Enhancing Flood Risk Management: A Review on Numerical Modelling of Past Flood Events

Abstract

Recent scientific literature has consistently highlighted a significant increase in both the frequency and intensity of flood events, primarily attributed to the effects of climate change. Projections suggest that this trend will likely intensify in the coming decades. In this context, enhancing our understanding of flooding dynamics becomes not only necessary but urgent. A critical component of this advancement lies in the numerical analysis of historical flood events, which provides valuable insights into flood behaviour across extended temporal and spatial scales. This approach enables two key outcomes: a significant improvement in conventional methods for estimating return periods and a reduction in the uncertainties associated with historical flood events by simulating multiple plausible scenarios to identify the most likely one. This paper presents a comprehensive review of the scientific literature focused on the numerical simulation and reconstruction of past flood events. Two main conclusions emerge from this review: First, the temporal scope of the studies is notably wide, covering events ranging from glacial periods to those occurring in the mid-20th century. Second, there exists a pronounced spatial imbalance in the geographical distribution of these studies, with certain regions significantly underrepresented. This review provides a valuable resource for researchers and practitioners working in flood risk assessment and hydrological modelling. By consolidating existing knowledge, it supports the development and refinement of decision-support tools aimed at improving mitigation strategies to reduce the impact of flooding on both populations and infrastructure.

1. Introduction

Recent scientific publications highlight that the world is currently experiencing one of the most intense periods of frequent flooding in recent decades, primarily driven by climate change [1,2]. There is clear evidence that both the frequency and intensity of extreme flood events are increasing in many regions worldwide [3,4]. As a direct consequence, the number of people affected by these events is expected to rise in the future. Recent flood disasters illustrate the devastating impact of such events. In July 2021, severe floods in Germany and Belgium resulted in more than 200 fatalities [5]. In March 2023, Cyclone Yaku triggered catastrophic flooding in Peru [6]. More recently, in October 2024, the extreme precipitations registered in Valencia (Spain) caused more than 200 deaths [7,8]. These events underscore the urgent need to improve our understanding of extreme flood dynamics to enhance preparedness, strengthen mitigation strategies, and adapt to the changing climate [9,10]. Addressing these challenges is a priority for the scientific community [10], but it requires a multidisciplinary approach. Fields such as meteorology, hydrology, and soil science all play a crucial role in advancing our knowledge and developing effective flood management strategies [11].

Two key tools contribute to achieving these objectives: Flood Early Warning Systems (FEWS) and the numerical analysis of past flood events. While the former was explored in detail by the authors in [12] through a comprehensive review of the most representative systems worldwide, this paper focuses on the latter. Understanding past flood events through numerical analysis is crucial for improving flood risk management. Historical floods provide valuable data that can reveal previously unidentified extreme events and offer deeper insights into known but poorly studied cases. By reconstructing the spatial and temporal evolution of these events, we can bridge critical knowledge gaps, leading to a more comprehensive understanding of flood dynamics [13,14,15,16,17]. This historical perspective is essential for refining flood return period calculations, a fundamental tool for predicting future scenarios. Additionally, studying past events helps enhance protective measures, ensuring better preparedness even for floods comparable to the most catastrophic events ever recorded. Learning from history allows us to anticipate and mitigate future disasters with greater precision.

The paper is structured as follows. First, in Section 2, an introduction is presented about numerical models used in flood analysis. Then, in Section 3, a review of the most important works focusing on the numerical analysis of flood events, along with a brief description of the methodology involved in the numerical methods, is presented. Finally, in Section 4, a series of conclusions are drawn.

2. Numerical Modelling of Flood Events

Numerical modelling is a fundamental tool for flood analysis, enabling accurate predictions of flood extent and arrival time [18]. These techniques facilitate the study of multiple flooding scenarios and provide critical data that are difficult or even impossible to measure directly, making them invaluable for hazard assessment. Numerical models solve mathematical equations that describe one or more natural processes, offering an approximation of the system’s behaviour. However, solving these equations can be computationally demanding, which may limit their applicability in certain contexts. Nonetheless, continuous advancements in computational power have significantly expanded the use of these models, enabling higher-resolution simulations and broader applications [14,15,16,19,20,21,22,23,24].

