Nat Hazards (2017) 85:1135–1150 DOI 10.1007/s11069-016-2625-1 ORIGINAL PAPER Analysis of influence of natural disaster on the economy and prediction of recovery time based on grey forecasting–difference comparison model: a case study in the upper Min River Cheng Miao1,2 · Mingtao Ding2 Received: 22 July 2016 / Accepted: 13 October 2016 / Published online: 21 October 2016 © Springer Science+Business Media Dordrecht 2016 Abstract After the 2008 Wenchuan earthquake, secondary geological disasters occurred frequently and caused huge economic losses in the upper reaches of Min River. In this paper, 2003–2012 GDP data of the upper Min River were divided into two states: no disaster (2003–2007) and disaster (2008–2012). With the support of Excel and Matlab7.0 software, the data were, respectively, used to construct no disaster GM (1,1) model and disaster GM (1,1) model. Then two forecasting models were compared to establish grey forecasting–difference comparison model on the regional economic effects of natural disasters (including Wenchuan earthquake and secondary mountain hazards) and pre- sumably analysed the influence degree and its recovery. Conclusions are drawn as follows: (1) The variation of 2003–2012 GDP in the upper reaches of Min River is shown as inclined “N”, so regional economy is affected by natural disasters significantly; (2) Using non-disaster or disaster of grey forecasting model to speculate 2008–2012 GDP and test c, p value, the results show the “good” rating that indicates the model can be used for pcrct rediction of regional GDP; (3) It obtains the I value from using grey forecasting-difference comparison model that shows a irregular “几” font variation around the 2008 year; (4) The development of natural disasters has different effects on regional economic recovery. The upper reaches of Min River can be restored to the level of non-disaster in 2014–2015. And the recovery time of these counties is that:Wenchuan County in 2015–2016, Li County in 2011–2012, Mao County in 2020–2021, Songpan Country in 2015–2016, Heishui County cannot be restored. The research results can serve as a guide and reference for the post- disaster of the regional social and economic development, overall planning and sustainability. & Mingtao Ding [email protected] Cheng Miao [email protected] 1 School of Geography and Planning, Sun Yat-sen University, Guangzhou, China 2 School of Environment and Resource, Southwest University of Science and Technology, Mianyang, China 123 1136 Nat Hazards (2017) 85:1135–1150 Keywords Disaster · Regional economic · Influence · Prediction · The upper reaches of Min River 1 Introduction At 14:28:04 local time on 12 May, 2008, an Ms 8.0 earthquake hit Yingxiu Town of Wenchuan County in Sichuan Province. The earthquake caused 100,000 km2 of severely affected area, a death toll of nearly 70,000 and a direct economic loss of 845.14 billion CNY (136.15 billion USD) (China Earthquake Administration). Among them, more than one-third of the losses were caused by the geo-hazards induced (Wu et al. 2009a). The upper Min River is a typical region of the fragile ecological environment and the incidence of geological disaster in the upper reaches of Yangtze River. In 2008, the basin suffered the invasion of the earthquake and was affected by a series of secondary disasters after the earthquake, which made the regional socio-economic fluctuation significant. Natural disasters have a significant impact on the socio-economy, especially in the time when the outbreak of disasters is more frequent. Most researchers focused on the natural attributes of disasters on the impact of a region, the socio-economics’ attributes were carried out late at home and abroad (Pan and Li 2002; Zheng 2010; Zhang et al. 2002). Dacy and Kunreuther (1969) discussed the impact of natural disasters on the economy in theory and found that the disaster had a positive effect on the economy. By discussing the impact of disaster on the Caribbean’s economy, Heger et al. (2008) obtained the contrary conclusion that the disaster caused a negative effect on the regional economy. In the twenty-first century, various theories and methods of intervention and multidisciplinary integration make the research refined. The obtained conclusion no longer tended to be in a certain direction and showed the neutral (Noy and Vu 2010; Loayza et al. 2012). Domestic research is relatively small and qualitative analysis is given priority, it mainly theoretically discussed the impact of natural disasters on the economy (Liu 1999; Su et al. 2005; Zhang 2012; Wu et al. 2009b). At the same time, China’s entry into the disaster-prone period, a qualitative evaluation of the impact of disasters on the social and economic has not clearly reflect the actual situation, so quantitative research methods gradually involved (Cheng et al. 2000; Shi 2009; Zhou 2013). Throughout domestic and foreign research present situation