Applicability of drought indices to
monitor multi-sector impacts:
“The Standardized Precipitation
Evapotranspiration Index – SPEI”
Sergio M. Vicente-Serrano, Santiago Beguería and Juan I. López-Moreno
Spanish National Research Council, CSIC, Zaragoza, Spain
Challenges for drought analysis and monitoring
• Drought is a complex natural phenomena without a general and commonly
accepted definition
• In contrast to other extreme events such as floods, which are typically restricted to
small regions and well-defined temporal intervals, droughts are difficult to pinpoint in
time and space, affecting wide areas over long periods of time.
• It is very difficult to isolate the beginning of a drought, as drought development is
slow and very often the drought is not recognized until human activities, or the
environment, are affected. Moreover, the effects of a drought can persist over many
years after it has ended.
• It is very difficult to objectively quantify their characteristics in terms of intensity,
magnitude, duration and spatial extent.
• We identify a drought by its effects at different levels, but there is not a physical
variable we can measure to quantify droughts.
Given the large dificulties to objectively quantify their characteristics
(duration, intensity, magnitude, spatial extent, onset, etc.) several drought
indices have been developed in the last decades (Heim, 2002: Bulletin of the
American Meteorological Society, 83: 1149-1165)
At present the two most widely used drought indices are:
Palmer Drought Severity Index
Palmer (1965)
Standardised Precipitation Index
McKee et al. (1993)
Based on a simplified water balance
equation.
Incorporates prior precipitation,
moisture supply, runoff and evaporation
demand at the surface level
Based on precipitation anomalies
sc-PDSI and 18-month SPI at Indore (India)
The importance of time-scales
• A critical issue in the study of the drought impacts is the multi-scalar nature of drought, since
the response of the hydrological (soil moisture, groundwater, river discharge, reservoir
storage, etc) and biological (crops, natural vegetation, etc) systems to water shortage varies
markedly and have different response times.
• This explains why severe drought conditions can be recorded in one system (e.g., low river
flows) whereas other systems in the same region (e.g., crops) have normal or even humid
conditions.
• The time period from the arrival of water inputs
to availability of a given usable resource differs
considerably. Thus, the time scale over which
water deficits accumulate becomes extremely
important,
and
functionally
separates
hydrological, environmental, agricultural and
other droughts. For this reason, drought indices
must be associated with a specific timescale to
be useful for monitoring and management of
different usable water resources.
• This explains the wide acceptance of the SPI.
SPI
SPI
SPI
SPI
The importance of time-scales
3
2
1
0
-1
-2
-3
3
2
1
0
-1
-2
-3
3
2
1
0
-1
-2
-3
3
2
1
0
-1
-2
-3
1-month
3-month
12-month
48-month
1950
1960
1970
1980
1990
2000
1.0
1.0
0.8
0.8
R-Pearson
R-Pearson
The importance of time-scales
0.6
0.4
0.2
SPEI
SPI
Inflows
0.6
0.4
0.2
0.0
SPEI
SPI
Storages
0.0
0
5
10
15
20
25
30
35
40
45
0
Time-scale
5
10
15
20
25
30
35
40
45
Time-scale
3
z-values
2
1
0
-1
-2
-3
1960
3-months SPEI
Inflows
1965
1970
1975
1980
1985
1990
1995
2000
2005
1970
1975
1980
1985
1990
1995
2000
2005
3
z-values
2
1
0
-1
-2
-3
1960
40-months SPEI
Reservoir storages
1965
Lorenzo-Lacruz, J., Vicente-Serrano, S.M., López-Moreno, J.I., Beguería, S., García-Ruiz, J.M., Cuadrat, J.M. (2010) The impact of droughts and water management on
various hydrological systems in the headwaters of the Tagus River (central Spain). Journal of Hydrology, 386: 13-26.
