Comparison of different threshold level methods for drought propagation analysis in Germany

Drought is a ‘creeping disaster’ (Mishra & Singh 2010) with complex and indirect mechanisms and impacts that are not trivial to study. Hydrological drought occurs when a meteorological drought starts to affect the terrestrial hydrosphere. When this happens, an abundance of processes and feedback mechanisms start to take effect that are yet to be fully understood. One way to deal with the complexity of the processes and feedbacks involved is the conceptualization of drought development as the propagation of negative hydro-climatic signals (i.e. meteorological droughts) through interconnected hydrological subsystems like the soil systems, surface water systems and groundwater bodies. Pinning down controls that slow down, speed up or deviate signal processing (i.e. catchment and climate controls) is one way to enhance process understanding as well as to determine an area's vulnerability to hydro-climatic extremes, i.e. droughts.

Within the drought propagation framework, one method to pin down patterns, processes and controls is to conduct comparative analysis on drought characteristics in the different levels of the hydrological cycle. Drought characteristics are features like drought duration, drought intensity (maximum deviation from threshold), deficit water volume (or severity) or the affected area. They can be obtained from the partial duration time series truncated by a threshold. This method is called the Threshold Level Method. Many studies on drought propagation use the Threshold Level Method in one way or another. This has to do with its ability to define drought characteristics in all possible hydrological variables in a uniform manner. This enables cross-variable frequency analysis of uniform statistical products (drought characteristics) which makes it a suitable tool for drought propagation studies (Van Loon 2013).

The Threshold Level Method was first introduced by Yevjevich (1967) and further elaborated by Zelenhasic & Salvai (1987) into an explicit drought definition approach, as it is used in drought analysis up to date. Two families of threshold level methods emerged: the Constant and the Variable Threshold Level Method. In the case of the constant threshold, as used for example by Tallaksen et al. (1997), Stahl (2001), Andreadis et al. (2005), Vidal et al. (2010), Sheffield et al. (2012) and Tallaksen & Stahl (2014), usually a single percentile of the long-term cumulative frequency distribution of the regarded hydrologic variable is used as a time invariant threshold. In the case of the variable threshold, which has been more widely used in recent years (Stahl 2001; Hirabayashi et al. 2008; Hannaford et al. 2011; Prudhomme et al. 2011; Tijdeman et al. 2012; Van Huijgevoort et al. 2012; Van Loon & Van Lanen 2012; Van Loon et al. 2014), the threshold level varies over the year, following the seasonal amplitude. It can be calculated in numerous ways, for example by taking a smoothed monthly (Van Loon & Van Lanen 2012) or a daily percentile as the varying threshold level (Stahl 2001; Hannaford et al. 2011). Commonly used percentiles for the threshold level for both constant and variable threshold methods range from the 70% percentile up to the 95% percentile (Van Loon 2013), with the 80% percentile being the most common choice. This is true for perennial rivers common in the climate zone regarded in this study (warm temperate, humid). Different percentiles might need to be chosen, for example for intermittent streams.

There are specific caveats for both methods. For example, provided there is a pronounced seasonality, as is the case in Germany, droughts will be defined almost exclusively during the dry season with the constant threshold. Now if droughts are viewed as below normal water availability – which is the most common definition (Mishra & Singh 2010) – then the constant threshold is not the correct way to define droughts, because deficits relative to the relative normal during the wet season can occur as well. From that perspective, a variable threshold is the better choice. On the other hand, drought can also be viewed as a social construct that defines specific periods of climate variability as a natural hazard in, from a physical perspective, a rather arbitrary manner. Which period this is, is defined by the impact it has on society. Therefore, we can technically only speak of drought when there is a real impact, which is during the dry season, mostly, when the absolute water deficit is highest. From that perspective, we actually could not speak of ‘droughts’ when we use the variable threshold, and should rather be calling it ‘relative water deficit’ (Stahl 2001), or use the constant threshold. In any case, a definite answer regarding to which drought definition scheme is the most suitable can only be given by ‘ground-truthing’ said methods by means of empirical impact data, by determining which framework can best predict impact occurrence. In this direction, recent efforts to build empirical impact databases are promising (e.g. Bachmair et al. 2015; Stahl et al. 2016).

