Estimating vertical wind power density by using tower observation and empirical models over varied desert steppe terrain in northern China

A complex and varied terrain has a great impact on the distribution of wind energy resources, resulting in uncertainty in accurately assessing wind energy resources. In this study, three wind speed distributions of kernel, Weibull, and Rayleigh type for estimating average wind power density were first compared by using meteorological tower data from 15 2018 to 2020 under varied desert steppe terrain contexts in northern China. Then three key parameters of scale factor (c) and shape factor (k) from the Weibull model and surface roughness (z0) were investigated for estimating wind energy resource. The results show that the Weibull distribution is the most suitable wind speed distribution over that terrain. The scale factor (c) in the Weibull distribution model increases with an increase in height, exhibiting an obvious form of power function. While there were two different forms for the relationship between the shape factor (k) and height: i.e., the reciprocal of the 20 quadratic function and the logarithmic function, respectively. The estimated roughness length (z0) varied with the withering period, the growing period, and the lush period, which can be represented by the estimated median value in each period. The maximum and minimum values of surface roughness length over the whole period are 0.15 m and 0.12 m, respectively. The power-law model and the logarithmic model are used to estimate the average power density values at six specific heights, which show greater differences in autumn and winter, and smaller differences in spring and summer. The gradient of the 25 increase in average power density values with height is largest in autumn and winter, and smallest in spring and summer. Our findings suggest that dynamic changes in three key parameters (c, k, and z0) should be accurately considered for estimating wind energy resources under varied desert steppe terrain contexts.


Introduction
Wind energy is a renewable, environmentally friendly, and popular alternative source of clean energy (Islam et al., 2013; brought global cumulative wind power capacity up to 743 GW in 2020. In the onshore market, 86.9 GW was installed, an increase of 59% compared to 2019. China and the United States remain the world's largest markets for new onshore installations (2021). To use this kind of nonpolluting energy, a lot of research has been conducted through a variety of different methods to develop an accurate and reliable wind energy evaluation model.

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The wind speed probability density function can effectively characterize wind speed. Therefore, the wind speed probability density function is of great significance in wind turbine site selection, wind farm design, generator design, determination of the dominant wind direction, and evaluation of wind conversion system management and operation (Masseran, 2015;Li and Shi, 2010). Wind shows great differences with various topographies, landforms, and meteorological conditions. The magnitude and direction of the wind speed exhibit significant differences when wind flows over rough ground or obstacles in 40 a complex terrain. In addition, the surface topography and roughness of the area around the location of the wind measurement tower will affect the predicted wind resources (Kim and Lim, 2017). Therefore, the wind speed probability density function and roughness are important input factors in the estimation of wind energy power density.

