S Journal of

O p s e s n Acce Geology and Geoscience

Case Report Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

Yen- Chieh Chen1*, Heng Tsai2, Quo-Cheng Sung3, Tsung-Yen Wang1 1Department of Tourism Management, Chia-Nan University of Pharmacy and Science, No.60, Erh-Jen Road, Sec.1, Jen-Te 717, Tainan, . 2Department of Geography, National Changhua University of Education, Changhua 50007, Taiwan. 3Institute of Geoinformatics and Disaster Reduction Technology, Chien-Hsin University of Science and Technology, No. 229, Chien- Hsin Rd., Jung-Li, Taoyuan 320, Taiwan.

Abstract In this study, we applied hypsometric curves (HCs) and elevation frequency histograms to reflect “topographic evolution stages” and “abundance distributions of basins’ residual land” in different topographic provinces in the Taiwan orogen. Results show that in the plain topographic area, basins in pure alluvial plains have S-type HCs and their elevation frequencies are widely distributed in the intermediate elevations. Additionally, basins in structural sinking basins have concave HCs and their elevation frequencies concentrate almost in the lowest elevation. In the western foothills, basin HCs adopt a concave type and their elevation frequencies have concentration in the low elevations. Owing to the continuous uplifting, basin HIs in the Western foothills will be gradually increasing. Their HCs will take on an S-type and the elevation frequencies will concentrate in the intermediate elevations. Moreover, basins on tablelands with continuous regional uplifting have convex HCs and match the young stage topography defined by [1]. In the central ranges, basins’ elevation frequencies are of normal distributions and the HCs are S-type. Therefore, in the central ranges, tectonics and denudation should reach the culminating stage defined by [2]. In the coastal ranges, the basin HIs are low, the rasin HCs are of concave types, basins’ elevation frequencies concentrate in the low elevations, and these characteristics of which are very similar to those of the western foothills. In summary, the Taiwan orogen, the basin HC patterns exhibit a “Taiwan orogen cycle”, which resemble the Ohmori cycle. Additionally, the elevation frequency histograms of this Taiwan orogeny cycle show the variations between the normal distributions and the distributions that concentrate in the low elevations. Keywords: steady-state range; morphotectonic index; χ2-test

Introduction utilized to facilitate rapid evaluation of these morphologic responses [12- 19].The hypsometric technique is considered Landform principally results from the combined action of a volumetric form index of 3-dimension; topography fractal endogenous processes, such as tectonics and volcanism, parameters and drainage basin asymmetry are considered areal and exogenous processes, such as weathering, erosion and form indices of 2-dimension; stream-gradient index, Hack deposition [3, 4]. In smaller scale but higher active convergent profile, mountain front sinuosity, river channel sinuosity, and orogenic belt, such as the Taiwan orogen, there exists strongly valley width-depth ratio are considered linear form indices dynamic negative feedback mechanisms of endogenous and of 1-dimension. With the speed and precision of Geographic exogenous processes [Willett and Brandon, 2002]. Typically, Information System (GIS) and Digital Terrain Model (DTM), the rates of tectonic activities are quite slow, and their effects the calculation of morphotectonic indices has become easier are usually only seen after long-term accumulation [5- 7]. [20- 23]. So, the morphotectonic indices have been widely Therefore, the long-term and large scale geological activities used in geomorphology and active tectonics. that may not be reflected by short-term geodetic measurements Since the late Miocene, roughly 6.5 million years ago, the such as GPS are aspects that cannot be neglected [8]. Taiwan orogen originated from the oblique arc- collision of the Topography features can reflect both “lithological or structural Luzon arc with the edges of the Eurasian continent between the variations of small and short time-space scales” and “tectonic Eurasian plate and the Philippine Sea plate (Figure 1) [24- 28]. activities of large and long time-space scales” [9- 11]. Morphotectonic is a subject that applies topographical analysis to indicate morphologic responses to lithologiy, structure and tectonism. Correspondence to: Yen-Chieh Chen, Tel: +886 9 21264027; E-mail address: chenycchna[AT]gmail[DOT]com

Numerous morphotectonic indices have been developed and Received: Jan 24, 2020; Accepted: Feb 19, 2020; Published: Feb 20, 2020

