Spatiotemporal variability of drought in Kohgilooyeh and Boyer Ahmad
Homa Razmkhah1, Eshagh Rostami1
1
Department of Water Engineering, College of Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran.
, +989177038490, Corresponding [email protected]
Abstract
The SPI is the most widely used drought index to provide good estimation of drought
characteristics. The objective of this study is to assess spatial and temporal variation of
meteorological drought properties as well as drought frequency, duration and value, using SPI
for 1, 3, 6, 12, 24 and 48 months lead times. Results showed that the frequency of drought
events decreases from SPI1 to 48 in all of the stations. Max drought duration of stations has an
increasing trend from SPI1 to 48 months moving average. The average duration of dry periods
change noticeably as a function of the time scales, as it increases from SPI1 to 48. Spatial
variation of average duration is considerable for long term drought. Max SPI value does not
follow any spatial and temporal variation, as it is constant for all lead times in all stations.
Average SPI value has a decreasing trend from SPI1 to 9, but increases from SPI9 to 48. Max
average of SPI value could be seen in short term drought, and the min for medium term. The
spatial variation of short, medium and long term drought could be considered in water resources
management to supply water for various demands.
Keywords: Drought, SPI, Spatiotemporal variations.
1. Introduction
Droughts are grate importance in the planning and management of water resources.
Drought are recognized as an environmental disaster which occures in virtually all climatic
zones, such as high as well as low rainfall areas and are mostly related to the reduction in the
amount of precipitation received over an extended period of time, temperature, low relative
humidity, timing and characteristics of rains, including temporal distribution of rainy days,
intensity and duration of rain, play a significant role in the occurance of droughts (Mishra and
1
Sing, 2010). Droughts impacts both surface and ground water resources and can lead to reduced
water supply, deteriorated water quality, crop failure, reduced range productivity, diminished
power generation and suspended recreation activities, as well as effect of economic and social
activities (Riebsame et al., 1990).
Due to the growth of population and expansion of agricultural, energy and industry, the
demand for water has been increased and even water scaring has been occuring almost every
year in many parts of the world. In recent years, floods and droughts have been experienced with
higher picks and severity levels. The droughts are generaly classified into four categories which
includes
Meteorological,
Hydrological,
Agricultural
and
Socio-economic
droughts.
Meteorological drought is defined as a lack of precipitation over a region for a period of time.
Hydrological drought is related to a period with inadequate surface, stream flow, subsurface and
ground water resources for established water uses of a given water resources management
system. Agricultural drought, refers to a period with declining soil moisture and consequent crop
failure. A decline of soil moisture depends on several factors which affect meteorological and
hydrological droughts along with differences between actual evapotranspiration and potential
evaporation increases. Several drought indices, based on a combination of precipitation,
temperature and soil moisture, have been derived to study agricultural droughts. Socio-economic
drought is associated with failure of water resources systems to meet water demands and occures
when the demand for an economic exceeds supply as a result of a weather related shortfall in
water supply (Mishra and Sing, 2010).
A number of different indices have been developed to quantify droughts, each with its own
stenghts and weaknesses, like Palmer drought index (PDSI; Palmer, 1965), rainfall anomaly
index (RAI; Van Rooy, 1965), deciles (Gibbs and Maher, 1967), crop soil moisture index (GMI;
Palmer, 1968), surface water supply index (SWSI; Shafer and Dezman, 1982), standardized
precipitation index (SPI; Mckee et al., 1993), reclamation drough t index (RDI; Weghorst, 1996)
and etc.
Based on the studies for drought indices, practically all drought indices use precipitation
either singly or in combination with other meteorological elements, depending upon the type of
requirments. Detailed description of drought indices, their usefullness, limitation and comparison
between them is explained by Mishra and Sing (2010) and Logan et al. (2010).
2
Several attempts have been made to compare indices to find the most suitable indices for
specific objectives of drought monitoring. Guttman (1999) showed that special characteristics of
PDVI varies from site to site while those of SPI don’t. PDI has a complex structure with an
exceptionally long memory, while SPI is an easily interpreted, simple moving average process.
In a comparison between performance of six indices, Morid et al. (2006) showed that SPI is able
to detect the onset and spatial and temporal variates of a drought consistently.
Yevjevich (1967) proposed the theory for identifying drought parameters and investigating
their statistical properties as duration, severity and intensity. Dogan et al. (2012) in a comparison
between rainfall-based drought severity indices of Percent of Normal (PN), Rainfall Decile based
Drought index (RDD), statistical Z-score, Chinaz Index (CZI), Standard Precipitation Index
(SPI) and Effective Drought Index (EDI) showed that SPI was more consistent in detecting
droughts for different time steps. Dracup et al. (1980) determined major components of a drought
as initiation time, termination time, duration, severity and intensity. Based on 14 well-known
drought indices using a weighted set of six evaluation criteria, Keyantash and Dracup (2002)
found that SPI was a valuable estimator of drought severity. The effect of drought often
accumulate slowly over a considerable period of time, the may linger for several years after the
drought period ends (Mishra et al., 2007).
The SPI is used in this study because a) SPI is based on rainfall alone, so drought
assessment is possible even if other hydrometeorological measurements are not available, b) It
could be computed in different time scale, which allows it to describe drought conditions
important for a range of meteorological, hydrological and agricultural applications (Hayes et al.,
1999), c) It is standardizate, which ensure that the frequency of extreme events at any location
and on any time scale are consistent (Mishra and Desai, 2006). SPI also detect moisture deficite
more rapidly than PDSI, which has a response time scale of approximately 8-12 months (Hayes
et al., 1999). The main advantage of the SPI in comparison with other indices is the fact that SPI
enables both determination of drought conditions at different time scales and monitoring of
different drought types (Vicento-Serrano and Lopez-Moreno, 2005). This is very important
because the time scale over which precipitation deficites accumulates functionally seperates
defferent types of drought (Mckee et al., 1993) and, therefor, allow to quantify the natural lags
between precipitation and other water usable sources such as the river discharge and the reservoir
3
storage (Vicento-Serrano and Lopez-Moreno, 2005). Therefor, SPI can be used as the primary
drought index, because it is simple, spatially invarient in its interpretation, and probabilistic, so it
can be used in risk and design analysis.
Bussay et al. (1999) and Szalai and Szinell (2000) assessed the utility of SPI for describing
drought in Hungary. They concluded that SPI was suitable for quantifying most types of drought
events. Stream flow was best described by SPIs with time scale of 2-6 months. Strong
relashionships to ground water level were found at time scales of 5-24 months. Agricultural
drought as well as deficite of soil moisture content was replicated by the SPI on a scale of 2-3
months. Long term scales filter out the effect on dought of short term predicties and seasonal
cycles, thus enhancing the long term variability (Bordi et al., 2009).
This paper focuses on meteorological drought using SPI for 1, 3, 6, 12, 24 and 48 months
lead times (moving average) to assess spatial and temporal variation of drought peoperties as
well as drought frequency, duration and value to be used in water resources management. The
reason for considering the total pecipitation for the returning periods of 1, 3, 6, 9. 12. 24 and 48
months in the present study is that a) drought has been classified as short, medium and long term,
based on SPI series. Thus SPI 1 and SPI 3 represent short term drought, SPI 6 and SPI 9
represent medium term drought and SPI 12, 24 and 48 months represent long term drought, b)
SPI series are strongly correlated with agjacent SPI series.
2. Methodology

2.1. Standardized Precipitation Index (SPI)
The SPI is calculated based on the long-term precipitation record for a desired period. This
long-term record is fitted to a propability distribution, which is transformed to a normal
distribution so that the mean SPI for the mean of SPI for the location and desired period is zer
(Mckee et al., 1993). The fundamental strenght of SPI is that it can be calculated for a variety of
time scales. This versatility allows SPI to monitor short-term water supplies, such as soil
moisture which is important for agricultural production, and long-term water resources, such as
ground water supplies, stream flow and lake and reservoir levels. Agricultural drought, proxied
by soil moisture content, is replicated best by SPI on a scale of 2-3 months (Szalai et al., 2000).
4
SPI has been used for studying different aspects of droughts, for example, forecasting
(Mishra and Desai, 2006), frequency analysis (Mishra et al., 2009; Cancelliere and Salas, 2010),
spatio temporal analysis (Gocic and Trajkoric, 2014; Logan et al., 2010; Bordi et al., 2009),
climate impact studies (Sarlak et al., 2009), Statistical modeling of Drought characteristics
(Sharma and Panu, 2014; Shiau, 2006; Kao and Govindaraju, 2010; Shiau and Modarres, 2009).
The length of precipitation record and nature of probability distribution play an important
role for calculating SPI and could be the SPI limitations (Mishra and Sing, 2010). A deficite of
precipitation impacts on soil moisture, stream flow, reservoir storage and ground water level and
etc on different time scale. Mckee et al. (1993) developed the SPI to quantify precipitation
deficite on multiple scales. The nature of the SPI allows ac analyst to determine the rariy of a
drought or an anomalously wet event at a particular time scale foe any lacation in the world that
has a precipitation record (Mishra and Deesai, 2006) A drought event occures at the time when
the volume of SPI is continuously negative. The event ends when the SPI becomes positive.
