# Possible Future Climate Change Impacts on the Hydrological Drought Events in the Weihe River Basin, China

Authors: Fei Yuan; Mingwei Ma; Liliang Ren; Hongren Shen; Yue Li; Shanhu Jiang; Xiaoli Yang; Chongxu Zhao; Hao Kong
Journal: Advances in Meteorology
 (2016)

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## Abstract

Quantitative evaluation of future climate change impacts on hydrological drought characteristics is one of important measures for implementing sustainable water resources management and effective disaster mitigation in drought-prone regions under the changing environment. In this study, a modeling system for projecting the potential future climate change impacts on hydrological droughts in the Weihe River basin (WRB) in North China is presented. This system consists of a large-scale hydrological model driven by climate outputs from three climate models (CMs) for future streamflow projections, a probabilistic model for univariate drought assessment, and a copula-based bivariate model for joint drought frequency analysis under historical and future climates. With the observed historical climate data as the inputs, the Variable Infiltration Capacity hydrological model projects an overall runoff reduction in the WRB under the Intergovernmental Panel on Climate Change A1B scenario. The univariate drought assessment found that although fewer hydrological drought events would occur under A1B scenario, drought duration and severity tend to increase remarkably. Moreover, the bivariate drought assessment reveals that future droughts in the same return period as the baseline droughts would become more serious. With these trends in the future, the hydrological drought situation in the WRB would be further deteriorated.


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## Body

## 1. Introduction

Nowadays our societies are in much more urgent need of water resources, particularly in the drought-prone territories in China and in other parts of the world. In such regions, increasingly frequent droughts are becoming a main threat to local socioeconomic and ecoenvironment systems [1]. Even in humid areas of South China, where droughts used to be less frequent, several long-lasting, severe, and widespread drought events were witnessed in the 2000s and 2010s, causing serious water shortage problems and sharp damage (e.g., the severe 2010 drought in Southwest China) [2, 3]. In Northern China, such as the Yellow River basin (YRB), drought situations can be even worse because of the semiarid to arid climatology and limited atmospheric water sources [4]. Therefore, the focus of this study is on the largest tributary of YRB, that is, the drought-prone Weihe River basin (WRB), where large human population, extensive areas of rainfall and/or irrigation-fed agriculture, rapid industrial and economic developments, and vulnerable ecological and environmental systems meet and conflict between water supply and demand. Several studies have shown that the WRB suffered from disastrous drought periods in history (e.g., 1962, 1972, 1987, and 1990s) and the drought trends of this region tend to deteriorate as well [5, 6]. For mitigation purposes, the water volume stored in river systems (e.g., streamflow) is often analyzed to define hydrological droughts. Based on the theory of runs, drought variables (e.g., duration and severity) can also be extracted to investigate their univariate and multivariate probabilistic properties and frequency analysis [7, 8]. However, the hydrological drought characteristics of the YRB have not yet been systematically investigated and reported. On the other hand, although [9–12] studied the variations of runoff/streamflow and its responses to climate change in the WRB, it is still unclear how potential climate change (especially the global warming) impacts future extreme hydrological drought events in this region.Therefore this study aims to propose an effective framework to evaluate historical (1961–1990 as baseline period) drought conditions and to project future (2011–2040 as climate change period) hydrological drought properties in the WRB. Specifically, the new framework consists of four components:(1) the Variable Infiltration Capacity (VIC) hydrologic model driven by climate outputs from three climate models (CMs) for future streamflow projections, (2) a drought variable identification model for drought severity and duration based on the theory of runs, (3) a probabilistic model for univariate drought assessment and frequency analysis (duration and severity) under historical and future climates, and (4) a copula-based model for bivariate drought assessment and joint frequency analysis. This framework provides quantitative evaluation of climate change impacts on hydrological drought characteristics in the WRB.Though [13] applied similar approaches to a river basin in USA, they adopted the Thornthwaite water balance model (a simple conceptual hydrologic model) to simulate future runoff and used the standardized streamflow index to define hydrological droughts. In this study, the authors employed the physically based VIC distributed hydrological model for historical streamflow simulations and future runoff projections. In addition, streamflow at certain levels was directly used as truncation thresholds to define hydrological drought duration and severity. This approach makes it more convenient to compare historical and future drought properties and to interpret climate change impacts on drought characteristics. Moreover, the adopted CMs and univariate and copula-based multivariate models are also quite different from those of [13]. In general, such a study using multimodels (climatic, hydrological, and multivariate probabilistic) has not been documented in the WRB. This work is expected to fill the research gap of future climate change impacts on hydrological droughts and to provide reliable data support for upgrading water resources management and adaptation strategies in response to changing environment in this region.


## 2. Study Area

The Weihe River is the longest tributary of the Yellow River in North China, with a drainage area of 1.348 × 105 km2 (Figure 1). The river basin is dominated by continental monsoon climate and characterized as semiarid region. The annual mean temperature ranges between 9.3°C and 14.4°C. The mean annual precipitation is 511.3~659.1 mm, with a distinct increase from northwest to southeast. Precipitation mainly occurs from June to November, which accounts for 70.8~74.2% of annual precipitation. Snow generally occurs in winter in the entire basin. The spatiotemporal distribution of runoff is similar to precipitation, with basin-averaged mean annual runoff depth being less than 100 mm. The basin is prone to droughts. Agricultural losses due to local drought disasters occupy over 50% of the total losses. Recent climate change has deteriorated the water shortage situation in the WRB and resulted in more severe drought events. Thus it is necessary to assess the possible climate change impacts on regional hydrological drought events. In this study, the area controlled by Huaxian streamflow station (upstream area of 1.065 × 105 km2, Figure 1) was selected as the study region.Figure 1
Map of study area.


## 3. Data and Methodology

### 3.1. Data

Historical meteorological data of thirteen weather stations within or nearby the basin (Figure1) were obtained from China Meteorological Administration. These data include daily records of maximum and minimum air temperature and precipitation during the period of 1961–2012. The whole basin was divided into 213 grid cells at a 0.25° resolution. All the station-based daily precipitation and air temperature data were interpolated to each 0.25° grid cell by the nearest neighbor method. Topographical effects were not considered in precipitation interpolation, while near-surface air temperature was assumed to decrease by 0.65°C per altitude rise of 100 m.China’s land-use/cover data sets with 5 or 10 yr intervals between 1980 and 2010 [14] were used to analyze the land-use change in the study area. It shows that cropland, the dominant land-use type in the region of the middle and lower reaches, has a downward trend since late 1980s. The cover ratio of woodland in the upstream region drops sharply since late 1980s and approximately trends to be stable after the 1990s. The built-up area increased notably since 1980, implying the rapid urbanization in this region. The coverage of water bodies, which refer to the lakes, reservoirs, ponds, and other water retaining projects for the irrigations, has also shown an upward trend. Furthermore, the Pettitt jump test for the annual runoff depth time series from 1961 to 2012 at Huaxian station indicates that the year 1990 is the abrupt change point in annual runoff with a significant decrease trend since 1990. Meanwhile, the consistency test with the double mass curve of the cumulative annual areal mean precipitation and observed runoff depth shows that runoff coefficient tends to decrease since 1990 as well. Therefore, considering the change patterns of land-use, precipitation and runoff, the period of 1961–1990 was defined as the baseline period for hydrological drought projections in this study.Climate data sets from three climate models (CMs) were adopted in this study. They are Australian Commonwealth Scientific and Research Organization (CSIRO) Mk 3.5 Global Climate Model (GCM), German Max Planck Institute for Meteorology (MPI) ECHAM 5 GCM, and Hadley Centre’s Providing Regional Climates for Impacts Studies (PRECIS) regional climate model (RCM). The CSIRO and MPI GCMs run at a spatial resolution of 1.875°  × 1.875° and 2.0°  ×  2.0°, respectively. The output of these two GCMs was statistically downscaled to a 50 km × 50 km resolution by the bilinear interpolation and quantile-mapping methods. The PRECIS RCM dynamically downscales the HadAM3H GCM data from the 1.25°  ×  1.875° resolution to 50 km × 50 km. The three CM data sets are composed of the simulated daily maximum and minimum air temperature and precipitation in the baseline period of 1961–1990 and in the years of 2011–2040 under A1B scenario of the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) [15]. The IPCC-SRES A1B shows rapid economic growth, especially in developing nations, with a balance across all energy sources for economic development, and it has been adopted as the most commonly used emission scenario for climate change studies in China [16, 17]. Furthermore, linear interpolation was performed to transform the three downscaled CM data sets (50 km × 50 km) to a 0.25° resolution. In this study, the observed historical climate data set in 1961–1990 was directly employed as the baseline climatology. To bias-correct the CM data sets, the delta-change method was used, which superimposes the mean monthly anomalies between the CM-simulated baseline and A1B climate data on the observed historical meteorology to represent future climate. In this way, three future climate data sets were finally constructed for three future scenarios, namely, A1B PRECIS, A1B CSIRO, and A1B MPI.


### 3.2. Variable Infiltration Capacity Hydrological Model

The Variable Infiltration Capacity (VIC) model [18, 19] is a state-of-the-art physically based distributed hydrological model. It simulates radiative fluxes, turbulent fluxes of momentum, sensible heat, unsaturated liquid water transport, saturated gravitational drainage, surface runoff, bottom drainage evapotranspiration, freezing, and thawing of soil ice at each land grid cell. Additionally, a conceptual streamflow routing model is included to route the computed runoff depth at each grid cell to the watershed outlets. The routing model simulates two processes: (1) runoff concentration on the outflow of each grid cell is represented by the linear reservoir method; (2) the routing effect of channel system connecting grid cells is represented by the Muskingum routing algorithm [20].In this study, the vegetation and soil parameters of the VIC model were spatially estimated a priori according to vegetation and soil texture classes at each grid cell. For each type of vegetation, the vegetation parameters, such as architectural resistancera (s/m), albedo α, minimum stomata resistance rsmin (s/m), leaf-area index LAI, roughness length z0 (m), and zero-plane displacement d0 (m), were derived on the basis of the vegetation parameter information from Land Data Assimilation Systems (LDAS, http://ldas.gsfc.nasa.gov/gldas/GLDASmapveg.php). The individual soil parameters used in VIC, such as porosity θs, saturated soil potential ψs, saturated hydraulic conductivity Ks, and bulk density BD, were derived according to the work of [21, 22]. In addition, two insensitive hydrologic parameters of VIC were estimated a priori according to the work of [23]. These parameters are the following: (1)Dsoil: soil depth of each soil layer (three layers in this study) is set as 0.1 m, 0.5 m, and 1.5 m, respectively; (2)Ws: the fraction of the maximum soil moisture (of the lowest soil layer) where nonlinear baseflow occurs is defined as 0.99. Other sensitive VIC hydrologic parameters (such as Dsmax, maximum baseflow that can occur from the lowest soil layer; Ds, fraction of Dsmax where nonlinear baseflow begins; and binf, coefficient defining the shape of the Variable Infiltration Capacity curve) and runoff routing parameters were calibrated by fitting the daily calculated streamflow time series against the observed records. These sensitive parameters are calibrated within the predefined rational physical value ranges by the Shuffled Complex Evolution (SCE-UA) automatic optimization method [24], with the log-transformed Nash-Sutcliffe model efficiency coefficient as the objective function.In this study, the gridded baseline and three future climate data sets were, respectively, used to drive the VIC model for daily streamflow simulations and projections at Huaxian station. Subsequently, the monthly simulated streamflow time series accumulated from the daily time series were analyzed to assess hydrological drought properties using univariate and bivariate drought distributions.


### 3.3. Univariate Drought Distribution Model

The VIC-simulated monthly streamflow time series were used to identify the hydrological drought events under the baseline (1961–1990) and three A1B (2011–2040) scenarios by the theory of runs. Following [25], three truncation levels of streamflow, Q0, Q1, and Q2 (Q0>Q1>Q2), were used to identify the hydrological drought events and relevant drought characteristics (Figure 2). As shown in Figure 2, four possible hydrological drought events (indicated as a, b, c, and d) are preliminarily identified during the period when the simulated monthly streamflow is below the truncation streamflow Q1. For the events with one-month duration (a and d in Figure 2), only the event a is finally identified to be a drought event as its monthly streamflow is below the truncation streamflow Q2, but the event d is rejected to be a hydrological drought with its monthly streamflow being above Q2. For the two sequential events with the interval time of one month (b and c in Figure 2), the two events b and c are combined to be one drought event on the condition that the monthly streamflow at the interval is below the truncation streamflow Q0; otherwise the events b and c are considered to be two independent drought events. For each identified drought event, the corresponding drought severity is the cumulative deviation below the truncation streamflow Q1 during the drought duration (Figure 2). According to Standard for Information and Hydrological Forecasting of China [26], the truncation streamflow Q0 in this study was defined to be the monthly mean of the simulated streamflow time series from 1961 to 1990 at Huaxian station, and Q1 and Q2 were assumed to be 10% and 20% below Q0, respectively.Figure 2
Diagram of drought identification using the theory of runs.Using the drought identification scheme (Figure2), the drought variables of duration and severity were derived for each drought event under the baseline and A1B PRECIS, A1B CSIRO, and A1B MPI scenarios. For the analysis using univariate drought distributions, the exponential and Weibull distributions were, respectively, used to fit the drought duration and severity samples under the baseline and three future scenarios, and the maximum likelihood method was used to estimate the distribution parameters. Additionally, the univariate return periods of drought events regarding only one variable (drought duration or severity) were also derived under the baseline and three A1B scenarios, which are shown as follows:(1)TD=EL1-FDd,TS=EL1-FSs,where D and S denote drought duration and severity, respectively; TD and TS represent the univariate return period for droughts with D≥d and S⩾s, respectively; E(L) is the mean interarrival time of droughts; FD(d) and FS(s) are the cumulative probability distribution functions of drought duration and severity, respectively.


### 3.4. Bivariate Drought Distribution Model

In reality, drought duration and severity are often significantly correlated. Therefore, the relevance between drought duration and severity should be carefully taken into account when using both drought variables for drought frequency analysis. Copulas are functions that link univariate distribution functions to form multivariate distributions [27, 28]. They are useful tools to effectively reflect the correlation features among multiple drought variables. With simple forms and good accuracies, the Archimedean copulas have been widely applied in drought studies [7, 13]. In this study, four Archimedean copulas were used to establish bivariate drought distribution that describes the joint probabilities of drought duration and severity. They are Gumbel-Hougaard, Clayton, Frank, and Ali-Mikhail-Haq copulas. Given the univariate distributions of drought duration and severity (FD(d) and FS(s)), the joint distributions for drought duration and drought severity using the four Archimedean copulas can be, respectively, formulated as follows:(2)FD,Sd,s=exp⁡--ln⁡FDdθ+-ln⁡FSsθ1/θ,(3)FD,Sd,s=FDd-θ+FSs-θ-1-1/θ,(4)FD,Sd,s=-1θln⁡1+e-θFDd-1e-θFSs-1e-θ-1,(5)FD,Sd,s=1-θFDdFSs1-θ1-FDd1-θ1-FDd-θFDdFSs,where FD,S(d,s) is the joint probability distribution of drought duration and severity; θ is the copula parameter representing the degree of association between FD(d) and FS(s).With the joint probability distribution of drought duration and severity, conditional probability can also be calculated. Given drought duration exceeding a certain thresholdd, the probability of drought severity is defined as(6)PS≤s∣D≥d=PS⩽s,D⩾dPD⩾d=FSs-FDSd,s1-FDd.In addition, two types of bivariate return periods, defined as TDSAND and TDSOR, were calculated. TDSAND represents the return period when both drought duration and severity exceed their specific values:(7)TDSAND=ELPD⩾d,S⩾s=EL1-FDd-FSs+FDSd,s,and TDSOR denotes the return period when drought duration is higher than a specific value or drought severity exceeds another specific value:(8)TDSOR=ELPD⩾dorS⩾s=EL1-FDSd,s.


