
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.

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 (SPI_{m}) 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 SPI_{m} 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 singlestation MDI of the 2288 stations in China one by one. We then obtain the weighted average of the singlestation 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 a_{i} 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 b_{i} 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. X_{max} and X_{min} 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 threshold 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.

There has been much interest in waterlogging indicators and assessment methods in recent years. Zhong et al. (2009) studied the spatiotemporal distribution of waterlogging by rain in Zhejiang Province during a period of concentrated precipitation. Zhang et al. (2009) analyzed the changes in waterlogging 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 waterlogging by rain based on the daily precipitation level.
First, we calculate the daily precipitation level index (R_{d}). The precipitation at a single station on one day (P) is divided into four levels:
Level 0 (R_{d} = 0): P < 50 mm;
Level 1 (R_{d} = n^{1/2}): 50 mm
$ \leqslant $ P < 100 mm for the nth consecutive day of a rainstorm;Level 2 (R_{d} = 2n^{1/2}): 100 mm
$\leqslant $ P < 200 mm for the nth consecutive day of a rainstorm;Level 3 (R_{d} = 3n^{1/2}): 200 mm
$ \leqslant $ P for the nth consecutive day of a rainstorm.We then calculate the monthly index for waterlogging 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, R_{d} 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 waterlogging 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 X_{max} and X_{min} are the maximum and minimum of X for all months from 1961 to 2016.
The weighted average of the 12month CMR in a year is normalized to give the arithmetic mean (Y). The result is a yearly index for waterlogging 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 a_{i} is the monthly weighted coefficient (2 for June, July, and August; and 1 for other months), and Y_{max} and Y_{min} 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.

The absolute temperature threshold, the relative threshold, and the probability distributionbased 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 threshold is a percentilebased 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 (T_{g}) and divide the daily maximum temperature (T_{max}) of a station into three levels:
Level 1 (T_{g} = 1): 35°C
$\leqslant $ T_{max} < 37°C;Level 2 (T_{g} = 2): 37°C
$\leqslant $ T_{max} < 40°C;Level 3 (T_{g} = 3): 40°C
$\leqslant $ T_{max}.We then calculate the daily minimum temperature level index (T_{d}) and divide T_{min} of a station into three levels:
Level 1 (T_{d} = 1): 25°C
$\leqslant $ T_{min} < 28°C;Level 2 (T_{d} = 2): 28°C
$\leqslant $ T_{min} < 30°C;Level 3 (T_{d} = 3): 30°C
$\leqslant $ T_{min}.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, T_{g} is the daily maximum temperature level index of a station on a single day, T_{d} is the daily minimum temperature level index of a station on a single day, D_{g} is the number of days when the daily maximum temperature of a station is continuously
$\geqslant $ 35°C, D_{d} 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 X_{max} and X_{min} are the maximum and minimum values of X for all months from 1961 to 2016.
We next average the 12month 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 Y_{max} and Y_{min} 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.

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 fiveday timescale to develop a cryogenic freezing index.
We compare the mean temperature anomaly in a fiveday 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 5day period,
$\overline {t} $ is the average temperature of the 5day period over 30 yr (1981–2010, a climatology period defined herein), and σ is the standard deviation of the temperature for the 5day period. The index mainly considers the average temperature of a fiveday 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 (I_{m}) and the cryogenic freezing index for winter (I_{y}) 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 5day 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.

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 6h 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 typhooninduced 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 (I_{t}) by weighting:
$${I_{\rm{t}}} = 0.4{I_{{\rm{mw}}}} + 0.6{I_{{\rm{pre}}}},$$ (12) where I_{mw} is the sum of the number of grid points in each interval of the wind factor, and I_{pre} 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.

Our calculation of a CRI for China is based on the monthly and yearly indices for waterlogging 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 waterlogging 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 CRI_{m} is China’s monthly climate risk index, N represents the number of disaster types, D_{i,j} is the index for disaster i and month j, and T_{i,j} is the weight of D_{i,j}. Using the multiyear average losses from meteorological disasters as the weight of the five yearly indices of meteorological disasters (waterlogging, 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 CRI_{y} is China’s yearly climate risk index, N represents the number of disaster types, D_{i} is the yearly index of disaster i, and T_{i} is the yearly weight of D_{i}.
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 12month 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 D_{i,j} represents the monthly index of a disaster and TD_{i,j} represents the weight of a disaster index in a month. TD_{i,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 CRI_{m} 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 CRI_{y} 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.
Search
Citation
Yujie WANG, Lianchun SONG, Dianxiu YE, Zhe WANG, Rong GAO, Xiucang LI, Yizhou YIN, Zunya WANG, Yaoming LIAO. Construction and Application of a Climate Risk Index for China[J]. J. Meteor. Res., 2018, 32(6): 937949. doi: 10.1007/s1335101981061 
Article Metrics
Article views: 489
PDF downloads: 43
Cited by: