- Email: [email protected]
Drought monitoring and analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI)
Accepted Manuscript Drought monitoring and analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI) S. Tirivarombo, D. Osupile, P. Eliasson PII:
S1474-7065(17)30054-2
DOI:
10.1016/j.pce.2018.07.001
Reference:
JPCE 2694
To appear in:
Physics and Chemistry of the Earth
Received Date: 3 April 2017 Revised Date:
6 June 2018
Accepted Date: 8 July 2018
Please cite this article as: Tirivarombo, S., , Osupile, D., Eliasson, P., Drought Monitoring and Analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI), Physics and Chemistry of the Earth (2018), doi: 10.1016/j.pce.2018.07.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Drought Monitoring and Analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI) 1
S. Tirivarombo*, 1D. Osupile, 1P. Eliasson
1
Department of Earth and Environmental Sciences Botswana International University of Science and Technology Email: [email protected], [email protected] *Corresponding author
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Abstract
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Although rainfall is a major indicator of the availability of water, temperature is also an
12
important factor that can influence the availability of water as it controls the rates of
13
evapotranspiration. Parameters such as rainfall and temperature can be used as indicators of
14
drought. These indicators are converted to drought indices which show the different
15
characteristics of a drought. This study compares two different drought indices in the Kafue
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Basin located in northern Zambia, where most of the socioeconomic livelihoods are dependent
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on water. The Standardised Precipitation Index (SPI) depends on precipitation as the single input
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variable while the Standardised Precipitation Evapotranspiration Index (SPEI) is derived from
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precipitation and temperature in the form of a simple water balance. By comparing time series
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plots (1960-2015) of the two indices, both indices were able to pick up temporal variation of
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droughts. SPI and SPEI agreed (R>0.5) on the direction of change but the effect on the drought
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condition was different. Compared to SPI, SPEI identified more droughts in the severe to
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moderate categories, with extended duration and increased intensity. On the other hand, SPI
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identified more droughts than SPEI under the extreme category, but with a shorter duration and
25
reduced frequency of occurrence compared to the severe to moderate droughts. The results
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suggest that temperature variability plays an important role in characterising droughts. SPI is
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useful in that it only requires rainfall as input and especially where temperature data is missing.
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However, the use of SPI to characterise drought should be done with caution.
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Key words: Drought analysis; drought indices; SPEI; SPI; Kafue basin
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1.0 INTRODUCTION
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Hydrologically extreme events such as floods and droughts are placed high on the list of climate-
35
related natural disasters. Drought in particular is one of the biggest threats to human survival,
36
imposing serious adverse impacts to social, economic and environmental sustainability (Sharma
37
et al., 2009). Defining a drought is complicated by the fact that droughts are spatially and
38
temporally variable, region-specific, context-dependent, and because they occur with varying
39
degrees of intensity, whilst their cumulative effect makes it difficult to identify their start and end
40
(Quiring and Papakryiakou, 2003). A drought can be defined simply as a recurrent and natural
41
climatic event caused by below normal precipitation compared to the long-term average and
42
extending over a long period of time (Kundzewicz, 1997; Pandey et al., 2007; Dai, 2011).
43
Compared to floods, droughts develop slowly over time and are only recognized once people and
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the environment start to feel their impact (Vicente-Serrano and Lopez-Moreno, 2005). As a
45
result, it is difficult to determine the onset and cessation of droughts. Defining droughts is also
46
complicated by the fact that they are widespread in occurrence and complex in nature. Initially
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occurring as a result of prolonged below normal precipitation, droughts may have implications
48
on other components of the hydrological cycle. Therefore, it is possible for one type of drought
49
to convert into another type under prolonged occurrence. In relation to water resources, drought
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can be considered as a multi-scalar phenomenon which is guided by catchment response time. It
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is worth noting that the hydrological responses of soil moisture, river discharge and groundwater
52
recharge as well as the biological response of crops and natural vegetation vary and have
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different response times (Lorenzo-Lacruz et al., 2010). Therefore the time over which the water
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deficits accumulate (timescale) is very important in determining the prevailing type of drought
55
(Wilhite and Glantz, 1985; Howard et al., 2014). Timescales functionally separate the different
56
types of droughts into meteorological (1 month timescale), agricultural (3-6 month timescale)
57
and hydrological droughts (12 month timescale) (Vicente-Serrano et al., 2010; Homdee et. al,
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2016). It is therefore important that droughts are classified by the specific timescales to allow
59
proper assessment of the drought.
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The rate of evapotranspiration is mainly influenced by temperature, atmospheric evaporative
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demand and the effect of heat waves (Beguería et al., 2014; Vicente-Serrano et al., 2015).
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Temperature is one of the major climatic factors that influences availability of water and also has
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consequent effects on the nature and occurrence of droughts (Rebetez et al., 2006; Dubrovsky et
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al., 2008, Sheffield and Wood, 2008. Already some studies project an increasing trend in global
65
mean annual temperatures (e.g. Trenberth et al., 2007; Dai, 2013; Trenberth et al., 2014).
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Moreover, in most arid and semi-arid regions of the world potential evapotranspiration is higher
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than annual precipitation such that a precipitation-only based drought index may not be sufficient
68
to monitor droughts (Howard et. al., 2014; Hogg, 1994). It is therefore important to incorporate
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temperature and/or other hydrological components in the determination of drought indices.
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Although it is difficult to identify the onset and cessation of droughts, their impacts can be
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averted through an understanding of their nature and occurrence. As such, appropriate and timely
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interventions to the impacts of droughts require monitoring tools that are able to objectively
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quantify the intensity, duration, magnitude and spatial extent of droughts (Smakhtin and Hughes,
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2004).
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Since drought is related to climatic events, variables such as rainfall, temperature and streamflow
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can provide good indicators of the occurrence or non-occurrence of drought. These indicators
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can then be converted to drought indices which show the occurrence, magnitude, intensity and
78
duration of a drought event (Zarger et al., 2011; Hayes, 2006). Drought indices can either be
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formed from a single input variable or from a combination of hydrological variables (Hao and
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Singh, 2015). Indices composed of a number of hydrological variables tend to provide more
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certain results, however, what variables to use depends on the situation to be addressed and the
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type of drought under analysis. Furthermore, selection of the drought index is guided by the
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region of interest and data availability (Smakhtin and Schipper, 2008).
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Several drought indices are in existence (Heim, 2002), but so far the most commonly used
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drought indices are the Palmer Drought Severity Index (PDSI, Palmer, 1968) and the
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Standardised Precipitation Index (SPI, Mckee et al. (1993). The PDSI is based on a simplified
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water balance with input parameters of precipitation, runoff, moisture supply and evaporation.
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On the other hand the SPI is a simplified index with only one input variable; precipitation
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(Vicente-Serrano et al., 2010). A drought index which is able to account for the different
90
timescales and the spatial scale at which drought occurs is considered to be multi-scalar in nature
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(Guttman, 1998). The SPI incorporates cumulative precipitation deficits at various spatio-
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temporal scales, thus rendering it multi-scalar (Hou et al., 2007). A major assumption in the
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computation of SPI is that droughts are largely driven by rainfall variability while other factors
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such as temperature are assumed to be stationary and as such do not change over time (Vicente-
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Serrano et al., 2010). The fundamental strength of SPI over other indices is that it is able to
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detect drought at different time scales (1, 3, 6, 12 and 24 months) implying that various types of
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drought (meteorological, agricultural and hydrological) can be monitored. However, the quality
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of a drought index result can only be as good as the input data (Tirivarombo and Hughes, 2011).
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Although the PDSI incorporates components of the hydrological cycle in its formulation, it falls
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short of the multi-scalar characterization of droughts because it is not capable of identifying
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drought for different timescales. Moreover, many parameters are required to calculate the index
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(Vicente-Serrano et al., 2010). The SPI is multiscalar but only incorporates precipitation to
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calculate the drought index. On the other hand, SPEI is a multi-scalar drought index which also
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takes into consideration both precipitation and temperature in addition to the ability to identify
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drought at different time scales. Because of its ability to incorporate both temperature and
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precipitation, SPEI may be a useful indicator of drought (Howard et. al., 2014), considering that
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evapotranspiration is the major form of water loss in dry regions where temperatures are high.
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The index is calculated based on the non-exceedance probability of the differences between
109
precipitation and potential evapotranspiration, adjusted using a three-parameter log-logistic
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distribution which accounts for common negative values (Středová et al., 2011; Vicente-Serrano
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et al., 2010).
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Droughts are a common and recurrent feature in southern Africa which can have detrimental
113
effects on the natural environment and agriculture with repercussions on human socio-economic
114
well-being. A large proportion of the population in the region depends solely on rain-fed
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agriculture for survival and in addition to agricultural demand there is increased pressure on
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water resources in the region due to population expansion and new developments. It is therefore
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important to have in place adequate drought assessment and monitoring tools that can produce
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reliable results to assist decision making at all levels. Because of the different formulations of the
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SPI and SPEI, this study seeks to compare the SPI and SPEI in characterizing droughts using a
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case example of the Kafue sub-basin which is found in Zambia. The basin drains into the
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Zambezi River and it is important because of its economic, social and ecological importance.
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About 50% of Zambia’s population lives in the basin and relies on the basin’s water resources
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for various uses such as mining, industry and agriculture. Despite heavy reliance on the basin’s
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water resources, the basin is under threat of high natural climatic variability which is amplified
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by climate change thus increasing the occurrence of hydrologically extreme drought events
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(Lweendo et al., 2017).
