We describe the implementation of a robotic SLODAR instrument at the Cerro Paranal observatory. The instrument measures the vertical profile of the optical atmospheric turbulence strength, in 8 resolution elements, to a maximum altitude ranging between 100 m and 500 m. We present statistical results of measurements of the turbulence profile on a total of 875 nights between 2014 and 2018. The vertical profile of the ground layer of turbulence is very varied, but in the median case most of the turbulence strength in the ground layer is concentrated within the first 50 m altitude, with relatively weak turbulence at higher altitudes up to 500 m. We find good agreement between measurements of the seeing angle from the SLODAR and from the Paranal DIMM seeing monitor, and also for seeing values extracted from the Shack-Hartmann active optics sensor of VLT UT1, adjusting for the height of each instrument above ground level. The SLODAR data suggest that a median improvement in the seeing angle from 0.689 arcsec to 0.481 arcsec at wavelength 500 nm would be obtained by fully correcting the ground-layer turbulence between the height of the UTs (taken as 10 m) and altitude 500 m.
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