Sea-level curves for the late Quaternary are typically reconstructed with data from reef tracts and terraces preserved along actively uplifting coastlines, recording highstands, and in some cases lowstands, of the world's oceans through time. As a result, sea-level curves reconstructed from these data are fixed at the maxima (highstands) and minima (lowstands), but either make no predictions about the intervening time or use arbitrary or free-hand methods of interpolation. These curves fail to meet the need of many applications of sea-level data for continuous, quantitative information.
A new method for calculating sea levels during intervening times produces a polynomial expression of sea level through time. LaGrange polynomial interpolation is used to fit a series of fourth-order equations to existing data of late Quaternary sea-level fluctuations, producing a systematic and realistic model of continuous sea-level elevations with time. The method is germane to any and all models of sea level based on discrete data points. Here the model advanced by Bloom et a1. is reexamined, and a new polynomial model which estimates eustatic sea levels continuously in the range 0-140 ka is developed from the Huon data. The method includes an error-analysis procedure that accounts for the effects of error in radiometric dates and theodolite measurements in the original data set, and extrapolates this error through the continuous model. Polynomial form and error estimation are indispensible to rigorous quantitative applications of sea-level data and supplant less-rigorous methods used to approximate sea level and rates of sea-level rise.