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Application of Quasi-Uniform B-Spline Surfaces with Different Degrees to Mesoscale Eddy Fitting.

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Title: Application of Quasi-Uniform B-Spline Surfaces with Different Degrees to Mesoscale Eddy Fitting.
Authors: Kong, Chunzheng1,2 (AUTHOR), Liu, Chuanfeng1,2 (AUTHOR), Zhou, Wei3 (AUTHOR) zhouwei@scsio.ac.cn, Lv, Xianqing1,2 (AUTHOR)
Source: Remote Sensing. Mar2026, Vol. 18 Issue 5, p735. 24p.
Subjects: Interpolation algorithms, Spline theory, Radar altimetry, Vortex motion, Ocean surface topography, Oceanography
Geographic Terms: Indian Ocean
Abstract: Highlights: What are the main findings? Based on the dense along-track observations from an eight-altimeter constellation (yielding approximately one data point per 40 km × 40 km area over a composite period), a 6-day optimal temporal window is identified for mesoscale eddy reconstruction in the South Indian Ocean, balancing data coverage against the physical advection of moving eddies. An application-oriented principle is established: the bi-quadratic B-spline is optimal for efficient sea surface height reconstruction, while the bi-quartic B-spline is essential for obtaining physically plausible vorticity fields. What are the implications of the main findings? The findings provide a methodological framework for selecting appropriate interpolation techniques based on specific scientific objectives, from operational eddy detection to advanced dynamical analysis. Leveraging the dense along-track observations from the current multi-satellite constellation, the demonstrated performance of B-spline methods offers a versatile and accurate tool for processing the new generation of high-resolution along-track satellite data (e.g., from SWOT), with significant potential for operational oceanography. Satellite altimetry technology provides along-track sea level anomaly (SLA) data for studying mesoscale eddies. However, accurately reconstructing their spatial structures from discrete and non-uniform along-track observations remains a significant challenge. This study systematically evaluates the performance of bi-quadratic, bi-cubic, and bi-quartic quasi-uniform B-spline surface fitting methods for mesoscale eddy reconstruction in the South Indian Ocean (60°S–30°S, 75°E–105°E). By combining idealized experiments with real satellite data, a comprehensive comparison is conducted across several dimensions, including fitting accuracy, computational efficiency, parameter robustness, error distribution, and the physical plausibility of derived vorticity fields. For SLA surface fitting, all three methods achieve comparable accuracy, but the bi-quadratic B-spline demonstrates marked advantages in computational efficiency. Its single-fit time is only 53% and 27% of that of the bi-cubic and bi-quartic methods, respectively, and it shows insensitivity to node configuration, highlighting its practicality. In contrast, vorticity field inversion, which relies on the second derivative of the fitted surface, requires higher-order continuity. Only the bi-quartic B-spline, with C3 continuity, produces physically credible and smooth vorticity fields, whereas lower-degree methods result in discontinuous or non-smooth fields. Based on these findings, this study proposes an application-oriented selection principle: the bi-quadratic B-spline is recommended for efficiency-focused tasks, such as eddy detection, while the bi-quartic B-spline is necessary for dynamic analyses involving vorticity. [ABSTRACT FROM AUTHOR]
Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Application of Quasi-Uniform B-Spline Surfaces with Different Degrees to Mesoscale Eddy Fitting.
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  Data: <searchLink fieldCode="AR" term="%22Kong%2C+Chunzheng%22">Kong, Chunzheng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Chuanfeng%22">Liu, Chuanfeng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhou%2C+Wei%22">Zhou, Wei</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> zhouwei@scsio.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Lv%2C+Xianqing%22">Lv, Xianqing</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Remote+Sensing%22">Remote Sensing</searchLink>. Mar2026, Vol. 18 Issue 5, p735. 24p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Interpolation+algorithms%22">Interpolation algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Spline+theory%22">Spline theory</searchLink><br /><searchLink fieldCode="DE" term="%22Radar+altimetry%22">Radar altimetry</searchLink><br /><searchLink fieldCode="DE" term="%22Vortex+motion%22">Vortex motion</searchLink><br /><searchLink fieldCode="DE" term="%22Ocean+surface+topography%22">Ocean surface topography</searchLink><br /><searchLink fieldCode="DE" term="%22Oceanography%22">Oceanography</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Indian+Ocean%22">Indian Ocean</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Highlights: What are the main findings? Based on the dense along-track observations from an eight-altimeter constellation (yielding approximately one data point per 40 km × 40 km area over a composite period), a 6-day optimal temporal window is identified for mesoscale eddy reconstruction in the South Indian Ocean, balancing data coverage against the physical advection of moving eddies. An application-oriented principle is established: the bi-quadratic B-spline is optimal for efficient sea surface height reconstruction, while the bi-quartic B-spline is essential for obtaining physically plausible vorticity fields. What are the implications of the main findings? The findings provide a methodological framework for selecting appropriate interpolation techniques based on specific scientific objectives, from operational eddy detection to advanced dynamical analysis. Leveraging the dense along-track observations from the current multi-satellite constellation, the demonstrated performance of B-spline methods offers a versatile and accurate tool for processing the new generation of high-resolution along-track satellite data (e.g., from SWOT), with significant potential for operational oceanography. Satellite altimetry technology provides along-track sea level anomaly (SLA) data for studying mesoscale eddies. However, accurately reconstructing their spatial structures from discrete and non-uniform along-track observations remains a significant challenge. This study systematically evaluates the performance of bi-quadratic, bi-cubic, and bi-quartic quasi-uniform B-spline surface fitting methods for mesoscale eddy reconstruction in the South Indian Ocean (60°S–30°S, 75°E–105°E). By combining idealized experiments with real satellite data, a comprehensive comparison is conducted across several dimensions, including fitting accuracy, computational efficiency, parameter robustness, error distribution, and the physical plausibility of derived vorticity fields. For SLA surface fitting, all three methods achieve comparable accuracy, but the bi-quadratic B-spline demonstrates marked advantages in computational efficiency. Its single-fit time is only 53% and 27% of that of the bi-cubic and bi-quartic methods, respectively, and it shows insensitivity to node configuration, highlighting its practicality. In contrast, vorticity field inversion, which relies on the second derivative of the fitted surface, requires higher-order continuity. Only the bi-quartic B-spline, with C3 continuity, produces physically credible and smooth vorticity fields, whereas lower-degree methods result in discontinuous or non-smooth fields. Based on these findings, this study proposes an application-oriented selection principle: the bi-quadratic B-spline is recommended for efficiency-focused tasks, such as eddy detection, while the bi-quartic B-spline is necessary for dynamic analyses involving vorticity. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/rs18050735
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 24
        StartPage: 735
    Subjects:
      – SubjectFull: Interpolation algorithms
        Type: general
      – SubjectFull: Spline theory
        Type: general
      – SubjectFull: Radar altimetry
        Type: general
      – SubjectFull: Vortex motion
        Type: general
      – SubjectFull: Ocean surface topography
        Type: general
      – SubjectFull: Oceanography
        Type: general
      – SubjectFull: Indian Ocean
        Type: general
    Titles:
      – TitleFull: Application of Quasi-Uniform B-Spline Surfaces with Different Degrees to Mesoscale Eddy Fitting.
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            NameFull: Kong, Chunzheng
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            NameFull: Liu, Chuanfeng
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            NameFull: Zhou, Wei
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            NameFull: Lv, Xianqing
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              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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