Drought Risk Assessment Based on Vulnerability Surfaces: A ... - MDPI

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Drought Risk Assessment Based on Vulnerability Surfaces: A Case Study of Maize Hao Guo 1,2 , Xingming Zhang 1,2,3 , Fang Lian 1,2 , Yuan Gao 1,2 , Degen Lin 1,2 and Jing’ai Wang 1,3,4, * 1

2 3 4

*

School of Geography, Beijing Normal University, Beijing 100875, China; [email protected] (H.G.); [email protected] (X.Z.); [email protected] (F.L.); [email protected] (Y.G.); [email protected] (D.L.) The Key Laboratory of Regional Geography, Beijing Normal University, Beijing 100875, China China Insurance Information Technology Management Co., Ltd., Beijing 100144, China The State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China Correspondence: [email protected]; Tel.: +86-10-5880-7454 (ext. 1632)

Academic Editor: Marc A. Rosen Received: 14 June 2016; Accepted: 11 August 2016; Published: 18 August 2016

Abstract: Agriculture is a sector easily affected by meteorological conditions. Crop yield reduction, even regional conflicts, may occur during a drought. It is extremely important to improve the state of our knowledge on agricultural drought risk. This study has proposed a new method (vulnerability surfaces) for assessing vulnerability quantitatively and continuously by including the environmental variable as an additional perspective on exposure and assessed global maize drought risk based on these surfaces. In this research, based on the Environmental Policy Impact Climate (EPIC) model, irrigation scenarios were adopted to fit “Loss rate-Drought index-Environmental indicator (L-D-E)” vulnerability surfaces by constructing a database suitable for risk assessment on a large scale. Global maize drought risk was quantitatively assessed based on its optimal vulnerability surface. The results showed an R2 for the optimal vulnerability surface of 0.9934, with coarse fragment content as the environmental indicator. The expected global average annual yield loss rate due to drought was 19.18%. The global average yield loss rate due to drought with different return periods (10a, 20a, 50a, and 100a) was 29.18%, 32.76%, 36.89%, and 38.26%, respectively. From a global perspective, Central Asia, the Iberian Peninsula, Eastern Africa, the Midwestern United States, Chile, and Brazil are the areas with the highest maize drought risk. The vulnerability surface is a further development of the vulnerability curve as a continuous expression of vulnerability and considers differences in environmental factors. It can reflect the spatial heterogeneity of crop vulnerability and can be applied in large-scale risk assessment research. Keywords: vulnerability surfaces; drought risk assessment; EPIC; maize

1. Introduction The Intergovernmental Panel on Climate Change (IPCC) 5th Assessment Report confirmed that, in general, global temperatures rose from 1880 to 2012, with a linear trend of 0.85 ◦ C/100a. Temperature increases are therefore expected to characterize global climate change in the 21st century. By the end of the 21st century, the global average temperature will have increased by at least 1.5 ◦ C compared with the period from 1850 to 1900 [1]. The probability of severe and persistent droughts may increase in the future under the influence of climate change and anthropogenic forcing [2,3]. Droughts may bring about food security problems or even regional conflicts [4]. Agriculture is dependent on climate conditions and is greatly influenced by climate change [5,6]. Reducing drought risk has therefore

Sustainability 2016, 8, 813; doi:10.3390/su8080813

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Sustainability 2016, 8, 813

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become an important topic in disaster risk research and is critical for promoting global food security and sustainable agricultural development. Risk assessment can generally be divided into hazard assessment and vulnerability assessment [7]. A number of drought indicators have been proposed for crop drought hazard assessment, such as the Palmer Drought Severity Index (PDSI) [8], the Standardized Precipitation Index (SPI) [9], the Vegetation Health Index (VHI) [10], and the Agricultural Reference Index for Drought(ARID) [11]. More recently, with the development of fuzzy mathematics in risk assessment [12], the quantitative evaluation of drought hazard has been generalized [13,14]. The most commonly and widely used methods of vulnerability assessment can be classified into three types: (1) vulnerability assessment based on historical disaster data, such as long-term data on precipitation, crop yield, and other factors [15–17]; (2) vulnerability assessment based on indicators [18–20]; and (3) vulnerability assessment based on the hazard–loss curve (also called the vulnerability curve), which can reflect the response of crop yield to drought from the aspects of crop physical properties [21–23]. Generally, case studies using the first two approaches may be limited if no long-term observational data are available. In addition, the first two methods provide only a qualitative or semi-quantitative vulnerability assessment. Risk assessment models also suffer from this limitation, and, as a result, they cannot directly estimate the probability of disaster losses [24]. A quantitative evaluation of crop vulnerability is clearly important to the quantitative assessment of agricultural drought risk [25]. The vulnerability curve can establish the quantitative functional relationship between hazard and loss. It provides a new method for quantitative evaluation of agricultural drought risk. Vulnerability curves first appeared in 1964 [26] and were used to provide a quantitative measurement of the interaction between hazard intensity and corresponding loss (loss rate) [27]. A vulnerability curve can quantitatively evaluate crop vulnerability. Studies have used the water requirement satisfaction index (WRSI) and loss rate to produce maize drought vulnerability curves for three countries (Kenya, Malawi, and Mozambique) [28]. With the development and application of crop models in disaster science, crop drought vulnerability assessments have adopted these models [22,29]. Yin [30] fitted maize drought vulnerability curves for 35 regions globally, using the water stress index and a maize yield loss rate simulation with the EPIC model. Agricultural drought risk assessment based on vulnerability curves calculates the losses (or loss rates) at different hazard intensities and is hence more quantitative and accurate than risk level evaluations based on indicators. However, the vulnerability curve involves only two dimensions, hazard intensity and loss, without considering environmental factors. Crop drought, however, is often influenced by more than just hazard intensity, which may vary among different environments. It is also difficult for vulnerability curves to express the continuous spatial variability of vulnerability. As a result, the spatial accuracy of risk assessment is limited, but can be improved by constructing a three-dimensional risk assessment method that includes loss rate, hazard intensity, and an environmental indicator. Surfaces have been commonly used for vulnerability assessments in earthquake disaster studies, in which fragility surfaces were fitted according to degree of damage and hazard intensity based on the structure of buildings or bridges. Lee [31] combined snow and earthquake hazards, both of which influence buildings, to fit fragility surfaces. Wang [32] considered the multiple hazards of earthquake and scour (flood and debris flow) to fit the fragility surface for a bridge. To date, few researchers have applied vulnerability surfaces to agricultural drought risk assessment. In fact, crop vulnerability varies among different locations. The evaluation under one environmental condition may not necessarily be applicable to other environments. The larger a study area, the greater is the variation in vulnerability, and the more important it becomes to fit continuous surfaces to express crop vulnerability. In this paper, a method of fitting three-dimensional vulnerability surfaces (“Loss rate-Drought index-Environmental indicator (L-D-E)”) is proposed. This method may provide a new way to evaluate crop vulnerability by considering exposure that vulnerability curves could not cover. This paper also assesses global maize drought risk quantitatively based on vulnerability surfaces.