Flood simulation models are generally categorized into two main types. On one hand, lumped models simplify the system by averaging its characteristics rather than explicitly considering spatial variations in topology [25]. This approach makes them computationally efficient but limits the level of detail they can provide. A refinement of these models is the semi-distributed approach, which divides the watershed into multiple sub-catchments (see Figure 1 as an illustrative example) to achieve a more accurate representation of the river system. Traditionally, lumped and semi-distributed models have been widely used in flood early warning systems, as they allow for rapid simulations at a catchment scale, ensuring timely responses [12]. Some of the most widely used models in this category include HEC-HMS [26,27] SWAT [28], and HBV [29].

On the other hand, distributed models explicitly account for topographical variations by discretizing the study area into a computational mesh. These models typically use 2D structured or unstructured meshes, although 1D approaches, such as HEC-RAS [30], remain popular due to their computational efficiency. Structured meshes, often composed of regularly shaped rectangular elements aligned with Cartesian coordinates, are relatively easy to generate and offer computational advantages [31]. In contrast, unstructured meshes, typically based on triangular elements, are better suited for representing complex topographies commonly found in flood scenarios. However, they tend to be more computationally demanding in terms of both generation and processing [32]. Figure 2 illustrates examples of structured and unstructured meshes with a characteristic mesh size of 3 m.

While distributed models provide higher accuracy, they are significantly more computationally expensive than lumped or semi-distributed models. Their computational cost depends on both the resolution and the type of mesh used. However, the development of numerical tools leveraging high-performance computing (HPC) techniques has greatly enhanced their efficiency. For example, the Iber model [33] has been optimized to utilize graphics processing units (GPUs), leading to computational speed increases of nearly 100 times compared to earlier versions, as seen in the Iber+ model [34]. Typically, these models solve the 2D Saint–Venant equations (also known as the shallow water equations) using numerical methods based on finite element or finite volume schemes. Numerous other distributed 2D models have been developed, including JFLOW [35], MIKE 21 [36], G-FLOW [19], and LISFLOOD-FP [37], among others.

Additionally, changes in terrain—in terms of elevation, land use, dam construction, bridges and walls—must be taken into account. Collecting and analysing this type of information is a challenging task, and only a limited number of countries or institutions have the capacity to undertake it. In Spain, for example, these changes can be detected using free GIS tools such as the PNOA Orthophoto Comparator (https://visualizadores.ign.es/comparador_pnoa/ accessed on 28 April 2025) or the Digital Fototeca (https://fototeca.cnig.es/fototeca/ accessed on 28 April 2025), which provide access to aerial images of Spain spanning from 1929 to 2022, depending on the study area. Figure 3 shows a snapshot from the PNOA Orthophoto Comparator, displaying aerial images of Madrid from 1956 (corresponding to the American Flight Series B) and 2018 (corresponding to the PNOA project, https://pnoa.ign.es/ accessed on 28 April 2025).

Other countries offer similar services, such as those provided by the Institut Géographique National in France (accessible at https://www.geoportail.gouv.fr/ accessed on 28 April 2025) and the United States Geological Survey (USGS) (available at https://earthexplorer.usgs.gov/ accessed on 28 April 2025). It is important to note that historical aerial imagery is limited to specific locations and generally covers the period from the early 20th century to the present. Additionally, this information is restricted to visual data, meaning that objective numerical data cannot be easily extracted.

Regarding land use, the CORINE Land Cover dataset, provided by the European Union Copernicus Land Monitoring Service (2018), offers an extensive database of European land use data from 1990 to 2018, which is freely accessible. Figure 4 illustrates the land use classifications for the watershed Miño-Sil, as defined in CORINE 2000. Similar datasets are available for various years between 1990 and 2018. A broader geographical data range is provided by the Global Land Cover Characterization (GLCC) from the Earth Resources Observation and Science (EROS) Center (https://doi.org/10.5066/F7GB230D accessed on 28 April 2025), enabling the global extension of land use data.

