the SW-NE direction and traverse over rocks formed during the Miocene-Pliocene periods.Other classes of χ md are dispersed and found to be between the major and minor basins that face east and northwest coastal areas.Between major basins, divides are stable, especially in the interior part of the island.However, the divide sections between major basins on the island's eastern side are predicted to be migrating at low to moderate levels.Though the χ md criteria presented in this study are arbitrary, they help illustrate the study's purpose.
Figure 4B shows the distribution and the direction of mobile divides' potential movements.14%, 40%, and 47% of divide sections are classified under a high, moderate, and low degree of potential mobility.Of the total identified mobile divide sections, 28% are moving in the N and NW directions, 5% towards the west, while 67% are heading towards the S, SE, and SW directions.Divide sections classified as highly mobile are moving in the northwest direction.These are the divides located at the headwaters of major basins that border minor basins facing the south.Six out of nine divide sections heading towards the south are moderately mobile.Of the ten divide sections inclined towards the southwest, seven divides have low mobility.

Disequilibrium basin and its river network
The elevation and χ profiles of streams found at both sides of a mobile divide give additional information on a basin's dynamics.The study illustrates this dynamic by selecting a divide section where χ shows a sharp anomaly across a divide, extracting two river profiles that meet at a divide, and investigating the χ values and the rivers' actual elevation profiles.Figure 5 shows the map view of two opposing river channels, which share an unstable divide predicted to migrate in a northwest direction and identifies the victim (low χ values) and the aggressor (high χ values) sides.The sharp color variation of χ across the divide section emphasized this χ anomaly (Figure 5A).The study noted earlier that smaller catchments along the southern coastal areas have a low χ value at their channel heads than the channel heads of major catchments located interior of the island.Both rivers discharge to the island's south coast, but their pathways and lengths differ.The victim river has a channel length of 78.3 km and is meandering towards its discharge point, while the aggressor stream extends to only 17.5 km long and goes straight to its outlet point.Both rivers have the same elevation drop, but their steady-state channel head elevation profiles have a difference of 367 m (Figure 5B).The inset histogram of Figure 5A shows a wide disparity of the χ values at the channel heads.

Hypsometric analysis at a basin and subbasin scales
Figure 6 shows the outputs of the hypsometric analysis, which emphasized HI variation at different scales.The study delineated 639 subbasins with catchment areas ranging from 0.09-2479.32hectares.The HI values vary from 0.1-0.6, and the spatial variation is notable in Figure 6A.The south-facing minor basins sharing divides with the larger basins show high HI values.There are patches of high HI areas in the western part of the island and the lower portion of the Wahig-Inabanga River Basin (Figure 6B).Considering the Wahig-Inabanga River Basin's high economic importance and intensive agriculture-related activities, the study selects the basin for a focused hypsometric analysis.Three subbasins are chosen with distinct HI values and hypsometric curves.Then, the subbasins' hypsometric features are compared with the larger basin's hypsometric attributes (Figure 6B).
Figure 6B shows the spatial variation of HI values across the Wahig-Inabanga River Basin and the selected subbasins' geographic locations.The larger basin and the subbasin 260 have low HI values of 0.19 and 0.28, respectively.In contrast,  subbasins 431 and 103 have higher HI values of 0.69 and 0.53, respectively.As HI values vary across the basin, the hypsometric curves also vary in terms of shape and pattern, which translate into stages of basin development: young (convex up), mature (S-shape), and old (concave up) (Strahler, 1952).The area below each hypsometric curve indicates the volume of the remaining landmass left after erosion.The higher the HI values, the more significant the remaining material volume and an indicator of still highly erosional landscape (Singh, 2009).The Wahig-Inabanga River Basin's hypsometric curve concaves upward while it crosses below the center of the diagram.Subbasin 431, located in the upstream portion of the basin, resembles a younger formation.Its curve is convex up and passes above the center of the diagram.Subbasin 260, located in the middle of the basin, has its hypsometric curve concaved up but is less concave than the larger basin, indicating an old subbasin.Lastly, subbasin 103 in the lower part of the basin has an S-shape curve.The curve suggests that subbasin 103 is transitioning to a mature stage.

