Stochastic Multiscale Climate Models

In climate models it will not be possible to capture all relevant processes through a higher resolution or better process description. Ocean models currently use already near eddy-resolving horizontal resolutions (e.g. 0.1°) but many important processes such as upper ocean turbulence and sub-mesoscale eddies, are not adequately captured at this resolution. 

To overcome this problem one needs to exploit the property that high-frequency components in the flow get into statistical equilibrium much faster than low-frequency components and, moreover, are locally determined by low-frequency components. This can be accomplished by coupling an implicit low-resolution model to an explicit high-resolution ocean model. One runs the high-resolution model alternatingly with the low-resolution model, for a short and long time period, respectively. 

In fact, we will run an instance of the high-resolution model for each grid cell of the low-resolution model, using initial and boundary values computed at low resolution. This leads to an embarrassingly parallelizable set of high-resolution models. 

Hence, very suitable for Exascale architectures. For each low-resolution grid cell, the statistics (mean, variance) resulting from these computations will be used to define a stochastic term (state-dependent) in the low-resolution model that parametrizes the behavior of the high-resolution model. 

This process is repeated until the model gets into statistical equilibrium. For the coupling of the models, we will extend the eScience tool OMUSE, developed by NLeSC in a recent project, to one which can deal with one low-resolution model that can interact with many high-resolution models.