Frequently used drought indices reflect different drought conditions on global scale

on global scale Niko Wanders1,2, Anne F. Van Loon3, and Henny A.J. Van Lanen4 1Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA 2Department of Physical Geography, Utrecht University, Utrecht, The Netherlands 3School of Geography, Earth & Environmental Sciences, University of Birmingham, United Kingdom 4Hydrology and Quantitative Water Management Group, Wageningen University, The Netherlands Correspondence to: N. Wanders (n.wanders@uu.nl)


Introduction
Drought is an abnormal and prolonged deficit in the available water and has a major impact on both natural and social hydrological resources (Wilhite, 2000;Tallaksen and Van Lanen, 2004;Mishra and Singh, 2010;Sheffield and Wood, 2011).Due to the large spatial and long temporal extent of drought events, they tend to have a large economic damage.The United states suffered an estimated agricultural loss of $5.5 billion for the 2012-2014 California drought alone (Howitt et al., 2014(Howitt et al., , 2015;;Medellín-Azuara et al., 2016).This drought was caused by lack of precipitation and snow accumulation in three consecutive years, leading to a significant reduction of the water levels in some of the major rivers and reservoirs affecting water security physical drought index needs to be identified to a specific drought impact to improve predictability of the impacts.
Most drought indices aim to subtract the normal seasonal variation in water availability or water state from the climatological variations and thereby quantify extreme events and thus drought.However, the difference in the drought calculation for the different drought indices (e.g.Keyantash and Dracup, 2002) results in uncertainty of which indices could be used under a given circumstance and for what affected sector.It is obvious that this will lead to confusion about what kind of index is to be used for a given impact.Expert knowledge is required to monitor drought with the correct index.Mostly, the focus of drought monitoring is put on precipitation and soil moisture drought while the impact of drought on various sectors goes beyond these domains of the hydrological cycle (Figure 1).There are other metrics that are more specifically related to monitoring reservoir levels, aquifer levels, deliveries of water to users, and the fraction of water demand that can be met.These metrics are often not monitored in operational systems since they are site-specific, user dependent and only available at local scales (e.g.river basins or reservoirs).The World Meteorological Organization (WMO) recommended the use of a more general index that derives drought conditions from anomalies in precipitation (World Meteorological Organization, 2009).However, WMO also states that a single precipitation derived index would not suffice to monitor drought conditions relevant to all possible impacted sectors.Another important effort is made by the National Drought Mitigation Center in the United States, to provide a weekly inventory of United States drought conditions.The maps that they produce are the result of a combination of drought indices (i.e.combined or composite index) that show the drought severity.This combined approach does take into account meteorological, soil moisture and discharge observations to estimate the drought conditions.A big advantage of this approach is that it combines all possible drought types.The European Drought Observatory (EDO) provides spatial information on their Combined Drought Index (CDI, Sepulcre-Canto et al., 2012).This index is derived from a combination of the Standardized Precipitation Index (SPI-3), soil moisture anomaly derived from the hydrological model LISFLOOD (SMA) and the fraction of absorbed photosynthetically active radiation (fAPAR) derived from remote sensing.EDO then uses three drought stages, namely the Watch, Warning and Alert Phases (Van Lanen, 2014).The meteorological SPI-3 is used to indicate a meteorological drought (Watch Phase), subsequently followed by a soil moisture drought (Warning Phase) and eventually the fAPAR will indicate a drought in the vegetation (Alert Phase).
Here we make an attempt to identify how physical drought indices capture the drought phenomena in different parts of the hydrological cycle, how these indices are capturing droughts within the different drought types (hence intrasubstitution), and the agreement between indices from different groups, from now on referred to as intersubstitution.We conduct the analysis on the global scale to cover climate differences using modelled data to provide the necessary input to compute the extensive suite of drought indices.Unfortunately, no consistent set of observations with high spatial coverage is available to do this analysis at continental and global scales.Moreover, the high-resolution data provided by the model allows us to assess the impact of the local climate of the correlation between drought indices.This will provide additional insight, as how we can determine meaningful indices for drought impact assessment at continental and global scales.
The objective of this study is to investigate: (i) intersubstitution of drought indices used for different drought types, (ii) intrasubstitution of drought indices used for the same drought type, and (iii) dependency of this intersubstitution and intrasubstitution on climatology.A conceptual hydrological model was used to simulate time series of hydrological variables to determine different drought indices.Time series of these indices were compared on a global scale.