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Figure 1: Steady-state ranges and geotectonic framework of Taiwan (Suppe, 1981; Ho, 1986; Teng, 1990; Dadson et al., 2003). (a) Plate tectonics of the Ryukyu-Taiwan-Luzon area. EP, Eurasian plate; PSP, Philippine Sea plate; MTr, Manila trench; RTr, Ryukyu trench; OT, Okinawa trough. (b) Schematic map of the time-space equivalence relationship model. The line of direction N20°E in the most southern tip of Taiwan is defined as 0km. Shallow gray is the mountain area of elevation between contours of 200m and 2000m. Dark gray is the mountainarea of elevation above ontour of 2000m. (c) Schematic map of the large-scale lithology and structures. CP, coastal plain; WF, Western Foothills thrust belt; HS, Hsuehshan Range; SL, slate belt; TS, Tananao schist; CoR, Coastal Range (d) Profile of the cross-section A-B in (c). The basal detachment zone is imaged using small earthquakes (Carena et al., 2002). CR, Central Range; CPF, Chelungpu fault; LVF, longitudinal valley fault.

As the collision time sequence proceeded from north to even stopping the orogenic movement in northern Taiwan, south, Taiwan’s mountain ranges started forming from collision in southern Taiwan had just started [32-34, 36]. uplifted ranges in northern Taiwan, and expanded gradually Thus, the ranges in southern Taiwan (about 0-120 km; southward at an propagation rate from 55 to 90 km/Ma equivalent to 0-1.33 Ma) are “growing ranges (pre-steady- [29]. Spatially, taking the maximum, the southern tip of tate)” with greater uplifting than denudation , and the ranges in the Taiwan ranges moved northward by 90 km, which was northern taiwan (about 290- 370 km; equivalent to 3.22-4.11 equivalent to an orogenic process for a million years (Figure Ma) are “decaying ranges (post-steady-state)” with greater 1b). Applying this “time-space equivalence” relationship to denudation than uplifting [36] (Figure 1). inspect the continuous rise in the height of Taiwan’s ranges from the southern tip to the north, it is found that at the 120- The unique tectonic framework of the Taiwan orogen is a 290 km zone (equivalent to 1.33-3.22 Ma) in the central good example for simultaneous investigation of hypsometric ranges (black bold line rectangle area in Figure 1b), the technique of pre-steady-state, steady-state, and post-steady- substance increase caused by tectonics and the substance state topography. Therefore, this study applies the hypsometric loss caused by denudation are balanced. The ranges can technique to the areas of different topographic characteristics in be called “steady-state ranges” [30, 31]. While the back- the Taiwan orogen and determines the hypsometric features for arc spreading of the Okinawa Trough was diminishing or different topographic evolution stages.

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Literature review of HCs have been widely applied to assess the geomorphic processes and identify the stages of topographic evolution The hypsometric integral (HI) applies an areal hypsometric curve (HC) model to describe the proportion of residual and [41, 42]. Furthermore, the topographic evolution stages are volume of a basin after erosion [37, 38]. It gives 3-dimensional always related to tectonic activities showed that a mountain is information for a 2- dimensional approach . Studies showed rapidly uplifted without serious denudation, and then increases that a strong relationship exists between the HI, tectonic uplift in dissection with a lowering in mean altitude by the ensuing rate, and some nature factors such as structural activities, erosion [43]. lithology, and climate features [39]. In addition, the HI scale- Therefore, basin HIs gradually decrease during the course of dependence was also widely discussed. Studies of the San topographic evolution. While young river basins have higher Gabriel Mountains, California by Lifton and Chase (1992) and HIs (HI>0.6) and convex HCs due to less denudation, mature the taiwan orogen by Chen et al. (2003a, b) clearly indicated and old river basins have intermediate HIs (0.4

Figure 2: HC patterns and cycle of topographic evolution stages. (a) and (b) are Strahler (1952) model: topographic evolution after a suddenly uplifting movement. Erosion becomes the main process. HIs will decrease, elevation drop will increase initially and then

uplifting and erosion. Both HIs and elevation drop will increase initially and then decrease. HCs will be concave to S-type. decrease, and HCs will be convex to S-type. (c) and (d) are Ohmori (1993) model: topographic evolution which is influenced by both

