Spatial counterfactuals to explore disastrous flooding

We selected the eleven river floods in Germany with the highest damage from the HANZE database (Paprotny et al 2018). We did not include events before 1950, as data availability, particularly for streamflow, is low in Germany prior to the 1950s. From this list, we deleted the Oder flood in 1997 and the flood in June 1994. The Oder marks the border between Germany and Poland and is not included in our flood model. For the 1994 flood the affected river basin is not given in the HANZE database, and our model does not show evidence of severe flooding during this period. However, we added the July 2021, i.e. the most expensive disaster in Germany. For each of these ten events, we define the start day of the flood event as given in the HANZE database and from available rainfall and streamflow data for the 2021 flood (table 1). To ensure that the event precipitation is captured completely across Germany, we define the shifting day as seven d prior to the event start day. Starting from the shifting day, we use the shifted precipitation to force the flood model. The selected floods contain winter, spring and summer events and represent the spectrum of flood timing in Germany.

For each of the ten events, we consider 25 precipitation scenarios, consisting of the observed (no-shift) precipitation and 24 shifted precipitation fields. To this end, we shift the observed precipitation in eight directions (N, NE, E, SE, S, SW, W, NW) by three distances (20, 50 and 100 km).

Shifting the event precipitation fields up to 100 km in all directions is well justified given the process scales and mechanisms involved. The paths of precipitation-generating low-pressure systems are dominated by non-linear interaction with synoptic- and larger-scale phenomena (at scales of ∼1 000 km or more). Cyclone tracks do not have fixed trajectories as previously assumed (van Bebber 1891). For example, Vb cyclone tracks can yield extreme precipitation at locations scattered across Central Europe, and the Atlantic winter cyclone path type impacts precipitation all over western Germany (Hofstätter et al 2016, Akhtar et al 2019).

Therefore, the precipitation fields of single events might unfold differently, given a slightly different synoptic situation. For example, the major moisture transport trajectory responsible for the 2021 flood was located on the western flank of a synoptic-scale persistent blocking system (Mohr et al 2023). A slight change in the blocking position or extension would have implied a shift in the moisture transport trajectory and the associated precipitation pattern of a few ten km, still influenced by orographic enhancement. The orography impacts the precipitation amounts in case of long-lasting events (>12 h), especially in the area of the Black Forest in southwest Germany, the Ore mountains in southeast Germany and the European Alps with length scales of ∼100 km and larger. This constraint is, however, less effective for precipitation events with larger return periods (e.g. five years, as demonstrated by Lengfeld et al 2021, using 20 years of German weather radar data).

We apply the grid-based mesoscale hydrologic model (mHM) (Samaniego et al 2010, Kumar et al 2013); specifically, the implementation of Samaniego et al (2019), which considers land use changes by using four historical land use layers, with spatial resolution of five km and daily time step. mHM is forced using the E-OBS product with spatial resolution of 0.25° covering Germany and the headwater parts in neighbouring countries for the period 01/1950–12/2021 at daily resolution. We interpolate the E-OBS data to obtain five km resolution as input for mHM. mHM utilizes a seamless multiscale parameterization regionalization to generate a spatially consistent set of regionalized model parameter fields, enabling a more accurate representation of the spatial patterns of hydrological processes.

To ensure the reliability of our findings, a multi-basin optimization is performed across a wide range of hydrologic regimes throughout Germany using twelve river gauges across the major river basins during the ten year period 01/2000–12/2009. The optimization utilizes the dynamically dimensioned search algorithm (Tolson and Shoemaker 2007) to calibrate 24 mHM transfer-function parameters globally. As objective function, the weighted Nash–Sutcliffe Efficiency (wNSE) that is highly focused on flood peaks is applied (Hundecha and Merz 2012).

In this way, we obtain a spatially consistent parameter set that can represent the hydrological processes across Germany. The performance of the calibrated model is assessed for 119 gauges across entire Germany over the period 01/1985–12/1994. Some smaller catchments show poor performance due to the coarse resolution of the meteorological forcing (0.25°) and the hydrological modelling resolution (5 km). However, the median values of wNSE (0.64) and KGE (0.44) indicate that the calibrated parameter set can effectively represent the observed discharge and especially the high flows for multiple catchments across Germany.

The validated mHM version is forced by observed precipitation for 01/1950–12/2021 to obtain the baseline flood situation for Germany. The spatial counterfactuals for a given event are generated by running mHM with observed precipitation until the specific shifting day. Then the observed precipitation is replaced by the shifted precipitation fields for a period of three weeks. In this way, the shifted precipitation fields are combined with the actual antecedent catchment conditions.