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2.0 MATERIALS AND METHODS
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2.1 Study area
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The Kafue basin (Figure 1) occupies an area of about 156 995 km2 which is about 20% of
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Zambia’s total land area. With a length of 1 300 km, the Kafue River is one of the major
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tributaries of the Zambezi River. Among other important features, the Kafue basin hosts the
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Kafue Flats, a wetland which falls under the RAMSAR Convention. The soils in the basin are a
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dark clayey montmorillonite characterized by high water holding capacity. The basin experiences
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two distinct seasons; a wet season and a dry season extending from November to April and from
136
May to October respectively. Mean daily temperatures range between 13 °C and 20 °C in winter
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and between 21 °C and 30 °C in summer. Rainfall is largely influenced by the Inter Tropical
138
Convergence Zone (ITCZ) which is a low-pressure system caused by the convergence of trade
139
winds. The position of the ITCZ varies from year to year thus influencing the precipitation
140
patterns in the basin. The annual rainfall ranges from 1300 mm/year in the north to 800 mm/year
141
in the southern parts of the basin. The basin experiences an average annual potential
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evapotranspiration rate of about 1300 mm/year with highest monthly values from August to
143
November at about 200-300 mm/month. Rainfall distribution is spatially variable in the Kafue
144
basin, decreasing in a north-south direction (Lweendo et al., 2017). Therefore, the northern sub-
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basins consisting of Lufwanyama, Luswishi, Lunga and to some extent Kafue 4 receive more
146
rainfall than the southern-most sub-basins.
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About 50% of Zambia’s population is concentrated in the Kafue basin and most of the communal
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livelihoods depend on rainfed agriculture for sustenance, implying that the basin community is
149
vulnerable to the impacts of changing rainfall patterns as a result of climate variability and
150
change. In addition, two major dams, the Itezhitezhi and the Kafue Gorge are found within the
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basin and are used for generating hydroelectricity. Other major activities in the basin include
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mining and industry which also impose a large water demand on the basin’s water resources
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(Mfalila et al., 2013).
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Figure 1: Location of Kafue basin. Sub-basins: (1) Lunga, (2) Luswishi, (3) Lufwanyama, (4) Kafue 4, (5) Kafue 3, (6) Kafue 2, (7) Kafue 1, (8) Nanzhila and (9) Kasaka
157
2.2 Climate data
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Due to sparse rainfall gauging networks this study used CRU TS4.00 data as an alternative
160
dataset which was obtained from the Climate Research Unit of the University of East Anglia
161
(Harris and Jones, 2017). The data set consists of 0.5° grids of monthly time series of different
162
climate variables including rainfall and temperature for the period 1901-2015. Ground station
163
datasets with a long enough time series which includes a base period of 1961-1990 are used to
164
calculate monthly normals after which the ground station data is converted into anomalies by
165
subtracting the 1961-1990 normal from the respective station’s time series data for each month
166
(Willmott and Robeson, 1995). The temperature and rainfall gridded datasets are obtained by
167
direct estimation through interpolation (as a function of latitude, longitude, and elevation) from
168
the ground station data (Harris et al., 2014) as obtained from the respective countries’
169
meteorological stations. To correct for inhomogeneity in data for any station, reference (1961-
170
1990) time series data from neighbouring ground observation stations are used for comparison
171
against the station in question. Anomalies relative to the 1961-1990 mean of the nearby ground
172
station data are interpolated and combined with the gridded anomalies. Using the angular
173
distance weighting method (New et al., 2000) these gridded anomalies are then combined with
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the mean monthly (1961-1990) climatology to obtain the monthly climate grids for the period
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1901-2015.
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The reliability of the CRU data was assessed based on ground rainfall stations (Table 1) that are
177
representative of the various sub-basins, with reasonably long time series (>30 years) and nearest
178
to selected grid points. The correlation results, which are a combination of all the stations used in
179
the analysis and averaged to represent a basin composite result for the various months are shown
180
in (Figure 2). In general most of the data points lie within the 95% confidence band and overall
181
the relationships between the CRU data and the ground station data are assumed to be reasonably
182
good (R2>0.5) thus providing confidence in the use of the CRU TS4.00 data.
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Table 1: Kafue ground stations used to validate the CRU TS4.00 data Sub-basin
Latitude -12.1
Longitude 26.4
Record years
-12.9
27.36
1951-1987
-13.2 -15.8
28.29 26.5
1906-1964 1919-1987
Kafue1
-15.87
27.76
1916-1986
Kasaka
-15.98
27.6
1946-1996
Lunga Luswishi Lufwanyama Kafue 2
1906-1994
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Analysis at the sub basin or basin scale requires catchment averaged rainfall which has an
186
advantage over point or gridded data because local variabilities associated with specific stations
187
are eliminated (WMO, 2000). For each sub-basin, the inverse distance weighting method (Wilk
188
et al., 2006) is used to calculate the weighted average rainfall and temperature from the CRU
189
climate grids found within each sub basin using the equation:
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=∑
∑
(1)
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where, R is the estimated rainfall for a specific sub basin, Ri is the rainfall at a grid point, i, and d
192
is the distance between the centroid of the area and the grid point.
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100
50
120
100
30
60
80
10
40
20
0
0 10
20
30
40
40
20 0
50
20
40
Local Rainfall (mm)
250
60
60
80
100
0
Local Rainfall (mm)
160
February 100 120
0
60
40 50
100
150
200
0
20
60
50
40
CRU Rainfall (mm)
60
80
20
80
100
0
30
20
10
100
0
10
20
40
50
4
8
12
16
Local Rainfall (mm)
80
120
140
160
June
10
5
0
5
10
15
20
25
Local Rainfall (mm)
10
August 8
6
6
4
2
0 20
100
Local Rainfall (mm)
15
60
CRU Rainfall (mm)
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0
30
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12
0
40
Local Rainfall (mm)
8
0
20
July
16
4
40
120
10
July
CRU rainfall (mm)
60
0
40
Local Rainfall (mm)
193
40
TE D
0
CRU Rainfall (mm)
CRU Rainfall (mm)
20
20
60
20
60
0
80
May
40
120
25
April 80
100
100
Local Rainfall (mm)
100
80
20
250
Local Rainfall (mm)
CRU Rainfall (mm)
0
60
SC CRU Rainfall (mm)
80
M AN U
CRU Rainfall (mm)
CRU Rainfall (mm)
150
50
40
March
140 200
100
20
Local Rainfall (mm)
120
January
RI PT
20
CRU Rainfall (mm)
80
CRU Rainfall (mm)
CRU Rainfall (mm)
40
0
December
November
October
4
2
0 0
2
4
6
8
Local Rainfall (mm)
10
0
2
4
6
8
10
Local Rainfall (mm)
194 195 196
Figure 2: Comparison of CRU TS4.00 rainfall data and local rainfall data (based on long-term mean monthly rainfall for various stations and averaged for the whole basin, lines show 95% confidence bounds)
197
Potential evapotranspiration was estimated by the Thornthwaite method (Thornthwaite, 1948).
198
This method was chosen due to the fact that out of the climatic variables required for estimating
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199
potential evapotranspiration we had temperature data at our disposal and the Thornthwaite
200
method requires only temperature as the input variable (equation 2). = 16
(2)
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where: T (°C) is the mean temperature for the month, d is the correction factor to account for the
203
unequal day length between months and is read from tables based on the latitude of the study
204
area.
205
I represents the annual thermal index and i is the monthly thermal index.
206
I=∑
207
=
.
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SC
202
! = 0.49 + 0.018' − 7.7 * 10+ ' + 6.7 * 10+, ' -
209
(3) (4) (5)
2.3 SPI and SPEI drought indices
211
A comparative analysis of SPI and SPEI is carried out in order to establish whether potential
212
evapotranspiration has an effect on the drought index. The analyses were done at different time
213
scales for the period 1960-2015. The different time scales (1, 3-6, and 12 months) represent
214
meteorological, agricultural and hydrological droughts respectively. The SPI and SPEI were
215
generated using the SPEI package (Berguria et al., 2014) found in the R software package which
216
is a free software environment for statistical computing and graphics, this package provides
217
different options for calculating SPI and SPEI.
218
2.3.1 SPI
219
The SPI was designed to assess drought conditions based on the probability distribution of long
220
term precipitation using the gamma function (Mckee et al., 1993). Precipitation is transformed
221
into normalised numerical values and the SPI is given as the number of standard deviations by
222
which the observed precipitation deviates from the long-term mean for a normally distributed
223
random variable (equation 6). It can thus be used to define and compare drought conditions in
224
different areas. The index gives a good and reliable estimate of the magnitude, severity and
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spatial extent of droughts. When precipitation is above the long term mean value the SPI is
226
positive and if precipitation falls below the long term mean the SPI is negative. Unlike other
227
drought indices, SPI is less cumbersome to use because it only requires a single input data series
228
of long term precipitation (Smakhtin and Hughes, 2004). Because it is based on normalised data,
229
the SPI is spatially invariant and droughts can be assessed in different regions (Guttman, 1998).
230
The index is calculated as follows:
231
. '=
232
where, xi is the precipitation of the selected period during the year i, x is the long term mean
233
precipitation and σ is standard deviation for the selected period.
234
2.3.2 SPEI
235
SPEI is calculated based on the non-exceedance probability of the differences between
236
precipitation and potential evapotranspiration, adjusted using a three-parameter log-logistic
237
distribution which accounts for common negative values (Středová et al., 2011; Vicente-Serrano
238
et al., 2010). SPEI uses a three-parameter distribution to capture the deficit values since it is most
239
likely that in arid and semi-arid areas the moisture deficit can be negative. For two-parameter
240
distributions as used in SPI, the variable x has a lower boundary of zero (0 > x < ∞) meaning that
241
x can only take positive values while for the three-parameter distributions used in SPEI, x can
242
take values in the range (γ > x< ∞) implying that x can also take negative values; γ is the
243
parameter of origin of the distribution (Vicente-Serrano et al., 2010). Therefore the Log-logistic
244
distribution was recommended for SPEI since it provides a better fit for the extreme negative
245
values (Hernandez and Uddameri, 2014). The SPEI is obtained by normalizing the water balance
246
into the Log-logistic probability distribution. For this study PET is estimated by the
247
Thornthwaite method ((Thornthwaite, 1948). The difference (Di) between precipitation (P) and
248
PET for the month (i) is given in equation 7.
