First of all, there is one more - vertical component of the wind. In some tasks this needs to be taken into account.

To calculate wind speed it's possible to average magnitude and direction separatly. You can average value of sine and cosine for wind direction and then use arcsine and arccosine to get wind direction.

The numerical value of wind speed dramatically depends on the location of the measuring device, the presence of nearby wind-disturbing objects, the altitude of placement, the altitude relief of the terrain and the design of the device. In particular, on the geometric dimensions of the device and the moment of inertia of its rotating elements. At small time intervals, wind speed is pink noise. Therefore, there are certain problems in comparing wind speed obtained by different devices using different methods. The difference can be two to four times or more.

Averaging wind data requires careful consideration of its vector nature, as both speed and direction are involved. There are two primary methods to average wind measurements: scalar averaging and vector averaging.

1. Scalar Averaging:

This method calculates the arithmetic mean of wind speeds without considering direction.

· Procedure:

o Sum all individual wind speed measurements.

o Divide by the total number of measurements.

· Formula:

Scalar Average Wind Speed=1N∑i=1Nwsi\text{Scalar Average Wind Speed} = \frac{1}{N} \sum_{i=1}^N ws_iScalar Average Wind Speed=N1​i=1∑N​wsi​

where wsiws_iwsi​ represents each wind speed measurement, and NNN is the total number of measurements.

· Consideration: This method does not account for wind direction. Consequently, winds blowing from opposite directions could result in a misleading average speed.

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2. Vector Averaging:

This method accounts for both wind speed and direction by averaging the vector components of the wind.

· Procedure:

1. Convert Wind Speed and Direction to Components:

§ Calculate the zonal (uuu) and meridional (vvv) components for each wind measurement: ui=wsi×cos⁡(θi)u_i = ws_i \times \cos(\theta_i)ui​=wsi​×cos(θi​) vi=wsi×sin⁡(θi)v_i = ws_i \times \sin(\theta_i)vi​=wsi​×sin(θi​) where θi\theta_iθi​ is the wind direction in radians, measured clockwise from north.

2. Average the Components:

§ Compute the mean of the zonal and meridional components: uavg=1N∑i=1Nuiu_{\text{avg}} = \frac{1}{N} \sum_{i=1}^N u_iuavg​=N1​i=1∑N​ui​ vavg=1N∑i=1Nviv_{\text{avg}} = \frac{1}{N} \sum_{i=1}^N v_ivavg​=N1​i=1∑N​vi​

3. Calculate the Average Wind Speed and Direction:

§ Speed: wsavg=uavg2+vavg2ws_{\text{avg}} = \sqrt{u_{\text{avg}}^2 + v_{\text{avg}}^2}wsavg​=uavg2​+vavg2​​

§ Direction: θavg=arctan⁡2(vavg,uavg)\theta_{\text{avg}} = \arctan2(v_{\text{avg}}, u_{\text{avg}})θavg​=arctan2(vavg​,uavg​) The function arctan⁡2\arctan2arctan2 computes the arctangent of the quotient, considering the signs of both components to determine the correct quadrant for the angle.

· Consideration: Vector averaging provides a more accurate representation of the mean wind by considering both speed and direction. It's particularly useful when wind direction is variable.

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Choosing the Appropriate Method:

· Scalar Averaging: Use when only the magnitude of wind speed is of interest, and direction is irrelevant.

· Vector Averaging: Use when both wind speed and direction are important, such as in applications involving wind-driven transport or dispersion.

In summary, vector averaging is generally preferred for a comprehensive understanding of wind behavior, as it accounts for variations in both speed and direction.