3. Methodology

The primary focus of this review is to provide a comprehensive and exhaustive overview of the most representative works on numerical modelling of past flood events. To ensure the article remains of manageable length while maintaining its relevance, the selection criteria were designed to highlight some of the most significant studies. The aim was to incorporate examples of past flood events spanning from the Holocene to the present day, thereby covering the widest possible temporal range. This broad time span is critical for understanding the long-term dynamics of flood events and their recurrence patterns. Moreover, the objective also sought to encompass a diverse range of spatial scales. This geographical breadth is essential for capturing the variability in flood events across different regions and contexts. In addition to these temporal and spatial considerations, a concerted effort was made to ensure comprehensive global representation by including examples from various regions worldwide, thus providing a holistic view of past flood events and their modelling.

The review process began with an extensive literature search of articles published in indexed journals, focusing on identifying studies related to past flood events. For this purpose, keywords such as “reconstruction”, “historical”, “past”, “flood”, “numerical”, and “modeling” were introduced in scientific databases, such as SCOPUS or Google Scholar. Additionally, other sources of information were also consulted in order to encompass all the representativeness objectives outlined above. Once the relevant documentation and information were gathered, the most representative examples, selected in accordance with the aforementioned criteria and with the goal of maintaining the article concise, were included in the review. Subsequently, the review presents a detailed description of the key characteristics of these flood events, the applications and numerical models employed, and the methodologies applied to each case, which are discussed in the following section. A brief depiction of the methodology presented in this section is shown in Figure 5.

4. Numerical Analysis of Past Flood Events

The study of past flood events is a crucial task in the field of hydrology, as it provides the foundation for understanding the mechanisms behind extreme and rare events. Gaining insight into flood dynamics can help anticipate similar occurrences, thereby reducing both human and material losses. European directives emphasize this need (E.D. 2007/60/C), highlighting the importance of considering extreme events when developing flood early warning systems to mitigate the most severe damage scenarios. This issue is also addressed in other European documents, such as [38,39].

Flood events can be classified in various ways. A fundamental classification based on location differentiates between riverine and coastal floods. Notable examples of historical coastal flood events include those analysed by [40,41], who examined tsunami-induced floods recorded in Chile (1960) and Portugal (1750), respectively. While coastal floods are significant, this study focuses on riverine floods, as they generally occur more frequently and result in greater economic and human losses than coastal events [42]. Furthermore, the effects of climate change—particularly the intensification of precipitation in certain regions—must be taken into account [43,44,45]. As a direct consequence, an increase in river flood events is expected. A comprehensive database of past and real-time flood events was compiled by [46], which aggregated flood data from social media sources. The results of this study are publicly accessible through the Global Flood Monitor (https://www.globalfloodmonitor.org/ accessed on 28 April 2025).

Analysing past flood events is a complex task that requires expertise in multiple subfields within hydrology. These range from paleoflood hydrology—in which the magnitude and frequency of past floods are reconstructed using geological evidence—to numerical simulations that model physical scenarios. Other disciplines, such as dendromorphology, can also be used to retrieve data on historical floods by analysing tree ring markings [47]. Data associated with historical flood events are usually scarce and difficult to obtain. It is important to note that instrumental flood records from gauge stations are typically limited to the industrial period, which generally begins around the 19th century [48]. As a result, data for earlier flood events are often unavailable.

Apart from the previously mentioned sources, additional data are required to cover a broader range of dates and to provide information on water levels and, in some cases, discharge values associated with flood events. For instance, studies [49,50] analysed historical flood events ranging from Roman times and highlighted the importance of information derived from existing epigraphic flood markers. A comprehensive description of historical flood data sources is provided by [51], which focused on floods of the Duero River in Zamora, Spain. They demonstrated that information on flood events can be obtained from ecclesiastical and municipal archives, historical city memoirs, flood marks, repair records of flood damage, and even relocations of religious communities due to major floods. Examples of such historical sources related to Zamora include works [52,53,54].