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basins always reflect the results of the concurrent tectonics hillslope processes with basin sizes. Where the basin area and denudation. Continuous tectonic activities always remain is small, hillslope processes would be dominant, and the the topographic evolution stages of river basins at young to HC would be convex with a HI close to 1. Conversely, with mature. Shih et al. (1980) analyzed the hypsometric features of increasing drainage area, the importance of river processes 30 main river basins with areas >10km2 in the Taiwan orogen, would increase, and the HC would become concave with a HI and concluded that most river basins were in the mature close to 0 (Willgoose and Hancock, 1998; Hurtrez et 1999; topographic evolution stages [44]. Sung and Chen, 2004). Under the concurrent tectonics and denudation, Ohmori Methodology (1993) identified three topographic evolution stages (Figure 2d). (1) The developing stage: altitude and relief of ranges The topographic provinces of the Taiwan orogen increase due to uplifting. (2) The culminating stage: ranges For discussion about large-scale HI features and HC patterns reach the highest altitude and relief. (3) The declining stage: in different topographic areas with special geology settings altitude and relief of ranges gradually decrease while uplifting in the Taiwan orogen (Figure 1c, d), this study defines four slows down or even stops. He also numerically simulated HCs main topographic provinces and several sub-provinces based and compared simulation results with real cases in Japan, and on the HI distribution (Chen et al., 2003a, b), geological demonstrated that HIs of river rasins have a fluctuating cycle features (Ho, 1986), and topographic features (Lin, 1969). The as the uplift rate changes. Additionally, HCs also have cycle four main topographic provinces are as follows. A is the Plain through concave, S-type, and concave again (Figure 2c), and topographic province, B is tthe Western foothill topographic this succession of HCs is the reverse of of Strahler’s diagram province, C is the Central range topographic province, and D (Ohmori, 1993) (Figure 2). is the Coastal range topographic province (Chen et al., 2006; Chang (1975) indicated that that in the Taiwan orogen, basins in Chen, 2008) (Figure 3). areas had HIs of 0.29-0.51 and concave to S-type HCs, whereas The sub-basins of the topographic sub-provinces are derived basins in mountainous areas ad HIs of 0.53-0.60 and S-type or from the processes reported by Chen et al. 2003a, b) and Chen minor convex HCs. The HCs also have scale-dependence features (2008). They derived sub-basins of Strahler order 1 from [45]. the Taiwan 40-m-resolution DTM with a flow accumulation Willgoose and Hancock (1998) proposed the HC scale- threshold of 3 km2 for large scale hypsometric analysis of dependences that may reflect the importance of river and this study. The Taiwan 40-m-resolution DTM, provided

Figure 3: HI distribution of the Taiwan orogen and topographic provinces (Chen et al., 2003a, b).