Different distribution functions have different fitting effects on the actual wind speed values in different study areas.
According to previous studies (Lo Brano et al., 2011;Celik, 2004;Masseran et al., 2012), seven wind probability density 45 functions have been widely used to fit the actual wind speed values: i.e., Weibull, Rayleigh, Lognormal, Gamma, Inverse Gaussian, Pearson type V, and Burr. These models exhibited different advantages and disadvantages for estimating wind probability density. For instance, (Celik (, 2004) used the Weibull and Rayleigh models to perform a statistical analysis of wind energy density in southern Turkey and found that the Weibull model not only fits the measured monthly probability density distribution better but also provides better power density estimation compared to the Rayleigh model. (Masseran et al. 50 (, 2012) used nine different wind speed probability density function models to describe wind speed conditions in different regions of Malaysia and found that Gamma, Weibull, and Inverse gamma models can fit the wind speed data better. (Chang (, 2011a) used six different probability density functions: namely Weibull, mixture Gamma and Weibull, mixture normal, mixture normal and Weibull, mixture Weibull, and maximum entropy principle distribution. They were tested on the wind data of three wind farms in Taiwan and it was found that, when the current wind speed distribution is unimodal, the fitting 55 effects of these six probability density functions are not significantly different. When the wind speed distribution is bimodal, the other five probability density functions are better than Weibull at describing wind characteristics. In addition, many other probability density functions have been invented to provide more accurate results for the estimation of wind power density in a specific area (Masseran, 2015;Carta et al., 2009;Jaramillo and Borja, 2004).
Among the above-mentioned various types of wind speed probability density functions, the Weibull and Rayleigh 60 distributions are still the more traditional and widely applicable typical wind speed distribution forms. The key issue in the study of the Weibull distribution is how to accurately determine the values of Weibull scale factor c and shape factor k (Azad et al., 2014;kaplan, 2017). Generally, six different methods, i.e., graphical method (Basu et al., 2009), empirical method (Costa Rocha et al., 2012;Kaoga et al., 2014), maximum likelihood method (Andrade et al., 2014;Azad et al., 2014), energy trend method (Chang, 2011b;Akdağ and Dinler, 2009), energy pattern method (Andrade et al., 2014), and the moment 3 method (Azad et al., 2014;kaplan, 2017;Costa Rocha et al., 2012), have been employed to calculate the c and k of the Weibull distribution model. But these methods perform differently in different regions. For instance, (kaplanKaplan (, 2017) found that the energy pattern method and the moment method were the best methods between 2009 and 2013 in the Hatay and Osmaniye regions. When the time series of wind data is provided, the maximum likelihood method is more robust and accurate than other methods (Seguro and Lambert, 2000;George, 2014). In addition, there is a strong time dependence and a 70 high change dependence for the changes in shape factor k and scale factor c (Lun and Lam, 2000;Justus and Mikhail, 1976): e.g., the scale factor c has a power-law functional relationship with height and the shape factor k has a reciprocal logarithmic functional relationship with height. Therefore, we can explore its general laws by studying the seasonal changes and height changes in shape and scale parameters in a specific area.
Roughness length plays a key role in estimating wind energy resources. For example, (Laporte (, 2010) pointed out that the 75 roughness estimation error can cause 5% to 10% of the wind energy resource estimation error. Current wind energy resource assessment is based on measured wind data at a height of 60 to 80 m from the ground, but the actual height of the hub may be greater than these heights. Therefore, we need to combine the surface roughness length and the known wind speed value of the measured height to extrapolate the wind speed value at the height of the hub (Nayyar and Ali, 2020). Theoretically, the surface roughness length z0 is the height at which the average wind decreases to zero with height. z0 varies with the 80 underlying surface (Davenport et al., 2000;Duan et al., 2021). Currently, three approaches (the analysis method, the Charnock method, and the statistical method) have been widely applied to estimate the surface roughness length of offshore wind energy (Golbazi and Archer, 2019). Among them, the statistical method is convenient, as it needs only three layers of wind speed data. After comparing the average value and median value of roughness z0, it is found that the median value is an order of magnitude closer to the roughness length calculated from the other two methods. Therefore, when using the field 85 measurement method to statistically determine the surface roughness length, attention should be paid to using the median value instead of the average value; otherwise huge errors will be generated when the wind speed is extrapolated to the height of the hub, which will have a huge impact on the evaluation of wind energy resources.
As an important production base of wind power energy in northern China, Inner Mongolia is under the influence of the westerly wind all year round. The types of underlying surfaces of wind power towers in China are complex and diverse, 90 including offshore, mountainous, urban outskirts, and grasslands. In Inner Mongolia, especially the desert grassland, the terrain is open, the vegetation is low and sparse, and its wind resources are very rich. So taking the Ningyuanbailiutu site as an example, in-depth data mining was carried out on the 4 heights of 10 m, 30 m, 50 m, and 70 m for the meteorological element data of a 100-meter wind tower from the autumn of 2018 to the summer of 2020 in Damaoqi, Baotou City, Inner Mongolia, China. The following three steps are used to study the three important key parameters that affect the evaluation of 95 wind energy resources: the surface roughness length z0, the scale factor c, and the shape factor k in the Weibull distribution function. Firstly, we need to determine the uniqueness and importance of the Weibull distribution function in the wind speed time series data in the Damaoqi area. This is reflected in the advances and shortcomings of the kernel distribution model, the Rayleigh distribution model, the Weibull distribution function, and the frequency distribution model using actual wind speed, which are used to calculate the monthly, seasonal, and all-time average power densities. Secondly, by studying the monthly 100 and seasonal changes in the surface roughness length and the changes in different incoming flow directions, we will gain a comprehensive understanding of the roughness of the site area in Inner Mongolia. Finally, by using two different models, namely the power-law model with scale parameter c and the logarithmic model with roughness information, the average wind power densities at six specific heights (75 m, 80 m, 85 m, 90 m, 95 m, and 100 m) per month, per season, and throughout the period are calculated. In this way, we discuss the application significance of the two models for wind energy 105 development, and provide a scientific reference for a further understanding of the wind energy resources in the region.
2 Study site, data, and methods