## 3.1. Data

Historical meteorological data of thirteen weather stations within or nearby the basin (Figure1) were obtained from China Meteorological Administration. These data include daily records of maximum and minimum air temperature and precipitation during the period of 1961–2012. The whole basin was divided into 213 grid cells at a 0.25° resolution. All the station-based daily precipitation and air temperature data were interpolated to each 0.25° grid cell by the nearest neighbor method. Topographical effects were not considered in precipitation interpolation, while near-surface air temperature was assumed to decrease by 0.65°C per altitude rise of 100 m.China’s land-use/cover data sets with 5 or 10 yr intervals between 1980 and 2010 [14] were used to analyze the land-use change in the study area. It shows that cropland, the dominant land-use type in the region of the middle and lower reaches, has a downward trend since late 1980s. The cover ratio of woodland in the upstream region drops sharply since late 1980s and approximately trends to be stable after the 1990s. The built-up area increased notably since 1980, implying the rapid urbanization in this region. The coverage of water bodies, which refer to the lakes, reservoirs, ponds, and other water retaining projects for the irrigations, has also shown an upward trend. Furthermore, the Pettitt jump test for the annual runoff depth time series from 1961 to 2012 at Huaxian station indicates that the year 1990 is the abrupt change point in annual runoff with a significant decrease trend since 1990. Meanwhile, the consistency test with the double mass curve of the cumulative annual areal mean precipitation and observed runoff depth shows that runoff coefficient tends to decrease since 1990 as well. Therefore, considering the change patterns of land-use, precipitation and runoff, the period of 1961–1990 was defined as the baseline period for hydrological drought projections in this study.Climate data sets from three climate models (CMs) were adopted in this study. They are Australian Commonwealth Scientific and Research Organization (CSIRO) Mk 3.5 Global Climate Model (GCM), German Max Planck Institute for Meteorology (MPI) ECHAM 5 GCM, and Hadley Centre’s Providing Regional Climates for Impacts Studies (PRECIS) regional climate model (RCM). The CSIRO and MPI GCMs run at a spatial resolution of 1.875°  × 1.875° and 2.0°  ×  2.0°, respectively. The output of these two GCMs was statistically downscaled to a 50 km × 50 km resolution by the bilinear interpolation and quantile-mapping methods. The PRECIS RCM dynamically downscales the HadAM3H GCM data from the 1.25°  ×  1.875° resolution to 50 km × 50 km. The three CM data sets are composed of the simulated daily maximum and minimum air temperature and precipitation in the baseline period of 1961–1990 and in the years of 2011–2040 under A1B scenario of the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) [15]. The IPCC-SRES A1B shows rapid economic growth, especially in developing nations, with a balance across all energy sources for economic development, and it has been adopted as the most commonly used emission scenario for climate change studies in China [16, 17]. Furthermore, linear interpolation was performed to transform the three downscaled CM data sets (50 km × 50 km) to a 0.25° resolution. In this study, the observed historical climate data set in 1961–1990 was directly employed as the baseline climatology. To bias-correct the CM data sets, the delta-change method was used, which superimposes the mean monthly anomalies between the CM-simulated baseline and A1B climate data on the observed historical meteorology to represent future climate. In this way, three future climate data sets were finally constructed for three future scenarios, namely, A1B PRECIS, A1B CSIRO, and A1B MPI.


## 3.2. Variable Infiltration Capacity Hydrological Model

The Variable Infiltration Capacity (VIC) model [18, 19] is a state-of-the-art physically based distributed hydrological model. It simulates radiative fluxes, turbulent fluxes of momentum, sensible heat, unsaturated liquid water transport, saturated gravitational drainage, surface runoff, bottom drainage evapotranspiration, freezing, and thawing of soil ice at each land grid cell. Additionally, a conceptual streamflow routing model is included to route the computed runoff depth at each grid cell to the watershed outlets. The routing model simulates two processes: (1) runoff concentration on the outflow of each grid cell is represented by the linear reservoir method; (2) the routing effect of channel system connecting grid cells is represented by the Muskingum routing algorithm [20].In this study, the vegetation and soil parameters of the VIC model were spatially estimated a priori according to vegetation and soil texture classes at each grid cell. For each type of vegetation, the vegetation parameters, such as architectural resistancera (s/m), albedo α, minimum stomata resistance rsmin (s/m), leaf-area index LAI, roughness length z0 (m), and zero-plane displacement d0 (m), were derived on the basis of the vegetation parameter information from Land Data Assimilation Systems (LDAS, http://ldas.gsfc.nasa.gov/gldas/GLDASmapveg.php). The individual soil parameters used in VIC, such as porosity θs, saturated soil potential ψs, saturated hydraulic conductivity Ks, and bulk density BD, were derived according to the work of [21, 22]. In addition, two insensitive hydrologic parameters of VIC were estimated a priori according to the work of [23]. These parameters are the following: (1)Dsoil: soil depth of each soil layer (three layers in this study) is set as 0.1 m, 0.5 m, and 1.5 m, respectively; (2)Ws: the fraction of the maximum soil moisture (of the lowest soil layer) where nonlinear baseflow occurs is defined as 0.99. Other sensitive VIC hydrologic parameters (such as Dsmax, maximum baseflow that can occur from the lowest soil layer; Ds, fraction of Dsmax where nonlinear baseflow begins; and binf, coefficient defining the shape of the Variable Infiltration Capacity curve) and runoff routing parameters were calibrated by fitting the daily calculated streamflow time series against the observed records. These sensitive parameters are calibrated within the predefined rational physical value ranges by the Shuffled Complex Evolution (SCE-UA) automatic optimization method [24], with the log-transformed Nash-Sutcliffe model efficiency coefficient as the objective function.In this study, the gridded baseline and three future climate data sets were, respectively, used to drive the VIC model for daily streamflow simulations and projections at Huaxian station. Subsequently, the monthly simulated streamflow time series accumulated from the daily time series were analyzed to assess hydrological drought properties using univariate and bivariate drought distributions.


## 3.3. Univariate Drought Distribution Model

The VIC-simulated monthly streamflow time series were used to identify the hydrological drought events under the baseline (1961–1990) and three A1B (2011–2040) scenarios by the theory of runs. Following [25], three truncation levels of streamflow, Q0, Q1, and Q2 (Q0>Q1>Q2), were used to identify the hydrological drought events and relevant drought characteristics (Figure 2). As shown in Figure 2, four possible hydrological drought events (indicated as a, b, c, and d) are preliminarily identified during the period when the simulated monthly streamflow is below the truncation streamflow Q1. For the events with one-month duration (a and d in Figure 2), only the event a is finally identified to be a drought event as its monthly streamflow is below the truncation streamflow Q2, but the event d is rejected to be a hydrological drought with its monthly streamflow being above Q2. For the two sequential events with the interval time of one month (b and c in Figure 2), the two events b and c are combined to be one drought event on the condition that the monthly streamflow at the interval is below the truncation streamflow Q0; otherwise the events b and c are considered to be two independent drought events. For each identified drought event, the corresponding drought severity is the cumulative deviation below the truncation streamflow Q1 during the drought duration (Figure 2). According to Standard for Information and Hydrological Forecasting of China [26], the truncation streamflow Q0 in this study was defined to be the monthly mean of the simulated streamflow time series from 1961 to 1990 at Huaxian station, and Q1 and Q2 were assumed to be 10% and 20% below Q0, respectively.Figure 2
Diagram of drought identification using the theory of runs.Using the drought identification scheme (Figure2), the drought variables of duration and severity were derived for each drought event under the baseline and A1B PRECIS, A1B CSIRO, and A1B MPI scenarios. For the analysis using univariate drought distributions, the exponential and Weibull distributions were, respectively, used to fit the drought duration and severity samples under the baseline and three future scenarios, and the maximum likelihood method was used to estimate the distribution parameters. Additionally, the univariate return periods of drought events regarding only one variable (drought duration or severity) were also derived under the baseline and three A1B scenarios, which are shown as follows:(1)TD=EL1-FDd,TS=EL1-FSs,where D and S denote drought duration and severity, respectively; TD and TS represent the univariate return period for droughts with D≥d and S⩾s, respectively; E(L) is the mean interarrival time of droughts; FD(d) and FS(s) are the cumulative probability distribution functions of drought duration and severity, respectively.