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by the Bureau of Forestry in the 1980s, is produced by HCs and elevation frequency histograms. The bottom and left photogrammetry and projected over a Universal Transverse axes are for the HCs, while the top and right axes are for the Mercator (zone 51) grid as as a Cartesian reference frame. elevation frequency histograms. Three types of basins have the Sung and Chen (2004) analyzed the fractal features of Taiwan same HI of 0.54, however, their HC patterns are S-type (or topography and proved that the Taiwan 40-m-resolution DTM concave-convex type), convex type, and convex-concave type was appropriate for basin topography analysis. (convex at high elevations and concave at low elevations), respectively (Figure 5). According to Figure 4a, the relative HC and Elevation Frequency Histogram abundance of basin with S-type HC is mainly concentrated in Strahler (1952) analyzed the elevations and areas of river the intermediate altitudinal classes (Figure 5a). The relative basins and plotted HCs (Figure 4b) in diagrams in which the abundance of which with straight-type HC (Liem et al., 2016) y-axis and the x-axis are the relative elevation ratio (h/H) and is thoroughly distributed to each altitudinal class (Figure 5b). the relative area ratio (a/A), respectively. In these diagrams, h The relative abundance of which with convex-concave HC is the elevation drop between a certain elevation and the lowest is mainly present in the lower and higher altitudinal classes elevation of river basin; H is the maximum elevation drop; (Figure 5c). Therefore, if studies consider the HC patterns a is the cross-sectional area of a certain elevation, and A is when analyzing the HIs, basins of the same HI should be the cross-sectional area of the lowest elevation. Mayer (1990) further differentiated and identified (Figure 5). divided the elevation drops of a river basins into 8 intervals Results and Discussion and plotted the histogram of areas between adjacent contour lines (Figure 4a). In this study, the elevation drop intervals are Figure 3 show that each main topographic province contains called “Altitudinal Class”, and the histogram is plotted using several topographic sub-provinces. Each topographic “Relative Abundance”. Relative abundance is defined as the sub-province contains several sub-basins, each of which has area between adjacent contour lines over the area of the whole a HC. Therefore, after plotting HCs of all sub-basins in each basin, and the “elevation frequency histogram” is formed by topographic sub-province, an “average hypsometric curve” these two parameters. If one calculates the proportion of an and “standard deviation curves” can be generated to simplify the HC patterns. The area under the average HC is called area “in and above” each interval to total basin area, “Relative “average HI”. Figures 6 to 9 present the results of HCs and area (a/A)” is generated and can be used when plotting HCs. elevation frequency histograms of the four main topographic This study divides elevation drop of river basins into 10 provinces and the detail discussion is as follows. intervals (Chen et al. 2005) to facilitate the plotting of HCs and elevation frequency histograms (Figure 4). Plain topographic province Theoretically, HIs only represent the areas under the HCs The average HIs of Choshui and Chianan Plains (A1), (Strahler, 1952) such that basins with the same HIs may have Basin (A2), and Pingtung Alluvial Fan (A8) are different HC patterns. Figure 5 presents a plot combining 0.42-0.47. Their average HCs are S-type, and the elevation

Figure 4: Conceptions of measurement of elevation frequency histogram and HC (Mayer, 1990).

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Figure 5: Comparison of elevation frequency histograms between different types of HCs with the same HI. Because the a/A values in the bottom X-axis increase with the decrease of the h/H values, the top X-axis (the altitudinal classes) is designed to be decrease with the increase of the a/A values. The basins under the diagrams are the cases that show the differences of relative abundance distributions among the altitudinal classes.

Figure 6: Plots of the HCs and the elevation frequency histograms of the Plain topographic province. The black curves are namely the average hypsometric, the dark grey curves are the positive and negative standard difference curves, and the grey curves are the individual hypsometric curve for each sub-basin. The black dashed lines are the diagonal lines and their HIs = 0.5.

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Figure 7: Plots of the HCs and the elevation frequency histograms of the Western foothill topographic province. The meanings of the black curves, the dark grey curves, and the grey curves are the same as those in Figure 6. frequencies are widely distributed among the intermediate be highly correlated with the concurrent high uplifting rate altitudinal classes. Choshui and Chianan Plains (A1) are the (>4.7 mm/yr) [47] and denudation (>5 mm/yr) (Dadson et al., western coastal plains in the foreland. They are of a young 2003). Basin (A3), Puli Basin (A4), Plain terrains (Simoes and Avouac, 2006) with a low erosion rate (A7), A9), Ilan Plain (A10), and Huatung (approximately 2-6 mm/yr) (Dadson et al., 2003). Due to the Valley (A11) have relatively lower average HIs of 0.27-0.33. influence of the Peikang basement high (Figure 3), Choshui Their average HCs are concave and the elevation frequencies and Chianan Plains (A1) were tilted slightly toward the west are mainly distributed in the low longitudinal classes. These with an uplifting rate of 0.5-4.4 mm/yr and a western horizontal hypsometric features imply that these topographic sub- shifting rate of 10-20 mm/yr [60, 46]. Therefore, they are provinces are situated in the structural sinking areas [52] or structural uplifting plains with lower erosion rate. Taichung the areas with lower uplifting rates [47]. Tainan Terrain (A5) basin (A2) is widely covered by the Wu River alluvial, and is only contains four sub-basins along the Tainan anticline. Tahu also a structural uplifting basin between the active Changhua Terrain (A6) lies southeast of Tainan Terrain (A5). and the Chelungpu faults. The average HC of Tainan Terrain (A5) is straight-type and The activity of the Changhua fault tilted Tatu Table l and (B6) that of Tahu Terrain (A6) is slightly S-type. The elevation and Pakua Tableland (B7) in the west of (A2), frequencies of Tainan Terrain (A5) and Tahu Terrain (A6) are and the active Chelungpu fault generated the disastrous Chi- distributed from the intermediate to high altitudinal classes.

