Performance of Drought Indices for Ecological, Agricultural, and Hydrological Applications

TL;DR: In this article, the performance of different drought indices for monitoring drought impacts on several hydrological, agricultural, and ecological response variables was evaluated. And the authors found that the SPEI was the index that best captured the responses of the assessed variables to drought in summer, the seas...

Abstract: In this study, the authors provide a global assessment of the performance of different drought indices for monitoring drought impacts on several hydrological, agricultural, and ecological response variables. For this purpose, they compare the performance of several drought indices [the standardized precipitation index (SPI); four versions of the Palmer drought severity index (PDSI); and the standardized precipitation evapotranspiration index (SPEI)] to predict changes in streamflow, soil moisture, forest growth, and crop yield. The authors found a superior capability of the SPEI and the SPI drought indices, which are calculated on different time scales than the Palmer indices to capture the drought impacts on the aforementioned hydrological, agricultural, and ecological variables. They detected small differences in the comparative performance of the SPI and the SPEI indices, but the SPEI was the drought index that best captured the responses of the assessed variables to drought in summer, the seas...

Summary

1. Introduction

• Drought is among the most complex climatic phenomena affecting society and the environment (Wilhite, 1993).
• As a result, at present there is high uncertainty among scientists, managers and end users of drought information when they aim to select one drought index for a specific purpose.
• For this purpose, the authors compare two of the most widely used drought indices, the Standardized Precipitation Index, SPI (McKee et al., 1993), and four versions of the Palmer Drought Severity Index, PDSI (Palmer, 1965).
• In addition, the authors also include in their comparison the recently developed Standardized Precipitation Evapotranspiration Index (SPEI), which has been claimed to outperform the two previous indices (Vicente-Serrano et al., 2010b).

2.1. Drought indices

• The PDSI was a landmark in the development of drought indices.
• It enables measuring both wetness (positive value) and dryness (negative values), based on the supply and demand concepts of the water balance equation, and thus incorporates prior precipitation, moisture supply, runoff and evaporation demand at the surface level.
• Therefore, in this study the authors have used the self-calibrated versions of the four Palmer drought indices, which are more suitable for drought quantification and monitoring at a global scale than the corresponding Palmer indices.
• The Standardized Precipitation Index (SPI) The Standardized Precipitation Index (SPI) was proposed by McKee et al. (1993) and it has been increasingly used during the two last decades because of its solid theoretical development, robustness and versatility in drought analyses (Redmond, 2002).
• Therefore, here the authors use the algorithm described by Vicente-Serrano (2006) and López-Moreno and Vicente-Serrano (2008) to calculate 1- to 48-month SPI values based on the Pearson III distribution and the L-moments approach to obtain the distribution parameters.

2.2. Datasets

• The six drought indices here assessed (PDSI, PHDI, WPLM, Z-index, SPI and SPEI) were computed globally based on the CRU TS3.1 climate dataset (Mitchell and Jones, 2005; available online at http://badc.nerc.ac.uk/data/cru/), covering the period 1901-2009 at a spatial resolution of 0.5º.
• 2011) the measurements at the different sites are recorded in the same units (% of the water field capacity) and given that each sample was compared independently with the different drought indices, the techniques of soil moisture measurements did not affect the analyses.
• Concerning tree growth data, the authors compiled 1840 annual tree-ring width series or mean site chronologies encompassing the period 1945-2009 and archived by the National Climate Data Center (NCDC) in the International Tree-Ring Data Bank, ITRDB (Grissino-Mayer and Fritts, 1997; available online at: http://www.ncdc.noaa.gov/paleo/treering.html) .
• Time series of annual crop productions in 173 countries were selected considering only those time series with a minimum of 15 years of records.