These historical sources can serve as input for numerical models as well as to validate model functioning in the areas under study. In this context, the application of the numerical models enables not only the reconstruction of past flood events but also the identification of their causes and consequences, thus facilitating the improvement of future event predictions and enhancing protection against their negative effects. Several studies have applied numerical models to analyse and reproduce significant historical flood events, taking into account the various sources of information that can be used to replicate these historical events. Wetter et al. [55] investigated floods since 1268 using a hydraulic model, comparing pre-industrial watermarks with modern instrumental data in the high Rhine basin. They classified events into catastrophic (>6000 m³/s) and severe (5000–6000 m³/s) categories, emphasizing the role of numerical modelling in improving return period accuracy and identifying flood causes. Ngo et al. [56] applied a coupled 1D–2D HEC-RAS model to reconstruct the 1374 flood near Cologne. Their findings suggested that previous studies overestimated peak discharge values, impacting return period estimations as [55] also observed. A related study [57] presented similar conclusions at the IAHR World Congress in Panama. Again, focusing on return period estimation, Ref. [58] simulated extreme floods of the Tiber River dating back to the 15th century using the 2D SMS hydrodynamic model. Their study revealed that flood variability is likely linked to climate change and suggested that traditional Gumbel-based [59,60] return period estimations may be inadequate for extreme events. Elleder et al. [61] reconstructed peak discharges of the Moldava River during the 1481 and 1825 floods using the empirical Manning equation, demonstrating strong agreement with modern reconstructions and highlighting the value of documentary data in flood modelling. By contrast, Ref. [62] examined flood events in the Ebro River Basin since 1600 CE, categorising them from large-scale, basin-wide floods to localised flash floods. Using HEC-RAS, HEC-GeoRAS, and Iber, they found that numerical models often yield higher peak flows than instrumental records, likely due to gauge station limitations during extreme conditions. This underscores the role of numerical modelling in refining flood risk assessments and return period calculations. Using the HEC-RAS model, Ref. [63] analysed historical floods recorded over the past 400 years in the Copiapó River, located at the southern limit of the Atacama Desert, to better understand the fluvial dynamics of the region and assess the rarity of extreme events observed in the present. Their findings suggest that the return periods currently in use can be improved by incorporating information derived from the analysis of historical flood events. Urban floods were also analysed. For example, Ref. [63] analysed the 1860 flood in Zamora using Iber, integrating meteorological data with historical records to reconstruct over 60 flood events from 1250 to 1871. Their study clearly demonstrated that numerical modelling of past floods can provide insights into future extreme events under climate change scenarios. Mancini et al. [64] provided guidance on the calibration of 2D models for historical urban floods, applying their methodology to the 1870 Rome flood. The authors emphasised the importance and complexity of accurately calibrating each parameter involved in 2D models and demonstrated how to constrain them by distinguishing among ‘static’, ‘dynamic’, and ‘global’ data, highlighting their respective roles in the calibration procedure. One of the key contributions of this study is the emphasis on the importance of considering historical events when attempting to reproduce urban floods. Elleder et al. [65] analysed the catastrophic 1872 flood in Central Bohemia (Czech Republic) using the Aqualog hydrological model. Based on historical documents (as no gauge data were available), they found that the combination of extreme precipitation and the collapse of approximately 100 ponds along the riverbed significantly contributed to the disaster. Their findings underscore the importance of understanding historical flood-modifying structures, which could also inform modern flood protection strategies, as exemplified by their analysis of Prague’s protective measures. A multidisciplinary methodology combining historical data and meteorological reanalysis was employed by [66] to reconstruct the 1874 Santa Tecla floods in Catalonia (Spain). Using HEC-RAS, the authors evaluated how precipitation data influenced peak flow. They emphasized the trade-offs between 1D models such as HEC-RAS, which provide rapid peak flow estimates, and 2D models like Iber, which offer more detailed flood extent maps. Their work underscored the need for further research on error quantification beyond precipitation data, particularly in relation to catchment characteristics. Another multidisciplinary methodology was applied in [14]. The authors analysed the 1876 floods in Badajoz, Spain—one of the most catastrophic flood events recorded in Europe—using a three-stage methodology. First, they estimated the precipitation in the Guadiana River basin during the days preceding the event based on data from two precipitation stations located in the western part of the basin. Second, they reconstructed the Guadiana River flow in Badajoz using the HEC-HMS model, driven by the precipitation estimates from the first stage. Third, they simulated the December 1876 flood in Badajoz using the 2D hydraulic model Iber+. This study highlighted the strong capability of the Iber+ model to reproduce historical extreme flood events. These works focus on the pre-20th-century period. For example, in the 20th-century period, [67] reconstructed the 1907 flood in Xerta (Spain, Ebro River Basin) using HEC-RAS and Iber models. Their study highlighted the importance of the Manning coefficient and water height in peak flow calculations, concluding that precise flood mark data are crucial for reducing errors in peak flow estimates. Ruiz-Bellet et al. [68] used DAN-W and FLO-2D to study a 1954 volcanic debris flow flood in Campania, Italy, finding that dual-model approaches enhance understanding of debris-laden flood dynamics. Fernández-Nóvoa et al. [16] used the Iber model to analyse the devastating 1967 flood in Quintas (Lisbon area), which resulted in over 100 fatalities. They estimated the probable peak flood by integrating available precipitation data into the Iber model and analysed several scenarios to detect the main causes that played a key role in the intensifying of the flood impact. Their simulations suggested that accumulated debris at a downstream bridge bottleneck significantly exacerbated the flood upstream, which helped to unravel the causes of the disaster. Ballesteros [69,70] used MIKE 21 and MIKE FLOOD to analyse roughness coefficients and flash floods in Spain, demonstrating that roughness parameter selection critically influences numerical outcomes. Denlinger et al. [71] applied TRIMR-2D to study two major floods of the Verde River (Arizona), comparing their numerical results with field data and obtaining good approximations by using roughness and discharge as constraint parameters in the model. The authors concluded that combining field observations of inundation and flow simulations with paleoflood constraints on maximum inundation limits over time provides a robust physical basis for quantifying flood hazards. Ruiz-Villanueva et al. [72] and Ruiz-Villanueva et al. [73], starting from historical reconstructions based on documentary sources and tree ring analysis, used Iber to investigate the effects of wood transport in mountain rivers, with a particular focus on bridge clogging caused by debris flows in urban areas. Their study centred on Arenas de San Pedro, Spain. A series of scenarios were developed based on the wood budget to simulate wood transport and deposition