1 INTRODUCTION

Inundations are among the most destructive disasters, with the potential to create dramatically negative impact on populations in terms of fatality, injury, displacement of people, and damage to infrastructure, cultural and environmental heritage, and economic activities (CRED-UNDRR, 2020; Doocy et al., 2013). Flooding can be induced by natural phenomena (such as river floods causing overflow or breaching of river embankments, coastal storms, tides, or intense rainfall in urban areas), or anthropic causes (such as incorrect operations of hydraulic structures, or uncontrolled release of water resulting from an accident, or the partial or total collapse of a dam). Over the last 20 years, floods have been the most recurrent type of natural disaster (accounting for 44% of all events recorded by CRED's Emergency Events Database during this period) and affected 1.65 billion people worldwide (the highest figure compared to the other disaster types), with $651 billion in economic losses (CRED-UNDRR, 2020).

Flooding creates a risk when anthropic and environmental systems can be potentially damaged. According to the EU Floods Directive (European Council, 2007), flood risk is defined as “the combination of the probability of a flood event and of the potential adverse consequences to human health, the environment and economic activity associated with a flood”. In analogy with the standard definition of risk of extreme events, flood risk is to be considered as the combination of three components (IPCC, 2012; Kron, 2002): flood hazard (i.e., flood frequency and severity); exposure (i.e., the presence of people, buildings, infrastructure, economic and social activities in floodable areas); and vulnerability (i.e., the propensity of exposed elements to be damaged by flooding). The increase in human settlements and economic assets in floodplains and coastal areas, along with the alteration in flood magnitude and frequency due to climate change, leads to a higher degree of flood risk (Hirabayashi et al., 2013), thus highlighting the need to adopt national and local risk reduction and adaptation strategies to improve the resilience of communities to the negative impacts of floods (Hammond et al., 2015; Nofal & van de Lindt, 2022).

Flood risk mapping is an effective, increasingly used tool in the risk-based approach to flood risk management (Sayers et al., 2013). Flood risk maps visualise the spatial distribution of flood risk, expressed in terms of expected damage and potential consequences for a given flooding event (Merz et al., 2007), and are essential to plan a prompt response to emergencies, prevent occurrence of new risks (by orienting land-use planning and land management), reduce existing risks (through the implementation of protection and mitigation measures), and increase public awareness of flood risk, thereby fostering the adaptation of society to changing risk factors (Martini & Loat, 2007).

On an international level, there exist many examples of flood mapping for purposes of flood risk management (de Moel et al., 2009; Klijn et al., 2008). Among these, the U.S. National Flood Insurance Program (NFIP, 2021; Luke et al., 2018); the French Flood Risk Prevention Plan (Decree 2019-715, 2019; Guillier, 2017); the Flood Risk Management Plan of the Rhine, Germany (ICPR, 2021); the Danube Flood Risk Management Plan (ICPDR, 2021); the plan PLUIES (Flood prevention and control and effects of floods on victims) in Wallonia, Belgium (PLUIES, 2003); the DREAM and UP DREAM programs in the Philippines (Santillan et al., 2016; UP DREAM, 2016); the recent update of hazard and flood risk maps for several thousand kilometres of river courses and coastal sectors in Spain (Olcina-Cantos & Díez-Herrero, 2021). The EU Floods Directive (European Council, 2007) requires member states to produce flood hazard and risk maps as a preparatory step to the development of flood risk management plans (de Moel et al., 2009).

Catalogues of interactive flood maps or databases are often made available on websites as a result of national flood mapping programs (e.g., Environment Agency, 2019; Géorisques, 2020; HORA, 2022; UmweltAtlas, 2022). Flood inundation maps for selected return periods are published in these online resources, thereby providing a flood hazard zonation based on flooding probability. Furthermore, various reports, guidelines and handbooks have been produced with the purpose of guiding flood risk assessment and management, typically targeted to a specific geographic area (e.g., CHARIM, 2021; Díez-Herrero et al., 2009; ESCAP, 1991; FEMA, 2013; FEMA, 2021; INTEGEMS, 2017; LAWA, 2006; Lumbroso et al., 2008; National Research Council, 2009; NSWG, 2005; The Mekong River Commission Secretariat, 2009), or offering an overview of the techniques used in different countries across the world (e.g., Prinos, 2008; Ranzi et al., 2011; van Alphen & Passchier, 2007). Recently, several national and international research programs have been devoted to investigating extreme flood events and promoting advances in methods, strategies, and flood simulation techniques to enhance flood risk management (e.g., FloodRISE: UCI, 2022; FLOODsite: FLOODsite, 2009 and Samuels et al., 2009; KULTURisk: KULTURisk, 2011; IMPACT: Morris & Hassan, 2005).

