In mid-July 2021, heavy precipitation caused flooding for multiple tributaries of the Meuse and Rhine rivers which resulted in many deaths and exceptional damage. The Ahr in Germany, the Vesdre in Belgium and the Geul in the Netherlands suffered the greatest damage in each country. The first step in reducing such high damage from international, minor catchments is to build an understanding of the flood event.

The goal of this study was to analyse how extreme several hydrological aspects of the flood event of July 13-16 were for the Ahr, Vesdre and Geul. Analysing the extremity of an event requires a description of that event which helps with building knowledge. Its extremity places that knowledge into context. A flood with a 10-year return period will require a different approach than one with a 1000-year return period to balance the risk reduction and required effort. Three international catchments have been selected as case studies to allow an in-depth analysis of catchments and compliment current research on the flood event with a transboundary perspective.

The hydrological aspects considered for this study concern the forcing, flow mechanisms and response. For the forcing and response, a data analysis has been performed to study the extremity of the origin, magnitude, spatial and temporal variation of the precipitation, as well as the magnitude of the flow. Characteristics of both were used to determine the flood type. The data analysis on flow magnitude and seasonality has been supplemented by historical information to give more insight. The flow mechanisms have been derived from two models with varying structure and spatial variation by analysing parameter values and internal states.

The origin of the precipitation is considered as extreme since the cold core low, a low pressure area with a cold centre, was accompanied by several factors in a rare combination that likely contributed to the high precipitation amounts. The precipitation amount of July 14, the wettest day of the event, was of extreme magnitude according to the return periods of over 1000 years for several gauges. Although there was a large spatial variation in precipitation and thus their return periods, the spatial pattern showed a positive correlation of medium strength with the climatic pattern and is thus not considered as extreme. The temporal variation of the event is also not extreme. So during the event, only the amount of precipitation was extreme, but the precipitation amount in the preceding month was also extreme.

The peak discharges have been estimated to be around 990, 600 and 90 $[m^3/s]$ at the downstream gauges of the Ahr, Vesdre and Geul. The higher peak discharges coincide with sharper hydrographs and a stronger relief and impermeable soils. The return periods of the peak discharges were over 1000 years. Such extreme return periods are not surprising as such discharges had never been measured before. However, historical reconstructions show that similar flood events have occurred at least once for the Ahr. The assumed rare occurrence of summer floods in the regions was also debunked by historical information as 21 to 44\% of the historical floods occurred during the summer half-year. Another assumption by reports on the flood event was the flood type identification of a flash flood. The large spatial and temporal scale, as well as lag times for downstream gauges of 13 to 24 hours, do not resemble a flash flood, but rather a long precipitation event with a fast response.

Two models, a lumped, simple model based on the HBV model and a distributed more complex model based on the SBM model, have been calibrated for several years preceding the flood event, resulting in a good performance. Their performance for the flood event was low due to a strong underestimation of the peak discharge. This underestimation was resolved by a re-calibration. The re-calibrated parameters and internal states of the models show an increase in fast responding mechanisms, up to unprecedented magnitudes. The SBM model includes more processes and shows a rare amount of overland flow due to saturation excess. The fast response mechanisms, both in magnitude and relative runoff contribution, were unprecedented and can be considered as extreme.

The magnitudes of the precipitation, flow mechanisms and discharge were extreme for the 2021 flood event. The extreme flows were possible due to fast flow mechanisms, most likely overland flow due to saturation excess, which can be linked to the extreme pre-conditions. The strong relief and impermeable soils also seem to play a role in this extreme response. All catchments are capable of a fast and strong runoff response and although the forcing of the event was extreme, a new flood event in the future can not be excluded and so a higher level of preparedness and protection is required.

This study should be considered as an exploratory first step for action on the flood event. In order to move forward and increase the protection of the region, more detailed research is required. Such research can focus on several areas. Varying the study regions could be helpful for specific purpose. Several examples are an analysis of the entire region for a precipitation analysis, one catchment study for flood measures, or a catchment comparison for detecting hydrological influences. The anthropogenic influences can also provide more insight and opportunities and could be included in these future researches. The use of models was limited in this research but their further development is essential for flood risk management. Uncertainty is another topic that deserves more attention. An important factor in decreasing the uncertainty is to construct robust and extensive measurement infrastructure. Nevertheless, without more international cooperation and data accessibility the additional data will not reach its full potential. International cooperation also provides more value to the previous recommendations. This research shows that the transboundary catchments of the case study can be compared and give more insights to the overall behaviour.