Detecting sea-level hazards: Simple regression-based methods for calculating the acceleration of sea level

This report documents the development of statistical tools used to quantify the hazard presented by the response of sea-level elevation to natural or anthropogenic changes in climate and ocean circulation. A hazard is a physical process (or processes) that, when combined with vulnerability (or susceptibility to the hazard), results in risk. This study presents the development and comparison of new and existing sea-level analysis methods, exploration of the strengths and weaknesses of the methods using synthetic time series, and when appropriate, synthesis of the application of the method to observed sea-level time series. These reports are intended to enhance material presented in peer-reviewed journal articles where it is not always possible to provide the level of detail that might be necessary to fully support or recreate published results.

The purpose of this report is to document and compare three simple methodologies that have previously been used to provide estimates with associated errors of the acceleration of sea-level elevation. These techniques have been used by coastal scientists and planners in assessing coastal risk over a wide range of spatial and temporal scales. Because relative sea-level (SL) elevation time series contain energetic fluctuations at many time scales, extracting what can be relatively small rate and acceleration signals (along with estimates of the error) from much larger “noise” has proven to be both difficult and controversial. Acceleration is a preferred measure of SL response to recent changes in the Earth’s climate because over time scales of 100 years or less slow vertical land motions (such as glacial isostatic adjustment) contribute only to the linear signal and not to acceleration, thus reducing the complexity of the analysis. Hence acceleration is useful if the goal of a study is to characterize and quantify the hazard associated with the changing relative elevation of water with respect to land on decadal time scales. Although in some cases it may be necessary to determine the cause of relative sea level rise, as a first step, it is important to accurately estimate the magnitude of the threat.

Most researchers agree that global sea level (GSL) rose persistently through much of the 20th century at about 1.5–2.0 millimeters per year (mm/yr). There is far less agreement about whether the rate of sea-level rise (SLR) is increasing (that is, an acceleration in SL).

Recent studies, and most of their predecessors, use tide gage data to quantify SL acceleration, A_SL(t). In the current study, three techniques were used to calculate acceleration from tide gage data, and of those examined, it was determined that the two techniques based on sliding a regression window through the time series are more robust compared to the technique that fits a single quadratic form to the entire time series, particularly if there is temporal variation in the magnitude of the acceleration. The single-fit quadratic regression method has been the most commonly used technique in determining acceleration in tide gage data. The inability of the single-fit method to account for time-varying acceleration may explain some of the inconsistent findings between investigators. Properly quantifying A_SL(t) from field measurements is of particular importance in evaluating numerical models of past, present, and future SLR resulting from anticipated climate change.