Analysis and Prediction of Tidal Measurement Data from Temporary Stations using the Least Squares Method

Andi Rusdin, Hideo Oshikawa, Andi M. A. Divanesia, Muksan P. Hatta


This research was conducted by equipping three temporary tidal stations located in three places inside Palu Bay with pressure-type tidal gauges. The stations recorded tidal series fluctuations for 4 months with a 5-minute sampling interval (Dt). Moreover, the simple and widely used least squares method (LSM) was applied to separate the harmonic constants of constituents, including amplitudes (Hi) and phases (gi), from the observed tidal series. A total of 11 dominant constituents were selected based on the largest magnitudes of tidal generating potential (CE), and these include M2, K1, S2, O1, P1, N2, Mf, K2, Mm, Q1, and Msf, which were diurnal, semidiurnal, and long-period constituents. The results showed that the semidiurnal constituents generated higher amplitudes than the diurnal constituents, while the long-period constituents produced quite small amplitudes. Furthermore, the ratios of amplitudes recorded showed that tidal in Palu Bay was mainly mixed with semidiurnal constituents. The difference between the observed and predicted values was quite small, and this showed the validity of the measurement conducted at the temporary tidal stations. The performance indicators applied also showed that LSM had acceptable accuracy compared to other methods. Moreover, tidal datums were calculated using the peak approach, and the average tidal range (RA) of Palu Bay was found to be 2.39 m.


Doi: 10.28991/CEJ-2024-010-02-03

Full Text: PDF


Palu Bay; Tidal; Least Squares Method; Coastal Engineering.


Gusman, A. R., Supendi, P., Nugraha, A. D., Power, W., Latief, H., Sunendar, H., Widiyantoro, S., Daryono, Wiyono, S. H., Hakim, A., Muhari, A., Wang, X., Burbidge, D., Palgunadi, K., Hamling, I., & Daryono, M. R. (2019). Source model for the tsunami inside palu bay following the 2018 palu earthquake, Indonesia. Geophysical Research Letters, 46(15), 8721–8730. doi:10.1029/2019GL082717.

Heidarzadeh, M., Muhari, A., & Wijanarto, A. B. (2019). Insights on the Source of the 28 September 2018 Sulawesi Tsunami, Indonesia Based on Spectral Analyses and Numerical Simulations. Pure and Applied Geophysics, 176(1), 25–43. doi:10.1007/s00024-018-2065-9.

Cai, S., Liu, L., & Wang, G. (2018). Short-term tidal level prediction using normal time-frequency transform. Ocean Engineering, 156, 489–499. doi:10.1016/j.oceaneng.2018.03.021.

Putera, F. H. A., & Sallata, A. E. (2015). Economic Valuation of Resources in Palu Bay, Palu City, Central Sulawesi Province. Journal of Maritime and Fisheries Socio-Economic Policy, 5(2), 83. doi:10.15578/jksekp.v5i2.1019. (In Indonesian).

Tjaija, A., Ali, M. N., Fadhliah, & Effendy. (2022). Development Strategy of Palu Bay Marine of Sustainable Tourism with the A’WOT Hybrid Method. Academic Journal of Interdisciplinary Studies, 11(1), 269–279. doi:10.36941/ajis-2022-0024.

Paulik, R., Gusman, A., Williams, J. H., Pratama, G. M., Lin, S. lin, Prawirabhakti, A., Sulendra, K., Zachari, M. Y., Fortuna, Z. E. D., Layuk, N. B. P., & Suwarni, N. W. I. (2019). Tsunami Hazard and Built Environment Damage Observations from Palu City after the September 28 2018 Sulawesi Earthquake and Tsunami. Pure and Applied Geophysics, 176(8), 3305–3321. doi:10.1007/s00024-019-02254-9.

ICSM (2021). Australian Tides Manual. Intergovernmental Committee on Surveying and Mapping (ICSM), Melbourne, Australia.

Gill, S. K., & Schultz, J. R. (2000). Tidal Datums and Their Applications. Silver Spring, Department of Commerce, Maryland, United States.