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2. Materials and Methods 2.1. Basic Idea and Research Framework 2.1.1. Assessment of Physical Vulnerability to Maize Drought The vulnerability of a system to climate change may be characterized as a function of the exposure, sensitivity, and adaptive capacity of the system [33]. Vulnerability is dynamic and complex and may vary with changes in both the biophysical and socioeconomic characteristics of a particular region. Biophysical vulnerability is an inherent attribute of the exposure or inventory, which can reflect the response of the crop to the disaster [22]. Further work is needed to integrate information about exposure, sensitivity, and adaptability to provide more detailed and quantitative information about the potential impacts of climate change and the relative degree of vulnerability of different regions, nations, and socioeconomic groups [33]. (1) Sensitivity is the degree to which a system is affected, either adversely or beneficially, by climate-related stimuli. The effects may be direct (e.g., a change in crop yield in response to a change in the mean, range, or variability of temperature) or indirect (e.g., damage caused by increased frequency of coastal flooding due to sea-level rise) and can be expressed by vulnerability curves; (2) Adaptation is the process of adjustment to actual or expected climate and its effects. In some natural systems, human intervention may facilitate adjustment to expected climate and its effects. In this study, human intervention (i.e., adaption, e.g., the possibilities for improvement of maize species, cultivation management, and other social factors) was not calculated as an influence index, but was considered as constant for lack of quantitative data; (3) Exposure is the presence of people, livelihoods, species or ecosystems, environmental functions, services, and resources, infrastructure, or economic, social, or cultural assets in places and settings that could be adversely affected [34]. In this study, location (planting area of maize) was assumed to be unchanged because it was difficult to simulate accurately. Overall, only the biophysical aspect of vulnerability was considered, and the adaptability and sensitivity of maize were assumed to be constant. Therefore, irrigation scenarios were set by changing the amount of irrigation in the crop model. According to the output of the model (water stress and yield) under different irrigation scenarios, 3D surfaces considering environmental factors (settings) were fitted. 2.1.2. Assessment of Drought Intensity and Risk Based on Crop Model Simulation With the development of crop models, many researchers have combined crop model simulation output with historical data and established indices to forecast drought risk [21,35]. This research suggests that a complex crop model can simulate the relationship between drought and crop productivity. In this study, yield and water stress index were simulated by the EPIC model. EPIC is a comprehensive model consisting mainly of hydrological, meteorological, erosion, nutrient cycling, soil temperature, crop growth, tillage, and economic modules. It can continuously simulate the growth processes of more than 100 kinds of crops using a daily time step and readily available inputs [36]. Productivity under climate change can be simulated effectively based on the model parameters and meteorological data. In this research, water stress indices (WS) were simulated to evaluate water insufficiency for the drought intensity calculation. The meteorological data used in the EPIC model contain observational data from 1971 to 2004 and forecast data calculated by the Global Climate Model (GCM) [37]. To reduce the uncertainty of the model prediction, the section of observation data from 1975 to 2004 was chosen for this study. The WS index over 30 years in each grid cell was simulated all over the world based on the data. Information diffusion theory was used to calculate the probability distribution of drought intensity from a few WS samples. The pattern of drought intensity in different regions can be expressed based on the calibrated model. The calculated risk is the result of both drought intensity assessment


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and vulnerability assessment and is defined in this paper as the probability of a given loss rate of maize yield. Sustainability 2016, 8, 813

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2.1.3. Research Framework

2.1.3. Research Framework The study was conducted in three steps. In Step 1, an EPIC model was calibrated by adjusting The study parameters. was conducted three Step an EPIC model calibrated adjustingwere several important IninStep 2,steps. basedInon the1,calibrated EPICwas model, otherbyvariables several important parameters. In Step 2, based on the calibrated EPIC model, other variables were controlled, and different irrigation scenarios were defined to obtain yields and water stress indices controlled, and different irrigation scenarios were defined to obtain yields and water stress indices (WS), which were normalized as yield loss rate (LR) and drought index (DI) respectively. LR, DI, (WS), which were normalized as yield loss rate (LR) and drought index (DI) respectively. LR, DI, and and environmental indicators (E) (such as elevation, slope, and soil parameters) were combined to environmental indicators (E) (such as elevation, slope, and soil parameters) were combined to obtain obtain vulnerability surfaces. In Step 3, historical data and the information diffusion theory were used vulnerability surfaces. In Step 3, historical data and the information diffusion theory were used to to obtain the of DI, DI, which whichwas wascombined combined with vulnerability surface obtain theprobability probability distribution distribution of with thethe vulnerability surface to to calculate risk risk (considered to be thethe probability 1). calculate (considered to be probabilityof ofLR) LR) (Figure (Figure 1). Historical scenario Management Data

Calibration Data

EPIC Model

Drought Index (DI)

Information Diffusion Theory

Possibilit y

DI

Calibrated EPIC model

RIsk

Calibration Drought Index (DI)

Environmental Data

Irrigation scenario Yield Loss Soil, elevation and slope Data

Figure 1. Overall study procedure. Figure 1. Overall study procedure.

2.2. Data

2.2. Data

The data were divided into three categories: geographical environment data, field management

The were divided three data,data and calibration datainto (Table 1). categories: geographical environment data, field management data, and calibration data (Table 1). Table 1. Study data. Data Category Data Category

Table 1. Study data.

Name DEM Name

Spatial Temporal Resolution Resolution United States Geological Survey (USGS) [38] 0.0833° × 0.0833°Temporal 1996 Source Spatial Resolution Resolution International Institute for Applied Systems Source

Slope DEM

Geographical Geographical environmental environmental data data

Field management data Calibration Field data management data

Analysis-Global Agro-Ecological United States Geological Survey Zones (GAEZ) ◦ 0.0833 [39] (USGS) [38] International Reference and Information InternationalSoil Institute for Applied Soil Centre (ISRIC) [40] Slope Systems Analysis-Global 0.0833◦ German Federal Ministry of Education Agro-Ecological Zones (GAEZ) [39] and Meteorological Research (BMBF):The ISIMIPand Fast Track project International Soil Reference Soil 0.0833◦ [41] Information Centre (ISRIC) [40] University of Wisconsin-Madison: Sustainability German Federal Ministry of Extent of maize and the Global Environment (SAGE) [42] Meteorological Education and Research (BMBF):The 0.5◦ Growth period University ofTrack Wisconsin-Madison Sustainability ISIMIP Fast project [41] of maize and the Global Environment (SAGE) [43] University of Wisconsin-Madison: Irrigation The University of Tokyo (OKI Laboratory) [44] ◦ Extent of maize Sustainability and the Global 0.0833 Land Use and the Global Environment (SAGE) [42]Environment (LUGE) Fertilizer [45] University of Wisconsin-Madison Growth period Actual yield of Sustainability and theOrganization Global 0.5◦ Food and Agriculture (FAO) [46] of maize global maize Environment (SAGE) [43] The University of Tokyo (OKI

◦

0.0833° × 0.0833° 2002 × 0.0833◦ 1996 0.0833° × 0.0833° 2012 × 0.0833◦ 2002 0.5° × 0.5° × 0.0833◦

