基于势能信息熵的黄土小流域地貌演化特征

黄土高原流域地貌系统的地貌演化特征十分复杂，尚有诸多科学问题有待进一步深入研究。以往研究大多集中在流域地貌演化的侵蚀和发育特征等某一方面，缺乏从流域地貌系统及其势能信息熵的视角深入剖析野外多岩土层黄土小流域地貌演化特征的研究。为此，基于系统论的观点和方法，构建多岩土层黄土小流域地貌系统及其势能信息熵的数学模型，并以辛店沟小流域为例，对其地貌演化特征进行研究。结果表明：（1）构建的野外多岩土层黄土小流域地貌系统的概念模型及其势能信息熵的数学模型能够有效对辛店沟小流域进行数值模拟。（2）以黄土侵蚀作用为主的辛店沟小流域从2000—2019年的地貌演化过程是其势能信息熵的熵减过程和黄土地貌不断侵蚀的过程。（3）辛店沟小流域的势能信息熵能较好地反映该小流域的地貌演化阶段和地貌侵蚀过程。

Geomorphic evolution characteristics of small loess watersheds based on potential energy information entropy

Research on the evolution characteristics of loess erosion and the development of watershed geomorphic systems in the Loess Plateau of China is a hotspot in the study of loess landforms, and many related scientific issues still need to be studied. Most previous studies have focused on the erosion and development characteristics of watershed geomorphology, but there is a lack of research on indepth analysis of the geomorphic evolution characteristics of loess small watersheds with multiple rock and soil layers in the field from the perspective of watershed geomorphology system and its potential energy information entropy (PEIE). Therefore, based on the viewpoint and method of system theory, mathematical models of the geomorphic system and its PEIE of a small loess watershed with multiple rock and soil layers were built. Taking the Xindiangou small watershed at Suide County, Shaanxi Province, China as the research sample area, the digital elevation model data of 5 periods from 2000 to 2019 were used to investigate the entropy change law of the PEIE and the characteristics of landform evolution in the watershed. The results show that from 2000 to 2019, the geomorphic evolution process dominated by loess erosion in the Xindiangou small watershed is the process of entropy reduction of its PEIE and continuous erosion of the loess landform. Combined with the entropy change of PEIE in the Xindiangou small watershed and the indoor small watershed, it is speculated that the watershed geomorphic system will form a W-shaped PEIE change curve in its complete geomorphic evolution process, and its PEIE can better indicate the watershed geomorphic development demarcation points in its infancy, maturity, and old age. The research results also confirm the effectiveness of the conceptual model of the loess watershed geomorphic system and its mathematical model of PEIE in the numerical simulation of the Xindiangou small watershed. This model is an extension of the existing mathematical model of PEIE of watershed geomorphic systems with homogeneous single loess layers, which can be used in heterogeneous multiple rock and soil layer loess watershed geomorphic systems and has wider applicability. The research results provide ideas for further research on the geomorphic formation mechanism and evolution law of the Xindiangou small watershed in the future and guide soil and water conservation, ecological restoration, and regional sustainable development of the Xindiangou small watershed, which has important theoretical significance and good application prospects.