# An agent-based modeling of rescue operations for the evaluation of short-range flash flood forecasts

Maryse Charpentier-Noyer, Olivier Payrastre, Eric Gaume, Pierre Nicolle, François Bouttier, Axelle Fleury, Hugo Marchal

► To cite this version:

Maryse Charpentier-Noyer, Olivier Payrastre, Eric Gaume, Pierre Nicolle, François Bouttier, et al. An agent-based modeling of rescue operations for the evaluation of short-range flash flood forecasts. Journal of Hydrology, 2025, 657, pp.133048. 10.1016/j.jhydrol.2025.133048. hal-05445015

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Research papers

# An agent-based modeling of rescue operations for the evaluation of short-range flash flood forecasts

Maryse Charpentier-Noyer<sup>a,b,D,*</sup>, Olivier Payrastre<sup>b,D,*</sup>, Eric Gaume<sup>b,D</sup>, Pierre Nicolle<sup>b,D</sup>, François Bouttier<sup>c,D</sup>, Axelle Fleury<sup>c,D</sup>, Hugo Marchal<sup>c,D</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Keywords:**

Flash-flood

Forecast

Agent based model

Rescue operations

## ABSTRACT

This paper presents the application of an agent based model to evaluate how short-range flood forecasts may improve the emergency management of a severe flash-flood event. The considered flood hit several inhabited areas in the Aude River basin, south-eastern France, in October 2018. Particularly, the capacity to trigger timely rescue operations at the right places is evaluated and compared, depending on the input information used in the emergency decision process: from rainfall observations up to flash flood impacts forecasts at the river reach scale. To achieve this evaluation, the field operations of firemen rescue teams are simulated in an agent-based model, which provides a detailed description of the complexity of the emergency situation: location and timing of flood damages, limited number of rescue teams, traveling times, decisions taken under uncertainty about the future evolution of the event. The flash flood impacts forecasts involved in the decisions are obtained using (i) three different short range (0-6h) quantitative precipitation forecast (QPF) products or a naive zero future rainfall scenario, (ii) a distributed hydrological model and (iii) a simple impacts model evaluating the number of flooded buildings. The presented results confirm that the efficiency of the rescue operations is generally improved when using QPFs as input of the decision chain, due to the increased anticipation. But they also illustrate how this added value can be highly altered by the combined effects of forecast uncertainties (false alarms) and limited available rescue means. In a fictive situation where rescue means are extremely limited, using a zero future rainfall scenario proves to be almost as efficient as using QPFs.

## 1. Introduction

Flash floods (FF) are responsible for an important proportion of the flood damages and fatalities over the world (Barredo, 2006; Llasat et al., 2013; Petrucci et al., 2019; WMO, 2020). The large impacts of flash floods can be mostly explained by their limited predictability (Georgakakos, 1986; Borga et al., 2008), their fast dynamics and high specific discharges (Gaume et al., 2009; Marchi et al., 2010), and their high spatio-temporal variability. Although several operational FF monitoring and warning systems are already implemented in several regions of the world (Javelle et al., 2016; Gourley et al., 2017; Corral et al., 2019), most of these systems rely on weather radar precipitation observations, which highly limits their anticipation capacities. Therefore, improving the anticipation capacity of flash floods, and consequently the efficiency of the flood emergency management, remains one of the main expected adaptation measure to be developed in the forthcoming years.

The use of short-range rainfall forecasts based on radar advection techniques and/or convection permitting numerical weather prediction models offers an interesting avenue to extend the anticipation lead times beyond the response times of the small watersheds hit by flash floods (Collier, 2007; Hapuarachchi et al., 2011; Zanchetta and Coulibaly, 2020). However, these approaches still suffer from significant uncertainties in the spatio-temporal representation of heavy precipitation (Roberts and Lean, 2008; Clark et al., 2016; Armon et al., 2020) and the subsequent occurrence of flash-floods (Silvestro et al., 2011; Vincendon et al., 2011; Furnari et al., 2020). These uncertainties can nevertheless be represented through ensemble forecast approaches, which have been widely developed and evaluated in the literature for FF forecast purpose (Vié et al., 2012; Alfieri and Thielen, 2012; Davolio et al., 2013, 2015; Hally et al., 2015; Nuissier et al., 2016; Amengual et al., 2017; Furnari et al., 2020; Poletti et al., 2019; Sayama et al.,

<footnote><sup>a</sup> SHECI-DPECI, DREAL Centre Val de Loire, Orléans, 45064, France</footnote>

<footnote><sup>b</sup> Univ Gustave Eiffel, GERS-LEE, Bouguenais, F-44344, France</footnote>

<footnote><sup>c</sup> CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, 31000, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: maryse.charpentier-noyer@developpement-durable.gouv.fr (M. Charpentier-Noyer), olivier.payrastre@univ-eiffel.fr (O. Payrastre).</footnote>
2020; Amengual et al., 2021; Lovat et al., 2022; Charpentier-Noyer et al., 2023; Godet et al., 2023).

However, due to the low occurrence frequency of extreme flash-
floods, the limited available discharge observations for these floods,
and the limited length of re-forecast chronicles for newly developed
ensemble rainfall forecasts approaches, the evaluations are still often
limited to single events and/or single locations (Charpentier-Noyer
et al., 2023), even if some contributions already tried to propose eval-
uations at regional scales (Silvestro and Reora, 2012; Davolio et al.,
2015; Anderson et al., 2019; Sayama et al., 2020; Charpentier-Noyer
et al., 2023; Godet et al., 2023). One common conclusion is that using
ensemble FF forecast may significantly increase anticipation with good
detection levels, but at the price of a significant number of false alarms.
Therefore, the added value of ensemble FF forecasts highly depends on
the end user's problematic, which fixes the respective benefits of an
increased anticipation, and costs of false alarms: integrating the end-
users objectives in the evaluation of FF forecasts is necessary to achieve
robust and objective evaluations (Charpentier-Noyer et al., 2023). The
evaluation of weather forecasts based on users decision-making has
been widely developed in the past through the concept of economic
value of forecasts (Katz and Murphy, 1997; Katz and Lazo, 2012), and
particularly the application of the cost/loss ratio decision model (Mur-
phy, 1977, 1985; Wilks, 2001; Zhu et al., 2002). However, these
approaches generally show a limited capacity to represent complex
decision-making situations realistically (Katz and Lazo, 2012). This pa-
per aims to advance one step further towards the representation of such
a complex real world problematic (i.e. the management of emergency
rescue operations), through the use of agent-based modeling.

