Wind Turbulence Intensity Characteristics at 10m Above Ground Along the Cotonou Coast, Benin

The characteristics of the wind turbulence intensity that are essential to know before installing a wind turbine at a site were investigated along the coast of Cotonou in Benin. The average speed, direction, roughness length, friction velocity, turbulence intensity and relationship between the roughness and wind turbulence intensity were evaluated as well. Using the estimators derived from a simple isotropic Gaussian model of turbulent wind fluctuations, we proposed modified models for estimating the turbulence intensity of wind components. Wind speed and direction data recorded at 10 m above ground level from 2011 to 2014 during the first Compact of the Millennium Challenge Account (MCA) in Benin were utilized. The results obtained indicated that the annual average roughness length is evaluated at 1.25×10 m, and the annual mean friction velocity is equal to 0.41 m.s. Peak values of the turbulence intensity vary from 0.3 to 0.6 except during the months of January, April, July, August and September. The high values obtained could jeopardize the production of wind energy during these months. The correlation between the turbulence intensity and roughness length ranging from 0.75 in January to 0.94 in August revealed that these two parameters are linked by an increasing linear function. Finally, modified formulations of the longitudinal and transversal wind turbulence intensity developed from the van den Hurk and de Bruin model and based on the best-fitting approach were proposed. The error estimators (MAE; RMSE) computed to validate these modified models vary respectively from (0.0099; 0.0141) to (0.0614; 0.0890).


Introduction
Electricity generation from wind turbines has gained momentum over the past two decades [1]. The worldwide cumulative installed wind capacity increased from 23,900 MW in 2001 to 539,581 MW in 2017 with a growth rate of about 2000%, which deserves to be valorized in underdeveloped countries [2,3] particularly in Benin. Moreover, this technology can contribute greatly to longterm economic growth of these countries, ensuring energy independence and boosting their local economy [4]. Wind power extraction involves using rotor blades which are the most important part of the aerodynamic device, owing to their profiles. Recently, Rafiee et al. (2016) and Boumrar (2016) [5,6] have shown that during their operation, and due to harsh and varied environmental conditions, those blades are exposed to complex cyclic loadings which induce static or even dynamic stresses. Thus, the decline in energy production, component failures inside and outside wind turbines, including motors, gears, and also cracks on wind turbine blades have occurred in the operation of wind turbines [7], reducing thus the performance of wind farms built offshore and onshore. As mentioned earlier, [1,[8][9][10][11][12][13][14][15][16][17][18][19][20] pointed out that wind turbulence effects at low frequencies have been the major cause of these problems. In addition, due to the sudden changes in wind direction and speed, these effects prompt blade fatigue which is the main source of reduction in the lifetime of wind turbines [21][22][23][24][25]. To better understand the behavior of such a turbulent system, therefore, a correct modeling of these fluctuations is crucial for estimating the fatigue loads on wind turbine blades [26]. Longitudinal and transversal wind fluctuations which provide important information on the turbulence properties in the atmospheric boundary layer [27] are therefore essential inputs for turbulence intensity estimation models that are instrumental in the design and operation of wind turbines [28]. The choice of turbines and their precise location, then, entail a more accurate determination of wind turbulence conditions, taking into account local factors [29]. Considering the major investment in this sector, with the installation of many large wind farms and other projects under planning, the blade design optimization is vital in order to improve their performance [30]. Thus, specific investigations into the local wind characteristics at lowfrequencies (which constitute an appropriate scale for wind energy production) [16,31] must be made whatever the site before wind turbine installation, as recommended by [32,33].
According to [31], West Africa is subject to significant wind fluctuations and seasonal changes due to the movement of trade winds (hot or humid air flow) and thermal winds. Likewise, Benin's coast, one with a considerable wind potential [34][35][36], is also exposed to this wind variability according to [37] and likely to reduce the life span of wind turbines. It is, therefore, imperative to conduct this study in this area of Benin where research work has focused on wind energy potential assessment only.
Our aim is to investigate the wind characteristics at 10 m above ground along the coast of Cotonou (Benin) ones, the knowledge of which is necessary before the installation of a wind turbine at a site. In this respect, the present article seeks to: 1. determine the wind direction and mean wind speed at low-frequency; 2. evaluate the roughness length, friction velocity and turbulence intensity; 3. establish the correlation between the roughness and turbulence intensity; 4. propose new estimators for the turbulence intensity of wind components.

Study Area Description
Benin is situated in the Gulf of Guinea (see Figure 1) between latitude 6°15' N and 12°30' N on the one hand and longitude 1°E and 3°40' E on the other. Its coastline is 125 km long and extends from Hillacondji in the West to Kraké in the East. This strip of land is located between latitude 6°15' N and 7°00' N.

