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J Geol Geosci Volume 4(1): 20201

Case RepoRt

Journal of Geology and Geoscience

Hypsometric Curve Patterns and Elevation Frequency Histograms of Active OrogenYen- 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, Taiwan.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.

AbstractIn 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

IntroductionLandform principally results from the combined action of endogenous processes, such as tectonics and volcanism, and exogenous processes, such as weathering, erosion and deposition [3, 4]. In smaller scale but higher active convergent orogenic belt, such as the Taiwan orogen, there exists strongly dynamic negative feedback mechanisms of endogenous and exogenous processes [Willett and Brandon, 2002]. Typically, the rates of tectonic activities are quite slow, and their effects are usually only seen after long-term accumulation [5- 7].

Therefore, the long-term and large scale geological activities that may not be reflected by short-term geodetic measurements such as GPS are aspects that cannot be neglected [8]. Topography features can reflect both “lithological or structural variations of small and short time-space scales” and “tectonic 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.

Numerous morphotectonic indices have been developed and

Correspondence to: Yen-Chieh Chen, Tel: +886 9 21264027; E-mail address: chenycchna[AT]gmail[DOT]com

Received: Jan 24, 2020; Accepted: Feb 19, 2020; Published: Feb 20, 2020

utilized to facilitate rapid evaluation of these morphologic responses [12- 19].The hypsometric technique is considered a volumetric form index of 3-dimension; topography fractal parameters and drainage basin asymmetry are considered areal form indices of 2-dimension; stream-gradient index, Hack profile, mountain front sinuosity, river channel sinuosity, and valley width-depth ratio are considered linear form indices of 1-dimension. With the speed and precision of Geographic Information System (GIS) and Digital Terrain Model (DTM), the calculation of morphotectonic indices has become easier [20- 23]. So, the morphotectonic indices have been widely used in geomorphology and active tectonics.

Since the late Miocene, roughly 6.5 million years ago, the Taiwan orogen originated from the oblique arc- collision of the Luzon arc with the edges of the Eurasian continent between the Eurasian plate and the Philippine Sea plate (Figure 1) [24- 28].

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

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As the collision time sequence proceeded from north to south, Taiwan’s mountain ranges started forming from uplifted ranges in northern Taiwan, and expanded gradually southward at an propagation rate from 55 to 90 km/Ma [29]. Spatially, taking the maximum, the southern tip of the Taiwan ranges moved northward by 90 km, which was equivalent to an orogenic process for a million years (Figure 1b). Applying this “time-space equivalence” relationship to inspect the continuous rise in the height of Taiwan’s ranges from the southern tip to the north, it is found that at the 120-290 km zone (equivalent to 1.33-3.22 Ma) in the central ranges (black bold line rectangle area in Figure 1b), the substance increase caused by tectonics and the substance loss caused by denudation are balanced. The ranges can be called “steady-state ranges” [30, 31]. While the back-arc spreading of the Okinawa Trough was diminishing or

even stopping the orogenic movement in northern Taiwan, collision in southern Taiwan had just started [32-34, 36].

Thus, the ranges in southern Taiwan (about 0-120 km; equivalent to 0-1.33 Ma) are “growing ranges (pre-steady- tate)” with greater uplifting than denudation , and the ranges in northern taiwan (about 290- 370 km; equivalent to 3.22-4.11 Ma) are “decaying ranges (post-steady-state)” with greater denudation than uplifting [36] (Figure 1).

The unique tectonic framework of the Taiwan orogen is a good example for simultaneous investigation of hypsometric technique of pre-steady-state, steady-state, and post-steady-state topography. Therefore, this study applies the hypsometric technique to the areas of different topographic characteristics in the Taiwan orogen and determines the hypsometric features for different topographic evolution stages.

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.

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of HCs have been widely applied to assess the geomorphic processes and identify the stages of topographic evolution [41, 42]. Furthermore, the topographic evolution stages are always related to tectonic activities showed that a mountain is rapidly uplifted without serious denudation, and then increases in dissection with a lowering in mean altitude by the ensuing erosion [43].