The importance of time-scales
3
SSI
2
1
0
-1
-2
-3
1950
1954
1958
1962
1966
1970
1975
1979
1983
1987
1991
1995
2000
2004
López-Moreno, J.I., S.M., Vicente-Serrano, J. Zabalza, S. Beguería, J. Lorenzo-Lacruz, C. Azorin-Molina, E. Morán-Tejeda. Hydrological response to climate variability at
different time scales: a study in the Ebro basin. Journal of Hydrology. Under review
The importance of time-scales
12
11
10
9
Month
8
7
6
PC
1
5
4
3
2
1
5
10
15
20
25
30
35
40
45
SPEI time-scale
12
11
10
9
Month
8
7
6
PC
1
5
4
3
2
1
5
10
15
20
25
30
SPEI time-scale
35
40
45
The importance of time-scales
Monthly 8 km. Global Inventory Modeling and
Mapping
Studies
(GIMMS)
Normalized
Difference Vegetation Index dataset obtained
from 25 years of daily NOAA-AVHRR satellite
data.
March 1993
March 1998
March 2003
March 2006
The importance of time-scales
North Mexico
20
18
14
12
10
8
16
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
20
18
14
12
10
8
16
20
18
14
12
10
8
16
8
6
4
4
2
2
2
2
Mar
Apr
May
Jun
J ul
Aug
Sep
Oct
Nov
D ec
Jan
Feb
Mar
Apr
May
Month
Jun
J ul
Aug
Sep
Oct
N ov
Jan
Dec
Feb
Mar
Apr
May
N-West Australia
South Africa
18
18
16
16
22
22
20
20
18
18
14
14
12
12
10
10
8
Sep
Oct
Nov
Dec
16
16
8
8
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
16
1
6
22
2
2
20
2
0
18
1
8
14
1
4
12
1
2
10
1
0
8
16
1
6
20
20
18
18
14
1
4
12
1
2
10
1
0
8
16
16
6
4
2
2
2
2
Au
Aug
g
Sep
O
Oct
ct
No
Nov
v
Dec
Jan
Feb
Mar
Ma r
Apr
Ap r
May
Ju
Jun
n
J ul
Month
Aug
Sep
Se p
Oct
O ct
N ov
Dec
De c
Ja n
Jan
Feb
Ma
Marr
Apr
May
Ma y
Jun
Jul
Ju l
Month
Aug
Au g
Sep
Oct
Nov
No v
Dec
Oct
N ov
Dec
Oct
O ct
N ov
Dec
De c
8
4
Ju
Jull
Sep
10
10
4
Month
Aug
12
12
4
Jun
J ul
14
14
4
May
Ma y
Jun
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
22
6
Apr
May
Kazakhstan
6
Mar
Ma r
Apr
24
24
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
6
Feb
Mar
Month
6
Ja n
Jan
Feb
Argentina
18
1
8
10
10
10
2
Feb
24
2
4
20
2
0
12
12
12
Month
22
2
2
14
14
14
4
Jan
24
2
4
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
SPEI Time-scale (month)
20
20
SPEI Ti me-scale (month)
22
22
Aug
East Africa
24
24
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
Jul
16
6
Month
Month
24
24
Jun
18
10
4
Feb
20
12
6
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
14
6
Jan
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
4
6
Ib. Pen.-Morocco
24
SPEI Ti me-scale (month)
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
SPEI Time-scale (month)
16
Sahel
24
SPEI Ti me-scale (month)
SPEI T ime-scale (month)
18
SPEI Ti me-scale (month)
20
SPEI Time-scale (month)
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
22
SPEI Ti me-scale (month)
N-East Brazil
24
24
SPEI Tim
Time-scale
e-scale (m
(month)
onth)
Canadian praires
24
2
Ja n
Jan
Feb
Ma
Marr
Apr
May
Ma y
Jun
Jul
Ju l
Month
Aug
Au g
Sep
Oct
Nov
No v
Dec
Jan
Feb
Mar
Ma r
Apr
Ap r
May
Jun
Ju n
J ul
Month
Aug
Sep
Se p
The importance of time-scales
The importance of time-scales
3.0
3.0
P.halepensis
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
19501955 1960 1965 1970 1975 1980 1985 1990 199520002005
3.0
Residual indices
2.5
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
Year
A.alba
3.0
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.3
3.0
0.2
J.thurifera
0.1
0.0
0.7
Year
P. sylvestris
Q. ilex
P. nigra
Q. faginea
J. thurifera
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1950 1955196019651970 1975 1980 1985 1990 1995 2000 2005
2.5
0.4
195019551960 1965 19701975198019851990199520002005
1950 1955196019651970 1975 1980 1985 1990 1995 2000 2005
2.5
0.5
1950 1955 1960 1965 1970 1975 1980198519901995 2000 2005
2.0
3.0
0.6
3.0
P.nigra
P. pinea
P. halepensis
0.7
0.0
0.0
2.5
0.8
P. pinea
Correlation
2.5
1950 1955 1960 1965 1970 1975 1980198519901995 2000 2005
0.0
3.0
Q.faginea