Cartwright, D. E., & Edden, A. C. (1973). Corrected Tables of Tidal Harmonics. Geophysical Journal of the Royal Astronomical Society, 33(3), 253–264. doi:10.1111/j.1365-246X.1973.tb03420.x.

Parker, B. B. (2007). Tidal analysis and prediction. Silver Spring, Department of Commerce, Maryland, United States.

Forrester, W. D. (1983). Canadian Tide Manual. Department of Fisheries and Oceans, Canadian Hydrographic Service, Ottawa, Canada.

Schureman, P. (1994). Manual of harmonic analysis and prediction of tides (No. 98). US Department of Commerce, Coast and Geodetic Survey, Washington, United States.

Horn, W. (1960). Some recent approaches to tidal problems. The International Hydrographic Review, XXXVII, No. 2, 65-88

Harris, D. L., Pore, N. A., & Cummings, R. A. (1965). Tide and tidal current prediction by high speed digital computer. The International Hydrographic Review, 95-103

Zetler, B. D. (1982). Computer applications to tides in the national ocean survey (No. 98). National Oceanic and Atmospheric Administration, National Ocean Survey, Silver Spring, Maryland, United States.

Foreman, M. G. G. (1977). Manual for tidal heights analysis and prediction. Institute of Ocean Sciences, Patricia Bay, British Columbia, Canada.

Ali, A. F. D. H., Rosli, R., & Basunia, M. A. (2023). Tidal harmonics in Brunei coastal water. AIP Conference Proceedings. doi:10.1063/5.0111545.

Mousavian, R., & Hossainali, M. M. (2012). Detection of main tidal frequencies using least squares harmonic estimation method. Journal of Geodetic Science, 2(3), 224–233. doi:10.2478/v10156-011-0043-6.

Boon, J. D., & Kiley, K. P. (1978). Harmonic analysis and tidal prediction by the method of least squares: A user's manual. Virginia Institute of Marine Science, Virginia, United States.

Yen, P.-H., Jan, C.-D., Lee, Y.-P., & Lee, H.-F. (1996). Application of Kalman Filter to Short-Term Tide Level Prediction. Journal of Waterway, Port, Coastal, and Ocean Engineering, 122(5), 226–231. doi:10.1061/(asce)0733-950x(1996)122:5(226).

Ahmed, A. A. M., Jui, S. J. J., AL-Musaylh, M. S., Raj, N., Saha, R., Deo, R. C., & Saha, S. K. (2024). Hybrid deep learning model for wave height prediction in Australia's wave energy region. Applied Soft Computing, 150, 111003. doi:10.1016/j.asoc.2023.111003.

Pan, H., Xu, T., & Wei, Z. (2023). A modified tidal harmonic analysis model for short-term water level observations. Ocean Modelling, 186, 102251. doi:10.1016/j.ocemod.2023.102251.

Meena, B. L., & Agrawal, J. D. (2015). Tidal level forecasting using ANN. Procedia Engineering, 116(1), 607–614. doi:10.1016/j.proeng.2015.08.332.

Abubakar, A. G., Mahmud, M. R., Tang, K. K. W., Hussaini, A., & Md Yusuf, N. H. (2019). A Review of Modelling Approaches on Tidal Analysis and Prediction. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XLII-4/W16, 23–34. doi:10.5194/isprs-archives-xlii-4-w16-23-2019.

Li, S., Liu, L., Cai, S., & Wang, G. (2019). Tidal harmonic analysis and prediction with least-squares estimation and inaction method. Estuarine, Coastal and Shelf Science, 220, 196–208. doi:10.1016/j.ecss.2019.02.047.

Setiyawan, Rusdin, A., Amaliah, T., & Olphino. (2022). Potential of tidal power plants on Tibo Beach with spektrum method. IOP Conference Series: Materials Science and Engineering, 1212(1), 012039. doi:10.1088/1757-899x/1212/1/012039.