249
2 =
250
The calculated D values are aggregated at different time scales as follows:
251
234 = ∑4+ +
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225
/ +/̅
(6)
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−
3+
−(
)3+
(7)
(8)
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252
where k is the timescale (months) of the aggregation and n is the calculation month.
253
The probability density function of a Log-logistic distribution is given as:
254
7(* ) = 9
255
where α, β and γ are scale, shape and origin parameters respectively for γ > D <∞. The
256
probability distribution function for the D series is then given as:
257
7(*) = [1 + (>/* − @)8 ]+
258
With f(x) the SPEI can be obtained as the standardized values of F(x) according to the method of
259
Abramowitz and Stegun (1965):
260
Where
.
261
and
B = I−2 ln( )
262
P is the probability of exceeding a determined Di value and is given as = 1 – 7(*) while the
263
constants are:
264
C0 = 2.515517, C1 = 0.802853, C2 = 0.010328, d1 = 1.432788, d2 = 0.189269, d3 = 0.001308.
265
Since SPEI is a standardized variable it can be used to compare droughts over different spatial
266
and temporal scales. Just like the SPI, continuously negative SPEI values define a drought period
267
based on intensity, severity, magnitude and duration (Byakatonda et. al, 2016).
268
2.3.3 Drought identification
269
The characterisation of droughts for both SPI and SPEI is based on the SPI scale (Mckee et al.,
270
1993). The SPI scale is used since the computation of both indices is based on the same
271
principles. This study places emphasis on moderate to extreme droughts and the SPI/SPEI index
272
scale is given as, extreme drought (≤ -2), severe drought (-2 to -1.5) and moderate drought (-1.5
273
to -1). It should be noted that a drought ends when the SPI/SPEI approaches zero and progresses
274
into a positive value. For this study, the duration of the drought is considered as the number of
275
months for which the drought has occurred while the magnitude of the indices indicates the
RI PT
(9)
SC
(10)
CD E CF GEC G
E F GE
G E HG H
for
≤ 0.5
(11) (12)
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'=B−
<
9
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+ /+: 8
;1 +
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8 /+: 8+
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severity of the drought. The comparison of SPI and SPEI, that is if both indices portray the same
277
pattern (irrespective of the magnitude), is assessed using the Pearson correlation coefficient, r,
278
which measures the strength of the statistical relationship between the SPI and SPEI. This
279
coefficient establishes whether a linear relationship exists between the indices at the 95%
280
confidence. The relationship coefficient (R) takes values between +1 and -1 where; +1: perfect
281
positive relationship, 0: no relationship and -1: perfect negative relationship. The magnitude of
282
the correlation shows the strength of the relationship and an R value ≥0.5 is deemed to be a
283
strong correlation (Taylor, 1990). R is calculated as follows: =
∑QRF(/ +/̅ )(P +PS)
SC
/P
T∑QRF(/ +/̅ ) (P +PS)
(13)
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284
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276
285
Where: n = number of observations, and for this study x and y represent the SPI and SPEI values
286
respectively.
287
3.0 RESULTS AND DISCUSSION
289
To demonstrate the temporal variation of drought at different time scales (3, 6 and 12 months) in
290
the Kafue, the SPIs and SPEIs for the different sub-basins were generated and presented in
291
Figures 3a and 3b. In general, and for all the sub-basins, both indices show the same pattern of
292
variability for each timescale but they differ in the duration and magnitude of the drought.
293
Variability in the droughts can be attributed to the fact that the sub-basin experiences high
294
natural variability in climate which is characteristic of the southern African region. Also, the
295
frequency of occurrence of the droughts is higher for the shorter timescale compared to the
296
longer timescales; it takes a shorter time (at most 1 month) of prevailing water deficiency for a
297
meteorological drought, thus the high variability of droughts. On the other hand, a longer period
298
of water deficit accumulation or depletion of water storage in rivers and reservoirs is required for
299
a hydrological drought to occur. Hence, the meteorological droughts (1 month timescale) show
300
the highest frequency of occurrence followed by agricultural droughts (3-6 month timescale) and
301
lastly the hydrological droughts (12 month time scale). However, at the higher timescales the
302
drought lasts longer and the magnitude increases.
AC C
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12
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ACCEPTED MANUSCRIPT
303 304 305
Figure 3a: SPEI and SPI at different timescales for the Kasaka, Lufwanyama, Luswishi and Nanzhila subbasins of the Kafue
13
AC C
EP
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M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
306 307 308
Figure 3b: SPEI and SPI at different timescales for the Lunga and Kafue1 to Kafue 4 sub-basins of the Kafue
14
ACCEPTED MANUSCRIPT
Given that it takes up to 6 months for most crops to be fully developed, a water deficiency
310
accumulation of at least 3 months, during the growing season, will adversely impact crop yields,
311
thus developing into an agricultural drought. Since drought develops over time, it can be
312
assumed that the extended period of drought at longer timescales may be a result of the after-
313
effects of accumulation of antecedent water scarcity over time and this situation may be
314
amplified with persistent and continuous periods of no rainfall. In addition, a drought can occur
315
if there is a shift in seasonal rainfall such that the rains are delayed thus causing impairment on
316
activities that normally depend on the onset of a rainfall event.
SC
317
RI PT
309
Apparent differences during some years and irrespective of the timescale were noted between the
319
SPI and SPEI. Longer droughts occurred under SPEI; here the duration of the drought is
320
extended as the counts of droughts increase in the yearly time series. For some of the years that
321
were already experiencing drought conditions under SPI, the magnitude of the drought was
322
amplified when detected by the SPEI. That SPEI produces droughts of increased magnitude can
323
be explained by the fact that evapotranspiration imposes a demand on the available water and the
324
impact is felt the most under conditions of water scarcity.
M AN U
318
TE D
325
Table 2 shows the number of droughts per year, including the drought categories for the Lunga
327
sub-basin. For the period under observation (1960-2015) the most common agricultural and
328
hydrological droughts were observed during the years 1964-1965, 1967, 1971-1973, 1981-1983,
329
1987, 1990-1992, 2001 and 2008, the same applies to all the other sub-basins of the Kafue.
330
Figure 4 shows that SPEI identified more droughts than SPI under the moderate to severe
331
drought categories across all sub-basins and for all time scales. The results show that even
332
though reduced precipitation is the major driver of droughts, the effect of temperature through
333
evaporative water demand has a role to play in the determination of droughts. Considering
334
rainfall alone, more droughts are classified as extreme compared to when including PET. Overall
335
Figure 4 shows that the highest number of droughts under 6 and 12 monthly timescales occurred
336
in the Nanzhila sub-basin which is located in the southernmost part of the Kafue basin.
337
Correlations between SPI and SPEI for the different sub-basins of the Kafue and under different
338
timescales are depicted in Figure 5. Statistically significant positive correlations (R>0.5) exist
339
between the two indices. Under climatic conditions with low inter-annual variability in
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15
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temperature compared to the variability in rainfall, the results imply that both indices will
341
predominantly respond more to the variations in precipitation suggesting that precipitation is the
342
major driver of water availability.
343 344
Table 2: Drought years and drought categories of SPI and SPEI at different time scales in the Lunga subbasin
4 -
1 1 1 -
1 2 -
1 1 2
3 3 3
2 1
-
-
4
4
-
1 2 -
1 2 1 1
2 1 2 3
3 4 5 4
1 -
3 -
3 -
2 -
1 -
2 -
1 1 -
1 -
1 2 -
2 1
1 -
3 2 2
6 2 3
1 1
1987 -
-
-
-
-
-
3
3
1990 1991 1992 1993 1994 1995 1996
-
2 1 -
-
2 1 -
1 1 3 -
2 2 1 -
2 1 1 3 -
4 3 2 4 1 3 -
1999 2 2000 2001 -
-
2 -
4 -
-
3
1
4
2003 2005 2006 2007 2008
1 1 -
1 -
4 2 -
1
1 1
2 4
3 6
-
-
-
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
-
-
-
-
2
1
-
3
-
-
-
-
2
1
3
-
-
-
-
-
-
-
-
-
-
-
-
7
38 68 113
4 3 3 3
2 4 5 7 6
-
-
-
-
2 -
1 7 -
7 3 9
8 12 9
5
9 -
3 -
-
12
1 2 -
7 3 1 -
2 10 2 4 6 9 9 10 10 10
M AN U 3 1 2 3
3 1 3 5 1
7 3 6 5 4
1
-
1
2
1 2 1 -
4 1 2 1 2
6 5 4
10 3 9 6 6
6 2
1 2
9 5
1 2 -
1 4 1
1
3
3 6 4
3 1
5 5
1 -
9 6
7 -
-
2 -
9 -
1 -
9 8
2 2 3
12 2 11
1
3
4
-
-
5
5
-
-
-
-
-
-
-
-
-
-
7
7
1 1 -
1 1 -
2 1 -
3 2 2 -
1 3 -
1 2 4 -
5 1 2 6
6 4 9 6
1 -
1 1 1 -
4 1 5 1 -
5 2 6 2 -
- - - - - 10 2 - 1
-
-
-
-
7 0 0
-
1 3
2 3
3 6
2 -
6 1 -
2 2 -
10 3 -
-
3
-
3
1 1 -
10 1 1 1 - -
12 3 -
-
-
-
-
0 5 -
-
-
3 -
3 -
2 -
1 -
2 3 -
5 3 -
1
5
3
9
-
-
-
1
2
6
9
TE D
EP
AC C
∑
1 -
Moderate
2 1 3 3
Severe
1 1 -
Extreme
4 3 -
∑
2 -
Moderate
1 3 -
Severe
1 -
Extreme
3 3 6 3 6
∑
3 4 2 4
Moderate
Severe
-
3 1 1 1
SC
1 -
12 9
Extreme
2 -
8
∑
4 3 5 3
Sum
Moderate
1 1 3 2
2015 2
Severe
1 1 1 1
2013 -
Extreme
2 3 -
2 1 1 -
2 1 -
∑
2 -
1981 1982 1983 -
Moderate
1 3
2 1 -
Severe
1 3 -
-
Extreme
Severe
1 -
1971 1972 1973 1974 1975
∑
Extreme
3 3 6 2 -
1 -
Moderate
∑
1 2 3 1 -
Severe
1 3 1 -
Extreme
1 1 -
1 -
1 1
SPEI 12
2 3 -
1962 1963 1964 1965 1966 1967
3 3 3 -
SPI 12
Moderate
SPEI 6
Severe
SPI 6
Extreme
SPEI 3
∑
SPI 3
3 -
Year
2011 -
345
SPEI 1 Moderate
SPI 1
RI PT
340
- - 10 10 - - - 12 10 11
-
29 15 21 43 79 13 18 26 57 10 30 43 83 15 26 35 76 12 40 48 100 28 17 24 69
346
The differences observed between SPI and SPEI for some months suggest that inclusion of
347
potential evapotranspiration is important especially given that evaporative water demand is quite
16
ACCEPTED MANUSCRIPT
important in determining water availability and in view of it being a major component of the
349
hydrological water balance. Moreover, water availability is also judged from available soil
350
moisture, of which potential evapotranspiration provides a reasonable indication of the soil water
351
losses.
