[MUSIC] Before the installation of a wind turbine or a wind farm, an on site feasibility study is always carried out. To forecast the potential electric production, it is important to know the characteristics of the wind on the site. For instance, suppose an industral plans to install a wind turbine whose height is 140 meters above the ground. Before launching the project, he needs to know what energy can be collected from the wind at this altitude over one year. For that purpose, he can use a remote measure instrument such as LIDAR, that measure directly, the wind at the needed altitude. But most often, it will just install a mast with cup anemometers whose height does not exceed 80 meters. In that situation, the wind is measured at the lower height than the altitude of interest and one needs to extrapolate the characteristics of the wind from the lower altitude to the higher altitude. You are going to perform such an analysis from the wind measurements that have been collected on the site of SIRTA with the LIDAR instrument. Here is a sample of the file Lidar_wind_40m_and_140m.txt that we'll use for the quiz. As previously, the three first columns contain the date, the fourth column contains the time in fraction of hour and the two last columns are the horizontal wind velocity at height 40 meters and 140 meters. Note that here, the wind velocity is a 10-minute average, thus you have six data per hour, and these wind measurements have been collected over one year. So with this data, you will study the annual variability of the wind. The first step you are going to go through is to plot the wind velocity distribution at the height of 40 meters. Here's the histogram that you will obtain. In that case, a suitable analytic representation of the wind distribution over one year is the Weibull distribution, whose probability density function is the following. It contains two parameters. c is the scale parameter in meters per second, and k, the shape parameter which is dimensionless. Here is the fit of the experimental measures to the Weibull distribution with the maximum likelihood estimate. Remember, to fit an empirical distribution to a Weibull law, there exists different methods to estimate the parameters k and c. You will use the Power Density method and the Maximum Likelihood Estimate. The knowledge of the probability distribution of the wind velocity allows to assess the energy that can be collected by the wind turbine. However, as we can see on the following graph, the wind distribution depends on the altitude. When we don't know the wind at a high altitude, say, z2, we need to extrapolate the wind distribution from what we know at the lower altitude, say, z1. Using the power of exponent alpha of the boundary layer and the parameters of the Weibull law at the altitude z1, formulae have been derived to compute the Weibull distribution at the altitude z2. In these formulae, the wind velocity is expressed in meter per second. Here, you can see in red, the curves of Weibull fit at the two different altitudes. And in green, the Weibull law, with the parameters extrapolated from 40 meters to 140 meters, using the the formulae of Justus and Mikhail. You are going to do this analysis yourself and will be able to discuss the accuracy of these formulae in a practical case. Now, you can move to the quiz to process yourself, the wind measurements data and investigate all the properties of the probability distribution of the wind velocity.