Landform dynamics and prioritization
The study uses χ md and hypsometric properties to identify and prioritize areas for a range of conservation goals.There are six divide sections with high χ md values across the study area, as shown in Figure 4A.These divide sections intersect with 24 subbasins whose HI values range from 0.24-0.69,as shown in Figure 7. Out of the 24 subbasins, six have HI values higher than 0.5.By considering only subbasins with HI = > 0.5, the list reduces to nine subbasins.The nine subbasins' hypsometric curves exhibit different shapes and patterns and suggest varying erosional processes (Strahler, 1952).An earthquaketriggered landslide in 2005 in subbasin 498 is still visible from satellite data of Google Earth.

Drainage divide stability with χ
Anomaly in χ values at the channel heads of opposing river networks sharing a common divide marks disequilibrium in drainage systems' topology and geometry (Willett et al., 2014;Menier et al., 2017;Forte & Whipple, 2018).In the study area, the state of drainage basins' divides and river networks vary as predicted by the χ values.Drainage divide mobility is imminent at the headwaters of major basins sharing boundaries with minor basins.Migrating drainage boundaries adjust and exchange areas with adjacent basins, leading to changes in river networks' topology as explained in Willett et al. (2014).In theory, χ is an inverse function of drainage area where lower χ values characterize a gain of drainage area while higher χ values indicate a loss of drainage (Fenta et al., 2017;Dahlquist et al., 2018).Dynamic river systems continuously change until an equilibrium condition between tectonic uplift and river erosion is met (Willett et al., 2014).The χ analysis points to areas in the study area, specifically the drainage divide sections in the upstream portion of major basins, striving to reach equilibrium with the neighboring basins.
The direction of divide migration also differs.However, most divide sections migrate northwest at the headwaters of large basins, especially the southernmost portion of Wahig-Inabanga River Basin.The predicted migration marks a loss of drainage area for the Wahig-Inabanga River Basin while the opposite minor basins are advancing their drainage areas.Upon examining the river networks sharing an unstable divide section, Figure 5B suggests the lateral migration of river channels in the river basin.As Willett et al. (2014) pointed out, the presence of laterally migrating river channels in river basins explains the plan view reorganization of drainage systems.As emphasized in the study of Johnson and Finnegan (2015), river basin lithology is the main difference between an actively meandering river stream and its adjacent straight neighbor.From here, the study infers that the meandering victim river could have passed through plains and rock walls, giving way to soft soil, allowing it to shift its banks and change courses towards the sea.In contrast, the straight aggressive stream could have crossed through mountains and carved steep-walled valleys where its course was set on rocks.However, further interpretation and comprehension of the rivers' sinuosity patterns are limited by the presently available data, which calls for more research in the future.Drainage divide migration is a slow process occurring over hundreds to thousands of years (Willett et al., 2014).However, Dahlquist et al. (2018) found that a divide migration can be activated by a single landslide-generating event such as an earthquake or a storm.As divide migration strives for equilibrium, the landscape redistributes its erosive energy (Dahlquist et al., 2018).The process becomes a host to potential natural hazards, including landslides (Scheingross et al., 2020).The study proposed a measure of the degree of divide mobility, χ md , to classify unstable divides, a parameter helpful in targeting migrating divides.Together with other geometric indices, the χ md can be used to facilitate the identification of hazard-prone areas.
The proposed χ md is a measure of the degree of drainage divide mobility and varies across the study area.The χ md becomes a property of a drainage divide shared by at least two basins and indicates the adjoined basins' dynamics relative to differential erosion rates across the divide.The variation of χ md can be attributed to geology and climate.However, there are limited details on the island's geology to associate a divide section's χ md with rock erodibility.On the other hand, climate change may influence this spatial difference of χ md as extreme climatic events such as strong typhoons often visit the island.Changes in climate regimes bring variations in overland flow erosion processes in river basin systems (Tucker & Slingerland, 1997).Nevertheless, since the island is relatively small and surrounded by other islands, it is interesting to look at the climate's contribution, if there are, to the χ md anomalies found.