Flood hazard is defined as the threat represented by a flood of certain frequency and magnitude to a particular location (de Moel et al., 2015; Nofal & van de Lindt, 2022); it is a key component of flood risk and can be evaluated via qualitative, semi-quantitative, or quantitative methods (Chen et al., 2015). Qualitative methods are heuristic and solely based on expert judgement. Semi-quantitative methods are based on the concept of ranking flood hazard by weighting the contributions of different geographic and morphometric factors. Typically, they exploit the potential of GIS (e.g., Albano et al., 2014; Albano et al., 2019; Araújo et al., 2019; Bathrellos et al., 2016; Bhat et al., 2019; Chen et al., 2015; Islam & Sado, 2000; Kittipongvises et al., 2020; Kourgialas & Karatzas, 2011; Kumar, 2016; Skilodimou et al., 2021; Toosi et al., 2019), and are very efficient, especially in large-scale (regional or basin-scale) analysis, or in situations characterised by scarcity of data. Finally, quantitative methods are based on hydrological scenarios and hydraulic modelling, and imply the definition and calculation of a suitable flood hazard index to be referred to in order to draw up a hazard level classification. Flood hazard indexes are usually defined by combining relevant flow parameters; therefore, applying such methods requires setting up complex hydrodynamic models and having a large number of input data available (elevation models, land use and cover data, etc.). In addition, a great computational effort is needed, especially when a large floodable area must be covered, and high accuracy and spatial resolution must be guaranteed (Banks et al., 2014). Figure 1 illustrates the main steps of quantitative flood hazard assessment. The hydrodynamic inundation model, usually based on the two-dimensional shallow water equations (FEMA, 2020; Mudashiru et al., 2021; Néelz & Pender, 2009; Teng et al., 2017), provides a physically based description of the flooding process for selected scenarios and allows predicting the relevant hydraulic parameters needed to characterise flooding intensity. The flooding parameters mostly used to quantify flood hazard are flood depth (FEMA, 2013; Martini & Loat, 2007; Merz et al., 2007; National Research Council, 2009) and flow velocity (Kreibich et al., 2009), taken separately or in combination to define a suitable flood hazard indicator (often, the product of flood depth and flow velocity; e.g., AIDR, 2017; Merz et al., 2007). In particular, flood depth is the most used intensity parameter in flood damage functions (Hammond et al., 2015; Merz et al., 2010; Nofal & van de Lindt, 2022). Other parameters relevant to flooding hazard assessment are flood arrival time, flood duration, flood depth rise rate (Ahmadisharaf et al., 2015; de Bruijn et al., 2015; FEMA, 2013; Merz et al., 2007; Muñoz et al., 2020; Naeem et al., 2021; Santillan et al., 2016; Vu & Ranzi, 2017), as well as standing water depth following the flood, erosive potential of the flooding (Luke et al., 2018), and debris or contaminant load.

Typical outcomes of quantitative flood hazard assessment are inundation and flood hazard maps (Figure 1), which depict the extent of the areas potentially subject to flooding and the spatial distribution of the flood hazard, respectively, for a selected hydrological scenario (Carrasco et al., 2012; de Moel et al., 2009; Merz et al., 2007; van Alphen & Passchier, 2007). However, lack of standardisation can be observed in flood hazard mapping (de Moel et al., 2009; van Alphen et al., 2009; van Alphen & Passchier, 2007). Probabilistic approaches have recently been proposed, which, unlike deterministic ones, provide information about the uncertainty associated with flood hazard predictions (e.g., Beven et al., 2015; Di Baldassarre et al., 2010; D'Oria et al., 2019; Vorogushyn et al., 2010).

