Modelling synthetic atmospheric turbulence profiles with temporal variation using Gaussian mixture model

The atmospheric turbulence profile plays a very important role for performance evaluation of wide-field adaptive optic systems. Since the atmospheric turbulence is evolving, the turbulence profile will change with time. To better model the temporal variation of turbulence profile, in this paper, we propose to use the extensive stereo-SCIDAR turbulence profile dataset from one observation site to train a Gaussian mixture model. The trained Gaussian mixture model can describe the structure of the turbulence profile in that particular site with several multidimensional Gaussian distributions. We cluster the turbulence profile data with the Gaussian mixture model and analyse the temporal variation properties of the clusters. We define the characteristic time as the time that the measured turbulence profile remains in a given profile. We find that normally the characteristic time is around 2 to 20 min and will change at different sites and in different seasons. With the statistical results of the characteristic time and the trained Gaussian mixture model, we can generate synthetic artificial turbulence profiles with realistic temporal variation to better test the performance of adaptive optics systems.