Interpolating Hydrologic Data Using Laplace Formulation
Interpolating Hydrologic Data Using Laplace Formulation
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DOI：
10.3390/rs15153844
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
Tian Xu;V. Merwade;Zhiquan Wang
中科院分区：
文献类型：
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作者：
Tian Xu;V. Merwade;Zhiquan Wang
空间插值技术在水文学中起着重要的作用，因为许多点观测需要被插值以创建连续的表面。尽管有几种工具和方法可用于插值数据，但并非所有工具和方法都适用于水文应用。其中一种技术是拉普拉斯方程，它在水文学中用于创建流网，但很少用于数据插值。本研究的目的是探讨拉普拉斯公式（LF）在水文应用中使用的数据（水文数据）插值的效率，并将其与其他广泛使用的方法，如反距离加权（IDW），自然邻居，和普通克里金法进行比较。LF插值与其他方法的性能进行评估，使用定量措施，包括均方根误差（RMSE）和系数的决定（R2）的准确性，表面质量的视觉评估，和计算成本的操作效率和速度。美国不同地区的地表高程、河流水深、降水量、温度和土壤湿度等数据均被使用。RMSE和R2结果表明，LF与其他方法的精度相当。LF易于使用，因为与反距离加权（IDW）和克里金法相比，它需要更少的输入参数。在计算上，当数据集不大时，LF在速度方面比其他方法更快。总的来说，LF提供了一个强大的替代现有的方法内插各种水文数据。需要进一步的工作，以提高其计算效率。
Spatial interpolation techniques play an important role in hydrology, as many point observations need to be interpolated to create continuous surfaces. Despite the availability of several tools and methods for interpolating data, not all of them work consistently for hydrologic applications. One of the techniques, the Laplace Equation, which is used in hydrology for creating flownets, has rarely been used for data interpolation. The objective of this study is to examine the efficiency of Laplace formulation (LF) in interpolating data used in hydrologic applications (hydrologic data) and compare it with other widely used methods such as inverse distance weighting (IDW), natural neighbor, and ordinary kriging. The performance of LF interpolation with other methods is evaluated using quantitative measures, including root mean squared error (RMSE) and coefficient of determination (R2) for accuracy, visual assessment for surface quality, and computational cost for operational efficiency and speed. Data related to surface elevation, river bathymetry, precipitation, temperature, and soil moisture are used for different areas in the United States. RMSE and R2 results show that LF is comparable to other methods for accuracy. LF is easy to use as it requires fewer input parameters compared to inverse distance weighting (IDW) and Kriging. Computationally, LF is faster than other methods in terms of speed when the datasets are not large. Overall, LF offers a robust alternative to existing methods for interpolating various hydrologic data. Further work is required to improve its computational efficiency.