Chi earthquake (ML=7.3) on September 21, 1999 in the east Both Tainan Terrain (A5) and Tahu Terrain (A6) are recently Taichung basin (A2) [40]. Due to the approximately equal emerged tablelands with terrain surfaces tilting westward [48]. forces of uplift [58] and denudation (Dadson et al., 2003), In these two areas, many folds and fault structures exist, and the HCs of Taichung basin (A2) presents S-type. The HC of the 20,000 years uplifting rate has reached 4-5mm/yr [47], Pingtung Alluvial Fan (A8) is also S-type, and this should

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Figure 8: Plots of the HCs and the elevation frequency histograms of the Central range topographic province. The meanings of the black curves, the dark grey curves, and the grey curves are the same as those in Figure 6.

Figure 9: Plots of the HCs and the elevation frequency histograms of the Coastal range topographic province. The meanings of the black curves, the dark grey curves, and the grey curves are the same as those in Figure 6.

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Table 1: χ2-test, skewness and kurtosis analysis results of elevation frequency histograms of the Central range topographic province and the pure alluvial plains. Topographic sub-provinces of the central range χ2 value p value Skewness Kurtosis North-Hsueshan Mountain (C1) 2.409 0.879 0.200 -0.719 Hsueshan Mountain (C2) 2.337 0.886 -0.089 -0.624 Back-Bone Range (C3) 2.244 0.896 -0.038 -0.605 Ali Mountain (C4) 1.230 0.942 -0.027 -0.740 Tawu Mountain (C5) 2.285 0.892 -0.064 -0.773 Hengchun Peninsula (C6) 1.113 0.981 0.198 -0.603 Topographic sub-provinces of the pure alluvial plains χ2 value p value Skewness Kurtosis Taichung Basin (A2) 5.039 0.539 0.251 -0.785 Choshui and Chianan Plains (A1) 2.759 0.838 0.158 -0.577 Pingtung Alluvial Fan (A8) 2.460 0.873 0.195 -0.790 demonstrating that these two terrains are the young stage Pakua anticlines. Ohmori(1993) indicated that different crustal topography. Therefore, their HIs are relatively higher. movements such as up-warping and tilting and the of newly emerged land will modify the course of change in the HCs. Although the topographic sub-provinces in the Plain Thus, we propose that the structural tilting could increase the topographic province all belong to the alluvial-plain category, basin’s elevation drop, and then intensified the river erosion they are affected by local tectonic activities and can be processes. Eventually, the intensified river erosion might cause categorized as “structural uplifting topography”, “sinking the lower HIs and concave which resemble the peneplain stage topography” and “recently emerged coastal plain terrains”. topography defined by Strahler (1952). The average HIs of Structural uplifting topography, such as Choshui and Chianan Plains (A1), Taichung Basin (A2) and Pingtung Alluvial Fan Hsinchu Hill (B4), Taichung Hill (B8), Toulio-Chiayi Hill (B9) (A8), have S-type average HCs and the elevation frequencies and Tainan Hill (B10) are 0.30-0.35. As well as the sinking are distributed in the intermediate altitudinal classes. Sinking topography in the Plain topographic province, their average topography, such as (A3), Puli Basin (A4), HCs are concave and their elevation frequencies are generally Kaohsiung Plain (A7), Pingtung Plain (A9), Ilan Plain (A10) in the low altitudinal classes. The four hills are located in the and Huatung alley (A11), have concave average HCs and western foothills. the elevation frequencies concentrate almost in the lowest The western foothills are the fold-thrust belts [51], and altitudinal class. Additionally, recently emerged coastal plain situated at the gradually uplifting mountain fronts (Figure 1c). terrains, such as Tainan Terrain A5) and Tahu Terrain (A6), Dadson et al. (2003) reported that in the Taiwan orogen, high have straight-type average HCs and the elevation frequencies erosion rates present at the mountain fronts, and the order- are roughly distributed to each altitudinal class (Figure 6). of-magnitude increased from north to south (approximately Western foothill topographic province 4-60 mm/yr). Therefore, we consider that the decreasing of HIs from north (Hsinchu Hill (B4), HI=0.35) to south (Tainan The average HIs of Linkou Tableland (B1), Taoyuan Tableland Hill (B10), HI=0.30) of the four hills should be caused by the (B2), Hukou Tableland (B3), and Houli Tableland (B5) are decadal-scale erosion patterns mentioned above. Moreover, 0.46-0.60. Their average HCs are convex to straight-type, the four hills with concave HC patterns that influenced by the and the elevation frequencies tend toward the high altitudinal gradually uplifting of the mountain fronts should resemble classes (Figure 7). The average HIs of Tatu Tableland (B6) the initial landform defined by Ohmori (1993). Tatun Volcano and Pakua Tableland (B7) are 0.36-0.39. Their average HCs (B11) is mainly composed of andesite, which is hard and resists are concave and the elevation frequencies are at the lowest erosion the influence time of erosion is not too long after the altitudinal classes (Figure 7). Linkou Tableland (B1), Taoyuan extinction of volcanoes (approximately 0.2Ma at least) [53], Tableland (B2), Hukou Tableland (B3), Houli Tableland (B5), generating an average HI of approximately 0.45, the average Tatu Tableland (B6), and Pakua Tableland (B7) are all lateritic HC is S-type, and the elevation frequencies are mainly in the soil tablelands that recently emerged by the active structures intermediate altitudinal classes (Figure 7). [59, 40, 35], but the manners in which they emerge from differ. Linkou Tableland (B1), Taoyuan Tableland (B2), Hukou Central range topographic province Tableland B3), and Houli Tableland (B5) as well as Tainan This province contains North-Hsueshan Mountain (C1), Terrain (A5) and Tahu Terrain (A6) are tablelands of entire Hsueshan Mountain (C2), Back-Bone Range (C3), Ali terrain uplifting, which resemble the young stage topography Mountain (C4), Tawu Mountain (C5), and Hengchun defined by Strahler (1952). Peninsula (C6). The average HCs for this area are consistently However, Tatu Tableland (B6) and Pakua Tableland (B7) are S-type, and their average HIs are 0.45-0.50. The elevation tilting [49, 50], and the tilting is associated with the Tatu and frequencies are principally in the intermediate altitudinal

