Energy is a key factor that contributes to populations’ socio-economic well-being. With the growing population coupled with development needs in terms of energy demand , the access to sustainable energy remains a major challenge. With the gradual depletion of traditional energy resources and their environmental impact, it is detrimental to align the energy sector development strategies with envronmental protection for sustainable development . In this context, the contribution of renewable energy to the global energy mix has steadily increased . Among the sources of renewable energy, wind power appears to be the most visible over these recent years because of its safety for the environment and its inexhaustible nature .
However, a study commissioned by the African Development Bank explicitly reveals that in the Sub-Saharan Africa and particularly in Burkina Faso, several major obstacles challenge the use and the development of this source of energy . One of these obstacles is the lack of dada on wind potential within the hub to estimate the resource available. More often, the wind resource available within the hub of a wind turbine (more than 10 m) is generally assessed through the installation of large towers or even more expensive equipment, including the LIDAR system (Light Detection And Ranging) or SODAR (Sonic Detection and Ranging) to perform the measurements. These tools used to assess the resource therefore increase the cost of wind projects by making them often economically unsustainable .
To address this difficulty, research has been directed towards the extrapolation of wind speeds measured by observing stations already available, from a standard measurement site (10 m altitude) to another site with energy interest (level of wind turbine hub) based on empirical models applicable only in the surface layer  . This is the case of the empirical formulas of the power law and the logarithmic law developed by several authors including  - . However, after having tested their reliability on other sites, the authors of   have obtained less satisfactory results. The authors therefore propose the establishment of a specific model for each site. In our study area, wind data in the hub of a wind turbine are not available, except the average NASA satellite data  calculated over a day at 50 m altitude. In addition, previous studies conducted on the assessment of wind resource at the study site by authors of  were limited to 10 m of altitude where data are measured every three hours.
Thus to solve this problem of lack of wind data on the study site at an altitude higher than 10 m, the NASA satellite data at 50 m and the data of the National Agency of Meteorology of Burkina (ANAM) at 10 m altitude were used. The best equations for estimating the wind speed at altitude from the power law and the logarithmic law are then established. Wind shear parameters contained in these models based on the atmospheric stability conditions were then determined and a comparative study between the models available in the literature and the data was made. The most suitable model for the site was used to extrapolate the vertical day and night wind profile based on data collected at 10 m above the ground. Based on the profile obtained, we assessed the wind potential in BoboDioulasso between 20 m and 50 m above the ground and studied its variability during the year.
2. Presentation of the Study Environment and Data Used
Burkina Faso, is a vast country of 274,200 square kilometers, located at the heart of West Africa, between parallels 9˚20' and 15˚05' of the North Latitude and meridians 2˚20' of the East Longitude and 5˚30' of the West longitude at an average altitude of 300 m above the sea level. It is a landlocked country surrounded by six (06) countries: Mali in the West and the North, Niger in the East, and by Benin, Togo, Ghana and Côte d’Ivoire in the South. According to the rainfall and temperatures recorded in Burkina Faso, there are 3 large climat zones. The Sahelian climat zone located in the North of the 14th parallel characterized by an annual rainfall of less than 650 mm. The Sudano-Sahelian climat zone located between the parallels 11˚30 and 14˚ of North latitude characterized by an annual rainfall ranging between 650 and 1000 mm. The Sudanese climate zone in the South with 11˚30' of North latitude, characterized by an annual rainfall above 1000 mm . Our study was conducted on the Bobo-Dioulasso site (Sudanian climat zone); data recorded and provided by the meteorological station of the Burkina Faso National Meteorological Agency (ANAM) during the period from January 2006 to December 2016 were used. The series of data used included those on wind speeds and temperature. The observation was made each every three hours using a cup anemometer placed on a 10 m pole above the ground. Ambient temperature was also measured on the site, at each every three hours. Daily wind speed data recorded at 50 m above the ground and provided by the NASA Prediction of Worldwide Energy Resource (POWER)  during the same measurement period were used. Figure 1 gives an overview of the study area and Table 1 gives the geographic coordinates of the site for the study.
