Drought caused the most widespread damage in China, making up over 50 % of the total affected area nationwide in recent decades. In the paper, a Standardized Precipitation Index-based (SPI-based) drought risk study is conducted using historical rainfall data of 19 weather stations in Shandong province, China. Kernel density based method is adopted to carry out the risk analysis. Comparison between the bivariate Gaussian kernel density estimation (GKDE) and diffusion kernel density estimation (DKDE) are carried out to analyze the effect of drought intensity and drought duration. The results show that DKDE is relatively more accurate without boundary-leakage. Combined with the GIS technique, the drought risk is presented which reveals the spatial and temporal variation of agricultural droughts for corn in Shandong. The estimation provides a different way to study the occurrence frequency and severity of drought risk from multiple perspectives.
The resilience of rural households is challenged by the uncertainties of climate risks (Barnett and Mahul, 2007; Hellmuth et al., 2009; Nieto et al., 2010; Trærup, 2012). Among all the natural disasters, drought influences agriculture production the most due to its long duration and high frequency (Li et al., 2015). The IPCC fifth report (Field et al., 2014) has shown that the drought-prone regions will be exposed to severer drought risks as the regional-to-global soil–moisture ratio will continue to decrease. In China, more than two million people have been plunged back to poverty with impact of the drought in southwest China (Sivakumar, 2010).
The drought is defined as a condition of moisture deficit (e.g. of precipitation, streamflow, soil moisture) in a specific time period (Kao and Govindaraju, 2009; McKee et al., 1993). The commonly used indicators for assessing the drought includes Standardized Precipitation Index (SPI) (McKee et al., 1995), Palmer Drought Severity Index (PDSI) (Palmer, 1965) and Vegetation Condition Index (VCI) (Kogan, 1995), etc. Among the indices, SPI shows a better performance in aspects of flexibility in time scale and geography (Alley, 1984; Guttman, 1998; Heim Jr., 2002; Mishra and Singh, 2010). To further increase the effectiveness of drought risk assessment, recent studies tend to analyse drought from multivariate aspects (Michele et al., 2013), which leads to the estimation the multivariate probability density functions (PDFs) by parametric and non-parametric methods (Santhosh and Srinivas, 2013). As pointed out by Santhosh and Srinivas (2013), non-parametric PDF estimation is more reliable for analyzing hydrological risk, while parametric models are recommended when the probability density of the underlying variable is known.
Of the various ways to estimate the PDF using non-parametric functions, kernel density estimation has gained the most recognition (Santhosh and Srinivas, 2013). It has been widely adopted in the frequency analysis of flood and drought (Dalezios et al., 2000; Kannan and Ghosh, 2013; Kim et al., 2006; Moon et al., 2010; Parviz et al., 2013). Among the different kernel density estimation methods, the standardized kernel function (e.g. Gaussian kernel density estimation (GKDE)) is known for its relatively straightforward computation scheme. However, one of the disadvantages for GKDE is the boundary leakage problem that may generate biased PDF for the case of large bandwidth or left skewed variable (Santhosh and Srinivas, 2013). Another concern is the bandwidth selection which can dramatically change the shape of the estimated PDF (Kannan and Ghosh, 2013). To overcome these, an alternative – the diffusion-based kernel density estimation (DKDE), has been proposed by Botev (2010). It is shown that the DKDE performs better compared to GKDE in the aspects of improving asymptotic bias, reducing computational cost and avoiding the boundary leakage problem for left-skewed variables (e.g. precipitation) (Botev et al., 2010; Ramsey, 2014; Santhosh and Srinivas, 2013).
In the study, a SPI-based drought risk analysis is carried out using historical rainfall data of 19 weather stations from 1951 to 2006 in Shandong province, China. In the analysis, both the bivariate GKDE and DKDE are used. The occurrence frequency and severity of drought risk per growth phase are derived by both methods. Comparison between the two density estimators is discussed based on the obtained results.
Shandong province is a part of the Northern China Plain located in the region
between longitudes 34–38
In despite of its reputation in grain production, the province is also known as one of the most drought prone regions in China. Xue (2004) identified drought as the key peril for crop production in Shandong. It is confirmed by analyzing the area with over 30 % yield loss at province level due to five key perils (drought, flood, frost, typhoon, and hail). The result shows that 64 % of the affected area was hit by drought over the period 1978–2011 in Shandong (Yearbook, 1979–2012) (Fig. 2).
