<p>The (statistical) variation is not the same as the gradient. The gradient is a measure how things change from here to a nearby point, or from now to a point in the near future. The variation, on the other hand, just says how often wind speeds of different magnitude happen.</p>

<p>For example: If the wind were to blow at exactly 30 km/h all the time, then the average wind velocity is going to be 30 km/h and the variation is zero. Conversely, if the average is 30 km/h and the variation is large, then the wind will blow at different speeds, typically quite different than 30 km/h, but so that the <em>average</em> is 30 km/h. </p>

<p>What's the importance in the context you're considering? If the variation were small, it would be fairly easy to design wind generators because they would only have to accommodate exactly one wind speed, which happens to be blowing all the time. On the other hand, if the variation is large, then you have to design wind generators so that they can produce electricity when there is little wind, when there is the average wind speed, and also when there is a storm. It's a bit like designing aircraft for (slow) take-off and (fast) cruise speeds -- it's complicated, as you can see with all of the flaps and levers moving on the wings of planes between start and cruise phase.</p>

CC BY-SA 4.0
2019-06-26T03:09:53.207Z
2019-06-26T03:09:53.207Z
Wolfgang Bangerth
<p>I have been reading some documents about meteorological data and many of them mention the <strong>second moment of wind velocity</strong>.
I guess it has to do with the way the wind is changing but in such case I would call it a gradient... Therefore, what is it's correct physical representation? </p>

CC BY-SA 4.0
2019-06-25T09:10:27.890Z
I understand it's the variance but does this mean how the wind is variating as well?
Federico Gentile
CC BY-SA 4.0
2019-06-25T09:16:43.420Z
ok thanks a lot :) I am still confused why they do not use something like the gradient though to represent how the wind is variating
Federico Gentile
CC BY-SA 4.0
2019-06-25T09:20:26.503Z
with common you mean that variance and gradient have same meaning?
Federico Gentile
CC BY-SA 4.0
2019-06-25T19:58:20.223Z
Lots of comments hovering around the answer here... I don't feel sufficiently expert on statistics and turbulence to give a good answer... hopefully somebody else does? :-)
Semidiurnal Simon
<meteorology><wind><weather-forecasting><statistics><turbulence>
What is the physical meaning of second moment of wind velocity?
Federico Gentile
# What is the physical meaning of second moment of wind velocity?

(Asked by: username_0 on 2019-06-25)

I have been reading some documents about meteorological data and many of them mention the **second moment of wind velocity**.
I guess it has to do with the way the wind is changing but in such case I would call it a gradient... Therefore, what is it's correct physical representation?

**Tags:** meteorology, wind, weather-forecasting, statistics, turbulence

> **Comments:**
> **username_0**: I understand it's the variance but does this mean how the wind is variating as well?  
> **username_0**: ok thanks a lot :) I am still confused why they do not use something like the gradient though to represent how the wind is variating  
> **username_0**: with common you mean that variance and gradient have same meaning?  
> **username_1**: Lots of comments hovering around the answer here... I don't feel sufficiently expert on statistics and turbulence to give a good answer... hopefully somebody else does? :-)  

---

## 1 answers

### Answer by username_2 on 2019-06-26. Score: 2 | Accepted answer

The (statistical) variation is not the same as the gradient. The gradient is a measure how things change from here to a nearby point, or from now to a point in the near future. The variation, on the other hand, just says how often wind speeds of different magnitude happen.

For example: If the wind were to blow at exactly 30 km/h all the time, then the average wind velocity is going to be 30 km/h and the variation is zero. Conversely, if the average is 30 km/h and the variation is large, then the wind will blow at different speeds, typically quite different than 30 km/h, but so that the *average* is 30 km/h.

What's the importance in the context you're considering? If the variation were small, it would be fairly easy to design wind generators because they would only have to accommodate exactly one wind speed, which happens to be blowing all the time. On the other hand, if the variation is large, then you have to design wind generators so that they can produce electricity when there is little wind, when there is the average wind speed, and also when there is a storm. It's a bit like designing aircraft for (slow) take-off and (fast) cruise speeds -- it's complicated, as you can see with all of the flaps and levers moving on the wings of planes between start and cruise phase.


---