Hydrological model
A conceptual hydrological model (Van Lanen et al., 2013) was used to simulate the catchment response to meteorological forcing.The model was used to simulate the hydrological cycle at a global scale with a resolution of 0.5 • for the period 1958-2001.The model incorporates snow, soil moisture and groundwater modules that enable the simulation of the hydrological response of the 0.5 • grid cell.Using a lumped approach, the model generates gridded time series of snow accumulation, soil moisture, groundwater and discharge.The precipitation, temperature and potential evapotranspiration data that are required as forcing were derived from the WATCH reanalysis dataset (Weedon et al., 2011).The conceptual model uses a fixed catchment parametrization which reflects a sandy-loam soil with an intermediate groundwater response time.The model has been successfully applied in previous studies (Van Lanen et al., 2013;Van Loon et al., 2014;Wanders and Van Lanen, 2015;Taufik et al., 2017).The conceptual model allows for isolation of the climatic signal from differences in catchment characteristics.This allow to focus on differences between drought indices, only with respect to different climate types.For a more detailed description of the model the reader is referred to Van Lanen et al. (2013); Wanders and Van Lanen (2015).

Sensitivity analysis
A sensitivity analysis was done to assess the robustness of the model parametrization with respect to the generated time series of soil moisture, discharge and derived drought indices.The sensitivity analysis by Van Lanen et al. (2013) showed that hydrological drought characteristics derived from simulated discharge, did not change significantly with changes parametrization.
However, here we evaluate the robustness of the model with respect to different drought indices.The sensitivity of the soil moisture and discharge simulations to changes in the parametrization was evaluated for a temperate climate (with seasonal snow impact).The relative difference in the variance and the mean of the soil moisture and discharge are related to the changes in parametrization.Thereafter, drought characteristics are calculated for different drought indices and the obtained timeseries are compared to a baseline scenario (sandy-loam soil with an intermediate groundwater response time).In order to assess the sensitivity of the model to the changes in the parametrization, we evaluated the correlation between the indices.

Drought indices
Drought in all parts of the hydrological cycle was evaluated using a selection of 10 frequently used drought indices, including the different lags resulting in a total of 20 indices (Table 1).These indices cover all drought types and strongly vary in calculation procedure and input data required, which were applied to detect drought conditions in the hydrological simulations.Here  the SPI-12, SPI-24 and SPEI-12 are classified as meteorological drought indices, however, these are often used as proxy for soil moisture or hydrological drought (Seneviratne et al., 2012).For drought indices that require only precipitation as input, the time series of the WATCH reanalysis dataset were used (Weedon et al., 2011).All indices were derived on a monthly time step and normalized time series for each index were calculated.For more information about the calculation procedure of each drought index the reader is referred to the individual papers mentioned in Table 1 and Wanders et al. (2010).
Indices were evaluated based on the correlations between indices that should indicate similar drought types or could be used to monitor similar impacts (Figure 1).The correlation between two meteorological drought indices (e.g.EDI and SPI-1) is referred to as intrasubstitution.The correlation between indices of different drought types (e.g.SPI-1 for meteorological and GRI for hydrological drought) is referred to as intersubstitution.In addition, the impact of climate types according to in the Köppen-Geiger classification was evaluated, to see if a dependency exist between the correlation and the climate type.

