As temporal and spatial resolution of the drought indicator and impact data, we selected monthly time series for the period 1970–2012, aggregated at the NUTS1 level (level 1 of the Nomenclature of Units for Territorial Statistics, a spatial unit used in the European Union). NUTS1 regions represent major socio-economic regions. This level of spatial aggregation was chosen because of a lack of sufficient data for analysis with finer-scale resolution. However, studies have shown that drought signals typically cover areas larger than NUTS1 regions (e.g., Hannaford et al., 2011). In Germany NUTS1 regions correspond to the federal states. In the UK there are 12 NUTS1 regions, in Germany 16 (see Table 1 for a list of NUTS1 regions considered for analysis and abbreviations used in this study, and Fig. 1 for the size of NUTS1 regions). Note that two NUTS1 regions in the UK and three in Germany were excluded from the analysis due to having insufficient impact data (see Sect. 2.3 for details).

As drought indicators we selected the SPI (McKee et al., 1993), the Standardized Precipitation Evaporation Index (SPEI) (Vicente-Serrano et al., 2010), and streamflow percentiles (Q). In addition, groundwater level percentiles (G) were included for Germany. For the SPI and SPEI, accumulation periods of 1–8, 12, and 24 months were chosen. Gridded SPI and SPEI data were calculated based on E-OBS (http://www.ecad.eu/download/ensembles/download.php) gridded data (version 9.0; 0.25∘ regular spatial grid; Haylock et al., 2008) using the R Package “SCI” (Stagge et al., 2015b). For the UK and Germany, the underlying station density of the gridded data is relatively high within Europe, and the data set is based on more European observing stations than in other European or global data sets (Haylock et al., 2008). The gamma distribution was used for the computation of the SPIs and the generalized logistic distribution for the SPEIs (reference period: 1971–2010). Potential evapotranspiration for the SPEI was estimated using the Hargreaves method (Hargreaves, 1994). For each NUTS1 region, regional averages of mean monthly SPI-n or SPEI-n were calculated. Here, n denotes the accumulation period. The mean was chosen since Bachmair et al. (2015) found little difference between the performance of different indicator metrics per spatial unit (e.g., mean vs. minimum, or 10th percentile vs. percent area with SPI or SPEI below a threshold). The reference period for calculation of streamflow percentiles is 1960–2012 in the UK, and 1970–2011 in Germany (also for groundwater).

The monthly streamflow percentiles are based on monthly mean streamflows. In Germany these are calculated from daily streamflow records for several gauging stations per federal state; monthly groundwater percentiles come from weekly to monthly readings of groundwater levels or spring discharge for several monitoring stations per state (data provision by different agencies of the German federal states; see Kohn et al., 2014). Many of these stations are used for the federal states' hydrological forecasting systems and thus represent stations with good data quality. Monthly streamflow records for the UK were taken from daily river flow records held on the UK National River Flow Archive (NRFA) (http://nrfa.ceh.ac.uk/). The UK Benchmark Network (Bradford and Marsh, 2003) of near-natural catchments was used, alongside the network of sites used in the National Hydrological Monitoring Programme (NHMP)(http://nrfa.ceh.ac.uk/nhmp). No groundwater measurements were used from the UK due to the limited number of NHMP borehole records available in many NUTS regions, reflecting the concentration of productive aquifers in the south and east of the country.

The streamflow gauging stations in the UK and Germany encompass both near-natural and anthropogenically influenced streamflow records. Since different drought impacts may occur in near-natural and regulated rivers it is necessary to have an indicator reflecting the drought signal in both natural and managed systems. Figure 1 displays the spatial location of Q and G measurement stations and the boundaries of the NUTS1 regions in the UK and Germany. The number of stations per NUTS1 region is displayed in Table 1. Regional average mean monthly Q and G values were calculated for each NUTS1 region, provided there was at least one station with non-missing observations in the region. As further predictors that may modify the drought indicators' power to explain drought impact occurrence we also selected the month of impact occurrence (M) and the year of impact occurrence (Y). For this purpose the series of months (1–12) was transformed into a sinusoidal curve shifted by 4 months (peak in July and lowest value in January).