Agent based models (ABMs) have been increasingly used in the last years to represent the complex interactions between flood spatio-temporal dynamics, institutional decisions, and human exposure and behavior (Zhuo and Han, 2020; Simmonds et al., 2020; Anshuka et al., 2022). ABMs were applied for a wide panel of objectives, falling mostly into two main categories: (i) long term flood adaptation and risk mitigation, and (ii) flood emergency management. The first category includes the assessment of different risk management policies, which may include insurance schemes, structural hazard reduction or vulnerability reduction measures, and/or flood risk communication and awareness (Dubbelboer et al., 2017; Jenkins et al., 2017; Haer et al., 2016, 2017; Crick et al., 2018; Tonn and Guikema, 2018; Abebe et al., 2019a,b; Haer et al., 2020; Han et al., 2020, 2022; Michaelis et al., 2020; Taillandier et al., 2021; Sung et al., 2022; De Ruig et al., 2023). The second category includes the evaluation of emergency flood management in terms of both human and economic losses. While some studies focused on the identification of factors governing the risks (Shabou et al., 2017; Zhu et al., 2019; Dai et al., 2020), other ones evaluated the efficiency of specific management measures, such as anticipated warnings, definition of shelter areas and/or evacuation, and local or property level temporary flood protections (Dawson et al., 2011; Du et al., 2017a,b; Higo et al., 2017; Lumbroso and Davison, 2018; Liu and Lim, 2018; Yang et al., 2018; Li et al., 2019; Shirvani et al., 2021; Novoa et al., 2023). All these studies revealed the potential of ABM for reflecting the complex human decision and behavior processes during floods, allowing to account for the response of populations to the developed policies or strategies. The agents are generally individuals or householders, sometimes complemented with institutional services. However, the review of literature suggests that up to now, none of these studies aimed to evaluate the efficiency of rescue operations, by integrating the emergency rescue teams as agents. This perspective seems interesting since ABM appears as an ideal tool to evaluate the capacity to trigger timely rescue interventions at the right places, and to account for the complexity of this process in an optimization perspective: multiple locations of flood damages, limited rescue means, decision under uncertainty about the future evolution of the event, possible travel difficulties for rescue teams, etc...

This paper proposes a first application of an ABM to evaluate the
added value of FF forecasts for a specific category of end users, i.e. the
emergency rescue services. The ABM enables representing the field
interventions of rescue teams, which are triggered based on varied
information, including FF forecasts. Through an explicit representation
of the rescue operations at the regional scale hit by the flood event, the
ABM should be able to measure the actual benefits of using anticipated
(but inaccurate) FF forecasts to trigger interventions, instead of waiting
for field observations or emergency calls. The approach can be used
to evaluate decisions taken based either on deterministic forecasts or
specific percentiles of ensemble forecasts. The main objective is to
illustrate how the efficiency of the emergency response may be altered
by (i) the uncertainties of hydrometeorological forecast information
used to anticipate flood risks, and (ii) the importance of available
resources for rescue operations (i.e. the number of rescue teams). The
presented case study corresponds to the October 2018 flood which hit
the Aude river watershed in south-eastern France.

The paper is organized as follows: Section 2 presents the structure of the ABM implemented for the study; sections 3 and 4 describe respectively the case study and the different FF risks forecasts used to feed the ABM; the results are presented and discussed in sections 5 and 6. The Section 7 finally includes the main conclusions of this work.

## 2. Principles of the agent-based model used for evaluation

The implemented ABM aims at estimating whether the emergency
rescue operations would be more efficient if the interventions were
triggered by forecasts, rather than by unanticipated field evidence.
The model represents individually each rescue team and its operations
during the flood event. The intervention decisions and the state of each
rescue team are updated every hour. Particularly, at each updating
time step, the situation has evolved, and a new forecast is available
to reassess its future evolution. Therefore, new decisions can be made
based on the priorities that emerge from this updated analysis.

The Fig. 1 summarizes the decision and action processes represented
in the ABM. The following three sections present in more details the
general principles of the ABM, as well as the model’s outputs and
criteria for evaluating the simulations.

2.1. *The agents: firemen rescue teams*

The choice is made to represent individually each rescue team as an agent in the model. The objective is to simulate the field interventions conducted in a territory including numerous river reaches and urban areas at risk. Initially, the rescue teams are dispatched over different locations in this territory (corresponding to local fire brigade stations). During the simulation, each team has the ability to travel anywhere within the territory (see Fig. 2.a), and its position is represented at the river reach scale (the river network is split in small river reaches). Each rescue team can assume four different states: Available, Traveling, Arrived at Site, and In operation. The “Available” status means that the team is ready for any new field intervention. This may happen when a team is still located at its initial position (fire station), or at a river reach, after an intervention has been completed (the number of flooded buildings has fallen back below a defined intervention threshold, see next section). The “Traveling” status indicates that the team is on its way to its next intervention river reach. For a realistic modeling, a travel delay on the road network is computed based on an average speed of 30 km/h. The travel time matrix is calculated prior to the simulation, considering all the centroids of river reaches and all the fire stations. The shortest routes are selected on the road network, and potential disruptions in traffic conditions during the event are not considered. The “Arrived at site” status shows that the team just arrived at its intervention river reach, and is getting prepared since the predicted flood did not occur yet. Lastly, the “In operation” status means that the team arrived at its intervention place and is performing
<figure><img src="image_3.png" /><figcaption>Fig. 1. General flowchart of the running of the ABM, for the representation of interventions decisions and related actions of rescue teams.</figcaption></figure>

rescue operations, since flood impacts do actually occur on the river reach.

The status of the rescue teams is monitored throughout the simulation with an hourly update (see Fig. 2.b). The teams with a traveling, arrived at site, or in operation status are referred as **mobilized teams** hereafter.

## 2.2. Decision criteria for rescue interventions

The decisions for rescue interventions are based on the expected level of flood impacts for each river reach. This modeling principle is relatively close to reality, since in practice the interventions of the rescue services are often triggered by on-site feedback (emergency calls), which reflect the actual impact level on inhabited areas. However, in the ABM the flood impacts are estimated using a hydrometeorological modeling chain, fed with either observed rainfall (i.e. with low anticipation, a principle which is close to the actual decision principle based on emergency calls), or ensemble rainfall forecasts. The number of flooded buildings is used as a measure of the impact level at each river reach. This hydrometeorological modeling chain will be further described in Section 4.

The decision to send a rescue team to a river reach depends on three parameters: Intervention threshold, Intervention capacity, and Reallocation of rescue teams. The Intervention threshold corresponds to the minimum expected number of flooded buildings which should be reached to trigger the allocation of a rescue team to an affected river reach. The Intervention capacity stands for the limited and defined number of buildings each team is capable of handling. Depending on the expected number of affected buildings, several rescue teams may be sent to a river reach. The Reallocation parameter defines whether the teams in operation can or cannot switch to the available status and be re-allocated to another place, once the rescue operations are achieved at one river reach or when the intervention means present on a river reach exceed the intervention needs according to the simulated impacts.

At each time step of the simulation, the river reaches where the number of observed or predicted flooded buildings exceed the intervention threshold are examined one by one (see Fig. 1). The reaches with the largest number of affected buildings are treated first. When at least one additional rescue team is needed for a reach, the nearest available team is selected and assigned to this river reach. This loop is repeated as long as there are intervention needs and available rescue teams.