Analysis of spatial patterns in drought indices
An example of the drought conditions in Africa on August 1984 is shown for all indices under study, to indicate the severity of the drought conditions and to explore difference between drought indices (Figure 3).It is clear that although the 1984 drought in Africa is known to be severe (e.g.Van Huijgevoort et al., 2012;Wada et al., 2013;Masih et al., 2014), not all indices show the dry conditions.There is a strong disagreement among the indices on the drought spatial pattern and the severity.Although not all indices have been developed to monitor the same drought type, similarities in the spatial patterns should be visible between indices of the same drought type.Especially since, most indices of the same type use similar input data.This example of a spatial drought pattern clearly shows that when it was monitored with a single index, the assessment of the natural hazard, could be significantly different from monitoring with another drought index of the same type.
A similar pattern is observed for the 1976 drought in Europe, another severe drought event (Perry, 1976).The extreme conditions for this drought, show large differences between the drought indices (Figure 4).We find extreme dry conditions for the SPEI for large parts of Europe; this could be driven by the strong increases in temperature and hence the strong increase in potential evaporation leading to strong negative values for this index.The inclusion of the potential evapotranspiration is one of the more important differences between the computation of the SPI and SPEI and could clearly explain the spatial differences for Eastern Europe.The SRI tends to follow the behaviour observed for the SPEI, which is interesting since it uses the same input data as the other hydrological indices.Here we see the impact of the standardization that is applied in the computation of the SRI, reducing the impact of the wet conditions for eastern Europe, compared to the other hydrological indices.

Analysis of temporal behaviour in drought indices
For a more detailed analysis we have selected a location close to Paris, in the heart of the 1976 drought, were we clearly see that all drought indices pick up on the extreme drought conditions (Figure 5).When we zoom in on the year 1976, we can 6

Intrasubstitution of drought indices
The correlation between drought indices within a drought type (intrasubstitution, Figure 6) is hypothesised to be high.It is striking to see that meteorological drought was characterized differently by the eleven relevant indices used in this study  (EDI, MAP, SPI-1,3,6,12,24, SPEI-1,3,6,12), resulting in the low median correlations over all climates (R = 0.1 − 0.75).

SPEI−3
An exception is found in the high correlation between SPI and SPEI with similar accumulation periods.Because most of the meteorological indices use only precipitation time series, the cause of any low correlation can fully be allotted to the way in which precipitation time series are transformed to meteorological drought.These indices were expected to have a high correlation because they should represent drought conditions for the same impacts.Any existing differences are largely caused by the way in which index calculations deal with this highly dynamic time series of precipitation, as can be clearly seen from the difference in the SPI and SPEI lag times.
The low average correlations (R = 0.25, Figure 6) found in the two soil moisture indices (PDSI and MAS) are a result of the different ways in which soil moisture drought is defined.Especially, in situations with snow accumulation (D and E climate type) the way in which the drought identification was performed is quite important.For example, PDSI does not account for 10 snow or delayed soil moisture availability caused by snow melt, which results in a different drought characteristics compared to MAS.
The intrasubstitution of three hydrological drought indices (SRI-1,3,6,12, GRI, TSDI, MAQ) was high as compared to the other drought types (R = 0.5−0.98, Figure 6, also seen in Figure 3).This suggests that one index might already suffice to correctly characterize hydrological drought events and their impacts (in contrast to meteorological or soil moisture drought).The fact that hydrological drought indices show the highest intrasubstitution could be related to the fact that the dynamics in groundwater and discharge time series is always lower than those of precipitation and soil moisture.This low dynamic behaviour results in a reduced impact of any smoothing or aggregation in the calculation of the drought index leading in consequence to higher correlations and agreement in the identification of drought events.Hydrological drought events often have long duration (Peters et al., 2003), whereas meteorological drought events are often shorter.

