The July 2021 flood in central Europe was one of the five costliest disasters in Europe in the last half century, with an estimated total damage of EUR 32 billion. The aim of this study is to analyze and assess the flood within an interdisciplinary approach along its entire process chain: the synoptic setting of the atmospheric pressure fields, the processes causing the high rainfall totals, the extraordinary streamflows and water levels in the affected catchments, the hydro-morphological effects, and the impacts on infrastructure and society. In addition, we address the question of what measures are possible to generate added value to early response management in the immediate aftermath of a disaster. The superposition of several factors resulted in widespread extreme precipitation totals and water levels well beyond a 100-year event: slow propagation of the low pressure system Bernd, convection embedded in a mesoscale precipitation field, unusually moist air masses associated with a significant positive anomaly in sea surface temperature over the Baltic Sea, wet soils, and steep terrain in the affected catchments. Various hydro-morphodynamic processes as well as changes in valley morphology observed during the event exacerbated the impact of the flood. Relevant effects included, among many others, the occurrence of extreme landscape erosion, rapidly evolving erosion and scour processes in the channel network and urban space, recruitment of debris from the natural and urban landscape, and deposition and clogging of bottlenecks in the channel network with eventual collapse. The estimation of inundation areas as well as the derived damage assessments were carried out during or directly after the flood and show the potential of near-real-time forensic disaster analyses for crisis management, emergency personnel on-site, and the provision of relief supplies. This study is part one of a two-paper series. The second part (Ludwig et al., 2022) puts the July 2021 flood into a historical context and into the context of climate change.

Heavy precipitation over western Germany and neighboring countries in July 2021 led to widespread floods, with the Ahr and Erft river catchments being particularly affected. Following the event characterization and process analysis in Part 1, here we put the 2021 event in the historical context regarding precipitation and discharge records and in terms of the temporal transformation of the valley morphology. Furthermore, we evaluated the role of ongoing and future climate change on the modification of rainfall totals and the associated flood hazard, as well as implications for flood management. The event was among the five heaviest precipitation events of the past 70 years in Germany. However, consideration of the large LAERTES-EU regional climate model (RCM) ensemble revealed a substantial underestimation of both return levels and periods based on extreme value statistics using only observations. An analysis of homogeneous hydrological data of the last 70 years demonstrated that the event discharges exceeded by far the statistical 100-year return levels. Nevertheless, the flood peaks at the Ahr river were comparable to the reconstructed major historical events of 1804 and 1910, which were not included in the flood risk assessment so far. A comparison between the 2021 and past events showed differences in terms of the observed hydro-morphodynamic processes which enhanced the flood risk due to changes in the landscape organization and occupation. The role of climate change and how the 2021 event would unfold under warmer or colder conditions (within a −2 to +3 K range) was considered based on both a pseudo global warming (PGW) model experiments and the analysis of an RCM ensemble. The PGW experiments showed that the spatial mean precipitation scales with the theoretical Clausius–Clapeyron (CC) relation, predicting a 7 % to 9 % increase per degree of warming. Using the PGW rainfall simulations as input to a hydrological model of the Ahr river basin revealed a strong and non-linear effect on flood peaks: for the +2 K scenario, the 18 % increase in areal rainfall led to a 39 % increase of the flood peak at gauge Altenahr. The analysis of the high-resolution convection-permitting KIT-KLIWA RCM ensemble confirmed the CC scaling for moderate spatial mean precipitation but showed a super CC scaling of up to 10 % for higher intensities. Moreover, the spatial extent of such precipitation events is also expected to increase.

Throughout its historical development, hydrology as an earth science, but especially as a problem-centred engineering discipline has largely relied (quite successfully) on the assumption of stationarity. This includes assuming time invariance of boundary conditions such as climate, system configurations such as land use, topography and morphology, and dynamics such as flow regimes and flood recurrence at different spatio-temporal aggregation scales. The justification for this assumption was often that when compared with the temporal, spatial, or topical extent of the questions posed to hydrology, such conditions could indeed be considered stationary, and therefore the neglect of certain long-term non-stationarities or feedback effects (even if they were known) would not introduce a large error.