RI PT
348
Timescale, 6 Months
Timescale, 1 Month
140 120
SC
100 80
M AN U
40 20 0 Timescale, 3 Months
140
Timescale, 12 Months
120 100
352 353 354
Severe
a
an ya ma Lu sw ish i Na nz hila Lu ng a
Ka sak
Lu fw
4
2
1
3
Ka f ue
Ka f ue
Ka f ue
Ka f ue
SPI SPEI
SPI SPEI
Moderate
ng a
an yam
Lu fw
3
4 Ka sak a
Ka fu e
2
Ka fu e
1 Ka fu e
AC C
Ka fu e
0
EP
20
Lu
40
Lu s
60
a wi s hi
TE D
80
Na nz hila
Count, months of drought
60
SPI SPEI Extreme
Figure 4: Number of drought events (1960-2015) at different time scales for the Kafue sub-basins. Left columns show SPI and right columns SPEI
17
ACCEPTED MANUSCRIPT
1 0.95 0.9 0.85
0.7 0.65 0.6 0.55 0.5 1
3
6
12
M AN U
Timescale (months) 355 356
Kafue 1 Kafue 2 Kafue 3 Kaue 4 Nanzhila Kasaka Lunga Luswishi Lufwanyama
RI PT
0.75
SC
R
0.8
Figure 5: Correlation between SPI and SPEI at different time scales for the Kafue sub-basins
357
4.0 CONCLUSION
359
This study compared SPI and SPEI in determining droughts. SPI is a precipitation-based index
360
while SPEI makes use of a water balance based on the difference between precipitation and
361
evapotranspiration. Both indices identified the temporal variability of droughts and were able to
362
identify different types of droughts as indicated by the different timescales. Compared to SPI,
363
SPEI captured more severe and moderate droughts under the study period of 1906-2015.
364
Although not very apparent, the SPEI droughts occurred with longer duration and increased
365
magnitude. This arises from the fact that temperature enhances the rates of potential
366
evapotranspiration, consequently increasing the evaporative water demand (Dubrovsky et al.,
367
2008) and therefore causing a water deficit. However, when considering precipitation alone, SPI
368
identified more extreme droughts compared to SPEI. Correlation analysis between SPI and SPEI
369
clearly indicates that precipitation is the major driver of drought. The results show that SPEI and
370
SPI have lower correlation for shorter timescales (meteorological followed by agricultural
371
droughts); that is, the indices pick up different signatures. However, the inclusion of potential
372
evapotranspiration becomes important at the longer timescales where the correlations are
373
stronger. Already it is largely accepted that precipitation plays a larger role in determining
AC C
EP
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358
18
ACCEPTED MANUSCRIPT
droughts and that evapotranspiration has considerable spatiotemporal effects on soil moisture
375
availability and consequently on agricultural droughts (Hao et al., 2018). It is because of this that
376
SPEI should be used in water resources planning in the face of drought. Hence, we suggest that
377
SPI must be used with caution while at the same time SPEI can be useful especially under
378
conditions where the effects of evapotranspiration are felt the most. Nonetheless, it should be
379
noted that this study aimed at establishing the difference between the two indices and since no
380
validation was performed on the results, conclusion cannot be drawn on which of the two is the
381
better indicator of drought.
SC
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374
382
ACKNOWLEDGEMENTS
384
The authors would like to thank the Climate Research Unit of the University of East Anglia for
385
availing the gridded climate data and the Meteorological Department of Zambia for providing
386
the ground station data for use in in this study. We are also grateful to the developers of the R-
387
statistical software package which made it easy to deal with large amounts of data in addition to
388
providing a platform on which to generate the indices for this study.
389
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391 392 393 394 395 396 397 398 399 400 401 402 403 404 405
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2 -
1981 1982 1983
-
1 1 -
1 -
1 2 -
2 1
1 -
3 2 2
6 2 3
1987
-
-
-
-
-
-
3
1990 1991 1992 1993 1994 1995 1996
-
2 1 -
-
2 1 -
1 1 3 -
2 2 1 -
2
4
-
-
∑
4 3 5 3
Moderate
1 1 3 2
Severe
1 1 1 1
Extreme
2 1 1 -
∑
2 3 -
Moderate
2 -
Severe
2 1 -
Extreme
∑
-
∑
Moderate
1971 1972 1973 1974 1975
Moderate
Severe
1 3
1 1
3 1 1 1
3 4 2 4
3 3 6 3 6
1 -
1 3 -
2 -
4 3 -
1 -
1 -
4 -
1 1 1 -
3 1 2 3
3 1 3 5 1
7 3 6 5 4
1
-
1
1 1
1 2 -
1 1 2
3 3 3
2 1
6 2
1 2
9 5
1 2 -
1 4 1
1
3
-
-
4
4
2 1 1 3 -
4 3 2 4 1 3 -
1 2 -
1 2 1 1
2 1 2 3
3 4 5 4
-
-
1
3
3
7
SPEI 12
Severe
Extreme
1 3 -
1 1 -
2 1 3 3
4 3 3 3
2 4 5 7 6
-
-
-
-
2 -
1 7 -
7 3 9
8 12 9
2
1 2 1 -
4 1 2 1 2
5 6 5 4
10 3 9 6 6
9 -
3 -
-
12
1 2 -
7 3 1 -
2 10 2 4 6 9 9 10 10 10
3
3 6 4
3 1
5 5
1 -
9 6
7 -
-
2 -
9 -
1 -
9 8
2 2 3
12 2 11
-
-
-
-
7
7
M AN U
1 -
RI PT
∑
3 3 6 2 -
SPI 12
Extreme
Moderate
1 2 3 1 -
TE D
1 3 1 -
SC
Severe
-
3 3 3 -
EP
Severe
1 1 -
SPEI 6
Extreme
Extreme
2 3 -
SPI 6
∑
∑
3 -
1999 2
Moderate
Moderate
1 -
-
1
3
4
-
-
5
5
-
-
-
-
-
-
1 1 -
1 1 -
2 1 -
3 2 2 -
1 3 -
1 2 4 -
5 1 2 6
6 4 9 6
1 -
1 1 1 -
4 1 5 1 -
5 2 6 2 -
10 -
2 1
10 10 - 12 10 11
-
-
-
-
-
-
-
-
2
6
2
10
-
-
-
-
1
10
1
-
-
-
-
AC C
Severe
1962 1963 1964 1 1965 1966 1967 -
Year
Extreme
Extreme
SPEI 3
∑
SPI 3
Moderate
SPEI 1
Severe
SPI 1
12
-
-
-
-
3
1
4
-
-
-
0 0
-
1 3
2 3
3 6
-
1 -
2 -
3 -
-
3
-
3
1 -
1 -
1 -
3 -
-
-
-
-
2003 2005 2 2006 2007 1 2008 -
1 1 -
1 -
4 2 -
1
1 1
2 4
3 6
2 -
1 -
2 -
0 5 -
-
-
3 -
3 -
2 -
1 -
2 3 -
5 3 -
1
5
3
9
-
-
-
-
1
2
-
3
2011
-
-
-
-
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2013
-
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
2015 2
1
-
3
-
-
-
-
2
1
-
3
-
-
-
-
2
1
Sum
12
9
29 15 21 43 79 13 18 26 57 10 30 43 83 15 26 35 76 12 40 48 100 28 17 24 69
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
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Figure 3a: SPEI and SPI at different time scales for the Lunga and Kafue 1 to Kafue 4 sub-basins of the Kafue
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Figure 3b: SPEI and SPI at different time scales for the Kasaka, Lufwanyama, Luswishi and Nanzhila sub-basins of the Kafue
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Highlights
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The Standardised Precipitation Index (SPI) and Standardised Evapotranspiration Index (SPEI) are compared for the Kafue Both SPI and SPEI capture the variability of droughts at different time scales but with different effects SPEI identified more droughts than SPI in the Kafue basin in Zambia Compared to SPI, SPEI records drought with increased duration and severity SPI should be used with caution since it only accounts for precipitation in the formulation of droughts
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S1474-7065(17)30054-2
DOI:
10.1016/j.pce.2018.07.001
Reference:
JPCE 2694
To appear in:
Physics and Chemistry of the Earth
Received Date: 3 April 2017 Revised Date:
6 June 2018
Accepted Date: 8 July 2018
Please cite this article as: Tirivarombo, S., , Osupile, D., Eliasson, P., Drought Monitoring and Analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI), Physics and Chemistry of the Earth (2018), doi: 10.1016/j.pce.2018.07.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Drought Monitoring and Analysis: Standardised Precipitation Evapotranspiration Index (SPEI) and Standardised Precipitation Index (SPI) 1
S. Tirivarombo*, 1D. Osupile, 1P. Eliasson
1
Department of Earth and Environmental Sciences Botswana International University of Science and Technology Email: [email protected], [email protected] *Corresponding author
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Abstract
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Although rainfall is a major indicator of the availability of water, temperature is also an
12
important factor that can influence the availability of water as it controls the rates of
13
evapotranspiration. Parameters such as rainfall and temperature can be used as indicators of
14
drought. These indicators are converted to drought indices which show the different
15
characteristics of a drought. This study compares two different drought indices in the Kafue
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Basin located in northern Zambia, where most of the socioeconomic livelihoods are dependent
17
on water. The Standardised Precipitation Index (SPI) depends on precipitation as the single input
18
variable while the Standardised Precipitation Evapotranspiration Index (SPEI) is derived from
19
precipitation and temperature in the form of a simple water balance. By comparing time series
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plots (1960-2015) of the two indices, both indices were able to pick up temporal variation of
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droughts. SPI and SPEI agreed (R>0.5) on the direction of change but the effect on the drought
22
condition was different. Compared to SPI, SPEI identified more droughts in the severe to
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moderate categories, with extended duration and increased intensity. On the other hand, SPI
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identified more droughts than SPEI under the extreme category, but with a shorter duration and
25
reduced frequency of occurrence compared to the severe to moderate droughts. The results
26
suggest that temperature variability plays an important role in characterising droughts. SPI is
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useful in that it only requires rainfall as input and especially where temperature data is missing.
