Keywords

1 Introduction

Due to the climate change, the natural disaster has been increased in South Korea. Snow disaster was the third major natural disaster in South Korea. In 2001, the roof top of Olympic Gymnastic stadium was fallen down by heavy snow. In 2004, the hall constructed by sandwich panel was collapsed by snow. In the accident, 103 people were injured and 10 people died. In Jan. 2016, the Jeju airport was closed for two days because of heavy snow and severe cold. It was an unexpected disaster because the winter daily average temperature in Jeju island was usually over 0 °C. Therefore, the necessity of snow disaster preparedness was increased. Many researches have been conducted to estimate snow damage in Korea. Oh et al. [1] said that the social and economic damage by heavy snow will be increased in South Korea.

Park et al. [2] conducted the vulnerability analysis by heavy snow in the Ulsan metropolitan city. The vulnerable area for the heavy snow was suggested for the disaster preparedness. Kim et al. [3] constructed snowfall forecasting model using neural networks and multiple regression analysis to consider nonlinear process of snowfall. Jeong et al. [4] estimated the snow damage using daily maximum fresh snow depth, snow days, population, GRDP, and area. Kwon and Chung [5] and Kwon et al. [6] also developed regression models to estimate snow damage using meteorological factors. Toya and Skidmore [7] developed a model to estimate the damage per GDP caused by natural disaster.

In this study, for the more accurate and applicable model, both of meteorological and socioeconomic factors were considered as input data to estimate snow damage. Regression models were developed using daily maximum fresh snow depth. The fresh snow depth was divided into six categories and different regression models were developed to improve the accuracy of the models.

2 Multiple Linear Regression Analysis

Multiple linear regression analysis is the linear model with more than two independent variables to estimate one dependent variable. The regression model to estimate \( Y \) with \( X_{0} ,X_{1} ,X_{2} , \ldots ,X_{i} \) (where \( i \) is the number of variables) independent variables were shown in Eq. (1).

$$ Y = \beta_{0} + \beta_{1} x_{1} + \beta_{2} x_{2} + \cdots + \beta_{j} x_{j} + \epsilon $$
(1)

where, \( \beta_{0} ,\beta_{1} ,\beta_{2} , \ldots ,\beta_{i} \) are regression coefficients, \( \epsilon \) is the random error.

The accuracy of the regression model is estimated using adjusted-\( R^{2} (R_{a}^{2} ) \). The adjusted-\( R_{{}}^{2} \) is shown in Eq. (2).

$$ R_{a}^{2} = 1 - \left( {\frac{n - 1}{n - k - 1}} \right)\frac{SSE}{SST} $$
(2)

where \( n \) is the number of data, \( k \) is the number of independent variables. \( SSE \) and \( SST \) are the sum of squared error and total sum of squares.

3 Data

3.1 Snow Damage Report

The snow damage data from 1994 to 2015 was collected from the Annual Natural Disaster Report published by Ministry of Public Safety and Security (MPSS) in South Korea. The damages were categorized with 23 types of damaged facilities. The number of snow damages during 22 years (1994–2015) in the administrative districts were drawn in Fig. 1. The frequently damaged areas were located in the mountainous areas or near ocean. The most damaged districts were Jeonlla, Chungcheong, and Kangwon-do. Among the 23 types of facilities, 33% of snow damage was occurred in the greenhouse. Therefore, the greenhouse is shown as the most vulnerable facility to the snow disaster.

Fig. 1
figure 1

The number of snow disasters for 22 years (1994–2015)

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3.2 Meteorological Data

In South Korea, snow damage is mostly caused by the snow loads over the roof [8]. The snow loads could be significantly changed depending on the humidity. The weight of 1 foot of fresh snow ranges from 3 lb per square foot for light and dry snow to 21 lb per square foot for heavy and wet snow [9]. Yu et al. [10] proposed that the light and dry snow is formed below −10 °C and the heavy and wet snow is formed between −1 and 1 °C. Therefore, the snow density depends on the relative humidity and temperature. In this study, snow depth (daily maximum fresh snow depth), relative humidity, daily minimum temperature, daily maximum temperature, and daily mean temperature were applied as the meteorological input data.

3.3 Socioeconomic Factors

As mentioned earlier, the most vulnerable facility to the snow disaster is greenhouse which is located in the agricultural area. According to Statics Korea, the average age of the agricultural area is 66.5 years in 2016 and increases very rapidly. Therefore, it is important to consider the agricultural district and the greenhouse area for the snow damage estimation. As the socioeconomic factors, the area of administrative districts, greenhouse area, number of farmers, and number of farmers over age 60 were considered in the regression model.

4 Results

The multiple linear regression model was developed using 541 historical snow damage data for the three provinces in South Korea, Jeonlla, Chungcheong, and Kangwon-do. The snow damage data was collected for the lasts 22 years. However, some damages were happened when snow depth was less than 10 cm which was not heavy snow. Therefore, it was assumed that the snow damage data with low snow depth might be caused by the maintenance mistake and cannot present the real disaster situation. The snow depth causing damage should be defined.

To find the appropriate thresholds of the snow depth, six different regression models were developed as Table 1. Case 1 is the snow damage estimation model when the snow depth was higher than 10 cm, that is, the snow depth less than 10 cm was discarded. As the same manner, case 6 discards the data with snow depth less than 25 cm. After less than 25 cm of snow depth data was discarded, the number of data considered in a multiple regression model was only 91.

Table 1 The number of data considered in the regression models and adjusted R2
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However, the expectation accuracy of the model is increased as the snow depth threshold become high. The most accurate model is case 6 with 0.7074 of adjusted R2. Therefore, it is concluded that the reliable snow damage could be estimated when the fresh snow depth is higher than 25 cm in case of South Korea. In Fig. 2, the observed and calculated snow damage in case 6 model was shown.

Fig. 2
figure 2

Comparison of observed (X-axis) and calculated (Y-axis) snow damage using multiple regression model (case 6) (unit: thousand dollar)

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The regression coefficients were listed in Table 2. The regression coefficients from the six different models did not have the regular sign for the dependent variables. For example, some of the models have the positive coefficients for the minimum temperature and relative humidity, whereas others do not.

Table 2 Regression coefficients of 6 models
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5 Conclusions

In this study, multiple linear regression models using both of meteorological and socioeconomic factors were developed to estimate snow damages. The snow depth thresholds were investigated using six different regression models for more accurate model estimation. Historical 541 snow damage cases from Jeonlla, Chungcheong, and Kangwon-do which had the largest snow damages were applied in the models. As the result, the regression models with higher than 25 cm of snow depth showed the most accurate estimation. However, the regression signs of the six models do not have consistency. The developed models are needed to be verified using the more number of data, however, the model could give the decision-maker the insight about the area or scale of the possible snow damage for the rapid disaster response.