Data Collection
We used a series of wind parameter measurements (wind speed and direction) performed by the Millennium Challenge Account (MCA) compact I and the Beninese Institute for Fishery and Oceanographic Research (IRHOB in French). This measurement campaign spans the period from June 1st, 2011 to April 30th, 2013 and that from December 1st, 2013 to April 30th, 2014. The measurements were recorded every 10-minute, using a cup anemometer and weather vane installed at 10 m above ground level. Figure 2 shows the wind sensor position together with the data logger (receiving station), both of which are located at the seaside.

Friction Velocity
In the surface layer, the flow is governed by the Monin-Obukhov similarity theory. Several methods have been used based on this theory to evaluate the statistical turbulence variables (friction velocity, surface roughness length, Obukhov length, etc.) [39][40][41][42][43][44]. We determined the surface friction velocity * u using the momentum flows ' ' u v (covariance of vertical and longitudinal wind component) and ' ' v w (covariance of vertical and transversal wind component) along with the Monin-Obukhov theory: where u is the longitudinal wind component and v the transversal wind component. We used the Cauchy-Schwarz inequality theory (where x and y are variables) to calculate the covariance. The wind vertical component in Equation (1) is not directly measured by our cup anemometer. Thus, we calculated its standard deviation ( ) w σ from the standard deviation of the horizontal wind speed ( ) U σ , using given by [45]: The cup anemometer provides the horizontal wind speed data and the weather vane provides the wind direction data. As, u and v are not directly measured, we used Equation (3) given by [46]: where U is the average horizontal wind and θ the Wind direction (in degrees).
The variances of the wind components (longitudinal ( where n is the observation number, u the longitudinal wind mean, and v the transversal wind mean.

Surface Roughness Length
In practice, it is difficult to determine this parameter experimentally with precision. But, we approximated it using the model of [48][49][50]: where g is the gravity, c α varies from about 0.011 on sea surface to 0.018 in coastal areas [51,52]. c α = 0.018 was used in this study.

Wind Turbulence Intensity
Here, we calculated the turbulence intensity ( ) I which is the ratio between the wind speed standard deviation and the horizontal wind module, every 10 minutes as was done by [31,[53][54][55], using Equation (8): The longitudinal and transversal wind turbulence intensity is, thus, respectively given by [56]:

Model for Estimating u I and v I
For estimating the fatigue loads on wind turbine blades, the turbulence intensity estimation models are input parameters. Several methods that can be used to estimate u σ and v σ from wind speed and direction statistics have been reported by [45,27]. These models are based on a simple isotropic Gaussian model of turbulent wind fluctuations. One of the best estimators for the fluctuations of wind components according to these authors is the model of [57]. It is expressed by: where θ σ is the standard deviation of wind direction.
Luhar (2010) [27] contends that this model clearly takes U σ into account and, therefore, its performance is much Ground Along the Cotonou Coast, Benin better. However, he noticed some inconsistencies, particularly the hypothesis about the equality between u σ and v σ in the van den Hurk and de Bruin model. He then proposed a more consistent set of relations for 2 u σ and 2 v σ (Equations (12) and (13)) based on the approach of [58], thereby assuming that U and θ are statistically independent and that θ is normally distributed: These models (Equations (11) to (13)) were used to estimate the components of wind turbulence intensity based on Equations (9) and (10). Next, these estimations were evaluated comparing them to our site data. From their respective performance, modified formulations were proposed according to an optimal approach. The method adopted to reach this objective is presented in section 3.2.5.

Correlation Test
We calculated the error estimators between the turbulence intensity models and data using the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) that measure the average magnitude of errors made by the forecast. We also evaluated a quantitative correlation between the turbulence intensity and the roughness using the Pearson correlation test. These estimators are the indicators used the most and calculated with the formulas below [59][60][61]: The smaller the error estimator value is and tends to zero, the better the model is (Akpinar and Akpinar 2007). As to R , it varies from 0 to 1. If 0 R = , there is no linear correlation between the estimations and observations. If 1 R = , the predictions have been perfectly correlated with the observations. When R is near 1, the correlation is very good.