In this study, daily precipitation of 19 weather stations from 1951 to 2006 is collected from National Meteorological Information Center (NMIC) is compiled in Table 1. The Thiessen Polygons (Thiessen, 1911) is introduced to cover the entire Shandong province by the 19 weather stations which served as seed points (Fig. 1).
Corn is the predominant crop normally planted in June and harvested in September (Fig. 3). Growth periods is phenologically divided into Emergence (Phase I: 6–13 June), Jointing (Phase II: 14–15 July), Anthesis (Phase III: 16 July–1 August), Grain Filling (Phase IV: 2–22 August) and Maturity (23 August–13 September) (Fig. 3). Due to the importance of pre-sowing soil moisture for germination, the farmers assess the soil moisture before planting. Excessive rainfall in Phase I affects the germination and emergence rate of corn, hence hindering the development of root system and cause the corn more vulnerable to drought in the following growth phases (Kranz et al., 2008). As a result, including Phase I introduces negative correlation between the drought index and the corn yield, which affects the accuracy and does not realistically reflect the drought exposure. Therefore, Phase I is not considered in the study.
For this study, the following approach is adopted to construct the SPI-based drought risk for corn in Shandong province: (i) data cleansing and detrending. Historical daily rainfall data of 19 weather stations in Shandong province are firstly cleansed and detrended for the calculation of the cumulative rainfall per growth phase, and then interpolated using Thiessen Polygons by the location of weather stations, (ii) SPI-based drought variables analysis. The SPI per growth stage of corn is developed for each region and converted into the drought duration, severity and intensity, (iii) univariate and bivariate PDFs of SPI drought variables estimation. The occurrence frequency and severity of drought risk per growth phase from multiple perspectives are conducted using DKDE and GKDE methods, (iv) joint return period analysis. The bivariate exceeding probability function is derived from the bivariate cumulative probability functions (CPFs) by integrating estimated PDFs constructed by DKDE and GKDE. By using the GIS spatial analysis tool, the spatial distribution of drought risk return periods at different drought intensities and drought durations are shown for the study region.
Meteorological data may contain trends caused by artificial influence
such as relocation of weather station (Hartell et al., 2006). In this
study, the historical rainfall records of stations
57 415/57 465/54 830/54 909 were relocated in the
1990s. Therefore, detrending is conducted to remove the
relocation-caused trend in prior to risk analysis. The conclusive
changes (e.g. increasing trending caused by relocation) in rainfall
will be identified with statistical regression to show the actual
structural trend (e.g. fluctuation of rainfall amount) (Hartell
et al., 2006). The rainfall data is assumed to be stationary in a long
time span. The linear detrending method (Hartell et al., 2006) is
adopted to decompose the rainfall data set
Following the method described in this section, the precipitation data for each of the 19 weather stations from year 1951 to year 2006 are cleansed and detrended. In the next section, the detrended rainfall will be used to compute the SPI.
The Standardized Precipitation Index (SPI) has been chosen to model the drought events considering its flexibility in time scale and tolerance in data geographical coverage. The calculation of the SPI is based on the probability density estimation of rainfall in a given time period. Theoretically, at least 30 years of continuous precipitation data is required for the calculation (McKee et al., 1993).
Firstly, the accumulated rainfall over a chosen period of time for each
insured area is fitted with a Gamma distribution (Eqs. 3 and 4) (McKee
et al., 1993). The shape and scale parameters are estimated by Maximum
Likelihood Estimation (Akaike, 1998). In this study, the length of each
phenological corn growth stages is chosen to be the time interval (Fig. 3).
Secondly, due to the difference of rainfall pattern in each region, the Gamma
cumulative distribution has different values of mean and standard deviation.
The variation will result in different drought characteristics. Hence, the
magnitude of drought events is incomparable across different regions. In
order to compare the drought severity across different regions, the Gamma
cumulative distribution function is transformed to the standardized Normal
cumulative distribution function with mean zero and standard deviation of
unity (Eq. 5) (Guttman, 1999; Sadat Noori et al., 2012). A positive SPI
indicates that rainfall amount is higher than mean value, while negative
value indicates the opposite. Since the resulting SPI is independent from
geographical and topographical difference (Manatsa et al., 2010), it can be
used to compare the magnitude of drought events across different regions.