Drought impact data come from the EDII (Stahl et al., 2016), which can be viewed online at http://www.geo.uio.no/edc/droughtdb/ (data extraction for this study: October 2014). The EDII defines a drought impact as a negative environmental, economic, or social effect experienced under drought conditions. Examples of drought impacts are crop losses, water supply shortages and hosepipe bans, increased mortality of aquatic species, reduced production at thermal or nuclear power plants due to a lack of cooling water, or impaired navigability of streams, to name a few. Drought conditions themselves (anomaly in precipitation, soil moisture, streamflow, groundwater levels, etc.), without a negative consequence or at least evoking serious concerns, are not considered an impact. The sources of EDII entries are text-based reports on drought impacts, e.g., governmental or NGO reports, books, newspapers, digital media, or scientific papers. Each impact report in the EDII contains the following information: (1) a spatial reference (different levels of geographical regionalization, including the European Union NUTS regions standard), (2) a temporal reference (at least the year of occurrence), and (3) an assigned impact category. The 15 categories, e.g., agriculture, water supply, are shown in Fig. 2. Each category subsumes several impact type sub-categories (see Stahl et al., 2016 for details).

For the analysis the qualitative information on drought impacts was transformed into monthly time series of number of drought impact occurrences per NUTS1 region. The same methodology as in Bachmair et al. (2015) was applied during the conversion of a “drought impact report” (EDII entry) into “drought impact occurrence” (hereafter termed I). In short, this entails the following (see Bachmair et al., 2015 for details):

Each impact report was assigned to a NUTS1 region. Impact reports with country-level information only were omitted from the analysis. An impact report was converted into several I if (1) the impact report stated impact occurrence in several NUTS1 regions or (2) an impact fell into several impact sub-types.

All the analyses were carried out using time series with monthly resolution. However, different subsets of periods for analysis were used. For each NUTS1 region separately, a subset of years within 1970–2012 was selected for analysis based on drought impact occurrence. Years with at least one impact occurrence in the region were selected. All months of the selected years were included in this censored time series. The censoring was undertaken to exclude years with drought conditions yet no impact reports in the EDII, similar to Bachmair et al. (2015). The search for impact reports in both countries focused on known drought events; the absence of impact reports in the EDII for years with drought conditions may therefore be attributable to either a lack of impact occurrence or simply a lack of drought impact reports, whether through not being discovered or not being published in the first place. Table 1 shows the length of time series per region and the percentage of months with impact occurrence in this censored time series. Despite the above-described censoring approach a considerable percentage of months with zero impact occurrence remained. The data analysis was only applied to regions with at least 10 months with impact occurrence, which led to the exclusion of Northern Ireland (NI) and Scotland (SCO) in the UK, and Bremen (HB), Hamburg (HH), and Thuringia (TH) in Germany (see Fig. 1). Additionally, a seasonal analysis was carried out based on the censored time series per NUTS1 region. For this purpose, only data for months occurring in the selected season were retained, in correct temporal sequence from one year to the next (see Sect. 2.3 for the definition of seasons).

First, we carried out a cross-correlation analysis between different drought indicators and the number of impacts, accounting for temporal autocorrelation in the indicator and/or impact time series. Spearman rank correlation coefficients (ρ) were calculated between time series of drought indicators and number of impact occurrences, for each NUTS1 region separately. Rank correlation was chosen over Pearson correlation since the counts of the impact data are not normally distributed. Correlations were undertaken between time series of different indicators on the one hand (mean SPI and SPEI for 1–8, 12, and 24 months; Q; G (DE only); month (M) and year (Y) of impact occurrence), and time series of number of impact occurrences for different impact subsets on the other:

total impacts (NI);

Second, we employed a machine learning approach utilizing an ensemble regression tree approach called “random forest” (Breiman, 2001). Similar to the cross-correlation analysis, the random forest approach also identifies drought indicators best linked to impact occurrence. In addition to extracting predictor importance, the random forest approach is used for obtaining splitting values as estimates of thresholds of impact occurrence, and to model drought impact occurrence.

A random forest (Breiman, 2001) is a machine learning algorithm, which constructs a large number of classification or regression trees (CARTs) on bootstrapped sub-samples of the data. For our analysis we applied the R package “randomForest” developed by Liaw and Wiener (2002). Details about the random forest (RF) methodology and model parameterization are given in the Appendix A. The RF predictors for each NUTS1 region included the same indicators as used in the correlation analysis. The response variable is the square root transformed monthly counts of impact data per NUTS1 region. We then ran models for the same subsets of impacts as in the correlation analysis if there were at least 10 months with impact occurrence: total impacts (NI), hydrological drought impacts (NIh), non-hydrological drought impacts (NIo), and impacts per impact category.

