## 1 Introduction  
In the feasibility study and microsite selection stage of wind farms, using the wind measurement data is a key step to evaluate the wind resources at the hub height. At present, wind farms are being developed towards low wind speed and high hub height. Since the height of existing wind mast towers is often lower than the hub height which results in a lack of wind data at high hub heights, it is important to develop a reliable method to evaluate the accurate wind resource for wind farm development. The motivation of wind speed extrapolation is to characterize the wind shear and the importance of wind shear characterization for wind speed calculation was mentioned in a number of studies [1; 2; 3]. Wind turbines typically operate at altitudes below 200 m, while the height of the convective boundary layer is on the order of 1000 m [4]. The wind shear within 100-200 m is a function of wind speed, atmospheric stability, surface roughness, and height spacing [5,6]. At present, the power law and logarithmic law are commonly used to extrapolate the wind speed. The logarithmic law can represent the vertical wind-speed profiles fairly well under neutral conditions [7] and was extended by using the Monin-Obukhov similarity theory [8] under stable or unstable conditions to include thermal stratification effects [9]. According to [PERSON] et al. [10], the logarithmic wind-speed profile based on the Monin-Obukhov similarity theory was found inaccurate under strong stable conditions due to the shallow surface layer. For unstable conditions, [PERSON] et al. [11] found that the power law is robust to give a realistic wind profile than the logarithmic law. In the near-surface layer, the wind speed affected by surface friction and atmospheric stability, varies significantly with the height [12]. [PERSON] [13] analyzed the 213-m-high Cabauw meteorological tower data and found that the measured wind profile was consistent with the Monin-Obukhov similarity theory (surface layer scaling) even for the height above 100 m. [PERSON] [14] investigated the relationship between the wind shear coefficient and atmospheric stability based on the dataset recorded from the met mast of Cabauw (Netherlands), and found that the [PERSON] and Dutton [15] model appeared particularly skillful during the diurnal unstable hours and during the nighttime under moderately stable conditions. [PERSON] and [PERSON] [16] summarized various methods for atmospheric stability classification. In the radiation method, the intensity of radiation is determined based on the amount of observed cloud which is difficult to obtain, and in the M-O length method, the heat flux data are required. In addition to these two methods, there are four methods based on the gradient Richardson number, horizontal wind standard deviation, vertical temperature gradient and wind speed ratio to classify the atmospheric stability. The parameters used in these methods can be calculated using measured wind speed, wind direction, and temperature data. [PERSON] and [PERSON] [17] analyzed the wind farm operating data and found that, when the atmosphere was stable and the wind speed was in the range of 5-8.5 m/s, the output power was obviously greater than that in unstable conditions with strong convection, and the average difference was close to 15%. [PERSON] et al. [18] applied the similarity theory to establish a new model for wind-speed profile by considering the effects of atmospheric stability, and the model was applied to the height of the entire atmospheric boundary layer in a flat terrain. [PERSON] and [PERSON] [19] proposed a model of vertical wind-speed extrapolation for improving the wind resource assessment using the WAsP (Wind Atlas Analysis and Application Program) software [20], and found that if the estimation is carried out with the fixed wind shear exponent, the overestimated wind speed in the day time (unstable atmosphere) and underestimated wind speed in the night time (stable atmosphere) are usually obtained.