Estimates of Cn2 from numerical weather prediction model output

The forecasts of small-scale turbulence are important for communication reliability, optical imaging systems, GPS performance, and many other related problems. Knowledge of these turbulent effects may be vital for testing of new and existing sensor systems at military test ranges, and for use of the sensors under combat conditions. In these applications the primary effect of the turbulence is to cause small scale changes in the atmospheric index of refraction (sometimes called scintillation). Scintillation magnitudes are typically measured in terms of the so-called refractive index structure constant, Cn2 . A reliable method for forecasting the scintillation levels would be highly desirable since that information could be used to modify the timing of an experiment at a test range, or even to cancel it.

Traditionally, estimates of Cn2 were produced using vertical gradients of temperature and humidity derived from soundings launched near the time of the test. Given the complex small scale structure of the turbulence, often confined to very thin vertical layers, methods based on vertical differences can be unreliable. Here we develop a technique to provide estimates of Cn2 from high-resolution numerical weather prediction (NWP) model output, not by using vertical differences from the model output, but rather by computing horizontal spatial structure functions of refractive index with corrections for the inherent smoothing and filtering effects of the underlying NWP model. The key assumptions are the existence of a universal statistical description of small-scale turbulence and a locally universal spatial filter for the model variables. Under these assumptions, spatial structure functions of the NWP model variables can be related to the structure functions of the atmospheric variables and extended to smaller under-resolved scales relevant to EM propagation. The shape of the universal spatial filter is determined by comparisons of model structure functions with the spatial structure function from aircraft data collected in the upper troposphere and lower stratosphere. This method of computing Cn2 has an important advantage over more traditional methods that are based on vertical differences since the structure-function based estimates avoid reference to the turbulence outer length scale. To evaluate the technique, NWP-model derived structure function estimates of Cn2 are compared to profiles of Cn2 derived from temperature structure function sensors attached to a rawinsonde (thermosonde) near Holloman Air Force Base in the US. The configuration of the NWP model is also discussed as it relates to the estimates of the turbulence metrics.