To identify the drought indicators best linked to impact occurrence we used the “variable importance” feature of the RF algorithm described in Liaw and Wiener (2002), which enabled us to use the ranks of percent decrease in accuracy as a variable importance measure (e.g., Strobl et al., 2009). Another output from the RF analysis are the splitting values for each predictor. The construction of each regression tree is based on recursively splitting the data into more homogenous groups (nodes). At each node, the best splitting variable and splitting value are determined, with multiple splits possible for the same variable (Strobl et al., 2009). For our analysis we extracted the splitting values corresponding to each predictor, considering all trees and nodes, and visualized their distribution as a box plot. We regard these splitting values as estimates of thresholds of impact occurrence. All RF models are based on multiple indicators. Therefore, indicator thresholds of individual indicators are conditional on predictor interactions.

The predictive potential of the random forest models was assessed in two ways. First, the overall model performance was evaluated based on a 10-fold cross-validation. The goal of this assessment (hereafter “RF predictions”) is to test the performance of RF models as a potential tool for predictive purposes, and to learn about the indicator–impact relationship. The data for cross-validation are the censored time series for each NUTS1 region, i.e., the time series based on the sub-selection of years with drought impact occurrence within 1970–2012. For each of the 10 model runs, the censored time series was split into 90 % for training and 10 % for prediction; impact occurrence of the left-out 10 % is predicted with a random forest model constructed on the training data. The cross-validation procedure allows evaluation of the predictive performance for unseen data excluded from model fitting. As model performance metrics we computed mean absolute error (MAE), root mean squared error (RMSE), and error components according to the Kling–Gupta efficiency (Gupta et al., 2009) modified by Gudmundsson et al. (2012): relative difference in mean (Δμ), relative difference in standard deviation (Δσ), and strength of correlation between observed vs. modeled number of impacts (r). Zero is the optimal value of Δμ and Δσ; negative and positive values indicate under- and over-prediction, respectively (Gudmundsson et al., 2012).

The second assessment (hereafter RF backwards learning) is the application of the RF models that were fitted to the censored time series to predict NI per NUTS1 region to those years that had been excluded, i.e., the years within 1970–2012 that have zero impact occurrence. The purpose of this second assessment is to scrutinize the impact data in the EDII database to backwards learn where a year without impacts may either be due to no impacts or due to the lack of reporting or finding reports. As the observations themselves are examined no model performance metrics are presented.

In the UK the strength of correlation between times series of NI and different indicators ranges between -0.65 and 0.51 (Fig. 3). Lower indicator values coincide with higher NI (negative correlation) for all drought indicators except for M, where positive values in summer concur with a higher NI (positive correlation). Overall, SPI and SPEI are very similar in terms of strength of correlation. For southern and central UK, accumulation periods of SPI and SPEI exceeding about 6 months show the strongest correlation with NI, whereas the more northern regions show the strongest correlation for short to intermediate accumulation periods. SPI-24 and SPEI-24 are the indicators with the strongest correlation for half of the NUTS1 regions (WAL, CWE, EE, SWE, and SEE), with ρ ranging between -0.38 and -0.65. Streamflow percentiles display a moderate and significant ρ in parts of eastern England, but for the other regions the correlation is weak to moderate and not significant at the 5 % level (two-sided test). There is mainly no or a weak (non-significant) correlation with Y, which varies in sign.

A split into Ih vs. Io, and a split by impact category reveal distinct differences in correlation patterns for some impact subsets (Fig. 3). The difference between I and Ih is rather minor. As can be seen in Fig. 2, Ih is the dominant impact type in the UK. Other drought impacts (Io) show a distinctly different pattern. With weak to moderate ρ for all indicators, no best SPI and SPEI timescale can be singled out. For agriculture, which mostly represents Io, only CEE and CWE show strong relationships, but for all accumulation periods. While the correlation patterns for water supply and freshwater ecosystem impacts are similar to Ih, shorter to intermediate accumulation periods of SPI and SPEI (4–8 months, for a few cases also 12 months) show the highest correlation with water quality impacts. For other impact categories correlation could only be determined for very few regions (wildfire, tourism, waterborne transportation), or not at all due to too few months with impact occurrence. A split by season (Fig. 4) also shows distinct differences, yet could not be determined for all regions given limited impact data if partitioned seasonally.