Monthly Average Distribution of the Horizontal Wind
The boxplot of the monthly average distribution of the horizontal wind speed is presented in Figure 3.  Figure 3 indicates that the average wind distribution is not homogeneous during the year, but has two peaks. We recorded the first peak in March with a monthly average speed of 5.02 m.s -1 and the second peak was observed in July with a monthly average speed of about 5.46 m.s -1 . The first peak would be due to the strong air mass convection observed during this hottest month of the year (Ogbonmwan et al. 2016). As to the second peak, it is due to the presence of the West African monsoon during this period of the year which pushes the intertropical front (ITF) towards the Sahel in the North [62] (Ogbonmwan et al. 2016). The least windy months are October, November and December, with the monthly average speeds between 3.88 and 3.94 m.s -1 . The gradual arrival of the north-east Asian trade winds (Harmattan) leading to a southward movement of the intertropical front (ITF) during this period of the year explains the low speeds observed. The lowest daily average speed during the year was observed in November and evaluated at 2.41 m.s -1 , but the highest speed was recorded in July with an average of about 5.92 m.s -1 . We also noted that the atypical wind speeds were estimated at 3 m.s -1 in April, and vary between 4.93 and 4.98 m.s -1 in July. These different results obtained reveal that the great wind variability at our site could cause energy production problems at the blade level. As it was stated above (see Equation (8)), fluctuations vary according to wind speed and turbulence intensity. Figure 4 presents the monthly daily distribution of the horizontal wind speed.     In Figure 5, we generally noted that the longitudinal wind component is low in January. But, from February to March, high longitudinal winds were recorded. These values vary from 01:00 to 10:00 in February and from 01:00 to 18:00 in March. High winds were also observed in April between 01:00 and 06:00, and they become relatively low during the rest of the day. In June, the longitudinal wind speeds increase again before reaching the maxima of the year observed between July and August and evaluated at 5.34 m.s -1 . From September, the longitudinal wind amplitude starts decreasing again until December. Negative values are also recorded for the longitudinal wind in December and January due to the predominance of the north-east trade winds during this period of the year. In Figure 6, the variations of the meridional wind are not similar to those of the longitudinal wind. Indeed, the peak of the year is observed between January and February with a speed estimated at 5.32 m.s -1 in February. From 01:00 to 13:00, the meridional wind reaches its lowest values whatever the period of the year, except January to March and in May between 00:00 to 02:00. From 13:00 to 23:50, the values were relatively higher. Between 06:00 and 08:00 from November to December the negative amplitudes of the meridional wind are noticed and due to the presence of northwesterly winds during this period. We present here the annual daily wind distribution of the longitudinal, transversal and horizontal wind components (see Figure 7).

Annual Daily Distribution of the Horizontal, Longitudinal and Transversal Wind
We noted that the annual average amplitude of the transversal wind increases during the day between 07:00 and 17:00 with a speed varying from 1.62 m.s -1 to 4.38 m.s -1 . After 17:00 the amplitude decreases until 07:00 and reaches its lowest daily speed evaluated at 1.62 m.s -1 . The opposite phenomenon was observed with the annual mean of the longitudinal wind. The peak of this component is reached early in the morning around 05:00 with a speed of 3.79 m.s -1 . During the rest of the time, the amplitude of the zonal wind decreases before increasing again after 22:00. From 10:00 to 01:00, the transversal wind dominates the longitudinal wind. This trend is reversed from 01:00 to 10:00. As to the annual average speed of the horizontal component, it has two peaks. The first peak is less noticeable around 01:40 with an average speed of 4.73 m.s -1 and the second one is recorded around 17:00 and corresponds to 5.05 m.s -1 . During the day from 08:30 to 17:00 we noticed an increase in the horizontal wind speed from 3.8 m.s -1 to 5.05 m.s -1 and, after 17:00, a progressive decrease down to 3.8 m.s -1 .

Wind Rose
The wind rose obtained at the Cotonou site is illustrated in Figure 8.  long dry season (December to March), long rainy season (April to July), short dry season (August to September) and short rainy season (October to November). It can then be noticed that the vast majority of winds come from the south. The southwest (SW) and south-southwest (SSW) directions are the most dominant ones whatever the seasons. Their frequency of occurrence varies from 25 to 45% with instantaneous wind speeds in the order of 5 to 15 m.s -1 . This predominance is caused by the frequent sea breezes on the coast of Benin and the West African monsoon prevailing in the study area at the end of May and extending until September [63]. Winds coming from the North (N) with a speed of 5 to 7.5 m.s -1 and those from the north-east (NE) with a speed between 10 and 15 m.s -1 were mostly observed in the long dry season-with a low frequency of the order of 5%. Some southeast (SE) winds occur with less than 5% as well as some westerly (W) winds noticed during the long dry and rainy seasons, with speeds varying from 5 to 10 m.s -1 . The presence of some westerly (W) and northwesterly (NW) winds was also noted in the study area. During the year except the long dry season there are practically no northerly winds. The arrival of Harmattan in our study area at the end of December until mid-January explains the rare occurrence of the prevailing southerly winds (25%) in the long dry season. Figure 9 shows the monthly daily wind fluctuations. In figure 9, the daily distribution of the horizontal wind fluctuations varies from 5 10 -4 to 1.51 m.s -1 whatever the period of year. The highest fluctuations of the horizontal wind were recorded between 08:00 and 14:00 during the months of February, March, May, June, October November and December. The peaks vary from 0.9 to 1.51 m.s -1 and were obtained in December and May respectively. The low values of the fluctuations were recorded in January, April, July, August and September. As pointed out by [31], these values are, then, indicative and reveal the presence of significant wind fluctuations in West Africa, particularly in Benin according to [37]. Likewise, the monthly average of the standard deviation varies from 0.17 m.s -1 in July to 0.55 m.s -1 in November.