## 3.4. Bivariate Drought Distribution Model

In reality, drought duration and severity are often significantly correlated. Therefore, the relevance between drought duration and severity should be carefully taken into account when using both drought variables for drought frequency analysis. Copulas are functions that link univariate distribution functions to form multivariate distributions [27, 28]. They are useful tools to effectively reflect the correlation features among multiple drought variables. With simple forms and good accuracies, the Archimedean copulas have been widely applied in drought studies [7, 13]. In this study, four Archimedean copulas were used to establish bivariate drought distribution that describes the joint probabilities of drought duration and severity. They are Gumbel-Hougaard, Clayton, Frank, and Ali-Mikhail-Haq copulas. Given the univariate distributions of drought duration and severity (FD(d) and FS(s)), the joint distributions for drought duration and drought severity using the four Archimedean copulas can be, respectively, formulated as follows:(2)FD,Sd,s=exp⁡--ln⁡FDdθ+-ln⁡FSsθ1/θ,(3)FD,Sd,s=FDd-θ+FSs-θ-1-1/θ,(4)FD,Sd,s=-1θln⁡1+e-θFDd-1e-θFSs-1e-θ-1,(5)FD,Sd,s=1-θFDdFSs1-θ1-FDd1-θ1-FDd-θFDdFSs,where FD,S(d,s) is the joint probability distribution of drought duration and severity; θ is the copula parameter representing the degree of association between FD(d) and FS(s).With the joint probability distribution of drought duration and severity, conditional probability can also be calculated. Given drought duration exceeding a certain thresholdd, the probability of drought severity is defined as(6)PS≤s∣D≥d=PS⩽s,D⩾dPD⩾d=FSs-FDSd,s1-FDd.In addition, two types of bivariate return periods, defined as TDSAND and TDSOR, were calculated. TDSAND represents the return period when both drought duration and severity exceed their specific values:(7)TDSAND=ELPD⩾d,S⩾s=EL1-FDd-FSs+FDSd,s,and TDSOR denotes the return period when drought duration is higher than a specific value or drought severity exceeds another specific value:(8)TDSOR=ELPD⩾dorS⩾s=EL1-FDSd,s.


## 4. Results

### 4.1. Historical Hydrological Streamflow Simulations

Historical daily streamflow in the baseline period (1961–1990) at Huaxian station was simulated using the VIC model fed with the observed precipitation and air temperature data (baseline climate data set). The VIC model was calibrated by fitting the calculated daily streamflow against the observed streamflow at Huaxian station with the aid of the Shuffled Complex Evolution (SCE-UA) automatic optimization method. Table1 and Figure 3 show that the VIC model can provide reasonable streamflow simulations in calibration and validation periods in terms of the log-transformed Nash-Sutcliffe model efficiency coefficient and the relative error (bias) between the simulated and the observed total runoff.Table 1
Performance of historical monthly streamflow simulations at Huaxian station.
Periods
Nash-Sutcliffe coefficient
Log-transformed Nash-Sutcliffe coefficient
Bias (%)
Calibration (1961–1980)
0.829
0.715
3.1
Validation (1981–1990)
0.902
0.809
7.3Figure 3
Observed and simulated monthly hydrographs at Huaxian station in the years 1961–1990.


### 4.2. Validation of Historical Hydrological Droughts

According to the theory of runs, the simulated monthly streamflow time series at Huaxian station in the baseline period (1961–1990) were used to derive the historical hydrological drought characteristics for univariate and bivariate drought analysis. For univariate drought analysis, the exponential and Weibull distributions were adopted to fit the identified historical drought duration and severity samples, respectively. The two-sample Kolmogorov-Smirnov (K-S) test was used to test whether the selected theoretical distributions are able to effectively represent the distributions of drought duration and severity, respectively. Figure4(a) shows that the Z-score of the K-S test statistics (ZK-S) is much lower than the critical Z-score (Zcri) at a 5% significance level, indicating that the historical drought duration and severity samples are in a good agreement with the exponential and Weibull distributions, respectively. To derive the joint distribution for the historical drought severity and duration, four copula functions were adopted. The root mean square error (RMSE) was used to calculate the biases between the empirical and theoretical joint distributions. Table 2 shows that the Clayton copula has the lowest RMSE among all the four copulas, and the Pearson correlation coefficient between the empirical probability and the Clayton-based theoretical joint probability is 0.991 in the baseline period (Figure 5(a)), implying that the Clayton copula is able to fit the joint duration-severity probability distribution for the historical drought events with very high accuracy.Table 2
RMSE of fitting four copula functions to joint distributions for drought severity and duration under baseline and three A1B scenarios.
Scenarios
RMSE
Gumbel-Hougaard
Clayton
Frank
Ali-Mikhail-Haq
Baseline
0.2334
0.0465
0.1655
0.8975
A1B PRECIS
0.2368
0.0536
0.1746
0.2117
A1B CSIRO
0.2313
0.0681
0.1682
0.1569
A1B MPI
0.2309
0.0703
0.1425
1.6671Figure 4
Theoretical distribution fitting for severity and duration under baseline and A1B scenarios with Z-score of two-sample Kolmogorov-Smirnov test statistics (ZK-S is the calculated Z-score of the K-S test statistics and Zcri is the critical Z-score at a 5% significance level).
(a)
Baseline
(b)
A1B PRECIS
(c)
A1B CSIRO
(d)
A1B MPIFigure 5
Empirical and theoretical joint probabilities of drought severity and duration under baseline and three A1B scenarios.
(a)
Baseline
(b)
A1B PRECIS
(c)
A1B CSIRO
(d)
A1B MPIGiven that the records of historical hydrological droughts were not available in the WRB, the findings of [29] were used to validate the feasibility of the univariate and bivariate probabilistic models in identifying historical hydrological droughts. Reference [29] made survey of statistics on the historical droughts in provincial administrative regions in China in the years 1949–2000 and defined drought situations regarding the annual reduction rate of grain yield. For instance, a severe drought year refers to the time period when local annual grain yield reduces by 5~7%, and an extreme drought year with a reduction rate of over 7%. Figure 1 indicates that Shaanxi and Gansu provinces occupy the WRB predominantly. Therefore, the annual records with severe droughts or extreme droughts in Shaanxi or Gansu were used for historical hydrological drought validation. As shown in Table 3, severe droughts or/and extreme severe droughts occurred in Shaanxi or/and Gansu for twelve years in the baseline period (1961–1990), and the top ten most severe drought events in the baseline period (1961–1990) identified by the univariate and bivariate drought models were compared with the severe and extreme drought records in Shaanxi and Gansu. Table 3 shows that the univariate and bivariate drought models in this study are able to effectively identify most historical drought years with severe and extreme drought conditions in Shaanxi and Gansu provinces. Although the historical agricultural drought records from [29] are mostly consistent with the modeling results, it is still necessary to collect the hydrological drought records for model validation in future studies so as to improve the credibility of the drought models.Table 3
Validation of univariate/bivariate model-based droughts against historical severe and extreme drought records in the baseline period (1961–1990).
Year
Historical drought conditions
Univariate model
Univariate model
Bivariate model
Shaanxi
Gansu
(Severity)
(Duration)
(Duration-severity)
1962
Severe
Extreme
Y
Y
Y
1966
Moderate
Severe
Y
Y
N
1969
Mild
Severe
Y
Y
Y
1971
Moderate
Extreme
Y
Y
Y
1972
Severe
Extreme
Y
Y
Y
1973
Mild
Extreme
Y
Y
Y
1979
Mild
Severe
N
Y
N
1980
Severe
Moderate
Y
Y
Y
1981
Moderate
Extreme
Y
Y
Y
1982
Moderate
Extreme
Y
Y
Y
1986
Severe
Moderate
Y
Y
Y
1987
Severe
Extreme
Y
Y
Y
Note: symbol “Y” indicates that the univariate or bivariate drought model is able to effectively identify the historical severe or extreme drought years in Shaanxi or Gansu province; and symbol “N” denotes that the drought model fails to identify the historical drought records in Shaanxi or Gansu.


