Since the 1960s, many rivers have been destroyed as a consequence of the process of rapid urbanization. As accurate figures are important to repair rivers, there have been many research reports on methods to obtain the exact river slope and elevation. Until now, many research efforts have analyzed the river using measured river topographic factors, but when the flow velocity changes rapidly, such as during a flood, surveying is not easy; and due to cost, frequent measurements are difficult. Previous research has focused on the cross section of the river, so the information on the river longitudinal profile is insufficient. In this research, using informational entropy theory, equations are presented that can calculate the average river slope, river slope, and river longitudinal elevation for a river basin in real time. The applicability was analyzed through a comparison with the measured data of river characteristic factors obtained from the river plan. The parameters were calculated using informational entropy theory and nonlinear regression analysis using actual data, and then the longitudinal elevation entropy equation for each river and the average river slope were calculated. As a result of analyzing the applicability of the equations presented in this study by R² and Root Mean Square Error, all R² values were over 0.80, while RMSE values were analyzed to be between 0.54 and 2.79. Valid results can be obtained by calculating river characteristic factors.

中文翻译：

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基于概率论的河流修复纵剖面研究

自 1960 年代以来，由于快速城市化进程，许多河流遭到破坏。由于准确的数字对于修复河流很重要，因此已经有许多关于获得准确河流坡度和高程的方法的研究报告。迄今为止，许多研究工作已经利用实测河流地形因素对河流进行了分析，但是当流速迅速变化时，例如在洪水期间，测量并不容易；并且由于成本原因，难以频繁测量。以往的研究主要集中在河流的横截面，因此河流纵剖面的信息不足。在本研究中，利用信息熵理论，提出了可以实时计算流域平均河流坡度、河流坡度和河流纵向高程的方程。通过与从河流规划中得到的河流特征因子实测数据进行比较分析其适用性。使用信息熵理论和非线性回归分析，利用实际数据计算参数，然后计算每条河流的纵向高程熵方程和平均河流坡度。作为分析本研究中提出的方程的适用性的结果，R²和均方根误差，所有R ²值都超过0.80，而RMSE值被分析为在0.54和2.79之间。通过计算河流特征因子可以得到有效的结果。