In Germany, the overall strength of correlation between times series of NI and different indicators is in a similar range as in the UK (-0.62 to 0.74). Contrary to the UK, shorter to intermediate accumulation periods of SPI and SPEI best correlate with impact occurrence (Fig. 5). Eleven of the 13 analyzed regions show the highest ρ for SPEI-2 to SPEI-4; for SPI-24 and SPEI-24 a non-significant correlation in inverse direction is found. The difference between SPI and SPEI is slightly more pronounced in Germany, with SPEI performing somewhat better (absolute difference in ρ up to 0.13). Q performs similar to SPI in many cases. Groundwater level percentiles show no or non-significant weak correlation with NI. In contrast, the sine expression of the month shows a higher and often significant ρ, especially in the northern NUTS1 regions. Similar to the UK, there is no or only a weak correlation with Y. As in the UK, there are regional differences, yet mostly regarding the strength of correlation. Most regions in the north and northeast of Germany display a noticeably lower strength of correlation (mostly weak ρ) than the central and southern regions.

Similar to the UK, a split into Ih and Io reveals differences in correlation patterns compared with I, yet the picture for Ih and Io is the opposite: while the correlation pattern for NIo is rather similar to NI, there is a noticeable shift towards higher correlation with longer SPI and SPEI timescales for Ih. NIo dominates over NIh in some German regions, in contrast to the situation in the UK (Fig. 2). A further split by impact category uncovered the following: agricultural impacts show the highest ρ for SPI and SPEI timescales of 1–4 months, yet most correlations are weak and not significant; there is a shift towards higher correlation with longer SPI and SPEI timescales for impacts on waterborne transportation in some NUTS1 regions; and for all other impact categories correlations could only be determined for one or two regions (BV or BW or RP) due to too little impact data. A seasonal split was also not possible to assess due to too few months with I in spring, fall, and winter; the majority of impacts in Germany occurred in summer (Fig. 2).

For the UK, the general picture from the random forest approach is very similar to the findings from the correlation analysis, both regarding I and different impact subsets (Ih, Io, and I per impact category) (Fig. 6). Long accumulation periods of SPI and SPEI (12 and 24 months) appear as the highest ranking predictors for most regions, except the more northern regions NEE, NEW, and YHU. Q does not show up as important predictor. Distinct differences compared with the correlation analysis include the following: (1) Y plays an important role for I and most impact subsets; (2) for Io, the RF predictor importance shows a shift to intermediate accumulation periods of SPI and SPEI (7 and/or 8 months). This shift is not as clearly discernible in the correlation patterns. The same holds true for the agricultural impacts.

In contrast to the UK, where the RF predictor importance plots look very similar to the correlation analysis plots, there is more variation for Germany (Fig. 7). The RF predictor importance patterns are spottier than the correlation analysis patterns with less smooth transitions between adjacent indicators. Nevertheless, the general tendency of best predictors is confirmed.

While splitting values of all indicators for all impact subsets (I, Ih, Io, different impact categories) were extracted, we only show the threshold distribution, i.e., splitting value distribution, for selected SPI and SPEI timescales (best performance for different regions and/or impact subsets) and streamflow and groundwater level percentiles (Figs. 8, 9). While we display the threshold distribution of individual indicators, it is important to remember they are conditional on multi-predictor interactions in the RF model.

For the UK, the threshold distribution for both meteorological indicators generally shows a considerable range, which decreases with increasing accumulation period. For the same accumulation periods of SPEI the range extends to less negative values. Apart from this, the differences between SPI and SPEI are negligible with interquartile ranges (IQR) predominantly between 0 and -2. When only focusing on the median of the distribution, SPI-8 and SPEI-8 values scatter around -1 for most NUTS1 regions. For SPI and SPEI of 12 and especially 24 month duration the scatter around -1 is slightly more variable. Regarding streamflow percentiles the splitting values cover almost the entire range, the IQR is distinctly larger than for SPI and SPEI, and the median ranges between 0.2 and 0.37. The split by impact category results in slightly narrower ranges of threshold distributions for many impact categories, and often a more negative median (not shown). All indicators show regional differences, however without systematic patterns.

