Terrain variability and channel network characteristics critically influence the hydrologic response of watersheds. Width function represents this response under idealized flow conditions of constant velocity and absence of losses, and can be estimated solely using the terrain data. However, the width function, in its graphical form, is less tractable for further analytical applications such as in the derivation of link-based geomorphological instantaneous unit hydrograph. In this study, we systematically redress these issues in the following manner: (a) develop a framework for the functional estimation of width functions using a mixture of truncated skew-normal distributions that captures a wide variety of distribution shapes, (b) provide a basis for model selection based on the Bayesian Information Criterion, (c) demonstrate the utility of a functional estimation approach by identifying hydrologically similar watersheds based on divergence measures applied to the width function estimates, and (d) illustrate the utility of efficient statistical estimation of geomorphic functions and metrics, which affords data reduction and can be scaled to very-large terrain datasets.

地形变异性和河道网络特征严重影响流域的水文响应。宽度函数表示在恒定速度和无损失的理想流动条件下的此响应，并且可以仅使用地形数据进行估算。但是，宽度函数以其图形形式对于进一步的分析应用（例如在基于链接的地貌瞬时单位水位图的推导中）较难处理。在这项研究中，我们通过以下方式系统地解决了这些问题：（a）使用截断的正态正态分布的混合物来开发宽度函数的函数估计框架，该正态分布可捕获各种各样的分布形状，（b）提供了基于贝叶斯信息准则的模型选择基础，