<caption>Table 1</caption>

Proportion of flooded buildings accounted for in the cost function, depending on the arrival time of rescue teams.

<table><thead><tr><td>Situation</td><td>Cost expressed in % of flooded buildings</td></tr></thead><tbody><tr><td>Team(s) on-site before flooding occurs</td><td>0% cost</td></tr><tr><td>Team(s) on-site between 0 and 1 h (included) after the onset of flooding</td><td>50% cost</td></tr><tr><td>No team(s) on-site 1 h (excluded) after the onset of flooding</td><td>100% cost</td></tr></tbody></table>

## 2.3. Output variables and evaluation criteria

The runs of the ABM lead to a detailed description of the activities of each rescue team, at each time-step (hour) during the event. The internal variables of the model include the positions and status of the rescue teams. For instance, the positions and number of teams in operation at river reaches where flood impacts are actually observed can be monitored (Fig. 2.a and dotted line on Fig. 2.b), as well as the total number of mobilized teams, i.e. including the teams traveling and arrived at site (solid line on Fig. 2.b). It is also possible to track the evolution of the number of flooded buildings receiving assistance, as illustrated in Fig. 2.c.

In order to evaluate the overall effectiveness of rescue decisions and operations, a cost function has been defined. Since the main objective assigned to rescue teams is to limit the threats to people, and to help exposed and vulnerable people to evacuate the areas at risks, it is considered that an efficient intervention can be achieved when a rescue team arrives at site before the beginning of flooding, provided that the teams are sufficiently formed and equipped to manage the rapid flooding of the area. Therefore, the number of flooded buildings for which rescue operations could not be achieved, or started too late, is counted (only the numbers of buildings exceeding the intervention threshold are counted). A cost level (proportion) is applied to each building, which depends on the delay between the onset of the flooding of the building and the arrival of the rescue team. The Table 1 presents the proposed percentages, ranging from 0% if a rescue team has arrived at-site before the flooding, to 100% if no rescue team is present on the site 1 h after the onset of flooding. The evolution of this cost function along the event is presented in Fig. 2.c.

The weighting of the costs, depending on the intervention delay, is essential in the ABM to reveal the added value of anticipated actions.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Illustration of the results of the ABM for the Aude 2018 event (decisions taken based on simulated flood impacts with observed rainfall): (a) location of the rescue teams in operation at 01:00, 04:00 and 09:00 am, (b) evolution in time of the total number of rescue teams mobilized (red solid line) and of the number of teams in operation (red dotted line), (c) evolution in time of the total number of inundated buildings (gray solid line), of the inundated buildings receiving assistance from a rescue team in operation (red solid line), and of the corresponding cost function (red dotted line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The selected cost proportion model (Table 1) is deliberately kept simple to facilitate the interpretation of the results.

# 3. Case study: the Aude River flash flood in october 2018

## 3.1. *The hydrometeorological event*

The Aude River basin is located in the southern of France, as depicted in Fig. 3. The basin has an 6074 km² drainage area, and receives an average of 850 mm of rainfall annually. While high discharges are common during Winter and Spring, the most severe floods usually occur during Autumn, due to possible occurrence of exceptionally intense and long-lasting convective rainfall events during this season in the French Mediterranean area. A particularly heavy rainfall event occurred during the night from the 14th to the 15th October 2018. The central part of the Aude River basin, downstream the town of Carcassonne, was particularly affected, with a maximum rainfall accumulation of more than 300 mm, among which 213 mm were recorded in six hours at Villegailhenc (estimated return period exceeding 100-years).

This rainfall had significant repercussions on the tributaries of the Aude river (Lauquet, Orbiel, Rieu Sec, Trapel), which all caused severe flooding. Additionally, on the main Aude river the stream gauge of Trèbes recorded a water level that had not been observed since 1891. Remarkably, this flood peak happened just nine hours after the onset of rainfall. These floods caused 14 deaths, approximately 100 injuries, and a total amount of insured damages estimated between 130 and 180 million euros (CCR, 2018).

The variability in both the spatial distribution and timing of the rainfall and runoff patterns observed during this event provides a compelling case study for evaluating the accuracy of short-term flood predictions.

## 3.2. *Local organization of rescue operations*

In France, the coordination of emergency operations falls under the responsibility of the Departmental Fire and Rescue Services (referred to as SDIS in French). In the Aude Department (administrative territory which encompasses the Aude River basin), the headquarters of the SDIS are located in Carcassonne, but the service is composed of a network of 42 local fire brigade stations distributed across the Department (red diamonds in Fig. 4).

A departmental risk analysis plan provides details about the specific resources allocated for the different types of emergencies, including fires, floods, and road accidents, and their distribution across the different local stations. Particularly, it describes the emergency response assets available in case of a flood event. The primary intervention vehicles used during floods are the firefighting tanker trucks. These all-terrain vehicles offer the advantage of being able to circulate even in adverse weather and traffic conditions. Across the department, there are a total of 92 vehicles of this type, dispatched to the local stations. The number of available vehicles in each center is indicated alongside each red diamond marker in Fig. 4.a. For realistic simulations, the settings of the ABM reference run have been fixed according to the content of the departmental plan. It was considered that the number of available all-terrain vehicles determines the number of rescue teams (i.e. 92 teams). The underlying assumption is that each local fire brigade has the requisite human resources to operate as many rescue teams as available vehicles.

According to the handbook of the SDIS, numerous rescue interventions were conducted during the floods of October 2018, visually depicted in Fig. 4.b. 32 different intervention areas are represented by black circles on the figure (each circle having a 2 km diameter). This representation accounts for the inherent inaccuracy in the provided locations (typically only the town name is available), and also the possible local traveling of the rescue teams in each intervention zone. The decisions regarding the interventions were primarily informed by
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** The Aude River basin, its river network, and the rainfall accumulations observed from 14 October 2018 00:00 to 15 October 2018 23:00, according to the Antilope J + 1 radar quantitative precipitation estimates (see Section 4.1).</figcaption></figure>

reports of observed flood situations. The initial instance of flooding, stemming from local runoff, was reported in the central part of Carcassonne around midnight on October 15th. A flood alert was officially declared for all the department at 0:30 a.m. The first reports concerning flooding in the northern region of Carcassonne were received around 1 a.m. External reinforcements from neighbor Departments contributed to enhancing the intervention capacities, but arrived at site early the next morning, several hours after the beginning of the floods. In total, a substantial number of emergency rescue operations were carried out on October 15th, including 211 preventive evacuations and 216 safety placements of people, and 91 direct rescues and 141 helicopter rescues of people in danger of death.

# 4. The hydrometeorological flash flood impact forecasting chains

This section describes the hydrometeorological modeling chain used as input of the agent-based model, to anticipate the flood impact level at the river reach scale, and take decision regarding rescue operations.