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
Q.ilex
0.7
P. sylvestris
A. alba
0.6
0.5
0.4
0.0
1950 1955196019651970 1975 1980 1985 1990 1995 2000 2005
1950 1955 1960 1965197019751980 1985 1990 1995 2000 2005
Years
Years
0.3
0.2
0.1
0.0
-0.1
0
5
10
15
20
25
30
35
40
45
Months
Pasho, E., J. Julio Camarero, Martín de Luis and Sergio M. Vicente-Serrano: Drought impacts on forest growth in a semi arid region in north-eastern Spain. Agricultural
and Forest meteorology. Under review.
The importance of time-scales
Promedio por especies
P. halepensis
Quercus sp.
Pasho, E., J. Julio Camarero, Martín de Luis and Sergio M. Vicente-Serrano: Drought impacts on forest growth in a semi arid region in north-eastern Spain. IAgricultural
and Forest meteorology. Under review.
The SPI calculation is based on two assumptions:
1. the variability of precipitation is much higher than that of other variables, such as temperature
and potential evapotranspiration (PET)
2. the other variables (PET) are stationary (i.e. they have no temporal trend).
In this scenario droughts are controlled by the temporal variability in precipitation. However, some authors
have warned against systematically neglecting the importance of the effect of temperature on drought
conditions.
There has been a general temperature increase (0.5-2°C) during the last past 150 years (Jones and
Moberg, 2003), and climate change models predict a marked increase during the 21st century (IPCC,
2007). It is expected that this will have dramatic consequences for drought conditions, with an
increase in water demand due to evapotranspiration (Sheffield and Wood, 2008; Dubrovsky et al.,
2008).
The use of drought indices which include temperature data in their formulation (such as the PDSI) is
preferable, especially for applications involving future climate scenarios.
However, the PDSI lacks the multi-scalar character essential for both assessing drought in relation to
different hydrological systems, and differentiating among different drought types.
We need a new drought index based on precipitation and PET and combining the sensitivity of
PDSI to changes in evaporation demand and the multi-temporal nature of the SPI. The index
must be suited to detecting, monitoring and exploring the consequences of global warming
on drought conditions.
The importance of the evapotranspiration processes on droughts
Syed et al. (2008): Water Resources Research, VOL. 44, W02433, doi:10.1029/2006WR005779, 2008
The importance of the evapotranspiration processes on droughts
Lobo, A. and Maisongrande, P., 2006. Hydrology and Earth System Sciences, 10: 151-164
The importance of the evapotranspiration processes on droughts
3
2
1
0
-1
-2
-3
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
3
2
1
0
-1
-2
-3
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
3
3
2
2
1
1
SPEI
SPI
SPEI
SPI
47ºN – 2º E
0
0
-1
-1
-2
-2
-3
-3
2002
2003
2004
2005
2002
2003
2004
2005
Sc-PDSI
6
4
2
0
-2
-4
-6
-8
Sc-PDSI
Under precipitation changes both the PDSI and the SPI are equally sensitive
6
4
2
0
-2
-4
-6
-8
Sc-PDSI-Original
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
4
Sc-PDSI
2010
Sc-PDSI-Precipitat ion change
2010
Difference
2
0
-2
-4
-6
SPI
3
2
1
0
-1
-2
-3
SPI
1910
3
2
1
0
-1
-2
-3
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPI (18 months)-Original
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPI (18 months)-Precipitat ion change
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
1.0
2010
Difference
SPI
0.5
0.0
-0.5
-1.0
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
PDSI and 18-month SPI at the Albuquerque (New Mexico, USA) observatory (1910−2007). Both indices were calculated from
precipitation series containing a linear reduction of 15% between 1910 and 2007. The difference between the indices is also
shown.