Sabhan, S., Badaruddin, Kurniawan, M., & Rusydi, M. (2021). Tidal and bathymetry characteristics after the 2018 earthquake and tsunami in Watusampu Waters, Palu Bay, Central Sulawesi. Natural Science: Journal of Science and Technology, 10(1), 26–30. doi:10.22487/25411969.2021.v10.i1.15505.

Susanto, R. D., Gordon, A. L., Sprintall, J., & Herunadi, B. (2000). Intraseasonal Variability and Tides in Makassar Strait. Geophysical Research Letters, 27(10), 1499–1502. doi:10.1029/2000GL011414.

Thomson, R. E., & Emery, W. J. (2014). Data Analysis Methods in Physical Oceanography (3rd Ed.). Elsevier Science, Amsterdam, Netherlands. doi:10.1016/C2010-0-66362-0.

Hall, P., & Davies, A. M. (2005). The influence of sampling frequency, non-linear interaction, and frictional effects upon the accuracy of the harmonic analysis of tidal simulations. Applied Mathematical Modelling, 29(6), 533–552. doi:10.1016/j.apm.2004.09.015.

UNESCO/IOC. (2006). Manual on Sea-level Measurements and Interpretation, Volume IV: Intergovernmental Oceanographic Commission of UNESCO, Paris, France.

Vassie, J. M., Woodworth, P. L., & Holt, M. W. (2004). An example of North Atlantic deep-ocean swell impacting ascension and St. Helena Islands in the Central South Atlantic. Journal of Atmospheric and Oceanic Technology, 21(7), 1095–1103. doi:10.1175/1520-0426(2004)021<1095:AEONAD>2.0.CO;2.

Joseph, A., Desa, E., Desa, E., Smith, D., Peshwe, V. B., Vijaykumar, & Desa, J. A. E. (1999). Evaluation of pressure transducers under turbid natural waters. Journal of Atmospheric and Oceanic Technology, 16(8), 1150–1155. doi:10.1175/1520-0426(1999)016<1150:EOPTUT>2.0.CO;2.

Mehra, P., Prabhudesai, R. G., Joseph, A., Vijaykumar, Agarvadekar, Y., Luis, R., Damodaran, S., & Viegas, B. (2009). A one year comparison of radar and pressure tide gauge at Goa, west coast of India. 2009 International Symposium on Ocean Electronics, SYMPOL 2009, 173–183. doi:10.1109/SYMPOL.2009.5664190.

Madah, F. A. (2020). The amplitudes and phases of tidal constituents from Harmonic Analysis at two stations in the Gulf of Aden. Earth Systems and Environment, 4(2), 321–328. doi:10.1007/s41748-020-00152-y.

US Coast and Geodetic Survey. (1965). Manual of tide observations. Publication 30-1. Special publication No. 196. Washington, United States.

SNI 7924:2013. (2013). Tidal station installation. Badan Standarisasi Nasional, Jakarta, Indonesia. (In Indonesian).

Arianty, N., Mudin, Y., & Rahman, A. (2017). Modeling of wave refraction and analysis of ocean wave characteristics in Palu Bay Waters. Gravitasi. 16 (2), 23–30.

SNI 7963:2014. (2014). Tidal Observation. Badan Standardisasi Nasional, Jakarta, Indonesia. (In Indonesian).

Foreman, M. G. G., & Henry, R. F. (1989). The harmonic analysis of tidal model time series. Advances in Water Resources, 12(3), 109–120. doi:10.1016/0309-1708(89)90017-1.

Annunziato, A., & Probst, P. (2016). Continuous Harmonics Analysis of Sea Level Measurements: Description of a new method to determine sea level measurement tidal component. Publications Office of the European Union, Luxembourg, Luxembourg. doi:10.2788/4295.

Stephenson, A. G. (2016). Harmonic analysis of tides using Tide Harmonics. The Comprehensive R Archive Network (CRAN). Available online: (accessed on June 2023).

Moore, R. A. (2020). Characterization of Seasonal Variability in Tides. Department of Mathematics, The University of Utah, Salt Lake City, United States.