This modeling chain follows the principle proposed by Le Bihan et al. (2017) for the anticipation of flash flood impacts. The chain is fed with high-resolution radar Quantitative Precipitation Estimates (QPEs) and/or short-range (0-6 h) ensemble Quantitative Precipitation Forecasts (QPFs). A spatially distributed hydrological model generates discharge forecasts for each river reach in the considered area. Then, a predefined discharge-impact relationship is applied for each river reach, enabling the conversion of discharge forecasts into corresponding impact projections (here the number of flooded buildings). The discharge-impacts relations are defined based on a library of inundation

scenarios covering a wide range of discharges for each river reach (Le Bihan et al., 2017).

Varied combinations of QPEs and QPFs products were used as input of the modeling chain, and their effectiveness was evaluated based on the outcomes of the ABM simulations (see Section 5).

## 4.1. Quantitative precipitation estimates and ensemble precipitation forecasts

The QPEs used in this study were obtained from the Antilope algorithm (Laurantin, 2008) developed by Météo-France. Antilope combines data from 30 operational weather radars and all available rain gauge observations, encompassing released in real-time or after a one-day delay. The resulting QPEs, referred to as Antilope J + 1, cover the whole French mainland, with a spatial resolution of 1 km by 1 km at an hourly time step. For the October 2018 flash flood event, the accumulated QPEs from Antilope J + 1 are presented in Fig. 3.

In addition to QPEs, three short-range ensemble QPFs, specifically developed for the anticipation of intense rainfall and flash flood events, were used and evaluated: AROME-EPS, pepi, and pertDpepi. All three QPFs products share uniform spatial and temporal resolutions - a grid of 0.025° by 0.025° and hourly updates -, and the same forecast range of 6 h ahead. A more detailed description of these products is provided in Charpentier-Noyer et al. (2023).

AROME-EPS is the ensemble forecast variant of AROME-France convection permitting NWP model (Bouttier et al., 2012; Raynaud and Bouttier, 2016). As of 2018, AROME-EPS comprised a 12-member ensemble forecast, forecasting up to two days ahead and updated four
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Overall organization and field interventions of the fire and rescue service (SDIS) during the Aude 2018 flood event: (a) Location of local centers and number of available intervention vehicles, (b) Location of the 32 municipalities where local rescue operations were achieved.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** From Charpentier-Noyer et al. (2023). Compared temporal evolutions of observed hourly rainfall rates (black dots), and 3-h lead time ensemble forecasts (boxplots): AROME-EPS (green), pepi (orange) and pertDpepi (purple). In the boxplots, whiskers reflect the min-max range and boxes the inter-percentile (25%-75%). All rainfall intensities are averaged over the Aude River basin (6074 km2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

times daily. The forecast ranges were then limited here to 6 h ahead, and the most recent runs were consistently used to obtain hourly updates.

**Pepi** is an experimental product combining AROME-EPS with AROME-NWC (Auger et al., 2015). AROME-NWC is a configuration of AROME-France updated every hour, providing forecasts up to 6 h ahead. AROME-NWC was used with time lagging, i.e. by considering the last 6 successive runs of AROME-NWC every hour. The resulting pepi product offers forecasts up to 6 h ahead, combining 12 members from the most recent AROME-EPS run with 1 to 6 members from AROME-NWC, depending on the lead time.

**PertDpepi** is another experimental product, where original pepi members are shifted 20 km in the four cardinal directions to increase ensemble spread in terms of the forecast rainfall uncertainties. This results in an ensemble with a larger number of members (ranging from 65 to 90) compared to pepi.

The Fig. 5 compares the hyetographs of the 14-15th October 2018 event for the Aude river basin, for the Antilope J + 1 and the three QPFs for a 3-h lead-time. It shows that the QPFs involved provide a relatively good anticipation of the rainfall event, at least for the shorter lead times.

## 4.2. The cinecar distributed hydrological model

Cinecar is a highly distributed hydrological model tailored specifically for simulating flash floods (Le Bihan, 2016; Naulin et al., 2013), which demonstrated its ability to provide accurate simulations of both the timing and intensity of flash flood occurrences. The model combines the Soil Conservation Service - Curve Number (SCS-CN) function to estimate runoff coefficients at the hill slope scale, and the kinematic wave and diffusive wave models to simulate hill slope transfers and flood propagation in the river network.

In the model's application to the Aude River basin, the basin was divided into 1174 sub-basins (hill slopes), with an average surface of 5 km². The CN values, initially assigned based on soil types and antecedent conditions, were further refined to achieve better agreement between simulated and observed peak discharges for the Aude 2018 flood (Hocini et al., 2021). The resulting model exhibited a consistent alignment with field observations, with deviations in peak discharges generally falling within a ±20% range. The resulting magnitudes of the 2018 floods, simulated by the Cinecar model with the Antilope J + 1 QPE, are presented in Fig. 6.a.

It must be noted that the calibration of the rainfall-runoff model to the 2018 flood event leads to reduce the flood prediction uncertainties if compared to a real world forecast application: i.e. the rainfall-runoff simulation uncertainties are neglected. But the proposed evaluation
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Illustration of the simulation results obtained when the modeling chain is forced with Antilope J + 1 QPE: (a) return periods of simulated peak discharges for each river reach, (b) maximum number of inundated buildings.</figcaption></figure>

method has to rely on a comprehensive knowledge of the flood impacts for all river reaches of the region, throughout the entire duration of the flood event. Such a comprehensive representation cannot be solely obtained from field data and is therefore reconstructed based on a reference simulation, that has been adjusted to closely resemble the actual event. Introducing realistic rainfall-runoff prediction uncertainties into the analysis, to assess if it could modify the conclusions on the usefulness of forecasts for improved event management, could be a subject of future developments.

### 4.3. Impacts modeling through a discharge-impact curve

This work aims at assessing the potential impacts of floods on the population and determining the corresponding rescue operations. Therefore, the number of potentially inundated buildings as been selected as a measure of the local impact, as it correlates with the number of possibly affected people. The buildings locations and characteristics can be obtained from the French BD TOPO® geographic database (https://geoservices.ign.fr/bdtopo). Residential and commercial buildings only were considered herein.

Discharge-impact (i.e. discharge-number of inundated buildings) curves were computed for the 1174 river reaches described in the Cinecar model, based on the crossing of the BD TOPO® building layer and of a comprehensive library of flood extent scenarios covering the whole Aude River basin and compiled in Nicolle (2021), Godet et al. (2024). This library includes seven flood scenarios corresponding to peak discharge return periods ranging from 5 to 1000 years. The flood extents were estimated based on a Lidar DTM and 2D steady state hydraulic computations with the Floodos model (Davy et al., 2017), at a 5 m resolution. The numbers of inundated buildings, with water levels exceeding 10 cm, were computed for each of the seven considered flood scenario and river reach. The discharge-impact relations were then linearly interpolated to obtain continuous curves. This linear interpolation may bring a significant uncertainty since 7 flood scenarios are considered. However, the shapes of the impact curves appeared sufficiently realistic in the presented case study. An alternative could have been here to increase the number of flood scenarios to limit the effect of interpolation.