1971–2099 2012

0.0833° × 0.0833° 2000 × 0.5◦ 1971–2099 0.5° × 0.5°

2010

0.5° × 0.5° × 0.0833◦ 0.5° × 0.5°

2010 2000

National × 0.5◦ (regional) unit ◦

2011 2010 2000–2004

Irrigation data included global DEM, global slope0.5 × global 0.5 2010 The geo-environmental [47], soil parameters [48], Laboratory) [44] and global meteorological [37] data as Global global data on the planting extent of maize [49]. The Land as Usewell and the Fertilizer 0.5◦ × 0.5◦ 2011 Environment (LUGE) [45] to 2099 and consisted of actual meteorological meteorological data contained daily data from 1971 Calibration fromActual of and Food forecast and Agriculture National observations 1971yield to 2004 data Organization based on global climate model from2000–2004 2005 to 2099. data global maize (FAO) [46] (regional) unit Daily values of maximum temperature, minimum temperature, precipitation, solar radiation, wind


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The geo-environmental data included global DEM, global slope [47], global soil parameters [48], and global meteorological [37] data as well as global data on the planting extent of maize [49]. The meteorological data contained daily data from 1971 to 2099 and consisted of actual meteorological observations from 1971 to 2004 and forecast data based on global climate model from 2005 to 2099. Daily values of maximum temperature, minimum temperature, precipitation, solar radiation, wind speed, and relative humidity were used in the EPIC model to assess the probability distribution of DI. Field management data included the growth period of global maize [50], global agricultural irrigation patterns [51], and global fertilizer application [52]. The irrigation and fertilizer data were defined as “maximum annual irrigation volume allowed” and “maximum annual nitrogen fertilizer application” for a crop respectively when running the EPIC model. The automatic options for fertilization and irrigation were applied in the EPIC model because it was impossible to obtain real fertilizer and irrigation schedules for each grid cell. The EPIC model requires all input data to have the same spatial resolution. Hence, the spatial resolutions of all data were converted into the same resolution as the meteorological data. The calibration data were the statistical yield of maize reported by FAO for each country (region) from 2000 to 2004, of which the data for 2000 were used to calibrate the model and the 2001–2004 data were used to validate it. 2.3. Methodology 2.3.1. Calibration of EPIC Model calibration is the basis for accurate simulation. For this study, risk was calculated by simulating the LR of maize yield under drought conditions produced by the EPIC model. Hence, it was important to simulate yield accurately. Moreover, the EPIC model parameters needed to be adjusted to suit different regions. The basic unit selected was the 0.5◦ × 0.5◦ grid, which is ideal for calibrating the model in each grid cell. However, when the model is calibrated in each grid cell, the cost of the calculation should be considered. Therefore, the country (region) was selected in this research as the basic unit to calibrate the EPIC model. Based on earlier studies [53–56], four parameters (WA (biomass-energy ratio), HI (harvest index), DLMA (maximum potential leaf area index), and DLAI (fraction of the growing season when leaf area declines)) were considered as key parameters of the EPIC model. In the calibration process, the parameters were adjusted for each country (region) that was considered as a homogeneous unit to create a suitable EPIC model. The parameters of each grid cell in each unit were adjusted at the same time (hence, each grid cell in a unit has the same parameters). Simulated yields of 2000 in each grid cell were obtained with the EPIC model and averaged in each unit to be compared with the statistical yield of each country (region). When the simulated yields of 2000 were close to the statistical yields, the calibration was completed. The results of model calibration for each unit were evaluated by comparing simulated maize yields with statistical yields for 2001–2004. Direction and step length are key factors in parameter adjustment. This study used the automatic adjustment method. The adjustment of each parameter in one unit can be described as three main steps. Step 1: define the default value of each parameter as the initial value in each unit. Simulate the yield of each grid cell using the initial value, and calculate the average yield of each unit. Calculate the RMSE between the simulated and statistical yields. Consider the initial parameter value as the optimum value if the RMSE is less than the threshold. Step 2: if the RMSE value is not less than the threshold, the parameter adjustment phase will work. First, consider the default value as the optimal parameter value and adjust it using Rule 1 if the number of cycles is less than 1. Step 3: carry out a new judgment if the condition in Step 2 is not satisfied. Assuming that the N-th cycle is the current cycle, adjust the parameter using rule 1 if the simulated yield in the (N-1)-st cycle is closer than that in the (N-2)-nd cycle to the actual yield, or adjust it using Rule 2 if not.


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Cycle through the adjustment process in the manner described above until the simulation results reach the output condition or the maximum number of cycles is reached; the optimal output parameters are assumed to 8, be813 obtained (Figure 2). Sustainability 2016, 6 of 22 Original Model Parameter C

EPIC Model

Simulation Yield Y Actual Yield Y0 RMSE＜Threshold？ Or Cycle Times＞Threshold？

Cycle Yes

Optimal Model Parameter C 0

Cycle NO

Cycle Times＜1？

No

Yes Simulation Yield closer to Y0？

No

Calculate Model Parameter (by Rule 2)

Yes

Optimal Yield and Parameter

Save Yield Y and Parameter C

Save Yield Y and Parameter C



Figure Figure 2. Parameter adjustment adjustment (assuming (assuming the the N-th N-th cycle cycle is is the the current current one): one): Rule Rule 1: 1: the step length length of of the 0.2, and and the the direction direction is the same as the (N-1)-st adjustment the N-th N-th adjustment adjustment == initial initial parameters parameters × × 0.2, (the (the default default is is positive positive ifif this this isis the the first firsttime). time). Rule Rule 2: 2: the step length length of of the the N-th N-th adjustment adjustment == [(parameter value of (N-1)-st adjustment) − (parameter value of (N-2)-nd adjustment)] × [(parameter value of (N-1)-st adjustment) − value of (N-2)-nd adjustment)] × 0.5, and the direction direction is is opposite opposite to to that that of of the the (N-1)-st (N-1)-st adjustment. adjustment.

Vulnerability Surface Surface 2.3.2. Fitting of the Vulnerability Based on the “Loss rate-Drought index-Environmental indicator (L-D-E)” samples generated by the calibrated calibrated EPIC EPIC model, model, the the drought drought vulnerability vulnerability surface surface of of maize maizehad hadthree threedimensions. dimensions. Waterstress stress(WS) (WS)isisan anEPIC EPICoutput outputfactor factorthat thatrepresents represents water shortage plants. The value Water water shortage forfor plants. The value of of WS ranges from 0 to the higher thevalue, value,the themore moreyield yieldisisaffected affectedby bydrought. drought. Twenty Twenty irrigation WS ranges from 0 to 1; 1; the higher the scenarios were defined to to obtain obtain “L-D-E” “L-D-E” samples. samples. First, the optimal level of irrigation (there are no irrigation level is is continuously continuously increased) was determined by significant changes in yield when the irrigation pre-testing. Second, Second,the the single-variable method to the keep the growth period, fertilizer pre-testing. single-variable method was was usedused to keep growth period, fertilizer addition addition and meteorological datawhile constant whilethe varying theofamount of irrigation to obtain WS rate, and rate, meteorological data constant varying amount irrigation to obtain WS and yield and yield under different irrigation scenarios. Twenty irrigation scenarios were defined to control the amount of irrigation, which uniformly increased from 0 to the optimal value in each grid cell. Third, WS and yield were simulated by EPIC under each scenario and then normalized to DI and LR. In this way, 20 samples of DI and LR were calculated in different grid cells that had different environmental conditions. DI and LR were then combined with the environmental indicators for each grid cell to