For quantifying the severity of flood events, we compile a dataset of 516 streamflow gauges (figure 1). We use the simulated streamflow, whereas mHM is driven by observed meteorology, to derive the annual maximum flow for each gauge. Then we estimate the flood frequency by fitting the generalised extreme value distribution to the annual maxima via the maximum likelihood method. These flood frequency curves are then used to assign a return period to each gauge for each flood event. We search for the highest streamflow value within three weeks after the event start day and transfer this streamflow value into the respective return period based on the flood frequency curve of the gauge.

To obtain a quantitative indicator of the severity of floods, that affect several rivers and tributaries, we introduce the severity indicator SI:

$$\begin{equation*}{\text{SI}} = { }\frac{1}{{{n_G}}}{ }\mathop {\mathop \sum \nolimits }\nolimits_1^n \frac{{Q_i^P}}{{Q_i^{10}}}{ }|{ }Q_i^P > Q_i^{10}\end{equation*}$$

where n_G = 516 (total number of gauges), $Q_i^P$ is the peak flow of the event maximum at gauge i, and $Q_i^{10}$ is the 10 year flood quantile at gauge i. SI considers only gauges that have a peak larger than the 10 year flood. Smaller peaks are assumed to be irrelevant for flood damages in Germany. SI combines the local severity (by considering the local flood peaks normalised by the 10 year flood) and the spatial extent of the event (by summing up the local severity of all gauges that are affected by a flood larger than the 10 year event).

The proposed indicator is similar to the flood severity indicator developed by Uhlemann et al (2010), however, it uses a higher threshold (10 year flood instead of 2 year flood) and does not weigh the severity with the length of the flood-affected river reach. We use a higher threshold, as the indicator of Uhlemann et al (2010) tends to label large-scale events with relatively small return periods as more severe than spatially confined events with very high return periods; the overall severity of floods thus tends to disagree with their impacts. Further, we refrain from weighting as our set of streamflow gauges is rather homogenous across Germany and we can thus assume that each gauge has a similar weight.

Here, we present the results for three important disasters in detail. The overall patterns of flooding are well represented by our model (figure 2, second row): the 1993 flood affected mainly the middle and lower parts of the Rhine basin, while the 2002 flood caused heavy damage in the Elbe and Danube catchments. The 2021 flood was exceptional as it occurred mostly as flash flooding in small rivers. Although our model works with a comparatively coarse space-time resolution, the overall spatial pattern of the event is well represented.

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Shifting the event precipitation creates upward and downward counterfactuals, i.e. less severe and more severe situations (figures 2(A1)–(C1)). Whether, and to which extent, the spatial shift aggravates the flood situation depends on the distance and direction of the shift. The larger the shifting distance, the larger the change in flood severity. The influence of direction is explained by the boundary effect. All three disasters occurred in regions close to the German border. Shifting the precipitation towards the center of Germany tends to increase the severity, as more gauges within Germany are flood-affected. For instance, the 2021 flood hit the border region of The Netherlands, Luxembourg, Germany and Belgium. In Germany, mostly rivers left to the Rhine were heavily affected (figure 2(C2)). Shifting it towards the border relaxes the flood situation for Germany; however, it aggravates the situation for the respective neighbouring countries. This effect, however, cannot be quantified as our hydrological model does not include the river network in the neighboring countries.

Shifting precipitation can create much more severe flooding than the historical realization. For instance, if the storm track that caused the 1993 Christmas flood had occurred 100 km towards northeast (figure 2(A4)), then the flooding would have been 35% more severe (when measured by SI.) The gauges that showed strong flooding (streamflow larger than the 50 year flood peak) in the historical realization would be similarly affected in this scenario—in addition, many other gauges with observed flood peaks smaller than the 50 year event would also show strong flooding.

Spatial counterfactuals can also create heavy flooding in regions that have been spared from havoc by the observed event. For instance, shifting the precipitation by 100 km towards northeast for the 1993 Christmas flood leads to flood peaks with return periods of up to 1 000 years in the Weser river basin (figure 3(A4)), which was only mildly affected in reality.