Therefore, basin HIs gradually decrease during the course of topographic evolution. While young river basins have higher HIs (HI>0.6) and convex HCs due to less denudation, mature and old river basins have intermediate HIs (0.4<HI<0.6) and S-type HCs (concave at high elevations and convex at low elevations). In the mature and old topographic evolution stages, if a sudden uplifting occurs, the topographic evolution stage will revert to the young stage. Otherwise, weathering and erosion will continuously reduce the residual land of the drainage basins, and the topography will develop to transitory monadnock phase (Strahler, 1952).

River basins at this terminal peneplain stage have power HIs (HI<0.4) and concave HCs (Figure 2a, b), and can be used as the initial landform of the next geomorphic cycle (Ohmori, 1993). However, in orogenic areas subject to continuous tectonic activities, such as Taiwan and Japan, HIs of river

Literature reviewThe hypsometric integral (HI) applies an areal hypsometric curve (HC) model to describe the proportion of residual and volume of a basin after erosion [37, 38]. It gives 3-dimensional information for a 2- dimensional approach . Studies showed that a strong relationship exists between the HI, tectonic uplift rate, and some nature factors such as structural activities, lithology, and climate features [39]. In addition, the HI scale-dependence was also widely discussed. Studies of the San Gabriel Mountains, California by Lifton and Chase (1992) and the taiwan orogen by Chen et al. (2003a, b) clearly indicated that tectonism strongly influenced the HI at larger scales of 30 km or range-wavelength, and a stronger influence of lithology at smaller scales of 10 km or below.

Moreover, Lifton and Chase (1992) suggested an inverse correlation between range-scale HI with varying climate and uplift rate, and a positive correlation is observed in the San Gabriel Mountains, California. Chen et al. (2018) also proposed a negative correlation between HI and rock uplift rate in the non-steady-state range front, and a positive correlation in the steady-state range interior in the south Coastal Range, Taiwan.

The HC represents the relative proportion of basin area above a given height (Strahler, 1952; Hurtrez et al., 1999). The patterns

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

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basins always reflect the results of the concurrent tectonics and denudation. Continuous tectonic activities always remain the topographic evolution stages of river basins at young to mature. Shih et al. (1980) analyzed the hypsometric features of 30 main river basins with areas >10km2 in the Taiwan orogen, and concluded that most river basins were in the mature topographic evolution stages [44].

Under the concurrent tectonics and denudation, Ohmori (1993) identified three topographic evolution stages (Figure 2d). (1) The developing stage: altitude and relief of ranges increase due to uplifting. (2) The culminating stage: ranges reach the highest altitude and relief. (3) The declining stage: altitude and relief of ranges gradually decrease while uplifting slows down or even stops. He also numerically simulated HCs and compared simulation results with real cases in Japan, and demonstrated that HIs of river rasins have a fluctuating cycle as the uplift rate changes. Additionally, HCs also have cycle through concave, S-type, and concave again (Figure 2c), and this succession of HCs is the reverse of of Strahler’s diagram (Ohmori, 1993) (Figure 2).

Chang (1975) indicated that that in the Taiwan orogen, basins in areas had HIs of 0.29-0.51 and concave to S-type HCs, whereas basins in mountainous areas ad HIs of 0.53-0.60 and S-type or minor convex HCs. The HCs also have scale-dependence features [45].

Willgoose and Hancock (1998) proposed the HC scale-dependences that may reflect the importance of river and

hillslope processes with basin sizes. Where the basin area is small, hillslope processes would be dominant, and the HC would be convex with a HI close to 1. Conversely, with increasing drainage area, the importance of river processes would increase, and the HC would become concave with a HI close to 0 (Willgoose and Hancock, 1998; Hurtrez et 1999; Sung and Chen, 2004).

MethodologyThe topographic provinces of the Taiwan orogen

For discussion about large-scale HI features and HC patterns in different topographic areas with special geology settings in the Taiwan orogen (Figure 1c, d), this study defines four main topographic provinces and several sub-provinces based on the HI distribution (Chen et al., 2003a, b), geological features (Ho, 1986), and topographic features (Lin, 1969). The four main topographic provinces are as follows. A is the Plain topographic province, B is tthe Western foothill topographic province, C is the Central range topographic province, and D is the Coastal range topographic province (Chen et al., 2006; Chen, 2008) (Figure 3).

The sub-basins of the topographic sub-provinces are derived from the processes reported by Chen et al. 2003a, b) and Chen (2008). They derived sub-basins of Strahler order 1 from the Taiwan 40-m-resolution DTM with a flow accumulation threshold of 3 km2 for large scale hypsometric analysis of 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).

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

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by the Bureau of Forestry in the 1980s, is produced by photogrammetry and projected over a Universal Transverse Mercator (zone 51) grid as as a Cartesian reference frame. Sung and Chen (2004) analyzed the fractal features of Taiwan topography and proved that the Taiwan 40-m-resolution DTM was appropriate for basin topography analysis.

HC and Elevation Frequency Histogram

Strahler (1952) analyzed the elevations and areas of river basins and plotted HCs (Figure 4b) in diagrams in which the y-axis and the x-axis are the relative elevation ratio (h/H) and the relative area ratio (a/A), respectively. In these diagrams, h is the elevation drop between a certain elevation and the lowest elevation of river basin; H is the maximum elevation drop; a is the cross-sectional area of a certain elevation, and A is the cross-sectional area of the lowest elevation. Mayer (1990) divided the elevation drops of a river basins into 8 intervals and plotted the histogram of areas between adjacent contour lines (Figure 4a). In this study, the elevation drop intervals are called “Altitudinal Class”, and the histogram is plotted using “Relative Abundance”. Relative abundance is defined as the area between adjacent contour lines over the area of the whole basin, and the “elevation frequency histogram” is formed by these two parameters. If one calculates the proportion of an area “in and above” each interval to total basin area, “Relative area (a/A)” is generated and can be used when plotting HCs. This study divides elevation drop of river basins into 10 intervals (Chen et al. 2005) to facilitate the plotting of HCs and elevation frequency histograms (Figure 4).

Theoretically, HIs only represent the areas under the HCs (Strahler, 1952) such that basins with the same HIs may have different HC patterns. Figure 5 presents a plot combining

HCs and elevation frequency histograms. The bottom and left axes are for the HCs, while the top and right axes are for the elevation frequency histograms. Three types of basins have the same HI of 0.54, however, their HC patterns are S-type (or concave-convex type), convex type, and convex-concave type (convex at high elevations and concave at low elevations), respectively (Figure 5). According to Figure 4a, the relative abundance of basin with S-type HC is mainly concentrated in the intermediate altitudinal classes (Figure 5a). The relative abundance of which with straight-type HC (Liem et al., 2016) is thoroughly distributed to each altitudinal class (Figure 5b). The relative abundance of which with convex-concave HC is mainly present in the lower and higher altitudinal classes (Figure 5c). Therefore, if studies consider the HC patterns when analyzing the HIs, basins of the same HI should be further differentiated and identified (Figure 5).

Results and DiscussionFigure 3 show that each main topographic province contains several topographic sub-provinces. Each topographic sub-province contains several sub-basins, each of which has a HC. Therefore, after plotting HCs of all sub-basins in each topographic sub-province, an “average hypsometric curve” and “standard deviation curves” can be generated to simplify the HC patterns. The area under the average HC is called “average HI”. Figures 6 to 9 present the results of HCs and elevation frequency histograms of the four main topographic provinces and the detail discussion is as follows.

Plain topographic province

The average HIs of Choshui and Chianan Plains (A1), Taichung Basin (A2), and Pingtung Alluvial Fan (A8) are 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).

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

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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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frequencies are widely distributed among the intermediate altitudinal classes. Choshui and Chianan Plains (A1) are the western coastal plains in the foreland. They are of a young terrains (Simoes and Avouac, 2006) with a low erosion rate (approximately 2-6 mm/yr) (Dadson et al., 2003). Due to the influence of the Peikang basement high (Figure 3), Choshui and Chianan Plains (A1) were tilted slightly toward the west with an uplifting rate of 0.5-4.4 mm/yr and a western horizontal shifting rate of 10-20 mm/yr [60, 46]. Therefore, they are structural uplifting plains with lower erosion rate. Taichung basin (A2) is widely covered by the Wu River alluvial, and is also a structural uplifting basin between the active Changhua and the Chelungpu faults.