2.3. Methods

• The different drought indices were calculated using the monthly precipitation and mean temperature of the CRU TS3.1 dataset.
• Therefore, the authors obtained one precipitation and one temperature series for each basin.
• The latitude necessary to obtain the SPEI and the Palmer indices, and the water field capacity used in the Palmer indices were also weighted for each country according to the percentage of surface cultivated by wheat.
• Therefore, the SPI and the SPEI were calculated at different time scales from 1 up to 48 months.
• Since the times of response to drought of the different systems is not known a priori, the Pearson correlation coefficients (r) between the time series of these variables and the 1- to 48-month SPI and SPEI series were computed, and the time-scale at which the strongest correlation was found was kept for further analyses.

3.1. Streamflow data

• Figure 2 shows a box plot illustrating the correlations obtained between the SSI series at 151 worldwide basins and the six assessed drought indices.
• In general, correlations tended to be higher for the SPI and the SPEI indices than for the Palmer ones (PDSI, PHDI, Z-index and WPLM).
• Figure 4 shows the spatial distribution of correlations between the SSI series and four of the most widely used drought indices (SPI, SPEI, PDSI, Z-index) either considering continuous series or separately for January and July monthly series.
• On the contrary, poor correlations were found in the Asian basins, mainly those that drain to the Arctic Ocean.
• In addition, in these zones it is clearly observed that differences between the SPI and SPEI correlations were important during the summer months, with the SPEI showing higher correlations than the SPI.

3.2. Soil moisture

• Figure 5 shows the box plots displaying the correlations between the different drought indices and the monthly soil moisture data obtained from April to October.
• Strong differences arise when comparing the SPI and the SPEI and the Palmer drought indices, with the first two indices outperforming the latter in all cases.
• The highest correlation between soil moisture and drought was found using the SPI or SPEI indices in a range of stations varying from 80% to 95% depending on the analyzed month, whereas in only 5 to 15% of the sites the highest correlation was found with the Palmer indices (Table 2).
• It was in the warmest months (July, August and September), in which evapotranspiration rates are the highest, when a much higher percentage of sites showed higher correlations with the SPEI than with the SPI.
• Higher correlations are found again with the SPI and the SPEI.

3.3. Tree-ring width series

• Correlations between tree-ring width series and the drought indices are depicted in Figure 7.
• The median of the correlations oscillated between 0.44 for the SPI and 0.30 for the PHDI.
• In humid sites of the East, North and North-West USA, where tree-ring growth is less constrained by drought, the authors obtain lower growth-drought correlations than elsewhere, independently of the selected drought index.
• Again, higher growth-drought correlation values were also found for the SPI and the SPEI than for the PDSI and Z indices.
• With a few exceptions, the highest correlations in the different forests corresponded to the SPI or the SPEI .

3.4. Wheat crop yields

• A summary of the relationship between the global wheat yields and the six different drought indices is illustrated in the Figure 10, which records the maximum correlation between the annual wheat yields and the drought indices independently of the month of the year in which the highest correlation was found.
• This approach minimizes the impact of the different crop cycles and harvest dates in the different parts of the world.
• Important differences were found between the Palmer indices since the Z-index provided much better results than the other three indices.
• Large differences in the influence of drought conditions on wheat crop productions are evident across the world.
• In any case, when the countries were classified according to the drought index showing the highest yield-drought correlation, the authors found that the wheat yields of most of the analyzed countries of the world were best correlated with the SPEI (49.5%) or with the SPI (34.3%).

4. Discussion and conclusions

• This study has provided the first global assessment of different indices to detect drought impacts on hydrological, ecological and agricultural systems.
• The magnitudes of the correlations between various hydrological, agricultural and ecological variables and the compared drought indices clearly show that the SPI and the SPEI are more capable to monitor drought conditions in different systems.
• This finding does not mean that the Palmer indices are not useful for some purposes.
• The difference in the percentage of maximum correlations between SPI and SPEI is about 10% higher for the SPEI than for the SPI in the different analyzed systems. ii).

Figures

Figure 4. Spatial distribution of correlation coefficients obtained between the Standardized Streamflow Index (SSI) and several drought indices (SPI, SPEI, PDSI and Z-index). A) Correlations considering continuous series from January 1948 up to September 2004, B) Correlations considering only the January series, C) Correlations considering only the July series, D) Drought index which presented the maximum correlation with the continuous (January 1948-September 2004), January and July SSI series.

Figure 9. Spatial distribution of correlation coefficients obtained between the tree-ring width chronologies and several drought indices (SPI, SPEI, PDSI and Z-index) in the USA. A) Maximum annual correlations independently of the month of the year, B) Correlations considering only the January (B) and July (C) drought series, D) Drought index showing the maximum correlation with tree growth for the annual, January and July drought series.

Figure 3. Box plots showing the correlations between the monthly series of the Standardized Streamflow Index (SSI) in 151 basins across the world and the six drought indices compared in this study.

Figure 10. Box plots showing correlation coefficients between the wheat yields in 173 countries and the six drought indices compared in this study. The graph represents the maximum correlations found for any of the twelve monthly series.

Figure 6: Spatial distribution of correlation coefficients obtained between the July soil moisture and several drought indices (SPI, SPEI, PDSI and Z-index) in North America. A) July correlations, B) Drought index which showed the maximum correlation with soil moisture in July

Table 2: Percentage of the 117 analyzed sampling points at which the maximum correlation with the standardized soil moisture series is found for any of the six drought indices compared. The percentages are given for the monthly series from April up to October.

Figure 7. Box plots showing correlation coefficients obtained between the tree-ring width series in 1840 worlwide forests and the six drought indices compared in this study. The graph represents the maximum correlations found for any of the twelve monthly series.

Figure 2. Box plots (the solid and dashed lines within the boxes correspond to the median and mean values, respectively) showing the correlations (Pearson coefficient) between the continuous series of the Standardized Streamflow Index (SSI) in 151 basins across the world and the six drought indices compared in this study.

Figure 11: Spatial distribution of correlation coefficients obtained between the annual wheat yields and several drought indices (SPI, SPEI, PDSI and Z-index). A) Maximum annual correlations independently of the month of the year, B) Drought index showing the maximum correlation with crop yield for the different monthly series of the drought indices. The countries with white areas lack wheat cultivation or do not have available long time series of wheat yields.

Figure 8. Box plots showing correlation coefficients obtained between the annual treering width series in 1840 forests located across the world and the monthly series of the six drought indices compared in this study.

Figure 5. Box plots showing the correlation coefficients obtained between the monthly series of the Standardized Soil Moisture data in 117 sampling points across the world and the six drought indices assessed in this study.

Figure 1. Response variables used in this study: A) Basins with monthly streamflow data for the period 1945-2004, B) soil moisture sample series with at least 10 years with data for the period 1950-2009, C) tree-ring width series with at least 25 years of data for the period 1945-2009, D) countries with series of wheat productions with at least 10 years of data for the period 1960-2009 (black outline). In D) the colors represent the percentage of lands cultivated by wheat, which was used as a weight to obtain the precipitation and temperature series, the water field capacity and the latitude used to obtain the time series of drought indices for each country.

Table 3: Percentage of the 1840 analyzed tree-ring width showing the maximum correlation is found for any of the six drought indices compared. The percentages are given for the annual maximum correlations, independently of the month of the year in which they are found, and for each one of the monthly series.

Table 1: Percentage of the 151 analyzed worldwide basins at which the maximum correlation with the SSI series is found for any of the six drought indices compared. The percentages are given for the continuous SSI series and for each one of the monthly series.

