J. Meteor. Res.  2018, Vol. 32 Issue (6): 937-949 PDF
http://dx.doi.org/10.1007/s13351-019-8106-1
The Chinese Meteorological Society
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#### Article Information

WANG, Yujie, Lianchun SONG, Dianxiu YE, et al., 2018.
Construction and Application of a Climate Risk Index for China. 2018.
J. Meteor. Res., 32(6): 937-949
http://dx.doi.org/10.1007/s13351-019-8106-1

### Article History

in final form September 25, 2018
Construction and Application of a Climate Risk Index for China
Yujie WANG1,2, Lianchun SONG2, Dianxiu YE2, Zhe WANG3, Rong GAO2, Xiucang LI2, Yizhou YIN2, Zunya WANG2, Yaoming LIAO2
1. Northwest Climate Center of Gansu Meteorological Bureau, Lanzhou 730020;
2. National Climate Center, China Meteorological Administration, Beijing 100081;
3. Caixin Insight Group, Beijing 100027
ABSTRACT: In the context of global warming, China is facing with increasing climate risks. It is imperative to develop quantitative indices to reflect the climate risks caused by extreme weather/climate events and adverse climatic conditions in association with different industries. Based on the observations at 2288 meteorological stations in China and the meteorological disasters data, a set of indices are developed to measure climate risks due to water-logging, drought, high temperature, cryogenic freezing, and typhoon. A statistical method is then used to construct an overall climate risk index (CRI) for China from these individual indices. There is a good correspondence between these indices and historical climatic conditions. The CRI, the index of water-logging by rain, and the high temperature index increase at a rate of 0.28, 0.37, and 0.65 per decade, respectively, from 1961 to 2016. The cryogenic freezing index is closely related to changes in the consumer price index for food. The high temperature index is correlated with the consumption of energy and electricity. The correlation between the yearly growth in claims on household property insurance and the sum of the water-logging index and the typhoon index in the same year is as high as 0.70. Both the growth rate of claims on agricultural insurance and the annual growth rate of hospital inpatients are positively correlated with the CRI. The year-on-year growth in the number of domestic tourists is significantly negatively correlated with the CRI in the same year. More efforts are needed to develop regional CRIs.
Key words: climate risk index     construction     economic activities     correlation     application and services
1 Introduction

The earth’s climate is closely related to human productivity and quality of life. Agricultural production, energy consumption, bulk commodity use, household consumption, health care, tourism, the sports and leisure industry, transportation, insurance, and finance are all affected by climatic conditions, especially extreme wea-ther and climate events. Over the last century, the earth’s warming climate has caused changes in the intensity, duration, and frequency of extreme events, such as heat waves, droughts, and heavy rains (IPCC, 2012), leading to increasing climate risks. Global extreme weather and climate events have become more frequent in recent years. Statistics show that 582 extreme weather and climate events occurred from 1980 to 2015, resulting in direct economic losses of 110 billion US dollars and affecting 170 million people (Zhai et al., 2016). Global climate change has led to increased uncertainty about the future climate, with negative effects on economic and social development, productivity and quality of life, and the development, implementation, and realization of national strategic objectives (Wang et al., 2016).

The purpose of climate risk management is to reduce the negative impacts of climate on the natural environment, human society, and the economy (Jones et al., 2014). To reduce climate risks, it is necessary to coordinate disaster risk management and adaptations to climate change and to closely link the driving factors, policy measures, and actors in climate risks (Saito, 2013; UNISDR, 2015). A climate risk index (CRI) is a scientific tool to quantitatively assess single or integrated climate risks by specifying the thresholds at which extreme weather and climate events cause disasters and to analyze actual disaster-induced losses based on historical climate data.

Karl et al. (1996) defined a climate extremes index for the United Sates, taking into account extreme temperatures, precipitation, and other indicators; this was later revised by Gleason et al. (2008). Hansen et al. (1998) proposed a climate change index after considering the heating degree days, the frequency of heavy rainfall events, and other indicators with practical application value. These indices are based on the calculation and analysis of a single or multiple climatic factors and indicators, giving little consideration to losses or impacts on society as a result of climate-induced disasters.

Germanwatch, a German non-governmental organization, releases a global CRI every year (e.g., Kreft et al., 2016) to quantify the impact of extreme weather and climate events based on data from the Munich Re Group. A comprehensive CRI is calculated for different countries by weighting 4 indicators: the number of deaths from climate disasters, proportion of deaths per 100,000 inhabitants, direct economic losses, and proportion of economic losses relative to the gross domestic product.

China has experienced some of the world’s most diverse, influential, frequent, and damaging climate disasters. Direct economic losses caused by extreme wea-ther and climate events have averaged over 200 billion yuan per year since the start of the 21st century and the trend is increasing year-on-year (Qin et al., 2015). Previous studies on climate risk in China have focused on the risk of climate disasters (Mo et al., 2012) or climate change (Wu et al., 2012), with only a few studies considering a comprehensive CRI or the impact of climate risks on the economy.

In this study, we select five major weather events (water-logging by rain, drought, high temperature, cryogenic freezing, and typhoon) as factors in constructing a CRI for China, based on observed data of these five types of weather and climate events and their resulting economic and social impacts. We use objective statistical methods to calculate the CRI, analyze the correlation between the CRI and economic activities, and explore the application of the CRI as a useful reference for the reduction of risk in industrial production and business activities from weather events.

