**3. Results**

### *3.1. Changing Temperature and Snowfall under Climate Change*

In this study, the winter snowfall, air temperature and wind data are used to assess the suitability of winter tourism in Jilin Province. The snowfall data were mainly used to analyze the influence of snow depth on winter sports, and the air temperature and wind determine the comfort level of outdoor sports. Several research studies show that snowfall and air temperature have changed significantly in Northeast China with climate change [31,61]. As part of Northeast China, the spatial distribution of snow, air temperature, and wind in Jilin province has also changed significantly. Revealing these changes can provide important informational support for winter tourism managemen<sup>t</sup> in Northeast China. Therefore, in this study, the spatial and temporal distribution of snow, air temperature, and wind in Jilin province were analyzed using meteorological data from 1971 to 2016 (from December to February of the next year).

Figure 2 shows the snowfall depth in Jilin Province varying from 5 to 30 cm, and the snowfall in winter increased by 1.3 mm/10a. Figure 3 shows that the temperature in Jilin Province varied from −16.4 ◦C to −9.2 ◦C, and the average temperature increased 0.27 ◦C/10a in the study area, including 0.25 ◦C/10a in the west, 0.26 ◦C/10a in the middle and 0.29 ◦C/10a in the east. The overall air temperature and snowfall change is beneficial to winter tourism. However, the annual temperature and annual snowfall fluctuated strongly. This will not be a disadvantage to winter tourism.

Climate change has favorable and unfavorable conditions for winter tourism. To avoid the influence of unfavorable factors, we need to distinguish the regions that are more suitable for development of winter tourism space. Therefore, the two indices, namely, MSI and SAI, were used to analyze the suitability of winter tourism space.

MSI evaluated comprehensively the suitability of meteorological environment using fuzzy inference. It is the weather index for suitable winter tourism. By coupling analysis of daily maximum air temperature, mean wind speed, air relative humidity, and visibility in winter, the spatial distribution of annual MSI was obtained in the study area from 1971 to 2016. The evaluation results (class (I)) were verified using the method provided by the literature [38] (class (II)) (Figure 4).

Figure 4 shows that the percentage difference between the two evaluation methods was 27.8%, 37.5% and 37.3% in the three grades of high (value1), medium (value1) and low (value3), respectively. Overall, 65.8% of the evaluation results are coincident. The major reasons are that visibility and relative humidity are considered in this study. Therefore, the degree of suitability predicted in this study is lower than that provided with the literature [38]. But in terms of temperature and wind speed, the evaluation results of the two methods are consistent.

By analyzing the mean value of annual MSI in the space, it is found that the maximum frequencies of high-suitability and medium-suitability degrees in the study area are 27.1% and 26.1%, respectively. The high frequency of high-suitability areas is mainly distributed in the eastern region and gradually decreases to the west, whereas the medium-suitability area is mainly distributed in the central region and gradually decreases to the east and west. It can avoid the inherent subjectivity of objective selection based on experience and make evaluation more scientific and reasonable. Compared with the analytic hierarchy process and risk matrix method, MSI calculated by fuzzy inference is more objective, and the evaluation results are closer to the actual situation.

**Figure 2.** Snow depth change from 1971 to 2016 in Jilin Province.

**Figure 3.** The temperature change from 1971 to 2016 in Jilin Province.

**Figure 4.** The cross validation of evaluation results in class (I) and class (II).

The SAI indicates the snow richness for outdoor activities in winter. It found an obvious spatial distribution difference between snow depth and duration in eastern, central and western Jilin province. The snow cover in the eastern region lasted for a long time, followed by the central plain area. The western region has the shortest snow cover time. The snow depth and snow cover decrease from southeast to northwest. The snow resource is mainly concentrated in the central-eastern study area. The maximum durations of snow depth exceeding 10 cm and 20 cm were reached at 35 and 79 days, respectively. In the central part of Jilin Province, the 10 cm snow depth lasted for 3–10 days, and the 20 cm snow depth lasted for 10–30 days. In the western part of Jilin, the duration of 10 cm snow is 1–5 days, and 20 cm snow depth is 5–10 days. By analysis of the snow depth contour exceeding 10 and 20 cm (Figure 5), it was found that the areas of 10 cm snow depth increased in the 1980s, 1990s, and 2010s, but the areas of 20 cm snow depth decreased in the same periods. This means that the number of heavy snow days is decreasing and that the number of light snow days increased in these periods.

