Practical implications in the interpolation methods for constructing the regional mean sea surface model in the eastern Mediterranean Sea

Milaa Zyad Murshan; Balaji Devaraju; Balasubramanian Nagarajan; Onkar Dikshit

doi:10.1515/jag-2023-0070

Article

Practical implications in the interpolation methods for constructing the regional mean sea surface model in the eastern Mediterranean Sea

Milaa Zyad Murshan , Balaji Devaraju , Balasubramanian Nagarajan and Onkar Dikshit

Published/Copyright: January 19, 2024

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From the journal Journal of Applied Geodesy Volume 18 Issue 3

Abstract

This investigation estimates a regional Mean Sea Surface (MSS) model, named SY21MSS, over the eastern Mediterranean Sea using satellite altimetry data from nine Exact Repeat Missions (ERM) and two Geodetic Missions (GM). Two interpolation methods, Least Squares Collocation (LSC) and Ordinary Kriging (OK), were employed, and statistical metrics were applied to assess their performance within a 15 km buffer from the coast. The comparison between LSC and OK techniques in the context of regional MSS modeling primarily centers on the covariance functions used by these methods. Furthermore, generalized cross-validation results indicate that OK outperforms LSC in this region. Consequently, the study recommends adopting the Kriging-based model for calculating regional MSS models in this region due to its superior performance. The investigation further explored the disparities between estimated regional MSS models and the global model DTU18MSS, highlighting a pronounced similarity between OK-SY21MSS and DTU18MSS, as evidenced by a lesser standard deviation (SD) difference compared to LSC-SY21MSS. The practical implications of this research underscore the importance of selecting an appropriate interpolation technique based on data characteristics and study area specifics. While both LSC and OK techniques are deemed viable for MSS modeling, the study emphasizes the superior performance of OK, particularly concerning covariance functions. Additionally, the results emphasize caution when applying global models in regions with significant local variations.

Keywords: regional mean sea surface model; Mediterranean Sea; satellite altimetry; Ordinary Kriging; Least Squares Collocation

Corresponding author: Milaa Zyad Murshan, Indian Institute of Technology Kanpur, Civil Engineering, Kanpur, India, E-mail: milaa@iitk.ac.in

Acknowledgments

The OpenADB team is acknowledged for making reprocessed altimetry data freely available, and the Overleaf team for providing helpful tools for making LATEX typesetting simple. We extend our heartfelt thanks to DTU for providing open access to their model data, allowing us to seamlessly access and utilize the model data seamlessly. Additionally, we appreciate the developers of the R programming language, which served as the primary platform for all computations and figures.

Research ethics: Not applicable.
Author contributions: Balaji Devaraju conceptualized and designed the research approach. Milaa Zyad Murshan performed the experiments, analyzed the data, and computed the models. Milaa Zyad Murshan and Balaji Devaraju analyze the outcome data. Milaa Zyad Murshan wrote the paper with assistance from Balaji Devaraju, Nagarajan Balasubramanian, and Onkar Dikshit. All authors have reviewed and approved the final version.
Competing interests: The authors state no conflict of interest.
Research funding: This research has received support from a grant from the Syrian Ministry of Higher Education and Scientific Research. Furthermore, the National Centre for Geodesy (NCG) at the Indian Institute of Technology Kanpur extended financial assistance for this research.
Data availability: The raw data can be obtained on request from the corresponding author.

References

1. Wang, YM. The satellite altimeter data derived mean sea surface GSFC98. Geophys Res Lett 2000;27:701–4. https://doi.org/10.1029/1999gl002375.Search in Google Scholar

2. Schaeffer, P, Faugére, Y, Legeais, J, Ollivier, A, Guinle, T, Picot, N. The CNES_CLS11 global mean sea surface computed from 16 years of satellite altimeter data. Mar Geodesy 2012;35:3–19. https://doi.org/10.1080/01490419.2012.718231.Search in Google Scholar

3. Yuan, J, Guo, J, Zhu, C, Li, Z. Mean sea surface model over the sea of Japan determined from multi-satellite altimeter data and tide gauge records. Rem Sens 2020;12:4168. https://doi.org/10.3390/rs12244168.Search in Google Scholar

