應用河川能量定律於集水區內河道剖面自動分區與支流覆蓋類型分類

Abstract

河川能量定律（Stream Power Law）是解釋河流縱剖面與受構造抬升驅動之地貌演化的常用理論框架。山區河流通常呈現三個地貌區段——崩積區、基岩區與沖積區，但這些區段間的轉換界線仍難以明確劃分。本研究提出一套自動化的河道縱剖面分區方法，結合坡度–集水面積分析、閾值式平滑處理及分段式迴歸擬合。過程中將自動判識區段分界之臨界集水面積，並為各區段率定河川能量定律之參數：曲度指數θ與陡度指數β。 藉由主流計算所得的θ值，支流縱剖面可轉換至χ–高程空間，以利一致性的比較。依據β值，支流再進一步透過K-means 分群與主流為基準的預測區間進行分類為基岩侵蝕型或覆蓋沉積型。對於沉積覆蓋型支流，則透過比對實測與模型預測之縱剖面，以估算基岩高程與沉積厚度。 為重建集水區地形，本研究於主流與支流坡面上套用等坡度的Eikonal 模型。在沖積區段中，為修正曲流影響，則引入基於曲流率的中心線調整。由於基岩參數化存在高度不確定性，目前集水區地形重建與沉積量推估尚屬初步結果。儘管如此，本研究所提出之框架，仍為進行形態分析與辨識集水區尺度沉積儲集模式提供了系統性基礎。

The stream power law is a widely used framework for interpreting river profiles and landscape evolution under tectonic uplift. Mountain rivers typically exhibit three geomorphic zones—colluvial, bedrock, and alluvial—but delineating transitions among them remains challenging. This study presents an automated method for river profile zonation using slope–area analysis, threshold-based smoothing, and piecewise regression fitting. Critical drainage areas separating geomorphic domains are automatically identified during this process, and stream power parameters—concavity θ and steepness β—are calibrated for each zone. Using the trunk-derived θ, tributary profiles are transformed into χ–elevation space to allow consistent comparison. Tributaries are classified as bedrock-incising or sedimentcovered based on β values, using both K-means clustering and a trunk-based prediction interval. For sediment-covered tributaries, bedrock elevations and sediment thickness are estimated by comparing observed and modeled profiles. To reconstruct watershed topography, a constant-slope Eikonal model is applied to hillslopes along both the trunk stream and its tributaries. In alluvial zones, channel centerlines are corrected for meandering using sinuosity-based adjustments. Due to large uncertainties in bedrock parameterization, both full watershed reconstruction and sediment quantification remain preliminary. Nevertheless, the framework provides a systematic basis for morphometric analysis and identifying sediment storage patterns at the catchment scale.