### 4.3. Projected Changes in Hydrometeorological Variables

The baseline mean monthly air temperature and precipitation were compared with the corresponding projected A1B values (Figures6(a) and 6(b)). It is found that the three CMs project a considerable increase in air temperature under A1B throughout the whole year, with a rise of 1.0~2.0°C for A1B PRECIS, 1.0~2.0°C for A1B CSIRO, and 0.7~1.6°C for A1B MPI. PRECIS projects no distinct changes in mean annual precipitation under A1B scenario, with a minor drop of 1.4 mm relative to the baseline level (559.3 mm), while the CSIRO and MPI GCMs simulate a considerable reduction of 47.9 mm (8.6%) and 51.1 mm (9.1%) in mean annual precipitation under A1B. Meanwhile, all the three CMs project obvious changes in seasonal precipitation. As shown in Figure 6(b), precipitation would generally undergo a substantial decrease in most months. However, PRECIS projects a significant precipitation increase in August and November–March; CSIRO simulates a considerable remarkable rise of precipitation in July and August; MPI projects an obvious increase in precipitation in January and February.Figure 6
Projected changes in precipitation, air temperature, evapotranspiration, and runoff under A1B scenarios relative to baseline period.
(a)
Air temperature change
(b)
Precipitation change
(c)
Evapotranspiration change
(d)
Runoff changeDriven by the baseline and three future climate data sets, the VIC model was used to simulate and project hydrological processes under baseline and A1B scenarios. Although the obvious increase in air temperature potentially promotes the atmospheric demand for evapotranspiration, actual evapotranspiration would undergo a slight reduction almost throughout the year under A1B CSIRO and A1B MPI (Figure6(c)). This is attributed to the phenomenon that both CSIRO and MPI project a considerable precipitation decrease in most months which is very likely to restrict the water supply for evapotranspiration. Using the A1B PRECIS climate data set as inputs, the VIC model projects a minor increase in evapotranspiration in spring and autumn and a slight decrease in summer. As shown in Figure 6(d), runoff would drop significantly in most months. Under A1B PRECIS, a substantial runoff increase would occur in February–April and August, mainly due to the projected remarkable precipitation rise in the same period. It is notable that although all the CMs generally project the WRB towards a drying trend in the future, the different magnitudes of air temperature and precipitation changes from different CMs are likely to lead to large uncertainties in the projected future runoff. This uncertainty may further largely impact the projections of hydrological drought events under future scenarios.


### 4.4. Projected Climate Change Impact on Hydrological Droughts

The simulated monthly streamflow at Huaxian station was used to derive the drought characteristics under baseline and A1B scenarios, and the identified properties of hydrological drought events were employed for univariate and copula-based bivariate drought analysis.


#### 4.4.1. Univariate Drought Analysis

According to the theory of runs, 39 hydrological drought events were identified for the baseline period, together with 38, 31, and 34 events under A1B PRECIS, A1B CSIRO, and A1B MPI scenarios, respectively. Relative to the baseline level, fewer hydrological drought events would occur under A1B. However, the means and medians of drought variables under all three future scenarios are projected to increase considerably. Figure7 shows that the mean drought severity and duration are 11.2 × 108 m3 and 4.8 months for the baseline period, while the values of these drought variables would increase to be 12.9 × 108 m3 and 5.5 months for A1B PRECIS, 18.5 × 108 m3 and 9.6 months for A1B CSIRO, and 18.3 × 108 m3 and 7.6 months for A1B MPI. Meanwhile, under A1B CSIRO and A1B MPI scenarios, much worse drought conditions are projected. In the baseline period, the most severe drought event was identified to be from November 1961 to April 1963, with the duration of 18 months and the severity of 29.8 × 108 m3. However, under A1B CSIRO, a long-term extreme drought is projected from October 2020 to June 2025, with the duration and severity being up to 57 months and 149.0 × 108 m3, respectively. In the case of A1B MPI, the most extreme drought would occur from June 2023 to June 2025, with the duration of 25 months and the severity of 57.7 × 108 m3; and a comparable extreme drought event is also projected under A1B PRECIS.Figure 7
Boxplots for drought severity and duration samples under baseline and A1B scenarios (the diamond symbol indicates the means of drought severity or duration).
(a)
Severity
(b)
DurationThe exponential and Weibull distributions were adopted to fit the drought duration and severity samples under three future scenarios, respectively. Figures4(b)–4(d) illustrate that the identified drought duration and severity samples preferably follow the exponential and Weibull distributions. With the univariate drought probabilistic models, drought severity and duration referring to different return periods were estimated. Table 4 shows that drought severity and duration in all return periods would increase remarkably under all three A1B scenarios, especially with the dramatic rise in the cases of A1B CSIRO and A1B MPI. Compared with the baseline situation, the 50-year drought severity would increase by 122.2% and 67.2% under A1B CSIRO and A1B MPI, and the 50-year drought duration is projected to rise by 17.4 and 7.7 months, respectively. This univariate drought analysis implies that future climate change under A1B would deteriorate the drought situation in the WRB, especially with increased frequencies of extreme hydrological drought events with higher severities and longer durations. It should be noted that the drought simulations as short as 30 years for both baseline and A1B scenarios may not sufficiently capture the changes in drought events at higher return period levels (such as 50 years) and a larger sample size of drought duration and severity data sets for both scenarios are required so as to reduce this uncertainty. In general, driven by the three CM data sets, the VIC hydrological model and the univariate probabilistic drought models project similar deteriorated drought conditions in the WRB under all three A1B scenarios, but with different magnitudes of changes in drought severity and duration. This uncertainty in drought projections might mainly result from the possible large uncertainties in climate data sets from different climate models.Table 4
Drought characteristics in different univariate return periods under baseline and A1B scenarios.
Return periods
Drought severity (108 m3)
Drought duration (month)
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
50 years
44.2
48.0
98.2
73.9
18.4
20.5
35.8
26.1
20 years
33.8
37.6
73.5
58.3
13.9
15.7
27.4
20.1
10 years
25.9
29.5
55.2
46.1
10.7
12.0
21.1
15.7
5 years
18.1
21.2
37.4
33.4
7.3
8.4
17.4
11.2


#### 4.4.2. Bivariate Drought Analysis

To derive the joint distributions of drought severity and duration under three A1B scenarios, four copula functions were adopted. Table2 and Figures 5(b)–5(d) show that the Clayton copula is able to effectively characterize the joint duration-severity distributions under all A1B scenarios. To quantify possible future climate change impacts on drought conditions, the joint probability, conditional probability, and joint return period under all future scenarios were compared with those of the baseline period.Figure8 shows the contours of joint probability for drought duration and severity under baseline and future scenarios. It demonstrates that large distance exists between the contours for baseline and A1B drought events at the same probability levels. On the basis of those contours, if the same duration or severity is given for both baseline and future events, the corresponding severity or duration values under all A1B scenarios are found to be considerably larger than those of baseline drought events. In consequence, more severe drought conditions are projected under three A1B scenarios, and the basin would experience the most serious hydrological drought situations under A1B CISRO and A1B MPI. This phenomenon can also be illustrated by the conditional distributions of drought severities given certain durations (Figure 9). For example, given a 6-month duration, the conditional probability of baseline drought events with severity less than or equal to 30.0 × 108 m3 is approximately 0.758 (Figure 9(a)). However, the same probability corresponds to the A1B PRECIS drought event with severity less than or equal to 33.1 × 108 m3 (Figure 9(a)), and such a probability is also in correspondence with the A1B CSIRO and A1B MPI drought events with severity less than or equal to 50.2 × 108 m3 (Figure 9(b)) and 45.4 × 108 m3 (Figure 9(c)), respectively.Figure 8
Bivariate joint probability of drought duration and severity under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure 9
Conditional probability of drought severity distributions with given durations of 3, 6, and 12 months under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure10 shows the contour plots of joint severity-duration return periods of TDSAND and TDSOR under baseline and three A1B scenarios. In comparison with the baseline situation, more serious drying conditions under the three A1B scenarios are projected in terms of the calculated joint return periods. For instance, the drought event with a 10-month duration and a 40.0 × 108 m3 severity leads to TDSAND of 41.3 years and TDSOR of 6.1 years in the baseline period. However, if the same drought event occurred under A1B PRECIS, such bivariate return periods would reduce to be 27.1 years and 5.0 years, respectively; TDSAND and TDSOR would further drop to be 7.7 years and 3.3 years under A1B MPI and to be 5.7 years and 2.8 years under A1B CSIRO.Figure 10
Bivariate joint return periods of drought duration and severity under baseline and A1B scenarios: (a)TDSAND defined by (7) and (b) TDSOR defined by (8).
(a)
T
D
S
A
N
D
(b)
T
D
S
O
R


