text: When generating a time series of wind speeds for a set of points across a surface, coherence needs to be taken into account. That is, the instantaneous wind speed at some point, A, will bear some resemblance to the wind speed at some other point, B. Clearly, the resemblance is influenced by the separation of points A and B. That is, two points separated by a large distance will show less similarity to each other than two neighbouring points on the surface. 
  In addition, one would expect low frequency components of the wind speeds at points A and B to show more correlation than high frequency components. As such, many coherence functions have been proposed: Davenport, Solari, etc. The Solari coherence spectrum is provided as an example:
  where  is a constant,  is the separation of points  and  on the surface,  is the frequency, and  and  are the mean wind speeds at points  and  respectively. The indices  and  run from 1 to n, and the index  covers the frequency range. From the coherence function stems the coherence matrix. To cover all relationships between all points, the coherence function must be an -by--by- matrix. Clearly, the coherence matrix is symmetric about the main diagonal if we are restricting ourselves to looking at the coherence function at a single frequency. This is because the spatial separation between points A and B is the same as the spatial separation between B and A. That is, for a n-by-n grid, only  elements need to be calculated for each frequency.
  It is worth noting at this point that whilst the coherence matrix is strictly a 3-dimensional matrix (i, j, and k), computer programmes which implement the Sandia method typically reduce the coherence matrix to a 2-dimensional matrix where the frequency dimension has been removed. This is to ease computational requirements. A 2-dimensional matrix is also required to perform some of the actions on the spectral matrix, such as a Cholesky decomposition, which is mentioned later. Of course, variation in frequency is still applied. However, the following process is carried out in full for one given frequency before proceeding to the next frequency. As such, in the following section, a power spectrum refers to the value of the power spectrum at a given frequency and not the full set of values across the frequency range being used. That is,
  and
  where an element of S,  , would have given the strength of the spectrum at a particular frequency  at a particular point in space.