TLDR: If you are planning to use the weibull curve for the power output of a wind turbine you'd better use yearly data and fit the curve.
Weibull distribution and shape factor
Weibull distribution has two parameters (in some variations):
- Scale: which is close to the concept of average. Its units are actually the units of the average (or m/s in this case).
- shape: which gives it a characteristic shape. Sometimes denoted with a k
Below you can see the effect of shape :
So for a given scale, the shape can be more skewed or symmetric.
Typically, wind velocity distributions have a skewed distribution so values are between 1.5 and 2.0.
For those parameters, usually the mean value is less than the Weibull scale factor. See example below:
The more skewed the distribution, the more the average will deviate from the scale factor.
Variation of wind speed velocity with time interval
As the measurement interval is decreased the wind speed will appear more jagged. As the measurement interval increases the wind speed will appear more smooth. See below for 1 min and 10 [min] comparison.
To capture that behaviour, in a wind data measurement even if the logger can measure (and can store in non volatile memory) every second, usually the data are stored in rows of either 10min or 1 hour intervals. And usually the following data for measurement interval is used:
- average wind speed for interval (or 1 hour average)
- standard deviation of wind speed for interval
- max gust of wind speed for interval
The importance of the above, is that the power output of the wind turbine will be completely different if there is high standard deviation in the wind speed. Wind turbines will perform more efficiently if the wind speed standard deviation is small i.e. constant speed.
Another thing is that you need to take into account is the seasonal variations. Wind speed through January, is not the same as in the other months. Following is the variation for 2018 in a single location.
How to proceed
According to your question you have data to the day for every month in the past couple of years. (following your comment I call yearly data all the data you collect in a year).
Assuming you are doing a Monte Carlo simulation or similar to predict power output, what you can do is take all that data and select one of the following:
- fit a Weibull distribution (e.g. with maximum likelihood method)
- calculate a kernel density estimation.
- Create a Markov chain
Another option (more accurate) would be to take all the data you have for each month separately, and perform one of the above. Then you will have created 12 Weibull distribution you can sample randomly.