Abubakar, A. G., Mahmud, M. R., Tang, K. K. W., & Husaaini, A. (2021). The Determination of Tidal Constituents using Wavelet Base Harmonic at The Strait of Malacca. IOP Conference Series: Earth and Environmental Science, 731, 012001. doi:10.1088/1755-1315/731/1/012001.

Doodson, A. T., & Lamb, H. (1921). The harmonic development of the tide-generating potential. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 100(704), 305–329. doi:10.1098/rspa.1921.0088.

Chelton, D. B., & Enfield, D. B. (1986). Ocean signals in tide gauge records. Journal of Geophysical Research: Solid Earth, 91(B9), 9081–9098. doi:10.1029/jb091ib09p09081.

Zetler, B. D., & Cummings, R. A. (1967). A harmonic method for predicting shallow-water tides. Journal of Marine Research, 25(1), 103–114.

Rossiter, J. R., & Lennon, G. W. (1968). An Intensive Analysis of Shallow Water Tides. Geophysical Journal of the Royal Astronomical Society, 16(3), 275–293. doi:10.1111/j.1365-246X.1968.tb00223.x.

Hanxing, X. (1984). A method for prediction of shallow water tides. Chinese Journal of Oceanology and Limnology, 2(1), 34–48. doi:10.1007/BF02888390.

Godin, G., & Taylor, J. (1973). A simple method for the prediction of the time and height of high and low water. The International Hydrographic Review, 50(2), 75-81.

Pugh, D. (1987) Tides, Surges and Mean Sea Level: A Handbook for Engineers and Scientists. John Wiley & Sons, Hoboken, United States.

Byun, D. S., & Hart, D. E. (2020). A monthly tidal envelope classification for semidiurnal regimes in terms of the relative proportions of the S2, N2, and M2 constituents. Ocean Science, 16(4), 965–977. doi:10.5194/os-16-965-2020.

Byun, D. S., Hart, D. E., Kim, S., & Ha, J. (2023). Classification of monthly tidal envelopes in mixed tide regimes. Scientific Reports, 13(1), 4786. doi:10.1038/s41598-023-31657-x.

Van der Stok, J. P. (1897). Wind and weather, currents, tides and tidal streams in the East Indian archipelago. G.P.O. Universiteitsbibliotheek Utrecht, Utrecht, Netherlands.

Courtier, A. (1939). Classification of tides in four types. The International Hydrographic Review, 50-58

Parker, B. B. (1977). Tidal hydrodynamics in the Strait of Juan de Fuca--Strait of Georgia (No. 69). Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, Silver Spring, Maryland, United States.

Amin, M. (1986). On the conditions for classification of tides. The International Hydrographic Review, 63(1), 161-174.

Daher, V. B., Paes, R. C. de O. V., França, G. B., Alvarenga, J. B. R., & Teixeira, G. L. G. (2015). Extraction of tide constituents by harmonic analysis using altimetry satellite data in the Brazilian coast. Journal of Atmospheric and Oceanic Technology, 32(3), 614–626. doi:10.1175/JTECH-D-14-00091.1.

Lee, S. H., & Chang, Y. S. (2019). Classification of the Global Tidal Types Based on Auto-correlation Analysis. Ocean Science Journal, 54(2), 279–286. doi:10.1007/s12601-019-0009-7.

Wright, E., Keller, J., Gallagher, D., & Ladd, D. (2023). Moon Phase and Libration, 2014. NASA’s Goddard Space Flight Center Scientific Visualization Studio, NASA, Washington, United States.

Hicks, S. D. (2006). Understanding tides. US Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Silver Spring, United States.

Parker, B. (2005). Tides. Encyclopedia of Coastal Science Encyclopedia of Earth Science Series. Springer, Cham, Switzerland.

Crawford, W. R. (1982). Analysis of fortnightly and monthly tides. The International Hydrographic Review, 59(1), 131-142.