using the Iber numerical model. The results enabled the identification of key infrastructure vulnerable to large wood passage and allowed for the simulation of the consequences of blockages, thereby improving flood hazard predictions. Garrote et al. [74] applied Iber to reconstruct the 1997 flash flood in Caldera de Taburiente National Park (Canary Islands, Spain), incorporating dendrogeomorphological evidence and utilising high-resolution topographic data (LiDAR) in the 2D hydraulic model Iber. The authors conclude that the combined use of numerical modelling with indirect evidence improves flood hazard management tools, allowing for more effective adaptation policies in national park management. González-Cao et al. [15] used Iber to analyse the 1997 floods in Badajoz (Spain), one of the most destructive flash floods in the Iberian Peninsula, employing the numerical model Iber+. Several scenarios were simulated to identify the main causes of the event. The authors concluded that the blockage of bridges was the primary cause of the flood, emphasising the importance of bridge maintenance as a key mitigation measure. A multimodel approach was adopted in [75] to study the 2000 flood in Crete, using Iber and HEC-RAS. The authors analysed two ungauged catchments (Ilingas and Sfakia), revealing that model calibration significantly impacts peak discharge estimates. Their study highlighted the influence of Manning coefficient selection on numerical results, demonstrating that improper calibration can lead to substantial discrepancies between models. Another application of numerical modelling in historical flood analysis was presented in a study conducted on the Yamuna River near Allahabad, India [76]. This study employed the Global Flood Monitoring System (GFMS) and GIS tools, alongside the HEC-RAS hydraulic model, to simulate water surface elevations across a series of historical flood events beginning in 1978. Historical floods were used in this case to calibrate and validate the model, thereby enhancing its reliability for future flood prediction and preparedness. This case underscores the value of historical flood modelling not only in evaluating flood risk but also in informing long-term urban planning and risk mitigation strategies in vulnerable areas. A significant example of historical flood hazard reconstruction is found in Morocco’s Ourika Valley, following the deadly flood that occurred in 1995 [77]. This tragic event revealed the vulnerability of communities in this semi-arid mountainous region and highlighted the urgent need for accurate flood risk mapping, especially in the absence of long-term hydrological records. To address this, the study employed hydraulic modelling using HEC-RAS to simulate the propagation of extreme floods, with the goal of reconstructing water levels and delineating floodplain extents. Crucially, the study evaluated the effect of digital elevation model (DEM) resolution on the accuracy of flood simulations by comparing the widely available 30 m ASTER DEM with a high-resolution (4 m) DEM derived from Pleiades satellite imagery. The results showed that the higher-resolution Pleiades DEM provided a more accurate representation of flood extent and water levels compared to the ASTER DEM, which significantly underestimated flood risk. This study illustrates how hydraulic modelling—when supported by high-resolution terrain data—can help characterise historical flood risk and guide future flood management. It also opens a path for integrating such models with vulnerability assessments to prioritise mitigation measures. In regions where instrumental records are sparse or absent, such reconstructions are vital for understanding past events and preparing for future extremes. Another relevant example of historical flood reproduction through numerical modelling is presented in a study of the Laigiang River basin in Central Vietnam [78]. The study employed the HEC-HMS hydrological model, supported by remote sensing data and GIS tools, to simulate flood dynamics associated with significant rainfall events and assess how historical changes in land use and land cover (LULC) influenced peak discharge and runoff volume. The results showed that the transformation of dense vegetation into areas of lower vegetation cover and increased urbanisation led to higher Curve Number (CN) values, which reduced infiltration and water retention capacity while increasing peak flows—ultimately contributing to greater flood risk. The model effectively reproduced historical flood behaviour, demonstrating the substantial impact of land cover evolution on flood severity. This case underscores the value of historical flood modelling not only for reconstructing past events but also for understanding the hydrological consequences of anthropogenic changes over time. Dahal and Kojima [79] evaluated three hydrological models for the analysis of flood events in the Bhutan region (located between India and China), specifically in the upper Wangchu River Basin. The three hydrological models assessed were the Integrated Flood Analysis System (IFAS), the Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS), and the Group on Earth Observations Global Water Sustainability (GEOGloWS) model. Two flood events were used for the calibration and validation of the models. Among the three, the GEOGloWS model demonstrated the best performance in replicating the observed results; however, further improvements are still necessary to enhance its accuracy and reliability. Bellos et al. [80] focused on the reconstruction of the November 2017 flood event in Mandra (Athens, Greece), which is part of the greater Sarantapotamos River system. The reconstruction was based on high water marks observed on sediments and building walls after the flood event. Two hydraulic models were employed: HEC-RAS and MIKE FLOOD. However, the results obtained were not entirely conclusive, indicating the need for further investigation and model refinement. Another example is [81]; this study focused on the town of Mandra (Greece), where the Agia Aikaterini stream frequently causes flooding. Due to the small size of the watershed, the objective was to develop an efficient early warning system tailored to small catchments. To achieve this, three hydrological models were evaluated: HYMOD, GR4H, and LRHM. Among them, the GR4H model, in combination with the HEC-RAS hydrodynamic model, was selected to develop a practical tool aimed at flood damage prevention. Sánchez-García et al. [82] focused on the Llobregat River (Llobregat and Ter Basins) in Spain, a region that has experienced multiple flood events. The research presents a hydraulic analysis using the HEC-RAS model to assess the applicability of Nature-based Solutions (NbSs) for flood mitigation. The results indicate that NbSs represent an effective tool for flood prevention in this area. In [83], the authors reconstructed the flood event that occurred on 18 September 2020 in the city of Karditsa, Greece, located within the Kaletzis river basin. The area is surrounded by two rivers, Gavrias and Karampalis, which contributed to the severe flooding. The reconstruction was carried out using CORINE land use data, the HEC-HMS hydrological model (Muskingum-Cunge routing), and the HEC-RAS hydrodynamic model. The study emphasises the value of integrating hydrological and hydrodynamic modelling with remote sensing data, as well as image, video, and eyewitness information provided by local residents. Finally, in [84], the authors compared various satellite-based tools and DEM-derived methods for near-real-time flood mapping, focusing on a 2022 flood event in Antananarivo, the capital of Madagascar. Satellite imagery from multiple sources was analysed using the HYDRAFloods tool. Among the configurations tested within HYDRAFloods, the Edge Otsu and Bmax Otsu algorithms produced the most accurate results. Additionally, a digital elevation model (DEM)-based analysis was conducted using the FwDET tool, which also yielded satisfactory outcomes.