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However, the use of SPI to characterise drought should be done with caution.
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Key words: Drought analysis; drought indices; SPEI; SPI; Kafue basin
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1.0 INTRODUCTION
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Hydrologically extreme events such as floods and droughts are placed high on the list of climate-
35
related natural disasters. Drought in particular is one of the biggest threats to human survival,
36
imposing serious adverse impacts to social, economic and environmental sustainability (Sharma
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et al., 2009). Defining a drought is complicated by the fact that droughts are spatially and
38
temporally variable, region-specific, context-dependent, and because they occur with varying
39
degrees of intensity, whilst their cumulative effect makes it difficult to identify their start and end
40
(Quiring and Papakryiakou, 2003). A drought can be defined simply as a recurrent and natural
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climatic event caused by below normal precipitation compared to the long-term average and
42
extending over a long period of time (Kundzewicz, 1997; Pandey et al., 2007; Dai, 2011).
43
Compared to floods, droughts develop slowly over time and are only recognized once people and
44
the environment start to feel their impact (Vicente-Serrano and Lopez-Moreno, 2005). As a
45
result, it is difficult to determine the onset and cessation of droughts. Defining droughts is also
46
complicated by the fact that they are widespread in occurrence and complex in nature. Initially
47
occurring as a result of prolonged below normal precipitation, droughts may have implications
48
on other components of the hydrological cycle. Therefore, it is possible for one type of drought
49
to convert into another type under prolonged occurrence. In relation to water resources, drought
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can be considered as a multi-scalar phenomenon which is guided by catchment response time. It
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is worth noting that the hydrological responses of soil moisture, river discharge and groundwater
52
recharge as well as the biological response of crops and natural vegetation vary and have
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different response times (Lorenzo-Lacruz et al., 2010). Therefore the time over which the water
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deficits accumulate (timescale) is very important in determining the prevailing type of drought
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(Wilhite and Glantz, 1985; Howard et al., 2014). Timescales functionally separate the different
56
types of droughts into meteorological (1 month timescale), agricultural (3-6 month timescale)
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and hydrological droughts (12 month timescale) (Vicente-Serrano et al., 2010; Homdee et. al,
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2016). It is therefore important that droughts are classified by the specific timescales to allow
59
proper assessment of the drought.
60
The rate of evapotranspiration is mainly influenced by temperature, atmospheric evaporative
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demand and the effect of heat waves (Beguería et al., 2014; Vicente-Serrano et al., 2015).
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Temperature is one of the major climatic factors that influences availability of water and also has
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consequent effects on the nature and occurrence of droughts (Rebetez et al., 2006; Dubrovsky et
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al., 2008, Sheffield and Wood, 2008. Already some studies project an increasing trend in global
65
mean annual temperatures (e.g. Trenberth et al., 2007; Dai, 2013; Trenberth et al., 2014).
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Moreover, in most arid and semi-arid regions of the world potential evapotranspiration is higher
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than annual precipitation such that a precipitation-only based drought index may not be sufficient
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to monitor droughts (Howard et. al., 2014; Hogg, 1994). It is therefore important to incorporate
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temperature and/or other hydrological components in the determination of drought indices.
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Although it is difficult to identify the onset and cessation of droughts, their impacts can be
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averted through an understanding of their nature and occurrence. As such, appropriate and timely
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interventions to the impacts of droughts require monitoring tools that are able to objectively
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quantify the intensity, duration, magnitude and spatial extent of droughts (Smakhtin and Hughes,
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2004).
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Since drought is related to climatic events, variables such as rainfall, temperature and streamflow
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can provide good indicators of the occurrence or non-occurrence of drought. These indicators
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can then be converted to drought indices which show the occurrence, magnitude, intensity and
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duration of a drought event (Zarger et al., 2011; Hayes, 2006). Drought indices can either be
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formed from a single input variable or from a combination of hydrological variables (Hao and
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Singh, 2015). Indices composed of a number of hydrological variables tend to provide more
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certain results, however, what variables to use depends on the situation to be addressed and the
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type of drought under analysis. Furthermore, selection of the drought index is guided by the
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region of interest and data availability (Smakhtin and Schipper, 2008).
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Several drought indices are in existence (Heim, 2002), but so far the most commonly used
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drought indices are the Palmer Drought Severity Index (PDSI, Palmer, 1968) and the
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Standardised Precipitation Index (SPI, Mckee et al. (1993). The PDSI is based on a simplified
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water balance with input parameters of precipitation, runoff, moisture supply and evaporation.
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On the other hand the SPI is a simplified index with only one input variable; precipitation
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(Vicente-Serrano et al., 2010). A drought index which is able to account for the different
90
timescales and the spatial scale at which drought occurs is considered to be multi-scalar in nature
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(Guttman, 1998). The SPI incorporates cumulative precipitation deficits at various spatio-
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temporal scales, thus rendering it multi-scalar (Hou et al., 2007). A major assumption in the
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computation of SPI is that droughts are largely driven by rainfall variability while other factors
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such as temperature are assumed to be stationary and as such do not change over time (Vicente-
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Serrano et al., 2010). The fundamental strength of SPI over other indices is that it is able to
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detect drought at different time scales (1, 3, 6, 12 and 24 months) implying that various types of
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drought (meteorological, agricultural and hydrological) can be monitored. However, the quality
98
of a drought index result can only be as good as the input data (Tirivarombo and Hughes, 2011).
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Although the PDSI incorporates components of the hydrological cycle in its formulation, it falls
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short of the multi-scalar characterization of droughts because it is not capable of identifying
101
drought for different timescales. Moreover, many parameters are required to calculate the index
102
(Vicente-Serrano et al., 2010). The SPI is multiscalar but only incorporates precipitation to
103
calculate the drought index. On the other hand, SPEI is a multi-scalar drought index which also
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takes into consideration both precipitation and temperature in addition to the ability to identify
105
drought at different time scales. Because of its ability to incorporate both temperature and
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precipitation, SPEI may be a useful indicator of drought (Howard et. al., 2014), considering that
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evapotranspiration is the major form of water loss in dry regions where temperatures are high.
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The index is calculated based on the non-exceedance probability of the differences between
109
precipitation and potential evapotranspiration, adjusted using a three-parameter log-logistic
110
distribution which accounts for common negative values (Středová et al., 2011; Vicente-Serrano
111
et al., 2010).
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Droughts are a common and recurrent feature in southern Africa which can have detrimental
113
effects on the natural environment and agriculture with repercussions on human socio-economic
114
well-being. A large proportion of the population in the region depends solely on rain-fed
115
agriculture for survival and in addition to agricultural demand there is increased pressure on
116
water resources in the region due to population expansion and new developments. It is therefore
117
important to have in place adequate drought assessment and monitoring tools that can produce
118
reliable results to assist decision making at all levels. Because of the different formulations of the
119
SPI and SPEI, this study seeks to compare the SPI and SPEI in characterizing droughts using a
120
case example of the Kafue sub-basin which is found in Zambia. The basin drains into the
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Zambezi River and it is important because of its economic, social and ecological importance.
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About 50% of Zambia’s population lives in the basin and relies on the basin’s water resources
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for various uses such as mining, industry and agriculture. Despite heavy reliance on the basin’s
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water resources, the basin is under threat of high natural climatic variability which is amplified
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by climate change thus increasing the occurrence of hydrologically extreme drought events
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(Lweendo et al., 2017).