Full text

PERFORMANCE OF DROUGHT INDICES FOR ECOLOGICAL, AGRICULTURAL AND
HYDROLOGICAL APPLICATIONS
Sergio M. Vicente-Serrano
1,
*, Santiago Beguería
2
, Jorge Lorenzo-Lacruz
1
, Jesús Julio Camarero
3
,
Juan I. López-Moreno
1
, Cesar Azorin-Molina
1
, Jesús Revuelto
1
, Enrique Morán-Tejeda
1
and Arturo
Sánchez-Lorenzo
4
1
Instituto Pirenaico de Ecología, Consejo Superior de Investigaciones Científicas (IPE-CSIC), Campus de
Aula Dei, P.O. Box 13034, E-50059, Zaragoza, Spain
2
Estación Experimental de Aula Dei, Consejo Superior de Investigaciones Científicas (EEAD-CSIC),
Zaragoza, Spain
3
ARAID-Instituto Pirenaico de Ecología, CSIC (Consejo Superior de Investigaciones Científicas), Campus
de Aula Dei, P.O. Box 13034, E-50059, Zaragoza, Spain
4
Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
* Corresponding author: svicen@ipe.csic.es
Abstract: In this study we provide a global assessment of the performance of different drought
indices for monitoring drought impacts on several hydrological, agricultural and ecological
response variables. For this purpose, we compare the performance of several drought indices (the
Standardized Precipitation Index, SPI; four versions of the Palmer Drought Severity Index, PDSI;
and the Standardized Precipitation Evapotranspiration Index, SPEI) to predict changes in
streamflow, soil moisture, forest growth and crop yield. We found a superior capability of the SPEI
and the SPI drought indices, which are calculated on different time-scales, than the Palmer indices
to capture the drought impacts on the aforementioned hydrological, agricultural and ecological
variables. We detected small differences in the comparative performance of the SPI and the SPEI
indices, but the SPEI was the drought index that best captured the responses of the assessed
variables to drought in summer, the season in which more drought-related impacts are recorded and
in which drought monitoring is critical. Hence, the SPEI index shows improved capability to
identify drought impacts as compared with the SPI one. In conclusion, it seems reasonable to
recommend the use of the SPEI if the responses of the variables of interest to drought are not known
a priori.

Key-words: Drought index, drought vulnerability, agricultural droughts, dendrochronology,
hydrological droughts, Standardized Precipitation Evapotranspiration Index (SPEI), Standardized
Precipitation Index (SPI), Palmer Drought Severity Index (PDSI).
1. Introduction
Drought is among the most complex climatic phenomena affecting society and the environment
(Wilhite, 1993). The root of this complexity is related to the difficulty of quantifying drought
severity since we identify a drought by its effects or impacts on different types of systems
(agriculture, water resources, ecology, forestry, economy, etc.), but there is not a physical variable
we can measure to quantify droughts. Thus, droughts are difficult to pinpoint in time and space
since it is very complex to identify the moment when a drought starts and ends, and also to quantify
its duration, magnitude and spatial extent (Burton et al., 1978; Wilhite, 2000).
These characteristics explain the vast scientific effort devoted to develop tools providing an
objective and quantitative evaluation of drought severity. The quantification of drought impacts is
commonly done by using the so-called drought indices, which are proxies based on climatic
information and assumed to adequately quantify the degree of drought hazard exerted on sensitive
systems. Many studies have shown strong relationships between the temporal variability of different
drought indices and response variables of natural systems such as tree growth (e.g., Orwig and
Abrams, 1997; Copenheaver et al., 2011; Pasho et al., 2011), river discharge (e.g., Vicente-Serrano
and López-Moreno, 2005; Hannaford et al., 2011), groundwater level (Khan et al., 2008; Fiorillo
and Guadagno, 2010), crop yields (e.g., Vicente-Serrano et al., 2006; Vergni and Todisco, 2011),
vegetation activity (e.g., Lotsch et al., 2003; McAuliffe and Hamerlynck, 2010; Vicente-Serrano,
2007), the frequency of forest fires (Littell et al., 2009; Drobyshev et al., 2012), etc. Drought
indices are currently used to monitor drought conditions in real time manner that is easily
understood by end users (Svoboda et al., 2002; Shukla et al., 2011). Indeed, drought monitoring has