Study site and data
In this study, long-term in-situ measurement was conducted in Damaoqi, Baotou City, Inner Mongolia (42°04'25.738"N,

Kernel, Weibull, and Rayleigh distributions
The kernel density estimator is the estimated probability density function (PDF) of a random variable. For any real values of v, the formula for the kernel density estimator is given by: where v1, v2, …, vi are random wind samples from an unknown distribution, n is the sample size, K(·) is the kernel smoothing function, and h is the bandwidth.
The probability density function of the Weibull distribution is given by: The Rayleigh model is a special and simplified case of the Weibull model. It is obtained when the shape factor k of the Weibull model is assumed to be equal to 2.
The maximum likelihood estimation method is a mathematical expression recognized as a likelihood function of the wind speed data in a time series format. In this method, a lot of numerical iteration can be required to determine the k and c parameters of the Weibull function. The parameter estimation formula of the maximum likelihood method is as follows: The average value and standard deviation of the wind speed can be obtained from the following formulas: respectively.
Alternatively, the mean wind speed can be determined from: if the probability density function is known.
If Eq. (2.7) is solved together with Eq. (2.2) making the substitution of for v, the following is obtained for the 145 mean wind speed: Note that the gamma function has the properties of

Power density
The mean power density for the kernel smoothing function becomes: The mean power density for the Weibull function becomes: The mean power density for the Rayleigh model is found to be: where ρ is the air density.

Weibull parameters
The relationship between scale factor c and height can be expressed as follows: Here c10 represents the scale factor at 10-m height, z represents the height, and  represents the power exponent parameter 160 to be estimated.
The relationship between scale factor k and height can be expressed as follows: where a, b  , and d are unknown parameters to be fitted to the quadratic function.
In addition, as shown in Figure 6c below, (Justus and Mikhail, 1976) gave the following formula for the shape factor k with 165 height: 10 10 (2.14) where k10 is the shape factor at a reference height of 10 m. At a reference height of 10 m, b = b10 is just some constant, whose value can be determined by a least squares fit of relation (2.14) to the data.

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When the wind speed at three or more heights is measured, the roughness length calculated by the least square regression (Archer and Jacobson, 2003;Archer, 2005;Golbazi and Archer, 2019) is: where zR is the reference height, zi is the height of the other three layers, N = 4 which represents 4 vertical layers, and Ui is the wind speed corresponding to the height of the other three layers. In most cases, it is a purely mathematical statistical 175 method, so this simple mathematical method does not require a physical explanation for roughness estimation.
In addition, the above-mentioned method is obtained from the logarithmic wind speed profile, which is a typical form of wind speed profile under neutral stratification. A calculation of the wind speed at other altitudes under the reference altitude can be obtained from the following formula (Golbazi and Archer, 2019;Archer and Jacobson, 2003): where z0 is the estimated surface roughness length, assuming that the friction speed near the ground does not change with height.

Comparisons of kernel, Weibull, and Rayleigh models
There are various statistical distribution functions for describing and analyzing wind data, including normal, lognormal,

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Rayleigh, and Weibull probability distributions (Fagbenle et al., 2011;Ozerdem and Turkeli, 2003). It has been found that the Weibull and Rayleigh distributions are the most accurate and adequate in wind analysis and in interpreting the actual wind speed data and in predicting the characteristics of the prevailing wind profile. A kernel distribution is a nonparametric representation of the PDF of a random variable. A kernel distribution is defined by a smoothing function and a bandwidth value, which control the smoothness of the resulting density curve (Kafadar et al., 1999). In fact, some scholars have used 190 the probability density distribution of wind speed to compare the advantages and disadvantages of the Weibull distribution and the Rayleigh distribution (Celik, 2004). However, in the present study, by quoting the kernel function distribution close to the actual distribution as a reference, two specified distribution functions are being compared with the kernel function to find out which one can better predict the wind speed data in the area.
The monthly, seasonal, and annual average wind speed values and standard deviations calculated using Eqs. (2.5) and (2.6) 195 for the available time series data are shown in Table 1. It can be seen from Table 1 Table 1. The shape factor k values of these three specific seasons are 2.18, 2.13, and 2.11 205 respectively, which are slightly higher than the shape factor k value of the Rayleigh distribution. In combination with Table   1, it is also found that the higher the value of the scale factor c, the smoother the three specific probability distribution curves.
In contrast, as shown in Figure 4d, its three specific probability density curves are very sharp. Finally, when these three specific probability density curves are fitted to the original wind speed data, the kernel distribution fitting the original wind speed data is not only the change trend or probability density estimate, but it is closer to the actual frequency distribution.

