Mathematical Model of Coastline Changes in the Ujung Pangkah Gresik Using the Polynomial Lagrange Approach

Hendrata Wibisana, Primasari Cahya Wardhani, Novie Handajani


Ujung Pangkah Gresik is an area where there is an estuary of a vast river, the Bengawan Solo river. This area annually sends sediment loads transported by the Bengawan Solo river to the Ujung Pangkah estuary so that gradually accumulation occurs, which results in changes in the morphology of the coast on the edge of the Ujung Pangkah coast, Gresik. This study seeks to see the side of shoreline changes on the Ujung Pangkah coast for five years. Then take the change model as a mathematical model that can describe the speed of shoreline change per year using the Lagrange polynomial interpolation method for degrees 1, degrees 2, and degrees 3. The results of shoreline changes that occur are obtained by the Lagrangge polynomial algorithm of degree 3 with R2 of 0.3747 which has a better correlation than degree 1 (0.0313) and degree 2 (0.3741). The results of this study obtained a mathematical model with a Lagrange polynomial approach where degree 3 has the best correlation among other models. This study concludes that by using a mathematical model, an overview of the process of change or natural phenomena can be obtained, where the existing model can predict future changes in the existing coastline.


Change of Coastline; Mathematical model; Lagrangge Polynomial; Ujung Pangkah Gresik

Full Text:



J. Liu, L. Zhou, Y. Tan, Q. Wang, Z. Hu, J. Li, X. Jiang, and Z. Ke, “Distribution of reactive aluminum under the influence of mesoscale eddies in the western South China Sea,” Acta Oceanologica Sinica, vol. 36, no. 6, pp. 95–103, jun 2017, doi: 10.1007/s13131-017-1046-7.

H. Phan, A. Reniers, T. Ye, and M. Stive, “Response in the Mekong deltaic coast to its changing sediment sources and sinks,” in Proceedings of Coastal Dynamics, 2017, pp. 311–322.

C. Wang, Y. Zhao, X. Zou, X. Xu, and C. Ge, “Recent changing patterns of the Changjiang (Yangtze River) Estuary caused by human activities,” Acta Oceanologica Sinica, vol. 36, no. 4, pp. 87–96, apr 2017, doi: 10.1007/s13131-017-1017-z.

U. U. Henry, J. Igbokwe, and A. C. Chukwocha, “Assessment of coastaline vulnerability for sustainable coastal development and planning in Nigeria using medium resolution satellite images and GIS,” International Journal of Engineering and Management Sciences, vol. 4, no. 4, pp. 408–416, 2013.

L. O. Dragomir, P. D. E. H. Petrosani, and S. Oncia, “Using satellite images LANDSAT TM for calculating normalized difference indexes for the landscape of Parang Mountains,” GeoCAD, 2012.

S. Zeinali, M. Dehghani, M. Rastegar, and M. Mojarrad, “Detecting shoreline changes in Chabahar Bay by processing satellite images,” Scientia Iranica, vol. 24, no. 4, pp. 1802–1809, aug 2017, doi: 10.24200/sci.2017.4271.

X. Li and M. C. Damen, “Coastline change detection with satellite remote sensing for environmental management of the Pearl River Estuary, China,” Journal of Marine Systems, vol. 82, pp. S54–S61, aug 2010, doi: 10.1016/j.jmarsys.2010.02.005.

A. Paytan, K. R. M. Mackey, Y. Chen, I. D. Lima, S. C. Doney, N. Mahowald, R. Labiosa, and A. F. Post, “Toxicity of atmospheric aerosols on marine phytoplankton,” Proceedings of the National Academy of Sciences, vol. 106, no. 12, pp. 4601–4605, mar 2009, doi: 10.1073/pnas.0811486106.

C. Zhong, W. P. Xiao, and B. Huang, “The response of phytoplankton to mesoscale eddies in western South China Sea,” Adv. Mar. Sci, vol. 31, no. 2, pp. 213–220, 2013.

T. R. Parsons, Y. Maita, and C. M. Lalli, A Manual of Chemical & Biological Methods for Seawater Analysis. Elsevier, 1984. ISBN 9780080302874 Doi: 10.1016/C2009-0-07774-5.

M. V. Khamutova, V. A. Kushnikov, and O. I. Dranko, “A mathematical model for choosing an action plan for the prevention and elimination of flood effects,” IFAC-PapersOnLine, vol. 55, no. 3, pp. 113–118, 2022, doi: 10.1016/j.ifacol.2022.05.020.

J. G. Wallwork, Mesh Adaptation and Adjoint Methods for Finite Element Coastal Ocean Modelling. PhD Thesis: Imperial College London, 2021.

T. Nguyen, J. Peterson, L. Gordon-Brown, and P. Wheeler, “Coastal changes predictive modelling: a fuzzy set approach,” World Acad Sci Eng Technol, vol. 48, pp. 468–473, 2008.

C. Chalons and A. Del Grosso, “Exploring different possibilities for second-order well-balanced Lagrange-projection numerical schemes applied to shallow water Exner equations,” International Journal for Numerical Methods in Fluids, vol. 94, no. 6, pp. 505–535, jun 2022, doi: 10.1002/fld.5064.

P. Othata and N. Pochai, “Irrigation Water Management Strategies for Salinity Control in the Chao Phraya River Using Sualyev Finite Difference Method with Lagrange Interpolation Technique,” Engineering Letters, vol. 29, no. 2, pp. 332–338, 2021.

R. Gens, “Remote sensing of coastlines: detection, extraction and monitoring,” International Journal of Remote Sensing, vol. 31, no. 7, pp. 1819–1836, apr 2010, doi: 10.1080/01431160902926673.

R. Bynoe, “Trekking the Shore: Changing Coastlines and the Antiquity of Coastal Settlement,” Quaternary Science Reviews, vol. 34, pp. 146–147, feb 2012, doi: 10.1016/j.quascirev.2011.12.016.

H. Wibisana, N. Handajani, and P. C. Wardhani, “The Mathematics Model Analysis of Distribution Concentration of Total Suspended Solid in Gresik Coastal Coast with Landsat 8 Satellite Imagery,” Nusantara Science and Technology Proceedings, pp. 288–294, 2021.

H. Wibisana and S. Zainab, “Time Series Analysis of Sea Surface Temperature With Aqua MODIS from 2011 to 2016. Case Studi: North Coast of Gresik and Madura,” IPTEK Journal of Science and Technology, vol. 28, no. 1, pp. 15–19, 2017.

P. Soille and M. Pesaresi, “Advances in mathematical morphology applied to geoscience and remote sensing,” IEEE Transactions on Geoscience and Remote Sensing, vol. 40, no. 9, pp. 2042–2055, sep 2002, doi: 10.1109/TGRS.2002.804618.


Copyright (c) 2023 Hendrata Wibisana, Primasari Cahya Wardhani, Novie Handajani

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Mathematics has been indexed by

>>>More Indexing<<<

Creative Commons License

Jambura Journal of Mathematics (e-ISSN: 2656-1344) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS. 

Editorial Office

Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia