In this study, a sexaxial figure of the Earth was created using randomly distributed 6400 control points on the geoid, which was generated by the EGM2008 gravity model. The shape of the sexaxial ellipsoid is defined by its six orthogonal axes. To construct the new geometric figure, eight triaxial ellipsoids were fitted to the Cartesian coordinates of control points in each octant of the geoid using the least squares method. Its geometric origin is constrained to coincide with the centre of mass of the geoid, and the ellipsoid has no net rotation with respect to the WGS84 coordinate system. This study demonstrates that the new geometric figure provides a customised fit to the control points in each octant.

Recent studies reported an ambiguous global sea level acceleration during the satellite altimetry (SA) era (1993-2017). New SA data created an opportunity to resolve this issue. In this study, two competing kinematic models to represent global mean sea level anomalies are compared. The first model consists of an initial velocity and uniform acceleration. The second model replaces the initial velocity and acceleration with a trend and a representation of a long periodic lunar subharmonic of period 55.8 y, which is determined to be statistically significant at globally distributed tide gauge records. The models also include parameters for the periodic effects of lunisolar origin with periods 18.6 y and 11.1 y annual, and biannual variations in 10-day average of globally SA measurements during 1993-2022. Generalized least squares solutions yielded updated statistically significant estimates for all the model parameters and their statistics for both models. However, the outcome failed to resolve the ambiguity of uniform acceleration in global mean sea level confounded with the long periodic lunar subharmonic of period 55.8 y during this period. This epistemic uncertainty will have a dire impact on climate change risk assessments as demonstrated through the prospective comparison of both kinematic models.

The analyses of the cumulative sums of the observed yearly averaged atmospheric CO2 concentrations revealed unambiguously two change points during 0-2021. The first abrupt change that occurred during 1830 delineated the starting epoch of the pre-industrial era, which is marked by a linear increase in concentrations (0.24 +/- 0.01 ppm/yr.) as described by the IPCC being driven by economic and population growth. Another notable change occurred during 1943 with the start of a uniform acceleration (0.028 +/- 0.000 ppm/yr(2)) since then. These findings bring not only clarity and precision into the IPCC's vague statement on the topic but also alleviates the bias introduced in estimating the trend (constant velocity) of the atmospheric concentrations, which is three times larger in magnitude (0.78 +/- 0.01 ppm/yr.) for the period 1830-2021 if the uniform acceleration since 1943 is not accounted for. If the increased concentrations of CO2 before 1943 are predominantly caused by the climate system, i.e. of non-anthropogenic origin, then the concentrations will continue to increase with the constant velocity estimated in this study despite the efforts to limit the anthropogenic contributions that are the source of the uniform acceleration since 1943.

Sub- and super-harmonics of luni-solar forcing are proxies for the natural variations in sea levels observed at tide gauge stations with long records as demonstrated in earlier studies. This study also identified their signatures in the noisy yearly misclosures of the global mean sea level budget for the period 1900–2018. The analyses of the yearly misclosures revealed a temporal linear systematic error of 0.08 ± 0.02 mm/year, which is not explained by the budget components. The estimate is statistically significant ( α = 0.05) but small in magnitude and accounts for only 11% (adjusted R 2 ) of the variations in the yearly misclosures. Meanwhile, the yearly misclosures have also a statistically significant constant bias as large as −12.2 ± 0.9 mm, which can be attributed to the lack of a common datum definition for the global mean sea level budget components. Modeling the low-frequency changes of luni-solar origin together with a trend and constant bias parameters reduces variability in the misclosures. Accounting for their effects explains 50% (adjusted R 2 ) of the fluctuations in the yearly misclosures compared to the 11% if they are not. In addition, unmodeled low-frequency variations in the yearly global budget closure assessments have the propensity of confounding the detection of a statistically significant recent uniform global sea level acceleration triggered by anthropogenic contributors.

This study establishes a predictive empirical model, the first of its kind, which is innately a cause-and-effect representation of the observed global mean sea level over time. The model uses the trends of its observed budget components, including the temporal variations in mass of glaciers, Greenland, Antarctic ice sheets, terrestrial water storage, steric effect, and astronomical forcings of luni-solar origin, as independent variables in representing global mean sea level anomalies, namely, the dependent variable. The model parameters are estimated using monthly globally averaged satellite altimetry measurements and the yearly rates of the budget components during 1993–2018 as a priori information. Prospective monthly global mean sea level anomalies are then quantified and tabulated together with their root mean square error of prediction at 5% significance level for the period 2018–2050.

Predicting coastal sea level rise during the 21st century is essential for risk assessments. It is, therefore, a central theme for numerous studies in predicting sea level rise at coastal regions using historical tide gauge measurements. However, these investigations rarely investigated if such an extrapolation of sea level rise at a coastal region is viable without evidence. This study proposes a broadly framed three-tier statistical validation approach for kinematic models that use tide gauge measurements in sea level predictions. It consists of a concurrent (contemporaneous) validation, retrospective (hindcast) validation and prospective (forecast) validation. The modus operandi for each stage is exemplified using sea level measurements at Brest tide gauge station since 1800. The proposed three-tiered validation process provide statistical information about the predictions to be made at this station.

The unambiguous detection of a uniform sea level acceleration at a tide gauge station is important under an increasingly warmer Earth for the long-term coastal risk assessments. Although the timescales needed for detecting mean sea level trends at tide gauges were well investigated in the past, very few studies addressed the same issue for the sea level accelerations in depth. In this study, we demonstrate that the ability to discern a uniform sea level acceleration at a tide gauge station depends on its magnitude, systematic and random sea level variations, the degree of autocorrelation of the random variations, the length of its historical record and the desired statistical significance level of its estimate. We offer a formulary to estimate the required minimum record lengths needed to detect a statistically significant prospective uniform acceleration at a coastal or Island tide gauge station based on the retrospective analyses of its sea level record. To demonstrate its effectiveness, the minimum record lengths required to detect statistically significant prospective uniform accelerations were calculated at 19 globally distributed tide gauge stations with long records.

Abstract Detection and quantification of sea level accelerations at tide gauge stations are needed for assessing anthropogenic contributions to the climate change. Nonetheless, uniform or non-uniform sea level accelerations/decelerations are particularly di˚cult to discern partly because of their small magnitudes and partly because of the low frequency sea level variations as confounders. Moreover, noisy excursions in the observed sea level variations also exacerbate reliability of estimated sea level accelerations. This study explores the uniformity of a sea level acceleration graphically that is left unmodeled in the residuals of a least squares solution using cumulative sum charts. Key West, USA tide gauge station’s record is studied for a demonstration. The cumulative sum charts of the residuals of a rigorous kinematic model solution without the acceleration parameter revealed its crisp and uniform signature experienced at this station since 1913.

Global mean sea level budget is rigorously adjusted during the period 2005–2015. The emphasis is to provide the best estimates for the linear rates of changes (trends) of the global mean sea level budget components during this period subject to the constraint: Earth's hydrosphere conserves water. The newly simultaneously adjusted trends of the budget components suggest a larger correction for the global mean sea level trend implicated by the other budget components' trends under the budget constraint. The simultaneous estimation of the linear trends of the budget components subject to the constraint for closure improves their uncertainties and enables a holistic assessment of the global mean sea budget, which has implications for future sea level science studies, including the future Intergovernmental Panel on Climate Change (IPCC) Assessment Reports, and the US Climate Assessment Reports.

Abstract Because oceans cover 71% of Earth’s surface, ocean warming, consequential for thermal expansion of sea water, has been the largest contributor to the global mean sea level rise averaged over the 20th and the early 21st century. This study first generates quasi-observed monthly globally averaged thermosteric sea level time series by removing the contributions of global mean sea level budget components, namely, Glaciers, Greenland, Antarctica, and Terrestrial Water Storage from satellite altimetry measured global sea level changes during 1993–2019. A baseline kinematic model with global mean thermosteric sea level trend and a uniform acceleration is solved to evaluate the performance of a rigorous mixed kinematic model. The model also includes coefficients of monthly lagged 60 yearlong cumulative global mean sea surface temperature gradients and control variables of lunisolar origins and representations for first order autoregressive disturbances. The mixed kinematic model explains 94% (Adjusted R2)1 of the total variability in quasi-observed monthly and globally averaged thermosteric time series compared to the 46% of the baseline kinematic model’s Adjusted R2. The estimated trend, 1.19±0.03 mm/yr., is attributed to the long-term ocean warming. Whereas eleven statistically significant (α = 0.05) monthly lagged cumulative global mean sea surface temperature gradients each having a memory of 60 years explain the remainder transient global mean thermosteric sea level changes due to the episodic ocean surface warming and cooling during this period. The series also exhibit signatures of a statistically significant contingent uniform global sea level acceleration and periodic lunisolar forcings.

The tide gauge record at Brest, France, along Eastern part of Atlantic coast is one of the longest records in Europe spanning 212 years (1807–2019). Analyzing these records has important ramifications in assessing anthropogenic impact of climate change at local and regional scales during this period. All the previous studies that analyzed Brest’s tide gauge record have used vaguely defined quadratics models and did not incorporate the effect of sea level variations at various frequencies, which confounded the presence or absence of a plausible uniform acceleration. Here, we entertained two competing kinematic models; one with a uniform acceleration representing 212 years of monthly averaged tide gauge data, the other is a two-phase trend model (Phase I is 93 years long and Phase II is 119 years long). Both models include statistically significant (α = 0.05) common periodic effects, and sub and super harmonics of luni-solar origin for representing monthly averaged sea level anomalies observed at Brest. The least squares statistics for both models’ solutions cannot distinguish one model over the other, like earlier studies. However, the assessment of Phase I segment of the records disclosed the absence of a statistically significant trend and a uniform acceleration during this period. This outcome eliminates conclusively the occurrence of a uniform acceleration during the entire 212-year data span of the tide gauge record at Brest, favoring the two-phase trend model as a sound alternative.

Abstract Global mean sea level budget is rigorously adjusted during the period 2005–2015 with an emphasis on closing the budget on a year by year basis as opposed to using linear trends of global mean sea level components. The adjustment also accounts for the effect of snow, water vapor, and permafrost mass components as a lump sum. The approach provides better resolution for evaluating individual contribution of each budget component year by year in tandem with the other components. Year by year budget misclosures and the confidence intervals of the year by year adjusted budget components are suggestive of an increasing non-linearity in satellite altimetry derived global mean sea level measurements starting in 2012, which are not present in the other components. The solution also generates time series iteratively for the lumped snow, water vapor, and permafrost mass components as well as an estimate for its linear trend, 0.06±0.59 mm/yr. Nonetheless, its standard error is markedly large because of the un-modeled variability in satellite altimetry observed yearly averaged global mean sea level anomalies.

Current studies in global mean sea level, GMSL, studies assess the closure/misclosure of the GMSL budget components and their uncertainties. Because Earth's hydrosphere conserves water, a closed global mean sea level budget with a consistent set of estimates and their statistics is necessary. An unclosed budget means that there are problems to be addressed such as biases in the budget components, unreliable error statistics about the estimates, unknown or known but unmodeled budget components. In a misclosed global mean sea level budget, as practiced in recent studies, the trend estimates for the budget components and their errors account only for the anomalies of each budget component in isolation. On the other hand, the trend of each series must consider the trends of the other series in tandem such that the global mean sea level budget is closed for a holistic assessment, which can only be achieved by adjusting global mean sea level budget components simultaneously. In this study, we demonstrate a statistical protocol to ameliorate this deficiency, which potentially have implications for future sea level science studies, including the future Intergovernmental Panel on Climate Change (IPCC) Assessment Reports, and the US Climate Assessment Reports.

Recent studies reported a uniform global sea level acceleration during the satellite altimetry era (1993–2017) by analyzing globally averaged satellite altimetry measurements. Here, we discuss potential omission errors that were not thoroughly addressed in detecting and estimating the reported global sea level acceleration in these studies. Our analyses results demonstrate that the declared acceleration in recent studies can also be explained equally well by alternative kinematic models based on previously well-established multi-decadal global mean sea level variations of various origins, which suggests prudence before declaring the presence of an accelerating global mean sea level with confidence during the satellite altimetry era.

This study demonstrates that absolute (geocentric) and relative sea level trends, sea level acceleration, low frequency sea level variations and linear trends in vertical crustal movements experienced at a tide gauge station can be estimated simultaneously using conflated satellite altimetry and tide gauge measurements without the aid of GPS measurements. The formulation is the first of its kind in sea level studies and its effectiveness is exemplified using tide gauge, and satellite altimetry measurements carried out in the vicinity of a tide gauge station.