For Germany, the splitting values in the different federal states range from roughly +1.5 to -2/-3 for both SPI and SPEI (Fig. 9). Absolute values of the IQR of German regions are similar to the UK. Contrary to the UK, a regional pattern exists regarding the median of the SPI and SPEI threshold distributions. The southern and most central federal states display a more negative median (mainly between -1 and -1.5) than the northern/northeastern states (with a median between 0 and -1). A small but noticeable gradient from SH to BV can be seen in Fig. 9. Streamflow percentiles show a similarly large spread of splitting values to the UK, yet the IQR is mostly smaller and the median is slightly lower (0.14–0.29). For groundwater level percentiles, the median per region ranges between 0.2 and 0.68; no regional pattern is found. The low amount of impact data for the RF analysis for several impact categories prevented a systematic intercomparison among impact categories.

RF predictions for the UK show that observed and modeled impacts agree well for the NUTS1 regions SWE, SEE, and EE (Fig. 10). In most central regions and LND there is more spread. The northern regions NEE and NEW show least agreement. The R2 ranges between 0.16 (NWE) and 0.73 (WAL) (Table 2). Due to the random component in the RF algorithm, model performance varies marginally for replications. Regional differences more or less reflect the length of each time series and the percentage of months with impact occurrence. That is, regions with R2> 0.6 generally have longer time series and a higher percentage of months with I than regions with lower R2 (Tables 1, 2). For Germany, observed and modeled impacts do not agree well compared to many UK regions (Table 2). However, much fewer data points for Germany than for the UK make a comparison difficult (Figs. 10, 11). Among the federal states of Germany, BV and BB show better agreement than other regions. The majority of federal states yielded an R2 between 0.33 and 0.54 (Table 2). Only four states show an R2> 0.6. Overall, the lower agreement between observations and predictions than in the UK concurs with the shorter time series of indicator and impact time series in Germany, and a smaller percentage of months with NI> 0 (Table 1).

The generally small difference in the mean (Δμ) of observed vs. modeled impacts for both the UK and Germany (Table 2) suggests that the central tendency is well modeled. However, a closer look at the time series of observed and modeled number of impact occurrences (Fig. 12, time series with gray background – RF predictions) reveals that small values are generally over-predicted and large values often under-predicted. The under-prediction of NI causes lower standard deviations for the modeled values than for the observed (Δσ between -0.22 and -0.52, see Table 2).

Furthermore, Fig. 12 shows that predictions and observations in the UK and Germany generally agree well both regarding initiation of impact occurrence and its subsequent temporal evolution. This is also reflected by a moderate to strong correlation between predictions and observations (Table 2). The blue line in Fig. 12 represents an impact threshold of one, as guidance for interpretation: modeled impacts smaller than one may be regarded as an absence of impacts. Taking this into account, the temporal dynamics agree even better, especially regarding impact onset. An obvious disagreement between dynamics of observations and predictions is found in many regions in the UK in 1991/92, where modeled NI is more dynamic than the observed static block of NI following an impact peak. The block-shaped data represent impacts due to a contraction of the stream network in large parts of the south and east of the UK during these years. In Germany, states with larger amplitude of NI (BV, BW, RP, and NW) tend to have a better agreement of temporal dynamics, especially when only focusing on values above the one-impact-threshold line. For states with low amplitude of NI, which often concurs with less negative splitting values (see Sect. 4.3), the temporal dynamics are not as well modeled (not shown).

The RF backwards learning predictions for all years with zero impact occurrence according to the EDII database are shown on white background in Fig. 12. They expose instances of potentially “false-positive impacts”, i.e., a positive number of impacts is modeled while there are no observed impacts. A clear example for the UK is the period 1972–1974, when drought conditions occurred, which would have caused impacts in many UK regions according to the RF model trained on the censored time series. Another example of false-positive impacts in the UK is found for many southern and central regions in the second half of the 1990s after a peak of NI in 1995. While for the UK two major, spatially coherent cases of false-positive impacts exist, the pattern for Germany is more diverse and region-specific.

