How does turbulence change approaching a rotor?

For load calculations on wind turbines it is usually assumed that the turbulence approaching the rotor does not change its statistics as it goes through the induction zone. We investigate this assumption using a nacelle-mounted forward-looking pulsed lidar that measures low-frequency wind fluctuations simultaneously at distances between 0.5 and 3 rotor diameters upstream. The measurements show that below rated wind speed the low-frequency wind variance is reduced by up to 10 % at 0.5 rotor diameters upstream and above rated enhanced by up to 20 %. A quasi-steady model that takes into account the change in thrust coefficient with wind speed explains these variations partly. Large eddy simulations of turbulence approaching an actuator disk model of a rotor support the finding that the slope of the thrust curve influences the low-frequency fluctuations.