A simple temporal and spatial analysis of flow in complex terrain in the context of wind energy modelling

A simple temporal and spatial analysis is done on wind speed and direction data from a number of meteorological towers separated by distances between roughly 1 and 100 kilometres. The analysis is done in the context of expect ed model error in wind energy calculations. The study first uses single poi nt statistics to show the evolution of mean values with time. It is shown t hat strong seasonal signals are present and that stable means are achieved only after averaging periods of a year or more. The study then uses discret e Fourier transforms to show that significant amounts of spectral energy re side in modes with periods of a few days to less than a day. Frequency depe ndent cross correlation values are then derived and used to show how correl ation between towers diminishes with increasing frequency. The mechanism re sponsible for this diminished correlation is shown through the comparison o f cross-correlation phase as a function of frequency and its relationship t o distance between towers. Error in wind energy estimates are shown to be s trongly related to correlation and therefore distance over which the predic tion is made. In summary, much of the inaccuracy in modelling flow in the c ontext of wind energy calculations is due to a lack of scale separation bet ween the deterministic part of the flow, which is well modelled, and that p art of the flow that is stochastic at the length and time scales modelled.