Ris, R. C., Holthuijsen, L. H., & Booij, N. (1999). A third-generation wave model for coastal regions 2. Verification. Journal of Geophysical Research: Oceans, 104(C4), 7667–7681. doi:10.1029/1998jc900123.

Ardhuin, F., Rogers, E., Babanin, A. V., Filipot, J. F., Magne, R., Roland, A., van der Westhuysen, A., Queffeulou, P., Lefevre, J. M., Aouf, L., & Collard, F. (2010). Semiempirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation. Journal of Physical Oceanography, 40(9), 1917–1941. doi:10.1175/2010JPO4324.1.

Akpinar, A., van Vledder, G. P., Kömürcü, M. I., & Özger, M. (2012). Evaluation of the numerical wave model (SWAN) for wave simulation in the Black Sea. Continental Shelf Research, 50–51, 80–99. doi:10.1016/j.csr.2012.09.012.

Mentaschi, L., Besio, G., Cassola, F., & Mazzino, A. (2013). Problems in RMSE-based wave model validations. Ocean Modelling, 72, 53–58. doi:10.1016/j.ocemod.2013.08.003.

Bryant, M. A., Hesser, T. J., & Jensen, R. E. (2016). Evaluation statistics computed for the wave information studies (WIS). Army Engineer Research and Development Center, Vicksburg, United States.

Ding, Y., Ding, T., Rusdin, A., Zhang, Y., & Jia, Y. (2020). Simulation and Prediction of Storm Surges and Waves Using a Fully Integrated Process Model and a Parametric Cyclonic Wind Model. Journal of Geophysical Research: Oceans, 125(7), 1-31. doi:10.1029/2019JC015793.

Yang, C. H., Wu, C. H., & Hsieh, C. M. (2020). Long Short-Term Memory Recurrent Neural Network for Tidal Level Forecasting. IEEE Access, 8, 159389–159401. doi:10.1109/ACCESS.2020.3017089.

Bradbury, M. C., & Conley, D. C. (2021). Using artificial neural networks for the estimation of subsurface tidal currents from high-frequency radar surface current measurements. Remote Sensing, 13(19). doi:10.3390/rs13193896.

Zhang, A., Lin, Y., Sun, Y., Yuan, H., Wang, M., Liu, G., & Hu, Y. (2022). Tidal current prediction based on fractal theory and improved least squares support vector machine. IET Renewable Power Generation, 16(2), 389–401. doi:10.1049/rpg2.12335.

Kusuma, H. A., Lubis, M. Z., Oktaviani, N., & Setyono, D. E. D. (2021). Tides Measurement and Tidal Analysis at Jakarta Bay. Journal of Applied Geospatial Information, 5(2), 494–501. doi:10.30871/jagi.v5i2.2779.

Palmer, K., Watson, C. S., Hunter, J. R., Hague, B. S., & Power, H. E. (2023). An improved method for computing tidal datums. Coastal Engineering, 184, 104354. doi:10.1016/j.coastaleng.2023.104354.

Masselink, G., & Short, A. D. (1993). The effect of tide range on beach morphodynamics and morphology: a conceptual beach model. Journal of coastal research, 785-800.

Djunarsjah, E., Nusantara, C. A. D. S., Putra, A. P., Wijaya, R. A., Sianturi, S. S., Anantri, N. M. K., Kusumadewi, D., & Julian, M. M. (2023). Prospects and Constraints of Lowest Astronomical Tide (LAT) as Determination of Sea Boundaries in Indonesia. The Egyptian Journal of Aquatic Research, 49(4), 444–451. doi:10.1016/j.ejar.2023.08.002.

ICSM. (2005). The Factors Contributing to the level of Confidence in the Tidal Predictions Accuracy of Tidal Predictions. Intergovernmental Committee on Surveying and Mapping (ICSM), Sydney, Australia.

Full Text: PDF

DOI: 10.28991/CEJ-2024-010-02-03


  • There are currently no refbacks.

Copyright (c) 2024 Andi Rusdin, Hideo Oshikawa, Andi Muthia Ardelia Divanesia, Muksan Putra Hatta

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