The reliability of single precision computations in the simulation of deep soil heat diffusion in a land surface model

Abstract

Climate models need discretized numerical algorithms and finite precision arithmetic to solve their differential equations. Most efforts to date have focused on reducing truncation errors due to discretization effects, whereas rounding errors due to the use of floating-point arithmetic have received little attention. However, there are increasing concerns about more frequent occurrences of rounding errors in larger parallel computing platforms (due to the conflicting needs of stability and accuracy vs. performance), and while this has not been the norm in climate and forecast models using double precision, this could change with some models that are now compiled with single precision, which raises questions about the validity of using such low precision in climate applications. For example, processes occurring over large time scales such as permafrost thawing are potentially more vulnerable to this issue. In this study we analyze the theoretical and experimental effects of using single and double precision on simulated deep soil temperature from the Canadian LAnd Surface Scheme (CLASS), a state-of-the-art land surface model. We found that reliable single precision temperatures are limited to depths of less than about 20–25 m while double precision shows no loss of accuracy to depths of at least several hundred meters. We also found that, for a given precision level, model accuracy deteriorates when using smaller time steps, further reducing the usefulness of single precision. There is thus a clear danger of using single precision in some climate model applications, in particular any scientifically meaningful study of deep soil permafrost must at least use double precision. In addition, climate modelling teams might well benefit from paying more attention to numerical precision and roundoff issues to offset the potentially more frequent numerical anomalies in future large-scale parallel climate applications.