The activity of the Changhua fault tilted Tatu Table l and (B6) and Pakua Tableland (B7) in the west of Taichung basin (A2), and the active Chelungpu fault generated the disastrous Chi-Chi earthquake (ML=7.3) on September 21, 1999 in the east Taichung basin (A2) [40]. Due to the approximately equal forces of uplift [58] and denudation (Dadson et al., 2003), the HCs of Taichung basin (A2) presents S-type. The HC of Pingtung Alluvial Fan (A8) is also S-type, and this should

be highly correlated with the concurrent high uplifting rate (>4.7 mm/yr) [47] and denudation (>5 mm/yr) (Dadson et al., 2003). Taipei Basin (A3), Puli Basin (A4), Kaohsiung Plain (A7), Pingtung Plain A9), Ilan Plain (A10), and Huatung Valley (A11) have relatively lower average HIs of 0.27-0.33. Their average HCs are concave and the elevation frequencies are mainly distributed in the low longitudinal classes. These hypsometric features imply that these topographic sub-provinces are situated in the structural sinking areas [52] or the areas with lower uplifting rates [47]. Tainan Terrain (A5) only contains four sub-basins along the Tainan anticline. Tahu Terrain (A6) lies southeast of Tainan Terrain (A5).

The average HC of Tainan Terrain (A5) is straight-type and that of Tahu Terrain (A6) is slightly S-type. The elevation frequencies of Tainan Terrain (A5) and Tahu Terrain (A6) are distributed from the intermediate to high altitudinal classes. Both Tainan Terrain (A5) and Tahu Terrain (A6) are recently emerged tablelands with terrain surfaces tilting westward [48]. In these two areas, many folds and fault structures exist, and the 20,000 years uplifting rate has reached 4-5mm/yr [47],

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.

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

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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.

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

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demonstrating that these two terrains are the young stage topography. Therefore, their HIs are relatively higher.

Although the topographic sub-provinces in the Plain topographic province all belong to the alluvial-plain category, they are affected by local tectonic activities and can be categorized as “structural uplifting topography”, “sinking topography” and “recently emerged coastal plain terrains”. Structural uplifting topography, such as Choshui and Chianan Plains (A1), Taichung Basin (A2) and Pingtung Alluvial Fan (A8), have S-type average HCs and the elevation frequencies are distributed in the intermediate altitudinal classes. Sinking topography, such as Taipei Basin (A3), Puli Basin (A4), Kaohsiung Plain (A7), Pingtung Plain (A9), Ilan Plain (A10) and Huatung alley (A11), have concave average HCs and the elevation frequencies concentrate almost in the lowest altitudinal class. Additionally, recently emerged coastal plain terrains, such as Tainan Terrain A5) and Tahu Terrain (A6), have straight-type average HCs and the elevation frequencies are roughly distributed to each altitudinal class (Figure 6).

Western foothill topographic province

The average HIs of Linkou Tableland (B1), Taoyuan Tableland (B2), Hukou Tableland (B3), and Houli Tableland (B5) are 0.46-0.60. Their average HCs are convex to straight-type, and the elevation frequencies tend toward the high altitudinal classes (Figure 7). The average HIs of Tatu Tableland (B6) and Pakua Tableland (B7) are 0.36-0.39. Their average HCs are concave and the elevation frequencies are at the lowest altitudinal classes (Figure 7). Linkou Tableland (B1), Taoyuan Tableland (B2), Hukou Tableland (B3), Houli Tableland (B5), Tatu Tableland (B6), and Pakua Tableland (B7) are all lateritic soil tablelands that recently emerged by the active structures [59, 40, 35], but the manners in which they emerge from differ. Linkou Tableland (B1), Taoyuan Tableland (B2), Hukou Tableland B3), and Houli Tableland (B5) as well as Tainan Terrain (A5) and Tahu Terrain (A6) are tablelands of entire terrain uplifting, which resemble the young stage topography defined by Strahler (1952).

However, Tatu Tableland (B6) and Pakua Tableland (B7) are tilting [49, 50], and the tilting is associated with the Tatu and

Pakua anticlines. Ohmori(1993) indicated that different crustal movements such as up-warping and tilting and the of newly emerged land will modify the course of change in the HCs. Thus, we propose that the structural tilting could increase the basin’s elevation drop, and then intensified the river erosion processes. Eventually, the intensified river erosion might cause the lower HIs and concave which resemble the peneplain stage topography defined by Strahler (1952). The average HIs of Hsinchu Hill (B4), Taichung Hill (B8), Toulio-Chiayi Hill (B9) and Tainan Hill (B10) are 0.30-0.35. As well as the sinking topography in the Plain topographic province, their average HCs are concave and their elevation frequencies are generally in the low altitudinal classes. The four hills are located in the western foothills.

