Question

In wind resource assessment, if a site follows a Rayleigh distribution, what is the specific relationship between the mean wind speed and the most frequent wind speed?

Accepted Answer

In wind resource assessment, wind speed frequency is often modeled using the Rayleigh distribution, which is a specific form of the more general Weibull distribution where the shape parameter is equal to two. The mean wind speed is the average value of all wind speeds recorded at a site over a given period, calculated as the sum of all speeds divided by the number of observations. The most frequent wind speed, also known as the mode, is the specific speed value that occurs more often than any other. In a Rayleigh distribution, the relationship is defined by the scale parameter, which determines the spread of the distribution. The mean wind speed is equal to the scale parameter multiplied by the square root of pi divided by two, which is approximately 1.253 times the scale parameter. The most frequent wind speed is exactly equal to the scale parameter itself. Therefore, the most frequent wind speed is calculated by dividing the mean wind speed by the square root of pi divided by two, or by multiplying the mean wind speed by approximately 0.798. This mathematical relationship shows that for a Rayleigh-distributed site, the most frequent wind speed is always lower than the mean wind speed because the distribution is positively skewed, meaning it has a longer tail on the side of higher wind speeds.

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In wind resource assessment, if a site follows a Rayleigh distribution, what is the specific relationship between the mean wind speed and the most frequent wind speed?