How Fast Is the Sea Rising Along India's Coast? Tide-Gauge Trends 1878–2025 With Serial-Correlation-Corrected Uncertainty, a Proof That the AR(1) Inflation Factor Is a Conservative Bound, and Why Station Trends Disagree
- 1Former Officer, CGGB
Abstract
Coastal designers in India need a defensible number for relative sea-level rise and an honest error bar. I use the annual Revised Local Reference records of the Permanent Service for Mean Sea Level for all Indian stations with at least 30 valid years and no station-level quality flag (eleven of 28 downloaded stations, 1878 to 2025). Year-to-year residuals are positively correlated, so ordinary least-squares standard errors are too small. I prove that for a linear trend with AR(1) errors the true variance of the slope, relative to the white-noise formula, is never larger than (1 + rho)/(1 − rho) and converges to it at rate 1/n, and I give the explicit error bound. Applying the factor widens the standard errors by 4 to 244 percent. Full-record station trends range from minus 2.98 mm per year at Saugor (1937 to 1987, not distinguishable from zero) to 3.84 at Diamond Harbour and are strongly inconsistent with a common value (Cochran Q 84.5 on 10 degrees of freedom). Over the common window 1971 to 2020, however, all ten stations with enough data lie between 1.66 and 2.94 mm per year and the inconsistency disappears (Q 5.5, p 0.79), with a pooled value of 2.36 mm per year. Most of the apparent disagreement between Indian gauges is therefore a matter of which years each gauge covers. The 147-year Mumbai record shows a statistically clear acceleration of 0.019 mm per year squared. A Monte Carlo study shows that the corrected interval still under-covers when the autocorrelation is estimated from short records, because the estimate is biased towards zero.
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BibTeX
@misc{aguru2026fast,
title = {{How Fast Is the Sea Rising Along India's Coast? Tide-Gauge Trends 1878–2025 With Serial-Correlation-Corrected Uncertainty, a Proof That the AR(1) Inflation Factor Is a Conservative Bound, and Why Station Trends Disagree}},
author = {Manoj Kumar Aguru},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23653378},
url = {https://zenodo.org/records/23653378},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - How Fast Is the Sea Rising Along India's Coast? Tide-Gauge Trends 1878–2025 With Serial-Correlation-Corrected Uncertainty, a Proof That the AR(1) Inflation Factor Is a Conservative Bound, and Why Station Trends Disagree
AU - Manoj Kumar Aguru
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23653378
UR - https://zenodo.org/records/23653378
AB - Coastal designers in India need a defensible number for relative sea-level rise and an honest error bar. I use the annual Revised Local Reference records of the Permanent Service for Mean Sea Level for all Indian stations with at least 30 valid years and no station-level quality flag (eleven of 28 downloaded stations, 1878 to 2025). Year-to-year residuals are positively correlated, so ordinary least-squares standard errors are too small. I prove that for a linear trend with AR(1) errors the true variance of the slope, relative to the white-noise formula, is never larger than (1 + rho)/(1 − rho) and converges to it at rate 1/n, and I give the explicit error bound. Applying the factor widens the standard errors by 4 to 244 percent. Full-record station trends range from minus 2.98 mm per year at Saugor (1937 to 1987, not distinguishable from zero) to 3.84 at Diamond Harbour and are strongly inconsistent with a common value (Cochran Q 84.5 on 10 degrees of freedom). Over the common window 1971 to 2020, however, all ten stations with enough data lie between 1.66 and 2.94 mm per year and the inconsistency disappears (Q 5.5, p 0.79), with a pooled value of 2.36 mm per year. Most of the apparent disagreement between Indian gauges is therefore a matter of which years each gauge covers. The 147-year Mumbai record shows a statistically clear acceleration of 0.019 mm per year squared. A Monte Carlo study shows that the corrected interval still under-covers when the autocorrelation is estimated from short records, because the estimate is biased towards zero.
ER -