How Do Skewness and Kurtosis Affect Wind Velocity Measurements?

[member 428835]

Hey PF!

I had a quick question for you about skewness and kurtosis. Suppose that I am measuring velocity in one dimension over time. Can you help me understand how positive or negative skewness relates to velocity? How about Kurtosis?

What if at two different points in space, say point 1 and point 2, and we collected a bunch of wind speeds (again, in one direction) and took the kurtosis of one point's 1 and 2 and found that kurtosis of point 1 was higher than point 2? What could explain this?

Let me know if I've been unclear in this.

Thanks a ton!

Josh

 

[FactChecker]

Skewness indicates if the tail on one side on the mean stretches out farther than on the other side. Suppose you were measuring the total velocities of dust particles in the air. Most dust is settled near the ground and the vast majority is moving slowly. So the mean is near zero. But there are fast moving dust particles going all the way up to the jet stream. So the PDF of velocities would have a very long tail on the fast side and a very short one on the slow side. The skew would be positive.
Kurtosis is always positive. It is closely related to variance. Usually a large kurtosis just indicates a large variance. In that case, the difference in variance should be understood first. But two distributions with the same variance can still have different kurtosis values. In that case, a larger kurtosis indicates that the PDF has fat tails while a small kurtosis indicates thin tails. So the first thing to do when comparing kurtosis of two PDFs is to explain any difference in variance. Then normalize them separately so they have the same variance. Then try to understand any difference in the kurtosis values of the normalized data.

 

[member 428835]

Ahh, thanks!

 

[Hornbein]

Hey PF!

I had a quick question for you about skewness and kurtosis. Suppose that I am measuring velocity in one dimension over time. Can you help me understand how positive or negative skewness relates to velocity? How about Kurtosis?

What if at two different points in space, say point 1 and point 2, and we collected a bunch of wind speeds (again, in one direction) and took the kurtosis of one point's 1 and 2 and found that kurtosis of point 1 was higher than point 2? What could explain this?

Let me know if I've been unclear in this.

Thanks a ton!

Josh

You want to compare the skewness of two samples, each from a different population. To me, the only way this would be meaningful would be to normalize the data from each population to mean zero and variance 1. Then positive skewness would tell you that there are more unusually high positive speeds than negative.

I think that the skewness and kurtosis numbers are not all that useful or meaningful. Usually we just look at a graph.

 

[blue_raver22]

Hi Josh,

Great question! Skewness and kurtosis are statistical measures that can help us understand the shape of a distribution of data. In your case, velocity in one dimension over time.

Skewness measures the asymmetry of a distribution. A positive skewness means that the tail of the distribution is longer on the right side, indicating a higher frequency of larger values. In terms of velocity, this could suggest that there are more instances of higher velocities over time.

On the other hand, a negative skewness means that the tail of the distribution is longer on the left side, indicating a higher frequency of smaller values. In terms of velocity, this could suggest that there are more instances of lower velocities over time.

Kurtosis, on the other hand, measures the "peakedness" of a distribution. A higher kurtosis value indicates a sharper peak and heavier tails, while a lower kurtosis value indicates a flatter peak and lighter tails. In your example, if the kurtosis of point 1 is higher than point 2, it could suggest that the wind speeds at point 1 have a higher concentration of values around the mean, with a few extreme values, while the wind speeds at point 2 have a more evenly distributed range of values.

Factors that could explain this difference in kurtosis between the two points could include differences in topography, climate, or other environmental factors that may affect wind patterns. It could also be due to differences in the measurement method or instrument used at each point.

I hope this helps clarify the relationship between skewness and kurtosis and how they can be applied in your specific scenario. Let me know if you have any other questions or need further clarification.

Best,
[Your name]