Interpolating Hydrologic Data Using Laplace Formulation
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...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/15/15/3844 |
| _version_ | 1797586011401748480 |
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| author | Tianle Xu Venkatesh Merwade Zhiquan Wang |
| author_facet | Tianle Xu Venkatesh Merwade Zhiquan Wang |
| author_sort | Tianle Xu |
| collection | DOAJ |
| description | 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 (R<sup>2</sup>) 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 R<sup>2</sup> 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. |
| first_indexed | 2024-03-11T00:17:15Z |
| format | Article |
| id | doaj.art-33b928ea6e014cb3bda734b6c0b02d01 |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-11T00:17:15Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-33b928ea6e014cb3bda734b6c0b02d012023-11-18T23:31:37ZengMDPI AGRemote Sensing2072-42922023-08-011515384410.3390/rs15153844Interpolating Hydrologic Data Using Laplace FormulationTianle Xu0Venkatesh Merwade1Zhiquan Wang2Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USALyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USADepartment of Computer Science, Purdue University, West Lafayette, IN 47907, USASpatial 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 (R<sup>2</sup>) 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 R<sup>2</sup> 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.https://www.mdpi.com/2072-4292/15/15/3844spatial interpolationhydrologic dataLaplace equationIDWnatural neighborordinary kriging |
| spellingShingle | Tianle Xu Venkatesh Merwade Zhiquan Wang Interpolating Hydrologic Data Using Laplace Formulation Remote Sensing spatial interpolation hydrologic data Laplace equation IDW natural neighbor ordinary kriging |
| title | Interpolating Hydrologic Data Using Laplace Formulation |
| title_full | Interpolating Hydrologic Data Using Laplace Formulation |
| title_fullStr | Interpolating Hydrologic Data Using Laplace Formulation |
| title_full_unstemmed | Interpolating Hydrologic Data Using Laplace Formulation |
| title_short | Interpolating Hydrologic Data Using Laplace Formulation |
| title_sort | interpolating hydrologic data using laplace formulation |
| topic | spatial interpolation hydrologic data Laplace equation IDW natural neighbor ordinary kriging |
| url | https://www.mdpi.com/2072-4292/15/15/3844 |
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