This paper analyses and models a wind farm using large amounts of measured data collected from every turbine in the farm over a full year. Spectral analysis of the power output of all turbine pairs in the wind farm first shows that their coherence is dependent on the distance between these turbine pairs. This gives a physical basis for a simple, hierarchical approach to wind farm modelling by aggregating turbines into groups based on their proximity. Comparison of the resulting wind farm models with measurement shows that the chosen number of aggregated turbine groups is a trade-off between modelling accuracy and use of more measured data. Further spectral analysis then reveals three distinct frequency regions in the wind farm power output. At the lowest frequencies, all the models and the measurements have similar power generation because the wind farm is compact relative to the length scales in the wind, and the scaling from any individual turbine to the entire wind farm is simply the number of turbines. At high frequencies, the turbines are uncorrelated because the length scales in the wind are now short, with another simple scaling for the total power generation. A third, transitional region sits between these two limits, with each turbine in the wind farm on average is more correlated with closer turbines and less correlated with more distant turbines. (C) 2020 Elsevier Ltd. All rights reserved.