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Next, we compare the severity of all selected disasters with their spatial counterfactuals in an aggregated way. To this end, we plot the SI ratio (figure 3), defined as the ratio of the severity index between the shifted and observed, no-shift, events. Shifting the event precipitation can transform a disaster into a non-flood situation with SI ratios of zero; i.e. there is no gauge that shows a peak larger than the 10 year flood. Shifting also generates much more severe situations. For instance, we obtain floods up to three times more severe for the January 1995 event. The most disastrous flood in German history, the 2021 flood, is aggravated by up to 2.4 times by shifting the event rainfall.

The sensitivity of flood severity to shifts in event precipitation varies strongly across the event set. The most sensitive event is the 1993 flood. Shifting the precipitation can reduce the disaster to a non-flood situation or increase its severity by 300%. The least sensitive event is the 2013 flood. Most of the spatial counterfactuals of this event show SI ratios between ±20%.

The different sensitivity is a consequence of boundary effects; shifting a precipitation event, that occurred close to the border, inwards (outwards) may strongly increase (decrease) the flood severity for Germany. Another factor influencing the sensitivity is the spatial variation of the antecedent state and the event precipitation. For instance, the small sensitivity of the 2013 flood is partially explained by the rather homogeneous antecedent state. In the weeks prior to the event, exceptional rain led to wet soils across large parts of Germany (Schröter et al 2015). The situation is different when the antecedent state is spatially heterogeneous; in that case, shifting the event precipitation may strongly affect the flood severity depending on whether it is shifted from a wet area to a dry area or vice versa.

Because unprecedented floods tend to overwhelm disaster management, we analyze to which extent the spatial counterfactuals lead to flood peaks higher than the flood-of-record. To this end, we first select four gauges from the major river basins and plot the counterfactual flood peaks along with the flood frequency curves (figure 4). In two out of four cases cases, we observe counterfactuals that are substantially larger than the flood-of-record, thus qualifying as unprecedeted flood. For the gauge Oberthau/Weiße Elster, we obtain a flood peak 35% larger than the flood-of-record. While the flood-of-record has a return period of 55 years, the largest counterfactual represents a 200 year event.

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Figure 5 shows how the spatial shifting of event precipitation generates unprecedented floods. At 369 gauges (72% of all gauges) we find at least one counterfactual flood that has a peak higher than the flood-of-record. At several gauges, particularly in the west of Germany, there are around 30 instances where counterfactuals exceed the flood-of-record. Obtaining unprecedented floods in 72% of all gauges demonstrates that spatial counterfactuals are an adequate means to develop exceptional floods, given that the ten observed disasters led to flood-of-records in only 24% of gauges (figure 5).

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Given that spatial counterfactuals produce many unprecedented events, we propose to use this approach to overcome people's reluctance to discuss exceptional floods. It could be a lever to overcome the availability bias, which is often a barrier to thinking about exceptional events, as people can more easily relate to an actual event that is used as starting point of the counterfactuals compared to a more abstract extreme scenario such as a 500 year flood. In addition, it might help to overcome the near-miss effect in risk perception. After a near-miss, i.e. an event with potentially serious adverse outcomes that did not materialize, people tend to feel safe and underestimate the risk (Bogani et al 2023). Demonstrating what could have happened if the storm track had taken a slightly different trajectory, might convince people that they just got lucky and that their feeling of safety is biased. However, people can show a place-based optimism bias and wrongly believe that an extreme event is more likely to hit nearby places instead of their own place (Klockow et al 2014). Hence, the role of spatial counterfactuals in the communication of flood risk and mitigation measures to lay people needs to be addressed in the future.

A potential weakness of our spatial counterfactual approach is a degree of subjectivity. Expert knowledge of the flood-triggering meteorological mechanisms in the given region is needed to exclude spatial shifts that are not plausible. Furthermore, flood generation depends on the interactions between atmospheric and land surface processes. A priori, it is not clear which shifts in terms of direction and distance cause the largest flood. Hence, one might need to simulate a large number of scenarios to identify the most severe response for a given region.

Our flood model used does not include the consequences of flooding in terms of inundation and losses. A counterfactual analysis including inundation areas and losses would be even more informative. Conceptually, it would be straightforward to extend the approach and to propagate the simulated streamflow through a hydrodynamic model providing inundation areas and through a loss model. For Germany, this could be achieved by the continuous simulation approach of the entire flood process chain (Sairam et al 2021). A computationally less demanding approach would be to transfer the point-based peak estimates into inundation areas by sampling and mosaicking the pre-computed inundation maps (Bates et al 2021). Such an extension would open the possibility to investigate counterfactuals that emerge at a later stage in the flood process chain. For instance, one could explore the effects of failing warning systems or evacuation plans on the flood situation.