I want to reconstructed a wind speed profile in 10 minutes. I have the average, minimum, maximum and deviation of the 10-minute wind speed profile. How to reconstructed it with the time step of 1 second?
If you only have 10 minute samples, then you don't have the needed information to generate information with a time resolution of 1 second. If you want that type of higher frequency content in your signal, you'll need to make some assumptions about the spectrum of wind. You could use some available assumptions, I outline how to do this in this paper: Control methodology to mitigate the grid impact of wind turbines
BG Rawn, PW Lehn, M Maggiore - IEEE Transactions on Energy Conversion, 2007. It's imperfect but would get you something.
The standard deviation is probably the only point of contact you can use to coordinate these types of models with each other. The max/min could be a kind of sanity check after.
Just a clarification before I may add my two-penny bit:
What exactly are you trying to do ? I saw your project summary, and it appears that you are attempting simulation of an electrical system at simulation time step of 1s, while you have wind data at intervals of 10min that you wish to include within your simulation.
Flow in the atmosphere is the classical example of high Reynolds number flow. Based on the existing evidence we know that fluctuations statistics for the velocity field are non-Gaussian and very intermittent. Despite of this fact most of practical calculations assume Gaussian statistics. The alternative, more realistic approach, is discussed in the paper
https://arxiv.org/pdf/nlin/0408005.pdf
The material discussed in this paper is particularly relevant for the studies of the wind field in the lower part of the troposphere in the context of wind energy and dispersion of atmospheric pollutants.
Actually, I want to get the output power of wind farm with 1Hz wind speed data, in order to analyze the reliability of electronic components in wind farm. Now I find a very good paper in attached below. Hope it could be helpful for others a the similar question.