As we can see, there are specific advantages and disadvantages of each method, depending on how we define drought. However, while there is some literature available that discusses severity-duration-frequency curves of streamflow for different Threshold Level Methods (Sung & Chung 2014; Sarailidis et al. 2015), as well as some recent non-peer-reviewed literature that discuss different Threshold Level Methods in some way (e.g. Boer et al. 2013; Beyene et al. 2015), to our knowledge no definite comparison of the constant and variable threshold has been published with regard to drought propagation. However, to choose the appropriate threshold method for one's study or management application, more clarity regarding the implication of the choice is essential. The aim of this study is therefore: (1) to evaluate the difference in drought characteristics and drought propagation patterns when analysis is undertaken with the constant and the variable threshold, respectively, and (2) to test if the findings of previous studies – which were based on modelling frameworks, mostly – are reproducible in an observation framework. To do this, this study compares drought propagation patterns under one prominent constant and one prominent variable threshold level method calculation procedure, respectively. The study was conducted for precipitation, discharge and groundwater head in various catchments in Germany. Drought propagation patterns were evaluated by means of drought duration frequency distributions (hereafter referred to as DFDs) and synoptic assessment of occurrence and strength of drought propagation patterns such as lag, lengthening and pooling in the hydrographs.

Streamflow and groundwater data were taken from a dataset collected by Kohn et al. (2014) for a national study on the low flow conditions of 2011. The data pool contained, amongst others, about 280 groundwater gauges and 350 stream discharge gauges across Germany, provided by the administrative departments of the federal states. The data were taken from locations with near-natural conditions. From this dataset, four streamflow gauges with matching unconfined groundwater gauges within their catchment boundaries were selected. These are used for the case study investigations of this study. The groundwater gauges were chosen according to the key borehole approach (Peters et al. 2006), where data from few or only one borehole are taken as a representative for the aquifer.

Precipitation data were taken from the freely available E-OBS dataset (Haylock et al. 2008) as 0.25° grid cell averages. The grid cell precipitation was then interpolated to the catchment area with the Thiessen Polygon method. Precipitation data, as well as streamflow data, were available on a daily basis. However, a larger share of the groundwater records had weekly or two-weekly measurements, which were linearly interpolated to daily resolution. The length of all time series is 36 years (1975–2011), with groundwater heads in units of m (a.s.l.), and stream discharge and precipitation normalized to catchment size, in units of mm/d.

For confirmation/validation purposes, an alternative, largest possible sample of 167 precipitation gauges, 217 streamflow gauges and 117 groundwater gauges was compiled from the above-mentioned sources. Here, selection criteria were less strict than for the case study selection: the data were required to be near-natural and within the 1975–2011 measurement period. The spatial distribution was on a 0.25° grid for precipitation, and randomly distributed for groundwater and streamflow.

The assessment of catchment and aquifer settings was undertaken using various sources of hydrogeological (meta-)data. These data were taken mainly from generalized mapping products as well as primary borehole profiles and stratigraphic cross profiles. Used mapping products were the HUEK200 (BGR & SGD 2011b), the GUEK200 (BGR & SGD 2011a) and the Hydrological Atlas of Germany HAD (Bundesamt für Gewässerkunde 2003), which are compilations of hydrogeological maps depicting, for example, geological setting, hydrological conductivities, soil properties, river network densities etc. Borehole profiles and stratigraphic cross sections were available for the Lachte and Oertze aquifers. Topographic data were taken from the HydroSHEDS DEM, a 100 × 100 m grid (Lehner et al. 2008).