2 Data and methods 2.1 Data

We use data from 2288 National Meteorological Information Center meteorological observation stations for daily precipitation, daily average temperature, daily maximum temperature, daily minimum temperature, and daily maximum wind speed from 1961 to 2016. The economic data are from the China Statistical Yearbook.

2.2 Drought index

Many indices are currently used to characterize drought, such as the percentage of precipitation anomaly, the number of consecutive days without precipitation, the Palmer drought severity index, the Z index, the standardized precipitation index (SPI), and the meteorological drought composite index (MCI) (Hayes et al., 1999; Wei and Ma, 2003; Yuan and Zhou, 2004; Wang et al., 2007). However, these indices are all based on a single station. We now construct a drought index to characterize the comprehensive intensity of drought over a region.

We first calculate the monthly SPI (SPIm) and classify it into the corresponding level based on its value. We then determine the daily drought index (DI) of a single station based on SPIm and add these values to obtain the monthly drought index (MDI) of the station:

 \begin{align}&{\rm DI}= \left\{ \;\; \begin{aligned}& 0, \quad\quad\quad\quad\quad\quad {{\rm SPI}_{\rm m} \geqslant - 1}\\& {{\rm SPI}_{\rm m} + 1,} \quad\quad\quad { - 1.5 \leqslant {\rm SPI}_{\rm m} < - 1}\\& {2 \times {\rm SPI}_{\rm m} + 2.5,} \quad { - 2 \leqslant {\rm SPI}_{\rm m} < - 1.5}\\& {3 \times {\rm SPI}_{\rm m} + 4.5,} \quad {\rm SPI_{\rm m} < - 2}\end{aligned}\right. \;\;; \\&{\rm{MDI}} = \sum\limits_{i = 1}^{{\rm{Day}}} {{\rm{DI}}_i}. \end{align} (1)

In this formula, “Day” represents the number of days with a daily average temperature > 0°C in the month, DI i represents the drought index of a station on a single day (average temperature > 0°C), and MDI represents the monthly drought index of a station in a single month. We calculate the single-station MDI of the 2288 stations in China one by one. We then obtain the weighted average of the single-station MDI while considering the regional and seasonal differences and normalize the monthly sequence to obtain an MDI for China (CMDI) that ranges between 0 and 10:

 $\begin{array}{l}X = \dfrac{{\displaystyle\sum\limits_{i = 1}^{2288} {{a_i} \times {b_i} \times {\rm{MDI}}{_i}} }}{{2288}};\\{\rm{CMDI}} = \dfrac{{\left({X - {X_{\min }}} \right)}}{{\left({{X_{\max }} - {X_{\min }}} \right)}} \times 10,\end{array}$ (2)

where ai represents the weight of station i (0 for the Tibetan Plateau and the central and western parts of Northwest China, 0.6 for the eastern part of Northwest China and the southwestern region, and 1 for other regions) and bi represents the monthly weight, which is determined based on the monthly precipitation and its possible impact. Precipitation in most parts of China is low in winter and therefore the impact of droughts will be small, so the weight for December, January, and February is 0.5. By contrast, precipitation is high in May, June, July, August, and September and there will therefore be a greater impact from droughts, so the weight for these months is 1.5. The weight for other months (March, April, October, and November) is 1. Xmax and Xmin are the maximum and minimum of the arithmetic mean X of all months from 1961 to 2016, respectively.

China’s yearly drought index (CYDI) is obtained by averaging the MDI for a single year and normalizing the results. Statistics show that the CMDI appears as an exponent and the CYDI is normally distributed. The thre-shold of the intensity level of droughts is determined by the percentile method based on the characteristics of the distribution functions. The CYDI is divided into 5 levels (mild, slightly mild, moderate, slightly severe, and severe) corresponding to 30%, 50%, 60%, 80%, and 100%, respectively.

2.3 Index for water-logging by rain

There has been much interest in water-logging indicators and assessment methods in recent years. Zhong et al. (2009) studied the spatiotemporal distribution of water-logging by rain in Zhejiang Province during a period of concentrated precipitation. Zhang et al. (2009) analyzed the changes in water-logging by rain in the Yellow and Yangtze River basins using an index based on the total amount of precipitation in 10 continuous days exceeding a certain value. The SPI developed by McKee et al. (1993) has been widely used in Canada (Bonsal and Regier, 2007). We now calculate an index for water-logging by rain based on the daily precipitation level.

First, we calculate the daily precipitation level index (Rd). The precipitation at a single station on one day (P) is divided into four levels:

Level 0 (Rd = 0): P < 50 mm;

Level 1 (Rd = n1/2): 50 mm $\leqslant$ P < 100 mm for the nth consecutive day of a rainstorm;

Level 2 (Rd = 2n1/2): 100 mm $\leqslant$ P < 200 mm for the nth consecutive day of a rainstorm;

Level 3 (Rd = 3n1/2): 200 mm $\leqslant$ P for the nth consecutive day of a rainstorm.

