The Yamartino method is an algorithm for calculating an approximation of the circular variance of wind direction during a single pass through the incoming data.
[1] The simple method for calculating circular variance requires two passes through the list of values.
Over the time interval to be averaged across, n measurements of wind direction (θ) will be made and two totals are accumulated without storage of the n individual values.
At the end of the interval the calculations are as follows: with the average values of sin θ and cos θ defined as Then the average wind direction is given via the four-quadrant arctan(x,y) function as From twenty different functions for σθ using variables obtained in a single-pass of the wind direction data, Yamartino found the best function to be where The key here is to remember that sin2θ + cos2θ = 1 so that for example, with a constant wind direction at any value of θ, the value of
radians for an almost uniform distribution of angles across all directions, while making minimal change to results for small dispersions.
Comparisons against Monte Carlo generated cases indicate that Yamartino's algorithm is within 2% for more realistic distributions.