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classes (Figure 8). (higher altitudinal classes). kurtosis is a measure of whether a probability distribution is heavy tailedness or light-tailedness The topographic evolution model from computer simulation relative to a normal distribution (kurtosis = 3). by Ohmori (1993) shows that when the ranges reach the culminating stage, the elevation frequencies will be in the Probability distribution with higher kurtosis (>3) tends to have intermediate altitudinal classes and similar to the normal heavy long tails naming the leptokurtic distribution, and that distribution. with lower kurtosis (<3) tends to have light short tails naming To determine whether the elevation frequency histograms are the platykurtic distribution. The skewness of Hsueshan ountain of normal distributions, this study applies normal distribution (C2), Back-Bone Range (C3), Ali Mountain (C4) and Tawu fitting to the elevation frequency histograms of the6 Mountain (C5) are all negative, indicating that the elevation topographic sub-provinces in the Central range topographic frequencies skew toward the high elevation. The skewness f province and the 3 pure alluvial plains (Choshui and Chianan North-Hsueshan Mountain (C1), Hengchun Peninsula (C6) Plains (A1), Taichung asin (A2), and Pingtung Alluvial Fan and all the pure alluvial plains are positive, indicating that the (A8)) in the Plain topographic province. Afterward, this study elevation frequencies skew toward the low elevation (Table 1). applies the χ2 (chi-square) test of goodness-of-fit for the 9 All the topographic sub-provinces in Table 1 have negative topographic sub-provinces [54]. The χ2 test can determine kurtosis, indicating that the elevation frequencies mostly whether the sample histogram or distribution belongs to a concentrate near the intermediate altitudinal classes than probability distribution function. Additionally, this study those of the normal distribution. In Table 1, from North- determines whether a difference exists between elevation Hsueshan Mountain (C1) southward and Hengchun Peninsula frequency histogram and the normal distribution function. The (C6) northward (Figure 3), the skewness vary from positive hypothesis of the χ2 test is as follows (the significance level α (lower altitudinal classes) to negative (higher altitudinal class) = 0.05). and narrow to -0.038 and -0.027, while the kurtosis narrow H : elevation frequency histogram belongs to the normal down to -0.605 and -0.740. These tendencies of skewness and 0 kurtosis causes the distribution of the elevation frequencies of distribution fitting. Back-Bone Range (C3) to be the most similar histogram to a normal distribution . H1 : rejects H0. Table 1 represents χ2 results for the 9 topographic sub- Combining the χ2 test analysis and the topographic evolution provinces. The p value is the probability value of a sample stages of the growing, steady-state and decaying ranges, when distribution belonging to a probability distribution function. It the ranges develop from growing to steady-state, the skewness of the elevation frequencies will narrow down from the low serves as a measure of the strength of evidence against H0 [55]. If the p value is quite low and even < α, the H0 will be rejected elevation toward the intermediate-to-high elevation, and the strongly. Simply, this test criterion means that a statistical kurtosis will increase. significance exists between the elevation frequency histogram Additionally, then the ranges develop from the steady-state to and the normal distribution fitting. However, if the elevation decaying, the skewness of the elevation frequencies will alter frequency histogram belongs to the normal distribution fitting, from the intermediate-to-high elevation to the low elevation, then p = 1. In Table 1, except Taichung Basin (A2), all the p and the kurtosis will decrease. Furthermore, according to values for the other topographic sub-provinces are very high the topographic evolution model by Ohmori (1993), when