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Although the kernel distribution also has specific parameters to control its probability density curve, it does not have the general form of wind speed distribution. Moreover, the k value of the Weibull distribution is~2. To select the specific wind speed distribution form suitable for the Ningyuanbailiutu site, therefore, the model prediction accuracies of the Weibull distribution and the Rayleigh distribution for average wind power need to be further compared.
In the present study, the differences between the kernel distribution, Weibull distribution, and Rayleigh distribution are 215 explored when calculating the average wind power density and the frequency distribution using the original wind speed data. The mean power densities calculated from the measured probability density distributions and those obtained from the models are shown in Figure 5. Analysis of residual error and average percentage error suggests that the average wind power density estimated by the Weibull distribution with specific parameter control is very similar to the kernel distribution, which is closest to the original 240 wind frequency distribution (Figure 5c). The lower limit of the 95% prediction interval is each predicted value minus 1.96 standard deviations, and the upper limit is each predicted value plus 1.96 standard deviations (Figures 5b-d). This suggests that the interval applicability of the three specific distribution models is good.
Although the mean wind power density calculated in this study is in good agreement with the actual grid-connected average power density assumed (Figure 5a), there is significant difference between the two values. This is because the wind turbines 245 are not connected to the grid due to failures, or other wind turbines are not within the range of the wind measurement tower.
As a result, the wind measured by a single wind tower will underestimate the wind speed of other wind turbines.
Analysis of residual error and average percentage error suggests that the average wind power density estimated by the Weibull distribution with specific parameter control is very similar to the kernel distribution, which is closest to the original wind frequency distribution (Figure 5c). The lower limit of the 95% prediction interval is each predicted value minus 1.96 250 standard deviations, and the upper limit is each predicted value plus 1.96 standard deviations (Figures 5b-d). This suggests that the interval applicability of the three specific distribution models is good. In general, we found that Weibull distribution is applicable for checking the wind speed distribution of the Ningyuanbailiutu site. Figure 6 shows the characteristic variation of the scale factor c and the shape factor k with height estimated from the Weibull 255 distribution for original wind speed data during the study period, exhibiting power exponential and quadratic function variations, respectively.  This shows that formula (2.12) has a better fitting effect in the winter of 2018, and a poor fitting effect in the winter of 2019. (Justus and Mikhail (, 1976) found that the mean value of  was 0.23. In the present study, the mean value of a for each month over the two whole years is 0.117, and the corresponding standard deviation is 0.016. Figures 6b and 6c indicate that the two different formula forms have a good fitting relationship for shape factor k and height.

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The RMSEs of Table 2 also suggest that the effect of the quadratic function fitting is better than the logarithmic reciprocal function of (Justus and Mikhail (, 1976). The RMSE of the quadratic function fitted to all data for two whole years is 0.0078, but the RMSE of the logarithmic reciprocal function is 0.0214, which is close to a multiple of 1:3. Both these two types of formula are basically applicable only to heights below 100 m. In addition, from a comparison of Figures 6b and 6c, it can be seen that there will be some different trends in the change in the k value with height, and the increasing or decreasing speed of the k value in the form of a quadratic function will be higher than that found by (Justus and Mikhail (, 1976) when the height is greater than 70 m. This different trend will lead to large errors in estimating wind energy resources above 70 m.
Therefore, it is necessary to intensively observe wind speeds above 70 m and below 100 m in future research, in order to establish a specific function of k varying with height applicable to the site.

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The shape of the wind profile is greatly affected by the surface roughness in the direction of the incoming flow. Thus, surface roughness is a key element in wind energy resource evaluation and forecasting models. In calculating aerodynamic roughness, especially in practical applications, the least squares approximation of the logarithmic profile equation to the measured wind speed profile method has been widely used, referred to as the logarithmic profile method.
After calculating the 15-minute continuous wind speed data using the above method, quality control of the data is carried out.