Sc-PDSI
6
4
2
0
-2
-4
-6
-8
Sc-PDSI
But under temperature changes only the PDSI is sensitive
6
4
2
0
-2
-4
-6
-8
Sc-PDSI-Original
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Sc-PDSI-Temperature change (2ºC)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
4
Sc-PDSI
2010
2010
Difference
2
0
-2
-4
-6
Sc-PDSI
1910
1920
1930
1940
1950
1960
1970
1980
6
4
2
0
-2
-4
-6
-8
1990
2000
Sc-PDSI-Temperature change (4ºC)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
4
Sc-PDSI
2010
2010
Difference
2
0
-2
-4
-6
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Evolution of the sc-PDSI at Albuquerque (New Mexico, USA) between 1910 and 2007, and under lineal temperature increase
scenarios of 2ºC and 4ºC during the same period. The difference between the indices is also shown.
The Standardized Precipitation Evapotranspiration Index (SPEI)
We describe here a simple multi-scalar drought index (the Standardised Precipitation
Evapotranspiration Index) that combines precipitation and temperature data.
The SPEI uses the monthly (or weekly) difference between precipitation and PET. This represents a simple
climatic water balance (Thornthwaite, 1948) which is calculated at different time scales to obtain the SPEI.
We followed the simplest approach to calculate PET (Thornthwaite, 1948), which has the advantage of only
requiring data on monthly mean temperature.
With a value for PET, the difference between the precipitation (P) and PET for the month i is calculated
according to:
Di = Pi-PETi,
The calculated D values are aggregated at different time scales:
k −1
D = ∑ Pn −i − PETn −i
k
n
i =0
where k (months) is the timescale of the aggregation and n is the calculation month.
The probability density function of a three parameter Log-logistic distributed variable is expressed as:
β ⎛ x −γ ⎞
f ( x) = ⎜
⎟
α⎝ α ⎠
β −1
⎛ ⎛ x −γ ⎞ ⎞
⎟
⎜1 + ⎜
⎜ ⎝ α ⎟⎠ ⎟
⎠
⎝
β
−2
where a, β and γ are scale, shape and origin parameters, respectively, for D values in the range (γ > D <∞ ).
Parameters of the Log-logistic distribution can be obtained following different procedures. Among them, the Lmoment procedure is the most robust and easy approach (Ahmad et al., 1988). When L-moments are
calculated, the parameters of the Pearson III distribution can be obtained following Singh et al. (1993):
2w1 − w0
β=
6w1 − w0 − 6w2
α=
where Γ(β) is the gamma function of β.
( w0 − 2 w1 )β
Γ(1 + 1 β )Γ (1 − 1 β )
γ = w0 − αΓ (1 + 1 β )Γ (1 − 1 β )
The probability distribution function of the D series according to the Log-logistic distribution is given by:
⎡ ⎛ α
F ( x ) = ⎢1 + ⎜⎜
⎢⎣ ⎝ x − γ
⎞
⎟⎟
⎠
β
⎤
⎥
⎥⎦
−1
F(x) values for the D series at different time scales adapt very well to the empirical F(x) values at the
different observatories, independently of the climate characteristics and the time scale of the analysis.