Groundwater levels at the groundwater gauges in the two lowland catchments Oertze and Lachte are close to the surface, ranging from 2 to 4.5 m below ground level (Table 2). The difference in altitude of the groundwater gauge relative to the closest stream branch is small, while groundwater levels are some 3–7 m above stream level, resulting in very small hydraulic gradients (Table 2), indicating high groundwater–surface water connectedness. In the two mountainous catchments, Salz and Spree, groundwater levels are deeper beneath the surface, with water levels ranging from 4.5 to 12 m below ground level (Table 2). Also, groundwater levels fluctuate on a magnitude twice as high as in the lowland gauges. As mountainous catchments, the height difference relative to the closest stream branch is much higher and groundwater levels are between 50 and 115 m above stream level. The distance to stream is not significantly shorter than in the two lowland catchments, resulting in relatively high hydraulic gradients (Table 2), indicating a lower groundwater–surface water connectedness.

Concerning aquifer characteristics, the Lachte and Oertze catchments stretch across the same large-scale, rather homogeneous aquifer system. It consists mostly of sand with some fraction of gravel. The aquifer depth of the top unconfined layer is about 20 m and conductivities range in the magnitude of about 10^–3 to 10^–4 m/s, according to the hydrological map HUEK200 (BGR & SGD 2011b). In the Salz and Spree catchments, aquifer characteristics are more heterogeneous. The Salz groundwater gauge is located on a small plateau above the Salz canyon about 120 m above the stream. According to HUEK200, conductivities in location of the gauge are about 10^–3 to 10^–5 m/s. The aquifer in the location of the Spree groundwater gauge is underneath a saddle in between three hills. The aquifer's material is slope debris with conductivities of about 10^–4 to 10^–6 m/s according to HUEK200, and the aquifer is significantly sloped, according to GUEK200 (BGR & SGD 2011a).

The overall approach was to study drought propagation on the basis of observed precipitation, streamflow and groundwater head records. Only observed data were used in contrast to many previous studies on drought propagation. The data were taken from four study catchments across Germany in order to account for catchment controls, following the comparative approach (Sivapalan 2009). The first step was to calculate drought durations according to the two threshold level methods. The second step was to calculate the drought DFDs. In addition to simple synoptic hydrograph analysis, the DFDs were used to assess the (change in) occurrence and strength of drought propagation patterns such as lag, lengthening and pooling.

Minor peaks can exceed the threshold for a short period of time, cutting droughts in half, thus producing two superficially independent, but actually dependent droughts (Zelenhasic & Salvai 1987). To minimize this effect, pooling procedures are needed (Fleig et al. 2006). First, minor droughts of less than 3 days duration are excluded. Second, an inter-event time criterion, whose sensitivity is disputed (Fleig et al. 2006; Van Loon 2013; Sarailidis et al. 2015), of 5 days was applied on groundwater, streamflow and precipitation. With these methods we follow Van Loon (2013), who discussed this choice in great detail.

It is interesting that slow and fast reacting patterns cannot be grouped according to classical catchment controls, e.g. lowland and mountainous topography, which typically distinguish large, fine grained (thus slow reacting) aquifers from smaller, coarse grained (thus fast reacting) aquifers, respectively. In particular, for the higher 70th percentile (Figure A2, available with the online version of this paper), streamflow in the two mountainous catchments Salz and Spree experience more tailing, i.e. longer droughts – especially under the constant threshold – than the two low-lying, flat catchments Lachte and Oertze. This is unexpected, since streamflow of sloped catchments should react flashier to rainfall events, interrupting drought events more frequently, thus leading to a prevalence of short droughts, not longer tails. This might be due to unexpectedly high storage capacities, however the long tails in the Salz and Spree streamflow DFDs also coincide with a long tail in their correspondent precipitation DFDs, indicating a drier, more continental climate in these two catchments (Figure A2).