We then calculate the monthly index for water-logging by rain (MR) of a single station. The MR of a station in a single month is the sum of its precipitation level index in that month:

 ${{\rm{MR}}} = \frac{{\displaystyle\sum\limits_{i = 1}^{{\rm{Day}}} {{{R_{\rm{d}}}}_{i}} }}{{{\rm{Day}}}},$ (3)

where “Day” is the number of days in the month, Rd is the daily precipitation level index of a station on a single day, and MR represents the MR of a single station in one month.

We then average the MR of 2288 stations in China and normalize the arithmetic mean (X). The result is a monthly index for water-logging by rain in China (CMR):

 $\begin{array}{l}X = \dfrac{{\displaystyle\sum\limits_{i = 1}^{2288} {{\rm{MR}}_{i}} }}{{2288}};\\{\rm{CMR}} = \dfrac{{\left({X - {X_{\min }}} \right)}}{{\left({{X_{\max }} - {X_{\min }}} \right)}} \times 10,\end{array}$ (4)

where Xmax and Xmin are the maximum and minimum of X for all months from 1961 to 2016.

The weighted average of the 12-month CMR in a year is normalized to give the arithmetic mean (Y). The result is a yearly index for water-logging by rain in China (CYR):

 $\begin{array}{l}Y = \dfrac{{\displaystyle\sum\limits_{i = 1}^{12} {{a_i}\times {\rm{CMR}}_{i}} }}{{12}};\\{\rm{CYR}} = \dfrac{{\left({Y - {Y_{\min }}} \right)}}{{\left({{Y_{\max }} - {Y_{\min }}} \right)}} \times 10,\end{array}$ (5)

where ai is the monthly weighted coefficient (2 for June, July, and August; and 1 for other months), and Ymax and Ymin are the maximum and minimum of Y of all years from 1961 to 2016.

Statistics show that the CMR appears as an exponent and the CYR is normally distributed. The threshold of intensity level is determined by the percentile method based on the characteristics of the distribution functions. The CMR is divided into 5 levels (mild, slightly mild, moderate, slightly severe, and severe) corresponding to 30%, 50%, 60%, 80%, and 100%, respectively, according to its distribution characteristics.

2.4 High temperature index

The absolute temperature threshold, the relative threshold, and the probability distribution-based statistical threshold are generally used for the quantitative analysis of high temperatures. The absolute temperature threshold defines a “high temperature day” as a day with a maximum temperature $\geqslant$ 35°C (Ding, 2013). The relative thre-shold is a percentile-based indicator used to identify extreme temperatures, and the indicators recommended by the World Meteorological Organization include cold day, cold night, warm day, and warm night (Frich et al., 2002; Alexander et al., 2006; Zhai, 2011; Zhai and Liu, 2012). The statistical threshold based on the probability distribution is mainly judged by whether the sample obeys a Gumbel distribution. If yes, the threshold for the daily maximum temperature of multiple years with a Gumbel distribution is calculated, and is then considered as the high temperature threshold (Jiang, 2015). However, the degree of heating is not only reflected by the maximum temperature but also closely related to the minimum temperature. We thus define a high temperature index based on the daily maximum temperature, the lowest daily temperature, and the duration.

We first calculate the daily maximum temperature level index (Tg) and divide the daily maximum temperature (Tmax) of a station into three levels:

Level 1 (Tg = 1): 35°C $\leqslant$ Tmax < 37°C;

Level 2 (Tg = 2): 37°C $\leqslant$ Tmax < 40°C;

Level 3 (Tg = 3): 40°C $\leqslant$ Tmax.

We then calculate the daily minimum temperature level index (Td) and divide Tmin of a station into three levels:

Level 1 (Td = 1): 25°C $\leqslant$ Tmin < 28°C;

Level 2 (Td = 2): 28°C $\leqslant$ Tmin < 30°C;

Level 3 (Td = 3): 30°C $\leqslant$ Tmin.

At the same time, a high temperature index (MT) for a station in a single month is constructed based on the daily maximum temperature level and the number of high temperature days at this level, as well as the daily minimum temperature level and the number of high temperature days at this level for the station in this month:

 ${\rm{MT}}=\frac{\displaystyle\sum\limits_{i=1}^{{\rm{Day}}}{{{T}_{\text{g}i}}}\times {{\left( {{D}_{\text{g}i}} \right)}^{0.5}}+\sum\limits_{j=1}^{{\rm{Day}}}{{{T}_{{\rm{d}}j}}}\times {{\left( {{D}_{{\rm{d}}j}} \right)}^{0.5}}}{{\rm{Day}}},$ (6)

where “Day” is the number of days of the month, Tg is the daily maximum temperature level index of a station on a single day, Td is the daily minimum temperature level index of a station on a single day, Dg is the number of days when the daily maximum temperature of a station is continuously $\geqslant$ 35°C, Dd is the number of days when the daily minimum temperature of a station is continuously $\geqslant$ 25°C, and MT is the monthly high temperature index of a station in a single month.

