# Fragility Analysis Based on Damaged Bridges during the 2021 Flood in Germany
## 2 Materials and Methods  
The July 2021 flood mainly affected Germany, Belgium and Luxembourg, causing over 200 deaths, including 184 fatalities in Germany and 38 in Belgium [43]. The 2021 summer flood was reported to be the costliest flood in Europe and the deadliest in the last 30 years [44]. The flood caused extensive damage to infrastructure, especially bridges, leading to the isolation of many communities in rural areas [45]. Intermodal transport was also affected, having destroyed railway lines, for example, in the Ahr valley, where the reconstruction of the railway is expected to last several years [46]. Furthermore, the failure of the warning chain and the damage to critical infrastructure highlighted the need for improving disaster management and infrastructure planning [47]. The rainfall event according to Figure 1 was particularly severe in the Ahr river catchment region, as the basin received more than 60 mm/24 h, with two thirds of the area registering more than 100 mm/day [48]. In 2016, another flood occurred in the river Ahr, registering a discharge value close to that of a 100 year return period, but in terms of precipitation, the event was milder than the flood of 2021. What caused the water level to rise in 2016 was the duration of the rainfall, which started a week before the flood event, reducing the soil absorption properties [46]. In the 2021 event, most of the rain fell within 24 h, causing all secondary reaches to peak [49]. The consequent discharge accumulated in the main reach. In addition, the antecedent soil moisture condition was affected by the persisting depression in that area. Indeed, although the rainfall's peak occurred on 14 July, the event started on 12 July, continuing in the area throughout 12-13 July. On 13 July, the depression moved towards the Baltic Sea, before reverting to the affected areas on 14-15 July. Certainly, one of the causes of such an extreme precipitation could be found in the increased evaporation due to an exceptionally high sea temperature, compared to the average of that period [46]. Therefore, one can affirm that a climatic shift, or change, was part of the ingredients which led to this unprecedented disaster. Figure 1: Daily accumulated precipitation (combined microwave-IR) 0.1 deg. (GPM GPM_3 IMERGDF v06), 14–15 July 2021 [48]. The highlighted area represents the accumulated daily precipitation, with values \(\geq\) 90 mm (darker region), 50 to 90 mm (intermediate), 30 to 50 mm (lighter region). Base map from NUTS250 [50], river shapefile from Waterbody-DE [51]. Before that event, the river gauge at Altenahr for a period of 100 years was estimated at 241 m\({}^{3}\)/s and through a regression it can be assumed to have been 265 m\({}^{3}\)/s for 200 years, with a R\({}^{2}\) = 0.99 (using discharge values for return periods of 2, 5, 10, 20, 25 and 50 years). However, as per Figure 2, the 2021 event's peak reconstructed by LfU was estimated at 991 m\({}^{3}\)/s [52]. This discrepancy posed additional open questions regarding the treatment of flood events, including the suitability of extreme value distributions and the role of inline structures in producing backwater effects when debris accumulation occurs. Concerning the first question, the highest discharges that occurred in the Ahr river were estimated to be 1200 m\({}^{3}\)/s at Dernau in 1804 and about 600 m\({}^{3}\)/s at Altenahr in 1910 [53]. Interestingly, these events were not included in the flood risk assessment of the local authority, which is debatable from a risk management perspective, given that in 2021 similar values were registered, as per Figure 2 [6]. On the other hand, these rare events, if examined using the extreme value theory, would have led to return periods of about 10\({}^{8}\) years, highlighting a limit of these statistical models [54]. The other issue concerns anthropogenic reductions to the river's cross-section (e.g., parking lot in Altenahr) and bridges, causing increased water levels upstream [6].