Introduction
With the increasing impact of climate change and anthropogenic activities,
droughts happen in more areas with higher frequency. Since the 1990s, drought
disasters have caused more than 11 million deaths and affected more than
2 billion people on the global level (United Nations International
Strategy for Disaster Reduction Secretariat, 2009). Since the 1970s, the areas where
droughts happened (PDSI < -3) have increased by 1.5 times in the
world (Dai et al., 2004). The probability of drought events that occurred in the
southern US in the late 19th century and 20th century has increased,
indicated by the analysis of the reconstructed precipitation series (Le Quesna et al.,
2009). The average annual economic losses that resulted from drought
disasters in the US range from 6 to 8 billion dollars. That amount reached up to
40 billion in 1988 (Federal Emergency Management Agency, 1995). The drought-related disasters caused more than
500 thousand deaths in Africa in the 1980s (Kallis, 2008). Given the growing influence
of climate change, which is mainly characterized by global warming, the
stability of the climate system is declining, and the impacts of drought and
other extreme climate events are increasing (Dai, 2011). The Special Report on Managing the Risks of Extreme Events Disasters to Advance Climate Change Adaptation showed that drought
would be persistent in many regions of the world in the future owing to
evaporation increase and soil moisture decrease; the United States,
southern Europe, southeastern Asia, Brazil, Chile, Australia, and Africa as
well as other countries and regions would be affected by persistent drought
severely (Intergovernmental Panel on Climate Change, 2012).
The drought occurrence and intensity in China demonstrate an increasing
tendency which is similar to the global trend. The drought problem has become
more and more prominent (Qin, 2009). Severe drought has happened every 2 to 3 years
on average (Weng and Yan, 2010). Over the past 500 years, several large-scale drought
disasters occurred in eastern China, as shown by historical records. Drought
disasters which happened from 1500 to 1730 and from 1900 until the present day have a
very wide spatial distribution (Dai, 2011). The areas where drought events and
drought disasters occurred have increased since the middle 21st century. The
annual average affected areas (the areas where crop yields decreased by over
10 % more than normal annual yields) and damaged areas (the areas where crop
yields decreased by over 30 % than normal annual yields) of drought
disasters were nearly 0.21 × 108 km2 and 0.10 × 108 km2 from 1950 to 2010, which were 2.19 times and 1.77 times of
the impacts of flood disasters, respectively (State Flood Control and Drought Relief Headquarters, 2010). Drought occurs
frequently not only in northern China, where water resources are short, but also in southern China, where water resources are relatively abundant. In recent years, several extreme drought events happened
frequently in China (Qin, 2009), such as the droughts that occurred in Sichuan
and Chongqing in 2006 (Qin, 2009), the drought that occurred in the winter
wheat region in northern China in 2008 (Qin, 2009), the drought that occurred
in southern China in 2009 (Weng and Yan, 2010) and the drought that occurred in the
middle and lower reaches of the Yangtze River in 2011.
The drought has become one of the major factors affecting sustainable
socioeconomic development. Government departments, the public and
researchers have paid more attention to the evolutionary rules and driving
mechanism of drought in the changing environment, as well as corresponding
strategies to cope with it. In addition, it is one of the emerging issues
and hot topics in the field of hydrology and water resources (State Flood
Control and Drought Relief Headquarters, 2010).
Drought is firstly a resource issue for its shortage of water resources, but as it develops it evolves into a disaster issue. Drought is one of the
extreme events in water cycle. Its evolution is affected by the
characteristics of water cycle in a particular region or basin. It is
characterized by the shortage of water resources resulting from the
subnormal precipitation continuously. It should follow the principle of
taking both natural water cycle and artificial water cycle into account in
order to cope with droughts (Yan et al., 2014).
Location of study area. Note: the numbers (1–64) present the assessment units. We divide the
Dongliao River basin into 64 assessment units. The methods are as the
following. Firstly, it is divided by the location of reservoirs in main
stream (i.e., the Erlongshan Reservoir) and the layout of the upper, middle
and lower reaches of the basin (i.e., the three segments of the Dongliao
River basin). Secondly, it is divided by the location of reservoirs (i.e.,
the Bayi Reservoir, the Jinman Reservoir et al.) or other main hydraulic
engineering in tributary streams. Lastly, it is divided by the irrigation
areas with considering the various crop planting structures.