River basin hypsometry
The hypsometric analysis provides information on erosion status across the study area.As shown in Figure 6A, the spatial variation of HI indicates varying geologic development that ranges from young to old stages.Most notably, the south and southwest portions of the island show highly erosional landscapes.The Wahig-Inabanga River Basin can be considered an old drainage unit.However, further examining the smaller subbasins within it, the study found areas of transient erosional landscapes where erosion rates vary from low to high.A prior erosion study in the upper Wahig-Inabanga River discovered considerable erosion rates in two monitored subbasins (Genson, 2006).Additionally, the study found high annual erosion rates from conventional agricultural practice (42.5 tons per hectare compared to the acceptable rate of 10 tons per hectare).Together with sediment measurements, such information can be adopted to prioritize areas for conservation measures (Singh, 2009).

Insights for area prioritization and conservation programs
Future divide migrations and the geologic development stage of a river basin are critical inputs to sustainable land and water management.They both describe potential erosion processes.In a seismically active landscape such as the Himalayans, Schwanghart et al. (2018) found that rivers with a high steepness index, Mχ (defined as dz⁄dχ), have a high probability of landslide-triggered earthquakes.The findings support the notion of Willett et al. (2014) that river network disequilibrium is associated with variations in weathering, soil production, and erosion rates.These potential events are detrimental to physical infrastructures like hydropower plants and irrigation dams adjacent to river channels.Therefore, the stability of river networks influences designs for engineering works such as hydropower plants (Geach et al., 2017;Schwanghart et al., 2018;Torrefranca et al., 2022).
The study by Dahlquist et al. (2018) assessed earthquake and storm-triggered landslides.It demonstrated a link to river channels, hillslopes, and ridges, leading to divide migration towards a steady-state position.The study area is one of the tectonically active islands in the country.Mobile divides are predicted by χ, and high erosion susceptibility is anticipated based on the hypsometric analysis.In the subbasins where χ values are high, the possibility of an earthquake-triggered landslide is also high.The 2005 Mayana landslide had occurred in one of these subbasins, as shown in Figure 8.The landslide started as a rockfall along a very steep northwest-trending fault scarp, triggered by a 4.9 magnitude earthquake about three months before the event (Catane et al., 2005).A seismic disturbance may not manifest instantaneously but may later come out as seismic processes generated and possibly increased rock formation instability, like the landslide event in Mayana.Extreme climatic conditions, such as large typhoons, may also be critical in initiating a divide migration phenomenon or progressing an existing motion towards a topographic steady-state.Dahlquist et al. (2018) have estimated that landslides triggered by large typhoons account for a minimum of 12%-15% of the movement of the Taiwan Central Range main divide toward a steady-state position.
Integration of information on the dynamic state of river basins measured at the drainage divide and the geologic development stage of a catchment area presents a new approach to identifying and prioritizing basins or subbasins for soil and water conservation programs and other developmental goals.The study identified subbasins with unstable divides and highly erosional areas.These subbasins are prioritized by ranking unstable divides based on χ md values and classifying the intersected subbasins' geologic development stages using HI values.Subbasins with divides having χ md > 255 and catchment areas having HI = > 0.5 are the highest priority areas.The study found nine subbasins with these parameter values, directing further field investigations.The study is a step toward understanding the evolution of a landscape shaped by tectonic and erosional processes.