We then average MT for the 2288 stations in China and normalize the arithmetic mean (X). The result is a monthly high temperature index for China (CMT):

 $\begin{array}{l}X = \dfrac{{\displaystyle\sum\limits_{i = 1}^{2288} {{\rm{MT}}_{i}} }}{{2288}};\\ {\rm{CMT}} = \dfrac{{\left({X - {X_{\min }}} \right)}}{{\left({{X_{\max }} - {X_{\min }}} \right)}} \times 10,\end{array}$ (7)

where Xmax and Xmin are the maximum and minimum values of X for all months from 1961 to 2016.

We next average the 12-month CMT for a single year and normalize the arithmetic mean (Y). The result is a monthly high temperature index for China (CYT):

 $\begin{array}{l}Y = \dfrac{{\displaystyle\sum\limits_{i = 1}^{12} {{\rm{CMT}}_{i}} }}{{12}};\\ {\rm{CYT}} = \dfrac{{\left({Y - {Y_{\min }}} \right)}}{{\left({{Y_{\max }} - {Y_{\min }}} \right)}} \times 10,\end{array}$ (8)

where Ymax and Ymin are the maximum and minimum of Y in all years from 1961 to 2016.

Statistics show that both the CMT and CYT appear as exponents. The threshold of intensity level is determined by the percentile method based on the characteristics of the distribution functions. The CMT is divided into 5 levels (mild, slightly mild, moderate, slightly severe, and severe) corresponding to 20%, 40%, 60%, 80%, and 100%, respectively. The CYT is also divided into 5 levels (mild, slightly mild, moderate, slightly severe, and severe) corresponding to 10%, 40%, 75%, 90%, and 100%, respectively.

2.5 Cryogenic freezing index

In China, studies on low temperature, freezing, and snowstorm indices generally focus on a certain region or crop. Mao et al. (2007) and Lou et al. (2009) developed a meteorological index for citrus frost damage (a major meteorological disaster that affects citrus production in China). This index is used as a standard in compensation for insurance against frost damage. Liu et al. (2010) proposed three levels of agricultural insurance against apple blossom frost damage in Shaanxi Province based on an apple blossom frost damage warning index, disaster data, and low temperature data. Zheng et al. (2011) proposed to use extreme minimum temperature as a weather insurance index for frost damage to tropical fruit in Taiwan. Yin et al. (2008) studied the meteorological index for frost damage and the corresponding reduction in output of Nanfeng tangerines and designed an insurance index for frost damage. Yi et al. (2015) designed a snow disaster weather index for pastoral areas.

The impact of low temperatures is, however, multifaceted; and low temperatures are often accompanied by rain, snow, and frost. Our work has taken into account the changes in temperature and the number of days with snow on a five-day timescale to develop a cryogenic freezing index.

We compare the mean temperature anomaly in a five-day period with its standard deviation σ. Assume that:

 $a = \left\{ {\begin{array}{*{20}{c}} {\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! 0, \quad{(\,t \,\,-\,\, }\overline {t} {\rm{\,) > - 1\sigma\,; }}} \\ { 1, \quad{ - 2\sigma < (\,t \,\,- \,\,}\overline {t} {\rm{\,)}} \leqslant { - 1\sigma\,; }} \\ { 2, \quad{ - 3\sigma < (\,t \,\,- \,\,}\overline {t} {\rm{\,)}} \leqslant { - 2\sigma\,; }} \\ { \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!3, \quad{(\,t \,\,-\,\, }\overline {t} {\rm{\,) \leqslant - 3\sigma\,. }}} \\ \end{array}} \right.$ (9)

The cryogenic freezing index of the station is then:

 ${I_{\rm{c}}} = a\,\, \times \,\, \left| \,\, {\frac{{{t \,\, - \,\,}\overline {t} }}{\sigma }} \right|,$ (10)

where t is the average temperature of a 5-day period, $\overline {t}$ is the average temperature of the 5-day period over 30 yr (1981–2010, a climatology period defined herein), andσ is the standard deviation of the temperature for the 5-day period. The index mainly considers the average temperature of a five-day period, but low temperatures are often accompanied by snow and other disastrous weather events, which may have a great impact on traffic and daily activities. The index is therefore weighted by (1 + Day/10) according to the number of days of snow. The impact of cryogenic freezing will be greater if the number of days of snow is greater. Cryogenic freezing in winter has a smaller effect in the northern region than in the southern region, and therefore the weight for the southern stations is 1 while the weight for the northern stations is 0.5. The impact of cryogenic freezing on daily activities in winter is greater in January and February during the travel rush of the Spring Festival, and therefore, the weight for December is 0.5 and the weight of both January and February is 1.

The formulas for the cryogenic freezing index of each month in winter (Im) and the cryogenic freezing index for winter (Iy) are:

 $\begin{split}{I_{\rm{m}}} = & \sum\limits_{j = 1}^{2288} {\sum\limits_{i = 1}^6 {{I_{\rm{c}}}(i,j)} };\\{I_{\rm{y}}} = & {I_{\rm{Jan}}} + {I_{\rm{Feb}}} + 0.5{I_{\rm{Dec}}}.\end{split}$ (11)

The cryogenic freezing index for each month (including 6 5-day periods, i.e., i = 1, 2, ..., 6) and the winter of the previous year is normalized to lie between 0 and 10.

