Modeling and Forecasting Long-Term Records of Mean Sea Level at Grand Isle, Louisiana: SARIMA, NARNN, and Mixed SARIMA-NARNN Models

Yeong Nain Chi


This study tried to demonstrate the role of time series models in modeling and forecasting process using long-term records of monthly mean sea level from January 1978 to October 2020 at Grand Isle, Louisiana. Following the Box–Jenkins methodology, the ARIMA(1,1,1)(2,0,0)12 with drift model was selected to be the best fit model for the time series, according to its lowest AIC value. Using the LM algorithm, the results revealed that the NARNN model with 9 neurons in the hidden layer and 6 time delays provided the best performance in the nonlinear autoregressive neural network models at its smaller MSE value. The Mixed model, a combination of the SARIMA and NARNN models has both linear and nonlinear modelling capabilities can be a better choice for modelling the time series. The comparative results revealed that the Mixed-LM model with 9 neurons in the hidden layer and 3 time delays yielded higher accuracy than the NARNN-LM model with 9 neurons in the hidden layer and 6 time delays, and the ARIMA(1,1,1)(2,0,0)12 with drift model, according to its lowest MSE in this study. Thus, this study may provide an integrated modelling approach as a decision-making supportive method for formulating local mean sea level forecast in advance. Understanding past sea level is important for the analysis of current and future sea level changes. In order to sustain these observations, research programs utilizing the resulting data should be able to improve significantly our understanding and narrow projections of future sea level rise and variability.

Article Metrics

Abstract: 50 Viewers PDF: 21 Viewers


Mean Sea Level; Time Series; Modeling; Forecasting; SARIMA; NARNN; Mixed SARIMA-NARNN Model; Levenberg-Marquardt Algorithm; Grand Isle, Louisiana.

Full Text:



M. H. Beale, M. T. Hagan, and H. B. Demuth, Howard B, “Deep Learning ToolboxTM: Getting Started Guide,” Natick, MA: The MathWorks, Inc., 2019.

G. Benrhmach, K. Namir, A. Namir, and J. Bouyaghroumni, “Nonlinear autoregressive neural network and extended Kalman filters do prediction of financial time series,“ Journal of Applied Mathematics, Vol. 2020, Article ID 5057801, 1-6, 2020.

D. Bolin, P. Guttorp, A. Januzzi1, D. Jones1, M. Novak1, H. Podschwit, L. Richardson, A. S¨arkk¨a, C. Sowder, and A. Zimmerman, “Statistical prediction of global sea level from global temperature,” Statistica Sinica, 25, 351-367, 2015.

G. E. O. Box, and G. M. Jenkins, “Time series analysis: forecasting and control,” Holden-Day, San Francisco, 1970.

G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, “Time series analysis: forecasting and control (5th ed.),” Hoboken, N.J.: John Wiley and Sons Inc., 2016.

A. Braakmann-Folgmann, R. Roscher, S. Wenzel, B. Uebbing, and J. Kusche, “Sea level anomaly prediction using recurrent neural networks,” In Proceedings of the 2017 Conference on Big Data from Space, pp. 297-300, 2017.

N. Bruneau, J. Polton, J. Williams, and J. Holt, “Estimation of global coastal sea level extremes using neural Networks,” Environmental Research Letters, 15(7), 074030, 1-11, 2020.

A. Cazenave, and W. Llovel, “Contemporary sea level rise,” Annual Review of Marine Science, 2, 145-173, 2010.

A. Cazenave, and G. L. Cozannet, G.L. “Sea level rise and its coastal impacts,” Earth’s Future, 2, 15–34, 2013.

J. A. Church, N. J. White, R. Coleman, K. Lambeck, and J. X. Mitrovica, “Estimates of the regional distribution of sea level rise over the 1950-2000 period,“ Journal of Climate, 17(13), 2609-2625, 2004.

J. A. Church, and N. J. White, “A 20th century acceleration in global sea-level rise,” Geophysical Research Letters, 33, L01602, 1-4, 2006.

J. A. Church, N. J. White, T. Aarup, W. S. Wilson, P. L. Woodworth, C. M. Domingues, J. R. Hunter, and K. Lambeck, “Understanding global sea levels: past, present and future,” Sustainability Science, 3, 9-22, 2008.