Concerning groundwater, we expected alluvial lowland aquifers to be slow responding and therefore experiencing few short droughts (since they are typically large, fine grained aquifers), and small mountainous aquifers to be fast responding, experiencing few long droughts (since typically smaller, coarser grained aquifers are located in this setting). However, exceptions exist in the data presented here, where one lowland and mountainous gauge experiences droughts with few and long durations including some multi-year droughts (Lachte and Salz, Figure 5, Table 3, Figure A2), and one lowland and mountainous gauge experiences many short drought durations (Oertze and Spree, Figure 5, Table 3, Figure A2). This suggests the existence of a slow responding aquifer system in Lachte (lowland) and Salz (mountainous), and a fast aquifer system in Oertze (lowland) and Spree (mountainous).

When different percentiles are taken as threshold level heights, a general pattern is observable. Moving from the 10th via the 20th to the 30th percentile, the drought onset generally shifts to an earlier date, while the drought termination shifts to a later date, resulting in longer drought durations (Figures A3–14, available with the online version of this paper), which is in accordance with the observed patterns in the DFDs (Figures A1–2). Also, additional droughts appear, and drought intensity increases, as the overall distance of hydrograph to threshold increases (Figures A3–14). This suggests that, while having a big impact on the unique drought characteristics themselves, the choice of the percentile as threshold level height is not a primary factor influencing the overall drought propagation patterns, though it does influence their magnitude. Different behaviour in lowlands and highlands when applying a different percentile are not apparent.

The first objective of this study was to evaluate the difference that the choice of Threshold Level Method makes. For this purpose, drought duration was chosen as it is directly derivable from all hydrological variables in a uniform manner, including groundwater head. The overall best drought characteristic to study drought propagation would be deficit volume, which, however, is not trivial to calculate for groundwater (Van Loon 2013). Also, Ko & Tarhule (1994) and Oosterwijk et al. (2009) showed that different drought characteristics are highly correlated, so drought duration can be taken as representative for other characteristics. This study revealed characteristic effects on drought DFDs that can be summarized as follows: when the variable instead of the constant threshold is applied, for streamflow and groundwater there is on average:

• a substantial increase in short droughts;

• a moderate decrease in droughts of medium duration;

• a minor increase in long droughts.

In contrast, precipitation droughts do not differ much between both threshold methods (Figure 7(a) and (b)). This is probably due to the generally flashy behaviour of precipitation, leading to sharp rises and descents in the hydrograph. This way, applying another type of threshold does not produce large differences in drought duration. In addition, precipitation DFDs are rather homogenous across all catchments (Figure 5). A possible explanation for this is the rather uniform climate conditions across Germany; presumably, there would be a higher variability if data were taken from a global dataset in contrasting climates, especially when considering climates with distinct seasonal precipitation patterns.

Furthermore, all DFDs are generally right-skewed. Skewness increases when the variable instead of the constant threshold is applied. This right-shift can be explained with the correspondence of the variable threshold with the overall seasonal amplitude. Any hydrological variable with inherent seasonality fluctuates around its seasonal amplitude, which corresponds to the variable threshold, thus more frequent threshold crossings produce shorter droughts in higher numbers, resulting in a higher right-skew in the associated DFD when the variable threshold is applied. All of the above-summarized patterns in the DFD statistics sustain for the threshold level height tested in this study (10th, 20th, 30th percentile), while overall drought numbers generally decreasing when moving from 30th via the 20th to the 10th percentile.

By means of the synoptic assessment of the normalised hydrographs (Figures 8–11), drought propagation patterns like pooling, lag and lengthening are comparatively stable in lowland catchments like the Lachte and Oertze (Figures 8 and 9) when another type of threshold is applied. In mountainous catchments like Salz and Spree, however, the differences between the two threshold level methods are more pronounced (Figures 10 and 11). As was shown, this was mainly due to streamflow, which crossed the respective threshold at completely different times and magnitudes when one or the other Threshold Level Method was applied. For example, in the Salz, we looked at a winter drought (Figure 10). Winter is the peak of the wet season in Germany, which obviously coincides with a peak in the variable threshold, thus the constant and variable threshold are far apart from each other during that time. This is true for the lowland catchments as well, but in the mountainous regions we additionally do not have reliable baseflow during that time, thus under precipitation deficits, the streamflow hydrograph can drop fast, which can result in very severe droughts with the variable threshold, though not with the constant threshold, which is much lower during that time. In contrast, in summer (see Figure 11), due to very low flows in general, we have the situation that quite small changes in the threshold can produce big differences in drought characteristics, simply because the range of values during this low flow season is narrow and often close to 0. Thus, in both cases the more ambivalent behaviour that we observed in mountainous catchments is probably due to a combination of a higher seasonal contrast and a lower baseflow.