4. Hamden, MH, Din, AHM, Wijaya, DD, Yusoff, MYM, Pa’suya, MF. Regional mean sea surface and mean dynamic topography models around Malaysian seas developed from 27 years of along-track multi-mission satellite altimetry data. Front Earth Sci 2021;9:665876. https://doi.org/10.3389/feart.2021.665876.Search in Google Scholar

5. Hernandez, F, Scheaffer, P, Andersen, O, Joel, D. Geoid recent improvements in altimetry: how MSS and MDT can benefit from it in combination with GOCE geoid? GOCE, Geoid Oceanogr 2004;569.Search in Google Scholar

6. Ghazavi, K, Nahavandchi, H. Mean Sea Surface and ocean circulation in North Atlantic and the Arctic Sea. J Geodetic Sci 2011;1:181–90. https://doi.org/10.2478/v10156-010-0021-4.Search in Google Scholar

7. Ophaug, V, Breili, K, Andersen, OB. A coastal mean sea surface with associated errors in Norway based on new-generation altimetry. Adv Space Res 2021;68:1103–15. https://doi.org/10.1016/j.asr.2019.08.010.Search in Google Scholar

8. Sevilla, M, Rodríguez-Velasco, G. Gravity and Mean Sea Surface in the Mediterranean Sea. Bol ROA 2000;3:225–9.Search in Google Scholar

9. Andersen, OB, Knudsen, P. DNSC08 mean sea surface and mean dynamic topography models. J Geophys Res: Oceans 2009;114. https://doi.org/10.1029/2008jc005179.Search in Google Scholar

10. Sun, W, Zhou, X, Yang, L, Zhou, D, Li, F. Construction of the Mean Sea Surface model combined HY-2A with DTU18 MSS in the Antarctic ocean. Front Environ Sci 2021;9:697111. https://doi.org/10.3389/fenvs.2021.697111.Search in Google Scholar

11. Wikipedia. In: Wikipedia, editor. Geography of Syria. Wikimedia Foundation; 2021. Available from: https://en.wikipedia.org/wiki/Geography_of_Syria.Search in Google Scholar

12. Schwatke, C, Bosch, W, Savcenko, R, Dettmering, D. OpenADB-an open database for multi-mission altimetry. In: EGU general assembly conference abstracts; 2010:12077 p.Search in Google Scholar

13. Bosch, W, Dettmering, D, Schwatke, C. Multi-mission cross-calibration of satellite altimeters: constructing a long-term data record for global and regional sea level change studies. Rem Sens 2014;6:2255–81. https://doi.org/10.3390/rs6032255.Search in Google Scholar

14. Cleveland, RB, Cleveland, WS, McRae, JE, Terpenning, I. STL: a seasonal-trend decomposition. J Off Stat 1990;6:3–73.Search in Google Scholar

15. Miller, J. Reaction time analysis with outlier exclusion: bias varies with sample size. Quart J Exp Psychol Sect A 1991;43:907–12. https://doi.org/10.1080/14640749108400962.Search in Google Scholar PubMed

16. Leys, C, Ley, C, Klein, O, Bernard, P, Licata, L. Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median. J Exp Soc Psychol 2013;49:764–6. https://doi.org/10.1016/j.jesp.2013.03.013.Search in Google Scholar

17. Cheng, Y, Andersen, O, Knudsen, P. An improved 20-year Arctic Ocean altimetric sea level data record. Mar Geodesy 2014;38:146–62. https://doi.org/10.1080/01490419.2014.954087.Search in Google Scholar

18. Rose, SK, Andersen, OB, Passaro, M, Ludwigsen, CA, Schwatke, C. Arctic Ocean sea level record from the complete radar altimetry era: 1991–2018. Rem Sens 2019;11:1672. https://doi.org/10.3390/rs11141672.Search in Google Scholar

19. Jin, T, Li, J, Jiang, W. The global mean sea surface model WHU2013. Geod Geodyn 2016;7:202–9. https://doi.org/10.1016/j.geog.2016.04.006.Search in Google Scholar

20. Yuan, J, Guo, J, Zhu, C, Li, Z, Liu, X, Gao, J. SDUST2020 MSS: a global 1′ × 1′ mean sea surface model determined from multi-satellite altimetry data. Earth Syst Sci Data 2022;15:155–69. https://doi.org/10.5194/essd-15-155-2023.Search in Google Scholar