## 4.1. Historical Hydrological Streamflow Simulations

Historical daily streamflow in the baseline period (1961–1990) at Huaxian station was simulated using the VIC model fed with the observed precipitation and air temperature data (baseline climate data set). The VIC model was calibrated by fitting the calculated daily streamflow against the observed streamflow at Huaxian station with the aid of the Shuffled Complex Evolution (SCE-UA) automatic optimization method. Table1 and Figure 3 show that the VIC model can provide reasonable streamflow simulations in calibration and validation periods in terms of the log-transformed Nash-Sutcliffe model efficiency coefficient and the relative error (bias) between the simulated and the observed total runoff.Table 1
Performance of historical monthly streamflow simulations at Huaxian station.
Periods
Nash-Sutcliffe coefficient
Log-transformed Nash-Sutcliffe coefficient
Bias (%)
Calibration (1961–1980)
0.829
0.715
3.1
Validation (1981–1990)
0.902
0.809
7.3Figure 3
Observed and simulated monthly hydrographs at Huaxian station in the years 1961–1990.


## 4.2. Validation of Historical Hydrological Droughts

According to the theory of runs, the simulated monthly streamflow time series at Huaxian station in the baseline period (1961–1990) were used to derive the historical hydrological drought characteristics for univariate and bivariate drought analysis. For univariate drought analysis, the exponential and Weibull distributions were adopted to fit the identified historical drought duration and severity samples, respectively. The two-sample Kolmogorov-Smirnov (K-S) test was used to test whether the selected theoretical distributions are able to effectively represent the distributions of drought duration and severity, respectively. Figure4(a) shows that the Z-score of the K-S test statistics (ZK-S) is much lower than the critical Z-score (Zcri) at a 5% significance level, indicating that the historical drought duration and severity samples are in a good agreement with the exponential and Weibull distributions, respectively. To derive the joint distribution for the historical drought severity and duration, four copula functions were adopted. The root mean square error (RMSE) was used to calculate the biases between the empirical and theoretical joint distributions. Table 2 shows that the Clayton copula has the lowest RMSE among all the four copulas, and the Pearson correlation coefficient between the empirical probability and the Clayton-based theoretical joint probability is 0.991 in the baseline period (Figure 5(a)), implying that the Clayton copula is able to fit the joint duration-severity probability distribution for the historical drought events with very high accuracy.Table 2
RMSE of fitting four copula functions to joint distributions for drought severity and duration under baseline and three A1B scenarios.
Scenarios
RMSE
Gumbel-Hougaard
Clayton
Frank
Ali-Mikhail-Haq
Baseline
0.2334
0.0465
0.1655
0.8975
A1B PRECIS
0.2368
0.0536
0.1746
0.2117
A1B CSIRO
0.2313
0.0681
0.1682
0.1569
A1B MPI
0.2309
0.0703
0.1425
1.6671Figure 4
Theoretical distribution fitting for severity and duration under baseline and A1B scenarios with Z-score of two-sample Kolmogorov-Smirnov test statistics (ZK-S is the calculated Z-score of the K-S test statistics and Zcri is the critical Z-score at a 5% significance level).
(a)
Baseline
(b)
A1B PRECIS
(c)
A1B CSIRO
(d)
A1B MPIFigure 5
Empirical and theoretical joint probabilities of drought severity and duration under baseline and three A1B scenarios.
(a)
Baseline
(b)
A1B PRECIS
(c)
A1B CSIRO
(d)
A1B MPIGiven that the records of historical hydrological droughts were not available in the WRB, the findings of [29] were used to validate the feasibility of the univariate and bivariate probabilistic models in identifying historical hydrological droughts. Reference [29] made survey of statistics on the historical droughts in provincial administrative regions in China in the years 1949–2000 and defined drought situations regarding the annual reduction rate of grain yield. For instance, a severe drought year refers to the time period when local annual grain yield reduces by 5~7%, and an extreme drought year with a reduction rate of over 7%. Figure 1 indicates that Shaanxi and Gansu provinces occupy the WRB predominantly. Therefore, the annual records with severe droughts or extreme droughts in Shaanxi or Gansu were used for historical hydrological drought validation. As shown in Table 3, severe droughts or/and extreme severe droughts occurred in Shaanxi or/and Gansu for twelve years in the baseline period (1961–1990), and the top ten most severe drought events in the baseline period (1961–1990) identified by the univariate and bivariate drought models were compared with the severe and extreme drought records in Shaanxi and Gansu. Table 3 shows that the univariate and bivariate drought models in this study are able to effectively identify most historical drought years with severe and extreme drought conditions in Shaanxi and Gansu provinces. Although the historical agricultural drought records from [29] are mostly consistent with the modeling results, it is still necessary to collect the hydrological drought records for model validation in future studies so as to improve the credibility of the drought models.Table 3
Validation of univariate/bivariate model-based droughts against historical severe and extreme drought records in the baseline period (1961–1990).
Year
Historical drought conditions
Univariate model
Univariate model
Bivariate model
Shaanxi
Gansu
(Severity)
(Duration)
(Duration-severity)
1962
Severe
Extreme
Y
Y
Y
1966
Moderate
Severe
Y
Y
N
1969
Mild
Severe
Y
Y
Y
1971
Moderate
Extreme
Y
Y
Y
1972
Severe
Extreme
Y
Y
Y
1973
Mild
Extreme
Y
Y
Y
1979
Mild
Severe
N
Y
N
1980
Severe
Moderate
Y
Y
Y
1981
Moderate
Extreme
Y
Y
Y
1982
Moderate
Extreme
Y
Y
Y
1986
Severe
Moderate
Y
Y
Y
1987
Severe
Extreme
Y
Y
Y
Note: symbol “Y” indicates that the univariate or bivariate drought model is able to effectively identify the historical severe or extreme drought years in Shaanxi or Gansu province; and symbol “N” denotes that the drought model fails to identify the historical drought records in Shaanxi or Gansu.


## 4.3. Projected Changes in Hydrometeorological Variables

The baseline mean monthly air temperature and precipitation were compared with the corresponding projected A1B values (Figures6(a) and 6(b)). It is found that the three CMs project a considerable increase in air temperature under A1B throughout the whole year, with a rise of 1.0~2.0°C for A1B PRECIS, 1.0~2.0°C for A1B CSIRO, and 0.7~1.6°C for A1B MPI. PRECIS projects no distinct changes in mean annual precipitation under A1B scenario, with a minor drop of 1.4 mm relative to the baseline level (559.3 mm), while the CSIRO and MPI GCMs simulate a considerable reduction of 47.9 mm (8.6%) and 51.1 mm (9.1%) in mean annual precipitation under A1B. Meanwhile, all the three CMs project obvious changes in seasonal precipitation. As shown in Figure 6(b), precipitation would generally undergo a substantial decrease in most months. However, PRECIS projects a significant precipitation increase in August and November–March; CSIRO simulates a considerable remarkable rise of precipitation in July and August; MPI projects an obvious increase in precipitation in January and February.Figure 6
Projected changes in precipitation, air temperature, evapotranspiration, and runoff under A1B scenarios relative to baseline period.
(a)
Air temperature change
(b)
Precipitation change
(c)
Evapotranspiration change
(d)
Runoff changeDriven by the baseline and three future climate data sets, the VIC model was used to simulate and project hydrological processes under baseline and A1B scenarios. Although the obvious increase in air temperature potentially promotes the atmospheric demand for evapotranspiration, actual evapotranspiration would undergo a slight reduction almost throughout the year under A1B CSIRO and A1B MPI (Figure6(c)). This is attributed to the phenomenon that both CSIRO and MPI project a considerable precipitation decrease in most months which is very likely to restrict the water supply for evapotranspiration. Using the A1B PRECIS climate data set as inputs, the VIC model projects a minor increase in evapotranspiration in spring and autumn and a slight decrease in summer. As shown in Figure 6(d), runoff would drop significantly in most months. Under A1B PRECIS, a substantial runoff increase would occur in February–April and August, mainly due to the projected remarkable precipitation rise in the same period. It is notable that although all the CMs generally project the WRB towards a drying trend in the future, the different magnitudes of air temperature and precipitation changes from different CMs are likely to lead to large uncertainties in the projected future runoff. This uncertainty may further largely impact the projections of hydrological drought events under future scenarios.