Groundwater was ambivalent as well, up to the degree that slow and fast reacting patterns could not be grouped according to classical catchment controls, e.g. lowland and mountainous topography, which typically distinguish large, fine grained (thus slow reacting) aquifers from smaller, coarse grained (thus fast reacting) aquifers, respectively. Instead, small-scale, within-catchment (or within-aquifer) variability plays a role. A good case for this point can be made by the Lachte and Oertze catchments. Even though both have near-identical hydrogeological settings, the Lachte groundwater gauge, being located in a groundwater recharge area next to a small stream tributary, experiences few and long droughts (Table 3, Figure 5). On the contrary, the Oertze gauge, located within the riverine valley 870 metres from the main river branch, i.e. in a groundwater transition zone, experiences many short droughts (Table 3, Figure 5). This is in agreement with Peters et al. (2006), who found that for the Pang catchment in the UK, droughts in groundwater head near the water divide were much more persistent than those near the stream, and points to the problem concerning representativeness of key boreholes as discussed further below. However, contrary to their explanation of faster aquifer response close to the stream, we hypothesise that it is more likely an effect of convergence. The Oertze gauge is located near the stream and thus has a larger ‘catchment’, i.e. experiences a high degree of accumulation from converging recharge areas (or rather aquifer volumes). In consequence, it shows a high seasonal regularity (Figure A15, available with the online version of this paper) due to steady inflow from these areas. The seasonal amplitude reliably exceeds the threshold during the wet season, thus no multi-year droughts occur in this location. The seasonal amplitude in the Lachte gauge is much less reliable, instead supra-annual patterns with cycles on longer timescales dominate the overall dynamics (Figure A15), coinciding with a twice as high Coefficient of Variation (0.66 for Lachte, 0.32 for Oertze). This is, hypothetically, because it receives a smaller portion of steady water inflow from ‘upstream’ converging aquifer volumes, and has therefore a higher vulnerability to climate fluctuations, which ultimately results in longer (multi-year) drought durations. Therefore, it is hypothesised that the main control here is a groundwater gauge's degree of convergence, which is in turn dependent on its location relative to areas of groundwater recharge, transition, and discharge within an aquifer.

The second objective of this study was to analyse observational data to evaluate possible agreement with those studies on the subject of drought propagation, on which the theoretical concepts were developed, and which are based almost exclusively on modelling experiments (Peters et al. 2003, 2006; Tallaksen et al. 2009; Di Domenico et al. 2010; Vidal et al. 2010; Van Loon & Van Lanen 2012; Van Loon et al. 2012). Only Eltahir & Yeh (1999) and Fendekova et al. (2011) took advantage of observational data, mostly. A further comparison with modelling results would require a model for each of the study catchments which was beyond the project's scope. Instead, we discuss the reproducibility of previously found forms of drought characteristic distributions and theoretical drought propagation patterns in an observational framework as presented in this paper.

The DFDs that were analysed show, in general, classical drought propagation patterns with decreasing numbers and increasing durations when moving from precipitation via streamflow to groundwater. This is in line with previous drought propagation studies (e.g. Tallaksen et al. 2006, 2009). Also, as already pointed out, drought propagation patterns like pooling, lag and lengthening of droughts are comparatively stable in lowland catchments like the Lachte and Oertze (Figures 8 and 9) when the other type of threshold is applied. Results in these areas are therefore in good agreement with previous studies as well (e.g. Van Loon & Van Lanen 2012; Van Loon et al. 2012; Van Loon 2013), while in mountainous catchments like Salz and Spree, the differences between the two threshold level methods are more pronounced (Figures 10 and 11). As pointed out, this was mainly due to a more ambivalent behaviour of streamflow due to less reliable baseflow conditions.