The western foothills are the fold-thrust belts [51], and situated at the gradually uplifting mountain fronts (Figure 1c). Dadson et al. (2003) reported that in the Taiwan orogen, high erosion rates present at the mountain fronts, and the order-of-magnitude increased from north to south (approximately 4-60 mm/yr). Therefore, we consider that the decreasing of HIs from north (Hsinchu Hill (B4), HI=0.35) to south (Tainan Hill (B10), HI=0.30) of the four hills should be caused by the decadal-scale erosion patterns mentioned above. Moreover, the four hills with concave HC patterns that influenced by the gradually uplifting of the mountain fronts should resemble the initial landform defined by Ohmori (1993). Tatun Volcano (B11) is mainly composed of andesite, which is hard and resists erosion the influence time of erosion is not too long after the extinction of volcanoes (approximately 0.2Ma at least) [53], generating an average HI of approximately 0.45, the average HC is S-type, and the elevation frequencies are mainly in the intermediate altitudinal classes (Figure 7).

Central range topographic province

This province contains North-Hsueshan Mountain (C1), Hsueshan Mountain (C2), Back-Bone Range (C3), Ali Mountain (C4), Tawu Mountain (C5), and Hengchun Peninsula (C6). The average HCs for this area are consistently S-type, and their average HIs are 0.45-0.50. The elevation frequencies are principally in the intermediate altitudinal

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 KurtosisNorth-Hsueshan Mountain (C1) 2.409 0.879 0.200 -0.719

Hsueshan Mountain (C2) 2.337 0.886 -0.089 -0.624Back-Bone Range (C3) 2.244 0.896 -0.038 -0.605

Ali Mountain (C4) 1.230 0.942 -0.027 -0.740Tawu Mountain (C5) 2.285 0.892 -0.064 -0.773

Hengchun Peninsula (C6) 1.113 0.981 0.198 -0.603Topographic sub-provinces of the pure alluvial plains χ2 value p value Skewness Kurtosis

Taichung Basin (A2) 5.039 0.539 0.251 -0.785Choshui and Chianan Plains (A1) 2.759 0.838 0.158 -0.577

Pingtung Alluvial Fan (A8) 2.460 0.873 0.195 -0.790

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classes (Figure 8).

The topographic evolution model from computer simulation by Ohmori (1993) shows that when the ranges reach the culminating stage, the elevation frequencies will be in the intermediate altitudinal classes and similar to the normal distribution.

To determine whether the elevation frequency histograms are of normal distributions, this study applies normal distribution fitting to the elevation frequency histograms of the 6 topographic sub-provinces in the Central range topographic province and the 3 pure alluvial plains (Choshui and Chianan Plains (A1), Taichung asin (A2), and Pingtung Alluvial Fan (A8)) in the Plain topographic province. Afterward, this study applies the χ2 (chi-square) test of goodness-of-fit for the 9 topographic sub-provinces [54]. The χ2 test can determine whether the sample histogram or distribution belongs to a probability distribution function. Additionally, this study determines whether a difference exists between elevation frequency histogram and the normal distribution function. The hypothesis of the χ2 test is as follows (the significance level α = 0.05).

H0 : elevation frequency histogram belongs to the normal

distribution fitting.

H1 : rejects H0.

Table 1 represents χ2 results for the 9 topographic sub-provinces. The p value is the probability value of a sample distribution belonging to a probability distribution function. It 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 strongly. Simply, this test criterion means that a statistical significance exists between the elevation frequency histogram and the normal distribution fitting. However, if the elevation frequency histogram belongs to the normal distribution fitting, then p = 1. In Table 1, except Taichung Basin (A2), all the p values for the other topographic sub-provinces are very high (p > 0.838 >> α), demonstrating that H0 is accepted strongly. In this study, the results of the χ2 test show that the elevation frequency histograms of these 9 topographic sub-provinces all belong to the normal distribution fittings. Additionally, the skewness (symmetry) and kurtosis (peakedness) are two important parameters for analyzing a probability distribution. Skewness is the degree to which a probability distribution is asymmetrical about its mean, and a perfectly symmetrical normal distribution (bell shape) having the value of 0.