Fig. 6.b shows the maximum computed numbers of flooded buildings simulated across the 1174 river reaches during the 2018 event. There is a relatively fair correspondence between these maximum computed impacts at the river reach level and the locations of the field

interventions of rescue teams. Apart from two cases, no intervention occurred on stream reaches with a maximum computed number of affected buildings lower than 25. Therefore, the threshold for deploying a rescue team has been set at 25 buildings in the ABM runs.

## 5. Results

### 5.1. The compared scenarios

For the ABM simulations presented in this paper, the parameters of the model have been set to the following values: the decision threshold was consistently fixed at 25 buildings; the intervention capacity of rescue teams was fixed to 100 buildings (which is a reasonable value considering that all flooded buildings do not systematically require emergency rescue operations); the number of available rescue teams was varied from 42 to an unlimited number, depending on the simulations, to illustrate the sensitivity of the results to this parameter.

Furthermore, the presented runs of the ABM systematically compare the results obtained with different information used to decide for rescue interventions. In a first reference scenario, the decisions are taken every hour according to QPE (observed rainfall) based impact simulation, which is assumed to represent the ground truth. This scenario, which will be called hereafter the “observation-based scenario”, represents a situation where decisions are taken with no anticipation. It is assumed to be close to a real world situation in which decisions are triggered either by emergency calls or field information. Alternatively, the FF impacts forecasting chain is run based on different rainfall scenarios, to obtain forecasts of the evolution of the flood impacts and better anticipate the intervention decisions :

- a no future rainfall scenario is first used to measure the anticipation capacity related to the propagation of the already generated runoff volumes along the stream network. This scenario will be referred to as “no future rainfall scenario”.

- one of the 3 different ensemble QPFs products presented in Section 4.1 is then used, to maximize the anticipation of FF impacts. These cases will be referred to as “QPF-based scenarios”, or “AROME EPS/pepi/pertDpepi scenarios”. Since the obtained FF impacts forecasts take the form of ensembles of different sizes, the 75% percentiles of these ensembles were systematically used in the ABM to compute decisions. The selection of the 75% percentile is based on Charpentier-Noyer et al. (2023), who showed
that the choice of this percentile highly limited the number of
missed anticipations of the 10-year peak discharge exceedance
for the considered QPFs and the 2018 event, and led to a good
balance between hits and false alarms. Although the results pre-
sented hereafter are limited to the 75% percentile, other choices
of decision percentiles could also be evaluated with the same ABM
model.

Considering that several of the involved QPF products are not yet
operational, the delivery times of forecasts can be only estimated for
each scenario. It has been assumed that in a real-time workflow, radar
QPFs would be available at H + 5 min, the QPFs would be available at
H + 35 min when involving AROME-NWS, or immediatly for AROME-
EPS (the members involved corresponding to the last available run),
and the computation times would be in a 1 to 10 min range, depending
on the number of members of the ensembles to be run, and provided
that parallel computing may accelerate the computation times for the
ensembles. Following these generic principles, the delivery times were
fixed to: 5 min for the observation-based scenario ; 6 min for the no
future rainfall scenario ; 10 min for the Arome-EPS scenario ; 40 min
for the pepi scenario ; and 45 min for the pertDpepi scenario.

According to the selected cost function (Table 1) and to the resulting dependence between costs and intervention delays, basing intervention decisions on forecasts may have two opposite consequences. The anticipation may reduce the intervention delays and the costs. But prediction errors may also unnecessarily mobilize intervention means, that will then not be available or waste precious time to intervene in the actually affected areas. The impact of prediction errors will clearly depend on the balance between rescue needs and resources.

5.2. *A first run with unlimited rescue means*

The initial simulation illustrates the ideal but unrealistic situation where an unlimited number of rescue teams is available in each of the 42 local fire brigade centers. The corresponding results are presented in Fig. 7, and more detailed illustrations are included in appendices A and B (Figs. A.1 and B.1), showing the positions and the status (available, traveling, arrived at site, in operation) of the rescue teams at different times along the flood event, for the 5 QPE/QPFs scenarios.

Since the rescue resources are unlimited, scenarios based on fore-
casts can only lead to reduce the computed costs: i.e. prediction errors
have no impact on the availability of rescue means and hence on the
intervention delays. Clearly, a much larger number of field emergency
operations are triggered when using QPFs, particularly at the start of
the event (Figs. 7.a and b, and Figs. A.1 and B.1). At the paroxysm
of the simulated interventions, 275 to 315 teams are mobilized simul-
taneously when QPF products are used in the ABM, compared to the
140 and 156 teams mobilized in the observation based and no future
rainfall scenarios respectively. In all scenarios, the peak mobilization
significantly surpasses the actual number of 92 available rescue teams
in the Aude region. This confirms, first that the generated results are
in line with the occurred event and that support from the surrounding
regions was in fact necessary and second, that this first run provides an
optimistic and unrealistic picture. The much higher number of required
teams in QPF-based scenarios is mostly explained by the high false
alarm rate, especially during the first part of the event. This is illus-
trated on the maps in Figs. 7.a and A.1 (Appendix A), and also on Fig.
B.1 (Appendix B) showing the detailed status of the rescue teams during
the event. At the start of the event (01:00), a large part of the mobilized
rescue teams in the QPF-based scenarios are still on their way. Then,
at 04:00, a significant proportion of the mobilized teams arrived at-
site and are waiting for potential flood impacts to occur, but are not
yet involved in rescue operations. At 09:00, a majority of these teams
are not considered as mobilized anymore, since the expected floods did
not occur and are not forecast anymore (false alarms). Consequently,
the maximum number of teams in operation remains largely lower than

the mobilized teams for all the QPF-based scenarios (Fig. 7.b). The gap
between the number of mobilized teams and the number of teams in
operation is largely lower for the observation-based scenario and for the
no future rainfall scenario. In these two simulations, the gap is rather
explained by the delays in intervention: a limited part of the mobilized
teams are on their way and hence not immediately effective during the
first part of the event.

Table 2 provides a summary of the effectiveness of rescue team allocation decisions, which can result in either incorrect allocations (due to false alarms) or timely or delayed arrivals of rescue teams at inundated sites. This table confirms at first that the observation-based scenario, by construction, can only lead to late arrival of rescue teams. Accounting for a no future rainfall scenario helps in anticipating the future impacts, which leads to an increase of timely arrivals, without any effects in terms of bad allocations (by construction, this scenario cannot result in false alarms). In the case of unlimited rescue teams, the QPF-based scenarios lead to a significant number of incorrect allocations: the corresponding rescue teams are traveling towards river sections where no rescue interventions are finally required, and then wait for another allocation decision, which represent a significant loss of time. However in the case of unlimited rescue teams, this has a limited effect on the efficiency of rescue operations, since other rescue teams remain available for other allocations. In parallel, the QPF-based scenarios greatly increase the timely arrival of rescue teams in affected areas (and reduce the late arrivals), which increases the global efficiency of rescue operations.