Table 1 Provides a drought classification based on SPI.
Table 1. Drought classification based on SPI

SPI value
Class
>2
Extremely wet
1.5 to 1.99
Very wet
1.0 to 1.49
Moderately wet
-0.99 to 0.99
Near Normal
-1 to -1.49
Moderately dry
-1.5 to -1.99
Severely dry
<-2
Extremely dry
SPI calculation
The SPI is computed by fitting a probability density function to the frequency distribution
of precipitation summed over the time scale of interest. This is performed seperately for each
5
month or other temporal basis, and for each location. Each probability density function is then
transformed in to the standardized distribution (Mishra and Desai, 2006).
The gamma distribution is defined by its frequency or probability density function is defined as
𝑔(𝑥) =
1
𝛽 𝛼 𝛤(𝛼)
−𝑥
𝑥 𝛼−1 𝑒 𝛽 ,
𝑓𝑜𝑟 𝑥 > 0
(1)
Where 𝛼 > 0 is a shape factor, 𝛽 > 0 is a scale factor, and 𝑥 > 0 is the amount of
precipitation. 𝛤(𝛼) is the gamma function which is defined as
∞
𝛤(𝛼) = ∫0 𝑦 𝛼−1 𝑒 −𝑦 𝑑𝑦
(2)
Fitting the distribution to the data require α and β to be estimated. Edwards and Mckee
(1997) suggesting these parameters using the approximation of Thom (1958) for maximum
likelihood as follows:
𝛼̂ =
1
4𝐴
(1 + √1 + )
4𝐴
3
(3)
𝛽̂ =
𝑥̅
𝛼̂
(4)
Where for n observations
𝐴 = 𝑙𝑛(𝑥̅ ) −
∑ 𝑙𝑛(𝑥)
𝑛
(5)
The resulting parameters are then used to find the cumulative probability of an observed
precipitation event for the given month and time scale:
𝑥
𝐺(𝑋) = ∫ 𝑔(𝑥)𝑑𝑥 =
0
1
𝛽̂ 𝛼̂ 𝛤(𝛼̂)
Substituting t for
x
̂
β
𝑥
̅
−𝑥
= ∫ 𝑥 𝛼̂−1 𝑒 𝛽̂ 𝑑𝑥
(6)
0
reduces equation to incomplete gamma fuction. Since the gamma
function is undefined for x = 0 and a precipitation distribution may contains zeros, the
cumulative probability becomes
6
𝐻(𝑋) = 𝑞 + (1 − 𝑞)𝑔(𝑥)
(7)
where q is the probability of zero precipitation.
The cumulative probability, H(x), is then transformed to the standard normal random
variable Z with mean zero and variance one, which is the value of SPI. Following Edwards and
McKee (1997), Hughes and Saunders (2002), we employ the approximate conversion provided
by Abramowitz and Stegun (1965) as an alternative:
𝑍 = 𝑆𝑃𝐼 = − (𝑡 −
𝑐0 + 𝑐1 𝑡 + 𝑐2 𝑡 2
),
1 + 𝑑1 𝑡 + 𝑑2 𝑡 2 + 𝑑3 𝑡 3
𝑓𝑜𝑟 0 < 𝐻(𝑥) ≤ 0.5
(8)
𝑍 = 𝑆𝑃𝐼 = + (𝑡 −
𝑐0 + 𝑐1 𝑡 + 𝑐2 𝑡 2
),
1 + 𝑑1 𝑡 + 𝑑2 𝑡 2 + 𝑑3 𝑡 3
𝑓𝑜𝑟 0.5 < 𝐻(𝑥) ≤ 1
(9)
𝑡 = √𝑙𝑛 [
𝑡 = √𝑙𝑛 [
And
1
(𝐻(𝑥))
2
],
1
(1 − 𝐻(𝑥))
𝑓𝑜𝑟 0 < 𝐻(𝑥) ≤ 0.5
2] ,
(10)
𝑓𝑜𝑟 0 < 𝐻(𝑥) ≤ 0.5
(11)
𝑐𝑜 = 2.515517, 𝑐1 = 0.802853, 𝑐2 = 0.010308, 𝑑1 = 1.432788, 𝑑2 = 0.189269, 𝑑3 =
0.001308.
2.2. Case Study
The study was carried out in the high basin of the Kohgilooye and Boyer Ahmad province,
including major patrs of the three important river basin of Karoon, Maroon-Jarahi and ZohrehHendijan river basins, located in the Sought West of Iran, Figure 1. The watershed boundaries
are 30° , 9′ to 31° , 32′ N and 49° , 57′ to 50° , 42′ E with 16249 km2 area.