The correlation analysis and the random forest approach revealed the following insights about the performance of drought indicators, which will be discussed in the context of expectations and literature: (1) the best-performing drought indicators are region and impact category specific, and in the UK season specific to some degree. While in the UK generally long accumulation periods of SPI and SPEI (12–24 months) performed best, short to intermediate accumulation periods (2–4 months) were best linked with drought impacts in Germany. However, there is spatial variability within each country, and differences among impact categories. (2) A comparison among indicators (SPI vs. SPEI vs. Q (vs. G in Germany)) uncovered that in the UK SPI and SPEI perform similarly to each other, and Q performs worse. In Germany SPEI often performed slightly better than SPI, the linkage with Q is better than in the UK, and there is low agreement between G and impact occurrence. (3) The largely congruent findings from the two different statistical approaches independently validate the results.

While much can be speculated about the drivers of region-, impact type-, and season-specific variability, it is nonetheless necessary to explore the underlying mechanisms for the observed differences to rule out purely data-driven, yet physically meaningless, indicator–impact relationships. Regional differences can result from both (1) real physical, spatial differences in geographic properties (e.g., climate, geology, soil, land use), vulnerability towards drought, and hazard characteristics, triggering impacts differing in type and response time, and (2) differences due to inherent spatial and temporal biases in the impact data (see Bachmair et al., 2015 on potential EDII error sources).

In the UK we found differences in best SPI and SPEI accumulation periods between most southern/central regions (long periods) vs. more northern regions (shorter periods). This corresponds well to known differences in the nature of the drought hazard, and impacts. Strong regional contrasts in drought occurrence across the UK have been noted previously, with a particular contrast between the upland northern and western UK, which is susceptible to short-term (6-month) summer half-year droughts, and the lowlands of the south-eastern UK that are susceptible to longer-term (18-month or greater) multi-annual droughts (Jones and Lister, 1998; Marsh et al., 2007; Parry et al., 2011). These findings reflect both the climatological rainfall gradient across the UK and the predominance of groundwater dominated catchments in the south-east (Folland et al., 2015). While we also found regional differences in indicator–impact–linkage patterns in Germany, they mostly relate to differences in strength of correlation (weaker correlation in northern/northeastern states). The smaller amplitude of impact time series in these states may explain weaker correlation in contrast to southern/central states with predominantly larger amplitude, i.e., pronounced impact peaks, as hypothesized by Bachmair et al. (2015).

The differences in indicator–impact relationships between the UK and Germany, and some of the within-country variability, are also very likely a result of the regional composition of drought impact types. It is common knowledge that impacts caused by different types of drought have different response times due to propagation through the hydrological cycle (e.g., Mishra and Singh, 2011; National Drought Mitigation Center, 2015; Wilhite and Glantz, 1985). In the UK impacts associated with drought conditions of surface waters and groundwater (Ih) clearly dominate (see Fig. 2). This agrees well with longer SPI and SPEI accumulation periods as best predictors in the UK compared with Germany. There, the fraction of non-hydrological drought impacts (Io) is distinctly larger than in the UK. Agricultural and forestry impacts in Germany account for roughly 20–70 % of impacts depending on the region, and this may explain why short to intermediate SPI and SPEI accumulation periods are the best predictors.

The identification of best-performing indicators for specific impact types is a key outcome of this study. For instance, agricultural and hydrological drought impacts were generally best linked to shorter and longer SPI and SPEI timescales, respectively. Here, shorter and longer refers to different absolute values: 1–4 (DE) and 7–8 months (UK) for agriculture, and 7 and/or 8 (DE) and 12 and/or 24 months (UK) for Ih. Perhaps unsurprisingly, a universal recommendation about best indicators hence cannot be inferred. However, the similar relative shift in best SPI and SPEI timescales suggests that there are likely to be typical patterns of response for given impact types, but that these are mediated by regional cause–effect mechanisms. This is in line with results of the studies by Blauhut et al. (2015) and Stagge et al. (2015a). Seasonal variation in linkage patterns as observed in our study for the UK further complicates recommendations regarding a single best drought indicator. Part of the variation across the seasons is likely to reflect differences in impact type distribution between the seasons (see Fig. 2). For example, the long SPI and SPEI timescales for winter and spring in permeable catchments in the southeastern lowlands (Fig. 4) reflect long groundwater droughts, which in turn affects groundwater-fed rivers. The winter half-year is the main recharge season and failure to recharge will trigger water use restrictions, while shrinking headwaters will result in freshwater ecosystem impacts. However, less permeable catchments are likely to respond more readily to winter rainfall as the evapotranspiration is low in this season. For the bulk of rivers, the SPI and SPEI timescales are therefore shorter, with impacts related to low absolute water levels mainly in summer and fall, although effects can be long-lasting.