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under different irrigation scenarios. Twenty irrigation scenarios were defined to control the amount of irrigation, which uniformly increased from 0 to the optimal value in each grid cell. Third, WS and yield were simulated by EPIC under each scenario and then normalized to DI and LR. In this way, 20 samples of DI and LR were calculated in different grid cells that had different environmental conditions. DI and LR were then combined with the environmental indicators for each grid cell to generate the “L-D-E” Sustainability 2016, 8, 813 samples (Figure 3). 7 of 22

Figure 3. Generation “L-D-E” samples samples in in each each grid grid cell. cell. Figure 3. Generation of of “L-D-E”

WS can be normalized by Equations (1) and (2): WS can be normalized by Equations (1) and (2):

DI  DI k = k

HI

HI max(( HHII )) max n n

WSi ), HI i ∑ ((WS  i) , =1

HI =

(1) (1)

(2) (2)

i 1

where WSi indicates the WS of maize on day i, n is the number of days that maize was influenced by where i indicates theHI WS on day i,value n is the number days growth that maize was max(HI) influenced by WS in aWS growth period, is of themaize accumulated of WS in oneofmaize period, is the WS in a growth HI isall theirrigation accumulated valueDI ofk WS inhazard one maize growth max(HI) is maximum value period, of HI under scenarios, is the index in gridperiod, cell k, and k is the the maximum value of HI under all irrigation scenarios, DI k is the hazard index in grid cell k, and k is grid cell identification number. the grid cell identification number. Yield can be normalized using Equation (3): Yield can be normalized using Equation (3): max(y) − y LR = max( y )  y ,, (3) LR  max(y) (3) max( y ) where y is the yield under one scenario, LR is the yield loss rate caused by drought, and max(y) is the where y is the yield under one scenario, LR is the yield loss rate caused by drought, and max(y) is the maximum yield. maximum yield. Two topographic indicators (elevation and slope) and seven soil indicators (coarse fragment Two topographic indicators (elevation and slope) and seven soil indicators (coarse fragment content (CFRAG), bulk density (BULK), water content at field capacity (TAWC), sand content (SDTO), content (CFRAG), bulk density (BULK), water content at field capacity (TAWC), sand content silt content (CLPC), organic carbon concentration (TOTC), and soil pH (PH)) were selected as (SDTO), silt content (CLPC), organic carbon concentration (TOTC), and soil pH (PH)) were selected environmental indicators for the study. as environmental indicators for the study. Twenty “L-D-E” samples for each grid cell were generated to fit a maize drought vulnerability Twenty “L-D-E” samples for each grid cell were generated to fit a maize drought vulnerability surface with DI as the x-axis, an environmental indicator as the y-axis, and LR as the z-axis. surface with DI as the x-axis, an environmental indicator as the y-axis, and LR as the z-axis. The The vulnerability surface was fitted by trend surface analysis (Equation (4)): vulnerability surface was fitted by trend surface analysis (Equation (4)): +bb)) ( a/ (a1 + (c× / 1b×bexp  exp c DI DI)) − a/ a / (11   LR = × d × ( E −2 e)2 + f , (4) LR  ( a/ (1 + b × exp (c)) − a/ (1 + b))   d  ( E  e )  f  (4)  a / 1  b  exp  c    a / 1  b   , where LR is the maize yield loss rate, DI is the hazard index, E is an environmental factor, and a, b, c, d, where is the maize yield loss rate, DI is the hazard index, E is an environmental factor, and a, b, c, e, f are LR parameters. d, e, f are parameters.

2.3.3. Drought Risk Assessment Based on the Vulnerability Surface Risk assessment can generally be divided into hazard assessment and vulnerability assessment [7]:


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2.3.3. Drought Risk Assessment Based on the Vulnerability Surface Risk assessment can generally be divided into hazard assessment and vulnerability assessment [7]: Risk = Hazard × Vulnerability,

(5)

Sustainability 813 8 of 22 where Risk 2016, is the8, maize drought risk, Hazard is the function of maize drought hazard, and Vulnerability is the function of maize drought vulnerability. Section 2.3.2 introduced the method of vulnerability vulnerabilityHazard assessment. Hazard was assessed usingprocess: a three-step process: data (1) historical (30 years assessment. was assessed using a three-step (1) historical (30 yearsdata (1975–2004)) (1975–2004)) were used to establish WS for different grid cells using the EPIC simulation; (2) WS was were used to establish WS for different grid cells using the EPIC simulation; (2) WS was normalized to normalized to DI (using a method similar to Equation (2)) to generate 30 years of DI samples for each DI (using a method similar to Equation (2)) to generate 30 years of DI samples for each grid cell; (3) the grid cell; (3)distribution the probability DI cells for different grid cells was obtained to complete the probability of DIdistribution for differentof grid was obtained to complete the hazard assessment hazardinformation assessmentdiffusion using information diffusion theory using theory [57,58] (Figure 4). [57,58] (Figure 4).

Hazards analysis

Normalization

WS data in gridn

DI

Information diffusion theory

DI data in gridn

……

EPIC model

DI data in grid1

……

WS data in grid1

……

Historical scenario: Data from 1975 to 2004

Probability distr ibution of DI in grid1 Probability

Probability distr ibution of DI in grid n Probability

DI

Figure Hazard assessment assessment in Figure 4. 4. Hazard in each each grid grid cell. cell.

In this thisresearch, research, samples 30 years were to found to be insufficient estimate the DIDI samples overover 30 years were found be insufficient to estimatetothe probability probability distribution each grid cell. Information diffusion theory provides a method to change distribution in each grid in cell. Information diffusion theory provides a method to change observations observations into normal fuzzy so that the probability of DI canThe be calculated. The into normal fuzzy sets so that thesets probability distribution of distribution DI can be calculated. basic principle basic principle of information diffusion theory was explained by Huang [12,57]. of information diffusion theory was explained by Huang [12,57]. a discrete Let U = {u11, u22,, uu33,,…, . . .u,nu} nbe } be a discreteuniverse universeofofDI DIthat thatcontains containsits itspossible possible values. values. According According thedefinition definitionofof maximum value Uand is 1,the and the minimum is 0.study, In this the to the DI,DI, thethe maximum value of U of is 1, minimum is 0. In this the study, resolution resolution of the discreteisuniverse is 0.0001. Therefore, U = {0, 0.0001, …,information 1}. The information of the discrete universe 0.0001. Therefore, U = {0, 0.0001, 0.0002, . . .0.0002, , 1}. The carried carried by therefore DI was therefore to uigrid in each grid cell the information diffusionshown function by DI was diffused diffused to ui in each cell using theusing information diffusion function in shown in Equation (6): Equation (6): # " 1 ( DIk − ui )2 2 f k (ui ) = √1 exp −  DI k 2 ui  , (6) f (u )  h 2π exp   2h , (6) k

i

2h 2

h 2

 where k is the grid cell identification number and h is called the normal diffusion coefficient and is calculated by Equation (7): where k is the grid cell identification  number and h is called the normal diffusion coefficient and is m=5 0.8146 ( b − a ) ,  calculated by Equation (7):      0.5960(b − a), m = 6    m= 75 0.4560(bb−aa),), m 0.8146(  h= (7) 0.3860(bb−aa),), m =8 , 0.5960( m6    0.3362(b − a), m = 9   0.4560(b  a ), m  7   0.2986(b − a), m = 10    bb−a a ), mm≥11 8 0.3860( , h   2.8651 n−1 , (7) b  a ),andmm is9the number of samples. In this paper, 0.3362( where b is the maximum value of DI, a isthe minimum, 0.2986(b  a ), m  10 m is 30 in each grid cell.  ba   2.8651 n  1 ,

m  11

where b is the maximum value of DI, a is the minimum, and m is the number of samples. In this paper, m is 30 in each grid cell. Information accumulation can be calculated using Equations (8) and (9): n

