Surface flux errors in asynchronous coupling of GCM

In coupled general circulation model, the accuracy of momentum and energy exchange at the air-sea interface is still a potential source of significant bias. In the framework of the COCOA project we investigate new methods (both mathematical and numerical) to have a more correct flux representation. One important source of error is the asynchronous coupling between oceanic and atmospheric model. Indeed, the time step of the coupling is generally longer than time steps used by either the atmospheric or the oceanic model. This introduces inconsistencies between the free evolution of the two models due to the exchange parameters that are held constant since the last coupling time step. In particular, non-synchronous exchange coefficients may lead to error in the diurnal evolution of the coupled system, or to bias in the ocean mixed layer temperature for period where surface fluxes increases or decrease linearly.

In order to evaluate the potential amplitude of this error, and its regional and sea- sonal distribution, we use the hourly fluxes that are available in the new ECMWF ERA5 re-analyses. The error due to asynchronous coupling is first evaluated by inspecting the flux difference between two successive time-steps. Results show more important differences over the western boundary currents and the circumpolar current for all the fluxes except for the solar flux. We also observe larger differences in summer compared to winter in the respective hemisphere. By taking in account the geometrical variation of the solar flux we show how we can reduce the error for the solar flux.

In a second time we are calculating the statistics for the linear increase and decrease of the flux for a fixed period (ig one day, two days...) over all the ocean for all the fluxes except the solar one. The results are showing coefficients that are decreasing as the period increase. We also use those coefficient in a simple mixed layer model to calculate the error made over the period of calcul. On the contrary we see the appearance of a plateau at two-three days on the impact of this linear bias. Finally, using the De Boyer de Montaigu climatology for the mixed layer height we show that the linear bias could lead to temperature change up to 0.1K.