been recognized as crucial for the implementation of drought plans (Wilhite, 1996; Wilhite et al.,
2007).
Recent works have reviewed the development of drought indices and compared their advantages
and drawbacks (Heim, 2002; Keyantash and Dracup, 2002; Mishra and Singh, 2010; Sivakumar et
al., 2010). However, very few studies have performed robust statistical assessments by comparing
different drought indices which may allow recommending the preferential use of one of them based
on objective criteria (Guttman, 1998; Keyantash and Dracup, 2002; Steinemann, 2003; Paulo and
Pereira, 2006; Quiring, 2009; Vicente-Serrano et al., 2010; Barua et al., 2011; Anderson et al.,
2011). In addition, few researchers have compared the relative performance of different drought
indices to identify drought impacts on several systems. In the case of drought impacts on
hydrological systems, Vasiliades et al., (2011) compared five drought indices in Greece. Lorenzo-
Lacruz et al. (2010) compared the performance of two drought indices to identify hydrological
droughts in river discharges and reservoir storages in central Spain, and Zhai et al. (2010) compared
the relationship between the Standardized Precipitation Index (SPI) and the Palmer Drought
Severity Index (PDSI) and streamflow data in ten regions of China. Sims et al. (2002) compared the
PDSI and the SPI to assess soil moisture variations in North Carolina, USA. In relation to
vegetation activity and crop productivity, Potop (2011) compared different indices to assess drought
impacts on corn yields in Moldava, and Mavromatis (2007) and Quiring and Papakryiakou (2003)
followed a similar approach by quantifying wheat production in Greece and the Canadian prairies,
respectively. Quiring and Ganesh (2010) compared drought indices to assess the responses of
vegetation activity to drought severity in Texas (USA). Kempes et al. (2008) assessed tree-ring
growth response to different drought indices in the southwestern USA. Recently, Drobyshev et al.
(2012) analyzed the correlation between different drought indices and fire frequency in Sweden.
The results of these studies are diverse, since the best drought index for detecting impacts changes
as a function of the analyzed system and the performance of the drought indices varied spatially. As

a result, at present there is high uncertainty among scientists, managers and end users of drought
information when they aim to select one drought index for a specific purpose.
To the best of our knowledge, at present there is no global study analyzing and comparing to which
degree the most widely used drought indices are able to identify drought impacts on vulnerable
systems. This task is necessary in order to have solid and objective criteria for selecting a drought
index to be used for specific tasks. In this study we provide the first global assessment of the
performance of different drought indices for monitoring drought impacts on streamflows, soil
moisture, forest growth and crop yields. For this purpose, we compare two of the most widely used
drought indices, the Standardized Precipitation Index, SPI (McKee et al., 1993), and four versions
of the Palmer Drought Severity Index, PDSI (Palmer, 1965). In addition, we also include in our
comparison the recently developed Standardized Precipitation Evapotranspiration Index (SPEI),
which has been claimed to outperform the two previous indices (Vicente-Serrano et al., 2010b).
2. Datasets and methods
2.1. Drought indices
a) The Palmer Drought Indices
The PDSI was a landmark in the development of drought indices. It enables measuring both wetness
(positive value) and dryness (negative values), based on the supply and demand concepts of the
water balance equation, and thus incorporates prior precipitation, moisture supply, runoff and
evaporation demand at the surface level. Although the PDSI presents several deficiencies (Alley,
1984; Karl, 1986; Soulé, 1992; Akimremi et al., 1996; Weber and Nkemdirim, 1998; Vicente-
Serrano et al., 2011), currently it is still one of the most widely used drought indices. The PDSI is
calculated based on precipitation and temperature data, as well as the water content of the soil. All
the basic terms of the water balance equation can be determined from those inputs, including
evapotranspiration, soil recharge, runoff, and moisture loss from the surface layer. The complete