We analyzed globally averaged satellite altimetry mean sea level time series during 1993 – 2018 and their future manifestations for the following 25 years using a kinematic model, which consists of a trend, a contingent uniform acceleration, and a random error model. The analysis of variance results shows that the model explains 71.7% of the total variation in global mean sea level for which 70.6% is by the secular trend, and 1.07% is due to a contingent uniform acceleration. The remaining 28.3% unexplained variation is due to the random errors, which are dominated by a first order autoregressive process driven mostly by oceanic and atmospheric variations over time. These numbers indicate more bumps and jumps for the future manifestations of the global mean sea level anomalies as illustrated using a one-step ahead predictor in this study. Our findings suggest preponderant random errors are poised to further confound and negatively impact the certitude of published estimates of the uniform global sea level acceleration as well as its prediction under an increasingly warmer Earth.

Knowledge of vertical crustal movement is fundamental to quantify absolute sea level changes at tide gauge locations as well as for satellite altimetry calibration validations. While GPS measurements at collocated tide gauge stations fulfill this need, currently only few hundred tide gauge stations are equipped with GPS, and their measurements do not span a long period of time. In the past, several studies addressed this problem by calculating relative and geocentric trends from the tide gauge and satellite altimetry measurements respectively, and then difference the two trends to calculate the rate of changes at the tide gauge stations. However, this approach is suboptimal. This study offers an optimal statistical protocol based on the method of condition equations with unknown parameters. An example solution demonstrates the proposed mathematical and statistical models' optimality in estimating vertical crustal movement and its standard error by comparing them with the results of current methods. The proposed model accounts for the effect of auto-correlations in observed tide gauge and satellite altimetry sea level time series, adjusts observed corrections such as inverted barometer effects, and constraints tide gauge and satellite altimeter measurement to close. The new model can accommodate estimating other systematic effects such as pole tides that are not eliminated by differencing.

Predicting sea level rise is essential for current climate discussions. Empirical models put in use to monitor and analyze sea level variations observed at globally distributed tide gauge stations during the last decade can provide reliable predictions with high resolution. Meanwhile, prediction intervals, an alternative to confidence intervals, are to be recognized and deployed in sea level studies. Predictions together with their prediction intervals, as demonstrated in this study, can quantify the uncertainty of a single future observation from a population, instead of the uncertainty of a conceivable average sea level namely a confidence interval, and it is thereby, better suited for coastal risk assessment to guide policy development for mitigation and adaptation responses.

This observational study reports that several globally distributed tide gauge stations exhibit a propensity of statistically significant sea level accelerations during the satellite altimetry era. However, the magnitudes of the estimated tide gauge accelerations during this period are systematically and noticeably smaller than the global mean sea level acceleration reported by recent analyses of satellite altimetry. The differences are likely to be caused by the interannual, decadal and interdecadal sea level variations, which are modeled using a broken trend model with overlapping harmonics in the analyses of tide gauge data but omitted in the analysis of satellite altimetry.

This is an exploratory investigation to search for the presence of an acceleration in global sea surface temperature rise, which is essential to identify anthropogenic contributions to the climate change during the 20th century. A weighted statistical model with an acceleration parameter was built progressively to reconstruct the variations in the global sea surface temperature data considering statistically significant confounders and autoregressive disturbances in the process. From the preliminary residual analysis of a weighted regression model, emerged a parsimonious model with first order autoregressive disturbances with a deterministic trend, acceleration and periodicity of 69 yr and its 138 yr subharmonic. The final model solution, selected from 29 alternative combinations of the model parameters using Mallows's C-p metric, revealed a statistically significant deterministic trend, 0.40 +/- 0.03 degrees C/c (p < 0.01), and acceleration, 0.67 +/- 0.11 degrees C/c(2) (p < 0.01) explaining 33% of the global sea surface temperature variations. The combined yearly trend and acceleration in global sea surface temperature as predicted by the model, exhibit a strong correlation with the yearly increase in the global CO2 concentrations observed during the 20th century. (C) 2018 Institute of Seismology, China Earthquake Administration, etc.