Conclusions
The study characterized the landform dynamics of Bohol Island in the central Philippines using divide migration metric and hypsometric analysis.It proposed a measure, χ md , to evaluate the degree of divide mobility.Integrating χ md of drainage divides with HI of subbasins sets the criteria that guide subbasins selection and prioritization.The study concludes the following: (1) The χ metric provides insights into a transient landscape revealing the state of drainage divides and the migration patterns.At the same time, the χ md indicates the degree of potential divide mobility.
(2) Across the study area, patterns of low to high erosional areas disclose different geologic development stages, indicating potential erosion risks.
(3) The integration of χ md and HI, characterizing the degree of drainage divide mobility and the erosional stages of a catchment, respectively, provides a rapid assessment tool for identifying and prioritizing subbasins for a range of conservation goals.For an area where natural disasters are commonplace, prioritization shall reconsider the dynamics of landforms shaped by tectonic and climatic forces.

Figure 1 .
Figure 1.The geographic location of the study site.
subbasins are selected to examine HI and hypsometric curves variation at different scales.Hypsometric curves and HI values were classified following El Hamdouni et al. (2008) and Pavano et al. (2019).The following classifications are adopted: hypsometric curves characterized by a downward concave curve with HI values greater than 0.6 indicate a youthful stage where a basin experiences an active base-level fall; hypsometric curves with an Sshape without any evidence of concavity and HI values between 0.35 and 0.6 show a mature stage; the curves with upward concavity and HI values less than 0.35 indicate a monadnock stage or an old phase.The study considers subbasins with HI = > 0.5 as highly erosional areas.

Figure 2 .
Figure 2. The flow of analysis.

Figure 3
Figure3shows the χ map of the study area, where χ values map the river networks.The color of the stream network shows the χ value variation across the study area, and a color contrast usually signals instability in the drainage divide.The contrasting colors of the opposite stream channels indicate disequilibrium at a divide section, while similar stream colors indicate divide stability.Figure3Ahighlights the major basins in the island and their drainage boundaries, emphasizing the χ similarity of a stable divide in Figure3Band χ differences of an unstable divide in Figure3C.The map's visual inspection found that drainage divides between the major basins show slight color differences.However, it is noteworthy that at the headwaters of major basins in the southern portion of the island, divide sections shared between major basins and minor basins facing the southern coast show highly contrasting colors indicating high χ anomalies, as highlighted by Figure3C.In the current study, histograms of stable and unstable divides are selected, as shown in Figures3B and 3C.To investigate the χ similarities and differences of the individual divide section quantitatively, Forte and Whipple (2018) use the histogram of χ values at the channel heads of either side of the divide.The histogram in Figure3Bshows the overlapping of χ values of the opposing channel heads.It also shows that the mean χ value of one side of the divide is within one standard deviation of the mean χ value of the other side, a conservative criterion for determining divide stability used byForte and Whipple (2018).The histogram in Figure3Cshows significant differences in χ values of the opposing channel heads, indicating that the mean χ value of one side of the divide is far from one standard deviation of the mean χ value of the other side.As predicted, this

Figure 3 .
Figure 3. χ map and the major basins in the study area.A) Highlights the major basins on the island.B) χ map of a stable divide and its histogram.C) χ map of an unstable divide and its histogram.

Figure 4 .
Figure 4. Divide sections' χ md and direction of migration.A) Divide sections colored according to χ md classification and laid over the area's geology.B) A rose diagram showing the direction of potential migration of unstable divides.

Figure 5 .
Figure 5. χ map of disequilibrium basins and the two opposing river networks' profiles that meet at the divide section.A) Map view of two opposing rivers' pathways (Inset: histogram showing a wide difference of the χ values).B) Longitudinal profile of the opposing streams.C) χ profile of the two opposing rivers.

Figure 6 .
Figure 6.Spatial variation of the hypsometric integral in A) island and the B) major basin.C) hypsometric curves of the basin and selected subbasins.Reference hypsometric curves in broken lines adopted from Pavano et al. (2019).

Figure 7 .
Figure 7. Map of the subbasins that share high χ md divide sections.The color indicates HI values (light to dark means low to high HI).The dark-colored subbasins have HI ≥ 0.5.In one of these subbasins, the 2005 Mayana landslide occurred.Inset is the latest satellite image of the landslide area extracted from Google Earth.Below are the hypsometric curves of the nine subbasins arranged from low to high HI values.