Previous studies have focused on events recorded from the 12th to the 21st century. Extreme paleofloods, such as the Pleistocene Missoula Flood, have also been studied using numerical models. Miyamoto et al. [85] developed a shallow-water model to analyse these cataclysmic events, and [86] used HEC-2 for similar reconstructions. Norris et al. [87] applied HEC-RAS to examine the Younger Dryas drainage of Lake Agassiz, concluding that this event had significant implications for Arctic meltwater transport—an insight relevant to modern climate change. Ref. [88] analyse Holocene catastrophic floods in the lower Yarlung Tsangpo River valley using the HEC-RAS model. Kidson et al. [89] analysed Holocene catastrophic floods in the lower Yarlung Tsangpo River valley using the HEC-RAS model. The authors also analysed paleofloods in the Mae Chaem catchment (Thailand). They carried out a very interesting analysis of the Manning coefficients of the area of study using data from recent flood events to estimate the discharge of a paleoflood event. In [90], the application of HEC-RAS provided essential insights into the hydraulic conditions responsible for the preservation of SWDs and deepened the understanding of historical flood behaviour at various sites. Moreover, the study incorporated Bayesian inference to enhance flood frequency analysis (FFA), which led to a reduction in the uncertainty associated with estimating extreme flood discharges. By integrating paleoflood data with gauged records, the model demonstrated how historical flood events can be reconstructed with greater accuracy, thus improving flood risk assessments. Despite some inherent uncertainties in hydraulic modelling, such as the potential for over- or under-estimation of paleoflood discharges due to variations in deposition depth, the HEC-RAS modelling in this study proved highly effective. The results reinforce the crucial role of hydraulic modelling in historical flood analysis.

