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題名：集水區測高特徵的尺度依賴性及其構造活動之推論－以台灣造山帶為例
作者：鄭光佑
作者(外文)：Cheng, Kuang-Yu
校院名稱：國立彰化師範大學
系所名稱：地理學系
指導教授：蔡衡
學位類別：博士
出版日期：2016
主題關鍵詞：面積高度積分；尺度依賴；地形均衡狀態；構造活動；台灣造山帶；Hypsometric Integral；Scale Dependence；Steady State Topography；Tectonic Activity；Taiwan Mountain Belt
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集水區測高分析普遍應用於描述集水區地形特徵、判斷集水區發育時期及推論地區構造活動等，已成為地形學的研究途徑（approach）之一。傳統上此一研究途徑有三大指導原則，即：（1）集水區面積高度積分（hypsometric integral, HI）與地形發育時間呈負相關、（2）集水區HI與地區構造抬升率呈正相關、（3）集水區測高特徵不受集水區尺度的影響（scale independence）。前人研究顯示集水區在一邊抬升一邊侵蝕的造山帶環境下，山脈由開始成長至達到抬升－侵蝕均衡狀態的過程，集水區測高曲線（hypsometric curve）會由凹形逐漸變成S形，HI值也會由低逐漸增高。此與前述原則（1）相反。另有前人研究顯示，在山麓前緣地區，其集水區HI會與地殼抬升率呈負相關，這也和原則（2）抵觸。而多篇研究報告也指出集水區測高特徵具有尺度依賴（scale dependence）的現象，則和前述指導原則（3）不符。
上述情況可理解為測高分析研究，已出現了一些與原研究途徑指導原則矛盾的現象。綜觀前人研究，發生矛盾現象的地方皆位於造山帶或構造活動頻繁的山麓前緣地帶。這些矛盾現象空間分布的一致性，可能暗示此三種矛盾現象成因具有關連性，且有重新檢討造山帶集水區測高特徵的地形意義，及山麓前緣地帶集水區測高特徵的解釋及應用方式的需要。
台灣為一造山地帶，西部麓山帶西翼及海岸山脈東翼可視為山麓前緣地帶，符合前述測高分析發生矛盾現象的區位特徵。而前人研究提議的中央山地由北向南的造山方向，可由山脈位置推論其發育年代帶先後，極適合用以觀察集水區測高特徵隨山脈發育時間的變化情形，並討論其所顯示的地形意義。海岸山脈則有前人海階定年提供的地殼抬升率資料，可用以討論集水區HI與地殼抬升率的關係。西部麓山帶的三義台地，亦有前人研究提出的地區構造活動模型，可供驗證集水區測高分析結果推論的構造活動是否合理。因此，本研究先以台灣中央山地、海岸山脈研究區，計測不同等級河流集水區測高特徵，觀察上述三項異常現象的分布情形，解釋發生矛盾現象的原因，並提出造山帶水區測高特徵的新分析方法，最後以新分析方法推論三義台地等三個造山帶測試樣區的構造活動特徵。
研究結果顯示，台灣中央山地由南向北集水區HI隨山脈發育年代的增加，由低逐漸增高，至中央山脈中部抬升－侵蝕均衡區時HI值達到最高（約0.5），往北則又隨著山脈的崩垮，HI逐漸降低，此結果的確和傳統認為的集水區HI與其發育時間呈負相關的觀念不同。中央山地的研究結果也顯示，集水區HI尺度依賴現象只會出現在非地形均衡地帶的集水區。顯示在尚未達到地形均衡地區，欲以集水區面積高度積分（HI）推論構造抬升率時，需考慮集水區的大小（size）也會影響積分值的表現。
海岸山脈的研究結果顯示，此一山麓前緣地帶，集水區HI有尺度依賴的現象，且HI與地殼抬升率呈負相關，的確和傳統指導原則牴觸。本研究認為山麓前緣地帶集水區HI與抬升率呈負相關，是因為高級河主集水區（面積較大）並非全面抬升，而是上游抬升較快，使集水區高差增大，因此導致集水區HI偏低，且該地區抬升率愈快，大集水區的高差愈大，其HI就愈低，使得集水區HI與地殼抬升率呈負相關。此外因低級河小集水區位置多位於上游，且其面積小故容易全面抬升，其集水區高差較小，所以得到較高HI。結果就會造成大集水區HI偏低，小集水區HI偏高的尺度依賴現象。因抬升速率愈快，尺度依賴程度愈高，所以本研究嘗試設計一個新的構造地形指標－集水區尺度依賴指數（scale dependence index, SDI），以用於山麓前緣地帶（或可視為非地形均衡區）的地殼抬升率推論。最後，本研究以台灣三義台地、中港溪流域及美國加州Point Reyes半島為例，運用SDI推論該地的構造活動，結果和前人提出的地區構造模型相符。本研究建議在山麓前緣地帶應以集水區SDI分析取代傳統的HI分析。
由以上測試與討論，本研究認為造山帶集水區測高特徵所表現的地形意義如下：
（1）凹形的集水區測高曲線、小於0.5的HI值與明顯的HI尺度依賴現象，表示該區位於造山帶的非地形均衡區。
（2）S形的集水區測高曲線、約0.5的HI值與無HI尺度依賴現象，表示該區位於造山帶的地形均衡區。
本研究建議造山帶集水區測高特徵推論區域構造抬升率的流程如下：
（1）檢測該區是否有集水區HI尺度依賴現象。
（2）若無尺度依賴現象，表示該區位於地形均衡區，可以傳統HI分析方法推論構造抬升率。
（3）若有尺度依賴現象，表示該區位於地形非均衡區（或山麓前緣地帶），則需以SDI分析法推論構造抬升率。
關鍵詞：面積高度積分、尺度依賴、地形均衡狀態、構造活動、台灣造山帶
The hypsometric analysis of drainage basins is a popular approach to depicting landform characteristics of a basin, to infering the development stages of a basin, and to deducing the tectonic uplift rate of an area. In tradition, this approach has three guiding principles that have been widely acknowledged. Firstly, there exists a negative correlation between basin hypsometric integral (HI) and basin development time. Secondly, there is a positive correlation between basin HI and tectonic uplift rates. Thirdly, the basin hypsometric characteristic is scale independent. Previous studies indicated that the hypsometric curve changes from concave shape to S-shape along with an increasing HI value through mountain building resulting from concurrent tectonics and denudation. This is against the first guiding principle. Other studies pointed out that there is a negative relation between basin HI and uplift rates in mountain front areas. These areas fail to comply with the second guiding principle. Many studies have also suggested that the basin HI is scale dependent, which conflicts with the third guiding principle. These discrepancies occur in cases where the hypsometric studies are applied to the orogenic belts and/or tectonically active mountain front areas. It suggests the above-mentioned conflicts may have some spatial and genetic relations. Therefore, this study will review in details the geomorphological meanings of basin hypsometry and will deduce a practical tool to resolve the conflicts that arise when basin hypsometry is applied to the morphotectonic study in the orogenic regions.