3.1. Vertical Extrapolation Method of the Wind Speed
Both most widely used wind speed extrapolation methods that take into account roughness and atmospheric stability conditions   were used, i.e. the log-linear law based on the similarity model and the power law    that were evaluated on our study site in order to choose the most optimal one.
3.1.1. The Log-Linear Law
This law takes into account the shear speed, the roughness length and the
Figure 1. Geographic location of the study site.
Table 1. Geographic coordinates of the sites studies.
Monin-obukhov length. It is expressed by the following formula  :
where L, is the Monin-Obukhov length, the roughness length, the friction speed in m/s, is the stability correction function, and the Von Karman constant assumed to be 0.4 and Z the height. The expression of the stability correction function is given by Paulson . We have the following equation for unstable atmospheric conditions :
In stable atmospheric conditions , the expression is given by the Equation (4).
The method used to calculate the Monin-Obukhov length that characterizes the stability of the surface layer is based on the expression from the Monin and Obukhov studies  and is given by the Equation (5):
where represents the covariance of the vertical wind component and the ambient air temperature, g the gravity, , the average temperature, Von Karman constant. Based on Cauchy-Schwarz inequality which is based on covariance mathematical properties, we therefore calculated . So we have  :
where is the variance of the air temperature and , the variance of the vertical wind component. According to , the standard deviation of the vertical wind component can be estimated from the parameter which is the standard deviation of the horizontal wind component:
where v is the horizontal wind speed recorded by the anemometer at 10 m above the ground. The results obtained with the Equation (5) during the day cycle were used to characterize the stable or unstable atmospheric conditions. Table 2 details the various atmospheric stability classes according to Obukhov length.
The roughness length and the friction speed can be calculated according to the various stability classes of the atmosphere by changing variables and using the Equation (1)  :
The equation (1) therefore becomes:
3.1.2. Power Law
Power law was proposed by G. Hellman and is based on experimentation. This method is easier to use in general for engineering studies  and thus enables to address difficulties encountered in using the linear-log law in terms of input
Table 2. Atmospheric stability class according to Obukhov length .
parameters. Therefore, we have    :
where is the wind speed at 10 m. α is the shear coefficient of the wind. It depends on atmospheric stability and roughness  and provides information on the variations of wind intensity according to the altitude. Based on the Equation (11), α can be calculated by the properties of logarithms  :
According to studies by Huang (1979)  reported by , the wind shear coefficient varies with unstable and stable atmospheric conditions. It is expressed by the equations (13) and (14), respectively.
Based on the power law and logarithmic law, parameters α, P and H are calculated by monthly and annual data fitting. Based on the values taken by these parameters, we therefore deduce the best wind speeds extrapolation equations in altitude, using statistical error estimation tests.
3.1.3. Model Validation Test
Statistical tests of the root mean squared error (RMSE) and mean absolute value (MAE) were used to assess the errors made by the prediction. These indicators are the most used and the model is better when they are close to zero . Using Equations (15) and (16), errors between speeds measured and those estimated are assessed    :
where represents observations, the various estimates or forecasts, and N the total number of observations of wind speed.
3.2. Wind Resource Assessment Method
3.2.1. Analysis of Statistic Distribution of Wind Speed Data
Over these recent years, several distribution functions are developed and tested by several researchers around the world to identify those best suited for wind energy applications. These include beta, Erlang, exponential, gamma, log-logistic, normal log, Pearson V, Pearson VI, uniform, and Weibull distribution functions   . On our study site, it has been demonstrated that the Weibull distribution with two parameters (shape parameter and scale parameter) developed in 1951 by Waloddi Weibull is suitable to analyze and represent the wind rate distribution. This distribution was therefore used and expressed as follows  .
where k is the dimensionless Weibull shape parameter, c the scale parameter in m∙s−1, v the wind speed in m∙s−1 and the probability of observing the wind speed v, or also called the frequency of occurrence. The corresponding Weibull cumulative density function is given in  :
The expressions of the mean wind speed v, and the standard deviation σ according to Weibull parameters are presented by the Equations (19) and (20), respectively:
is the gamma function expressed by the Equation (21):
Several methods are used to determine Weibull parameters   . The one used in this study to calculate the Weibull parameters is the maximum likelihood method  . The parameters of form k and scale c are estimated using the Equations (22) and (23), respectively:
where is the wind speed at the course of time i and n is the non-zero wind speed observation number. Equation (22) can be solved using an iterative procedure (k = 2 is the appropriate initial conjecture), then Equation (23) is solved explicitly. Equation (22) must be used for non-zero wind speed data points only.