J. A. Church, and N. J. White, “Sea-level rise from the late 19th to the early 21st century,” Surveys in Geophysics, 32, 585-602, 2011.

G. Foster, and P. T. Brown, “Time and tide: analysis of sea level time series,” Climate Dynamics, 45, 1-2, 291-308, 2014.

H. P. Gavin, “The Levenberg-Marquardt algorithm for nonlinear least squares curve-fitting problems,” Department of Civil and Environmental Engineering Duke University, 19 pp., 2020. Retrieved from:

M. Haasnoot, J. Kwadijk, J. Alphen, D. Bars, B. Hurk, F. Diermanse, A. Spek, G. O. Essink, J. Delsman, and M. Mens, “Adaptation to uncertain sea-level rise; how uncertainty in Antarctic mass-loss impacts the coastal adaptation strategy of the Netherlands,” Environmental Research Letters, 15, 034007, 1-15, 2020.

B. P. Horton, R. E. Kopp, A. J. Garner, C. C. Hay, N. S. Khan, K. Roy, and T. A. Shaw, “Mapping sea-level change in time, space, and probability,” Annual Review of Environment and Resources, 43, 481-521, 2018.

IPCC, “Climate Change 2014: Synthesis Report,” Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, PachauriR.K., & Meyer, L.A. (eds.)], IPCC, Geneva, Switzerland, 151 pp., 2014.

R. E. Kopp, B. P. Horton, A. C. Kemp, and C. Tebaldi, “Past and future sea level rise along the coast of North Carolina, USA,” Climatic Change, 132, 693–707, 2015.

R. E. Kopp, C. C. Hay, C. M. Little, and J. X. Mitrovica, “Geographic variability of sea-level change,” Current Climate Change Reports, 1, 192–204, 2015.

S. A. Kulp, and B. H. Strauss, “New elevation data triple estimates of global vulnerability to sea-level rise and coastal flooding,” Nature Communications, 10, 4844, 1-12, 2019.

G. M. Ljung, and G. E. O. Box, “On a measure of lack of fit in time series models,” Biometrika, 65(2), 297-303, 1978.

O. Makarynskyy, D. Makarynska, M. Kuhn, and W. E. Featherstone, “Predicting sea level variations with artificial neural networks at Hillarys Boat Harbour, Western Australia. Estuarine,” Coastal and Shelf Science, 61(2), 351–360, 2004.

D. C. Montgomery, C. L. Jennings, and M. Kulahci, “Introduction to time series analysis and forecasting,” Hoboken, N.J.: John Wiley & Sons. Inc., 2008.

P. K. Srivastava, T. Islam, S. K. Singh, G. P. Petropoulos, M. Gupta, and Q. Dai, “Forecasting Arabian sea level rise using exponential smoothing state space models and ARIMA from TOPEX and Jason satellite radar altimeter data,” Meteorological Applications, 23, 633-639, 2016.

U.S. Global Change Research Program (USGCRP), “Climate science special report: Fourth National Climate Assessment, Volume I,” [Wuebbles, D. J., Fahey, D. W., Hibbard, K. A., Dokken, D. J., Stewart, B. C., and Maycock, T. K. (eds.)], U.S. Global Change Research Program, Washington, DC, USA, 470 pp., 2017.

H. Visser, S. Dangendorf, and A. C. Petersen, “A review of trend models applied to sea level data with reference to the “acceleration-deceleration debate,” Journal of Geophysical Research: Oceans, 120(6), 3873-3895, 2015.

W. Wang, and H. Yuan, “A tidal level prediction approach based on BP neural network and Cubic B-Spline Curve with Knot Insertion Algorithm,” Mathematical Problems in Engineering, 2018, Article ID 9835079, 9 pp., 2018.

G. P. Zhang, “Time series forecasting using a hybrid ARIMA and neural network model,” Neurocomputing, 50, 159-175, 2003.


  • There are currently no refbacks.


Journal of Applied Data Science

2723-6471 (Online)
Published by Bright Publisher
Puri Mersi Baru, Jl.Martadireja II, Gang Sitihingil 3 Blok A No 2, Purwokerto Timur, Jawa Tengah
Website :
Email :

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0