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Since 1900, a number of indices have been developed to quantify a drought,
and they could be classified into three stages.
During the first stage (1900–1964), drought indices could be
divided into four types. Firstly, they were established based on the
precipitation records, such as the Munger index (Munger, 1916), the Kincer index
(Kincer, 1919), the Blumenstock index (Blumenstock, 1942), the standard deviation index (Xu, 1950) and
the antecedent precipitation index (McQuigg, 1954). Secondly, they were constructed
based on the evaporation records, such as the moisture adequacy index (McGuire and Palmer, 1957).
Thirdly, they were proposed based on the precipitation and temperature
records, such as the Marcovitch index (Marcovitch, 1930) and the Demartonne index (De Martonne, 1926).
Fourthly, they were put forward based on the precipitation and evaporation
records, such as aridity index (Ma et al., 2003). Drought indices in this stage were
established based on one or two factors, in accordance with the
particular region. They were simple to calculate, but lacking the
universality and the mechanism of the water cycle.
During the second stage (1965–1992), drought indices could
also be divided into four types. Firstly, they were also proposed based on
the precipitation records, such as the precipitation anomaly percentage index
(National Meteorological Center of CMA, 1972), the drought area index (Bhalme and Mooley, 1980) as well as the positive and negative
anomaly index (Liu and Wei, 1989). Secondly, they were produced based on the runoff
records, such as the hydrological drought severity index (Dracup et al., 1980a, b)
and the surface water supply index (Shafer and Dezman, 1982). Thirdly, they took surface conditions
into consideration, such as Keetch–Byram drought index (Keetch and Byram, 1968), soil
thermal inertia index (Wang and Guo, 2003). Fourthly, they were put forward based on the
soil water balance principle, such as the Palmer drought severity index
(Palmer, 1965, 1967) and the Palmer revised surface-water supply index (Garen, 1993). Drought
indices in this stage were established based on multiple factors. Drought indices in this
stage considered water cycle elements and processes with some physical mechanism to some degree.
During the third stage (1993 till now), with the development of computers
and hydrological models, drought indices not only contained multiple factors
of the water cycle, but also integrated multiple indices (GB/T 20481-2006, 2006). Furthermore,
different drought parameters which included intensity, duration, severity
and spatial extent were assessed (Serinaldi et al., 2009; Shiau and Modarres, 2009). Some drought indices can
compute on various time scales, like standard precipitations index (SPI)
(McKee et al., 1993). They could be divided into three types. Firstly, they integrated
multiple indices, such as the comprehensive drought index (GB/T 20481-2006, 2006) and
the meteorological drought index (Yan et al., 2009). Secondly, they were proposed based on
a distributed hydrological model (Xu et al., 2008), such as the Palmer drought severity
index, which is based on a geomorphology-based hydrological model. Thirdly, they were
created based on remote sensing, such as the vegetation–temperature condition
index (Wang et al., 2001), the temperature–vegetation dryness index (Sandholt et al., 2002), the vegetation
supply water index (Mo et al., 2006), the perpendicular drought index (Ghulam et al.,
2007a, b), the standard vegetation index (Peters et al., 2002), the short-wave infrared perpendicular water
stress index (Ghulam et al., 2007c).
Advantages and disadvantages of the common drought indices.
Name
Main parameters
Advantages
Disadvantages
Reference
Munger
Precipitation
Higher sensitivity and suitable for
Mainly used for forest fire warning, but
Munger
short-term drought
seldom used in agriculture and others
(1916)
Kincer
Precipitation
Emphasizing seasonal distribution of
Only considering precipitation, but not
Kincer
precipitation and considering the
the universality
(1919)
climate of annual precipitation
Marcovitch
Precipitation
Considering total days and precipitation
Not being universal
Marcovitch
temperature
at the same time and higher than 32.2 ∘C
(1930)
in summer
Blumenstock
Precipitation
Higher sensitivity and suitable for
Not being universal
Blumenstock
short-term drought
(1942)
Antecedent
Precipitation
Wide application
Subjective parameter determination
McQuigg
Precipitation
(1954)
Index
Moisture
Evapotranspiration
Considering the water balance, soil
Much data needed; complex
McGuire and
Adequacy
characteristics and crop growths
computation
Palmer (1957)
Index
Palmer
Precipitation
Considering rainfall, latent evaporation,
Complex computation
Palmer (1965)
Drought
Evapotranspiration
antecedent soil moisture and runoff;
Severity
Runoff
quickly reflecting the change of soil
Index
et al.
