Droughts are serious natural hazards, especially in semi-arid regions. They are also difficult to characterize. Various summary metrics representing the dryness level, denoted drought indices, have been developed to quantify droughts. They typically lump meteorological variables and can thus directly be computed from the outputs of regional climate models in climate-change assessments. While it is generally accepted that drought risks in semi-arid climates will increase in the future, quantifying this increase using climate model outputs is a complex process that depends on the choice and the accuracy of the drought indices, among other factors. In this study, we compare seven meteorological drought indices that are commonly used to predict future droughts. Our goal is to assess the reliability of these indices to predict hydrological impacts of droughts under changing climatic conditions at the annual timescale. We simulate the hydrological responses of a small catchment in northern Spain to droughts in present and future climate, using an integrated hydrological model calibrated for different irrigation scenarios. We compute the correlation of meteorological drought indices with the simulated hydrological time series (discharge, groundwater levels, and water deficit) and compare changes in the relationships between hydrological variables and drought indices. While correlation coefficients linked with a specific drought index are similar for all tested land uses and climates, the relationship between drought indices and hydrological variables often differs between present and future climate. Drought indices based solely on precipitation often underestimate the hydrological impacts of future droughts, while drought indices that additionally include potential evapotranspiration sometimes overestimate the drought effects. In this study, the drought indices with the smallest bias were the rainfall anomaly index, the reconnaissance drought index, and the standardized precipitation evapotranspiration index. However, the efficiency of these drought indices depends on the hydrological variable of interest and the irrigation scenario. We conclude that meteorological drought indices are able to identify years with restricted water availability in present and future climate. However, these indices are not capable of estimating the severity of hydrological impacts of droughts in future climate. A well-calibrated hydrological model is necessary in this respect.

In semi-arid regions, droughts are a serious natural hazard,
often causing tens of millions of Euros of damage

Droughts have a wide range of impacts, and are often difficult to define.
They have been classified in four main categories

and

In addition to the identification of drought periods, these meteorological
drought indices are also good indicators of various drought impacts in
present climate, based on the results of a range of studies. For example,
text recollections of droughts, such as newspaper articles, are linked with
different drought indices, indicating a relationship between the social
impacts of droughts and drought-index values

Hence, meteorological drought indices are correlated with hydrological and
agricultural impacts of meteorological droughts. Consequently, they are also
correlated with hydrological or agricultural droughts. Many of the drought
impacts cited above, such as changes in groundwater levels or discharge,
could also be conceptualized as an indicator of hydrological or agricultural
droughts. For example, groundwater levels could be transformed to a drought
indicator such as the standardized groundwater level index (SGI,

The relationship between meteorological drought indices and drought impacts
is valid for many drought indices in present climate, including simpler
indices using one input variable, such as precipitation. However, the
suitability of drought indices has not been tested under a changing climate.
The ongoing increase in air temperature was not taken into account. Because
climate change will probably impact drought intensity and frequency

A large number of drought indices have been used in recent climate-impact
studies. For instance, the standardized precipitation index was often used to
study future droughts

A summary of the drought indices used in this study.

To study the validity of drought indices in future climate, we chose seven
well-known drought indices (Table

A fully integrated hydrological model of a small catchment, the Lerma
catchment, in northeastern Spain, is used to simulate the hydrological
responses to the meteorological forcing. This catchment has recently
undergone a monitored transition from rainfed to irrigated agriculture, in
which the irrigation water is imported from the Yesa reservoir located
outside of the catchment

The remainder of this paper is structured as follows: first, we present the methodology used in this study. Specifically, we briefly describe the study area, the hydrological model, the drought indices, and the methods used to compare them. Secondly, we discuss the climate and the irrigation scenarios. We also compare the frequency distribution of drought indices computed from measurements and based on the outputs of the weather generator. Next, we summarize an analysis of the correlation coefficients between hydrological variables and drought indices for two different land uses (with/without irrigation), and for present and future climate scenarios. Afterwards, we investigate changes in the relationship between these drought indices and the hydrological variables. We then use these results to predict relevant changes in drought risks in the study area in future climate. Finally, we discuss the usefulness of drought indices in climate-impact studies.

The main objective of this paper is to test the suitability of several
meteorological drought indices to estimate the impacts of climate change on
the water cycle of a small catchment. Seven drought indices, described in
Sect.