1.0
1.0
1.0
Albuquerque
Albuquerque
0.8
Albuquerque
(12 months)
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.0
-300
-200
-100
0.0
-400
0
-300
P-PET
-200
-100
0.0
-700
0
-500
-200
0.0
-1200
-100
Sao Paulo
(6 months)
(12 months)
0.8
0.8
0.4
0.2
0.2
0.2
0.2
0.0
0.0
0.0
-200
800
1000
-200
0
200 400
P-PET
200 400 600 800 1000 1200 1400 1600
0.8
0.6
F(x)
F(x)
0.6
0.4
0.4
0.4
0.2
0.2
0.2
100
P-PET
200
300
0.0
-200
0.0
0
200
P-PET
400
(24 months)
0.8
0.2
0
2000
Helsinki
(12 months)
0.4
0.0
-100
1500
1.0
Helsinki
(6 months)
0.6
F(x)
0.6
1000
F(x)
0.8
500
P-PET
1.0
Helsinki
(3 months)
0
P-PET
1.0
Helsinki
(24 months)
0.0
0
P-PET
1.0
0.8
600 800 1000 1200 1400
-200
F(x)
F(x)
0.4
600
-400
0.6
0.4
400
-600
Sao Paulo
0.8
0.4
200
-800
P-PET
0.6
F(x)
0.6
0
-1000
1.0
Sao Paulo
(3 months)
F(x)
-300
1.0
Sao Paulo
0.6
-400
P-PET
1.0
0.8
-600
P-PET
1.0
(24 months)
0.8
0.6
F(x)
0.6
F(x)
0.6
1.0
Albuquerque
(6 months)
0.8
F(x)
(3 months)
F(x)
0.8
0.0
0
200
400
P-PET
600
800
0
200
400
600
800
1000
1200 1400
P-PET
Theoretical according the Log-logistic distribution (black line) vs. empirical (dots) F(x) values for D series at
time scales of 3, 6, 12 and 24 months for the observatories at Albuquerque, Sao Paulo and Helsinki.
With F(x) the SPEI can easily be obtained as the standardized values of F(x). For example, following the
classical approximation of Abramowitz and Stegun (1965).
Sc-PDSI
3
2
1
0
-1
-2
-3
1930
1940
1950
1960
SPEI
SPI
3
2
1
0
-1
-2
-3
1920
3
2
1
0
-1
-2
-3
SPEI
SPI
3
2
1
0
-1
-2
-3
SPI
1910
3
2
1
0
-1
-2
-3
SPEI
Sc-PDSI
6
4
2
0
-2
-4
-6
3
2
1
0
-1
-2
-3
SPI (3 months)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
1990
2000
2010
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
SPEI (12 months)
1910
SPI (24 months)
1980
SPEI (3 months)
1910
SPI (12 months)
1910
1970
1920
1930
1940
1950
1960
SPEI (24 months)
1910
1920
1930
1940
1950
1960
sc-PDSI, 3-, 12- and 24-month SPI and SPEI at Sao Paulo (1910−2007).
Under warming conditions…
0.8
1. 0
Albuquer que
(3 months)
0. 8
(6 months)
0.8
F(x)
0.4
0. 4
0.4
0.2
0. 2
0.2
0.0
0. 0
0.0
-800
-50
0
50
100
-300
-200
P-PET
0.8
0
1. 0
Sao Paulo
(3 months)
0. 8
1.0
Sao Paulo
(6 months)
0.8
F(x)
F(x)
0. 4
0.4
0.2
0. 2
0.2
200
400
0. 0
-200
600
0
200
400
P -PE T
0.8
1. 0
(3 months)
0. 8
600
800
1000
1.0
1.0
( 6 months)
500
0.8
1. 0
Helsinki
(12 months)
F(x)
0. 2
0.0
-100
0. 0
-200
0.0
300
400
1. 0
(3 months)
0. 8
1.0
Albuquerque
0.8
200
400
600
800
0
1.0
Albuquerque
(12 months)
0.8
F(x)
F(x)
0. 4
0.4
0.4
0.2
0. 2
0.2
0.2
0.0
0. 0
0.0
-150
-100
-50
0
50
-600
-400
-200
P -P E T
0.8
-800
