The Schmidt hammer as a Holocene calibrated-age dating technique: Testing the form of the R-value-age relationship and defining the predicted-age errors

Most recent developments of Schmidt-hammer exposure-age dating (SHD) as a calibrated-age dating tool have been limited by the use of locations at two age control points. This has necessitated: (1) making assumptions about a linear R-value-age relationship; and (2) basing predictions of age errors only on R-value variance at the two age control points. This paper analyses 9900 R-values obtained from multiple-age control points on a sequence of glacio-isostatically raised shorelines with well constrained ages (Skuleskogen High Coast World Heritage Site and environs, Gulf of Bothnia, northern Sweden) ranging from modern to 10.5 ka in age. The sampling design involved 30 measurements on granite beach boulders from 30 sites at 11 age control points. The R-value-age relationship is best described by a linear function (ordinary least squares, OLS) with an R-2 of 0.89 (p < 0.0001). Predicted-age errors are calculated using two approaches: (1) OLS regression, which takes account of the uncertainties associated with the regression line and the age control points; and (2) weighted total least squares (WTLS) regression which, in addition, takes account of possible shoreline age errors and the heteroscedasticity of R-value residuals with increasing age. With both approaches, 95% predicted-age errors are relatively modest: +/- 355-455 years and +/- 300-515 years, respectively, with larger R-value variance and hence uncertainty for older surfaces, and the possibility of further improvement from a more selective field sampling scheme that differentiates between age-related and non-age-related rock-surface variability. Our results also indicate that for certain lithologies and weathering environments, it is possible to construct reliable calibrated-age curves from relatively few age control points.