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In this study, we have eliminated wind speeds greater than or equal to 6.0 m/s at 50 m, and the estimated abnormal roughness data is infinitely large or infinitely small. Figure 7 shows that both the average and median monthly roughness According to the Davenport land type roughness classification (Davenport et al., 2000) and summary of roughness length over the wind-tower sites and the corresponding types (Li et al., 2021), in the case of land types with less vegetation and cropland, the roughness length is generally estimated to be a slightly rough open area of about 0.10 m. The area we studied 295 belongs to the grassland vegetation type, and the roughness estimate should be around 0.13 m, and it will not be classified as rough; that is, the roughness length is as high as 0.25 m. In addition, in a study (Golbazi and Archer, 2019) on the estimation of sea surface roughness length in coastal waters, it is mentioned that the statistical method uses a single constant value of z0 in the representative area, and the median value can be worth recommending. Figure 8 shows the variation in the estimated roughness length in 12 different incoming wind directions. When the wind direction is 120°or 240°, the estimated roughness length is highest, and the median value and average value are about 0.23 m and 0.30 m, respectively. Secondly, when the wind direction is 30°or 300°, the estimated roughness length is lowest, and the median value and average value are about 0.08 m and 0.18 m, respectively. Therefore, between the highest and lowest estimated roughness lengths, there is a specific trend of increasing or decreasing. The above phenomenon can be explained in conjunction with Figure 1 and Figure 3. There is a hillside to the west of the wind tower. Therefore, when the incoming 305 wind direction is 120°or 240°, it is on the windward side or leeward side, respectively, of the wind measuring tower. In this way, there will be a pressure difference, which will increase friction loss and increase the estimate of the effective roughness length. When the incoming wind direction is 30°or 330°, it is found that the wind passing through the wind measurement tower will not be greatly affected by the terrain. The terrain is relatively flat, and the estimated roughness length is close to the normal value of 0.10 m. In addition, in the plot of roughness length estimation with wind direction, there are obviously 310 more data points in the wind directions from 180°to 330°than in the other wind directions. The 240°wind direction has the most data points, which also shows that the site has a southwesterly wind blowing all year round.

Extrapolation of the average wind power density
With the scale factor c changing with height in the form of a power function, and shape factor k changing with height in the What is consistent is that the difference between the two specific extrapolation models increases gradually with height.
Generally speaking, the difference between the estimated average power density values is very small. However, the data and methods used in the estimation of the two models are different. The result of this estimation gives us important guidance for studying two Weibull parameters, namely the scale factor c and the shape factor k, and the surface roughness length 335 parameter.

