‘Diatoms and pH reconstruction’ (1990) revisited

Abstract

The 167 sample lake-water pH-diatom calibration data-set created as part of the Palaeolimnology Programme within the Surface Water Acidification Project (SWAP) is re-analysed numerically using nine different numerical methods, six based on simple two-way weighted-averaging (WA), and the other three involving Gaussian logit regression (GLR) and maximum-likelihood (ML) calibration, the modern analogue technique, or weighted-averaging partial least-squares regression and calibration. Root mean squared error of prediction and maximum bias were estimated for all nine methods based on 10,000 internal and 10,000 external cross-validations involving a training-set, an optimisation-set, and a test-set. The results show that WA with a monotonic deshrinking spline equals or slightly outperforms WA with linear inverse deshrinking, especially in external cross-validation. Methods that employ tolerance downweighting generally have an inferior performance except when combined with monotonic deshrinking. It appears that simple two-way WA extensively used in SWAP cannot be significantly bettered. Thanks to increased computing power, better software, and more rigorous cross-validations, GLR shows good performance, especially in external cross-validation.