Iterative Schwarz Method to Couple Ocean and Atmosphere in a Global Climate Model

For historical and practical reasons, present-day coupling algorithms implemented in ocean-atmosphere models are primarily driven by the necessity to conserve energy and water at the air-sea interface. However the asynchronous coupling algorithms currently used in ocean-atmosphere do not allow for a correct phasing between the ocean and the atmosphere.

In an asynchronous coupling algorithm, the total simulation time is split into smaller time intervals (a.k.a. coupling periods) over which averaged-in-time
boundary data are exchanged. For a particular coupling period, the average atmospheric fluxes are computed in the atmospheric model using the oceanic surface properties computed and averaged by the oceanic model over the previous coupling period. Therefore, for a given coupling period, the fluxes used by the oceanic model are not coherent with the oceanic surface properties considered by the atmospheric model. The mathematical consistency of the solution at the interface is not guaranteed.

The use of an iterative coupling algorithm, such as Schwarz methods, is a way to correct this inconsistency and to properly reproduce the diurnal cycle when the coupling period is less than one day. In Lemarié et al. (2014), preliminary numerical experiments using the Schwarz coupling method for the simulation of a tropical cyclone with a regional coupled model were carried out. In ensemble simulations, the Schwarz iterative coupling method leads to a significantly reduced spread in the ensemble results (in terms of cyclone trajectory and intensity), thus suggesting that a source of error is removed with respect to the asynchronous coupling case.

In the present work, the Schwarz iterative method is implemented in IPSLCM6, a state-of-the-art global ocean-atmosphere coupled model used to study past, present and future climates. We analyse the convergence speed and the quality of the convergence. A partial iterative method is also tested: in a first phase, only the atmosphere physics and the vertical diffusion terms are computed, until the convergence. This provide a first guess for the full model which is then iterated until convergence of the whole system. The impact on the diurnal cycle will also be presented.