According to the winter cryogenic freezing index of the years from 1961 to 2016, the index value is between 0.5 and 6.0. Among the 56 yr, the winter cryogenic freezing index of 43 yr (about 80%) is within this range, whereas the index for 6 yr is < 0.5 and the index for a further 6 yr is > 6, accounting for about 10% of the total samples. Therefore, the winter cryogenic freezing index is divided into 5 levels (< 0.5, 0.5–1.5, 1.5–3.5, 3.5–6.0, and > 6.0) corresponding to mild, slightly mild, moderate, slightly severe, and severe. The frequency of each level obeys a normal distribution.

2.6 Typhoon index

Gray (1990) and Gray et al. (1992) proposed a hurricane destruction potential index to study the characteristics of Atlantic tropical cyclones (TCs). This index is based on the sum of the squares of the maximum wind speeds near the center of TCs in which every 6-h intensity reaches hurricane level in a certain period. Bell et al. (2000) improved this index and defined the accumulated cyclone energy index. Emanuel (2005) proposed an index of potential destructiveness based on the dissipation of power. Yin et al. (2011) proposed the TC potential impact index. These indices take into account the intensity, frequency, and duration of TCs, but do not take into account the disasters caused. Our typhoon index is based on the weighted average of the coverage area of different levels of wind and rain. The daily maximum wind speed (mw) is taken as the wind factor and the daily precipitation (pre) is taken as the rain factor.

Considering the uneven distribution of meteorological stations, the data are first interpolated into a 0.5 × 0.5 grid and the typhoon-induced precipitation and wind speed are separated from the grid data. We then count the number of points of wind and rain factors in each interval and calculate their weighted average to obtain the wind and rain indices. The weighted average wind and rain indices are normalized to give the typhoon index.

The typhoon index is compared with typhoon disasters and the yearly and monthly typhoon indices are divided into different levels. To eliminate the favorable impacts of typhoons, mw and pre are divided into five intervals with 9 m s–1 and 50 mm as the starting point, respectively. Based on a single typhoon, we then assign a weight of 0.4 to the wind factor and 0.6 to the rain factor and calculate the typhoon index (It) by weighting:

 ${I_{\rm{t}}} = 0.4{I_{{\rm{mw}}}} + 0.6{I_{{\rm{pre}}}},$ (12)

where Imw is the sum of the number of grid points in each interval of the wind factor, and Ipre is the sum of the number of grid points in each interval of the rain factor. According to the date of a single typhoon, we then add into the typhoon indices the corresponding year and month to obtain the yearly and monthly indices. We then normalize the yearly and monthly indices.

According to the actual distribution characteristics of the yearly typhoon index and the monthly typhoon index, we divide the yearly and monthly typhoon indices into 5 levels (mild, slightly mild, moderate, slightly severe, and severe) based on the 15th, 30th, 50th, and 80th percentile. During the statistical period, the stronger the wind and rain factors and the wider the range of influence, the longer the typhoon remains in the area and the greater the potential impact.

2.7 CRI for China

Our calculation of a CRI for China is based on the monthly and yearly indices for water-logging by rain, drought, high temperature, cryogenic freezing, and typhoon. As a result of the impact of the monsoon climate, there are large differences in the climate of different seasons and the factors affecting climate risks are also different. For example, the factors affecting climate risk in the summer half of the year are mainly water-logging by rain, typhoon, and high temperature, but the main factors affecting climate risk in the winter half of the year are drought and low temperature. As a result of these seasonal differences in climate, the climate risk in summer is higher than in winter. Statistical analysis of China’s monthly losses from meteorological disasters in the last 10 years shows that the climate risk in June to September is significantly higher than in other months. Therefore, we normalize the logarithmic function of the monthly losses from disasters and obtain the weights of the monthly indices. China’s CRI is calculated as:

 ${\rm{CRI}}_{\rm{m}} = \sum\limits_{i = 1}^N {{D_{i, j}} \times {T_{i, j}}},$ (13)

where CRIm is China’s monthly climate risk index, N represents the number of disaster types, Di,j is the index for disaster i and month j, and Ti,j is the weight of Di,j. Using the multi-year average losses from meteorological disasters as the weight of the five yearly indices of meteorological disasters (water-logging, drought, high temperature, cryogenic freezing, and typhoon), we obtain:

 ${\rm{CRI}}_{\rm{y}} = \sum\limits_{i = 1}^N {{D_i} \times {T_i}},$ (14)

where CRIy is China’s yearly climate risk index, N represents the number of disaster types, Di is the yearly index of disaster i, and Ti is the yearly weight of Di.

In terms of a single yearly index, we first calculate the average of the monthly indices and then take the square root of the average of the monthly indices as the weight of the monthly indices. We then sum up the 12-month indices, each multiplied by the weight, and obtain the yearly index. The specific formula is:

 ${D_i} = \sum\limits_{j = 1}^{12} {{D_{i, j}} \times {\rm{TD}}_{i, j}},$ (15)

where Di,j represents the monthly index of a disaster and TDi,j represents the weight of a disaster index in a month. TDi,j is set to be the square root of the average of the monthly disaster indices from 1980 to 2010 (a base climatology period).