Parallel to the explanation of a more ambivalent streamflow in mountainous settings, an additional problem is posed by the key borehole approach. The modelling frameworks generally reproduce a catchments storage as a whole, while with the key borehole approach, as used in this study, data from few or only one borehole are taken as a representative for the aquifer. This approach has disadvantages since drought characteristics are highly variable within an aquifer (Peters et al. 2006). Still, the key borehole approach was a necessity because the availability of groundwater gauges is scarce and groundwater modelling is time and cost intensive and is subject to many assumptions. Also, we did not have access to data from dense gauging grids. In any case, the conclusions made with data from key boreholes have limited explanatory power for aquifers in its entirety, since evidence exists that the ability to adequately characterise an aquifer's behaviour in its entirety on grounds of only one or few gauges is disputable (Peters et al. 2006). Thereby, the explanatory power is lower in the mountainous gauges (Salz and Spree), which represent only a subset of multi-aquifer storage systems that consists of a variety of smaller storage units of different size, texture etc. The explanatory power is higher for the lowland gauges (Lachte and Oertze) due to flat and rather homogenous aquifer conditions, which is more representative concerning the whole groundwater storage in the respective catchment.

The study has shown the characteristic effects of the two investigated threshold level methods. Those are, under the variable relative to the constant threshold: (1) a substantial increase in short droughts, (2) a moderate decrease in intermediate droughts and (3) a minor increase in long droughts. This holds for streamflow and groundwater, but not precipitation. Also, all DFDs are right-skewed under the constant threshold and skewness increases even more under the variable threshold. These patterns generally sustain in DFD statistics for the different thresholds considered (10th, 20th and 30th percentile). Additionally it was shown how different hydrogeological settings can impact propagation patterns. Most prominently, it was found that the two lowland groundwater gauges showed significantly different response patterns, hypothetically due to different degrees of convergence, i.e. the amount of aggregated water they receive.

Still, it is the lowland setting where the main results of previous studies on drought propagation can be generally confirmed, while in the mountainous catchments, theoretical drought propagation patterns were less often true, mainly due to lower baseflow. This study gives insight how, especially in the mountainous catchments, while different percentiles for the threshold did not change drought propagation patterns in a major way, the drought propagation patterns can be instable across threshold methods since drought characteristics like onset, intensity and duration of droughts change significantly when another type of threshold is applied. This happens up to the extent that individual droughts disappear completely or emerge at entirely different times. The effect is most pronounced in streamflow, less extreme in groundwater and least extreme in precipitation. The differences in the occurrence of actual events are to some extent averaged out in the statistics, such as the DFDs we studied, where drought propagation patterns were more stable, even when different percentiles were chosen as threshold levels. Still, this points to the risk of diverging inference that can be drawn from the same data, especially in hydrograph discussion, depending on which type of threshold, constant or varying, is applied. Thus, in any application, our results suggest that the distinct advantages and disadvantages of each method have to be weighed carefully because they can lead to diverging inferences from the results.

This study was supported through a scholarship from the Rosa Luxemburg Foundation to the first author. The authors would like to thank the three reviewers, who provided very helpful suggestions and added quality to the study. Streamflow and groundwater data were collected by Kohn et al. (2014) with special thanks to the following federal and regional state authorities of Germany, who provided the data: LfU, DWD, HLUG, LANUV, LfULG, LLUR, LUA, LUBW, LUGV, LUNG, LUWG, LHW, LKNM, NLWKN, StALU-MS, StALU-VP, StALU-WM and TLUG. For the precipitation data, we further acknowledge the E-OBS dataset from the EU-FP6 project ENSEMBLES (http://ensembles-eu.metaoffice.com) and the data providers in the ECA&D project (www.ecad.eu).