Surface elevation of the Lerma catchment (m a.s.l.). The
observation wells drilled in 2010 are indicated by blue circles and the ones
drilled in 2008 are indicated by white circles. The gray line represents the
limits of the surface flow domain. Vertical exaggeration:

The time series of the drought impacts listed above are obtained using the
outputs from a calibrated, integrated, pde-based, hydrological model
(Sect.

These time series are directly used to represent the drought impacts on
hydrology. They are compared to the time series of meteorological drought
indices (Sect.

This study is focused on annual droughts. We choose the annual timescale
because it is often used when predicting future droughts

Soil and hydrogeological zones for the year 2009. Vertical
exaggeration:

The Lerma catchment is situated within the Ebro basin in Spain with an
altitude varying between 330 and 490

The catchment underwent a rapid transition from non-irrigated to irrigated
agriculture between 2006 and 2008. The majority of the fields within the
catchment are now irrigated, with an annual irrigation of 286

To simulate the hydrological response of the Lerma catchment, we use
HydroGeoSphere

The conceptual model of our study area and its calibration have also been
presented by

We calibrated the parameters of the model using three computational grids of
increasing resolution

More than 150 drought indices have been developed in the past

the standardized precipitation index (SPI): SPI

The standardized precipitation evapotranspiration index (SPEI):
the computation of SPEI

The rainfall anomaly index (RAI): RAI

The effective drought index (EDI): EDI

The Palmer drought severity index (PDSI): PDSI is a widely used drought
index that was developed to measure the cumulative departure of moisture
supply during dry periods

The Palmer hydrological drought index (PHDI): PHDI is an index similar
to PDSI, which was developed to better represent hydrological droughts

The reconnaissance drought index (RDI): the computation of RDI

We present the selected indices in more detail in the Supplement and provide
a summary in Table

Potential evapotranspiration (ET

To compare how well the drought indices can predict the chosen hydrological
variables in present and future climate, we use two approaches. First, we
compute Pearson's linear correlation coefficient

Pearson's correlation coefficient indicates the degree of linear dependence
between two variables. However, if this correlation coefficient is calculated
under different climatic conditions, it does not indicate possible changes in
the coefficients of the (assumed) linear dependencies. To investigate the
changes in the linear dependency between the two climates, we perform a
linear regression between a drought index and a hydrological variable in the
present climate. Then, we use this linear relationship to predict the
hydrological variables from the same drought index in future climate. We
conduct this analysis for each combination of drought index and hydrological
impact in all irrigation scenarios. By this, we aim to investigate whether
drought indices in future climate represent on average a similar drought
(i.e., a drought with similar hydrological impacts) than in present climate.
This is important because many drought studies

To quantify the changes in the linear dependencies between hydrological
variables and drought indices, two performance metrics were selected: the
relative model bias

The NRMSE is the root mean square error divided by the standard deviation of
the least-square regression in present climate

In the present climate, the variability of the differences between the
outputs from the hydrological model and the linear regression is smaller than
12 % of the average difference between model outputs and the linear
regression. Hence, the error of the linear model in the present climate can
be considered homoscedastic; i.e.,

The climate scenarios used in this study have been presented by

Our future climate scenarios cover the time period of 2040–2050, using the
A1B IPCC emission scenario

The chosen downscaling procedure has the advantage of producing longer time series, compared to the relatively short (23-year) climate record in the Lerma catchment. Moreover, it reproduces future changes in the precipitation variability, and not only in the precipitation mean, which is an important criterion when studying future droughts.

Name and acronym of the regional climate models used in this study.
Adapted from

Nevertheless, the downscaling of climate model outputs is a complex task and
the choice of a particular downscaling method can have a large impact on the
results

In addition to the reproduction of the meteorological forcing mentioned in
Sect.

All seven drought indices used in our study are normalized (Sect.

To compute each drought index, we use the measured time series, which has a
length of 23 years (1988–2011). In addition, we compute the drought indices
using the simulated data. To get a comparable length between measured and
modeled data, the time series of drought indices based on the weather
generator are separated into 15 periods with a duration of 23 years each
(totaling 354 years). The final length of this time series is chosen such
that it is about twice the length of the hydrological simulations
(180 years). We then prepare 15 empirical cumulative distribution functions
(

The

Consistent with our earlier study

scenario NOIRR: without irrigation and without agriculture;

scenario PIRR: with present cropping patterns and present irrigation; and

scenario FUTIRR: with the present cropping pattern but with an updated
irrigation volume to account for future climatic conditions. To create this
scenario, we assume that the irrigation efficiency will not change in future
climate. In addition, we assume that the increase in irrigation will only
depend on the increase in ET

Empirical cumulative distribution function (

Empirical cumulative distribution functions of daily precipitation for present and future climate scenarios.