Characteristics of the Statistical Turbulence Variables
Based on Equations (1) to (7), the daily variations of the roughness length and the surface friction velocity at the site of Cotonou on a monthly scale have been respectively presented in Figures 10 and 11. Ground Along the Cotonou Coast, Benin  The surface roughness obtained during the year reached the values of 10 -4 to 10 -3 m. During the diurnal cycles the values were on average higher than those in the nocturnal cycle. The low roughness values were obtained from July to September with a peak of about 6×10 -4 m recorded in July. In the other months, the roughness values are higher. The peaks observed in May, November and December vary from 3 10 -3 m to 4 10 -3 m. The annual average roughness length was estimated at 1.25 10 -4 m. The low roughness values obtained at our site could be due to the wind sensor position which is located by the seaside (as shown in Figure 2). Moreover, the most frequent wind directions at the site come from the sea (south-southwest, southwest direction as illustrated in Figure 8). These results are close to those obtained by [49,64], who worked on similar sites and proposed values of about 10 -4 m. The variations in the friction velocity indicate that this parameter reached a peak of 1.45 m.s -1 in November. The monthly average varies between 0.20 m.s -1 in August and 0.61 m.s -1 in December. The annual average was estimated at 0.41 m.s -1 . These different results are also close to those found by [65,66] at coastal sites and estimated at 0.55 m.s -1 and 0.43 m.s -1 respectively.

Characteristics of the Wind Turbulence Intensity
The wind turbulence intensity was calculated and the different daily distributions are exemplified in Figure 12. The wind turbulence intensity and the surface roughness have the same daily distribution which correlates with the friction velocity (see Figure 12). The highest values of the turbulence intensity were observed in May, October as well as November and evaluated at 0.6. The lowest values were obtained in January, April, July, August, and September with the peak value (0.19) recorded in January. During the other months (February, March, June, and December), the peak values obtained were evaluated at 0.3. Martin et al. [13] showed that the turbulence is high when the peak value exceeds 0.2. Moreover, experimentally, [7] concluded that the threshold value of the turbulence intensity to be used with respect to the optimal planning of wind turbine installation is 0.2. [8-11, 15, 16, 67, 68] asserted that high values of the turbulence intensity have a negative influence on wind turbine blades, especially their lifetime, and lead to a fall in energy production. In conducting wind tunnel experiments, [11] showed that when the wind turbulence intensity increases from 5% to 25%, the wind turbine performance decreases nearly from 23% to 42%. As to the work of [69], the authors believe that a site with higher turbulence intensity has a lower wind power potential and, thus, is less attractive for wind power application. Relying on their work, we can therefore conclude that February, March, May, June and October to December are unfavourable for an efficient use of this energy source. On the other hand, January, April, July, August and September are favourable for wind energy production. Before the installation of wind turbines at our study site, we then suggest taking into account the fatigue loads induced by high turbulence levels observed at the site in the design of wind turbine blades in order to optimize energy production and ensure a long lifetime of wind turbines. Ground Along the Cotonou Coast, Benin Figure 13 shows the monthly correlation between the turbulence intensity and roughness. Different linear equations for estimating the turbulence intensity based on the roughness length were proposed. Pearson's correlation coefficient was determined in order to validate these equations.