21. Klos, A, Bos, MS, Bogusz, J. Detecting time-varying seasonal signal in GPS position time series with different noise levels. GPS Solut 2018;22:1–11. https://doi.org/10.1007/s10291-017-0686-6.Search in Google Scholar

22. Klos, A, Kusche, J, Fenoglio-Marc, L, Bos, MS, Bogusz, J. Introducing a vertical land motion model for improving estimates of sea level rates derived from tide gauge records affected by earthquakes. GPS Solut 2019;23:102. https://doi.org/10.1007/s10291-019-0896-1.Search in Google Scholar

23. Dermanis, A. Kriging and collocation – a comparison. Manuscripta Geod 1984;9:159–67.10.1007/BF03655053Search in Google Scholar

24. Schaffrin, B. Equivalent systems for various forms of Kriging, including least-squares collocation. Z Vermess 2001;2:87–93.Search in Google Scholar

25. Ligas, M, Lucki, B, Banasik, P. A crossvalidation-based comparison of kriging and IDW in local GNSS/levelling quasigeoid modelling. Rep Geodesy Geoinf 2022;114:1–7. https://doi.org/10.2478/rgg-2022-0004.Search in Google Scholar

26. Andersen, OB, Knudsen, P. Global marine gravity field from the ERS-1 and Geosat geodetic mission altimetry. J Geophys Res: Oceans 1998;103:8129–37. https://doi.org/10.1029/97jc02198.Search in Google Scholar

27. Sansò, F, Venuti, G, Tziavos, I, Vergos, G, Grigoriadis, V, Vergos, G. Geoid and Sea Surface Topography from satellite and ground data in the Mediterranean region-a review and new proposals. Bull Geod Geomat 2008;67:155–201.Search in Google Scholar

28. Haran, T, Haran, T, editors. ICESat/GLAS and WGS-84 ellipsoid and geoid conversions, sidads.colorado.edu (2004). University of Colorado Boulder; 2004. Available from: ftp://sidads.colorado.edu/pub/DATASETS/icesat/tools/idl/ellipsoid/README_ellipsoid.txt.Search in Google Scholar

29. Reyes, R, Noveloso, D, Rediang, A, Passaro, M, Bringas, D, Nagai, M. Tide gauge and satellite altimetry data for possible vertical land motion detection in south east Bohol trench and fault. Int Arch Photogramm Rem Sens Spatial Inf Sci 2019;42:369–76.10.5194/isprs-archives-XLII-4-W19-369-2019Search in Google Scholar

30. Zůvala, R, Fišerová, E, Marek, L. Mathematical aspects of the kriging applied on landslide in Halenkovice (Czech Republic). Open Geosci 2016;8:275–88. https://doi.org/10.1515/geo-2016-0023.Search in Google Scholar

31. Wu, CY, Mossa, J, Mao, L, Almulla, M. Comparison of different spatial interpolation methods for historical hydrographic data of the lowermost Mississippi River. Ann GIS 2019;25:133–151. https://doi.org/10.1080/19475683.2019.1588781.Search in Google Scholar

32. Statistics, S. In: Statology, editor. Kolmogorov-Smirnov test in R (with examples). Statology; 2021. Available from: https://www.statology.org/kolmogorov-smirnov-test-r/.Search in Google Scholar

33. Prism. In: Prism, editor. Interpreting results: Kolmogorov-Smirnov test. GraphPad Prism 9 Statistics Guide; 2020. Available from: https://www.graphpad.com/guides/prism/latest/statistics/interpreting_results_kolmogorov-smirnov_test.htm.Search in Google Scholar

34. Massey, FJ. The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 1951;46:68–78. https://doi.org/10.1080/01621459.1951.10500769.Search in Google Scholar

Received: 2023-08-21

Accepted: 2024-01-03

Published Online: 2024-01-19

Published in Print: 2024-07-26

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Articles in the same Issue

https://doi.org/10.1515/jag-2023-0070

Keywords for this article

regional mean sea surface model; Mediterranean Sea; satellite altimetry; Ordinary Kriging; Least Squares Collocation