3.     Possible solutions for flood event attribution

The challenge of non-linear relations between extreme precipitation and flooding applies to all flood cases, and thus also to cases of near-natural hydrology, where hydrological changes during the time interval of interest can be neglected (Fig. 2). We argue that for these simpler cases an approach that can be explored is the expansion of the existing framework of probabilistic extreme event attribution.
On the other hand, cases where relevant hydrological changes have occurred, i.e., land-cover changes and human hydrological interventions, present the additional challenge that the effect of these flood drivers overlaps with the effect of climate change. For these more complex cases, we argue that it is necessary to establish a multi-driver framework for conditional event attribution.

3.1 Possible solution for near-natural cases

The methods of probabilistic event attribution can be expanded to include representation of the relevant hydrological and hydrodynamic processes, by explicitly using flood data and flood modelling. This allows overcoming the problem posed by the non-linearity between precipitation and floods, in two main respects. First, explicit flood attribution overcomes the errors associated with the initial step of event definition. When using precipitation as a proxy for floods, the precipitation event needs to be defined in terms of intensity and extent in space and time, such that it most closely captures the generation of the flood. This involves arbitrary choices (van Oldenborgh et al., 2021). For example, after consultation with local experts and consideration of impacts, it can be defensible to define the triggering event as the cumulative precipitation over either 2 or 5 days, and over an area of either 500 or 2000 km2. However, the results of the attribution may strongly diverge in either case (Angélil et al., 2018), requiring sensitivity tests (Luu et al., 2021). If, instead, the definition is an observed metric of flood hazard, this problem is largely negated. Second, explicit flood attribution addresses the issue of antecedent conditions. Multi-year hydrological simulations, followed by flood simulations, can adequately reproduce the state of, e.g., soil moisture and snow pack.
In the following, we explore possible solutions for: the definition of an appropriate flood metric; the availability of suitable flood data; and the flood modelling.

3.1.1 Flood metric

Adding explicit consideration of floods to attribution means that all analysis is based on a metric of flood hazard, instead of precipitation. As established in event attribution science, the event definition should be closely informed by the socio-economic impacts of the event. For any type of exposed element, the impact is primarily determined by the depth of the flood waters. Other relevant quantities are the flow velocity, flood duration, and any pollution or sediment carried by the water (Vogel et al., 2018). The total impact of the event is determined by the sum of the impacts at each point over the flooded area. Therefore, a flood metric that reasonably relates to the total impact is the total flood area. However, since exposure widely varies over the territory, to better approach impacts, a finer analysis should take into account the location of population and of valuable and critical assets.

3.1.2 Flood data

Probabilistic extreme event attribution requires the following categories of data: 1) observed magnitude of the event, for the event definition; 2) time-series of observations, for trend detection; 3) model-based time-series, representing both factual and counterfactual climates, for the actual attribution (Philip et al., 2020).
For the magnitude of the flood event, it is ideal if collaboration with the local relevant institutions is established; the change is then higher that data from remote sensing, gauges or field surveys can be accessed. Sometimes, local measurements are compromised by the flood (Kreienkamp et al., 2021). In the absence of local data, recent products at continental or global scale are potentially suitable replacements:
For future events, ongoing developments in remote sensing are promising. New flood observation data are becoming available, e.g., in the Fractional Water data from NASA’s Soil Moisture Active Passive satellite (Du et al., 2021). New algorithms may soon reconstruct near-real time observations of flood area, integrating imaging from satellite and aerial sensors with elevation maps (Muñoz et al., 2021).
Time-series of local observations should have sufficient length for trend detection, ideally covering the whole period of climate change, i.e., the last 150 years, or as a minimum the last 4-5 decades, to capture most of climate change. The key issue is that complete, uniform time-series of floods are very rare. For a few locations, the data listed in the previous section may contain a short time-series of historical floods. Failing that, the next best option is to resort to a flood proxy better than precipitation: river discharge. If that is also not available, the best approach is to use modelling reconstructions that are based on observations or on climate reanalysis. The key datasets are:

3.1.3 Flood modelling

Flood modelling should be used to produce time-series of flood events, based both on observed and on modelled boundary conditions. In probabilistic attribution, the former are needed in the step of trend detection, and the latter are needed in the model-based attribution step that compares floods in factual and counterfactual climates.
To produce an observation-based flood time-series, the modelling chain needs to include both a hydrological and a hydrodynamic modelling step. The hydrological model uses meteorological observations on precipitation and temperature, typically at daily time-step; solve key processes like evapotranspiration, infiltration, exchanges between storage in snow, soil and groundwater; and produce time-series of discharge or runoff at a suitable resolution. In turn, the discharge or runoff series are used in the hydrodynamic model, which solves processes related to the surface flow of water more accurately than the hydrological model, and yields peak discharge and flood metrics.
To produce the entirely model-based flood time-series representing factual and counterfactual climate, the modelling chain is the same, but will take precipitation and temperature from climate models. These could come from the simulations coordinated by the Coupled Model Intercomparison Project Phase 6 (CMIP6). CMIP6 includes simulations called ‘piControl’, i.e., ‘pre-industrial control’, reflecting the counterfactual climate of AD 1850 (Eyring et al., 2016), unaffected by anthropogenic greenhouse gas emissions, using constant forcing along the whole duration, of at least 100 years. The factual climate is addressed by the ‘historical’ simulations of CMIP6. These simulations are transient, meaning that increasing levels of greenhouse gas are applied to reflect the history of anthropogenic emissions during 1850-2014. To extend the series until the present, results of the ‘scenarioMIP’ experiments of CMIP6 can be used. CMIP6 results are available at https://esgf-node.llnl.gov/projects/cmip6/. Such results have been used to globally simulate high-resolution floods for the pre-industrial (counterfactual) climate (Scussolini et al., 2020), and both pre-industrial and modern (factual) climates (project ISIMIP2b; Lange et al., 2020).
Additionally, to force flood models at higher resolution, results from regional climate models can be used. A group of dynamical downscaling experiments using different regional climate models is coordinated by CORDEX (Diez-Sierra et al., 2022; https://cordex.org/data-access/). These experiments cover 14 continental domains, at resolution between 12 and 50 km. Simulations start at 1950, and thus do not include the pre-industrial, fully counterfactual climate. Also, they are presently based on CMIP5 global climate models, but results based on CMIP6 will become available in the near future.
However, it is necessary to consider whether the meteorological input from global or regional climate models has adequate resolution and skill, especially with respect to convective precipitation events. These fine-scale events are not adequately represented by parameterisation schemes in those models (Coppola et al., 2020). This can be overcome by the recent emergence of convection-permitting climate models, with resolution finer than 4 km (Luu et al., 2022; Manola et al., 2018). Such input into the flood modelling can improve skills in reproducing flood properties. However, this comes at massive computing costs; hence cannot be performed over a large area or for a large ensemble and their application is rare (Pichelli et al., 2021).
Hydrological simulations for attribution should be carried out continuously for multiple years, as first evidenced by Schaller et al. (2016). This is the only way to capture antecedent conditions, as it allows the hydrological model to adjust to long term effects on, e.g., storage of snow, lakes and groundwater (Ajami et al., 2014). Thus, results will also include floods generated by moderate precipitation, for example, when it coincides with snow-melt, or when it occurs after prolonged cold/wet conditions that have saturated the soil in the basin. Ideally, simulations should be run continuously over the whole interval covered by the multi-decadal climate time-series available. If that is computationally too expensive, and if long-term changes in water storage are negligible, a reasonable choice is to apply a threshold to extract extreme events from the precipitation time-series, and to simulate hydrology and floods during multi-year intervals culminating with these events.
The step of model evaluation should include, besides precipitation and temperature, comparison of modelled floods and discharge with the respective observations, both for the event and for historical time-series. For this, the datasets mentioned above can be used.

3.2 Possible solution for complex cases

When relevant hydrological change has occurred, changes in flood occurrence have more than one driver. This is not contemplated in the probabilistic attribution framework, where the question is a variant of “has anthropogenic climate change increased the frequency of events like this one?” (NASEM, 2016).

3.2.1 A multi-driver framework for conditional event attribution

A multi-driver framework should be formulated to address driver-specific questions that condition the attribution on the states of the other drivers. By systematically including and excluding, in the hydrological and hydrodynamic modelling steps, the effect of land-cover change and of human hydrological interventions, explicit flood attribution can disentangle the relevance of each driver, including climate change. Such framework takes inspiration from and goes beyond emerging literature on storyline attribution for flood management (de Bruijn et al., 2016; Sillmann et al., 2021).
The core steps should be: event definition; definition of hydrological drivers; evaluation of the modelling chain; conditional model-based attribution. Whereas in probabilistic attribution the step of trend detection is essential to determine if attribution even makes sense, in a multi-driver framework this is not pertinent, as any driver-specific trends are confounded by the effects of the other drivers. The event definition and the evaluation of the modelling chain present the same challenges as in the near-natural cases discussed above. We here discuss available data about hydrological changes, to inform the definition of the relevant hydrological drivers, and how to represent hydrological changes in models, to enable the conditional model-based attribution.