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 CMIP6 intercomparison project, 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 Schwarz methods. Despite the fact that the computational cost is large compared to standard coupling methods, which makes the method impractical as is for production runs, Schwarz algorithms are 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. A new coupling scheme based on such iterative method has been implemented in the IPSL coupled model. Comparisons between coupled solutions obtained with this new scheme and the standard IPSL coupling scheme show large differences at sunrise and sunset, when the external forcing (insolation at top of 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 time step, 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. A thorough design of the first guess to initialize the iterative process may yield a solution that reduces the error with only one iteration. 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 the time coupling schemes. It is a very practical tool to test new approaches like Schwartz methods that enable correcting the mismatch in between components due to asynchronous coupling through an iterative method (Marti et al, 2020) and to assess the effect of different coupling algorithms from purely sequential to asynchronous. It is also an interesting tool to assess the effect of surface flux parameterizations on both ocean and atmospheric boundary layers.…”

Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients

“…[22] suggested that the convergence is insensitive to variations of ν j (z) at large frequencies. Indeed, in the ω → ∞ limit, regardless of the viscosity profile, the S 1 S 2 product, with S j defined in either (28), (30), or (34), converges towards the same value…”

“…for the so-called shallow-water equations [31,36], or for the ocean primitive equations [1]. At a more practical level, the dynamical core of at least one Earth system numerical model relies on a SWR algorithm for its domain decomposition method [35], and empirical studies have been undertaken for including Schwarz methods in ocean -atmosphere couplers [30]. Generally speaking, the theoretical convergence analysis of SWR algorithms is restricted to relatively simple linear model problems, often approximating space-varying quantities as constant coefficients, assuming that scalar variables are independent from each other, so that all the conditions to apply Fourier and Laplace transformations are met.…”