0
-600
-400
P-P E T
1. 0
Sao Paulo
(3 months)
0. 8
(6 months)
0.8
-200
Sao Paulo
(12 months)
0.4
0.4
0. 2
0.2
0.2
0.0
-400
0. 0
-400
0.0
-400 -200
400
600
-200
0
200
0.8
600
800
1000
1. 0
Helsinki
(3 months)
0. 8
1.0
( 6 months)
0.8
0.4
0. 4
0.4
0.2
0. 2
0.2
0.0
-100
0
100
P -P E T
200
400
200
300
600 800 1000 1200 1400
0. 0
-200
-500
1. 0
Helsinki
(12 months)
0
100
P-P E T
500
200
300
400
1000
1500
2000
Helsinki
( 24 months)
0. 8
0. 6
0. 4
0. 2
0.0
-100
0
P -P ET
0.6
F(x)
0. 6
F(x)
0.6
(24 months)
P -P ET
Helsinki
-200
0.0
0
P -P E T
F(x)
1.0
400
-400
F(x)
200
-600
0.6
0. 4
P -PE T
1400
Sao Paulo
0.8
0.2
0
1200
P -PE T
1.0
0.4
-200
1000
(24 months)
0.0
-1600 -1400 -1200 -1000 -800
0
0.6
F(x)
0. 6
F(x)
0.6
1.0
Sao Paulo
800
Albuquerque
P -PE T
F(x)
1.0
600
F(x)
-200
400
0.6
0.4
-250
200
P -P E T
0.6
0. 6
F(x)
0.6
( 24 months)
P -P E T
(6 months)
2000
0. 0
0
P-P E T
Albuquer que
1500
F(x)
0.8
200
1000
0. 6
0. 4
1.0
500
Helsinki
0. 8
0.2
100
0
P -P ET
0.4
0
(24 months)
0.0
-500
1000
0.6
-100
-200
0.2
0
0. 2
300
-400
0.4
0. 4
200
-600
0.6
0.2
100
-800
P -P ET
Helsinki
P -P E T
-1000
Sao Paulo
0.8
0.4
0
-1200
P -P E T
(12 months)
0.0
-500
1200
0. 6
F(x)
0.6
0. 0
-1400
0
Sao Paulo
P -P E T
Helsinki
-200
F(x)
1.0
-400
F(x)
0
0. 2
-600
0.6
0.4
-200
0. 4
P -P E T
0. 6
0.0
( 24 months)
0. 6
P-P E T
0.6
B)
-100
Albuquerque
0. 8
F(x)
1.0
(12 months)
F(x)
-100
1. 0
Albuquer que
0.6
0. 6
F(x)
0.6
1.0
Albuquerque
F(x)
1.0
F(x)
A)
0. 0
0
200
400
P -P E T
600
800
0
200
400
600
800
1000 1200 1400
P -P E T
Theoretical according the log-logistic distribution (black line) vs. empirical (dots) F(x) values for D series at time scales of
3, 6, 12 and 24 months for the observatories at Albuquerque, Sao Paulo and Helsinki. A) Temperature increase of 2ºC.
B) Temperature increase of 4 ºC.
Sc-PDSI
8
6
4
2
0
-2
-4
-6
-8
Sc-PDSI
8
6
4
2
0
-2
-4
-6
-8
Sc-PDSI
8
6
4
2
0
-2
-4
-6
-8
SPI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
Sc-PDSI
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Sc-PDSI + 2ºC
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Sc-PDSI + 4ºC
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
SPI (18 months)
1910
1920
1930
1940
1950
1960
SPEI (18 months)
1910
1920
1930
1940
1950
1960
SPEI (18 months) + 2ºC
1910
1920
1930
1940
1950
1960
SPEI (18 months) + 4ºC
1910
1920
1930
1940
1950
1960
Evolution of the sc-PDSI, and 18-month SPI and SPEI in Abashiri (Japan). The original series
(1910−2007) and the sc-PDSI and SPEI were calculated for a temperature series with a lineal increase
of 2ºC and 4ºC throughout the analyzed period.