The probability density function of CRIm for China from 1981 to 2010 shows that the indices are mainly concentrated below the 20th percentile. With the 20th, 40th, 60th, and 80th percentiles as the basis for dividing the levels, 5 levels (low, slightly low, medium, slightly high, and high) account for 56%, 20%, 12%, 9%, and 3% of the risk, respectively. The probability density function of CRIy for China from 1981 to 2010 shows that the indices are mainly concentrated between the 30th and 70th percentiles. With the 20th, 40th, 60th, and 80th percentiles as the basis for dividing the levels, 5 levels (low, slightly low, medium, slightly high, and high) account for 23%, 30%, 27%, 17%, and 3% of the risk, respectively. The monthly and yearly CRIs agree with China’s actual historical climatic conditions.

3 Analysis of results

Figure 1 shows the changes in the monthly and yearly drought indices for China from 1961 to 2016, and a spatial distribution of the yearly drought index over China in 2001. The drought indices are highest in September 1966 (10.0), November 1979 (8.87), and May 1981 (9.21), giving a good reflection of the actual degree of drought (Fig. 1a). On the annual timescale (Fig. 1b), the drought index can also reflect the actual degree of drought. For example, in 1997, a summer to autumn drought occurred in North China (figure omitted), and the annual drought index reached the highest value of 10 in that year. The drought index reached 9.71 in 2001, corresponding to the drought in northern China and the Yangtze River basin (see Fig. 1c). The annual drought index reached 8.95 in 2011, corresponding to the severe autumn and winter drought in the winter wheat region of northern China and the severe winter and spring drought in the middle and lower reaches of the Yangtze River (figure omitted).

 Figure 1 (a) Monthly and (b) annual evolutions of the drought index for China during 1961–2016, and (c) spatial distribution of the yearly drought index over China in 2001. The dashed line in (b) shows the linear trend, and the dots in (c) denote the provincial captical cities of China.

Figure 2 shows the changes in the monthly and yearly indices for water-logging by rain in China. The monthly indices for water-loggin by rain are high in summer and autumn but low in winter and spring, which is closely related to the seasonal distribution of precipitation in China. The yearly index of water-logging by rain is a good reflection of the actual water-logging disasters. For example, this index reached a historical high in 1998 (10.0) when China’s Yangtze River, Nenjiang River, Huanghuai area, and North China were affected by historically rare, wide-ranging, and persistent storms and floods in summer. This index was 9.53 in 2016, ranking the second. As a result of the super strong El Niño event in 2016, the Yangtze River, Huanghuai area, and North China were again affected by historically rare storms and floods. Based on the long-term trend, the yearly index of water-logging by rain of China is increasing at a rate of 0.37 per decade, indicating that the risk of water-logging by rain in China has been increasing since 1961.

 Figure 2 As in Fig. 1, but for the index of water-logging by rain.

Figure 3 shows the changes in the monthly and yearly high temperature indices for China from 1961 to 2016. The most severe high temperature and heatwave disaster since 1961 struck southern China in 2013 and the wide-ranging and persistent high temperatures had a great impact on agriculture, electricity, water resources, and human health. The high temperature index reached a maximum of 10.0 that year. China’s Yangtze River basin was affected by over 40 consecutive days of high temperatures in 2016 and the yearly high temperature index reached 9.53, ranking the second in history. Based on the long-term trend, the high temperature index of China increases at a rate of 0.65 per decade from 1961 to 2016. The average yearly high temperature index from 1981 to 1998 is 2.53 and increases to 5.43 from 1999 to 2016, showing that China’s risk of high temperatures has significantly increased.

 Figure 3 As in Fig. 1, but for high temperature index.

Figure 4 shows the changes in the monthly and yearly cryogenic freezing indices for China from 1961 to 2016. The cryogenic freezing index was highest in December 1971 (9.87), February 1964 (9.61), and February 1969 (8.96). There was a wide-ranging blast of cold weather in eastern and southern China in December 1975. The average temperature in South China and southwestern China was 7–9°C lower than in the same period of an average year, and the extreme minimum temperature in many regions was the lowest since 1949. Eastern China experienced large-scale frost damage in mid-to-late February 1964. Most areas in China were affected by a cold spell from the end of January to early February 1969 and there was nationwide frost damage. The yearly cryogenic freezing index was highest (10.0) in 1977. The temperature in most areas of China continued to decrease significantly in the winter of 1976–77 and it was bitterly cold all over the country, which was a rare event. The yearly cryogenic freezing index in 2008 was 6.25 as a result of frost damage, ranking the fourth since 1961. Based on the long-term trend, the yearly cryogenic freezing index of China is decreasing at a rate of 0.61 per decade.

 Figure 4 As in Fig. 1, but for cryogenic freezing index.

Figure 5 shows the monthly and yearly typhoon indices for China from 1961 to 2016. The correlation coefficient between the yearly typhoon index and yearly typhoon disasters from 2000 to 2016 is 0.74, at the significance level of 0.001. The typhoon indices are highest in 1985 (10.0), 1994 (9.94), and 2016 (8.48). A total of 9 powerful typhoons made landfall in concentrated areas of China in 1985. In 1994, 11 typhoons made landfall 15 times over China and the frontal Typhoon 9415 affected Shandong and Liaoning, so this year witnessed serious losses. In 2016, 8 typhoons made landfall in China, and 6 of which were super typhoons.