found that the home and abroad scholars study the effect of disasters on regional economic growth is to discuss its influence, rarely involved in the specific analysis of the influence degree of changes and recovery of timeliness. Therefore, based on the existing researches (Ni et al. 2014; Miao and Ding 2015;Dingand Miao 2015;DingandWang 2016;Dingetal.2016), the article focused on the upper reaches of Min River. Combining GDP data of 2003–2012, we constructed a grey forecasting–difference comparison model to discuss the impact of natural disasters on regional economic growth and the forecast of recovery time, the conclusions will provide guidance and reference for regional post-disaster overall planning and the sustainable development of social economy. 2 Study area The upper reaches of Min River refer to the reaches above Dujiangyan and its tributaries, including Wenchuan County, Mao County, Li County, Songpan County, the major part of Heishui County in Aba Tibetan Autonomous Prefecture and a small part of Dujiangyan 123 Nat Hazards (2017) 85:1135–1150 1137 City. It is located in the northwest of Sichuan Basin, east area of Qinghai–Tibet Plateau and east margin of Hengduan Mountain. The area is the transition zone between Hill Mountains around Sichuan Basin and Qinghai–Tibetan Plateau, it is at 30°45′N–33°09′N and 102°35′ E–103°56′E (Fig. 1). The research area is located in the alpine ravines of the eastern margin of the Qinghai– Tibet Plateau. The terrain is complex; the difference of the physiognomy is significant. Ground elevation generally is 2000–4000 m. Due to the relative height, it is great disparity between the ridge and the valley, the average longitudinal gradient of the valley reaches about 10 ‰ and the run-off is rapid and strong, causing the valleys to be deeply undercut in the region. Fracture of the upper reaches of Min River develops well, and neotectonic movement is strong. Therefore, the regional earthquake activity is frequent and secondary disaster happens repeatedly. The exposed strata are from the Proterozoic to the Cenozoic in the region. The upper reaches of Min River is the transition zone between the sea-land monsoon zone and the plateau monsoon zone. The annual rainfall is uneven, and there is a clear distinction between the dry season and the rainy seasons. In the area, annual mean Fig. 1 Location and DEM map of the study area 123 1138 Nat Hazards (2017) 85:1135–1150 temperature is 5.7 to 13.5 °C. Annual precipitation is 400 to 800 mm, of which 80 % is concentrated in May to October. Run-off is mainly formed by rainfall and also has sec- tional alpine snowmelt supplies. Annual run-off is quite stable, the annual variation is small. 3 Data sources Wenchuan earthquake-related information and data from China Earthquake Administration. Sichuan Province statistical yearbook published by the Bureau of Sichuan Province and NBS survey office in Sichuan Province and jointly edited with China Statistics Press (2004–2013), which provides 2003–2012 GDP data of the upper reaches of Min River (Wenchuan County, Li County, Mao County, Songpan County and Heishui County). 2003–2012 social and economic data of the upper Min River is provided by the national economic and social development statistical bulletins of five counties (Wenchuan County, Li County, Mao County, Songpan County and Heishui County). 4 Methods Grey forecasting–difference comparison model is a combination of both the grey fore- casting model and the difference comparison method. The grey forecasting model is a method to predict the system with uncertain factors, it shows that a small amount of disordered raw data will be transformed to a regular data sequence and the prediction results maintain a high accuracy (Xu 2002). The difference comparison method is a research method of semi-qualitative and semi-quantitative, and the method has a good performance to study the effect of a certain factor on the main body, which reflects the direct impact and long timeliness of factors to the subject (Ni and Liu 2005). To combine the two, grey forecasting–difference comparison model keeps the advantages of grey forecasting model and difference comparison method and also shows the new significance of the comprehensive consideration of the state and process; therefore, it can be very good to show the impact of a certain factor on the main body. In this article, both a small amount of data to predict and the immediate and long-term impact of the disaster on regional economy are required to reflect. Therefore, grey forecasting–difference comparison model is used to study the impact of natural disasters on regional economic growth and the forecast of recovery time on the damage. Original data sequence no xð0Þ ¼ xð0Þð1Þ; xð0Þð2Þ; ...; xð0ÞðtÞ t ¼ 1; 2; ...; n ð1Þ ð0Þ where 2003–2007 GDP data sequence constitutes x1 (no disaster), t = t1; 2008–2012 GDP ð0Þ data sequence constitutes x2 (disaster), t = t2.