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Yamartino method

The Yamartino method is an algorithm for calculating an approximation to the standard deviation σ_θ of wind direction θ during a single pass through the incoming data.^[1] The standard deviation of wind direction is a measure of lateral turbulence, and is used in a method for estimating the Pasquill stability category.

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The typical method for calculating standard deviation requires two passes through the list of values. The first pass determines the average of those values; the second pass determines the sum of the squared differences between the values and the average. This double-pass method requires access to all values, and special consideration must be made for a discontinuous variable such as wind direction.

The single-pass method is used as a rapid way to compute a standard deviation, although this method is not practical for angular data such as wind direction.

The Yamartino method avoids the need to have access to the original n values of wind direction. The United States Environmental Protection Agency (EPA) has chosen it as the preferred way to compute the standard deviation of wind direction.^[2]

Algorithm

During the single pass through n values of wind direction measurements (θ) two values are computed; the average values of sin θ defined as

$s_a=n^{-1}\sum_{i=1}^n \sin \theta_i,$

and average cos θ

$c_a=n^{-1}\sum_{i=1}^n \cos \theta_i.$

The average wind direction is then given as

$\theta_a=\tan^{-1} \left (\frac{s_a}{c_a} \right ).$

From twenty different functions for θ using variables obtained in a single-pass of the wind direction data Yamartino found the best function to be

$\sigma_\theta = \sin^{-1} \left (\varepsilon) \right [1.0+0.1547 \varepsilon^3],$

where

$\varepsilon=\sqrt{1-(s^2_a+c^2_a)}.$

Comparisons against the correct double-pass σ_θ indicates that Yamartino's algorithm is within 2%.

References

^ Yamartino, R.J. (1984). "A Comparison of Several "Single-Pass" Estimators of the Standard Deviation of Wind Direction". Journal of Climate and Applied Meteorology 23: 1362-1366.
^ Meteorological Monitoring Guidance for Regulatory Modeling Applications (section 6.2.1)

Category: Boundary layer meteorology