3.2.2. Wind Power Density
Wind energy power density is the most important feature of wind. It represents the amount of mechanical energy produced by wind. Assuming that S is the cross-cutting section through which wind blows perpendicularly, the mean wind power density is given by the relation (24)  :
With representing the power carried by the wind speed v.
By integrating Equation (24), we get the expression of the average available power density given by the relation (25).
where represents the density of the air according to the altitude. In this study, we will keep air density constant because its variation is not significant so that it does not impact the calculation of the wind resource .
4. Results and Discussions
4.1. Characteristics of the Wind Speed in the Surface Boundary Layer in the Study Area
4.1.1. Vertical Profile of the Wind Speed
The results obtained on the characteristics of wind speed in the surface boundary layer in the study area are summarized as follow. Figure 2 shows the vertical wind speed profile fitting curves for a typical day, then for the whole month, based on the power law and logarithmic law. Table 3 summarizes the values of parameters P and H obtained after monthly fitting. The fitting coefficients (α, P, H) obtained is different from one month to another and show that the vertical profile of the wind does not produce the same variations depending on the altitude during the year. The analysis of Figure 2 shows that the vertical profile of the wind speed fitted by the power law and the logarithmic law corresponds to the measurements whatever the period of the year. RMSE values and MAE coefficients obtained and summarized in Table 4 are very low and very close. This very low value can be explained by the limited number of measurement level of the wind speed (10 m and 50 m in our study).
Despite this limit, these low values enable us to validate these various fitting equations based on the power law model and the logarithmic law as extrapolation models of the wind speed at the Bobo-Dioulasso site. Both laws can therefore be used to model the profile of the vertical wind speed at our study site as reported by the studies in  . Near the ground, there is a significant wind speed variation that would be due to the impact of roughness and obstacles encountered on the ground, which decreases with altitude. Figure 3 shows the annual best-fit line of the vertical wind profile by applying both laws and the fitting equations. The average annual speed at 10 m above ground using data is 3.02 m/s and 4.39 m/s at 50 m. The estimation errors (RMSE, MAE) between both laws and data measured are very small as abovementioned, i.e. 1.40 × 10−15; 1.33 × 10−15
Figure 2. Fitting of monthly wind speed vertical profile from January to December (2006-2016).
Table 3. Parameters to fit log-linear and power law models on Bobo-Dioulasso site.
Figure 3. Fitting of the annual wind velocity vertical profile (2006-2016).
and 8.88 × 10−16; 8.86 × 10−16 respectively for power law and logarithmic law.
4.1.2. Parameters of the Model
Figure 4 shows the average monthly variations of the wind shear parameters. This is the wind shear coefficient (Figure 4(a)), the roughness length of the surface (Figure 4(b)), and the wind friction speed (Figure 4(c)). The coefficients of correlation between the wind shear coefficient and the friction speed, the roughness and the friction speed, as well as the wind shear coefficient and the roughness are estimated at 0.64, 0.55 and 0.90, respectively. These variations show that these three parameters are correlated, notably the shear and the roughness of the soil.
Roughness is an increasing function of wind shear and ground friction speed near the surface. The highest values of these three parameters are observed in March and October, estimated at 0.28; 0.61 m; 0.4 m/s and 0.29; 0.68 m; 0.35 m/s, respectively. In August, the lowest values of the wind shear coefficient, the
Figure 4. Mean wind shear parameters, (a) mean shear coefficient, (b) mean roughness length, (c)mean shear velocity (2006-2016).
