Partitioned time discretization for atmosphere-ocean interaction

Numerical algorithms are proposed, analyzed and tested for improved efficiency and reliabil-ity of the dynamic core of climate codes. The commonly used rigid lid hypothesis is assumed,which allows instantaneous response of the interface to changes in mass. Additionally, mois-ture transport is ignored, resulting in a static interface. A central algorithmic feature is thenumerical decoupling of the atmosphere and ocean calculations by a semi-implicit treatmentof the interface data, i.e. partitioned time stepping. Algorithms are developed for simpli-fied continuum models retaining the key mathematical structure of the atmosphere-oceanequations. The work begins by studying linear parameterization of momentum flux in terms of windshear, coupling the equations. Partitioned variants of backward-Euler are developed allowinglarge time steps. Higher order accuracy is achieved by deferred correction. Adaptations aredeveloped for nonlinear coupling. Most notably an application of geometric averaging isused to retain unconditional stability. This algorithm is extended to allow different size timesteps for the subcalculations. Full numerical analyses are performed and computationalexperiments are provided. Next, heat convection is added including a nonlinear parameterization of heat flux interms of wind shear and temperature. A partitioned algorithm is developed for the atmo-sphere and ocean coupled velocity-temperature system that retains unconditional stability.Furthermore, uncertainty quantification is performed in this case due to the importance ofreliably calculating heat transport phenomena in climate modeling. Noise is introduced in two coupling parameters with an important role in stability. Numerical tests investigate thevariance in temperature, velocity and average surface temperature. Partitioned methods are highly efficient for linearly coupled 2 fluid problems. Exten-sions of these methods for nonlinear coupling where the interface data is processed properlybefore passing yield highly efficient algorithms. One reason is due to their strong stabilityproperties. Convergence also holds under time step restrictions not dependent on mesh size.It is observed that two-way coupling (requiring knowledge of both atmosphere and oceanvelocities on the interface) generates less uncertainty in the calculation of average surfacetemperature compared to one-way models (only requiring knowledge of the wind velocity)