C 

f (u )


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Information accumulation can be calculated using Equations (8) and (9): Sustainability 2016, 8, 813

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n

Ck =

∑

i=1

f k ( ui )

F ( DI k , u j ) 

f k (u j )

(8)

, (9) f k (C u jk) F ( DIk , u j ) = , (9) C where Ck is the information accumulation of the k-thk sample and F(DIk,uj) is the normalized where Ck is the informationofaccumulation of the k-thpoint sample F(DIk ,uall the normalized information information distribution sample DI. For each uj, and summing normalized information, the j ) is distribution sample DI. Forcame eachfrom pointthe uj , given summing all normalized information, the information information of gain at uj, which sample DI, was obtained. The information gain is gain at in uj ,Equation which came shown (10): from the given sample DI, was obtained. The information gain is shown in Equation (10): m

qq((uujj))=  DIi ,i ,uuj )j.) . ∑ FF((DI m

(10) (10)

 11 jj =

The The diffusion diffusion information information of of the the sample sample was was obtained obtainedby bysumming summingq(u q(uj j)) (Equation (Equation (11)): (11)): nn

Q=  Q ∑ qq((uujj)). .

(11) (11)

j j = 11

was estimated estimated so so that that the the Next, the the occurrence occurrence probability probability of of aa drought drought disaster disaster of of magnitude magnitude uuj was Next, j probability distribution of DI could be assessed: probability distribution of DI could be assessed:

 pp((uujj))=

q(u )

q(u j )j . Q Q

(12) (12)

Based on onthe theprobability probability distribution ofand DI the andvulnerability the vulnerability themaize global maize Based distribution of DI surface,surface, the global drought drought risk was assessed (Figure 5). risk was assessed (Figure 5).

Figure 5. 5. Flowchart of maize maize drought drought risk risk assessment. assessment. Figure

The optimal optimal surface surface with with the the highest highest R R22 was The was chosen chosen to to assess assess the the global global drought drought risk risk for for maize. maize. For each grid cell, a pair of coordinates (x,y) was determined by a spatial query based on the overall For each grid cell, a pair of coordinates (x,y) was determined by a spatial query based on the overall planting extent extent of of maize. maize. According According to to the the coordinates, coordinates, the the DI DI probability probability distribution distribution curve curve of of the the planting grid cell was also identified. The function relating DI and LR was obtained by the intersection of grid cell was also identified. The function relating DI and LR was obtained by the intersection of EE (an environmental environmental indicator) indicator) and and the the optimal optimal vulnerability vulnerability surface. surface. The The function function was was then then combined combined (an with the the probability probability distribution distribution of of DI DI to to calculate calculate the the probability probability distribution distribution of of LR with LR for for the the grid grid cell. cell. According to the probability distribution of LR, which represents the probability of different levels According to the probability distribution of LR, which represents the probability of different levels of of LR, the expected risk was calculated. The LR risk at different return periods could also be obtained, LR, the expected risk was calculated. The LR risk at different return periods could also be obtained, where the the probability probability of of aa 10a, 10a, 20a, 20a, 50a, 50a, and and 100a 100a return return period period corresponds corresponds to to 0.1, 0.1, 0.05, 0.05, 0.02, 0.02, and and where 0.01, respectively. 0.01, respectively.

3. Results 3.1. Calibration Results By comparing Sustainability 2016, 8, 813the simulated and actual yields (from FAO statistics) for the national (regional) 10 of 22 units from 2001 to 2004, scatter plots were drawn, and a correlation analysis was completed (Figure 6). 3. Results Both actual and simulated global maize yields are concentrated in the vicinity of the 1:1 line. All R2 values are greater than 0.7. The Pearson correlation coefficients between simulated and actual 3.1. Calibration Results yields from 2001 to 2004 were 0.898, 0.867, 0.857, and 0.860, respectively, and were significant at the By comparing the simulated and yields actual are yields (from FAO statistics) for actual the national 0.01 level. It can be seen that simulated significantly correlated with yields,(regional) meaning unitsthe from 2001calibration to 2004, scatter were drawn, and a correlation analysis was completed (Figure 6). that model resultplots is positive.

(a)

(b)

(c)

(d)

Figure 6. Scatter plots of simulated and actual yield of global maize over four years: (a) 2001; (b) 2002; Figure 6. Scatter plots of simulated and actual yield of global maize over four years: (a) 2001; (b) 2002; (c) 2003; (d) 2004. (c) 2003; (d) 2004.

3.2. “L-D-E” Vulnerability Surface of Maize Both actual and simulated global maize yields are concentrated in the vicinity of the 1:1 line. slope, andthan seven (CFRAG, BULK, TAWC, SDTO, CLPC, TOTC, and 2 values are All RElevation, greater 0.7.soil Theproperties Pearson correlation coefficients between simulated and actual PH) were selected as2004 environmental to fit the0.860, drought vulnerability of maize (Table yields from 2001 to were 0.898,indicators 0.867, 0.857, and respectively, andsurface were significant at the 2). Table 2 shows that the surface-fitting accuracy is generally good. The vulnerability surface with 0.01 level. It can be seen that simulated yields are significantly correlated with actual yields, meaning 2 of 0.99342 and an CFRAG as the environmental indicator has the best fitting accuracy, with an R that the model calibration result is positive. RMSE of 2.89062. 3.2. “L-D-E” Vulnerability Surfacevulnerability of Maize According to the optimal surface (Figure 7) for global maize, under the same CFRAG, LR rises significantly with an increase in DI. When DI does not change, LR decreases at first, Elevation, slope, and seven soil properties (CFRAG, BULK, TAWC, SDTO, CLPC, TOTC, and PH) reaching a minimum when CFRAG is approximately 10%, and then increases. were selected as environmental indicators to fit the drought vulnerability surface of maize (Table 2). Table 2 shows that the surface-fitting accuracy is generally good. The vulnerability surface with CFRAG as the environmental indicator has the best fitting accuracy, with an R2 of 0.99342 and an RMSE of 2.89062.


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Table 2. Parameters of the drought vulnerability surface of maize.

Indicator

Table Parameters the drought vulnerability surface maize. Table 2.2. Parameters ofof the drought vulnerability surface ofof maize. 2 a

b

a

c

b

d

c

e

d

f

R

RMSE

2 f RMSE f99.12 R2R RMSE 0.99339 2.89636 99.12 0.99339 2.89636 97.98 0.99339 0.99338 2.89636 2.89996 99.12 98.88 0.99338 0.99342 2.89996 2.89062 97.98 0.99338 2.89996 97.98 2.62 0.95518 7.54344 98.88 0.99342 0.99342 2.89062 2.89062 98.88 64.82 0.95620 7.45699 2.62 0.95518 0.95518 7.54344 7.54344 2.62 99.34 0.99338 2.89889 64.82 0.95620 7.45699 99.80 0.95620 0.99334 7.45699 2.90779 64.82 99.34 0.99338 2.89889 103.81 0.99342 2.89104 99.34 0.99338 2.89889 21.87 0.95589 2.90779 7.48403 99.80 0.99334 CLPC −421.92 0.36 3.37 −0.0015 6.91 99.80 0.99334 2.90779 TOTC 103.86 103.86 0.35 0.35 3.38 3.38 −0.00019 −0.00019 171.47 171.47 103.81 103.81 0.99342 0.99342 2.89104 2.89104 TOTC PH 0.44 0.30 3.49 0.02 −54.39 21.87 0.95589 7.48403 0.44 vulnerability 0.30 3.49 surface 0.02 (Figure −54.39 21.87 maize, 0.95589 7.48403 AccordingPH to the optimal 7) for global under the same CFRAG,

Indicator

Indicator 384.01a Elevation 0.35b 3.39c 1.09 ×d10−7 5 −7 Elevation 384.010.35 0.353.39 3.39 3.91 1.09 × −10 −7 Slope −90.22 ××10 Elevation 384.01 0.35 3.39 1.09 10 −5 CFRAG − 15.65 0.36 3.36 0.007 Slope −90.22 0.35 0.35 3.39 3.39 3.91 3.91 × 10 −5 Slope −90.22 × 10 BULK 0.44 0.29 3.52 0.41 CFRAG −15.65 −15.65 0.36 0.36 3.36 3.36 0.007 0.007 CFRAG 3.52 0.0008 TAWC 9.71 0.29 BULK 0.44 0.29 0.29 3.52 3.52 0.41 BULK 0.44 0.41 3.40 −0.00018 SDTO 100.32 0.35 TAWC 9.71 0.29 3.52 0.0008 CLPC − 421.92 0.36 3.37 − 0.0015 TAWC 9.71 0.29 3.52 0.0008 SDTO 103.86 100.320.35 0.353.38 3.40 − −0.00018 TOTC 0.00019 SDTO 100.32 0.35 3.40 −0.00018 0.02 PH CLPC 0.44−421.920.30 0.363.493.37 −0.0015

e

e 1167.23 1167.23 −164.39 1167.23 10.94 −164.39 −164.39 − 13.75 10.94 10.94 −184.18 −13.75 −13.75 26.51 −184.18 6.91 −184.18 26.51 171.47 26.51 −6.91 54.39

LR rises significantly with an increase in DI. When DI does not change, LR decreases at first, reaching a minimum when CFRAG is approximately 10%, and then increases.

(a)(a)

(b) (b)

Figure 7. “L-D-E”vulnerability vulnerability surfacewith with CFRAGasasenvironmental environmental indicator. (a,b)represent represent Figure Figure 7. “L-D-E” “L-D-E” vulnerability surface surface with CFRAG CFRAG as environmental indicator. (a,b) (a,b) represent different perspectives; vulnerability surfaces with other environmental indicators are shown different environmental indicators are are shown inin different perspectives; perspectives; vulnerability vulnerabilitysurfaces surfaceswith withother other environmental indicators shown Appendix A. Appendix A. A. in Appendix

3.3. MaizeDrought Drought Riskonona Global a Global Scale 3.3. 3.3. Maize Maize Drought Risk Risk on a Global Scale Scale According to information diffusion theory, theprobability probability ofdifferent different droughtintensities intensities was According According to to information information diffusion diffusion theory, theory, the the probability of of different drought drought intensities was was calculated ineach each gridcell cell basedonon30-year 30-year historicaldata data (Figure8).8). calculated calculated in in each grid grid cell based based on 30-year historical historical data (Figure (Figure 8).

(a)(a)

(b) (b) Figure 8. Cont.

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(c)

(d)

Figure 8. Global drought intensity for maize by different return periods: (a) 10-year return period; (b) 20-year return period; (c) 50-year return period; (d) 100-year return period. The darker areas have a higher probability of maize drought.

Global maize drought (c) risk was calculated according to the optimal (d) vulnerability surface (CFRAG), as shown in Figure 9. Figure 8. drought intensity for byby different return periods: (a) (a) 10-year return period; (b) Figure 8. Global Global drought intensity formaize maize different return periods: 10-year return period; The expected global yield loss rate for maize is 19.18%. The rate rises with increasing return 20-year return period; (c) 50-year return period; (d) 100-year return period. The darker areas have aa (b) reaching 20-year return period; (c) 50-year returnand period; (d) 100-year return period. The50-year, darker areas period, 29.18%, 32.76%, 36.89%, 38.26% in a 10-year, 20-year, andhave 100-year higher probability of maize drought. probability of maize drought. returnhigher period, respectively (Appendix B). Globally, areas with high maize drought risk (red zone) are located in mid-latitude regions (30°–50°), mainly including Peninsula, the Midwestern Global maize drought risk was calculated accordingthe to Iberian the optimal vulnerability surface Global maize drought risk was Central calculated according to the optimal vulnerability surface (CFRAG), United States, northwestern China, Asia, eastern Brazil, Chile, Spain, and certain low-latitude (CFRAG), as shown in Figure 9. as shown in Figure 9. regions the Equator, and northeastern Brazil. Thenear expected global including yield lossEast rateAfrica for maize is 19.18%. The rate rises with increasing return period, reaching 29.18%, 32.76%, 36.89%, and 38.26% in a 10-year, 20-year, 50-year, and 100-year return period, respectively (Appendix B). Globally, areas with high maize drought risk (red zone) are located in mid-latitude regions (30°–50°), mainly including the Iberian Peninsula, the Midwestern United States, northwestern China, Central Asia, eastern Brazil, Chile, Spain, and certain low-latitude regions near the Equator, including East Africa and northeastern Brazil.

Figure 9. 9. Global Globalexpected expectedannual annualmaize maizedrought droughtrisk. risk.Red Redareas areashave haveaahigher higherrisk riskof ofmaize maizedrought, drought, Figure indicating that droughts yield loss rates of maize in these regions, whereas greengreen areas indicating droughtscan canlead leadtotohigh high yield loss rates of maize in these regions, whereas have a lower risk, meaning that maize in these less is affected by droughts. This figure areas have a lower risk, meaning that maize in areas these is areas less affected by droughts. This shows figure only the expected risk map; return period period maps are shown in Appendix B. shows only the expected riskthe map; the return maps are shown in Appendix B.