Table 1. Main characteristics of referenced papers.

Id. Number	Reference	Location	Country	Continent	Hydraulic Model
1	[67]	Xerta	Spain	Europe	HEC-RAS, Iber
2	[16]	Quintas-Lisbon	Portugal	Europe	Iber
3	[66]	Santa Tecla	Spain	Europe	HEC-RAS
4	[65]	Central Bohemian	Czech Republic	Europe	Aqualog
5	[75]	Crete	Greece	Europe	HEC-RAS, Iber
6	[62]	Ebro river	Spain	Europe	HEC-RAS, HEC-GeoRAS, Iber
7	[56]	Cologne	Germany	Europe	HEC-RAS
8	[57]	Cologne	Germany	Europe	HEC-RAS
9	[51]	Zamora	Spain	Europe	Iber
10	[55]	Cologne	Germany	Europe	FLUX/FLORIS2000
11	[58]	Rome	Italy	Europe	SMS
12	[61]	Prague	Czech Republic	Europe	Manning Eq.
13	[72]	Arenas de San Pedro	Spain	Europe	---
14	[68]	Campania region	Italy	Europe	DAN-W, FLO-2D
15	[74]	Canary island	Spain	Europe	Iber
16	[64]	Rome	Italy	Europe	HEC-RAS
17	[69]	Spanish Central System	Spain	Europe	MIKE 21
18	[70]	Navaluenga	Spain	Europe	MIKE FLOOD
19	[73]	Arenas de San Pedro	Spain	Europe	Iber
20	[15]	Badajoz	Spain	Europe	Iber
21	[14]	Badajoz	Spain	Europe	Iber, HEC-HMS
22	[80]	Athens	Greece	Europe	HEC-HMS
23	[81]	Mandra	Greece	Europe	HYMOD, GR4H, LRHM, HEC-RAS
24	[82]	Llobregat River	Spain	Europe	HEC-RAS
25	[83]	Karditsa	Greece	Europe	HEC-RAS HEC-HMS
26	[71]	Arizona	USA	North America	TRIMR-2D
27	[85]	Missoula	USA	North America	Developed by authors
28	[86]	Missoula	USA	North America	HEC-2
29	[87]	Lake Agassiz	Canada	North America	HEC-RAS
30	[63]	Copiapó River	Chile	South America	HEC-RAS
31	[88]	Tibetan Plateau	China	Asia	HEC-RAS
32	[89]	Chiang Mai	Thailand	Asia	HEC-RAS
33	[76]	Allahabad	India	Asia	HEC-RAS
34	[78]	Laigiang River basin	Vietnam	Asia	HEC-HMS
35	[79]	Wangchu River Basin	Buthan	Asia	HEC-HMS
36	[77]	Ourika Valley	Morocco	Africa	HEC-RAS
37	[84]	Antananarivo	Madagascar	Africa	HYDRAFloods
38	[90]	Southeast Queensland	Australia	Oceania	HEC-RAS