Future precipitation (Fig.

Because of the higher temperature, potential evapotranspiration (ET

The hydrological responses of the Lerma catchment to climate change under
different irrigation conditions have been modeled previously by

In this section, we analyze the correlation between the different drought
indices for the 180 years of each scenario and the corresponding simulated
mean annual discharge, water deficit, and hydraulic heads. For this purpose,
we use the Pearson linear correlation coefficient

The values of the correlation coefficients between the hydrological variables
and the drought indices depend on the drought indices. For example, the
correlation coefficient between water deficit and EDI is 0.47, while the
correlation coefficient between this variable and RAI is 0.78 in the present
climate. However, the correlation coefficients for a particular drought index
and a particular hydrological variable are similar for all irrigation
scenarios in present and future climate. For example, let us consider the
correlation coefficients between drought indices and discharge
(Fig.

Water deficit exhibits a similar behavior to discharge when correlation
coefficients are examined. When the absolute values of correlation
coefficients are large in present climate, they will be similarly large in
future climate or in another irrigation scenario. SPEI, RDI, and RAI have the
largest correlation coefficients with water deficit in all scenarios (

Correlation coefficients between drought indices and groundwater heads in a particular observation well are similar for all drought indices considered. However, the correlation coefficients are very different from one observation well to another (see the Supplement for more information).

Seasonal differences in the correlation coefficients are not considered here, even though these correlations might be influenced by the annual cycle. Our analysis is focused on annual droughts.

Correlation coefficient

The previous section has shown that the linear correlations between drought indices and hydrological variables are relatively similar under all climatic and irrigation conditions. Hence, a particular drought index is able to identify the dry periods in present and future climate. However, this does not indicate whether the droughts in future climate have similar hydrological impacts to those in present climate. Correlation coefficients quantify how well a relationship between two variables can be expressed by an (assumed) linear equation, without considering the actual coefficients of the linear equation. The latter are commonly evaluated by linear regression.

Identifying changes in the regression coefficients of the relationships
between drought indices and hydrological variables is important when making
hydrological predictions based on meteorological drought indices in a
changing climate. Only when the regression coefficients do not change does
the same value of a drought index have the same hydrological impact. To this
end, we compare changes in the (assumed) linear regressions between drought
indices and discharge or water deficit (Sect.

The stability of the relationship between drought indices and hydrological
variables strongly depends on the chosen drought index and the irrigation
scenario. In Fig.

As outlined above, we use two different performance metrics to quantify this
bias, the relative model bias

Performance of SPEI in future climate for annual discharge. The blue
line is the linear regression between SPEI and discharge in present climate.
Top panel: NOIRR scenario, large model bias. Second panel: FUTIRR scenario,
no significant model bias. Bottom panel: the two coefficients of the linear
regression between

Relative model bias and NRMSE in the NOIRR and PIRR/FUTIRR
irrigation scenarios. The results are based on the average of the outputs of
the four regional climate models (Table

Present and future (2040–2050) droughts predicted by the seven
drought indices, using the outputs from the weather generator. See
Table

For discharge, model bias depends strongly on the irrigation scenario
(Fig.

For the water deficit (Fig.

The drought indices with the lowest model bias and a correlation coefficient

In Sects.

Our definition of a drought is identical for present and future climate.
Practically, we standardize the drought indices in the present climate and
keep the same standardization (explained in Sect.

Figure

When we compare the changes in drought indices between present and future
climate, significant differences can be observed between the different
climate scenarios (based on the four regional climate models). Indices that
only contain precipitation (RAI, SPI, and EDI) predict a small increase in
droughts or a small decrease depending on the climate scenario
(Fig.