moisture
Keetch–Byram
Precipitation
Considering precipitation, temperature
No distinguishing between soil texture
Keetch and
Index
Temperature
and land use at the same time;
and climate conditions
Byram (1968)
Land use
effectively determining the onset of
drought; reflecting the cumulative
effects of drought by recurrence method
Drought
Precipitation
Simple calculation; eliminating
Considering the precipitation as normal
Bhalme and
Area
differences caused by different climate
distribution without considering the
Mooley (1980)
Index
types; effectively reflecting regional and
evaporation and land use
seasonal scales of the water status
Hydrological
Runoff
Analyzing the time integral flow of
Low resolution
Dracup et
Drought
concrete section of the river
al. (1980a, b)
Severity Index
Surface Water
Runoff
Representing water supply conditions
Complex analysis due to necessary
Shafer and
Supply Index
Water supply
for different hydrological zones
consideration of the probability
Dezman
distribution change and the weight of
(1982)
each factor
Standard
Precipitation
Quantifying the impacts of different
Assuming that droughts in all sites
McKee et
Precipitation
precipitation shortages to different
occurred with the same frequency, so
al. (1993)
Index
water resources on different time scales
spatial distribution features cannot be
identified
Temperature
Surface temperature
Directly obtaining the parameters from
Only representing the relative values of
Sandholt et
and Vegetation
Normalized
the image data; simple and convenient
the same image moisture state but not
al. (2002)
Index
differential
calculation
comparable in time
vegetation index
Meteorological
Precipitation
Combing the advantages of SPI and
Neither reflecting the relationship
Yan et al.
Drought Index
Temperature
PDSI
between drought disaster area and
(2009)
runoff nor considering ecosystem and
economic environment
Palmer wetland
Precipitation
Being suitable to evaluate wetland
Complex computation; being not of
Yuan et
drought index
Surface inflow
drought caused by the integrated effects
universality; much data needed
al. (2014)
Evapotranspiration
of precipitation, surface inflow, and
Outflow
water volume, especially that influenced
The amount of
strongly by human activities
water stored in
the wetlands
In light of the advantages and disadvantages of the above indicators (Table 1),
we propose the generalized drought assessment index (GDAI) based on
water resources systems for assessing drought events.
This study is organized as follows. Section 2 describes the methodology,
including the water and energy transfer process model in the Dongliao River
basin (Sect. 2.2), the method of generalized drought assessment index (GDAI)
(Sect. 2.3), the theory of runs (Sect. 2.4), and the assessment
method of the standard precipitation index (SPI), Palmer drought severity
index (PDSI) and rate of water deficit index (RWD) (Sect. 2.5). Section 3
presents the results, including the generalized drought times (Sect. 3.1),
the generalized drought duration (Sect. 3.2), and the generalized drought
severity (Sect. 3.3) of the Dongliao River basin. Section 4 assesses the
differences between the GDAI, the SPI, the PDSI, and the RWD. The study
concludes in Sect. 5.
Methodology
Case study
The Dongliao River basin (DRB) is located in northeastern China. It covers an
area of 11 306 km2 (Fig. 1). It is roughly divided into three
segments. The upper reaches are the segment above Erlongshan Reservoir,
which is a low-mountain and hilly area with an altitude from 200 to 600 m,
primarily consisting of dark brown soil and planosol; the middle reaches are
the segment from Erlongshan Reservoir downwards to Chengzishang Hydrological
Station, which is a hilly area with an altitude from 100 to 300 m, mainly
including black soil and meadow soil; the lower reaches are the segment from
Chengzishang Hydrological Station downwards to the Sanjiangkou iron bridge on
the Siping–Qiqihar railway line, which is a plain area with an altitude from 0m
to 200 m, primarily consisting of meadow soil, salinized chernozem soil and
steppe aeolian sandy soil.