A surprising result is that streamflow did not appear as an important drought indicator in the UK, even after a separation of hydrological drought impacts. In Germany, groundwater level percentiles played only a minor role. There are several possible reasons for these discrepancies. For groundwater level percentiles the mismatch is likely attributable to a lagged groundwater response (Bachmair et al., 2015). One probable reason for the lack of relationship between I and Q may be the nature of the spatially aggregated streamflow data, which represents different catchments varying in size and characteristics (including degree of human influence), lumped over a large administrative area, which does not coincide with catchment boundaries. A further reason may be the nature of the EDII data, especially regarding the sub-divisions of Ih. While in Germany the fraction of instream impacts of Ih is larger (e.g., impaired navigability of streams, water quality, and reduced power production due to a lack of cooling water), water supply impacts dominate Ih in the UK. For groundwater or reservoir-fed water supply systems these impacts are, to a certain extent, disconnected from river flows (the purpose of reservoirs being to smooth out variations in instream water availability).

Overall, despite a rather complex picture in terms of best drought indicator for impact occurrence, the empirical evaluation of drought indicators with text-based impact information proved to be a feasible approach. Given the minor differences in the outcomes of the correlation and the random forest analysis for the UK, both methods appear recommendable. Generally, the strength of the random forest algorithm is that it can handle interactions and nonlinearities among variables, and thus identify non-intuitive relationships (Evans et al., 2011; Hastie et al., 2009). Furthermore, random forests are robust to noise (Breiman, 2001; Hastie et al., 2009), and the bootstrap sampling provides a way to account for the uncertainty of the impact data. Nevertheless, the black-box nature of the RF model (Breiman, 2001) may not be as useful when an intuitive method for the choice of best drought indicator is needed (e.g., when working with a wide range of stakeholders from different backgrounds). For Germany, systematic differences in indicator–impact–linkage patterns were easier to perceive in the correlation plots than in the RF predictor importance plots. For large data sets, the RF algorithm has the potential to detect relatively complex structures; for small data sets, however, this is unlikely to be the case (Maindonald and Braun, 2006).

The analysis of splitting values used in the random forest construction highlighted a large spread. Yet, when focusing on the median there are differences between the countries and among the regions (medians around -1 for SPI and SPEI of different accumulation periods in the UK, and in DE between ca. 0 and -1 (north/northeast) and -1 and -1.5 (southern/central states)) and, to some extent, impact categories.

We regard splitting values during recursive partitioning as estimates of thresholds of impact occurrence because they provide guidance on critical predictor values triggering a consequence. Nevertheless, the uncertainty of the text-based impact data clearly must be taken into account in the search for meaningful thresholds. One cause of the large spread of the threshold distributions is the uncertain timing of actual impact occurrence, especially regarding its termination. Second, in the UK there are impacts appearing as blocks following an impact peak in 1990. They arise from EDII reports citing long-lasting impacts without an exact known end-point or temporal evolution of the severity of the impact (i.e., low-flow anomalies in eastern and southern UK causing a contraction of the stream network and thus impacts on aquatic species reported for the years 1990–1992). Third, hosepipe bans and drought orders do not represent direct impacts of drought, but are triggered (and canceled) by an administrative/political decision as an intermediate step. The onset and termination of the impacts they are meant to reflect may therefore be more uncertain than those for other, more direct impacts. These issues highlight the necessity to separately consider phases of drought development and recovery for drought M&EW (Parry et al., 2016; Steinemann and Cavalcanti, 2006). Fourth, differences in impact reporting between Germany and the UK also need to be considered. In the UK, a significant proportion of impacts for later droughts (2004–2006 and 2010–2012) were sourced from weekly drought management briefs by the Environment Agency (EA). In Germany there is no continuous information on drought impacts, and no unifying impact-reporting scheme exists within the federal state structure.