(p > 0.838 >> α), demonstrating that H0 is accepted strongly. the ranges reach the culminating stage, the average HIs will In this study, the results of the χ2 test show that the elevation be the maximum, the HCs will be S-type, and the elevation frequency histograms of these 9 topographic sub-provinces frequencies will be in the intermediate altitudinal classes all belong to the normal distribution fittings. Additionally, with a normal distribution. Thus, the Back-Bone Range (C3) the skewness (symmetry) and kurtosis (peakedness) are two should already reach the culminating stage. Additionally, the important parameters for analyzing a probability distribution. distribution pattern of the HI in North-Hsueshan Mountain Skewness is the degree to which a probability distribution (C1) presents a northward decrease (Figure 5), indicating that is asymmetrical about its mean, and a perfectly symmetrical denudation becomes the main process due to the back-arc normal distribution (bell shape) having the value of 0. spreading of the Okinawa Trough. The skewness value can be positive or negative. For a Therefore, North-Hsueshan Mountain (C1) is in the declining probability distribution, positive skew commonly indicates stage. Hengchun Peninsula (C6) and Tawu Mountain (C5) are that the tail is on the right side of the distribution, and negative ranges in the developing stage for which uplifting exceeds skew indicates that the tail is on the left [56]. In this study, the erosion. Their distribution patterns of the HIs increase northward upper x-axis for the elevation frequency histogram (Altitudinal (Figure 5), indicating that they are gradually developing toward Class) is defined to be increasing from right to left (Figure 8). the culminating stage. North-Hsueshan Mountain (C1) and Therefore, positive skewness causes the histogram to skew Hengchun Peninsula (C6) both have S-type HCs; however, their toward the right (lower altitudinal classes), and the negative topographic evolution stages are different. Thus, it’s difficult to skewness causes the histogram to skew toward the left distinguish whether a ranges growing or decaying only from the