The skewness value can be positive or negative. For a probability distribution, positive skew commonly indicates that the tail is on the right side of the distribution, and negative skew indicates that the tail is on the left [56]. In this study, the upper x-axis for the elevation frequency histogram (Altitudinal Class) is defined to be increasing from right to left (Figure 8). Therefore, positive skewness causes the histogram to skew toward the right (lower altitudinal classes), and the negative skewness causes the histogram to skew toward the left

(higher altitudinal classes). kurtosis is a measure of whether a probability distribution is heavy tailedness or light-tailedness relative to a normal distribution (kurtosis = 3).

Probability distribution with higher kurtosis (>3) tends to have heavy long tails naming the leptokurtic distribution, and that with lower kurtosis (<3) tends to have light short tails naming the platykurtic distribution. The skewness of Hsueshan ountain (C2), Back-Bone Range (C3), Ali Mountain (C4) and Tawu Mountain (C5) are all negative, indicating that the elevation frequencies skew toward the high elevation. The skewness f North-Hsueshan Mountain (C1), Hengchun Peninsula (C6) and all the pure alluvial plains are positive, indicating that the elevation frequencies skew toward the low elevation (Table 1).

All the topographic sub-provinces in Table 1 have negative kurtosis, indicating that the elevation frequencies mostly concentrate near the intermediate altitudinal classes than those of the normal distribution. In Table 1, from North-Hsueshan Mountain (C1) southward and Hengchun Peninsula (C6) northward (Figure 3), the skewness vary from positive (lower altitudinal classes) to negative (higher altitudinal class) and narrow to -0.038 and -0.027, while the kurtosis narrow down to -0.605 and -0.740. These tendencies of skewness and kurtosis causes the distribution of the elevation frequencies of Back-Bone Range (C3) to be the most similar histogram to a normal distribution .

Combining the χ2 test analysis and the topographic evolution stages of the growing, steady-state and decaying ranges, when the ranges develop from growing to steady-state, the skewness of the elevation frequencies will narrow down from the low elevation toward the intermediate-to-high elevation, and the kurtosis will increase.

Additionally, then the ranges develop from the steady-state to decaying, the skewness of the elevation frequencies will alter from the intermediate-to-high elevation to the low elevation, and the kurtosis will decrease. Furthermore, according to the topographic evolution model by Ohmori (1993), when the ranges reach the culminating stage, the average HIs will be the maximum, the HCs will be S-type, and the elevation frequencies will be in the intermediate altitudinal classes with a normal distribution. Thus, the Back-Bone Range (C3) should already reach the culminating stage. Additionally, the distribution pattern of the HI in North-Hsueshan Mountain (C1) presents a northward decrease (Figure 5), indicating that denudation becomes the main process due to the back-arc spreading of the Okinawa Trough.

Therefore, North-Hsueshan Mountain (C1) is in the declining stage. Hengchun Peninsula (C6) and Tawu Mountain (C5) are ranges in the developing stage for which uplifting exceeds erosion. Their distribution patterns of the HIs increase northward (Figure 5), indicating that they are gradually developing toward the culminating stage. North-Hsueshan Mountain (C1) and Hengchun Peninsula (C6) both have S-type HCs; however, their topographic evolution stages are different. Thus, it’s difficult to distinguish whether a ranges growing or decaying only from the

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

J Geol Geosci Volume 4(1): 202011

types of HCs. Other parameters, such as average height, relief, and orogenic age, should be associated with the HCs to identify the topographic evolution stage of ranges.

Coastal range topographic province

This topographic province contains three topographic sub-provinces, North Coastal Range (D1), central Coastal Range (D2), and South Coastal Range (D3). The average HCs of the three topographic sub-provinces are all concave. The average HI is low (=0.34) in North Coastal range (D1), high (=0.39) in Central Coastal Range (D2), and intermediate (=0.37) in South Coastal range (D3). The elevation frequencies all tend toward the low altitudinal classes (Figure 9), and are similar to the patterns of the hills in the Western foothill topographic province (Figure 9).

Lin (2000) determined that the earliest uplift area along the coastal range is North Coastal Range (D1) (1.1 Ma), followed by Central Coastal Range (D2) (0.77 Ma), and the last is South Coastal Range (D3) (0.22Ma).