A reason why we consider tree splitting values as meaningful thresholds of impact occurrence is because Bachmair et al. (2015) found similar threshold patterns for Germany using the same impact data but a different methodological approach based on extracting indicator values concurrent with past impact onset. Both approaches revealed differences in indicator thresholds between northern/northeastern vs. southern/central German federal states. These differences were speculated to result from differences in geographic properties and thus different vulnerability to drought (Bachmair et al., 2015). The northern/north-eastern states tend to have more sandy soils with lower water holding capacity than in the south, and lower natural water availability (Bundesamt für Gewässerkunde, 2003; Bundesanstalt für Geowissenschaften und Rohstoffe, 2007). This could explain the impact occurrence for less negative SPI and SPEI thresholds.

Despite possible shortcomings of EDII data and the method to derive indicator thresholds, we recommend further efforts to empirically validate indicator thresholds with impact data. Drought indicator thresholds informed by impact data may complement and allow comparison with local-scale decision-making on drought triggers, which is usually based on past hydrological data, stakeholder knowledge and the experience of individuals (e.g., Steinemann, 2014). In our study the median of the SPI and SPEI threshold distribution ranged around -1 in the UK, which correspond to the transition between mild and moderate drought according to the SPI classification by McKee et al. (1993). At the same time, the differences in median of the SPI and SPEI threshold distributions for Germany (lower values for SPEI) demonstrate that, despite the standardized nature of such indices, the same thresholds (and corresponding statistical return periods) are not necessarily equally meaningful for drought impact occurrence. To improve that knowledge base, more studies should systematically evaluate and make public the delineation rules of different drought severity classes by using drought impacts (as e.g., Sepulcre-Canto et al., 2012) or by stakeholders' experience (as e.g., Steinemann and Cavalcanti, 2006).

The two parts of the random forest modeling exercise exposed that (1) there are differences among regions in terms of predictive power, with RF models for regions with better impact data (longer censored time series, a higher percentage of non-zero data, and larger amplitude of the impact time series) showing good agreement between observations and predictions; (2) while the temporal dynamics of impact occurrence were reasonably reproduced, over- and under-prediction of small and large values, respectively, are an issue; and (3) backwards learning about impact occurrence for years with no observations (through RF models trained on drought years) provided valuable insights into time periods that potentially lack impact data in the EDII.

Overall, the analysis revealed that RF models generally represent a suitable tool for drought M&EW, yet further model tuning is possible (e.g., reduction of predictors, grouping several regions for increasing the number of observations, and impact category specific models). The finding that there is good agreement between observed and predicted number of drought impact occurrences for regions with good data availability is promising. It underlines the benefit of spending time and resources on impact data collection. The necessity of expanding impact data collection and its benefit for drought M&EW has also been reported by others (Lackstrom et al., 2013; Stahl et al., 2015; Wilhite et al., 2007).

Despite the promising predictive capability of RF models for some regions, the under-prediction of peaks is an issue. One reason for this may be an inherent bias of the random forest algorithm with high values being under-predicted and low values being over-predicted, as observed by others (Ordoyne and Friedl, 2008). This is because the RF algorithm computes averages over a large number of model predictions and hence reduces the range and variance of predictions compared with observed values (Liaw and Wiener, 2002; Ordoyne and Friedl, 2008). Another reason may be an impact-reporting bias caused by impact-reporting increasing during peaks of events. We hypothesize that drought impacts may go unreported during the early stages of a drought, but once a certain threshold of public attention and media coverage is exceeded there is a tendency for more complete reporting. Also, the chances of finding information on drought impacts are higher for recent events due to better online availability of reports and new media channels compared with decades ago.

The RF backwards learning assessment provided a way to scrutinize whether an absence of data in the EDII for certain time periods reflects a true absence of drought impacts, or simply missing data. For the UK, we discovered two prominent examples of droughts that are more severe in modeled impacts than observed EDII impacts: the early 1970s and late 1990s. Both are well-documented droughts, but previous studies suggest the former genuinely had fewer impacts (Cole and Marsh, 2006), in part due to a wet summer in 1973. In contrast, the late 1990s is likely to represent missing impact data. For the 1995–1997 drought, impacts from the hot, dry summer of 1995 are captured in the EDII; the summer drought had very severe water supply impacts, triggering public enquiries, and was thus very extensively reported. However, a protracted groundwater drought, with water restrictions in some areas, extended into 1997 (Cole and Marsh, 2006). However, no formal drought report was issued on the latter phases of the drought, so these impacts have not been captured by the EDII. Altogether, false-positive impacts identified with the RF backwards learning assessment provide guidance on which time periods to focus on when searching for additional impact information.