## 4.4. Projected Climate Change Impact on Hydrological Droughts

The simulated monthly streamflow at Huaxian station was used to derive the drought characteristics under baseline and A1B scenarios, and the identified properties of hydrological drought events were employed for univariate and copula-based bivariate drought analysis.


### 4.4.1. Univariate Drought Analysis

According to the theory of runs, 39 hydrological drought events were identified for the baseline period, together with 38, 31, and 34 events under A1B PRECIS, A1B CSIRO, and A1B MPI scenarios, respectively. Relative to the baseline level, fewer hydrological drought events would occur under A1B. However, the means and medians of drought variables under all three future scenarios are projected to increase considerably. Figure7 shows that the mean drought severity and duration are 11.2 × 108 m3 and 4.8 months for the baseline period, while the values of these drought variables would increase to be 12.9 × 108 m3 and 5.5 months for A1B PRECIS, 18.5 × 108 m3 and 9.6 months for A1B CSIRO, and 18.3 × 108 m3 and 7.6 months for A1B MPI. Meanwhile, under A1B CSIRO and A1B MPI scenarios, much worse drought conditions are projected. In the baseline period, the most severe drought event was identified to be from November 1961 to April 1963, with the duration of 18 months and the severity of 29.8 × 108 m3. However, under A1B CSIRO, a long-term extreme drought is projected from October 2020 to June 2025, with the duration and severity being up to 57 months and 149.0 × 108 m3, respectively. In the case of A1B MPI, the most extreme drought would occur from June 2023 to June 2025, with the duration of 25 months and the severity of 57.7 × 108 m3; and a comparable extreme drought event is also projected under A1B PRECIS.Figure 7
Boxplots for drought severity and duration samples under baseline and A1B scenarios (the diamond symbol indicates the means of drought severity or duration).
(a)
Severity
(b)
DurationThe exponential and Weibull distributions were adopted to fit the drought duration and severity samples under three future scenarios, respectively. Figures4(b)–4(d) illustrate that the identified drought duration and severity samples preferably follow the exponential and Weibull distributions. With the univariate drought probabilistic models, drought severity and duration referring to different return periods were estimated. Table 4 shows that drought severity and duration in all return periods would increase remarkably under all three A1B scenarios, especially with the dramatic rise in the cases of A1B CSIRO and A1B MPI. Compared with the baseline situation, the 50-year drought severity would increase by 122.2% and 67.2% under A1B CSIRO and A1B MPI, and the 50-year drought duration is projected to rise by 17.4 and 7.7 months, respectively. This univariate drought analysis implies that future climate change under A1B would deteriorate the drought situation in the WRB, especially with increased frequencies of extreme hydrological drought events with higher severities and longer durations. It should be noted that the drought simulations as short as 30 years for both baseline and A1B scenarios may not sufficiently capture the changes in drought events at higher return period levels (such as 50 years) and a larger sample size of drought duration and severity data sets for both scenarios are required so as to reduce this uncertainty. In general, driven by the three CM data sets, the VIC hydrological model and the univariate probabilistic drought models project similar deteriorated drought conditions in the WRB under all three A1B scenarios, but with different magnitudes of changes in drought severity and duration. This uncertainty in drought projections might mainly result from the possible large uncertainties in climate data sets from different climate models.Table 4
Drought characteristics in different univariate return periods under baseline and A1B scenarios.
Return periods
Drought severity (108 m3)
Drought duration (month)
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
50 years
44.2
48.0
98.2
73.9
18.4
20.5
35.8
26.1
20 years
33.8
37.6
73.5
58.3
13.9
15.7
27.4
20.1
10 years
25.9
29.5
55.2
46.1
10.7
12.0
21.1
15.7
5 years
18.1
21.2
37.4
33.4
7.3
8.4
17.4
11.2


### 4.4.2. Bivariate Drought Analysis

To derive the joint distributions of drought severity and duration under three A1B scenarios, four copula functions were adopted. Table2 and Figures 5(b)–5(d) show that the Clayton copula is able to effectively characterize the joint duration-severity distributions under all A1B scenarios. To quantify possible future climate change impacts on drought conditions, the joint probability, conditional probability, and joint return period under all future scenarios were compared with those of the baseline period.Figure8 shows the contours of joint probability for drought duration and severity under baseline and future scenarios. It demonstrates that large distance exists between the contours for baseline and A1B drought events at the same probability levels. On the basis of those contours, if the same duration or severity is given for both baseline and future events, the corresponding severity or duration values under all A1B scenarios are found to be considerably larger than those of baseline drought events. In consequence, more severe drought conditions are projected under three A1B scenarios, and the basin would experience the most serious hydrological drought situations under A1B CISRO and A1B MPI. This phenomenon can also be illustrated by the conditional distributions of drought severities given certain durations (Figure 9). For example, given a 6-month duration, the conditional probability of baseline drought events with severity less than or equal to 30.0 × 108 m3 is approximately 0.758 (Figure 9(a)). However, the same probability corresponds to the A1B PRECIS drought event with severity less than or equal to 33.1 × 108 m3 (Figure 9(a)), and such a probability is also in correspondence with the A1B CSIRO and A1B MPI drought events with severity less than or equal to 50.2 × 108 m3 (Figure 9(b)) and 45.4 × 108 m3 (Figure 9(c)), respectively.Figure 8
Bivariate joint probability of drought duration and severity under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure 9
Conditional probability of drought severity distributions with given durations of 3, 6, and 12 months under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure10 shows the contour plots of joint severity-duration return periods of TDSAND and TDSOR under baseline and three A1B scenarios. In comparison with the baseline situation, more serious drying conditions under the three A1B scenarios are projected in terms of the calculated joint return periods. For instance, the drought event with a 10-month duration and a 40.0 × 108 m3 severity leads to TDSAND of 41.3 years and TDSOR of 6.1 years in the baseline period. However, if the same drought event occurred under A1B PRECIS, such bivariate return periods would reduce to be 27.1 years and 5.0 years, respectively; TDSAND and TDSOR would further drop to be 7.7 years and 3.3 years under A1B MPI and to be 5.7 years and 2.8 years under A1B CSIRO.Figure 10
Bivariate joint return periods of drought duration and severity under baseline and A1B scenarios: (a)TDSAND defined by (7) and (b) TDSOR defined by (8).
(a)
T
D
S
A
N
D
(b)
T
D
S
O
R