The sources of the differences between the climate scenarios, which result in
the aforementioned differences in the values of drought indices, are
uncertain. Nevertheless, two factors are often cited when discussing
differences in future climate scenarios with identical emission scenarios:
modeling of cloud cover

In addition to the differences related to the chosen climate scenario, the
choice of the drought index has a large influence on the prediction of future
droughts. These differences in drought prediction are largely the reflection
of the differences in the linear relationships between drought indices and
hydrological variables discussed in Sect.

Average hydrological impacts of present and future (2040–2050)
droughts. From left to right: relative changes in mean annual precipitation,
ET

If we analyze the hydrological impacts of meteorological droughts (defined
here as periods with an SPI and SPEI value of lower than 1), the general
behavior is similar in present and future climate (Fig.

Outputs from global or regional climate models are often used to predict changes in droughts in future climates because these outputs are easy to obtain and relatively simple to analyze. In most cases, the analysis is based on the computation of meteorological drought indices. To use drought indices in climate-impact studies, it is necessary to choose a particular set of indices. Based on the assessment of correlation coefficients and the stability of the relationships between hydrological variables and drought indices, the drought indices RDI, RAI, and SPEI are the most suitable indices in our case study. However, their performance strongly depends on the assumed irrigation scenarios and may thus be different in other climates and land uses. Other drought indices might perform better in more humid or colder climates. However, based on this study, these three indices are the most suitable for climate-impact studies in the Mediterranean climate.

On a broader level, we propose to use drought indices with a certain caution in climate-impact studies and advise against using a single drought index. A hydrological model is a more direct way to analyze hydrological drought impacts in future climate and it should be used whenever possible in such studies. Unfortunately, the development and the parameter calibration of hydrological models is a complicated task and depends on the availability of hydrological measurements such as discharge and hydraulic heads.

If the development of a hydrological model is not an option, our results
suggest that outputs from drought indices should be analyzed in detail with
respect to three issues, regardless of the set of the chosen drought indices.

The importance of potential evapotranspiration (ET

Correlation coefficients are not always sufficient to compare drought indices:
our comparison of the correlation coefficients between hydrological variables
and drought indices (Sect.

The hydrological impacts of droughts depend on climate change:
this has been previously explored in other studies, notably in studies
focusing on hydrological droughts. For instance,

The interpretation of changes in meteorological drought indices
between future and present climates can be considerably compromised by the
assumption that the relationship between the drought indices and the
hydrological variables (which represent the effects of drought) is identical
in present and future climates. The same drought-index value might lead to
different drought consequences in present and future climates. Results can be
further compromised by neglecting the increase in ET

As a summary, in the Lerma catchment, drought indices are useful indicators of dry periods in all tested climate scenarios and land uses. However, a change in a particular drought index in future climate cannot easily be transferred to hydrological effects of droughts. In a stationary climate, the relationships between drought impacts and drought indices are usually reliable, and so the hydrological consequences of droughts can be assessed from the drought indices. However, these relationships may change in a non-stationary climate and their evolution strongly depends on the particular combination of drought index and land use. Hence, projections of future droughts using only one drought index may result in misleading estimation of the possible drought impacts.

Because drought indices can be estimated directly from the outputs of climate
models, they are popular metrics of droughts even though they cannot be
related uniquely to hydrological or even ecological impacts of droughts.
Rather than relying on these indices, we recommend using a hydrological model
to study hydrological effects of future droughts whenever possible. If
setting up a hydrological model is not feasible, we advise considering more
than a single drought index and choose drought indices that take both
precipitation and ET

Regardless of the chosen drought index or the climate scenarios, this study,
and many previous studies

Hydrological data from the Lerma catchment have been collected and are owned
by the Spanish Geological Survey

We show our appreciation to H. Fowler and S. Blenkinsop for providing the weather generators and for their support. Moreover, we thank the Spanish meteorological national agency (AEMET) for providing us with the meteorological data. In addition, we acknowledge the ENSEMBLES project, funded by the European Commission's 6th Framework Programme (contract number: GOCE-CT-2003-505539), for providing us with the outputs from the regional climate models. Research in the Lerma catchment is supported by the Spanish Ministry of Economy and Competitiveness within the framework of project AgroSOS (FEDER funds [EU], grant CGL2015-66016-R). The publication of this article is supported by the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen. This study was performed within International Research Training Group “Integrated Hydrosystem Modeling” (grant GRK 1829/1 of the Deutsche Forschungsgemeinschaft). Edited by: P. Saco Reviewed by: S. Bachmair and one anonymous referee