The DRB is controlled by the Pacific low pressure and Siberian high pressure
with four distinctive seasons. The precipitation decreases from the upper to
lower reaches. The multi-year average precipitation is reduced from 710 to
450 mm from 1960 to 2011. It is distributed unevenly within the year. It
accounts for 75 % of annual precipitation from June to September. It
accounts for 50 % in July and August. Inter-annual precipitation change decreases from west to east. The temperature decreases from southwest
to northwest. The multi-year average temperature decreases from 6.7 to
5.6∘ (1960–2011). The evaporation increases from upper to
lower reaches. The multi-year average evaporation changes from 850 to
1200 mm (1960–2011). The runoff decreases from upper to lower reaches.
The multi-year average runoff decreases from 150 to 25 mm (1960–2011), with
that from June to September taking up 80 % of annual runoff.
The observed drought disaster records in Lishu County were listed below.
Maize growth was affected by drought disaster starting from 18 April 1994.
The affected areas account for 30 % in 25 June 1994. The damaged
areas of the maize were 1487 km2, and the yields were reduced by
10 % during 11 May to 12 June 1996. They were 1133 km2 which
accounted for 63 % from 21 April to 16 May 1997. They accounted for
88 % until 30 July 1997. They were 2440 km2 from 1 to 28 June 2000.
The yields were reduced by 70 % until 9 August 2000.
The observed drought disaster records in Gongzhuling city were listed below.
The damaged areas of the maize were 1200 km2 and the disaster areas
(the areas that crop yields decreased by over 80 % than normal annual
yields) were 300 km2 during 8 June and 30 July 1997. They were
667 km2 which accounted for 70 % during 2 and 20 July 2000.
The water and energy transfer process model in the DRB
The water and energy transfer process (WEP) model (Jia et al., 2001) is chosen to simulate
the elements of natural and artificial water cycle in the DRB, and then to
calculate the water supply and water demand of the assessment units based on
water resources systems. The WEP model has been successfully applied in
several watersheds in Japan, Korea, and China with different climate and
geographic conditions (Jia and Tamai, 1998; Jia et al., 2001, 2002, 2004, 2005; Kim et al., 2005; Qiu et al., 2006).
Model input data and their source.
No.
Type
Name
Description
Center
1
Digital elevation
Elevation, slope, aspect,
1 : 250 000 national fundamental geographic
National Geomatics Center of
data
flow direction, digital river,
information system
China
catchment, etc.
2
Soil data
Soil depth, soil texture, etc.
1 : 1 000 000 soil database in China
National Second Soil Survey
Observed soil data
China Soil Scientific Database
(http://www.soil.csdb.cn/)
3
Land use data
Land use data in 1954, 1986,
MODIS, TM images from 1980 to 2010
Institute of Geographic Sciences
2000, 2005
and Natural Resources Research
4
Meteorological and
Precipitation, wind speed,
Observed daily meteorological data of
China Meteorological Data Sharing
hydrological data
temperature, sunshine hours,
Kaiyuan, Changling, Shuangliao, Siping,
Service System
relative humidity
Changchun, Panshi, Qingyuan, Meihekou
(http://cdc.cma.gov.cn)
stations
Monthly runoff
Observed and restored monthly runoff
Dongliao Water Resources
records from the Erlongshan Reservoir and the Wangben and
Commission, Ministry of Water
Quantai hydrological stations from 1956 to
Resources
2000
Daily runoff
Observed daily runoff records from the Wangben,
Quantai and Liaoyuan hydrological stations from
2006 to 2010
5
Hydraulic
Distribution of reservoir and
Erlongshan reservoir operation manual in
Dongliao Water Resources
engineering data
irrigation
1986
Commission, Ministry of Water
Resources
Hydrological yearbook in the DRB
6
Socioeconomic
Water supply, water use,
Water resources integrated planning in China
Dongliao Water Resources
data
water consumption,
in 2006
Commission, Ministry of Water
irrigation schedule, etc.
Resources
Water resources bulletin in the Dongliao Basin
from 1990 to 2010
Comparing the simulated and observed restored monthly runoff from 1960 to 2000.