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2.0 MATERIALS AND METHODS
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2.1 Study area
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The Kafue basin (Figure 1) occupies an area of about 156 995 km2 which is about 20% of
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Zambia’s total land area. With a length of 1 300 km, the Kafue River is one of the major
132
tributaries of the Zambezi River. Among other important features, the Kafue basin hosts the
133
Kafue Flats, a wetland which falls under the RAMSAR Convention. The soils in the basin are a
134
dark clayey montmorillonite characterized by high water holding capacity. The basin experiences
135
two distinct seasons; a wet season and a dry season extending from November to April and from
136
May to October respectively. Mean daily temperatures range between 13 °C and 20 °C in winter
137
and between 21 °C and 30 °C in summer. Rainfall is largely influenced by the Inter Tropical
138
Convergence Zone (ITCZ) which is a low-pressure system caused by the convergence of trade
139
winds. The position of the ITCZ varies from year to year thus influencing the precipitation
140
patterns in the basin. The annual rainfall ranges from 1300 mm/year in the north to 800 mm/year
141
in the southern parts of the basin. The basin experiences an average annual potential
142
evapotranspiration rate of about 1300 mm/year with highest monthly values from August to
143
November at about 200-300 mm/month. Rainfall distribution is spatially variable in the Kafue
144
basin, decreasing in a north-south direction (Lweendo et al., 2017). Therefore, the northern sub-
145
basins consisting of Lufwanyama, Luswishi, Lunga and to some extent Kafue 4 receive more
146
rainfall than the southern-most sub-basins.
147
About 50% of Zambia’s population is concentrated in the Kafue basin and most of the communal
148
livelihoods depend on rainfed agriculture for sustenance, implying that the basin community is
149
vulnerable to the impacts of changing rainfall patterns as a result of climate variability and
150
change. In addition, two major dams, the Itezhitezhi and the Kafue Gorge are found within the
151
basin and are used for generating hydroelectricity. Other major activities in the basin include
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mining and industry which also impose a large water demand on the basin’s water resources
153
(Mfalila et al., 2013).
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Figure 1: Location of Kafue basin. Sub-basins: (1) Lunga, (2) Luswishi, (3) Lufwanyama, (4) Kafue 4, (5) Kafue 3, (6) Kafue 2, (7) Kafue 1, (8) Nanzhila and (9) Kasaka
157
2.2 Climate data
159
Due to sparse rainfall gauging networks this study used CRU TS4.00 data as an alternative
160
dataset which was obtained from the Climate Research Unit of the University of East Anglia
161
(Harris and Jones, 2017). The data set consists of 0.5° grids of monthly time series of different
162
climate variables including rainfall and temperature for the period 1901-2015. Ground station
163
datasets with a long enough time series which includes a base period of 1961-1990 are used to
164
calculate monthly normals after which the ground station data is converted into anomalies by
165
subtracting the 1961-1990 normal from the respective station’s time series data for each month
166
(Willmott and Robeson, 1995). The temperature and rainfall gridded datasets are obtained by
167
direct estimation through interpolation (as a function of latitude, longitude, and elevation) from
168
the ground station data (Harris et al., 2014) as obtained from the respective countries’
169
meteorological stations. To correct for inhomogeneity in data for any station, reference (1961-
170
1990) time series data from neighbouring ground observation stations are used for comparison
171
against the station in question. Anomalies relative to the 1961-1990 mean of the nearby ground
172
station data are interpolated and combined with the gridded anomalies. Using the angular
173
distance weighting method (New et al., 2000) these gridded anomalies are then combined with
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the mean monthly (1961-1990) climatology to obtain the monthly climate grids for the period
175
1901-2015.
176
The reliability of the CRU data was assessed based on ground rainfall stations (Table 1) that are
177
representative of the various sub-basins, with reasonably long time series (>30 years) and nearest
178
to selected grid points. The correlation results, which are a combination of all the stations used in
179
the analysis and averaged to represent a basin composite result for the various months are shown
180
in (Figure 2). In general most of the data points lie within the 95% confidence band and overall
181
the relationships between the CRU data and the ground station data are assumed to be reasonably
182
good (R2>0.5) thus providing confidence in the use of the CRU TS4.00 data.
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Table 1: Kafue ground stations used to validate the CRU TS4.00 data Sub-basin
Latitude -12.1
Longitude 26.4
Record years
-12.9
27.36
1951-1987
-13.2 -15.8
28.29 26.5
1906-1964 1919-1987
Kafue1
-15.87
27.76
1916-1986
Kasaka
-15.98
27.6
1946-1996
Lunga Luswishi Lufwanyama Kafue 2
1906-1994
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Analysis at the sub basin or basin scale requires catchment averaged rainfall which has an
186
advantage over point or gridded data because local variabilities associated with specific stations
187
are eliminated (WMO, 2000). For each sub-basin, the inverse distance weighting method (Wilk
188
et al., 2006) is used to calculate the weighted average rainfall and temperature from the CRU
189
climate grids found within each sub basin using the equation:
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=∑
∑
(1)
191
where, R is the estimated rainfall for a specific sub basin, Ri is the rainfall at a grid point, i, and d
192
is the distance between the centroid of the area and the grid point.
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100
50
120
100
30
60
80
10
40
20
0
0 10
20
30
40
40
20 0
50
20
40
Local Rainfall (mm)
250
60
60
80
100
0
Local Rainfall (mm)
160
February 100 120
0
60
40 50
100
150
200
0
20
60
50
40
CRU Rainfall (mm)
60
80
20
80
100
0
30
20
10
100
0
10
20
40
50
4
8
12
16
Local Rainfall (mm)
80
120
140
160
June
10
5
0
5
10
15
20
25
Local Rainfall (mm)
10
August 8
6
6
4
2
0 20
100
Local Rainfall (mm)
15
60
CRU Rainfall (mm)
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0
30
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12
0
40
Local Rainfall (mm)
8
0
20
July
16
4
40
120
10
July
CRU rainfall (mm)
60
0
40
Local Rainfall (mm)
193
40
TE D
0
CRU Rainfall (mm)
CRU Rainfall (mm)
20
20
60
20
60
0
80
May
40
120
25
April 80
100
100
Local Rainfall (mm)
100
80
20
250
Local Rainfall (mm)
CRU Rainfall (mm)
0
60
SC CRU Rainfall (mm)
80
M AN U
CRU Rainfall (mm)
CRU Rainfall (mm)
150
50
40
March
140 200
100
20
Local Rainfall (mm)
120
January
RI PT
20
CRU Rainfall (mm)
80
CRU Rainfall (mm)
CRU Rainfall (mm)
40
0
December
November
October
4
2
0 0
2
4
6
8
Local Rainfall (mm)
10
0
2
4
6
8
10
Local Rainfall (mm)
194 195 196
Figure 2: Comparison of CRU TS4.00 rainfall data and local rainfall data (based on long-term mean monthly rainfall for various stations and averaged for the whole basin, lines show 95% confidence bounds)
197
Potential evapotranspiration was estimated by the Thornthwaite method (Thornthwaite, 1948).
198
This method was chosen due to the fact that out of the climatic variables required for estimating
8
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199
potential evapotranspiration we had temperature data at our disposal and the Thornthwaite
200
method requires only temperature as the input variable (equation 2). = 16
(2)
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where: T (°C) is the mean temperature for the month, d is the correction factor to account for the
203
unequal day length between months and is read from tables based on the latitude of the study
204
area.
205
I represents the annual thermal index and i is the monthly thermal index.
206
I=∑
207
=
.
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! = 0.49 + 0.018' − 7.7 * 10+ ' + 6.7 * 10+, ' -
209
(3) (4) (5)
2.3 SPI and SPEI drought indices
211
A comparative analysis of SPI and SPEI is carried out in order to establish whether potential
212
evapotranspiration has an effect on the drought index. The analyses were done at different time
213
scales for the period 1960-2015. The different time scales (1, 3-6, and 12 months) represent
214
meteorological, agricultural and hydrological droughts respectively. The SPI and SPEI were
215
generated using the SPEI package (Berguria et al., 2014) found in the R software package which
216
is a free software environment for statistical computing and graphics, this package provides
217
different options for calculating SPI and SPEI.
218
2.3.1 SPI
219
The SPI was designed to assess drought conditions based on the probability distribution of long
220
term precipitation using the gamma function (Mckee et al., 1993). Precipitation is transformed
221
into normalised numerical values and the SPI is given as the number of standard deviations by
222
which the observed precipitation deviates from the long-term mean for a normally distributed
223
random variable (equation 6). It can thus be used to define and compare drought conditions in
224
different areas. The index gives a good and reliable estimate of the magnitude, severity and
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spatial extent of droughts. When precipitation is above the long term mean value the SPI is
226
positive and if precipitation falls below the long term mean the SPI is negative. Unlike other
227
drought indices, SPI is less cumbersome to use because it only requires a single input data series
228
of long term precipitation (Smakhtin and Hughes, 2004). Because it is based on normalised data,
229
the SPI is spatially invariant and droughts can be assessed in different regions (Guttman, 1998).
230
The index is calculated as follows:
231
. '=
232
where, xi is the precipitation of the selected period during the year i, x is the long term mean
233
precipitation and σ is standard deviation for the selected period.
234
2.3.2 SPEI
235
SPEI is calculated based on the non-exceedance probability of the differences between
236
precipitation and potential evapotranspiration, adjusted using a three-parameter log-logistic
237
distribution which accounts for common negative values (Středová et al., 2011; Vicente-Serrano
238
et al., 2010). SPEI uses a three-parameter distribution to capture the deficit values since it is most
239
likely that in arid and semi-arid areas the moisture deficit can be negative. For two-parameter
240
distributions as used in SPI, the variable x has a lower boundary of zero (0 > x < ∞) meaning that
241
x can only take positive values while for the three-parameter distributions used in SPEI, x can
242
take values in the range (γ > x< ∞) implying that x can also take negative values; γ is the
243
parameter of origin of the distribution (Vicente-Serrano et al., 2010). Therefore the Log-logistic
244
distribution was recommended for SPEI since it provides a better fit for the extreme negative
245
values (Hernandez and Uddameri, 2014). The SPEI is obtained by normalizing the water balance
246
into the Log-logistic probability distribution. For this study PET is estimated by the
247
Thornthwaite method ((Thornthwaite, 1948). The difference (Di) between precipitation (P) and
248
PET for the month (i) is given in equation 7.