Figure 13. (a-l) Linear adjustment between turbulence intensity and roughness length from January to December (2011-2014).
Analysis of Figure 13 reveals that the turbulence intensity and roughness length generally display a pretty good correlation. Indeed, Pearson's correlation coefficient varies from 0.75 in January to 0.94 in August. During May, August, September, and November the correlation between the two parameters evaluated at (0.92; 0.94; 0.92; 0.91) respectively is good and better than that in other months. In February, March, June, July, October and December this correlation is moderately good. Pearson's correlation coefficient varies from 0.80 to 0.89. In January and April we noticed that the correlation is less good compared to the other months and between 0.75 and 0.77. These different values of Pearson's correlation coefficient allow us to validate the use of the different linear adjustments proposed to calculate the turbulence intensity based on the roughness at our site. In short, turbulence intensity is an increasing function of roughness. This observation is consistent with the findings obtained by [70][71][72][73].

Fitting of the Turbulence Intensity of Wind
Components In Figure 14, we compared the adjustment curves of the longitudinal and transversal wind turbulence intensity distribution obtained from van den Hurk and Bruin, Luhar models (Equations (9) to (13)) and from turbulence intensity data. In Table 1 are presented the error estimators (MAE, RMSE) between models existing in the literature and the measurements. Analysis of Figure 13 and Table 1 reveal that the error estimators obtained with van den Hurk and the Bruin model are lower than the ones of Luhar, except the months of June, September, October, November for the longitudinal turbulence intensity and the months of January for the transversal turbulence intensity. The performance of these models is therefore better than that of Luhar's for most of the months. However, the inconsistencies pointed out by Luhar could be the cause of the gap observed between the data and estimation during some months. In order to correct them and unlike the Luhar approach, we modified the existing formulation of [57] by introducing fitting parameters. Using Equations (9) and (11), the modified formulations of u I and v I are then expressed as follows: From the algorithm fminsearch developed under Matlab, we determined the fitting coefficients, k fminsearch function (based on the nonlinear least squares method) which allows finding the parameters that minimize the gap between the theoretical models and the experimental data from an initial estimate was used on Matlab R2013a (8.1.0.604) to determine these adjustment constants. The algorithm of this function uses the simplex search method of [74]. In Figure 15, we present the evaluation of the modified turbulence intensity formulations. In Tables 2 and 3 are presented the values of the fitting constants and the errors (MAE; RMSE) between the estimations obtained from the modified formulations and the measurements. Moreover, the estimation error reduction rate resulting from the modified formulations was evaluated. Analysis of Figure 14 and Tables 2 and 3 show that the proposed modified formulations better reflect the distribution of the wind turbulence intensity ( u I and v I ) at our study site whatever the period of the day and year. Low values of the error estimators (MAE; RMSE) were recorded and vary from (0.0099; 0.0141) in January to (0.0577; 0.0801) in December for the longitudinal turbulence intensity and from (0.0136; 0.0190) in September to (0.0614; 0.0890) in December for the transversal turbulence intensity. The estimation error reduction rates obtained from these modified formulations vary between 6.06% and 83.13%. These two modified models therefore constitute reliable inputs for the evaluation of the loads induced by wind fluctuations on wind turbine blades.

Conclusions
The wind characteristics at 10 m above ground level along the Cotonou coast (Benin) that are essential to know before the installation of a wind turbine at a site have been studied and new estimators for the turbulence intensity of wind components have been proposed. The following concluding remarks can be made: 1. The highest monthly average speed are obtained in July and evaluated at (5.92 ± 0.17) m.s -1 , and the lowest one are recorded in November and estimated at (2.41± 0.55) m.s -1 . The most frequent winds come from southwest (SW) and south-southwest (SSW) directions whatever the season. 2. The annual average roughness length is evaluated at 1.25 10 -4 m and the annual average friction velocity at 0.41 m.s -1 . 3. The turbulence intensity observed indicates high values in February, March, May, June, October, November, and December with peaks ranging from 0.2 to 0.6. On the other hand, during January, April, July, August and September, the values are low, especially in August where they do not exceed 0.12. These months are more suitable for an efficient exploitation of the wind resource available at the site. 4. The turbulence intensity observed at our site is an increasing linear function of the surface roughness. Pearson's correlation coefficient of the linear adjustment varies from 0.75 in January to 0.94 in August. 5. Finally, modified formulations of the longitudinal and transversal wind turbulence intensity obtained from the van den Hurk and de Bruin model and based on a bestfitting approach are proposed. The error estimators (MAE; RMSE) obtained to validate these modified models vary respectively from (0.0099; 0.0141) in January to (0.0614; 0.0890) in December respectively. For optimal exploitation of wind energy at our study site, we suggest that the fatigue loads induced by the high turbulence levels observed at the site during the design of wind turbine blades should be taken into account. In the future, the turbulence integral length scale and the turbulence power spectra will be examined based on high-frequency wind data.