Hydrological
Observed
Simulated
Deviation
Nash–Sutcliffe
Correlation
station
restored
annual
(%)
model
coefficient
annual
average
efficiency
average
runoff
coefficient
runoff
(m3 s-1)
(m3 s-1)
Erlongshan Reservoir
166.16
171.98
3.50
0.812
0.932
Wangben
282.99
291.20
2.90
0.775
0.900
Quantai
91.56
87.08
-4.89
0.805
0.937
Note: The Nash–Sutcliffe model efficiency coefficient is used to assess the
predictive power of hydrological models. It is defined as
E=1-∑t=1TQot-Qmt2∑t=1TQot-Qo‾2,
where Qo is the mean of observed discharges, and Qm is modeled
discharge. Qot is observed discharge at
time t. Its definition is identical to the coefficient of determination
R2 used in linear regression.
Model input
The WEP model has the following main characteristics: (1) combining modeling
of hydrological processes and energy transfer processes; (2) considering the
land use heterogeneity inside a computation unit by adopting the mosaic
method; and (3) incorporating the runoff generation theory of various source
areas into the model through a numerical simulation in groundwater flows to
directly reflect the topography's effects in runoff generation, thus capable of
modeling infiltration excess, saturation excess and mixed runoff generation
mechanism (Jia et al., 2006).
The WEP model consists of the vertical structure within a grid cell and the
horizontal structure within a watershed. Each grid cell in the vertical
direction, from top to bottom, includes nine layers, namely an interception
layer, a depression layer, three upper soil layers, a transition layer, an
unconfined aquifer and two confined aquifers. Land use is divided into five
groups, namely the soil vegetation (SV) group, the non-irrigated farmland (NF)
group, the irrigated farmland (IF) group, the water body (WB) group, and the impervious
area (IA) group. The SV group is further classified into bare soil land,
tall vegetation (forest or urban trees) and short vegetation (grassland).
The IA group consists of impervious urban cover, urban canopy and rocky
mountain (Jia et al., 2006).
The simulated hydrological processes include snow melting,
evapotranspiration, infiltration, surface runoff, subsurface runoff,
groundwater flow, overland flow, river flow and water use. The simulated
energy transfer processes include short-wave radiation, long-wave radiation,
latent heat flux, sensible heat flux, and soil heat flux. Adopted modeling
approaches for hydrological and energy processes are referenced in Jia et al. (2001); snow-melting processes and water-use processes are not.
WEP-DRB model input data consists of six types: digital elevation data,
soil data, land use data, meteorological and hydrological data, hydraulic
engineering data, and socioeconomic data (Table 2). They are treated by
spatial interpolation and formatting before applying the model.
Model verification and validation
The DRB is divided into 11 catchments and 64 assessment units. The
simulated time step of the WEP–DRB model is 1 day. Firstly, the WEP–DRB model is
verified by using observed and restored monthly runoff records from the
Erlongshan Reservoir and the Wangben and Quantai hydrological stations from 1956 to
2000. The warm-up period is from 1956 to 1959, and the verified period is
from 1960 to 2000. Secondly, the WEP–DRB model is validated by using observed
daily runoff records from the Wangben, Quantai, and Liaoyuan hydrological stations
from 2001 to 2010. The warm-up period is from 2001 to 2005, and the verified
period is from 2006 to 2010.
Comparing the simulated and observed restored monthly runoff from 1960 to
2000 (Table 3), the result shows that the maximum deviation is -4.89 % at
the Quantai Hydrological Station and the minimum is 2.90 % at the Wangben
Hydrological Station. Nash–Sutcliffe model efficiency coefficients are all
over 0.70, and they range up to 0.812 at the Erlongshan Reservoir Hydrological
Station. Comparing the simulated and observed monthly runoff from 1960 to
2000 (Table 4), the result shows that the maximum deviation is -6.32 % in
Quantai Hydrological Station and the minimum is 0.47 % at the Erlongshan
Reservoir Hydrological Station. Nash–Sutcliffe model efficiency coefficients
are all over 0.70, and they range up to 0.830 at the Quantai Hydrological Station.