Considering the rescued buildings and related costs (Fig. 7.c), this first simulation clearly reveals the potential added value of hydrometeorological forecasts. The anticipation provided by the QPFs, but also, to a lesser extent, by the rainfall-runoff simulations (no future rainfall scenario), helps providing timely assistance to the flooded areas and largely reduces the intervention delays for this specific case-study. The computed costs remain therefore close to 0 when QPFs are used, and are drastically reduced in the case of the no future rainfall scenario if compared to the observation-based scenario. The small difference in the computed costs between QPF-based scenarios and the no future rainfall scenario, may appear surprising at first glance, especially when the number of mobilized rescue teams are compared. This is explained by the fact that the no future rainfall scenario provides useful forecasts on river reaches with large upstream drainage areas and high times of concentration: i.e. the downstream reaches of the river network. According to the selected cost function, the zero-rainfall scenario already offers sufficient anticipation to trigger timely rescue operations for these downstream river reaches, where the largest towns with the highest numbers of buildings exposed to flooding are located. However, QPFs remain crucial for fast-reacting headwater streams. And the cost function could also be adapted in future works to account for a larger spectrum of safety operations requiring more time than the evacuation and assistance to inhabitants.

5.3. *Run with a realistic number of rescue teams*

To provide a more realistic picture, the second simulation involves
the actual number of rescue teams available in the Aude department
(i.e. 92 teams). The simulation results are summarized in Fig. 8, the
maps showing the locations of the rescue teams at 3 different stages
of the flood event are presented in Fig. A.2 (Appendix A), and the
temporal evolution of the status of the 92 rescue teams during the event
is presented in Fig. B.2 (Appendix B), for the five QPE/QPF products.

Unlike the former run, the maximum numbers of rescue teams sent
in intervention (Fig. 8.b) do not differ here between the five different
QPE/QPFs scenarios: all available rescue teams are mobilized, however
more or less rapidly, during the course of the flood. In the case of
QPF-based scenarios, all rescue teams are already mobilized at 01:00
because of the better anticipation. The negative effect of false alarms
is still visible here, but appears highly reduced in comparison with the
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Results of the ABM for an unlimited number of rescue teams: (a) locations of the rescue teams arrived at site and in operation during the event (case of the pepi forecasts), (b) evolution of the numbers of mobilized rescue teams (solid lines) and of teams in operation (dotted lines), and (c) evolution of the total number of inundated buildings (gray solid lines), of the inundated buildings receiving assistance from a rescue team in operation (color solid lines), and of the corresponding cost functions (color dotted lines). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Results of the ABM in a realistic case where 92 rescue teams are available in the 42 local firemen centers: (a) locations of the rescue teams arrived at site and in operation during the event (case of the pepi forecasts), (b) evolution of the numbers of mobilized rescue teams (solid lines) and of teams in operation (dotted lines), and (c) evolution of the total number of inundated buildings (gray solid lines), of the inundated buildings receiving assistance from a rescue team in operation (color solid lines), and of the corresponding cost functions (color dotted lines). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<caption>**Table 2**</caption>

Detailed results of allocation decisions of rescue teams, considering 5 forecast scenarios and 3 different levels of rescue means (unlimited, 92 and 42 teams): bad allocations (due to false alarms), timely arrivals (before inundation), or late arrivals (after beginning of inundation) of rescue teams.

<table><thead><tr><th>Scenario</th><th>No. of rescue teams</th><th>No. of alloc. decisions</th><th>No. of bad allocations</th><th>No. of timely arrivals</th><th>No. of late arrivals</th></tr></thead><tbody><tr><td rowspan="3">Obs. based</td><td>Unlimited</td><td>178</td><td>0</td><td>0</td><td>178</td></tr><tr><td>92</td><td>144</td><td>0</td><td>0</td><td>144</td></tr><tr><td>42</td><td>86</td><td>0</td><td>0</td><td>86</td></tr><tr><td rowspan="3">No future rain</td><td>Unlimited</td><td>179</td><td>0</td><td>98</td><td>81</td></tr><tr><td>92</td><td>138</td><td>0</td><td>40</td><td>98</td></tr><tr><td>42</td><td>73</td><td>0</td><td>20</td><td>53</td></tr><tr><td rowspan="3">Arome-EPS</td><td>Unlimited</td><td>346</td><td>117</td><td>177</td><td>52</td></tr><tr><td>92</td><td>152</td><td>15</td><td>81</td><td>56</td></tr><tr><td>42</td><td>88</td><td>7</td><td>37</td><td>44</td></tr><tr><td rowspan="3">Pepi</td><td>Unlimited</td><td>345</td><td>117</td><td>182</td><td>46</td></tr><tr><td>92</td><td>166</td><td>23</td><td>65</td><td>78</td></tr><tr><td>42</td><td>89</td><td>12</td><td>24</td><td>53</td></tr><tr><td rowspan="3">PertDpepi</td><td>Unlimited</td><td>300</td><td>82</td><td>179</td><td>39</td></tr><tr><td>92</td><td>146</td><td>8</td><td>77</td><td>61</td></tr><tr><td>42</td><td>71</td><td>0</td><td>39</td><td>32</td></tr></tbody></table>

run with unlimited means: the number of teams that finally provide actual rescue operations is close to the number of mobilized teams. This is explained by the maps presented on Fig. A.2: at 04:00, no rescue teams are present in the south-western part of the Aude basin, whereas numerous teams were arrived at site in this area for the simulation with unlimited means (Fig. A.1). The false alarms are present in this area for both simulations, but since the expected impacts are limited in this upstream part of the watershed, when the rescue means are limited the teams are rather sent in other places, where the forecast impacts are higher. Finally, the number of rescue teams in operation is larger for QPF-based scenarios if compared to QPE-based scenarios (observation based and no future rainfall scenarios) until 06.00 a.m. and the start of the recession of the flood event (Fig. 8.b).

Table 2 confirms that when 92 rescue teams are available, the number of bad allocations is largely reduced for QPF-based scenarios. These few remaining bad allocations directly limit the number of rescue teams available for other operations. However, the positive effect of no future rainfall and QPF-based decisions in terms of timely arrivals of rescue teams is still clearly visible. The balance between the gains in anticipation related to accurate predictions, and the costs induced by false alarms and the corresponding losses of time, remains positive as far as intervention decisions are considered. This may be explained by the limited effect of false alarms, and also by the fact that a significant part of the first damaging floods occur on upstream catchments with short response times. In the case of the no future rainfall scenario, the rescue teams may often arrive too late on these streams. It can also be observed on Fig. B.2 that around 05.00 a.m., i.e. at the paroxysm of the event, a significant part of the teams are still traveling for the observation-based scenario, which limits the number of teams providing rescue operations at this time. For all other scenarios, at the same time, the number of teams in operation is close to the maximum number of 92 teams. The gains related to the better anticipation is clearly visible here.