249
2 =
250
The calculated D values are aggregated at different time scales as follows:
251
234 = ∑4+ +
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225
/ +/̅
(6)
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−
3+
−(
)3+
(7)
(8)
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252
where k is the timescale (months) of the aggregation and n is the calculation month.
253
The probability density function of a Log-logistic distribution is given as:
254
7(* ) = 9
255
where α, β and γ are scale, shape and origin parameters respectively for γ > D <∞. The
256
probability distribution function for the D series is then given as:
257
7(*) = [1 + (>/* − @)8 ]+
258
With f(x) the SPEI can be obtained as the standardized values of F(x) according to the method of
259
Abramowitz and Stegun (1965):
260
Where
.
261
and
B = I−2 ln( )
262
P is the probability of exceeding a determined Di value and is given as = 1 – 7(*) while the
263
constants are:
264
C0 = 2.515517, C1 = 0.802853, C2 = 0.010328, d1 = 1.432788, d2 = 0.189269, d3 = 0.001308.
265
Since SPEI is a standardized variable it can be used to compare droughts over different spatial
266
and temporal scales. Just like the SPI, continuously negative SPEI values define a drought period
267
based on intensity, severity, magnitude and duration (Byakatonda et. al, 2016).
268
2.3.3 Drought identification
269
The characterisation of droughts for both SPI and SPEI is based on the SPI scale (Mckee et al.,
270
1993). The SPI scale is used since the computation of both indices is based on the same
271
principles. This study places emphasis on moderate to extreme droughts and the SPI/SPEI index
272
scale is given as, extreme drought (≤ -2), severe drought (-2 to -1.5) and moderate drought (-1.5
273
to -1). It should be noted that a drought ends when the SPI/SPEI approaches zero and progresses
274
into a positive value. For this study, the duration of the drought is considered as the number of
275
months for which the drought has occurred while the magnitude of the indices indicates the
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(9)
SC
(10)
CD E CF GEC G
E F GE
G E HG H
for
≤ 0.5
(11) (12)
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'=B−
<
9
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+ /+: 8
;1 +
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8 /+: 8+
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severity of the drought. The comparison of SPI and SPEI, that is if both indices portray the same
277
pattern (irrespective of the magnitude), is assessed using the Pearson correlation coefficient, r,
278
which measures the strength of the statistical relationship between the SPI and SPEI. This
279
coefficient establishes whether a linear relationship exists between the indices at the 95%
280
confidence. The relationship coefficient (R) takes values between +1 and -1 where; +1: perfect
281
positive relationship, 0: no relationship and -1: perfect negative relationship. The magnitude of
282
the correlation shows the strength of the relationship and an R value ≥0.5 is deemed to be a
283
strong correlation (Taylor, 1990). R is calculated as follows: =
∑QRF(/ +/̅ )(P +PS)
SC
/P
T∑QRF(/ +/̅ ) (P +PS)
(13)
M AN U
284
RI PT
276
285
Where: n = number of observations, and for this study x and y represent the SPI and SPEI values
286
respectively.
287
3.0 RESULTS AND DISCUSSION
289
To demonstrate the temporal variation of drought at different time scales (3, 6 and 12 months) in
290
the Kafue, the SPIs and SPEIs for the different sub-basins were generated and presented in
291
Figures 3a and 3b. In general, and for all the sub-basins, both indices show the same pattern of
292
variability for each timescale but they differ in the duration and magnitude of the drought.
293
Variability in the droughts can be attributed to the fact that the sub-basin experiences high
294
natural variability in climate which is characteristic of the southern African region. Also, the
295
frequency of occurrence of the droughts is higher for the shorter timescale compared to the
296
longer timescales; it takes a shorter time (at most 1 month) of prevailing water deficiency for a
297
meteorological drought, thus the high variability of droughts. On the other hand, a longer period
298
of water deficit accumulation or depletion of water storage in rivers and reservoirs is required for
299
a hydrological drought to occur. Hence, the meteorological droughts (1 month timescale) show
300
the highest frequency of occurrence followed by agricultural droughts (3-6 month timescale) and
301
lastly the hydrological droughts (12 month time scale). However, at the higher timescales the
302
drought lasts longer and the magnitude increases.
AC C
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288
12
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ACCEPTED MANUSCRIPT
303 304 305
Figure 3a: SPEI and SPI at different timescales for the Kasaka, Lufwanyama, Luswishi and Nanzhila subbasins of the Kafue
13
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SC
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ACCEPTED MANUSCRIPT
306 307 308
Figure 3b: SPEI and SPI at different timescales for the Lunga and Kafue1 to Kafue 4 sub-basins of the Kafue
14
ACCEPTED MANUSCRIPT
Given that it takes up to 6 months for most crops to be fully developed, a water deficiency
310
accumulation of at least 3 months, during the growing season, will adversely impact crop yields,
311
thus developing into an agricultural drought. Since drought develops over time, it can be
312
assumed that the extended period of drought at longer timescales may be a result of the after-
313
effects of accumulation of antecedent water scarcity over time and this situation may be
314
amplified with persistent and continuous periods of no rainfall. In addition, a drought can occur
315
if there is a shift in seasonal rainfall such that the rains are delayed thus causing impairment on
316
activities that normally depend on the onset of a rainfall event.
SC
317
RI PT
309
Apparent differences during some years and irrespective of the timescale were noted between the
319
SPI and SPEI. Longer droughts occurred under SPEI; here the duration of the drought is
320
extended as the counts of droughts increase in the yearly time series. For some of the years that
321
were already experiencing drought conditions under SPI, the magnitude of the drought was
322
amplified when detected by the SPEI. That SPEI produces droughts of increased magnitude can
323
be explained by the fact that evapotranspiration imposes a demand on the available water and the
324
impact is felt the most under conditions of water scarcity.
M AN U
318
TE D
325
Table 2 shows the number of droughts per year, including the drought categories for the Lunga
327
sub-basin. For the period under observation (1960-2015) the most common agricultural and
328
hydrological droughts were observed during the years 1964-1965, 1967, 1971-1973, 1981-1983,
329
1987, 1990-1992, 2001 and 2008, the same applies to all the other sub-basins of the Kafue.
330
Figure 4 shows that SPEI identified more droughts than SPI under the moderate to severe
331
drought categories across all sub-basins and for all time scales. The results show that even
332
though reduced precipitation is the major driver of droughts, the effect of temperature through
333
evaporative water demand has a role to play in the determination of droughts. Considering
334
rainfall alone, more droughts are classified as extreme compared to when including PET. Overall
335
Figure 4 shows that the highest number of droughts under 6 and 12 monthly timescales occurred
336
in the Nanzhila sub-basin which is located in the southernmost part of the Kafue basin.
337
Correlations between SPI and SPEI for the different sub-basins of the Kafue and under different
338
timescales are depicted in Figure 5. Statistically significant positive correlations (R>0.5) exist
339
between the two indices. Under climatic conditions with low inter-annual variability in
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15
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temperature compared to the variability in rainfall, the results imply that both indices will
341
predominantly respond more to the variations in precipitation suggesting that precipitation is the
342
major driver of water availability.
343 344
Table 2: Drought years and drought categories of SPI and SPEI at different time scales in the Lunga subbasin
4 -
1 1 1 -
1 2 -
1 1 2
3 3 3
2 1
-
-
4
4
-
1 2 -
1 2 1 1
2 1 2 3
3 4 5 4
1 -
3 -
3 -
2 -
1 -
2 -
1 1 -
1 -
1 2 -
2 1
1 -
3 2 2
6 2 3
1 1
1987 -
-
-
-
-
-
3
3
1990 1991 1992 1993 1994 1995 1996
-
2 1 -
-
2 1 -
1 1 3 -
2 2 1 -
2 1 1 3 -
4 3 2 4 1 3 -
1999 2 2000 2001 -
-
2 -
4 -
-
3
1
4
2003 2005 2006 2007 2008
1 1 -
1 -
4 2 -
1
1 1
2 4
3 6
-
-
-
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
-
-
-
-
2
1
-
3
-
-
-
-
2
1
3
-
-
-
-
-
-
-
-
-
-
-
-
7
38 68 113
4 3 3 3
2 4 5 7 6
-
-
-
-
2 -
1 7 -
7 3 9
8 12 9
5
9 -
3 -
-
12
1 2 -
7 3 1 -
2 10 2 4 6 9 9 10 10 10
M AN U 3 1 2 3
3 1 3 5 1
7 3 6 5 4
1
-
1
2
1 2 1 -
4 1 2 1 2
6 5 4
10 3 9 6 6
6 2
1 2
9 5
1 2 -
1 4 1
1
3
3 6 4
3 1
5 5
1 -
9 6
7 -
-
2 -
9 -
1 -
9 8
2 2 3
12 2 11
1
3
4
-
-
5
5
-
-
-
-
-
-
-
-
-
-
7
7
1 1 -
1 1 -
2 1 -
3 2 2 -
1 3 -
1 2 4 -
5 1 2 6
6 4 9 6
1 -
1 1 1 -
4 1 5 1 -
5 2 6 2 -
- - - - - 10 2 - 1
-
-
-
-
7 0 0
-
1 3
2 3
3 6
2 -
6 1 -
2 2 -
10 3 -
-
3
-
3
1 1 -
10 1 1 1 - -
12 3 -
-
-
-
-
0 5 -
-
-
3 -
3 -
2 -
1 -
2 3 -
5 3 -
1
5
3
9
-
-
-
1
2
6
9
TE D
EP
AC C
∑
1 -
Moderate
2 1 3 3
Severe
1 1 -
Extreme
4 3 -
∑
2 -
Moderate
1 3 -
Severe
1 -
Extreme
3 3 6 3 6
∑
3 4 2 4
Moderate
Severe
-
3 1 1 1
SC
1 -
12 9
Extreme
2 -
8
∑
4 3 5 3
Sum
Moderate
1 1 3 2
2015 2
Severe
1 1 1 1
2013 -
Extreme
2 3 -
2 1 1 -
2 1 -
∑
2 -
1981 1982 1983 -
Moderate
1 3
2 1 -
Severe
1 3 -
-
Extreme
Severe
1 -
1971 1972 1973 1974 1975
∑
Extreme
3 3 6 2 -
1 -
Moderate
∑
1 2 3 1 -
Severe
1 3 1 -
Extreme
1 1 -
1 -
1 1
SPEI 12
2 3 -
1962 1963 1964 1965 1966 1967
3 3 3 -
SPI 12
Moderate
SPEI 6
Severe
SPI 6
Extreme
SPEI 3
∑
SPI 3
3 -
Year
2011 -
345
SPEI 1 Moderate
SPI 1
RI PT
340
- - 10 10 - - - 12 10 11
-
29 15 21 43 79 13 18 26 57 10 30 43 83 15 26 35 76 12 40 48 100 28 17 24 69
346
The differences observed between SPI and SPEI for some months suggest that inclusion of
347
potential evapotranspiration is important especially given that evaporative water demand is quite
16
ACCEPTED MANUSCRIPT
important in determining water availability and in view of it being a major component of the
349
hydrological water balance. Moreover, water availability is also judged from available soil
350
moisture, of which potential evapotranspiration provides a reasonable indication of the soil water
351
losses.