Comparing the simulated and observed daily runoff from 2006 to 2010 (Table 5),
the result shows that the maximum deviation is -7.91 % in Liaoyuan
Hydrological Station and the minimum is 2.90 % at the Wangben Hydrological
Station. Nash–Sutcliffe model efficiency coefficients are also all over 0.70,
and they range up to 0.763 at the Wangben Hydrological Station.
Comparing the simulated and observed monthly runoff from 1960 to 2000.
Hydrological
Observed
Simulated
Deviation
Nash–Sutcliffe
Correlation
station
annual
annual
(%)
model
coefficient
average
average
efficiency
runoff
runoff
coefficient
(m3 s-1)
(m3 s-1)
Erlongshan Reservoir
157.21
157.95
0.47
0.720
0.899
Wangben
226.19
238.22
5.32
0.800
0.913
Quantai
84.52
79.18
-6.32
0.830
0.937
Comparing the simulated and observed daily runoff from 2006 to 2010.
Hydrological
Observed
Simulated
Deviation
Nash–Sutcliffe
Correlation
station
annual
annual
(%)
model
coefficient
average
average
efficiency
runoff
runoff
coefficient
(m3 s-1)
(m3 s-1)
Wangben
181.54
186.81
2.90
0.763
0.916
Quantai
111.62
105.37
-5.60
0.754
0.923
Liaoyuan
69.23
63.76
-7.91
0.732
0.908
Classification of the GDAI, SPI, PDSI, and RWD.
Index
Normal or wet
Mild drought
Moderate drought
Severe drought
Extreme drought
spell
GDAI
-1.0 < GDAI
-2.0 < GDAI ≤ -1.0
-3.0 < GDAI ≤ -2.0
-4.0 < GDAI ≤ -3.0
GDAI ≤ -4.0
SPI
-0.5 < SPI
-1.0 < SPI ≤ -0.5
-1.5 < SPI ≤ -1.0
-2.0 < SPI ≤ -1.5
SPI ≤ -2.0
PDSI
-1.0 < PDSI
-2.0 < PDSI ≤ -1.0
-3.0 < PDSI ≤ -2.0
-4.0 < PDSI ≤ -3.0
PDSI ≤ -4.0
RWD
-1.0 < RWD
-2.0 < RWD ≤ -1.0
-3.0 < RWD ≤ -2.0
-4.0 < RWD ≤ -3.0
RWD ≤ -4.0
Overall, the simulation accuracy of the model has reached the requirement to
obtain good simulation results. The model can be used to simulate water
supply and water demand of water resources systems to calculate the
generalized drought assessment index (Yan et al., 2014).
Generalized drought assessment index
The DRB is an important production base of commodity grain. The cultivated land
and forest land account for 88.03 % of its total watershed area.
Therefore, agricultural system and ecosystem in the DRB are chosen to be
evaluated. Then water demand (DW) per assessment unit is the sum of them.
Water supply (SW) represents sum of surface effective evapotranspiration
and special water resources per assessment unit in the DRB. The water resources
shortage D is
D=SW-DW.
In order to let Eq. (1) be used to compare water resources shortage in
different assessment units and different assessment periods, the climatic
characteristic coefficient K is considered here by referring to the PDSI.
That is
K′=1.6log10((DW‾/SW‾+2.8)/|D|‾)+0.5K=329.37×K′/∑136(|D|‾×K′),
where DW‾ is the average water demand of 10 days; SW‾ is the
average water supply of 10 days; |D|‾ is the average absolute D.
The water resources shortage index Z is
Z=K⋅D.
Then, the generalized drought assessment index (GDAI) DI (generalized drought assessment index) is
DI(i)=0.91DI(i-1)+Z(i)/25.0,
where DI(i), Z(i) is the DI , Z
for the ith 10 days, respectively; DI(i - 1) is the DI for
the (i - 1)th 10 days. The classification of drought (wet)
still follows the standard of Palmer drought severity index (Palmer, 1965), as
shown in Table 6.
To verify the reasonability and representativeness of the GDAI, the results
simulated by GDAI using Eq. (4) were compared with the observed drought
disaster records from 1960 to 2010 in Gongzhuling City and Lishu County in the DRB.
Comparing the results evaluated by the GDAI and the observed drought
disaster records in Lishu County (Fig. 2a) and Gongzhuling City (Fig. 2b),
we could see that the GDAI is able to assess the characteristics of
droughts in the DRB.