Theoretically, the SPI represents how much the observed precipitation data
departs from the mean with regards to Gamma density function. The degree of
the departure has been quantified and expressed as the SPI representing
numbers of standard deviation from mean in normal distribution. For example,
the cumulative probability of one negative standard deviation (SPI
The theory of The drought duration Drought severity The drought intensity
To quantify the drought risk during a corn growth period, both drought duration and intensity are analysed using the DKDE and GKDE estimators. The K-S test is used to estimate the effectiveness of the two. This section provides a brief introduction of GKDE and DEKE.
Kernel density estimation is firstly introduced by Rosenblatt (1956)
and the general form is given by Härdle (1991). Let
(
The bandwidth is determined under the assumption that the underlying true
density is normally distributed and targets to minimize the asymptotic mean
integrated square error (AMISE) between the kernel density and the target
density (Silverman, 1986). When the Gaussian function is adopted in
multivariate case, the optimal bandwidth
The rescaled SPI-based variables, duration and intensity, are denoted
by
The estimation of
After the estimation of the joint PDFs of the duration and intensity,
the joint return period is calculated from the bivariate cumulative
probability functions (CPFs) by aggregating the joint PDFs for
different drought events. The return period
To examine the performance of the DKDE and GKDE, both methods are applied to SPI per growth phase of the19 weather stations in Shandong province. The data from Weather station 57 414 is taken as an example. The joint return period of drought duration and drought intensity based on the DKDE is developed for the spatial drought risk analysis in Shandong province. The performance of the DKDE and GKDE is examined by comparing the SPI-based corn drought risk for all the four growth phases in two aspects: drought duration and drought intensity.
The monthly SPI per year and SPI of Phase II to V of each weather
station are separately calculated and plotted in Fig. 5. The
fluctuation of SPI per growth phase from 1951 to 2006 indicates that
the lowest SPI is around
Figure 6 shows the bivariate PDF of drought intensity and duration for Phases
II–V estimated by DKDE and GKDE separately. One thing can be observed from
the figure is that the DKDE performances better than the GKDE in terms of the
boundary leakage or boundary bias problem. For example, Fig. 6b shows that
the PDF estimated by GKDE results in negative drought intensity, and the left
boundary of GKDE marginal PDF estimation extends into the negative region of
drought intensity in Fig. 6c. Furthermore, the K-S test at 95 %
confidence level is shown in Table 3. It indicates that DKDE has a better
goodness of fit for univariate PDF for drought intensity compared to the one
using GKDE. It is shown that 92 % of the
The bivariate exceeding probability is shown in Fig. 7. It is later used to obtain the joint return period of drought duration and drought intensity. Comparison of the joint return period estimated by DKDE and GKDE is shown in Fig. 8. The figure indicates that the drought intensity estimated by GKDE is higher than that of DKDE given the same drought duration and vice versa. Figure 9 shows the joint return period of drought duration and intensity in Phases II, III, IV and V estimated by DKDE for weather station 57 414.
The joint return period by DKDE for Shandong Province is computed under the
condition of 1
Regions around the weather station 54 936 show that the highest return
period (6.7
Better understanding of the occurrence frequency and severity of drought risk can help financial institutions and governments to capture the potential losses and compensate the uncertainties of caused by extreme drought events. Therefore, it is necessary to conduct ample studies for the related risks beforehand.
The study provides an alternative to understand the occurrence and severity of drought risk from multiple perspectives. As shown in Sect. 4, the DKDE is more effective than GKDE in estimating the bivariate PDFs of drought risk in terms of accuracy and the ability to avoid boundary-leakage problem. Combined with GIS spatial analysis techniques, spatial and temporal variations of agricultural droughts for corn in Shandong province are revealed. It is shown that the central region is less vulnerable to drought compared to the other regions. Therefore, using the DKDE function to analyze agricultural drought will eventually help the financial institutes determine compensation by providing a reference for identifying regional drought risk vulnerability, and offer important technological support for drought management for government.
Locations and daily rainfall data records of 19 weather stations in Shandong province.
Drought categories based on Standardized Precipitation Index.
Location of Shandong province in China (top), Shandong province (below) with 19 weather stations (points) and Insured Areas by Thiessen polygons.
Sown agricultural area affected by drought, flood, and other
perils in Shandong province from 1978 to 2011 (1 ha = 15
Corn phenological growth stages in Shandong province.
Standardized Precipitation Index (SPI)-based drought duration
SPI per corn Growth Phase II
Weather station 54 714
Joint return period of drought duration and drought severity for corn growth phase II, III, IV and V (weather station 57 414).
Map of Shandong province with joint return period with
drought duration of 1
Map of Shandong province with joint return period with
drought duration of 1