Based on Figure 9 (Table 3),loss the rate risk for gridiscells in each country waswith averaged. The results The expected yield for all maize 19.18%. The rate rises increasing return Figure 9. Globalglobal expected annual maize drought risk. Red areas have a higher risk of maize drought, suggest that the average yield loss rate may exceed 50% when Chile, Afghanistan, Iraq, Spain, and period, reaching 29.18%, 32.76%, 36.89%, and 38.26% in a 10-year, 20-year, 50-year, and 100-year return indicating that droughts can lead to high yield loss rates of maize in these regions, whereas green certain other countries suffer from a drought disaster. Themaize average yield risk loss (red ratezone) of maize in the period, respectively (Appendix B). Globally, areas withareas high drought located areas have a lower risk, meaning that maize in these is less affected by droughts. This are figure ◦ ◦ United States and Australia is about 30%–40%, whereas that in China and Brazil is less than 20%. The in mid-latitude regions (30 risk –50map; ), mainly including the Iberian Peninsula, the B. Midwestern United shows only the expected the return period maps are shown in Appendix highest values among the countries in Table 3 are about 80%–90%. The differences in maize drought States, northwestern China, Central Asia, eastern Brazil, Chile, Spain, and certain low-latitude regions risk countries are obvious. Some offor these countries areeach major grain-producing countries, and Based on Figure 9 (Table 3),Africa the risk all grid cellsBrazil. in country was averaged. The results nearamong the Equator, including East and northeastern suggest thatonthe average yield3), loss exceed 50% when Afghanistan, Iraq, The Spain, and Based Figure 9 (Table therate riskmay for all grid cells in eachChile, country was averaged. results certain countries a drought disaster. average loss rate Iraq, of maize in and the suggestother that the averagesuffer yieldfrom loss rate may exceed 50%The when Chile,yield Afghanistan, Spain, United Statescountries and Australia about 30%–40%, whereas in China less than 20%. The certain other sufferisfrom a drought disaster. Thethat average yieldand lossBrazil rate ofismaize in the United highest values among the countries in Table 3 are about 80%–90%. The differences in maize drought risk among countries are obvious. Some of these countries are major grain-producing countries, and


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States and Australia is about 30%–40%, whereas that in China and Brazil is less than 20%. The highest values among the countries in Table 3 are about 80%–90%. The differences in maize drought risk among countries are obvious. Some of these countries are major grain-producing countries, and food shortages may occur once they have suffered a severe loss in yield. Therefore, countries with higher maize drought risk should strengthen their predictive capabilities for drought disasters to minimize the economic losses caused by droughts. Table 3. Expected value of maize yield loss rate in high-risk countries. Country

Maximum Yield Loss Rate (%)

Minimum Yield Loss Rate (%)

Average Yield Loss Rate (%)

Afghanistan Australia Brazil Chile China Iraq Spain United States

93.85 92.23 83.32 100 99.97 99.48 98.91 97.26

0 0.45 0 0.06 0 7.96 0 0.03

67.63 48.00 11.59 64.64 19.75 70.32 51.46 30.52

4. Discussion 4.1. Relationship between CFRAG and Crops In this research, the “L-D-E” vulnerability surface was best fitted with coarse fragment content (CFRAG) as the environmental indicator. With increasing CFRAG, LR of maize first decreased and then increased under the same hazard condition. A higher CFRAG is helpful for soil permeability because it makes it easier for water to reach plant roots and be absorbed. When CFRAG exceeds a threshold value, however, the water-holding capacity of the soil decreases, soil moisture is more likely to evaporate, and plants are more vulnerable to drought. Some CFRAG studies have proposed that CFRAG is negatively correlated with maize yields [59]. According to Grewal’s experiment with different levels of gravel content (18%, 28%, and 40%) as CFRAG, an increasing proportion of gravel led to decreasing soil nutrient content and soil water-holding capacity and a yield that showed a downward trend [60]. Driessen described the quantitative effect of CFRAG on a productivity index (decreasing from 100% to 0% with gravel contents of 10% to 70%), but the effect was due to the reduction of available plant water rather than rooting depth [61]. When CFRAG is higher than the threshold value, it will negatively affect soil moisture and nutrition, resulting in yield reduction and higher crop vulnerability. 4.2. Significance of Vulnerability Surfaces In a similar study, researchers calculated the global drought risk for maize by fitting vulnerability curves for different areas [30]. However, two-dimensional vulnerability curves can only express the relationship between hazard intensity and yield loss, without considering the environmental dimension. Environmental differences can be embodied only by artificially dividing the study area into different units. The vulnerability surface is different from the vulnerability curve. Its significant advantage lies in its consideration of the differences in environmental elements. Therefore, different environmental elements correspond to different relationships between hazard intensity and yield loss rate, and errors in research results caused by artificial division into different environment zones are thus avoided. Another advantage of the vulnerability surface is that it can be incorporated into multi-scale studies. This means that the maize drought vulnerability surface calculated based on a 0.5◦ × 0.5◦ grid in this study can be converted into vulnerability assessment results at different scales according to the research resolution requirement or the resolution of relevant environmental indicators, which may even be higher than 0.5◦ × 0.5◦ .


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For risk assessment studies based on the vulnerability curve, the vulnerability surface can 14 of 22 of vulnerability curves according to different environmental indicators. The vulnerability surface can be considered as an infinite number of vulnerability curves. For risk using the integrals the vulnerability curves.index, The larger the integral assessment values, the can more assessment studies of based on the vulnerability the vulnerability be vulnerable completed crops shown of in the Figure 10, vulnerability under types was calculated andvulnerable classified usingare. the As integrals vulnerability curves. The different larger thesoil integral values, the more according to the maize “L-D-E” vulnerability surface (based on 0.5° × 0.5° data) and soil data (0.0833° crops are. As shown in Figure 10, vulnerability under different soil types was calculated and classified ◦ ◦ ×according 0.0833°) curves, thus the vulnerability assessment resolution can be converted from lower (0.5° × to the maize “L-D-E” vulnerability surface (based on 0.5 × 0.5 data) and soil data ◦ ) curves, 0.5°) to ◦higher (0.0833° × 0.0833°). (0.0833 × 0.0833 thus the vulnerability assessment resolution can be converted from lower Sustainability be divided2016, into8, a813number

(0.5◦ × 0.5◦ ) to higher (0.0833◦ × 0.0833◦ ).

◦ Figure 10. 10. Vulnerability Vulnerability of global maize to drought 0.0833◦ ). The Thevulnerability vulnerability assessment assessment Figure drought (0.0833 (0.0833° × × 0.0833°). results were based on on thethe method of natural breaks (jenks) in ArcGIS. The redder results were divided dividedinto intofive fivelevels levels based method of natural breaks (jenks) in ArcGIS. The the areathe in area the picture, the larger integral of the corresponding vulnerability curve, curve, and theand higher redder in the picture, the the larger the integral of the corresponding vulnerability the the vulnerability. If the value is smaller, the vulnerability is lower. higher the vulnerability. If the value is smaller, the vulnerability is lower.