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types of HCs. Other parameters, such as average height, relief, and Tawu Mountain (C5) have HIs that will increase gradually and orogenic age, should be associated with the HCs to identify due to their properties of growing ranges. Hsueshan Mountain the topographic evolution stage of ranges. (C2), Back-Bone Range (C3) and Ali Mountain (C4) have reached the culminating stage with the properties of steady- Coastal range topographic province state ranges. North-Hsueshan Mountain (C1) has HIs that will This topographic province contains three topographic sub- decrease gradually due to its property of decaying ranges. provinces, North Coastal Range (D1), central Coastal Range Comprehensively, all of these generate the mountain cycle (D2), and South Coastal Range (D3). The average HCs of the (red arrows in Figure 10). (2) Hsinchu Hill (B4) and Taichung three topographic sub-provinces are all concave. The average Hill (B8) that are located in the northern and central Western HI is low (=0.34) in North Coastal range (D1), high (=0.39) foothill topographic province have higher HIs than Tainan in Central Coastal Range (D2), and intermediate (=0.37) in Hill (B10) that are located in the southern Western foothill South Coastal range (D3). The elevation frequencies all tend topographic province due to the lower erosion rates and their toward the low altitudinal classes (Figure 9), and are similar relatively longer period of tectonic activities. Additionally, to the patterns of the hills in the Western foothill topographic the hypsometric features of the Western foothill topographic province (Figure 9). province now are transitioning toward the culminating stage Lin (2000) determined that the earliest uplift area along the (purple arrows in Figure 10). The HIs of this topographic coastal range is North Coastal Range (D1) (1.1 Ma), followed province will gradually increase due to the continuous by Central Coastal Range (D2) (0.77 Ma), and the last is South tectonic uplifting, and the HCs will gradually develop toward Coastal Range (D3) (0.22Ma). S-shape. (3) Combining the results of (1) and (2) above, we may figure out a “Taiwan orogen cycle” (black arrows in Theoretically, the average HIs of topographic sub-provinces Figure 10), which develops under the concurrent tectonics and should increase with their emerged ages (Ohmori, 1993). denudation, resembling the Ohmori cycle. (4) The topographic However, the erosion and uplifting rates act as the key factors evolution model of the Coastal range topographic province is of the hypsometric features in the coastal range topographic different from the Central range. Due to continuously strong province. Dadson et al. (2003) reported that the erosion rate denudation, the hypsometric features of the Coastal range in the coastal range area is higher than 10 m/yr, and the mean topographic province will remain in the state of low HIs and annual coastal suspended sediment flux in the north is about 31 concave HCs (green arc-mark in Figure 10) (Figure 10). Mt/yr, the central is about 22 Mt/yr, and the south is up to 88 Mt/yr. Hsieh et al. (2004) demonstrated that the uplifting rates Conclusion in the coastal range area are less than 4 mm/yr in the north, The Taiwan orogen is a young terrain, and shows various 4-7mm/yr in the central and up to 7-9 mm/yr in the south, shapes of HCs with HIs from 0.27 to 0.60. The Central range and the most southern 10 km may reach 10 mm/yr. Therefore, topographic province with the highest elevation has higher HI the concave HCs in the Coastal range topographic province and S-type HC due to its relatively longer period of tectonic should be caused by the high erosion rates, and the relatively activities. However, the Western foothill topographic province lower suspended sediment flux and intermediate uplifting rate situated at the gradually uplifting mountain fronts has lower may cause the Central Coastal Range (D2) to have a relatively HI and concave HCs due to the higher erosion rates and its higher HI. relatively shorter period of tectonic activities. Additionally, The Taiwan orogen cycle from the HCs except the recently emerged tablelands with convex to straight-type HCs, all the topographic sub-provinces of the A summary of the development of HCs of the Central range, Western foothill topographic province and the Coastal range the Western foothill, and the Coastal range topographic topographic province have concave HCs. provinces indicates the follows. (1) Hengchun Peninsula (C6)

Figure 10: Plot of the “Taiwan orogen cycle” from the average HCs of the Central range, the Western foothill, and the Coastal range topographic provinces. The black dashed line is the diagonal line and its HI = 0.5.

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Figure 11: Elevation frequency histogram patterns of topography evolution of the Taiwan orogen. A: the old stage topography (the sinking or subsidence basins or plains), B: the developing and declining stage topography (the foothills, growing ranges and decaying ranges), C: the culminating stage topography (steady state ranges), and D: the young stage topography (the recently emerged tablelands).

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Citation: Chen YC, Tsai H, Sung QC, Wang T (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen. J Geol Geosci 4: 001-014. Copyright: © 2020 Chen YC. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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