average surface roughness length and the friction speed are estimated at 0.16, 0.04 m and 0.20 m/s, respectively. On an annual basis, the values of the shear coefficient, the average surface roughness length and the friction speed are estimated at 0.23; 0.28 m and 0.34 m/s, respectively. The low values observed for roughness could be due to changes in the soil surface coverage on the site (tree Savannah). The wind direction also influences this variability, notably the various obstacles encountered on the ground (buildings or other structures) and which would be source of cause the high values noticed in March and October. Using the studies in the , Hellmann coefficient value indicated for such a zone (tree Savannah) is estimated between 0.24 and 0.33. This result is close to that found on our study site and estimated, on average, between 0.16 and 0.29. When referring to the study by Landry et al.  on the Burkina Wind Atlas, the roughness length value in this area is between 0.1 m and 1.5 m without taking into account the stability conditions. Our results show that the roughness length values are close to those abovementioned and vary from 0.04 to 0.68 under the same conditions. This gap could be explained by the model (commercial anemoscope Software) and the input data (climate data, topographic data, land use data) used to make estimates in .
4.1.3. Comparative Study of Wind Speed Extrapolation Models
Figure 5 and Figure 6 show a comparison between some wind speed extrapolation models taken in literature, fitting equations requiring fewer parameters and data. It should be noted that the wind shear parameters obtained without taking into account the stability conditions of the atmosphere on our site were used in these extrapolations models. MAE error estimators assessed between measures and models are presented in Table 5. The analysis of the results obtained shows that, throughout the year, the fitting equation gives the best fitting of the vertical wind profile with the lowest values of MAE shown in Table 5. Considering the annual wind profile, Mikhail model and power 1/7 model underestimate the empirical data while the models by Justus and Mikhail, Kasbadji, and that of the variable coefficient overestimate data, as shown in Figure 6. However, in February, April, May, October, November, December, Kasbadji model produces a
Figure 5. Monthly comparison of wind speed vertical extrapolation models (2006-2016).
Figure 6. Annual comparison of wind speed vertical extrapolation models (2006-2016).
Table 4. Square root of the mean squared error (RMSE) and the Mean Absolute Error (MAE) for various laws corresponding to the operating range 10 - 50 m (2006-2016).
Table 5. Mean Absolute Error (MAE) between models and the measure corresponding to the extrapolation range of 10 to 50 m (2006-2016).
good fitting with data. The estimation of MAE errors gives 0.003; 0.01; 0.01; 0.02; 0.01; 0.03, respectively. Justus-Mikhail model also provides a good approximation of the wind profile for February, March and November. The estimated MAE values for these months are 0.09; 0.04 and 0.01, respectively. In short, this comparative study also confirms the results of     that propose the establishment of an empirical wind extrapolation model for each site.
4.1.4. Vertical Profile of Day and Night Wind Cycle
Figure 7 shows Obukhov length variation during its day and night cycle. Obukhov length is calculated using Equation (5). Referring to Table 2, an analysis of the graphs in this figure shows that from 10 am to 6 pm, the atmosphere is generally unstable while it is stable over the other periods of the day. These results are confirmed by a large number of studies such as those by   which show that the atmosphere is unstable during the day.
The lowest values on our study site, recorded in January, February, March,
Figure 7. Monthly variation of day and night cycle of Obukhov length for typical day for the Bobo-Dioulasso site (2006-2016).
Table 6. Shear coefficient values according to the atmospheric stability.
April, May and June, which correspond to the great part of the dry season in the study area (Bobo Dioulasso), are of −0.47 m, −0.65 m, −0.79 m, −1.16 m, −2.59 m and −0.83 m, respectively. However we record low values in September and October which are −1.75 m and −1.34 m, respectively. The highest values recorded during the unstable period of a typical day in July and August, which correspond to rainy season periods , are −0.23 m and −0.15 m, respectively. These results show that during the day and periods of high temperature at the ground level, such as in dry season, the atmosphere is more unstable due to intense convection of air masses. This is consistent with the statements by  . In addition, in November and December, months of dry season, values close to those obtained during the rainy season are recorded. They are estimated at −0.19 m, −0.17 m, respectively. These values obtained in November and December could be explained by the gradual arrival of the Harmattan in the study area. Regarding the stable period of the day (from 18:00 to 10:00), highest values are recorded from January to May and vary from 1.5 m (February) to 7.54 m (March) while the months of the rainy season record values that vary between 0.67 m and 1.13 m. Based on these observations, the average vertical wind profile is presented during the daytime cycle between 10:00 and 18:00 and the average profile of the night cycle between 18:00 and 10:00 am. From the power law requiring fewer parameters (Equations (11), (13) and (14)), the wind shear coefficient and wind data recorded at 10 m from the ground, the profiles can be determined by extrapolation following atmospheric stability conditions. Table 6 summarizes the values of the shear coefficients according to atmospheric stability conditions.