Therefore, the vulnerability vulnerabilitysurface surfacefurther furtherconsiders considers differences in environmental elements, Therefore, the differences in environmental elements, and and can be converted to different scales due to its ability to express continuous changes in can be converted to different scales due to its ability to express continuous changes in vulnerability. vulnerability. It has certain advantages foraslarge-scale (such as or global) vulnerability or risk It has certain advantages for large-scale (such global) vulnerability risk assessment. assessment. 4.3. Validity of Risk Assessment Results Based on the Vulnerability Surface 4.3. Validity of Risk Assessment Basedcome on thefrom Vulnerability Surface The planting range dataResults for maize the Center for Sustainability and the Global Environment (SAGE), University Wisconsin-Madison [49]. Thesefor data were combined with The planting range data forofmaize come from the Center Sustainability and thenational, Global state, and county statistical data that described the harvested area of 175 crops (spatial resolution: Environment (SAGE), University of Wisconsin-Madison [49]. These data were combined with ◦ ). In this research, the spatial resolution was resampled to 0.5◦ × 0.5◦ to unify research 0.0833◦ ×state, 0.0833and national, county statistical data that described the harvested area of 175 crops (spatial resolution. The risk was assessed as long as maize was planted in thewas gridresampled cell. Note that the×planted resolution: 0.0833° × 0.0833°). In this research, the spatial resolution to 0.5° 0.5° to proportion of each grid cell was not considered risk Indeed,ingross production or unify research resolution. The risk was assessed in as the long as assessment. maize was planted the grid cell. Note planted proportion has littleof effect yield each grid cell. Therefore, this study, whichgross used that the planted proportion eachon grid cellloss wasrate notinconsidered in the risk assessment. Indeed, yield loss rate represent risk, would be little influenced. production or to planted proportion has little effect on yield loss rate in each grid cell. Therefore, this Cases ofused global maize drought risk assessment areberare. researchers have calculated study, which yield loss rate to represent risk, would little Some influenced. precipitation, moisture, other indicators for different under various scenarios according Cases of soil global maizeand drought risk assessment are months rare. Some researchers have calculated to different climate models to assess future drought severity due to climate change [62,63]. The results precipitation, soil moisture, and other indicators for different months under various scenarios show that to thedifferent United States, Amazon Basin,future and Europe areseverity future arid in different climate according climatethe models to assess drought dueregions to climate change [62,63]. The results show that the United States, the Amazon Basin, and Europe are future arid regions in different climate models. Other researchers have considered the Palmer Drought Severity Index (PDSI) and other drought-related indices on a global scale to evaluate the frequency [64], trend [65], and soil moisture and temperature changes [66] associated with future drought. Overall, most


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models. Other researchers have considered the Palmer Drought Severity Index (PDSI) and other drought-related indices on a global scale to evaluate the frequency [64], trend [65], and soil moisture and temperature changes [66] associated with future drought. Overall, most research results show that serious drought areas will be distributed mainly in central Asia, southwestern Europe, southern Africa, western and central North America, and northeastern South America. To test the validity of the results reported in this paper, those reported by Li [64] were chosen for comparison. A correlation analysis (Table 4) was completed between the pattern of maize drought risk reported in this paper (the sum of the expected loss rates for each continent) and Li’s results (DRI of baseline for each continent). The correlation coefficient was 0.717, which shows a significant relationship at the 0.05 level. Table 4. Comparison of results with those of Li’s research [64]. Continent

Normalized Value of Risk in This Study

Normalized Value of Risk in Li’s Study

North America Europe Africa South America Oceania Southern Asia South East Asia Eastern Asia Middle East

1 0.64 0.96 0.64 0.15 0.07 0 0.56 0.80

0.30 0.22 1 0.37 0 0.25 0.22 0.29 0.43

Therefore, the results of this study, which are based on the maize vulnerability surface, are close to the pattern of existing results at continental scale. However, the evaluation results may be different in regional areas as a result of different methods and data. 5. Conclusions The influence of drought on agriculture is serious. Research on crop response to drought can provide significant information to reduce agricultural losses caused by drought and promote sustainable agricultural development. In this research, a 3D vulnerability surface was fitted, and the global maize drought risk was evaluated. It was concluded that the vulnerability surface incorporating variations in environmental factors can express the continuous functional relationship between “Hazard”, “Loss (Loss rate)”, and “Environment”. In addition, the vulnerability assessment results can be converted into different scales based on the vulnerability surface due to its ability to express continuous changes in vulnerability. Last but not least, the vulnerability surfaces can be used for quantitative drought risk assessment that directly denotes the probability of crop yield loss. The research provides a new method for research into biophysical vulnerability assessment. In our previous studies, EPIC was used to simulate “Drought hazard-Crop yield loss” vulnerability curves to assess the drought risk of different crops (maize [67], wheat [68], and rice [69]). This study has proposed a new method for assessing vulnerability quantitatively and continuously by including the environment variable as an additional perspective on exposure. This method could be used for different crops, climate scenarios, and periods. It might constitute a promising direction for further research that could assess vulnerability comprehensively and quantitatively by studying the location change or adaption of different crop species. Acknowledgments: This study was supported by the National Basic Research Program of China (973 Project): Relationship between Global Change and Environmental Risks and its Adaptation Paradigm (No. 2012CB955403) and the National Key Research and Development Program (No. 2016YFA0602402). This paper was improved by comments from Matthew Turner and A.-Xing Zhu from the University of Wisconsin-Madison. The valuable comments and suggestions from the editor and anonymous reviewers are also greatly appreciated. Author Contributions: Hao Guo conceived the entire paper, analyzed the data, and wrote the paper; Xingming Zhang designed and performed the experiments and analyzed the data; Fang Lian and Yuan Gao polished the text of the paper; Degen Lin provided technical support; Jing’ai Wang polished the text and provided project support.


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Conflicts of Interest: The authors declare no conflict of interest.

Appendix A Appendix A Similar to Figure 7, “L-D-E” vulnerability surfaces were fitted with other environmental Similar to Figure 7, “L-D-E” vulnerability surfaces were fitted with other environmental indicators, indicators, as shown in Figure A1. as shown in Figure A1.

(a)

(b)

(c)

(d)

(e)

(f) Figure A1. Cont.

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(g)

(h)

Figure A1. “L-D-E” vulnerability surfaces fitted with environmental indicators other than CFRAG: (a) Figure A1. “L-D-E” (g) vulnerability surfaces fitted with environmental indicators other than CFRAG: (a) (h)PH. elevation; (b) slope; (c) BULK; (d) TAWC; (e) SDTO; (f) CLPC; (g) TOTC; (h) elevation; (b) slope; (c) BULK; (d) TAWC; (e) SDTO; (f) CLPC; (g) TOTC; (h) PH. Figure A1. “L-D-E” vulnerability surfaces fitted with environmental indicators other than CFRAG: (a) Appendix B (b) slope; (c) BULK; (d) TAWC; (e) SDTO; (f) CLPC; (g) TOTC; (h) PH. elevation;

SimilarBto Figure 9, global maize drought risk was mapped for different return periods, as shown Appendix Appendix B in Figure B1. Similarto toFigure Figure9,9,global globalmaize maizedrought droughtrisk riskwas wasmapped mappedfor fordifferent differentreturn returnperiods, periods,as asshown shown Similar inFigure FigureB1. B1. in

(a) (a) Figure B1. Cont.

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(b)

(c) Figure B1. Cont.


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(d) Figure B1. Global maize drought risk for different return periods: (a) 10-year return period; (b) 20Figure B1. Global maize drought risk for different return periods: (a) 10-year return period; (b) 20-year year return period; (c) 50-year return period; (d) 100-year return period. return period; (c) 50-year return period; (d) 100-year return period.

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