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Why doesn monthly mean wind speed match the square root of the sum of the squares of the monthly U and V winds?

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Why doesn monthly mean wind speed match the square root of the sum of the squares of the monthly U and V winds?

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This applies to data sets with winds of higher temporal resolution, such as daily. Wind speed over a month should be calculated ideally by averaging the wind speed at a higher temporal frequency (e.g., daily). By deriving wind speed from the monthly average U and V winds, a significant part of the wind speed is missed. You might notice this when making wind vector plots from our various web pages. For some data sets, a wind speed variable is made available that is separately calculated from higher temporal frequency U and V winds. You should use that if available. Note that the vector wind direction will be correct when using the monthly mean U & V winds, although the speed will not.

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