It is a mountainous area, with a wide range of altitudes, from 4409 m in Dena mountain to
less than 500m in Lishtar, complex topography and dominated by steep slope. In the low
7
elevated areas the mean annual precipitation is 350 mm and in the elevated areas more than 800
mm. Temperature variation range in low lands is between 10℃ to 47℃ and in elevated areas
between −10℃ to 37℃ .
Figure 1. Kohgilooyeh Boyer Ahmad Province, Iran.
o Precipitation Data
The knowledge of temporal and spatial precipitation distribution is crucial when selecting
the stations. In the Kohgilooyeh and Boyer Ahmad province (site of study) 14 meteorological
stations within the region were selected to see spatial distribution. All of these gauges had to
have continuous record in the common observation period 1999-2009. The precipitation gauges
8
were chosen to be spatially representative in terms of the precipitation regime in this large basin.
A list of selected gauges is provided in Table 2.
Table 2. Selected precipitation Gauges
Mean Monthly
Stand. Dev. of
Precipitation (mm)
Precipitation (mm)
Margoon
54.62
Tal Chogha
Station
Lat. (m)
Long. (m)
Elevation
85.95
3422034
509553
2220
59.6
100.25
3416494
527128
1520
Ghaleah Reiesi
77.69
117.3
3398053
527128
760
Chitab
75.7
123.28
3414689
531866
1610
Tolian
39.9
69.21
3405454
531894
1760
Darshahi
97.43
172.12
3316658
541731
1580
Sisakht
55.32
91.88
3144728
543020
2140
Charou Sagh
69.2
111.27
3399952
543079
1940
Sepidar
35.4
70.12
3298546
543142
2100
Shah Mokhtar
58.73
97.84
3396860
549479
1640
Dehdasht
38.63
71.82
3367417
552107
795
Gachsaran
78.05
114.15
3212879
552166
699
Cheshmeh Chenar
55.34
88.42
3396343
560652
2200
Ghalat
115.89
225.97
3381595
565530
1870
3. Results
To avoid inhomogenieties in the data (Peterson et al., 1998) the homogeneity of
precipitation series was tested by means of the Mann-Whitney test. The temporal gaps (<10%)
in the meteorological stations were completed using grid fit upon the reference series.
9
Figure 2 shows the continuous evolution of SPI at different time scales in Margoon Station.
At shorter time scales like 1 months, the dry (SPI<0) and wet (SPI>0) show a high temporal
frequency, whereas when the time scale increases the frequency of dry period decreases. At the
time scale of 3 months 11 important dry periods are recognised whereas at SPI 24 months only 2
important dry periods, the years (1999-2000) and (2008-2009).
The average duration of dry periods change noticeably as a function of the time scales. At
the time scale of 3 months the average duration is 5.1 months, at the time scale of 9 months is 7.2
months and the longest mean duration is recorded at the time scale of 48 months with an average
duration of more than 38 months.
3
SPI-1 Months (Margoon)
1
0
-1
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
2
-2
Month (1999-2009)
2
SPI-3 Months (Margoon)
0
-1
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
1
-2
Months (1999-2009)
10
11
SPI
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
-1
-2
-1
-2
1
-1
-2
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
-2
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
2
1
SPI-6 Months (Margoon)
0
-1
Month (1999-2009)
2
SPI-9 Months (Margoon)
1
0
Month (1999-2009)
2
SPI- 12 Months (Margoon)
1
0
Month (1999-2009)
2
SPI- 24 Months (Margoon)
0
Month (1999-2009)
SPI- 48 Months (Margoon)
2
0
-1
-2
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
SPI
1
Month (1999-2009)
Figure 2. Evolution of the SPI at different time scales in Margoon Station
The SPI charachteristics of all stations are extracted and presented in Figure 3(a-e); number
of drought events in Figure (a); max drought duration in (b); average drought duration in (c);
max SPI value in (d) and average SPI value in (e). It could be seen that the frequency of drought
events decreases from SPI 1 to 48 months lead time in all stations. The difference of stations
drought frequency in SPI 1 to 12 (short and medium term drought) is more than others. Max
drought frequency in most of the SPI lead times has been occurred in Ghalat station, Figure 3(a).