Across all scenarios, the limited number of rescue teams finally constrains the number of flooded buildings receiving assistance, which remains largely lower than the total number of flooded buildings (Fig. 8.c). This results in costs largely higher than those observed in the former simulation (unlimited rescue means). Finally, the added-value of decisions based on QPFs forecasts is notably diminished in this context when compared to the no future rainfall scenario. This is due to the reasons exposed above: the no future rainfall scenario offers a significant anticipation for the downstream river reaches where the larger impacts are observed, and the gains associated with the better anticipation offered by QPFs correspond mostly to upstream watersheds where the impacts are limited, and this better anticipation is counterbalanced by

the consequences of false alarms (even if reduced here). However, the three QPF-based scenarios still perform significantly better than the no future rainfall forecast, as demonstrated by the final values of the cost function (reduced by ≈10 % when decisions are guided by the QPFs).

### 5.4. Run with a highly limited number of rescue teams

In this last run, it is assumed that the number of available rescue teams is significantly reduced, while the same number of firemen centers is maintained: only one rescue team is placed in each of the 42 local centers at the beginning of simulation. This new scenario aims at illustrating what could be obtained in case of much limited rescue means, compared to the actual situation. The results of this run are summarized in Fig. 9, and the detailed positions and status of the rescue teams for the five QPE/QPF scenarios are presented in Figs. A.3 and B.3 (appendices A and B).

This new simulation shows similar trends as the former one. The 42 rescue teams are rapidly mobilized for all the five scenarios, but 2–3 h earlier for QPF forecasts (Fig. 9.a and b, and appendices A and B). Overall, the numbers of rescue teams in operation reach peak values that are relatively close to the maximum number of available rescue teams (42). The limited number of rescue teams leads here to focus the interventions on river reaches with the larger impacts, more often located on downstream river reaches in the basin. On these river reaches, the uncertainties of forecasts are lower due to the flood’s propagation times, which contributes to attenuate the effects of false alarms when using QPFs. Moreover, the anticipation is less crucial for these river reaches since they are close to the firemen centers, which attenuates the effects of limited anticipation when using QPE based scenarios. All of this contributes to bring closer the efficiency of QPE and QPFs based scenarios. However, Fig. B.3 still shows a slight effect of false alarms for the pepi scenario (some teams arrived at site at 05.00 and then traveling to other places), and of limited anticipation for the observation based scenario (teams still traveling at 05.00). Table 2 confirms that a limited number of bad allocations still remain in this case for the pepi and AROME-EPS scenarios. It also shows that timely arrivals of rescue teams become much more similar between QPF-based and no future rainfall scenarios. Table 3, which presents the effectiveness of rescue team allocation decisions for two different categories of upstream drainage areas (<500 km² or >500 km²), confirms that bad allocations (due to false alarms) and timely arrivals are concentrated on smaller catchments for QPF-based scenarios. Conversely, for the no future rainfall scenario, timely arrivals of rescue teams are mostly located on larger drainage areas.
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Results of the ABM in a pessimistic case where only 1 rescue team is available in each of the 42 local firemen centers: (a) location of the rescue teams arrived at site and in operation during the event (case of the pepi forecasts), (b) evolution of the numbers of mobilized rescue teams (solid lines) and of teams in operation (dotted lines), and (c) evolution of the total number of inundated buildings (gray solid lines), of the inundated buildings receiving assistance from a rescue team in operation (color solid lines), and of the corresponding cost functions (color dotted lines). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<caption>**Table 3**</caption>

Detailed results of allocation decisions of rescue teams, in the case of limited rescue means (42 teams): bad allocations (due to false alarms), timely arrivals (before inundation), or late arrivals (after beginning of inundation) of rescue teams.

<table><thead><tr><th>Upstr. drain. area</th><th>Scenario</th><th>No. of alloc. decisions</th><th>No. of bad allocations</th><th>No. of timely arrivals</th><th>No. of late arrivals</th></tr></thead><tbody><tr><td rowspan="5">&lt;500 km²</td><td>Obs. based</td><td>46</td><td>0</td><td>0</td><td>46</td></tr><tr><td>No future rain</td><td>36</td><td>0</td><td>7</td><td>29</td></tr><tr><td>AROME-EPS</td><td>55</td><td>7</td><td>34</td><td>14</td></tr><tr><td>Pepi</td><td>50</td><td>12</td><td>17</td><td>21</td></tr><tr><td>PertDpepi</td><td>36</td><td>0</td><td>22</td><td>14</td></tr><tr><td rowspan="5">&gt;500 km²</td><td>Obs. based</td><td>40</td><td>0</td><td>0</td><td>40</td></tr><tr><td>No future rain</td><td>37</td><td>0</td><td>13</td><td>24</td></tr><tr><td>AROME-EPS</td><td>33</td><td>0</td><td>3</td><td>30</td></tr><tr><td>Pepi</td><td>39</td><td>0</td><td>7</td><td>32</td></tr><tr><td>PertDpepi</td><td>35</td><td>0</td><td>17</td><td>18</td></tr></tbody></table>

The consequence illustrated on Fig. 9.c is a relatively close evolution of the buildings receiving assistance during the flood for the 5 scenarios, even if the same tendencies as in the former simulation can still be observed: advantage to the QPF forecasts during the raising phase of the event because of larger anticipation, and advantage of the no future rainfall forecast at the end of the event (after 07 a.m.), because of the good anticipation of the propagation of the flood towards the downstream river reaches where the impacts are the largest. Logically, the number of buildings receiving assistance is globally lower, and the cost function higher here than in the former run, because of the highly limited number of rescue teams (42 against 92). But the other and less expected consequence of this reduction of rescue means is the proximity of all the scenarios in terms of costs, with a difference in the final value of the cost function limited to 20% between the observation-based scenario and the pertDpepi forecast. Note also that the no future rainfall scenario leads in this case to a very similar cost than the pepi scenario, showing that the added value of the better anticipation provided by QPFs may be almost completely annihilated in some specific situations.

This case finally reveals how QPF scenarios may progressively lose their interest, in cases where rescue means are severely constrained and thus concentrated on locations where the impacts are larger, located downstream and close to the emergency centers, which limits the complexity of the optimization of rescue operations.

# 6. Discussion

## 6.1. The added-value of the ABM model

Even if still simplified, the ABM model presented in this paper shows an interesting capacity to represent the complex dynamics of rescue operations, in a fast evolving and uncertain situation. It helps in explicitly identifying important (and sometimes unexpected) limiting factors, such as the uncertainties of forecasts of course, but also the quantity of available rescue means, the location of the main impacts in the territory, and the times required to access these impacted places. Owing to the explicit representation of all these factors and their
detailed interactions, the developed ABM offers the capacity to analyze and objectively evaluate the cost-benefits balance of using ensemble QPFs as input of the emergency decision chain, due respectively to the increased anticipation and the presence of uncertainties leading to false alarms.