Intersubstitution of drought indices
The potential intersubstitution of drought indices is even lower than the intrasubstitution (Section 3.3), which is to be expected The results suggest that substitutes (meteorological drought indices that should approximate another drought type), cannot be used to study different drought types.For example, the intersubstitution of drought indices is always lower than the intrasubstitution found for each of the three hydrological drought indices.This indicates, for instance, that differences amongst hydrological drought indices are smaller than differences with possible substitutes, e.g.SPI-12 or SPI-24 (R = 0.3 − 0.7).
Although computational effort and complexity of the calculations might be decreased by selection of a substitute for all drought types, this does not provide useful information for impacted sectors.When the SPI is used to monitor hydrological drought (because of lack of observed discharge data), this leads to different drought severity patterns (see Figure 3).
An impact of snow accumulation is found for the snow-affected (D) and polar (E) climate where the intersubstitution of meteorological and hydrological drought indices is lower than for other climate types.Similar to the result obtained for meteorological drought indices, the intersubstitution between soil moisture and hydrological drought indices is hampered in snow-affected (D) and polar (E) climate regions.This clearly illustrates that snow should be accounted for in these regions, when soil moisture or hydrological drought is considered.In snow affected (D) climates, snowmelt can end drought events by increased water availability in spring, which could lead to different behaviour for indices that either include snow accumulation or not.Moreover, a meteorological drought in winter is not directly visible in groundwater or discharge (Van Loon et al., 2014).Indices that do not include snow accumulation and snow melt are highly affected by this condition and show low correlations in snow-affected regions.In the desert climate (B) all indices are affected by long periods with no precipitation or recharge; for these regions the definition of a drought remains challenging and should be done carefully to avoid a confusion between drought and aridity (i.e.normal climatic conditions).Intersubstitutionality of drought indices is higher in tropical (A) and temperate (C) climate regions than in the dry and cold climates (B, D and E).

Sensitivity analysis of hydrological model
To test the sensitivity of the results we have altered the model parameterization to simulate both a coarse sand and sandy loam soil to analyse potential differences in correlation between indices as a results of the model parameterization.In addition, we have altered the groundwater response parameters to reflect a groundwater system that has a 10% faster or slower response time (Figure 2).From this sensitivity analysis, we see that the parametrization of the conceptual model only has a minor impact on the simulated drought indices and hence it hardly influences the comparison between indices time series.Since for all indices, changes in the parameterization will also result in changes in the drought characterization baseline, the overall impact of the changes in parameterization remains small.We found change in the correlations between drought indices that were less than 0.005 for all indices under study, at all locations.This clearly shows that the impact of the model parametrization on the conclusions of this study is negligible.
The in general low correlations between drought indices (Figure 6) show that it is very important to select the right physical index for monitoring, forecasting and predicting a drought type relevant for an impacted sector.Since drought impacts are related to different parts of the hydrological cycle (Figure 1), every index provides specific information and hence is viable to monitor drought condition for certain impacts.Additionally, the different spatial patterns between indices for a known drought event show the need to be cautious when using a single drought index to identify specific conditions even for one drought type (Figure 3).
Time series of different drought indices are often used to derive trends in drought characteristics.However, intercomparison of the outcome of these studies should be done with extreme caution since the used indices might capture different drought types, or were computed in different ways leading to differences in the predicted trends (e.g. the PDSI; Dai, 2013;Sheffield et al., 2012).Trend analysis based on a single index creates the illusion that the phenomenon drought is studied in general, but the drought is not captured by one index and consequently only the trend for some impacts is studied.Single index studies can be used to capture trends in a single type of drought (e.g.meteorological or hydrological), although this should also be done with care since using a different index could lead to different results (see intrasubstitution potential, Section 3.3).
We believe that researchers should not try to fulfil this quest to one ultimate drought index, since such an index can never cover the full width of the multi-faced drought phenomenon.Every impact requires a different type of index and although some impacts can be studied with the same physical drought index, this is certainly not a standard procedure (Bachmair et al., 2016a).
As was described by Bachmair et al. (2016b) and confirmed in this work, we see that not every index can capture every drought impact.When physical indices are related to drought impacts, it is important to find an index that is as close as possible to the drought impact of interest.In addition we show that the performance of an index is also dependent on climate type, indicating that the desire for one global index certainly cannot be fulfilled.
A distinction can be made between indices used for drought awareness usually on a large scale (e.g. the European Drought Observatory, Sepulcre-Canto et al., 2012) and indices for operational drought management on a river basin scale (e.g.Andreu et al., 2009).We argue that indices for public awareness could be dimensionless and do not require a direct connection with an impacted sector.For example, the SPI with different accumulation periods can be used to monitor anomalies throughout the hydrological cycle, since it gives an indication on the duration and severity of the drought.However, indices like the SPI are not applicable to calculate drought deficits since only standardized anomalies are provided.The SPI or similar indices can be used to increase public drought awareness due to their easy interpretation.Similar calculation procedures as the SPI have been applied to other hydro-meteorological time series to study drought propagation in for example runoff (Standardized Runoff Index, Shukla and Wood, 2008) and groundwater (Standardized Groundwater Index, Bloomfield and Marchant, 2013).For operational purposes, however, a threshold approach would be more suitable, since it can directly be translated into drought deficits, water shortages or storage deficits.The threshold approach is easily applicable throughout the hydrological cycle and therefore suitable for propagation studies (e.g.Peters et al., 2003Peters et al., , 2006;;Tallaksen et al., 2009;Van Loon and Van Lanen, 2012;Van Loon et al., 2014).Additionally, the threshold can also be used to study at quantitative changes in drought characteristics for long historical periods or future projections (e.g.Wanders et al., 2015;Wanders and Wada, 2015).These changes can be directly related to changes in water storage or deficits.The calculated deficits are not meant for the general public unless values are standardised, e.g. by the mean flow.
Results of this study impact the way in which drought should be monitored and forecasted.Since indices are not intrasubstitutional, different indices are required for different impacts.Additionally, studying drought in snow-affected regions should be done with more care and a realistic representation of snow accumulation should be included in indices used for these regions (Staudinger et al., 2014).In this study, we show that drought indices show large difference in drought identification and therefore drought indices should be related to the impacted sector under study.Drought indices are hardly intra-and intersubstitutional and therefore a careful selection of the drought index is required.Using a single index to study global trends for all drought types is impossible and unrealistic.

