Modeling refractivity fluctuations with random functions

Fluctuations in the refractive index n can be characterized with the refractive structure function index Cn². Cn² is often modeled as decreasing exponentially with height and having a dependence on latitude and season. A subset of the components of Cn² are at scales below that which can be resolved with the grid spacing of large eddy simulation (LES). The output of mesoscale numerical weather prediction (NWP) models can be wholly outside those scale lengths. When electromagnetic (EM) parabolic equation (PE) models are run using refractivity from a mesoscale NWP model, a troposcatter model is often run within the PE model to add what amounts to sub-grid fluctuation n′(r, z) to the NWP output n(r, z) where r is range and z is height.