Sc-PDSI
8
6
4
2
0
-2
-4
-6
-8
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
SPEI
3
2
1
0
-1
-2
-3
Sc-PDSI
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (1 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (3 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (6 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (12 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (18 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
SPEI (24 month)
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Evolution of the sc-PDSI, and 1-, 3-, 6-, 12-, 18- and 24-month SPEI at Tampa
(Florida, USA) under a 4ºC temperature increase scenario relative to the origin
• According to the sc-PDSI, under global warming temperature will play a more important role than precipitation in
explaining drought conditions. This phenomenon can also be assessed using the SPEI, which was very similar to the
sc-PDSI under the two temperature increase scenarios tested. This suggests that the SPEI should be used in
preference to the sc-PDSI, given the former index’s simplicity, lower data requirements and multi-scalar properties.
• The SPEI can account for the possible effects of temperature variability and temperature extremes beyond the
context of global warming. Therefore, given the minor additional data requirements of the SPEI relative to the SPI,
use of the former is preferable for the identification, analysis and monitoring of droughts in any climate region of the
world.
• The SPEI fulfils the requirements of a drought index since its multi-scalar character enables it to be used by
different scientific disciplines/sectors to detect, monitor and analyze droughts. Like the sc-PDSI and the SPI, the SPEI
can measure drought severity according to its intensity and duration, and can identify the onset and end of drought
episodes. The SPEI allows comparison of drought severity through time and space, since it can be calculated over a
wide range of climates, as can the SPI. The SPEI is statistically robust and easily calculated, and has a clear and
comprehensible calculation procedure.
• A crucial advantage of the SPEI over the most widely used drought indices that
consider the effect of PET on drought severity is that its multi-scalar characteristics
enable identification of different drought types and impacts in the context of global
warming.
Advantages of the SPEI
Moscow (Russia)
3
2
SPI
1
0
-1
-2
-3
1960
1970
1980
1990
2000
2010
1960
1970
1980
1990
2000
2010
3
SPEI
2
1
0
-1
-2
-3
2000
2010
2000
2010
Advantages of the SPEI
Advantages of the SPEI
Advantages of the SPEI
Advantages of the SPEI
3
2
1
0
-1
-2
-3
SSI
PDSI
z-units
Mississippi
6
4
2
0
-2
-4
-6
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
z-units
z-units
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
3
2
1
0
-1
-2
-3
(sc)PDSI
4-month SPEI
3
2
1
0
-1
-2
-3
17-months SPEI
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
3
2
1
0
-1
-2
-3
SSI
PDSI
z-units
St. Lawrence
6
4
2
0
-2
-4
-6
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
z-units
z-units
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
3
2
1
0
-1
-2
-3
31-month SPEI
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
(sc)PDSI
3
2
1
0
-1
-2
-3
14-months SPEI
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Tools and datasets
http://sac.csic.es/spei/
Tools and datasets
http://sac.csic.es/spei/
Tools and datasets
Updates and improvements:
Method of calculation of the log-logistic parameters: unbiased estimator,
maximum likelihood.
Including different options to obtain the PET (Hargreaves, Penmann).
Dataset updated to 2009.
Real time monitoring from global products.
References:
Vicente-Serrano S.M., Santiago Beguería, Juan I. López-Moreno, (2010) A Multiscalar drought index sensitive to global warming: The Standardized Precipitation
Evapotranspiration Index – SPEI. Journal of Climate 23: 1696-1718.
Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I., Angulo, M., El Kenawy,
A. (2010): A new global 0.5° gridded dataset (1901-2006) of a multiscalar drought
index: comparison with current drought index datasets based on the Palmer
Drought Severity Index. Journal of Hydrometeorology. 11: 1033–1043
Beguería, S., Vicente-Serrano, S.M. Angulo, M., (2010): A multi-scalar global
drought data set: the SPEIbase: A new gridded product for the analysis of
drought variability and impacts. Bulletin of the American Meteorological Society.
91, 1351-1354
Vicente-Serrano, S.M., Juan I. López-Moreno, Santiago Beguería, Jorge
Lorenzo-Lacruz, Cesar Azorin-Molina and Enrique Morán-Tejeda (2011):
Accurate computation of a streamflow index. Journal of Hydrologic Engineering
doi:10.1061/(ASCE)HE.1943-5584.0000433