Sub-Scalar Parameterization in Multi-Level Simulation

Sub-scalar parameterization refers to substituting processes that are too small-scale or complex to be physically represented in a simulation model by parameters. A typical example for a sub-scalar parameterization is the representation of clouds in climate models. Unfortunately, not all of these parameters can be measured directly. Hence, it is often necessary to calculate sub-scalar parameters (for the primary simulation) using additional models, like special small-scale simulations (secondary simulations). In many applications a dynamic exchange of data between both simulation during runtime is necessary: The high-resolution model iteratively calculates new parameter values using information from the aggregated model. Using such an approach in the climate example, the secondary model would calculate cloud distributions on the basis of simulation results from the primary climate model (e.g. based on global or local average temperatures). However, there is a certain amount of inherent uncertainty in the data flow from aggregated to a high-resolution models. If the output of the secondary high-resolution model is sensitive to this uncertainty, sub-scalar parameterization is at least questionable. The paper formally defines this problem in order to systemize its investigation.