## 4.4.1. Univariate Drought Analysis

According to the theory of runs, 39 hydrological drought events were identified for the baseline period, together with 38, 31, and 34 events under A1B PRECIS, A1B CSIRO, and A1B MPI scenarios, respectively. Relative to the baseline level, fewer hydrological drought events would occur under A1B. However, the means and medians of drought variables under all three future scenarios are projected to increase considerably. Figure7 shows that the mean drought severity and duration are 11.2 × 108 m3 and 4.8 months for the baseline period, while the values of these drought variables would increase to be 12.9 × 108 m3 and 5.5 months for A1B PRECIS, 18.5 × 108 m3 and 9.6 months for A1B CSIRO, and 18.3 × 108 m3 and 7.6 months for A1B MPI. Meanwhile, under A1B CSIRO and A1B MPI scenarios, much worse drought conditions are projected. In the baseline period, the most severe drought event was identified to be from November 1961 to April 1963, with the duration of 18 months and the severity of 29.8 × 108 m3. However, under A1B CSIRO, a long-term extreme drought is projected from October 2020 to June 2025, with the duration and severity being up to 57 months and 149.0 × 108 m3, respectively. In the case of A1B MPI, the most extreme drought would occur from June 2023 to June 2025, with the duration of 25 months and the severity of 57.7 × 108 m3; and a comparable extreme drought event is also projected under A1B PRECIS.Figure 7
Boxplots for drought severity and duration samples under baseline and A1B scenarios (the diamond symbol indicates the means of drought severity or duration).
(a)
Severity
(b)
DurationThe exponential and Weibull distributions were adopted to fit the drought duration and severity samples under three future scenarios, respectively. Figures4(b)–4(d) illustrate that the identified drought duration and severity samples preferably follow the exponential and Weibull distributions. With the univariate drought probabilistic models, drought severity and duration referring to different return periods were estimated. Table 4 shows that drought severity and duration in all return periods would increase remarkably under all three A1B scenarios, especially with the dramatic rise in the cases of A1B CSIRO and A1B MPI. Compared with the baseline situation, the 50-year drought severity would increase by 122.2% and 67.2% under A1B CSIRO and A1B MPI, and the 50-year drought duration is projected to rise by 17.4 and 7.7 months, respectively. This univariate drought analysis implies that future climate change under A1B would deteriorate the drought situation in the WRB, especially with increased frequencies of extreme hydrological drought events with higher severities and longer durations. It should be noted that the drought simulations as short as 30 years for both baseline and A1B scenarios may not sufficiently capture the changes in drought events at higher return period levels (such as 50 years) and a larger sample size of drought duration and severity data sets for both scenarios are required so as to reduce this uncertainty. In general, driven by the three CM data sets, the VIC hydrological model and the univariate probabilistic drought models project similar deteriorated drought conditions in the WRB under all three A1B scenarios, but with different magnitudes of changes in drought severity and duration. This uncertainty in drought projections might mainly result from the possible large uncertainties in climate data sets from different climate models.Table 4
Drought characteristics in different univariate return periods under baseline and A1B scenarios.
Return periods
Drought severity (108 m3)
Drought duration (month)
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
Baseline
A1B PRECIS
A1B CSIRO
A1B MPI
50 years
44.2
48.0
98.2
73.9
18.4
20.5
35.8
26.1
20 years
33.8
37.6
73.5
58.3
13.9
15.7
27.4
20.1
10 years
25.9
29.5
55.2
46.1
10.7
12.0
21.1
15.7
5 years
18.1
21.2
37.4
33.4
7.3
8.4
17.4
11.2


## 4.4.2. Bivariate Drought Analysis

To derive the joint distributions of drought severity and duration under three A1B scenarios, four copula functions were adopted. Table2 and Figures 5(b)–5(d) show that the Clayton copula is able to effectively characterize the joint duration-severity distributions under all A1B scenarios. To quantify possible future climate change impacts on drought conditions, the joint probability, conditional probability, and joint return period under all future scenarios were compared with those of the baseline period.Figure8 shows the contours of joint probability for drought duration and severity under baseline and future scenarios. It demonstrates that large distance exists between the contours for baseline and A1B drought events at the same probability levels. On the basis of those contours, if the same duration or severity is given for both baseline and future events, the corresponding severity or duration values under all A1B scenarios are found to be considerably larger than those of baseline drought events. In consequence, more severe drought conditions are projected under three A1B scenarios, and the basin would experience the most serious hydrological drought situations under A1B CISRO and A1B MPI. This phenomenon can also be illustrated by the conditional distributions of drought severities given certain durations (Figure 9). For example, given a 6-month duration, the conditional probability of baseline drought events with severity less than or equal to 30.0 × 108 m3 is approximately 0.758 (Figure 9(a)). However, the same probability corresponds to the A1B PRECIS drought event with severity less than or equal to 33.1 × 108 m3 (Figure 9(a)), and such a probability is also in correspondence with the A1B CSIRO and A1B MPI drought events with severity less than or equal to 50.2 × 108 m3 (Figure 9(b)) and 45.4 × 108 m3 (Figure 9(c)), respectively.Figure 8
Bivariate joint probability of drought duration and severity under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure 9
Conditional probability of drought severity distributions with given durations of 3, 6, and 12 months under baseline and three A1B scenarios.
(a)
Baseline VS A1B PRECIS
(b)
Baseline VS A1B CSIRO
(c)
Baseline VS A1B MPIFigure10 shows the contour plots of joint severity-duration return periods of TDSAND and TDSOR under baseline and three A1B scenarios. In comparison with the baseline situation, more serious drying conditions under the three A1B scenarios are projected in terms of the calculated joint return periods. For instance, the drought event with a 10-month duration and a 40.0 × 108 m3 severity leads to TDSAND of 41.3 years and TDSOR of 6.1 years in the baseline period. However, if the same drought event occurred under A1B PRECIS, such bivariate return periods would reduce to be 27.1 years and 5.0 years, respectively; TDSAND and TDSOR would further drop to be 7.7 years and 3.3 years under A1B MPI and to be 5.7 years and 2.8 years under A1B CSIRO.Figure 10
Bivariate joint return periods of drought duration and severity under baseline and A1B scenarios: (a)TDSAND defined by (7) and (b) TDSOR defined by (8).
(a)
T
D
S
A
N
D
(b)
T
D
S
O
R


## 5. Conclusions and Discussion

In this study, a modeling system for projecting the potential future climate change impacts on hydrological drought events in the WRB in North China is presented. This modeling system includes the VIC hydrological model driven by climate outputs from PRECIS RCM, CSIRO GCM, and MPI GCM for future streamflow projections, a univariate probabilistic model for drought severity and duration assessment, and a copula-based model for bivariate drought assessment and joint frequency analysis under historical and future climates. Driven by the observed climate data, the modeling system is able to effectively identify most historical severe and extreme severe droughts in the WRB. The VIC model fed with three CM data sets, in general, projected a considerable runoff reduction under IPCC-SRES A1B scenario. This further triggers much worse drought conditions in the future. It is found in the univariate drought assessment that although fewer hydrological drought events would occur under A1B scenario, such drought variables as duration and severity were projected to increase considerably. The bivariate drought assessment using copula reveals that if historical droughts at a certain return period reoccurred under the future scenarios, the corresponding joint return periods would decrease remarkably. With these trends in the future, the hydrological drought situation in the WRB would be further deteriorated, and effective water saving techniques and rational water resources management strategies should be carried out for drought disaster mitigations.It should be noted that, with the projected streamflow at Huaxian station being adopted for univariate and bivariate drought assessments, only the general drought conditions in the upstream area controlled by Huaxian hydrological station were projected in this study. To consider the spatiotemporal variations of drought conditions in the WRB, future work will be carried out to analyze the VIC-calculated runoff depth at each grid cell within the study area with the similar methodology in this study.It is interesting to notice that although all modeling runs with different CM data sets consistently project future droughts to be deteriorated in the WRB, the projected drought conditions under A1B CSIRO and A1B MPI tend to be more serious than the case of A1B PRECIS. Several studies [30–32] found that CMs are the dominant uncertainty source, influencing future streamflow projections. Given that the VIC model is able to accurately reproduce the historical monthly streamflow at Huaxian station (Table 1 and Figure 3), the uncertainties of streamflow from CMs are very likely to predominantly further affect future hydrological drought projections in this study. Consequently the uncertainty in drought projections might mainly originate from the uncertainties of CMs. Therefore, it is necessary to quantitatively evaluate the effects of the CM uncertainties on future drought projections. Furthermore, the PRECIS and CSIRO climate data sets under the IPCC-SRES B1 scenario were also adopted for future drought projections in this study (the results are not shown in this paper). It shows that the WRB would experience deteriorated drought conditions under B1, but the drying magnitude is less severe than that under A1B. This implies that the uncertainty from the adopted emission scenarios is nonignorable as well, which should be quantified in future studies. In addition, currently the new projected future climate data sets from the Coupled Model Intercomparison Project phase 5 (CMIP5) are available, which employed the latest generation of GCMs under the scenarios of Representative Concentration Pathways (RCPs) [33]. Therefore, it is encouraged to use this latest climate projection product for drought projections in future studies.



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*Source: 2905198-2015-12-24.xml*