 Figure 5 As in Fig. 1, but for typhoon index.

Figure 6 shows the CRI for China from 1961 to 2016. The CRI was highest in 1994 (10.0), 2016 (9.70), and 2013 (8.09). In 1994, large-scale rainstorm disasters in South China and south of the Yangtze River, the severe spring drought in North China, the severe summer drought in the Yangtze–Huaihe region, and frequent typhoons, all caused significant losses. China’s annual average precipitation in 2016 was the highest since 1961; the middle and lower reaches of the Yangtze River, regions south of the Yangtze River, South China, and southwestern China were successively affected by torrential rain, severe convection, and super typhoons. Many areas in northern China were hit by severe rainstorms and floods in 2013 and South China experienced the most severe high temperature and heatwave since 1961. Based on the long-term trend, the CRI for China increased at a rate of 0.28 per decade from 1961 to 2016, with an average of 3.69 from 1981 to 1998 and an average of 4.69 from 1999 to 2016, indicating that China’s climate risk has increased significantly in this century.

 Figure 6 As in Fig. 1, but for climate risk index (CRI).
4 Application of the climate risk indices 4.1 Cryogenic freezing index and food prices

The consumer price index (CPI) is one of the most important macroeconomic indicators. In addition to being closely related to people’s lives, the CPI is an important reference index for macroeconomic analysis and decision-making, in which the CPI for food is particularly important. There are many factors that affect changes in the CPI for food and the determinants of the price changes for different commodities are also different, but the impact of climatic conditions on food prices cannot be neglected. Southern China was hit by severe frost damage in early 2008, affecting food production, transportation, and sales. The CPI for food increased by 18.2% and 23.3%, respectively, on a year-on-year basis in January and February 2008, the highest in the last 20 years.

Cryogenic freezing is the most important source of climate risk in winter. A comparative study of the relationship between the increase in the CPI for food in January and February and the cryogenic freezing index in the corresponding month shows that they are highly synchronized (Figs. 7a, b) with correlation coefficients of 0.72 and 0.77, respectively, passing the 99% confidence level. The year-on-year increase in the CPI for food in January and February and the cryogenic freezing index are more highly synchronized if they are averaged, with a correlation coefficient of 0.89 (Fig. 7c).

 Figure 7 Relationship between the cryogenic freezing index (blue) and the CPI for food (red) for (a) January, (b) February, and (c) the average of January and February.
4.2 High temperature index and energy consumption

Most of China lies in the northern temperate zone. Except in some high-altitude areas, high temperatures are universal and frequent in the summer months. The consumption of electricity by the industrial and agricultural sectors increases if temperatures are high in July and August. High temperatures in summer also increase the demand for energy by domestic consumers for air conditioning, which costs more electricity than other electrical appliances in summer. The year-on-year growth rate for household electricity consumption from July to August is positively correlated with high temperature indices for these months (Fig. 8a) with a correlation coefficient of 0.73. The summer temperatures were high in 2013 and 2016 and the growth in household electricity consumption in summer also accelerated in these years. High temperatures in summer increase not only household electricity consumption, but also sales of electrical appliances (air conditioners, refrigerators, and electric fans) and food. Air conditioners have become increasingly popular in recent years; the correlation coefficient between the annual sales of air conditioners and the high temperature index is 0.44 (Fig. 8b). This is because the average temperature in spring and summer is high if the temperatures in a particular year are high, increasing the likelihood of consumers buying air conditioners. High summer temperatures are to some extent predictable, so consumers will buy air conditioners in advance based on climate predictions.

 Figure 8 Relationship between the high temperature index (blue) and (a) domestic electricity consumption (red) and (b) air conditioning sales (red).
4.3 Climate risk index and tourism

Public demand for tourism has increased rapidly with economic development and improvements in the national income in China. The number of tourists, the rate of travel, and per capita spending have maintained steady growth. The average annual growth rate in the number of domestic tourists since 2007 is 13% and the average annual growth rate of the number of outbound tourists is over 20%. The main driving force for the development of tourism is the increase in disposable income and spare time; the exchange of ideas and improvements in tourist facilities and services are also important factors.

The impact of climatic conditions on the development of tourism cannot be ignored. Summer rainstorms, floods, and typhoons pose serious threats to the safety of tourists; both high and low temperatures and droughts will increase the discomfort of travel and affect the number of tourists. Tourists are mainly concentrated in the high tourist season of May to October in most provinces, which is highly coincident with the months with the most frequent meteorological disasters. There is a significant negative correlation between the year-on-year growth in domestic tourism and the CRI in that year (Fig. 9). Tourists are more inclined to cancel or change travel plans in years with a high climate risk.

 Figure 9 Relationship between the climate risk index (blue) and the growth rate of number of domestic tourists (red).

In addition to the impact of the overall climate risk on tourism, attention should also be paid to the impact of climate imbalances in different regions. High temperatures in some areas in summer will promote the flow of tourists to areas with lower temperatures, whereas low temperatures and snowfall in the north in winter will increase the attractiveness of this region to tourists from the south. Heavy rains and typhoons place great constraints on travel, but droughts may increase the popularity of tourist attractions such as coastal regions and forests. The impact of climate factors on tourist flows in different regions will be included in future studies.