4.2. Variability of Wind Energy Potential on the Study Site
4.2.1. Weibull Distribution Parameters
Table 7 shows the variation of Weibull parameters according to the altitude during the months of the year. We have noticed that both Weilbull parameters (c and k) are an increasing function of the altitude. However, the shape parameter k increases very few according to the altitude, contrary to the scale parameter. The shape parameter k varies from 2.30 in September at 20 m to 2.93 in January at 50 m. The low values of k ( ) show the predominance of weak winds, k = 2 of isotropic conditions, for k values between 1 and 2, winds are scattered in all directions (widespread distribution), while values higher than 2 show the privileged direction (limited distribution) . High k values are encountered during the windiest months while the low ones are during the least windy months. Regarding the scale parameter c, it varies from 3.68 m∙s−1 in September at 20 m to 5.58 m∙s−1 in March at 50 m.
4.2.2. Variation of Wind Energy Density
In Figure 8, the average monthly wind energy density is presented monthly and annually. The wind energy density at the Bobo-Dioulasso site, belonging to the Sudanian climate zone varies according to the months of the year and is strongly influenced by the various seasons of the year (dry season and rainy season). The graph in Figure 8 shows two peaks obtained during the year. The first peak appears on the site in March or May and the second peak in October or December depending on the altitude. The site shows an increase in wind energy from January to May, followed by a decrease from June to August. From September to December, there is an increase again. These various variations were observed between 20 and 30 m altitude. From 40 m to 50 m, the first peak is obtained in March. The period of the year during which wind energy production is at the highest level is therefore from January to June and in December. The unfavorable period of production is from July to November on the study site.
The amount of energy available at 20 m from the ground at the Bobo sites varies from 36.43 W∙m−2 (August) to 71.13 W∙m−2 (May). At 50 m from the ground, the power density varies from 45.29 W∙m−2 (August) to 118.82 W∙m−2 (March). The average annual power density value is estimated at 53.13 W∙m−2 at 20 m and at 84.05 W∙m−2 at 50 m, accounting for 36.78% growth rate.
These various results were compared with studies of   carried out on similar sites in West Africa. As a result, in the West African Savanna and Sahelian
Table 7. Shape and scale parameters for the Bobo-Dioulasso site for 20 m, 30 m, 40 m and 50 m.
Figure 8. Monthly distribution of the average power density on the Bobo-Dioulasso site from 20 m to 50 m (2006-2016).
zones, particularly in Northern Côte d’Ivoire, Mali, Chad and Niger, wind potential varies from one place to another. This is the case of the Korhogo site in the Savannah zone in Northern Côte d’Ivoire, which wind potential on a monthly basis is more favorable in May, estimated at 29.28 W∙m−2 at 10 m, while on our study sites (Bobo Dioulasso), the maximum value is 49.80 W∙m−2 (May) at the same altitude of 10 m. Our value is therefore higher than that obtained on the site of Korhogo in the North of Côte d’Ivoire. Didane et al.  conducted a study on the wind potential in Chad and have elaborated a complete wind map of the country. The results show that power density values vary considerably from one area of the country to another. For example, for the Abéché, Am’Timan, Ati, Bokoro, Bousso, Doba, Faya-Largeau, Mao, Mongo, Moundou, N’Djamena, Pala and Sarh sites, the annual wind potentials are 68.80 W∙m−2, 8.04 W∙m−2, 10.06 W∙m−2, 12.21 W∙m−2, 6.73 W∙m−2, 26.03 W∙m−2, 45.29 W∙m−2, 24.07 W∙m−2, 50.54 W∙m−2, 31.41 W∙m−2, 64.63 W∙m−2, 54.80 W∙m−2, 16.58 W∙m−2 at 10 m. As for the Sahelian sites of Goundam, Niafunke, Timbuktu, Koro, Kayes, Gao, Nioro, Bandiagara, Mopti, San, Kangaba, Kadiolo in Mali (day wind potential and night wind potential) at 50 m, the average annual wind potentials are 185 W∙m−2, 170 W∙m−2, 136 W∙m−2, 136 W∙m−2, 122W∙m−2, 119 W∙m−2, 110 W∙m−2, 101 W∙m−2, 95 W∙m−2, 92 W∙m−2, 60 W∙m−2, 51 W∙m−2, respectively. At the Bobo-Dioulasso site (Burkina Faso), the annual wind energy potential is estimated at 84.05 W∙m−2 at 50 m. The differences between our values