Figure 1 .
Figure 1.Different types of droughts and their impact on society and nature.meteo: meteorological drought, soil: soil water drought, and hydro-GW and hydro-Q refer to hydrological droughts in Groundwater (GW) and discharge (Q). 5

Figure 2 .
Figure 2. Model set-up of the synthetic hydrological model.The model consists of three partitions, Snow, Soil and Groundwater.Psn snowfall, Pra rainfall, ETp potential evapotranspiration, ETa actual evapotranspiration, Sn snow storage, SS soil storage, SSmax maximum soil storage, Qsn snow melt, Qs recharge to the groundwater from the unsaturated zone, Q b bypass flow, R ch total recharge to groundwater, SG groundwater storage, j groundwater response parameter, Qout groundwater discharge and t is the time index.

Figure 3 .
Figure 3. Drought conditions over Africa in August 1984 for selected drought indices under study.Colours indicate the normalized drought severity, where negative values show drought conditions and positive values wetness, and the lower/higher the values the more extreme the drought/wetness.

Figure 4 .
Figure 4. Drought conditions over Europe in August 1976 for selected drought indices under study.Colours indicate the normalized drought severity, where negative values show drought conditions and positive values wetness, and the lower/higher the values the more extreme the drought/wetness.

Figure 5 .
Figure 5. Drought conditions around Paris for the period 1974-1983 for selected drought indices under study.Colours indicate the value of the normalized drought severity, where negative values show drought conditions and positive values wetness, and the lower/higher the values the more extreme the drought/wetness.

Figure 6 .
Figure 6.Correlations between indices for the period 1958-2002, where the colours of bars and histograms indicate average correlations between indices.In this cross-correlation diagram, each row and column provide the data of one index, as indicated in the diagonal.Bar plots (above diagonal) indicate the average cross-correlation between index separated for locations with a tropical (A), desert (B), temperate (C), Snow (D), or Polar (E) climate types, and (All) gives the global average (upper left cell gives sequence of climate types for the histograms) For each climate type we have aggregated all the locations that are located in a specific climate type and computed the average cross-correlation.Global cross-correlation distribution (below diagonal) indicates the global average of the correlations where no distinction is made between climate types and the full distribution is provided.The colours of each bar of histogram correspond to the value of the histogram bar (above the diagonal) or the global average cross-correlation (below the diagonal).10 Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-512Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 17 August 2017 c Author(s) 2017.CC BY 4.0 License.