RI PT
348
Timescale, 6 Months
Timescale, 1 Month
140 120
SC
100 80
M AN U
40 20 0 Timescale, 3 Months
140
Timescale, 12 Months
120 100
352 353 354
Severe
a
an ya ma Lu sw ish i Na nz hila Lu ng a
Ka sak
Lu fw
4
2
1
3
Ka f ue
Ka f ue
Ka f ue
Ka f ue
SPI SPEI
SPI SPEI
Moderate
ng a
an yam
Lu fw
3
4 Ka sak a
Ka fu e
2
Ka fu e
1 Ka fu e
AC C
Ka fu e
0
EP
20
Lu
40
Lu s
60
a wi s hi
TE D
80
Na nz hila
Count, months of drought
60
SPI SPEI Extreme
Figure 4: Number of drought events (1960-2015) at different time scales for the Kafue sub-basins. Left columns show SPI and right columns SPEI
17
ACCEPTED MANUSCRIPT
1 0.95 0.9 0.85
0.7 0.65 0.6 0.55 0.5 1
3
6
12
M AN U
Timescale (months) 355 356
Kafue 1 Kafue 2 Kafue 3 Kaue 4 Nanzhila Kasaka Lunga Luswishi Lufwanyama
RI PT
0.75
SC
R
0.8
Figure 5: Correlation between SPI and SPEI at different time scales for the Kafue sub-basins
357
4.0 CONCLUSION
359
This study compared SPI and SPEI in determining droughts. SPI is a precipitation-based index
360
while SPEI makes use of a water balance based on the difference between precipitation and
361
evapotranspiration. Both indices identified the temporal variability of droughts and were able to
362
identify different types of droughts as indicated by the different timescales. Compared to SPI,
363
SPEI captured more severe and moderate droughts under the study period of 1906-2015.
364
Although not very apparent, the SPEI droughts occurred with longer duration and increased
365
magnitude. This arises from the fact that temperature enhances the rates of potential
366
evapotranspiration, consequently increasing the evaporative water demand (Dubrovsky et al.,
367
2008) and therefore causing a water deficit. However, when considering precipitation alone, SPI
368
identified more extreme droughts compared to SPEI. Correlation analysis between SPI and SPEI
369
clearly indicates that precipitation is the major driver of drought. The results show that SPEI and
370
SPI have lower correlation for shorter timescales (meteorological followed by agricultural
371
droughts); that is, the indices pick up different signatures. However, the inclusion of potential
372
evapotranspiration becomes important at the longer timescales where the correlations are
373
stronger. Already it is largely accepted that precipitation plays a larger role in determining
AC C
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358
18
ACCEPTED MANUSCRIPT
droughts and that evapotranspiration has considerable spatiotemporal effects on soil moisture
375
availability and consequently on agricultural droughts (Hao et al., 2018). It is because of this that
376
SPEI should be used in water resources planning in the face of drought. Hence, we suggest that
377
SPI must be used with caution while at the same time SPEI can be useful especially under
378
conditions where the effects of evapotranspiration are felt the most. Nonetheless, it should be
379
noted that this study aimed at establishing the difference between the two indices and since no
380
validation was performed on the results, conclusion cannot be drawn on which of the two is the
381
better indicator of drought.
SC
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374
382
ACKNOWLEDGEMENTS
384
The authors would like to thank the Climate Research Unit of the University of East Anglia for
385
availing the gridded climate data and the Meteorological Department of Zambia for providing
386
the ground station data for use in in this study. We are also grateful to the developers of the R-
387
statistical software package which made it easy to deal with large amounts of data in addition to
388
providing a platform on which to generate the indices for this study.
389
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391 392 393 394 395 396 397 398 399 400 401 402 403 404 405
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2 -
1981 1982 1983
-
1 1 -
1 -
1 2 -
2 1
1 -
3 2 2
6 2 3
1987
-
-
-
-
-
-
3
1990 1991 1992 1993 1994 1995 1996
-
2 1 -
-
2 1 -
1 1 3 -
2 2 1 -
2
4
-
-
∑
4 3 5 3
Moderate
1 1 3 2
Severe
1 1 1 1
Extreme
2 1 1 -
∑
2 3 -
Moderate
2 -
Severe
2 1 -
Extreme
∑
-
∑
Moderate
1971 1972 1973 1974 1975
Moderate
Severe
1 3
1 1
3 1 1 1
3 4 2 4
3 3 6 3 6
1 -
1 3 -
2 -
4 3 -
1 -
1 -
4 -
1 1 1 -
3 1 2 3
3 1 3 5 1
7 3 6 5 4
1
-
1
1 1
1 2 -
1 1 2
3 3 3
2 1
6 2
1 2
9 5
1 2 -
1 4 1
1
3
-
-
4
4
2 1 1 3 -
4 3 2 4 1 3 -
1 2 -
1 2 1 1
2 1 2 3
3 4 5 4
-
-
1
3
3
7
SPEI 12
Severe
Extreme
1 3 -
1 1 -
2 1 3 3
4 3 3 3
2 4 5 7 6
-
-
-
-
2 -
1 7 -
7 3 9
8 12 9
2
1 2 1 -
4 1 2 1 2
5 6 5 4
10 3 9 6 6
9 -
3 -
-
12
1 2 -
7 3 1 -
2 10 2 4 6 9 9 10 10 10
3
3 6 4
3 1
5 5
1 -
9 6
7 -
-
2 -
9 -
1 -
9 8
2 2 3
12 2 11
-
-
-
-
7
7
M AN U
1 -
RI PT
∑
3 3 6 2 -
SPI 12
Extreme
Moderate
1 2 3 1 -
TE D
1 3 1 -
SC
Severe
-
3 3 3 -
EP
Severe
1 1 -
SPEI 6
Extreme
Extreme
2 3 -
SPI 6
∑
∑
3 -
1999 2
Moderate
Moderate
1 -
-
1
3
4
-
-
5
5
-
-
-
-
-
-
1 1 -
1 1 -
2 1 -
3 2 2 -
1 3 -
1 2 4 -
5 1 2 6
6 4 9 6
1 -
1 1 1 -
4 1 5 1 -
5 2 6 2 -
10 -
2 1
10 10 - 12 10 11
-
-
-
-
-
-
-
-
2
6
2
10
-
-
-
-
1
10
1
-
-
-
-
AC C
Severe
1962 1963 1964 1 1965 1966 1967 -
Year
Extreme
Extreme
SPEI 3
∑
SPI 3
Moderate
SPEI 1
Severe
SPI 1
12
-
-
-
-
3
1
4
-
-
-
0 0
-
1 3
2 3
3 6
-
1 -
2 -
3 -
-
3
-
3
1 -
1 -
1 -
3 -
-
-
-
-
2003 2005 2 2006 2007 1 2008 -
1 1 -
1 -
4 2 -
1
1 1
2 4
3 6
2 -
1 -
2 -
0 5 -
-
-
3 -
3 -
2 -
1 -
2 3 -
5 3 -
1
5
3
9
-
-
-
-
1
2
-
3
2011
-
-
-
-
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2013
-
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
2015 2
1
-
3
-
-
-
-
2
1
-
3
-
-
-
-
2
1
Sum
12
9
29 15 21 43 79 13 18 26 57 10 30 43 83 15 26 35 76 12 40 48 100 28 17 24 69
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
M AN U
TE D EP
8
AC C
2000 2001
RI PT
-
SC
ACCEPTED MANUSCRIPT
7
38 62 107
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 3a: SPEI and SPI at different time scales for the Lunga and Kafue 1 to Kafue 4 sub-basins of the Kafue
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
Figure 3b: SPEI and SPI at different time scales for the Kasaka, Lufwanyama, Luswishi and Nanzhila sub-basins of the Kafue
ACCEPTED MANUSCRIPT
Highlights
RI PT
SC M AN U TE D
• • •
EP
•
The Standardised Precipitation Index (SPI) and Standardised Evapotranspiration Index (SPEI) are compared for the Kafue Both SPI and SPEI capture the variability of droughts at different time scales but with different effects SPEI identified more droughts than SPI in the Kafue basin in Zambia Compared to SPI, SPEI records drought with increased duration and severity SPI should be used with caution since it only accounts for precipitation in the formulation of droughts
AC C
•