## 1. Introduction

[2] The rapid expansion of wind power in recent years has led to the need for suitable descriptions of wind speed. Various expressions have been used [*García et al.*, 1998], amongst which the Weibull distribution has gained widespread acceptance [*Sahin*, 2004]. This function has two adjustable parameters whose values determine its appearance; hence analyses of this function and the methods of parameter calculation always prove to be of interest.

[3] *Pérez et al.* [2004] used 1 month of observations to analyze wind behavior in the low atmosphere and to calculate, among other variables, Weibull parameters by four methods, which may be considered typical from the analysis of references cited in that paper. One restriction of this study is the size of the database. Other methods have also recently been used to calculate Weibull parameters, evidencing the fact that this research line is active, since new methods are being proposed which need to be tested. This paper aims to pursue such relatively unexplored lines of investigation using a sufficiently wide enough database as to observe daily and seasonal parameter evolution.

[4] The computational procedure to obtain the Weibull parameters may be key when a wide database is involved and the calculation complexity can be used to establish a simple classification based on the following three classes: direct methods, methods based on order statistics and iterative procedures. Some of the methods are direct since their values are provided by simple expressions involving little handling of data. This is the case with the method of moments, based on the mean and the standard deviation of data [*Justus*, 1978]. Other methods are based on order statistics, and slow down calculation when extremely long data series are concerned, although the expression used for the parameters may be simple. An easy example of this second kind is the method based on median and quartile wind speeds [*Justus et al.*, 1978]. Finally, iterative procedures imply more complex calculation, which may also prove slower with wide databases, such as the maximum-likelihood method, which is sometimes considered [*Seguro and Lambert*, 2000]. In any case, the wide diversity of methods currently used evidences the fact that there is no single universally accepted procedure to calculate the Weibull parameters and that the choice of whatever method should be conditioned by computational requirements.

[5] In this paper two approaches have been adopted. The first is a theoretical analysis of the Weibull distribution to obtain and condense information into useful expressions. This approach is not common, as most papers simply present the Weibull distribution without any further consideration. However, we have followed a numerical calculation in order to gain an insight into the behavior of this function. Moreover, the domain of the Weibull parameters is another key point, since considerations concerning this function with parameters far from their usual values hold no interest in terms of practical application.

[6] The second approach compares the values of the Weibull parameters using three methods corresponding to the classification considered above. Two of the procedures have rarely been used, justifying their study in an attempt to gain a better understanding of them. The third method is proposed as an alternative which may prove as useful as the more well-known and applied procedures.

[7] The database considered is obtained from a sodar. Extensive experience related to this technique is available at present [*Coulter and Kallistratova*, 2004] and offers two main advantages. First, no hypothesis or upscaling of data in height is required as is usually the case in wind analysis [*Altaii and Farrugia*, 2003; *Archer and Jacobson*, 2003], since data are provided by the device. Second, it provides information on an atmospheric region which is close to the ground, although as yet not well researched, since most analyses are restricted to only a few tenths of meters in height, corresponding to the surface layer.

[8] Finally, random samples have been generated to calculate the accuracy of the Weibull parameters and to investigate a possible trend in this accuracy.