and those obtained at similar sites could be due to the measurement time scale of the wind data used to perform these various studies or to slightly different climate conditions or the extrapolation models used by some authors. To characterize the sites likely to host wind turbines or large scale wind applications, the  studies reported by , authors believe that sites can be classified based on their wind power density. Thus, from this table and at 50 m, the areas given in class 1 (0 W∙m−2 to 200 W∙m−2) are generally not suitable for large-scale and economically justifiable wind turbine applications, while class 2 areas (200 W∙m−2 to 300 W∙m−2) are marginal. Areas that can be classified in Class 3 (300 W∙m−2 to 400 W∙m−2) or higher are suitable for most wind turbine applications  . Given these and the results presented in Figure 8, the study site is not suitable for large scale electrical power generation. But it could be suitable for the installation of small and medium size wind turbines to address electricity deficit in rural areas.
This study was conducted in two steps, the first of which consisted of developing specific extrapolation models at the Bobo-Dioulasso site belonging to the Sudanese climate zone in Burkina Faso. The second consists of using these various extrapolation models to assess wind resource at 20 m and 50 m. The power law and the logarithmic law models were therefore assessed for the various classes of atmospheric stability. Parameters of these models were estimated, then these models were compared to the models available in the bibliography. The best model adapted to the site was then used to extrapolate the vertical profile of the day and night cycle from the data measured at 10 m from the ground. The main results of our study on the first phase of our study are summarized as follows:
Power law and logarithmic law give the best fitting of the mean wind speed on a monthly and annual bases. On the site, the atmosphere is generally unstable from 10:00 to 18:00 and stable during the other periods of the day. The mean annual shear coefficients of the wind during the convective day and night cycle are estimated at 0.17 and 0.23, respectively.
The comparative study between wind extrapolation models and data shows that the best fit equation used is always in agreement with data of low MAE values. The development of a model per site is therefore recommended in order to reduce errors in the estimation of wind potential at altitude.
The study of the assessment and the variability of the wind potential between 20 m and 50 m was conducted during months of the year by using the results obtained on the vertical wind profile. The following conclusions can be drawn: Months of the dry season, notably April and May are the windiest of the year.
Wind potential assessed reveals that the largest amounts of energy are generally recorded during months corresponding to the dry season with peaks in March, May or June depending on sites. The amount of energy available in terms of power density at 20 m from the ground at the site varies from 36.43 W∙m−2 (August) to 71.13 W∙m−2 (May). At 50 m from the ground, the power density varies from 45.29 W∙m−2 (August) to 118.82 W∙m−2. The average annual quantity of power density is estimated at 53.13 W∙m−2 at 20 m and at 84.05 W∙m−2 at 50 m, accounting for 36.78% increase rate.
With regard to the power density values, our study site is only suitable for small and medium size wind turbines, producing electrical energy. Specifically, wind turbines with a starting speed ranging between 2 and 3 m∙s−1 will be valuable. This production can therefore provide people with energy autonomy, particularly in rural areas for activities including pumping water, heating water and generating electricity. It should be noted that it will be possible to identify a limited number of sites with acceleration effects, located near an existing network, on which a wind farm of medium size and economically feasible can be constructed. These results are therefore useful for those who want to invest in wind energy to efficiently use this source of energy in our country. In the future, the fitting performance of the power and logarithmic laws will be considered for high resolution temporal and multi-level data. This will lead to an optimization of wind energy resource estimate.