summarises the main aspects of the references described in this section, and in Figure 6, the locations of the flood events described in this section are depicted.

5. Conclusions

• This study provides a comprehensive review of scientific literature focused on the numerical analysis of past flood events, which is a key component in enhancing flood risk management strategies.
• Numerical modelling emerges as an invaluable tool for reconstructing and evaluating past flood events, particularly in improving the understanding of extreme and/or (very) rare events in which data are scarce. These events may become more frequent in the future due to the implications of climate change, making their analysis increasingly relevant.
• Several types of past flood events and some characteristics of the numerical models applied to reproduce them can be found in this review. In most cases, numerical reproduction is the only feasible approach to extracting information from these historical events, as the available data are often extremely limited.
• The available information on past events is often restricted to brief descriptions in ancient texts, ecclesiastical records, or similar sources. The initial input data required for the numerical reproduction of such events is also subject to the same limitations. For instance, land use conditions at the time of the event are often uncertain, and current digital elevation models (DEMs) are unlikely to accurately represent the topography of the event period, given that landscape modifications over time are almost inevitable.
• Numerical simulation tools allow us to overcome these challenges by accounting for possible variations in these key variables, thereby generating a range of potential outcomes. This enables a more detailed understanding of the event under study. Based on this information, appropriate measures can be implemented to mitigate the adverse effects of such events.
• Furthermore, numerical simulation methodologies can significantly enhance the conventional methods used to estimate return periods associated with these events. Traditional approaches rely on discharge data obtained from control station records, where discharge values are derived from rating curves that establish a relationship between water surface elevation and discharge using an equation typically developed under mean river conditions. Consequently, these estimations often lack reliability under extreme flow conditions.
• Additionally, in many cases, numerical models contributed to resolving the uncertainties that existed in the development of historical floods by simulating various possible scenarios of occurrence and detecting the most plausible, thereby contributing to gaining knowledge and improving adaptation to mitigate flood events.
• The review highlights two key findings. On the one hand, it reveals a wide temporal coverage in the literature, ranging from glacial-era events to the mid-20th century. On the other hand, it also highlights a significant spatial imbalance: most studies are concentrated in Europe, with limited representation in North America. More strikingly, few relevant studies have been identified in Asia, South America, or Oceania.
• Significant data gaps were also detected across various regions of the world, particularly in developing and least-developed areas. Limited access to the necessary tools and resources often makes it economically unfeasible to conduct studies such as the one presented in this work. One potential strategy to overcome this limitation is the use of tools like the 2D hydrodynamic model Iber, which is freely accessible and available for download at no cost, in combination with global Digital Elevation Models (DEMs), which are also freely available. The adoption of such tools represents a viable pathway to reducing disparities in data and resource availability, thereby enabling the implementation of similar studies in underrepresented regions. This would help close research gaps and support local flood mitigation efforts.
• This gap presents a promising research line in these geographic regions, where efforts should be directed towards identifying and reconstructing ancient flood events. Thus, future research should prioritise the reconstruction of historical floods in underrepresented regions. Doing so will not only improve our understanding of flood mechanisms but also contribute to the global knowledge of climate change impacts.
• Therefore, this work, along with the first part of the paper focusing on Flood Early Warning Systems (FEWSs), provides a very useful literature review to scientists and engineers involved in flood analysis to improve and develop support tools to help improve mitigation measures to reduce flood damage both for people and property.