A Schwarz iterative method to evaluate ocean–atmosphere coupling schemes: implementation and diagnostics in IPSL-CM6-SW-VLR

Abstract

State-of-the-art Earth system models, like the ones used in the Coupled Model Intercomparison Project Phase 6 (CMIP6), suffer from temporal inconsistencies at the ocean–atmosphere interface. Indeed, the coupling algorithms generally implemented in those models do not allow for a correct phasing between the ocean and the atmosphere and hence between their diurnal cycles. A possibility to remove these temporal inconsistencies is to use an iterative coupling algorithm based on the Schwarz iterative method. Despite its large computational cost compared to standard coupling methods, which makes the algorithm implementation impractical for production runs, the Schwarz method is useful to evaluate some of the errors made in state-of-the-art ocean–atmosphere coupled models (e.g., in the representation of the processes related to diurnal cycle), as illustrated by the present study. IPSL-CM6-SW-VLR is a low-resolution version of the IPSL-CM6 coupled model with a simplified land surface model, implementing a Schwarz iterative coupling scheme. Comparisons between coupled solutions obtained with this new scheme and the standard IPSL coupling scheme (referred to as the parallel algorithm) show large differences after sunrise and before sunset, when the external forcing (insolation at the top of the atmosphere) has the fastest pace of change. At these times of the day, the difference between the two numerical solutions is often larger than 100 % of the solution, even with a small coupling period, thus suggesting that significant errors are potentially made with current coupling methods. Most of those differences can be strongly reduced by making only two iterations of the Schwarz method, which leads to a doubling of the computing cost. Besides the parallel algorithm used in IPSL-CM6, we also test a so-called sequential atmosphere-first algorithm, which is used in some coupled ocean–atmosphere models. We show that the sequential algorithm improves the numerical results compared to the parallel one at the expanse of a loss of parallelism. The present study focuses on the ocean–atmosphere interface with no sea ice. The problem with three components (ocean–sea ice–atmosphere) remains to be investigated.