calculation procedure of the PDSI can be consulted in many publications (e.g., Karl, 1983 and
1986; Alley, 1984).
The modified Palmer Drought Severity Index (WPLM) was proposed by the National Weather
Service Climate Analysis Center for operational meteorological purposes (Heddinghaus and Sabol
1991), modifying the original rules of accumulation during wet and dry spells.
The Palmer Hydrological Drought index (PHDI) was derived from the PDSI to quantify the long-
term impact of drought on hydrological systems. Values of the PHDI tend to be negative for up to
several months after PDSI have returned to normal levels, i.e. it usually returns to near-normal
levels more gradually than the PDSI (Karl et al., 1987). Therefore, the PHDI is considered a
measure of long-term hydrological drought since streamflows, reservoir storages and groundwater
tend to stay below normal values for some time after a meteorological drought ends. Finally, the
Palmer Z-Index is also derived from the Palmer model and it is much more responsive to short-term
moisture deficiencies than the PDSI. The Palmer Z-Index shows how monthly moisture conditions
depart from normal, and it is sensitive to unusual wet (and dry) months even in extended dry (or
wet) spells. Therefore, the Palmer Z-index is usually used for the detection of short term droughts.
One of the main problems of the Palmer indices is that the parameters necessary to calculate them
were determined empirically and mainly tested in the USA, which restricts its use in other regions
(see Akimremi et al., 1996) and limits the geographical comparisons based on the PDSI (Heim,
2002; Guttman et al., 1992). This problem was solved by developing of the self-calibrated Palmer
indices (Wells et al., 2004), which are spatially comparable and report extreme wet and dry events
at frequencies expected for rare conditions. Therefore, in this study we have used the self-calibrated
versions of the four Palmer drought indices, which are more suitable for drought quantification and
monitoring at a global scale than the corresponding Palmer indices.
b) The Standardized Precipitation Index (SPI)

Frequently asked questions

Q1. What have the authors contributed in "Performance of drought indices for ecological, agricultural and hydrological applications" ?

In this study the authors provide a global assessment of the performance of different drought indices for monitoring drought impacts on several hydrological, agricultural and ecological response variables. For this purpose, the authors compare the performance of several drought indices ( the Standardized Precipitation Index, SPI ; four versions of the Palmer Drought Severity Index, PDSI ; and the Standardized Precipitation Evapotranspiration Index, SPEI ) to predict changes in streamflow, soil moisture, forest growth and crop yield. The authors detected small differences in the comparative performance of the SPI and the SPEI indices, but the SPEI was the drought index that best captured the responses of the assessed variables to drought in summer, the season in which more drought-related impacts are recorded and in which drought monitoring is critical. 

Q2. What is the reason why Zhao and Running have recently shown that the annual ANPP decreased?

Zhao and Running (2010) have recently shown at a global scale that between 2000 and 2009 the annual ANPP decreased because of the combined effects of severe drought stress and high temperatures which induced high autotrophic respiration levels, indicating that ANPP decreases because of warming-associated drying trends. 

Q3. How is the drought a quantitative measure of the degree of hazard?

The quantification of drought impacts is commonly done by using the so-called drought indices, which are proxies based on climatic information and assumed to adequately quantify the degree of drought hazard exerted on sensitive systems. 

Q4. What is the role of temperature in the onset of drought?

The strong role of temperature as a major driver of drought severity was evident in the devastating 2003 central European heat wave, which drastically reduced tree growth and the Aboveground Net Primary Production (ANPP) across most of the continent (Ciais et al., 2005). 

Q5. What is the percentage of countries with the highest correlation with the Palmer indices?

The percentage of countries in which the highest correlation was found with one of the different Palmer indices was quite low (2.9% for the PDSI, 5.7% for the PHDI, 2.9% for the Z-index and 4.8% for the WPLM). 

Q6. What is the correlation between soil moisture and drought?

It is interesting to note that correlations between soil moisture and drought indices were higher from July to October than for other months, being the former a period in which soils tend to be less saturated by water than in spring. 

Q7. Did the techniques of soil moisture measurements affect the analyses?

Although the world soil moisture network uses different instruments and techniques (Dorigo et al., 2011) the measurements at the different sites are recorded in the same units (% of the water field capacity) and given that each sample was compared independently with the different drought indices, the techniques of soil moisture measurements did not affect the analyses.