Applicability of Weibull, Rayleigh models
There are various statistical distribution functions for describing and analyzing wind data, including normal, lognormal, Rayleigh, and Weibull probability distributions (Fagbenle et al., 2011;Ozerdem and Turkeli, 2003). It has been found that 340 the Weibull and Rayleigh distributions are the most accurate and adequate in wind analysis and in interpreting the actual wind speed data and in predicting the characteristics of the prevailing wind profile. A kernel distribution is a nonparametric representation of the PDF of a random variable. A kernel distribution is defined by a smoothing function and a bandwidth value, which control the smoothness of the resulting density curve (Kafadar et al., 1999). In fact, some scholars have used the probability density distribution of wind speed to compare the advantages and disadvantages of the Weibull distribution 345 and the Rayleigh distribution (Celik, 2004;Celik, 2004;Pishgar-Komleh et al., 2015). In our present work, the kernel function exhibits the feature of the smooth function, and also is closer to the actual frequency distribution (Figure 4), which can be used to fit the original wind speed data. Therefore, the kernel function is employed as a medium to compare the pros and cons of the Weibull and Rayleigh functions in the desert steppe area.In our present work, the kernel function also exhibits the feature of the smooth function, and is closer to the actual frequency distribution (Figure 4), which can be used to 350 fit the original wind speed data. Therefore, the kernel function is employed as a medium to compare the pros and cons of the Weibull and Rayleigh functions in the desert steppe are Celik (2003) usemployed the Weibull function to analyzeanalyse wind power density in 6 different regions ofall over the world, and the average percentage errors obtained were relatively low. The reason may be that the scale factor c representing the average wind and the shape factor k are relatively small, the original wind speed is relatively stable and fluctuates little, 355 and also the Weibull function has strong applicability. Celik (2004Celik ( , 2011  compare the applicability of various wind speed distribution functions in the studylocal area. In general, we found that Weibull distribution is applicable for checkdepicting the wind speed distribution ofat the Ningyuanbailiutu site in the northern China. In addition, Aalthough the mean wind power density calculated in this study is in good agreement with the actual gridconnected average power density assumed (Figure 5a), there is significant difference between in these two values. This is 370 because the wind turbines are not always connected to the grid, due to failures, or other wind turbines are not withinout the range of the wind measurement tower. As a result, the wind measured by a single wind tower will underestimate the wind speed of other wind turbines. The limitation of this study is that only one a single wind tower data was derivedmeasured data.
In the future wind energy density estimation, it is worth advocating to erectcollect more wind towers to obtain a more realistic wind resource distribution in the study area.  Table 2 show the spatiotemporal variability of scale factor c, shape factor k, and surface roughness z0, which can be attributed to the following three aspects: (a) The type of surface land and meteorological conditions (Golbazi and Archer, 2019); (b) uncertainty of Weibull parameters calculated using maximum likelihood method (Mohammadi et al., 2016) and uncertainty of roughness length calculated using statistical mathematical methods (Kim and 380 Lim, 2017); (c) limitations of extrapolating high-level Weibull parameters methods (Justus and Mikhail, 1976). The shape factor k varies with height not only inexhibits the form of not only the reciprocal of the logarithmic function but also the form of the quadratic function with height. From the RMSE in Table 2, it can be seen that the quadratic function is the most suitable for this study area. Therefore, to use the Weibull function to evaluate the high-level wind speed distribution in a certain research area in the future, we should consider encrypted high-density observations or usewith more fitting methods 385 to obtain the best functional form of the Weibull parameter varying with height. Table 3 reviews scale factor c, shape factor k, surface roughness z0, and yearly mean absolute percentage erroraverage relative error (ARE) over different topography, showing obvious regional differences, due to various climate and topography context with different method. For exmapleIn Table 3, Pishgar-Komleh et al. (2015) used a constant surface roughness value of 0.14 to extrapolate wind speed, ignoring the dynamic changes in surface roughness throughout the year. The calculated annual mean absolute percentage error 390 relative is much higher than the value calculated afterby the dynamic surface roughness was introduced in this study.
Therefore, the large difference in the annual mean percent error in mean power density suggests that we should take dynamic roughness information into account and that it is better to use based on a reliable and accurate topographic map, rather than assuming surface roughness as a constant.
The differences and uncertainties between the logarithmic and power-law models can also be seenfound in Figure 9. Its 395 uncertainty is manifested in the absence of verification of actual high-level wind speeds. The reason for the difference is that the shape factor k in the winter of 2018 and in July and August of 2020 shows a decreasing trend with height, and according to formula (2.10), the average wind energy density is inversely proportional to the shape factor k, according to formula (2.10). Therefore, the limitation of this paper is that the extrapolated results need to be further confirmed by future encrypted observations of high-level wind speed data. SecondIn addition, the encouraging news is that this gives us two reliable 400 options for future extrapolation of high-level wind energy density, in the case of non-Weibull winds, only the logarithmic model can be considered, and in the case of Weibull winds, both the logarithmic model and the power-law model All are good choices.

Conclusions
The present work investigated the scale factor c and the shape factor k that affect the Weibull distribution of wind speed, by 405 directly estimating the energy potential of the wind speed resource at four different heights, and the surface roughness length parameter which directly affects the shape and law of the wind profile. The main conclusions are given as follows: The In general, under a carbon-neutral background, the determination of the potential for economical and clean wind energy resources is an important scientific issue in the development of renewable energy worldwide. Our research has determined the possible relationship between Weibull natural wind mesoscale parameter c and shape factor k with height under the 430 conditions of a desert steppe terrain in northern China, which has great potential in wind power generation, but there is a lack of comprehensive investigations into key parameters for estimating wind power density from tower data. In the present study, we have gained an enhanced understanding of the seasonal changes in the surface roughness of the desert grassland and the changes in the incoming wind direction. Our findings also have important implications for the assessment of wind energy resources for the establishment of new wind farms in areas experiencing varied desert steppe terrains throughout the world.

Code availability
The model and all implementation and analysis codes in this paper are based on MatLab and python, which can be available upon request to the author (20191203039@nuist.edu.cn).

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The data in this paper comes from an observation wind tower, which can be available upon request from the author (20191203039@nuist.edu.cn).

Author contributions
YY and ZG were responsible for conceptualization, supervision and funding acquisition. SZ developed the software and prepared the original draft. SZ and YY developed the methodology and carried out formal analysis. XX and SZ validated 445 data. ZG,YY, XX, ZD, and YL were reviewed and edited the text. SZ was responsible for visualization. All authors have read and agreed to the published version of the paper.

Competing interests
The authors declare that they have no conflict of interest.   Table 3. Review of scale factor c, shape factor k, surface roughness z0, and yearly mean absolute percentage error (MAPE)yearly average percent relative error (ARE) on over different underlying topography.