Research article    |    Open Access
Acta Natura et Scientia 2025, Vol. 6(2) 121-138

Statistical Characterization of Residual Interannual Fluctuations for Sea Level From ARIMA Modeling of Adjusted NOAA Data

Mostafa Essam Eissa

pp. 121 - 138   |  DOI: https://doi.org/10.61326/actanatsci.v6i2.349

Publish Date: December 11, 2025  |   Single/Total View: 0/0   |   Single/Total Download: 0/0


Abstract

Sea level rise, a critical consequence of global climate change, poses significant challenges to coastal communities worldwide. While long-term trends in sea level rise garner considerable attention, understanding and predicting interannual variability fluctuations are equally crucial for effective coastal management and adaptation. This research investigates detrended annual variability of adjusted sea level data, focusing on the unpredictable fluctuations superimposed on long-term trends. By employing Autoregressive Integrated Moving Average (ARIMA) modeling, this study aims to quantify and forecast these interannual variations, providing a statistical baseline that underscores the challenge of interannual variability prediction for coastal management. Utilizing adjusted annual sea level measurements from the National Oceanic and Atmospheric Administration (NOAA) spanning 1993 to 2019, this research isolates residual interannual fluctuations by removing the influence of long-term trends and other components through data adjustment. This adjustment process, typically incorporating corrections for factors like glacial isostatic adjustment (GIA) and vertical land motion (VLM), enables a focused analysis of the residual fluctuations. The adjusted sea level data was imported into the Minitab web platform for analysis. The “Forecast with Best ARIMA Model” tool within Minitab’s “Stat” menu was employed to automatically identify, fit and diagnose the most appropriate ARIMA model. This tool explores a range of potential ARIMA models, varying the order of autoregressive (AR), integrated (I) and moving average (MA) components, using the Akaike Information Criterion with correction (AICC) to select the best-fitting model while penalizing complexity. The results of this analysis reveal that, after an extensive screening of the ARIMA parameter space, the ARIMA(0,1,0) model, also known as the random walk with drift, emerged as the optimal representation of the adjusted sea level data. This suggests that the residual interannual variability, after accounting for factors removed during data adjustment, is largely unpredictable within the ARIMA framework. The selected model was then used to generate 100-year forecasts, from 2020 to 2119, along with 95% confidence intervals to quantify forecast uncertainty. The standard error of the forecasts was also analyzed, revealing a clear increase in uncertainty with longer forecast horizons. In conclusion, this research demonstrates that while the adjusted sea level exhibits significant annual variability, this variability is largely unpredictable using ARIMA models. This finding underscores the importance of separating the analysis of these kinds of fluctuations from the long-term sea level rise trend, which must be modeled using different approaches. The 100-year forecasts and associated confidence intervals provide valuable information for coastal communities to better prepare for and manage the risks associated with interannual sea level fluctuations, even if precise predictions are not possible. Concurrence of AICC, AIC and BIC provide strong support for validity of the model, reinforces the principle of parsimony, suggests genuine random walk behavior in the adjusted sea level data and increases confidence in the interpretation of the results. While the ARIMA(0,1,0) serves as a robust baseline for understanding the inherent unpredictability of adjusted sea level variations, future research could explore the potential of incorporating predictors, such as climate indices or employing non-linear time series models to further refine understanding and predictive capabilities concerning interannual sea level changes.

Keywords: AICC, ARIMA, GIA, NOAA, Sea level, VLM


How to Cite this Article?

APA 7th edition
Eissa, M.E. (2025). Statistical Characterization of Residual Interannual Fluctuations for Sea Level From ARIMA Modeling of Adjusted NOAA Data. Acta Natura et Scientia, 6(2), 121-138. https://doi.org/10.61326/actanatsci.v6i2.349

Harvard
Eissa, M. (2025). Statistical Characterization of Residual Interannual Fluctuations for Sea Level From ARIMA Modeling of Adjusted NOAA Data. Acta Natura et Scientia, 6(2), pp. 121-138.

Chicago 16th edition
Eissa, Mostafa Essam (2025). "Statistical Characterization of Residual Interannual Fluctuations for Sea Level From ARIMA Modeling of Adjusted NOAA Data". Acta Natura et Scientia 6 (2):121-138. https://doi.org/10.61326/actanatsci.v6i2.349

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