χ-maps and Hypsometric Analysis for River Basin Management and Prioritization: The Case of Bohol River Basins, Central Philippines

14 Topographic indices represent and simplify complex surficial processes fundamental to 15 characterizing landform dynamics and to prioritizing river basin conservation and 16 management goals. A method of characterizing landform dynamics integrating the 17 steady-state river channel elevation and the hypsometric analysis is presented. The chi 18

( ) metric, a proxy for the steady-state river channel elevation, gages the stability of 19 drainage divides while hypsometric analysis quantifies the stages of basin geological 20 development. Using a 30m SRTM DEM and the TopoToolbox tool in MATLAB, - 21 values along stream networks are computed. At the channel heads of opposing stream 22 networks of a divide section, equalvalues indicate a stable divide while across 23 difference in -values suggest unstable divide with a potential to migrate from low 24 values towards the highvalues side of the divide. To classify the degree of 25 potential divide mobility, the quantity called mean chi difference ( ) is proposed. 26 The features of the aggressive and victim river streams are visually differentiated using 27 their elevation profiles, map-view arrangement and pathways to discharge points. 28 Hypsometric analysis examines the erosional stages of basins indicated by the 29 hypsometric integrals (HI) and hypsometric curves. A basin and its subbasins show 30 different levels of geologic development that the disaggregation of large basin into 31 small hydrologic units enables the identification of areas of different erosional stages. 32 The prioritization of subbasins considers the intersection of highly mobile divides and 33 highly erosional areas. Over the study area, nine subbasins are identified which are all 34 located at the headwaters of major basins in the island. A considerable earthquake- 35 triggered landslide has been found in one of the identified subbasins. The study presents 36 a new approach in the initial characterization of landforms in order to facilitate the 37 identification and prioritization of highly erodible areas for high consideration 38 especially at the local or village level.
Landforms are functional regions on the earth's surface, and are bounded segments 43 and may be discontinuous [1] that change shape overtime. Landform evolution and its 44 unique characteristics is a time-integrated product of extremely long periods of 45 weathering and surface processes [2], driven primarily by tectonics and climate [3,4]. 46 These processes, operating at varying intensities in distinct climate and tectonic 47 systems, formed highly regionalized associations between landforms, ground 48 conditions, geohazards and resources characterizing a geomorphological environment 49 [2]. The current topography is a fingerprint of these processes and is fundamentally the 50 basis of landform dynamics analysis constituting modern geomorphic analysis. 51 Advances in the quantitative characterization of terrain and processes, and  [7], facilitate geo-hazard assessment [8,9], predict spatial patterns of soil 56 properties [10,11] [14]. 79 The development of themetric as a measure of divide stability by Willet et al 80 [21] is fundamentally based on the 'differential rates of river channel erosion on 81 opposite sides of a divide'. It was argued that when disequilibrium exists between 82 opposing river channels, the shared drainage divide is set in motion until equilibrium is 83 reach. is an integral solution to the stream power model proposed by [22] and is 84 expressed as: This study is set out to explore the integration of the -metric [27] and the 159 commonly used hypsometric analysis [15] as rapid assessment tools in river basin  Table 1. The minimum accumulation area is used to define stream 213 initiation. The theta_ref or the reference concavity is a constant for calculating and 214 the 'min_elevation' parameter is use to set minimum elevation for base level. 215 To evaluate across divide stability for a selected divide section, the 216 AcrossDivide function is used. The function allows the selection of a divide, 217 segmentation of a heterogenous divide into sections, and the calculation of quantities. 218 In this study, the standard deviation is used as the criteria to define whether a divide is  Figure 2B and 2C, respectively. 319 The histogram in Figure 2B shows  For the selected divides predicted to be migrating, the distribution and the direction 354 of potential movement is shown in Figure 4B.   Figure 5A shows the spatial distribution of where a sharp 386 discontinuity across the landscape is emphasized. It is noted that smaller catchment 387 along the coastal area has low -value compared to a major catchment located interior 388 of the island. Both rivers discharge to the southern coast of the island but their pathways 389 and lengths differ remarkedly. The victim side has a channel length of 78.3 km and is meandering towards its discharge point. On the other hand, the aggressor side extends 391 its length to only 17.5 km long and goes straight to its outlet point. Figure

Hypsometric analysis at different scales
Hypsometric analysis provide information on the erosion status of basins which 416 is used as the basis for prioritizing areas for conservation measures [14]. Figure 6 shows 417 the results of the hypsometric analysis in the island and across a major basin, and the 418 hypsometric curves of a major basin and selected subbasins within it. The spatial pattern 419 of landform changes in the island is notable in Figure 6A. to reconsider the dynamics of landforms shape by tectonic and climatic forces. 499 The study presents a method which integrates a proxy for steady state channel   Figure 1 Geographic location of the study site. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 2
Flow of analysis and the methods. Figure 3 χ -map and the major basins in the study area. A) Highlights the major basins in the island. B) χ -map of a stable divide and its histogram. C) χ -map of an unstable divide and its histogram. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. Figure 5 χ-map of disequilibrium basins and the pro les of the two opposing river networks that meet at the divide. A) Map view of the pathways of two opposing rivers (Inset: histogram showing wide difference of the chi values). B) Longitudinal pro le of the opposing streams. C) χ-transformed pro le of the two opposing rivers. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 7
Map of the subbasins that share with high χmd 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 had 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. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.