Correction: Timing of the Last Glacial Maximum from observed sea-level minima

Nature, 406, 713–716 (2000).

In this Letter, a statement on page 715 that the eustatic sea level Δζ_eus(t) differs from the ice-volume-equivalent sea level Δζ_e(t) is erroneous. We thank W. R. Peltier for drawing this error in interpretation to our attention. The two definitions were initially introduced to distinguish changes in sea level that were the result of ice mass being added to the oceans from other changes caused by thermal expansion, for example. The erroneous statement was the result of a programming error that was introduced into the program in 1998 when it was modified to deal with shelf ice more accurately and to introduce the time dependence of the coastlines in the evaluation of the equivalent sea-level change through equation (3). This evaluation requires a knowledge of the location of the shoreline at each time step, of the grounding line of the ice and of the part of the shelf ice that floats or grounds as a result of sea level change and shelf-ice thickness change. The error was introduced at the end of each iteration of the sea-level equation, when the value of sea level change was integrated over the ocean and the resulting volume was compared with the change in ice volume for the corresponding interval. The eustatic sea level at this stage was defined as the global average of sea-level change but, because we allow sea level to be non-zero on land so as to be able to compute the tilting of lakes or the changing elevations of tree lines, the averaging should have been restricted to the ocean. Fortunately, the error does not enter into any other part of the model predictions because the estimate of global sea level rise is based on the ice volume change in equation (3) throughout the core program. Thus calculations of the isostatic correction Δζ_i(j,t) in equation (1) and of the ice-volume-equivalent sea level Δζ_e(t) are correct, as are the results illustrated in Fig. 2. The matter arises in the two sentences in parentheses of the penultimate paragraph of the main text (page 715), in a discussion of the difference between our Barbados results and those of Peltier. The first sentence in parentheses remains correct, but our attempt to explain it in the second sentence is not. The cause for the disagreement must be sought elsewhere, possibly in the different ice and/or earth models used.