4.4 Climate risk index and insurance

The insurance industry is very closely related to climate risk. Increased climate risk will directly increase claims for relevant types of insurance. Historical weather disasters and predictions of future climatic conditions will affect the levels of insurance premiums. Among the various types of insurance, we select property insurance and agricultural insurance as representatives to study the effect of climate risk indices.

Our results show that water-logging by rain and typhoons have the most direct impact on property loss, whereas losses in agricultural production are related to water-logging by rain, droughts, high temperatures, low temperatures, and typhoons. As there is a temporal gap of several months between indemnification and the occurrence of disasters and losses, we only analyze the annual data. Since 2004, the year-on-year increase in household property insurance claims is highly correlated with water-logging by rain and typhoon disasters in that year (Fig. 10) with a correlation coefficient of 0.70. The growth rate for agricultural insurance claims in most years is related to the overall CRI (Fig. 10b) with a correlation coefficient of 0.20. However, there are differences in climate risk between different regions. From a long-term perspective, regions with high climate risk have high premium levels and should also have high rates of insurance coverage.

 Figure 10 Relationship between household property insurance (red) and (a) sum of the index of water-logging by rain and the typhoon index (blue) and (b) the climate risk index (blue).
4.5 Climate risk index and health

There are many factors that affect human health, including climatic conditions. Abnormal weather conditions can cause discomfort, increase the risk of disease, and increase the number of both hospital outpatients and inpatients; severe disasters may even increase the mortality rate. There are concentrated occurrences of some health conditions under particular weather conditions. For example, people are prone to heatstroke and intesti-nal disorders in high temperature seasons; low temperature conditions have an adverse effect on patients with cardiovascular disease; and infectious diseases often peak after floods. Physical damage and psychological distress are often related to long-term conditions caused by climate disasters.

China has made rapid developments in medicine over the last 15 years. Public concerns over health have improved, treatment conditions have improved, and the number of hospital inpatients and outpatients and medical expenses show an upward trend. Limited by the data available on specific diseases, we take the total number of inpatients as a health index. Because the factors affecting the hospitalization of patients are complex and there are differences in the impact of different climate risks, we do not distinguish between specific climate risks and analyze the overall climate risk. There is a positive correlation between the annual growth rate of inpatients and the CRI with a correlation coefficient of 0.15. The correlation has been particularly significant in the last five years (Fig. 11).

 Figure 11 Relationship between the year-on-year increase in inpatient numbers (red) and the climate risk index (blue).
5 Conclusions and discussion

We use statistical methods to quantitatively calculate the indices for climate risks caused by water-logging, drought, high temperature, cryogenic freezing, and typhoon. These indices are used to characterize major extreme weather and climate events and unusual climatic conditions on different timescales in China. The overall climate risk for China is also derived and calculated. The application of these climate risk indices to relevant industries are analyzed and our conclusions are as follows.

(1) From 1961 to 2016, China’s CRI, the index of water-logging by rain, and the high temperature index increase at a rate of 0.28, 0.37, and 0.65 per decade, respectively; whereas the cryogenic freezing index decreases at a rate of 0.61 per decade. There is no significant change in the drought index. No change is found in the typhoon index either.

(2) The average yearly growth rate of the CPI for food during January–February is highly correlated with the average cryogenic freezing index during the same time period, with a correlation coefficient of 0.89. The correlation coefficient between the year-on-year growth rate in the total household electricity consumption from July to August and the average high temperature index from July to August is 0.73. Since 2004, the correlation coefficient between the year-on-year growth in claims on household property insurance and the sum of the water-logging by rain index and the typhoon index in the same year is 0.70. The growth rate in claims for agricultural insurance and the annual growth rate for hospital inpatients are both positively correlated with the CRI with a correlation coefficient of 0.20 and 0.15, respectively. The yearly growth in the number of domestic tourists is negatively correlated with the CRI for a particular year.

(3) Research into and the development of indices for China’s climate risks should be more closely linked to the relevant industries to meet the demands for climatic products of the investors, producers, and consumers. Considering the vast territory and complex climatic conditions of China, descriptions based on average results may underestimate the impact of major climate risks in some areas. There are significant differences in the economic structure of different regions and differences also exist in the impact of same-level climate risks on the economy. We therefore need to study and develop regional CRIs to establish better links between the climate risk and the economy in different economic zones/sectors. For example, agricultural production and climatic conditions are inseparable, therefore we need to study the climatic conditions suitable for different crops, so as to develop CRIs for crop yield and price under certain climate expectations. We need to make the climate index an important tool with which to modulate and facilitate the farming and the produce market.

(4) The main use of a climate index is to reduce or prevent future meteorological disasters. By using the precursory signals in global sea surface temperature, the western Pacific subtropical high, monsoon circulation, and land ice and snow changes, together with the outputs of climate models, we can predict the main climate elements (such as temperature and precipitation) for China on the country scale at a lead time of three months. The climate risk indices can then be calculated to predict trends in the CPI for food, insurance claims, and the tourists demand. Although there are uncertainties in the current climate models as well as uncertainties due to human factors, climate indices are significantly useful in many industries.

References