**Figure 5.** The contour of 10 and 20 cm snow depths in the 1980s, 1990s and 2010s.

### *3.2. The SAI and SMI Joint Probability*

To obtain stable income, a suitable area for winter tourism development should be located where the meteorological factors steadily change annually and the winter tourism resources are suitable for development. Therefore, the coupling of annual MSI and SAI from 1971 to 2014 was used to analyze the suitability of winter tourism. To analyze the spatial coupling relationship between the annual SAI and SMI, the joint probability of the two indices was calculated based on Copula functions, and then the winter tourism suitability degree was established. In this study, the annual SAI and SMI were used to establish the copula function. The RMSEs determined by all of the observed samples identified the most appropriate copula function. By comparing the copula functions in Table 1, the results show that the RMSEs are 0.298 (Clayton), 0.241 (Frank), and 26.264 (Gumbel) at the 0.05 significance level (Figure 6). Therefore, the Frank copula function was selected to calculate the joint probability, and *θ* = −1.471 was calculated using the study area sample data. Through analysis, it is found that the high-suitability region is located in central and eastern Jilin Province (the joint probability >60%), the low-suitability region is located in west Jilin province (the joint probability <40%), and Yushu–Jiutai–Yitong–Dongliao is the boundary line. In central and eastern Jilin Province, the spatial distribution matching degree of the annual MSI and SAI is high and winter tourism resources are abundant (Figure 6). According to the two indices, the western region is weak for developing winter tourism because of low air temperature and the lack of snow resources.

**Figure 6.** The verification results of copula functions.

Snow-based winter tourism has long been dealing with variability in natural snowfall and seasonal temperatures, which has led to early adaptive interventions and investments [62]. Figure 7 shows that winter tourism suitability in western Jilin is low, mainly due to lower air temperature in the winter (annual air temperature below −13 ◦C, and annual rainfall below 10 cm), so it is not suitable for development of ice and snow tourism. Due to current limitations on temperatures for snowmaking (usually below −2 ◦C) [63], western Jilin Province is suitable for artificial snowmaking. However, due to the lack of regional competitiveness, the attractiveness of its scenic spots is not as attractive as that of the central and eastern region. The most suitable areas for development of ice and snow tourism are the central and eastern regions of Jilin Province, mainly because they are rich in snow resources (snow depth is over 15 cm) and annual air temperature (over −10.4 ◦C) suitable for outdoor activities and long snow retention time (over 150 days), which makes for less restrictions on the development of tourism and for higher winter tourism income. This is the most advantageous area for the development of the ice and snow industry. There are 38 large ski resorts in Jilin province, and all are located in this area. Jilin province has designated 27 key winter tourist attractions, 94% of which are located in the region. These analysis results are consistent with the actual Jilin Province situation.

Copula functions characterize the spatial interdependence of two factors. It could analyze the joint recurrence probability of the two indices in space in this study. The higher the joint recurrence probability is, the better the spatial suitability of winter tourism is, which means that this area was less affected by climate change, and it is suitable for the development of winter tourism. Compared with the traditional comprehensive evaluation method (e.g., weighted overlay), the parameters of this method are obtained by calculating historical data, which can avoid the shortcomings of subjectivity in the weighted overlay.

**Figure 7.** The joint probability spatial distribution of the SAI and MSI in the study area. The suitability degrees were classified as 0.00–0.20 (very low), 0.21–0.40 (low), 0.41–0.60 (medium), 0.61–0.80 (medium-high), and 0.81–1.00 (high).