The Taiwan Mountain Range resulted from an arc-continent collision which has propagated southward during the past 5 My, and the age of collision and the duration of sub-aerial erosion have increased progressively towards the north. The duration of the evolution of the sub-aerial landscape is assumed to be equivalent to the distance from the southern tip of the island. Taking advantage of the space-for-time substitution concerning the building process of Taiwanese mountains, this study sampled major drainage basins for hypsometric analysis, from the southern tip of the island to the northern end, to explore the relation between the hypsometric integral(HI) and the development stage of drainage basins. In the Coastal Range, previous studies have provided data on crustal uplift rates, which can be used to discuss the relation between the basin HI and uplift rates. In the San-yi Tableland, a previous study has suggested a regional tectonic model which can be used to validate the new basin hypsometric analysis we proposed. Finally, we used the new method to discuss the tectonic inferences in western foothills, Taiwan and Point Reyes, California.
The results of this study showed that the characteristics of basin hypsometry in steady state topography of the Taiwan Mountain Range can be summarized as the HI for a main basin and its subordinate basins having values greater than 0.5 and the S-shaped hypsometric curve. From the southern end to the middle part in the Central Range, there is a positive relationship between the basin HI and the basin development time. The higher order the drainage basin, the longer the development time. We also suggested that the HI is scale free (particularly size independent) for basins of steady state topography, while the HI is scale dependent for basins at a pre-steady state of topography or for basins with topography where the steady state has been destroyed. The results from the Coastal Range showed that the basin HI has scale dependence in the mountain front area. And the basin HI is negatively correlated with uplift rates in the range front area. The results differ from the traditional guiding principles. We suggested that the origin of the negative relation between the basin HI and uplift rates lies in the fact that the major, bigger basin in the mountain front area is not entirely uplifted as a whole. It is uplifted only on the upper reaches, so the elevation drop increases and the basin HI decreases. The higher the uplift rate is in the upper reaches, the lower basin HI will be. In addition, the lower order basins are usually in the upper reaches with small areas, so they may have been entirely uplifted. The entire uplift results in a lower elevation drop and higher basin HI. Therefore, the small basins have higher HI and bigger basins have lower HI in the mountain front area, that is, the scale dependence phenomenon of the basin HI. We also suggested that the basins which have higher uplift rates will have higher degrees of HI scale dependence.
Therefore, we propose a new basin hypsometric index to show the degree of HI scale dependence, and we name it the scale dependence index (SDI). The SDI will be used to infer tectonic uplift rates in the range front area. We used the SDI method to infer tectonic activity in San-yi Tableland, and the result is consistent with the previous study proposed by Ota et al. (2006). We also applied the SDI method to infer tectonic activities in Chung-kang drainage and in Point Reyes peninsula of California, USA, with improved results over the traditional HI method. Therefore, in the range front area, we suggest substituting the SDI method for the traditional method of basin hypsometry analysis.
This study concluded that the morphotectonic implications of basin hypsometry can be summarized as below, when being applied to orogenic regions:
1. If a basin is located in the area of non-steady state topography, it is characterized by a concave hypsometric curve, a HI less than 0.5, and an apparent scale dependence.
2. If a basin locates in the area of steady state topography, it is characterized by a S-shaped hypsometric curve, a HI of 0.5, and a scale independence.
This study further suggested that the steps for inferring the uplifting rate of the orogenic region using basin hypsometry be as follows:
1. The scale dependence of basin hypsometry should be tested in the region.
2. If drainage basins in the region show scale independence in terms of basin hypsometry, the regional topography may be considered to be in a steady state. The traditional hypsometric analysis can, then, be applied to infer the uplifting rate in the region.
3. If drainage basins in the region show scale dependence in terms of basin hypsometry, the regional topography may be considered to be in a non-steady state. The SDI method should be applied to infer the uplifting rate in the region.
Keyword: Hypsometric Integral, Scale Dependence, Steady State Topography, Tectonic Activity, Taiwan Mountain Belt
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