In comparison to the conventional economic value approaches (Katz and Murphy, 1997; Katz and Lazo, 2012), the ABM approach offers here the possibility to represent a much more complex real world situation, where the consequences of the decisions are difficult to appraise, and cannot not be easily summarized in terms of cost and benefit to build synthetic metrics. Thus, ABM appears as an interesting tool for the evaluation of benefits of uncertain weather forecasts in complex decision-making problems, such as the one examined in this paper.

## 6.2. Current limits and possible improvements of the ABM model

Since the model applied in this paper remains highly simplified, its realism could certainly be largely improved through reasonable efforts. Particularly, different choices and assumptions made for the representation of the rescue operations and emergency decisions should probably still be questioned. For instance, the results appeared sensitive to several parameters governing the decisions (intervention threshold, intervention capacity), and it is therefore important that these parameters remain representative of reality. The question of redeployment of rescue teams should also be examined since this possibility may not be representative of real world situations: field interventions taking time, and progressively altering the capacity of rescue teams due to tiredness. Finally, the cost function should also probably be discussed with operational emergency services to evaluate which delay is reasonable to define a "timely" rescue operation (1-h considered here).

More important and ambitious evolution of the ABM model presented here may also be envisaged. At first, the difficulties encountered by the rescue teams to access to the impacted locations, due to the development of the flood, could be represented by using specific models simulating the road closures during the flood (Naulin et al., 2013). Second, the current version of the model only represents the rescue teams as agents, and does not explicitly account for the location, dynamics, and behavior of the population receiving assistance. A combined representation of the rescue teams and population would also be feasible in a multi-agent model, leading to much more complex simulations but also probably a more realistic representation of the actual crisis situation, as suggested by former applications of ABM for flood crisis management purpose (Zhuo and Han, 2020; Anshuka et al., 2022).

## 7. Conclusions

The case study presented in this paper shows how ABM may help in evaluating the value of short-range FF forecasts to optimize the decision-making and crisis management processes. Through an explicit representation of the rescue operation processes, the proposed ABM offers a new and meaningful insight on the combined effects of increased anticipation and forecast uncertainties (leading to false alarms), and on the resulting efficiency of a complex decision and action chain (i.e. rescue operations). Since the presented ABM approach remains highly simplified, further work is still needed to improve its realism and to further validate its outputs against actual rescue operations data.

Despite these remaining possible improvements, the results obtained in this first case study show that impact-based FF forecasts based on short-range QPFs may be sufficient to highly increase the efficiency of rescue operations, under the assumption of unlimited rescue means. Unfortunately, this benefit can also be largely limited by the combined effects of the limited intervention capacities (number of teams), the loss of time due to uncertainties of forecasts (false alarms), and also the location of the mains impacts on downstream river reaches, where

significant anticipation is possible without using QPFs. The added value of using short-range QPFs remained nevertheless perceptible in all the presented simulations, even if it was often close to the benefits offered by a no future rainfall forecast, which offers less anticipation, but brings less uncertainty. The ABM model may also be helpful in drawing a hierarchy between different QPF products, even if the three tested products led here to close performances, which is consistent with the results obtained by Charpentier-Noyer et al. (2023). However, the conclusions we obtained in the presented case study are likely to be event dependent. Drawing robust conclusions about the actual added value of flash-flood forecasts and the hierarchy between the QPFs products used as input would require to run the ABM model for a much larger set of events, including a large and statistically representative variety of event characteristics (with different locations, intensities, durations, and spatio-temporal variabilities).

Finally, this work confirms that the evaluation of FF forecasts and of new QPF products may not exclusively rely on statistical evaluation metrics, but could also account for the real world situations and problems, and the efficiency of decisions taken by the users of forecasts. ABM should probably be considered as an interesting avenue to achieve this objective.

## CRediT authorship contribution statement

**Maryse Charpentier-Noyer:** Writing – original draft, Visualization, Validation, Software, Methodology, Conceptualization. **Olivier Payrastre:** Writing – original draft, Visualization, Supervision, Methodology, Conceptualization. **Eric Gaume:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Pierre Nicolle:** Software, Methodology, Conceptualization. **François Bouttier:** Writing – review & editing, Resources, Data curation. **Axelle Fleury:** Resources, Data curation. **Hugo Marchal:** Resources, Data curation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

The Agence Nationale de la Recherche (ANR) provided financial support for this research, as part of the PICS project (https://pics.ifsttar.fr, grant no. ANR-17-CE03-0011) and of the MUFFINS project (https://muffins-anr-project.hub.inrae.fr, grant no. ANR-21-CE04-0021). Financial support was also provided by the French Ministry of Ecology (DGPR/SCHAPI) for the PhD of Maryse Charpentier-Noyer. Rainfall observations (QPE) and forecasts (QPF) data were provided by Météo-France and CNRM. Peak discharge data for the Aude 2018 flood event were obtained as part of the HyMeX research program (http://hymex.org), with financial support from the CNRS (MISTRALS program) and of the Ministry of Ecology (DGPR/SCHAPI). The authors also thank the Aude Departmental Fire and Rescue Service (SDIS de l'Aude), for the provided data about the actual rescue management organization during the Aude 2018 flood.

## Appendix A. Location of the rescue teams during the ABM simulations

See Figs. A.1–A.3.

## Appendix B. Evolution of team assignment over time

See Figs. B.1–B.3.
<figure><img src="image_13.png" /><figcaption>Fig. A.1. Locations of the rescue teams arrived at site and in operation during the event for the simulation with unlimited rescue means: (a) AROME-EPS scenario, (b) pertDpepi scenario, (c) no rainfall scenario and (d) observation-based scenario.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. A.2. Locations of the rescue teams arrived at site and in operation during the event for the simulation with 92 rescue teams: (a) AROME-EPS scenario, (b) pertDpepi scenario, (c) no rainfall scenario and (d) observation-based scenario.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. A.3. Locations of the rescue teams arrived at site and in operation during the event for the simulation with 42 rescue teams: (a) AROME-EPS scenario, (b) pertDpepi scenario, (c) no rainfall scenario and (d) observation-based scenario.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. B.1.** Evolution of the status of rescue teams in a case of unlimited number of rescue teams: (a) AROME-EPS scenario, (b) pepi scenario, (c) pertDpepi scenario, (d) no rainfall scenario and (e) observation-based scenario.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. B.2.** Evolution of the status of rescue teams in the case of 92 rescue teams: (a) AROME-EPS scenario, (b) pepi scenario, (c) pertDpepi scenario, (d) no rainfall scenario and (e) observation-based scenario.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. B.3. Evolution of the status of rescue teams in the case of 42 rescue teams: (a) AROME-EPS scenario, (b) pepi scenario, (c) pertDpepi scenario, (d) no rainfall scenario and (e) observation-based scenario.</figcaption></figure>

## Data availability

Data will be made available on request.

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