Representative optical turbulence profiles for ESO Paranal by hierarchical clustering

Knowledge of the optical turbulence profile is important in adaptive optics (AO) systems, particularly tomographic AO systems such as those to be employed by the next generation of 40 m class extremely large telescopes (ELTs). Site characterisation and monitoring campaigns have produced large quantities of turbulence profiling data for sites around the world. However AO system design and performance characterisation is dependent on Monte-Carlo simulations that cannot make use of these large datasets due to long computation times. Here we address the question of how to reduce these large datasets into small sets of profiles that can feasibly be used in such Monte-Carlo simulations, whilst minimising the loss of information inherent in this effective compression of the data. We propose hierarchical clustering to partition the dataset according to the structure of the turbulence profiles and extract a single profile from each cluster. This method is applied to the Stereo-SCIDAR dataset from ESO Paranal containing over 10000 measurements of the turbulence profile from 83 nights. We present two methods of extracting turbulence profiles from the clusters, resulting in two sets of 18 profiles providing subtly different descriptions of the variability across the entire dataset. For generality we choose integrated parameters of the turbulence to measure the representativeness of our profiles and compare to others. Using these criterion we also show that such variability is difficult to capture with small sets of profiles associated with integrated turbulence parameters such as seeing.