Compared the results evaluated by the GDAI and the
observed drought disaster records (1960–2010). Note: parts in
gray were the periods of the observed drought disaster records.
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Theory of runs
Generalized drought times (GDT), generalized drought duration (GDD), and
generalized drought severity (GDS) are calculated by theory of runs (Dracup et al.,
1980a; Feng and Zhu, 1997). The generalized drought duration DD is expressed in
10 days during which a drought parameter is continuously below the critical
level. In other words, it is the time period between the initiation and
termination of a drought event. That is the positive run-length. The
generalized drought severity S indicates a cumulative deficiency of a
drought parameter below the critical level. -DI is defined by using the
logarithm of the GDAI. X0, X1, and X2 are thresholds of the
GDAI. For mild drought, they are 0, 1.0, 2.0; for moderate drought, they are
1.0, 2.0, 3.0; for severe drought, they are 2.0, 3.0, 4.0; for extreme
drought, they are 3.0, 4.0, 5.0, respectively.
Figure 3 shows that “g” is a drought event because DI is more than
X1. “h” is not a drought event because the GDD is only one unit and
DI is less than X2, though it is more than X1. “p” is a
drought event because DI is more than X1, though there is one unit of
GDD below X1 between DD1 and DD2, say
DD = DD1 + DD2 + 1, S = S1 + S2. More details can be found in the
studies by Lu et al. (2010).
Recognition methods of GDD and GDS. Note: L is drought inter-arrival time between
(n + 1)th drought and nth drought.
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SPI, PDSI and RWD
The GDAI is constructed based on the elements of water resources systems and
the “natural–artificial” dualistic water cycle which includes natural water
cycle and artificial water cycle. It is evaluated by comparing with the
standard precipitation index (SPI), the Palmer drought severity index (PDSI)
and the rate of water deficit index (RWD).
The SPI for 1- and 12-month time scales, the PDSI for 1-month, and the RWD
for 1–10 days of 64 assessment units from 1960 to 2010 are
calculated. The inter-annual differences between the results assessed by the
GDAI, the SPI, the PDSI, and the RWD are compared. Moreover, the annual
difference is also compared from 1999 to 2001 because drought disasters have
occurred continuously in the DRB during this period.
The method of the SPI can be found on Zhang and Gao (2004) and Yuan and Zhou (2004a). The method of the
PDSI can be found on Palmer (1965), Yuan and Zhou (2004b) and GB/T 20481-2006 (2006). The evaporation is estimated
by Thornthwaite's method (GB/T 20481-2006, 2006). The available moisture stored in surface
layer (0–20 cm) at the beginning of the month is 40 mm, and
the available moisture stored in underlying levels (20–100 cm) at the
beginning of the month is 150 mm (Liu et al., 2004). The method of the RWD
is similar to the GDAI. The differences are that the RWD is defined as the
ratio of the water resources shortage and the water demand, and the water
supply here did not consider surface effective evapotranspiration, it equals
to special water resources.
Spatial distribution of the GDT of different drought
levels in various periods.
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According to the results simulated by the GDAI and theory of runs, the
spatial distribution of the GDT, the GDD, and the GDS of different drought
levels (i.e., mild drought, moderate drought, severe drought, extreme
drought) in different periods (i.e., 1960s, 1970s, 1980s, 1990s, 2000s) were
compared with each other. For the GDT of various drought levels, assessment
units were chosen when their GDT were greater than or equal to the minimum
of average GDT of 64 assessment units in 5 decades. For the GDD
or GDS of various drought levels, the maximum GDD (MGDD) or GDS (MGDS) of
each unit was calculated firstly. Assessment units were chosen when their
GDD or GDS were greater than or equal to the minimum of average MGDD or MGDS
of 64 assessment units in 5 decades. Then, their centers of
gravity were calculated.