Theoretically, the average HIs of topographic sub-provinces should increase with their emerged ages (Ohmori, 1993). However, the erosion and uplifting rates act as the key factors of the hypsometric features in the coastal range topographic province. Dadson et al. (2003) reported that the erosion rate in the coastal range area is higher than 10 m/yr, and the mean annual coastal suspended sediment flux in the north is about 31 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 in the coastal range area are less than 4 mm/yr in the north, 4-7mm/yr in the central and up to 7-9 mm/yr in the south, and the most southern 10 km may reach 10 mm/yr. Therefore, the concave HCs in the Coastal range topographic province should be caused by the high erosion rates, and the relatively lower suspended sediment flux and intermediate uplifting rate may cause the Central Coastal Range (D2) to have a relatively higher HI.

The Taiwan orogen cycle from the HCs

A summary of the development of HCs of the Central range, the Western foothill, and the Coastal range topographic provinces indicates the follows. (1) Hengchun Peninsula (C6)

and Tawu Mountain (C5) have HIs that will increase gradually due to their properties of growing ranges. Hsueshan Mountain (C2), Back-Bone Range (C3) and Ali Mountain (C4) have reached the culminating stage with the properties of steady-state ranges. North-Hsueshan Mountain (C1) has HIs that will decrease gradually due to its property of decaying ranges. Comprehensively, all of these generate the mountain cycle (red arrows in Figure 10). (2) Hsinchu Hill (B4) and Taichung Hill (B8) that are located in the northern and central Western foothill topographic province have higher HIs than Tainan Hill (B10) that are located in the southern Western foothill topographic province due to the lower erosion rates and their relatively longer period of tectonic activities. Additionally, the hypsometric features of the Western foothill topographic province now are transitioning toward the culminating stage (purple arrows in Figure 10). The HIs of this topographic province will gradually increase due to the continuous tectonic uplifting, and the HCs will gradually develop toward S-shape. (3) Combining the results of (1) and (2) above, we may figure out a “Taiwan orogen cycle” (black arrows in Figure 10), which develops under the concurrent tectonics and denudation, resembling the Ohmori cycle. (4) The topographic evolution model of the Coastal range topographic province is different from the Central range. Due to continuously strong denudation, the hypsometric features of the Coastal range topographic province will remain in the state of low HIs and concave HCs (green arc-mark in Figure 10) (Figure 10).

Conclusion The Taiwan orogen is a young terrain, and shows various shapes of HCs with HIs from 0.27 to 0.60. The Central range topographic province with the highest elevation has higher HI and S-type HC due to its relatively longer period of tectonic activities. However, the Western foothill topographic province situated at the gradually uplifting mountain fronts has lower HI and concave HCs due to the higher erosion rates and its relatively shorter period of tectonic activities. Additionally, except the recently emerged tablelands with convex to straight-type HCs, all the topographic sub-provinces of the Western foothill topographic province and the Coastal range topographic province have concave HCs.

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.

Chen YC (2020) Hypsometric Curve Patterns and Elevation Frequency Histograms of Active Orogen

J Geol Geosci Volume 4(1): 202012

We summarize a topographic evolution model of the active collision orogenic belt from the elevation frequency histograms as follows. 1) The topography that is subjected to concurrent tectonics and denudation: the Central range topographic province and the hills in the Western foothill topographic province belong to this type. As the growing of ranges and hills, the elevation frequencies will develop from the low elevation (right skewness) to normal distribution (from curve B to C in Figure 11). Afterward, if the arc-continent collision diminishes or even stops as the decaying ranges of the northern Taiwan, the topographic elevation frequencies will gradually develop from normal distributions back to the low elevation (right skewness) (from curve C to B in Figure 11).

(2) The topography that emerged rapidly: Tainan Terrain (A5), Linkou Tableland (B1) and Houli Tableland (B5) belong to this type. The HCs are convex that conform to the Strahler’s young stage, and the elevation frequencies will remain in the high elevation (left skewness) (curve D in Figure 11) due to the continuous regional uplifting.

(3) The topography of alluvial-plain: the sinking terrains and the pure plains of the Plain topographic province belong to this type. The hypsometric features of the sinking terrains should conform to the Strahler’s old stage, and the elevation frequencies will remain in the lowest elevation (curve A in Figure 11) due to the continuous regional subsidence. However, because the pure plains are also influenced by concurrent tectonics and denudation, the hypsometric features of this foreland topography are similar to those of the growing ranges in the Central range topographic province (Figure 11).

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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.

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