Max drought duration of stations has an increasing trend from SPI 1 to 48 months moving
average ans max value could be seen in Ghalat staion again, Figure 3(b). The difference of max
drought duration varies in different SPI lead times, as for SPI 1, 3 (short term) and 48 (long term)
there is not any significant difference among the stations but for SPI 6 and 9 (medium term
drought) the variation is not neglectable. Figure 3(c) shows that average drought duration
increases from SPI 1 to 48. Spatial variation of the average duration is considerable for SPI 12,
24 and 48 (long term drought). Max SPI value does not follow any spatial and temporal
variation, as it is constant from SPI 1 to 48 in all stations, Figure 3(d). Average SPI vaue has a
decreasing trend from SPI 1 to 9, but increases from SPI 9 to 48. This trend could be seen in all
stations, Figure 3(e). Max of average SPI value could be seen in SPI 1 and 3 (short term) and
min for SPI 6 and 9 (medium term). The difference of this drought character is considerable for
all SPI lead times moving average, in all of the stations.
12
Number of Drought Events
20
Margoon
18
Tal Chogha
Ghaleah Reiesi
16
Number of Drought Events
Chitab
14
Tolian
12
Darshahi
Sisakht
10
Charou Sagh
8
Sepidar
6
Shah Mokhtar
Dehdasht
4
Gachsaran
2
Cheshmeh Chenar
Ghalat
0
SPI 1
SPI 3
SPI 6
SPI 9
SPI 12
SPI 24
SPI 48
SPI
a
Max Drought Duration
45
Margoon
Tal Chogha
40
Ghaleah Reiesi
Max Drought Duration (month)
35
Chitab
Tolian
30
Darshahi
25
Sisakht
Charou Sagh
20
Sepidar
15
Shah Mokhtar
Dehdasht
10
Gachsaran
5
Cheshmeh Chenar
Ghalat
0
SPI 1
SPI 3
SPI 6
SPI 9
SPI 12
SPI
b
13
SPI 24
SPI 48
Average Drought Duration
45.0
Margoon
Tal Chogha
40.0
Average Drought Duration (month)
Ghaleah Reiesi
35.0
Chitab
Tolian
30.0
Darshahi
25.0
Sisakht
Charou Sagh
20.0
Sepidar
15.0
Shah Mokhtar
Dehdasht
10.0
Gachsaran
5.0
Cheshmeh Chenar
Ghalat
0.0
SPI 1
SPI 3
SPI 6
SPI 9
SPI 12
SPI 24
SPI 48
SPI 24
SPI 48
SPI
c
Max SPI value
0.00
SPI 1
SPI 3
SPI 6
SPI 9
SPI 12
Margoon
Tal Chogha
-0.50
Ghaleah Reiesi
Chitab
Tolian
Max SPI value
-1.00
Darshahi
Sisakht
-1.50
Charou Sagh
Sepidar
-2.00
Shah Mokhtar
Dehdasht
Gachsaran
-2.50
Cheshmeh Chenar
-3.00
Ghalat
SPI
d
14
Average SPI value
0.0
SPI 1
SPI 3
SPI 6
SPI 9
SPI 12
SPI 24
SPI 48
Margoon
Tal Chogha
Ghaleah Reiesi
-0.5
Chitab
Average SPI value
Tolian
Darshahi
-1.0
Sisakht
Charou Sagh
-1.5
Sepidar
Shah Mokhtar
Dehdasht
-2.0
Gachsaran
Cheshmeh Chenar
Ghalat
-2.5
SPI
e
Figure 3(a-e). Drought characteristics in the stations
4. Conclusion
As precipitation is an important water resources supply component, an analysis of
precipitation deficite charachteristics is a critical component in drought risk. SPI is based only on
the precipitation field, it is standardized and can be computed on different time scales, allowing
to monitor the varius kinds of drought. In this paper the SPI drought indices for 1 to 48 months
lead times was computed and its charachteristics was extracted in all of the meteorological
stations in Kohgilooyeh and Boyer Ahmad Province, Iran.
Evaluation of SPI charachteristics highlighted the spatial and temporal variations of the
meteorological drought occuring frequency, duration and values in the province. The frequency
of drought events decreases from SPI 1 to 48 months lead time in all of the stations. Max drought
15
duration of stations has an increasing trend from SPI 1 to 48 months moving average. The
average duration of dry periods change noticeably as a function of the time scales as it increases
from SPI 1 to 48. Spatial variation of the average duration is considerable for long term drought.
Max SPI value does not follow any spatial and temporal variation, as it is constant for all lead
times in all of the stations. Average SPI value has a decreasing trend from SPI 1 to 9, but
increases from SPI 9 to 48 in all of the stations. Max average of SPI value could be seen in short
term drought and min for medium term. The spatial variation of short, medium and long term
drought could be considered in water resources management to supply water for various
demands.
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