Results
Distribution of the generalized drought times
The centers of gravity of the GDT of various drought levels in various
periods are all distributed in the middle reaches of the DRB (near Erlongshan
Reservoir) (Fig. 4). For mild drought, the center of gravity moved toward the
southeast from the 1960s to the 1970s. The reason may be that the GDT in
upper reaches are increasing while decreasing in lower reaches. It moved
toward the southwest, east, and west from the 1970s to the 1980s, the 1980s to
the 1990s, and the 1990s to the 2000s, respectively. For a moderate drought,
the center of gravity moved toward southeast from the 1960s to the 1990s,
though it moved toward northwest from the 1990s to the 2000s. For a severe
drought, it moved toward southeast from the 1960s to the 1970s, then toward
northwest from the 1970s to the 2000s. For an extreme drought, it moved
toward southwest, northwest, and southeast from the 1960s to the 1970s, the
1970s to the 1990s, and the 1990s to the 2000s, respectively.
Spatial distribution of the MGDD of different drought
levels in various periods.
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Distribution of the generalized drought duration
The centers of gravity of the MGDD of various drought levels in various
periods are also all distributed in the middle reached of the DRB (Fig. 5).
For mild drought, the center of gravity moved toward southeast, northwest,
southeast, and northwest from the 1960s to the 1970s, the 1970s to the
1980s, the 1980s to the 1990s, and the 1990s to the 2000s, respectively. For
a moderate drought, it moved toward southeast, northwest, east, and
southeast from the 1960s to the 1970s, the 1970s to the 1980s, the 1980s to
the 1990s, and the 1990s to the 2000s, respectively. For a severe drought,
the movement direction of the center of gravity is similar to a mild
drought, but the movement distance is short from the 1960s to the 1970s. For
an extreme drought, it moved toward southwest and southeast from the 1960s
to the 1970s and the 1970s to the 1980s, respectively, but the movement
distance is short. It moved toward northwest and southeast from the 1980s to
the 1990s and the 1990s to the 2000s, respectively.
Distribution of the generalized drought severity
The centers of gravity of the MGDS of various drought levels in various
periods are also all distributed in the middle reaches of the DRB (Fig. 6).
For a mild drought, the center of gravity moved toward southeast, northwest,
southeast, and northwest from the 1960s to the 1970s, the 1970s to the
1980s, the 1980s to the 1990s, and the 1990s to the 2000s, respectively. For
a moderate drought, it moved toward southeast, northwest, and southeast from
the 1960s to the 1970s, the 1970s to the 1980s, and the 1980s to the 2000s,
respectively. For a severe drought, it moved toward southwest, northwest,
southeast, and northwest from the 1960s to the 1970s, the 1970s to the
1980s, the 1980s to the 1990s, and the 1990s to the 2000s, respectively. For
an extreme drought, it moved toward northwest, northeast, and southeast from
the 1960s to the 1980s, the 1980s to the 1990s, and the 1990s to the 2000s, respectively.
Conclusions
Drought is firstly a resource issue with a shortage of water resources, but
with its development it evolves into a disaster issue which affects natural
and socioeconomic systems. The occurrences of drought events usually
feature determinacy and randomness. The basic principle of
natural-artificial water cycle should be followed. This study has proposed
the generalized drought assessment index (GDAI) from the perspective of
water resources systems for assessing drought events.
Spatial distribution of drought frequency simulated by the RWD in the DRB.
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To demonstrate this new drought assessment approach, a drought-prone case
study site, the Dongliao River basin in northeastern China was selected.
Temporal distribution of drought events and spatial distribution of drought
frequency from the GDAI were compared with the traditional approach
(i.e., the SPI, the PDSI, and the RWD). The differences of them were analyzed from
driving forces (i.e., NCV, ACC, UCC, and HER), water cycle elements
(i.e., precipitation, evaporation, and soil water), water cycle processes
(i.e., natural water cycle and artificial water cycle), water supply
(i.e., surface water resources, groundwater resources, and soil water resources), and water
demand (i.e., agricultural system and ecosystem).
Generalized drought times (GDT), generalized drought duration (GDD), and
generalized drought severity (GDS) were calculated by theory of runs. The
distribution of the centers of gravity of the GDT, the maximum GDD (MGDD),
and the maximum GDS (MGDS) of various drought levels in various periods was
analyzed. They were all distributed in the middle reaches of the DRB, and
changed at various drought levels in various periods.
The proposed drought assessment methodology will provide water managers a
tool to distinguish between natural and human effects and adapt their
management accordingly. This would help adapt to droughts and reduce their
negative impact.