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

Abstract

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.

Assessment of the sea surface temperature diurnal cycle in CNRM-CM6-1 based on its 1D coupled configuration

“…Such 1D coupled configurations are particularly relevant to perform studies related to time coupling schemes. It is a very practical tool to test new approaches like Schwartz methods that enable correcting the mismatch between components due to asynchronous coupling through an iterative method (Marti et al, 2021) and to assess the effect of different coupling algorithms from purely sequential to asynchronous. Using a Schwartz algorithm for coupling would enable properly assessing the rectification effect in coupled mode.…”

AWI-CM3 coupled climate model: description and evaluation experiments for a prototype post-CMIP6 model

“…In the production mode both the atmosphere and the ocean components compute their own surface update at time t n based on time-lagged information at t n−1 of the other component. The physical inconsistencies resulting from this double-sided-lag method are small compared to those stemming from, e.g., spatial and temporal truncation and are generally accepted in the climate modeling community as they allow for parallel execution of model components (Lemarié et al, 2015;Marti et al, 2021).…”

“…AWI-CM3 can also be run in a sequential atmosphere-first mode, updating the ocean at time step t n with atmospheric fluxes from t n . In this mode climate models can get very close to what would be a converged solution of an iterative coupling at the atmosphere-ocean interface (Marti et al, 2021). Integration of a Schwarz iterative method for fully converged surface coupling is not planned due to the high computational cost compared to small reduction in model error.…”

AWI-CM3 coupled climate model: Description and evaluation experiments for a prototype post-CMIP6 model

“…The physical inconsistencies resulting from this double-sided-lag method are small compared to those stemming from e.g. spatial and temporal truncation and are generally accepted in the climate modelling community, as they allow for parallel execution of model components (Lemarié et al, 2015;Marti et al, 2021). AWI-CM3 can also be run in a sequential atmosphere-first mode, updating the ocean at timestep t n with atmospheric fluxes from t n .…”

“…AWI-CM3 can also be run in a sequential atmosphere-first mode, updating the ocean at timestep t n with atmospheric fluxes from t n . In this mode climate models can get very close to a converged solution at the atmosphere ocean interface (Marti et al, 2021). Integration of a Schwarz iterative method for fully converged surface coupling is not planned, due to the high computational cost compared to small reduction in model error.…”