*2.2. Methods*

This study is mainly based on natural conditions (weather and snow) to assess the suitability of regional winter tourism development. To analyze the meteorological conditions and snow resources of Jilin province, the data sources include remote sensing images and local meteorological records. The snow depth data were extracted from the long-term snow depth dataset of China [46]. The original snow data sources are passive microwave images since 1980 obtained from the US National Snow and Ice Data Center (NSIDC). The original long time series dataset of China snow is (1) passive microwave remote sensing SMMR (1980–1987), (2) SSM/I (1987–2007) and (3) SSMI/S (2008–2014). Meteorological data include daily air temperature and wind speed (2 m height) obtained from the Chinese Meteorological Administration (daily data from 1971 to 2016).

### 2.2.1. Meteorological Suitability Index (MSI)

Air temperature and wind speed are two important factors that directly influence snow quality and outdoor snow sports in winter. When the mean air temperature is about −12 ◦C, and air relative humidity less than 80%, it will form power snow which is suitable for skiing. The hardness and softness of snow are closely related to air temperature. When the temperature rises, the snow surface will melt gradually under the action of sunlight and the continuous rolling of skis, which cause snow becomes soft; while the extreme cold weather will lead to water condensation and even a thicker ice crystalline layer in the snow, which cause snow to become hard. The present study indicates that when the air temperature is too low (≤−20 ◦C) tourists feel uncomfortable [37,47,48], and when it is too high (≥2 ◦C), it influences snow quality and snow cover days [47,49]. Outdoor snow sports are directly restricted by high wind speed. When wind speed reaches a certain level, outdoor activities are limited. When there is wind, the body temperature will be lower. Therefore, when the minimum temperature reaches −16 ◦C, visitors feel significantly uncomfortable. When the wind-force is less than scale 2 to 3, the skiing is suitable, and when the wind-force is more than scale 5, the skiing will

be dangerous. Air relative humidity and visibility also limit outdoor activities [37]. The influence of weather on the spatial and temporal distribution of winter tourism is analyzed by the coupled analysis of air temperature, and wind speed in this study. The classification of a single factor is referred to the meteorological skiing index issued by the Chinese Meteorological Administration [37]. In this study, the fuzzy inference and following steps are used to analyze MSI.

Step 1: Determining the evaluation factors and their grades.

Four factors daily maximum temperature (T), wind speed (W), air relative humidity (H) and visibility (V) were selected to describe meteorological suitability. The factors and their grades are shown in Table 1.


**Table 1.** The factors and their grades in MSI.

Step 2: Constructing the fuzzy membership function of factors

The Gaussian membership function, Z-shaped, and S-shaped membership function were used to establish the fuzzy membership of factors. The symmetric Gaussian function depends on two parameters *σ* and *c* as given by:

$$f(x, \sigma, c) = e^{\frac{-(x-c)^2}{2\sigma^2}}\tag{1}$$

Z-shaped and S-shaped membership are spline-based functions. The parameters *a* and *b* locate the extremes of the sloped portion of the curve as given by:

$$g(x,a,b) = \begin{cases} 1 & x \le a \\\ 1 - 2\left(\frac{x-a}{b-a}\right)^2 & a \le x \le \frac{a+b}{2} \\\ 2\left(\frac{x-b}{b-a}\right)^2 & \frac{a+b}{2} \le x \le b \\\ 0 & x \ge b \end{cases} \tag{2}$$

$$h(\mathbf{x}, a, b) = \begin{cases} 0 & \mathbf{x} \le a \\\ 2\frac{(\frac{\mathbf{x} - \mathbf{a}}{b - a})^2}{b - a} & a \le \mathbf{x} \le \frac{a + b}{2} \\\ 1 - 2\left(\frac{\mathbf{x} - \mathbf{a}}{b - a}\right)^2 & \frac{a + b}{2} \le \mathbf{x} \le b \\\ 1 & \mathbf{x} \ge b \end{cases} \tag{3}$$

The parameters *σ*, *c*, *a* and *b* will be established based on the boundary value in Table 1.

Step 3: Determining the weights of factors

Previous studies have shown that air temperature, wind speed, and visibility are all restrictive factors of outdoor activities, and they play an equally important role in winter tourism [37]. The air relative humidity is a non-restrictive factor of winter tourism. Therefore, the weight of this study is assigned as

$$\mathbf{A} = [0.3, 0.3, 0.3, 0.1]$$

Step 4: By using the membership formula, the daily fuzzy membership of each meteorological factor of MSI at different levels can be obtained using Equation (4):

$$B = A^{\circ}R$$

where ◦ is fuzzy operator symbols, A is a row matrix of factor weights, *R* is a matrix of fuzzy sets, which is calculated using Table 2. The MSI is divided into three levels and assigned value 1, 2 and 3. The values 1, 2 and 3 mean high-suitability, medium-suitability, and low-suitability, respectively. The daily MSI is determined according to the principle of maximum membership degree (Equation (5)). To facilitate the calculation of MSI, this study compiled the MSI using MATLAB 2016b (MathWorks, Natick, MA, USA).

$$MSI = \max\left(B\right) \tag{5}$$


**Table 2.** The membership functions for factors.

### 2.2.2. Snow Abundance Index (SAI)

The abundance of snow resources in a region is mainly expressed by snow thickness and duration. Therefore, daily snow depth and duration are used to calculate the snow abundance index. Winter tourism depends on the amount of snow, only when the snow reaches a certain depth and lasts for a period of time can tourists be attracted. Experience and researchers have found that only when the snow depth reaches more than 10 cm, can greatly reduce the cost of artificial snowfall in the ski resort and ge<sup>t</sup> economic benefits [40,50]. It is generally considered that snow sports need at least 30 cm of snow depth [40]. Witmer [51] suggested that a skiable area with at least 30 cm snow depth and 100 days duration per year would be suitable for the skiing industry. If the snowfall is reduced in one year, scenic areas can make snow artificially to satisfy tourists. The snowfall determines the snowmaking cost and tourism income. Therefore, the winter tourism industry needs to obtain the spatial distribution of snow resources. At present, several studies have obtained large-scale spatial snow resources based on remote sensing images and proved their feasibility [32–34]. Based on the snow data obtained from local remote sensing images, the snow abundance index was designed by coupling daily snow depth and duration in this study (Equation (6)). Several studies have provided a method to classify snow depth [52]. In this study, based on previous researches [50–52] and according to the actual situation of snow depth in Jilin Province, the snow depths were divided into <10, 10–20 and >20 three classes:

$$MSI = \begin{cases} \begin{array}{l} 1 \quad SD \ge 20 \landAND \text{ SC} \ge 60\\ 2 \quad SD \ge 10 \landAND \text{ SC} \ge 30\\ 3 \quad \text{others} \end{array} \tag{6}$$

where *SD* is the snow depth (cm) and *SC* is the snow cover days (d). The values 1, 2 and 3 mean high-abundance, medium-abundance, and low-abundance, respectively.