According to Dooge (1986) intermediate-scale catchments are systems of organized complexity, being too organized and yet too small to be characterized on a statistical/conceptual basis, but too large and too heterogeneous to be characterized in a deterministic manner. A key requirement for building structurally adequate models precisely for this intermediate scale is a better understanding of how different forms of spatial organization affect storage and release of water and energy. Here, we propose that a combination of the concept of hydrological response units (HRUs) and thermodynamics offers several helpful and partly novel perspectives for gaining this improved understanding. Our key idea is to define functional similarity based on similarity of the terrestrial controls of gradients and resistance terms controlling the land surface energy balance, rainfall runoff transformation, and groundwater storage and release. This might imply that functional similarity with respect to these specific forms of water release emerges at different scales, namely the small field scale, the hillslope, and the catchment scale. We thus propose three different types of "functional units" – specialized HRUs, so to speak – which behave similarly with respect to one specific form of water release and with a characteristic extent equal to one of those three scale levels. We furthermore discuss an experimental strategy based on exemplary learning and replicate experiments to identify and delineate these functional units, and as a promising strategy for characterizing the interplay and organization of water and energy fluxes across scales. We believe the thermodynamic perspective to be well suited to unmask equifinality as inherent in the equations governing water, momentum, and energy fluxes: this is because several combinations of gradients and resistance terms yield the same mass or energy flux and the terrestrial controls of gradients and resistance terms are largely independent. We propose that structurally adequate models at this scale should consequently disentangle driving gradients and resistance terms, because this optionally allows equifinality to be partly reduced by including available observations, e.g., on driving gradients. Most importantly, the thermodynamic perspective yields an energy-centered perspective on rainfall-runoff transformation and evapotranspiration, including fundamental limits for energy fluxes associated with these processes. This might additionally reduce equifinality and opens up opportunities for testing thermodynamic optimality principles within independent predictions of rainfall-runoff or land surface energy exchange. This is pivotal to finding out whether or not spatial organization in catchments is in accordance with a fundamental organizing principle.

Applying metrics to quantify the similarity or dissimilarity of hydrographs is a central task in hydrological modelling, used both in model calibration and the evaluation of simulations or forecasts. Motivated by the shortcomings of standard objective metrics such as the Root Mean Square Error (RMSE) or the Mean Absolute Peak Time Error (MAPTE) and the advantages of visual inspection as a powerful tool for simultaneous, case-specific and multi-criteria (yet subjective) evaluation, we propose a new objective metric termed Series Distance, which is in close accordance with visual evaluation. The Series Distance quantifies the similarity of two hydrographs neither in a time-aggregated nor in a point-by-point manner, but on the scale of hydrological events. It consists of three parts, namely a Threat Score which evaluates overall agreement of event occurrence, and the overall distance of matching observed and simulated events with respect to amplitude and timing. The novelty of the latter two is the way in which matching point pairs on the observed and simulated hydrographs are identified: not by equality in time (as is the case with the RMSE), but by the same relative position in matching segments (rise or recession) of the event, indicating the same underlying hydrological process. Thus, amplitude and timing errors are calculated simultaneously but separately, from point pairs that also match visually, considering complete events rather than only individual points (as is the case with MAPTE). Relative weights can freely be assigned to each component of the Series Distance, which allows (subjective) customization of the metric to various fields of application, but in a traceable way. Each of the three components of the Series Distance can be used in an aggregated or non-aggregated way, which makes the Series Distance a suitable tool for differentiated, process-based model diagnostics. After discussing the applicability of established time series metrics for hydrographs, we present the Series Distance theory, discuss its properties and compare it to those of standard metrics used in Hydrology, both at the example of simple, artificial hydrographs and an ensemble of realistic forecasts. The results suggest that the Series Distance quantifies the degree of similarity of two hydrographs in a way comparable to visual inspection, but in an objective, reproducible way.

The organization of drainage basins shows some reproducible phenomena, as exemplified by self-similar fractal river network structures and typical scaling laws, and these have been related to energetic optimization principles, such as minimization of stream power, minimum energy expenditure or maximum "access". Here we describe the organization and dynamics of drainage systems using thermodynamics, focusing on the generation, dissipation and transfer of free energy associated with river flow and sediment transport. We argue that the organization of drainage basins reflects the fundamental tendency of natural systems to deplete driving gradients as fast as possible through the maximization of free energy generation, thereby accelerating the dynamics of the system. This effectively results in the maximization of sediment export to deplete topographic gradients as fast as possible and potentially involves large-scale feedbacks to continental uplift. We illustrate this thermodynamic description with a set of three highly simplified models related to water and sediment flow and describe the mechanisms and feedbacks involved in the evolution and dynamics of the associated structures. We close by discussing how this thermodynamic perspective is consistent with previous approaches and the implications that such a thermodynamic description has for the understanding and prediction of sub-grid scale organization of drainage systems and preferential flow structures in general.