This article systematically reviews existing quantitative flood hazard assessment methods either prescribed by national government authorities or developed by academic institutions during research programs, with a special focus on the criteria proposed for flood hazard level classification. Despite recent valuable efforts to provide critical reviews on various aspects of flood risk modelling (e.g., Cea & Costabile, 2022; Moreira et al., 2021), a comprehensive review on quantitative flood hazard assessment methods is still missing in the literature. Stability conditions for people and vehicles are not considered here since they identify two possible states only (i.e., safe/unsafe) without introducing an actual classification in different flooding hazard levels. Besides, extensive reviews of these stability conditions are already available, for both people (Jonkman & Penning-Rowsell, 2008; Xia et al., 2014) and vehicles (Bocanegra et al., 2020; Martínez-Gomariz et al., 2018; Shah et al., 2021), often with particular reference to urban flooding (Mignot & Dewals, 2022).

The methods reviewed here are categorised in terms of basic approach (heuristic, conceptual, empirical); exposed element (people, buildings, vehicles); and field of application (riverine or coastal flooding, dam-break, levee breach, debris flow, etc.). For each method, the indicator used to express flood hazard is specified along with the parameters involved.

2 STATE OF THE ART ON QUANTITATIVE FLOOD HAZARD ASSESSMENT METHODS

The quantitative flood hazard methods retrieved during the literature review are divided into two main categories and listed in two distinct tables. Table 1 shows the methods based on flood intensity only, which do not explicitly include information on frequency of flooding in the flood hazard classification. The resulting hazard maps represent the spatial distribution of the hazard index for a specific flood event (historical or synthetic). Table 2 includes the methods that take into account probabilistic information (i.e., the return period of the flood event or the probability of the flooding scenario), as well as the intensity of flooding. In this case, the flooding hazard maps represent the spatial distribution of flood hazard assessed on the basis of intensity-probability matrices. The methods usually adopted for the identification of river hazard zones also belong to this category. In both tables, the methods are listed in chronological order.

The tables consist of nine columns.

Column 1 reports a progressive number for the reader's convenience.

Column 2 indicates which government authority or national guidelines prescribe or suggest the method; state-of-the-art methods proposed in academic research projects are labelled as “N/A”.

Column 3 provides the fundamental references of each method, especially those where they were first proposed (if available).

In Column 4, the methods are classified according to the basic approach: (a) “heuristic”, if the flood hazard classification is defined on the basis of the author's expertise, well-established local uses, or choices made in previous studies, without providing specific supporting reasons; (b) “conceptual”, if the flood hazard classification is defined on the basis of theoretical stability models specifically designed for the exposed element considered; and (c) “empirical”, if the flood hazard classification is defined on the basis of experimental data.

Column 5 lists the hydraulic parameters and flooding variables involved in the definition of the flood hazard indicator for each method considered.

The flood hazard index used to provide a quantitative measure of flood hazard is specified in Column 6, while the related flood hazard classification is detailed in Column 7. The complexity of the classification is mainly related to the number of flooding parameters involved and the inclusion of information on flood frequency.

The exposed elements considered with each method are specified in Column 8 (people, buildings, vehicles, etc.).

Finally, Column 9 reports the fields of application of the methods, along with some references in which the methods are applied to real cases. In this column, “flooding” indicates the application to generic inundation events having various causes (severe rainfall, river overflow, coastal storm); labels “levee breach” and “dam-break” indicate the application of the method to flooding caused by levee system- and dam-failure, respectively; “debris flow” indicates the application to debris flow events. Hazard assessment methods specifically proposed for debris flows are listed at the bottom of Tables 1 and 2.

3 DISCUSSION

The present review shows that a large number of quantitative flood hazard assessment methods have been proposed in the past decades and are currently in use. These methods differ in many respects, including the basic approach (heuristic, conceptual, or empirical), the indicator used to assess flood hazard, and details on flood hazard ranking. Table 3 reports some statistics regarding the entire set of methods listed in Tables 1 and 2.

Most of these methods (i.e., the 50 listed in Table 1 out of 72 total, approximately 7 out of 10) are based on estimating the hazard through flooding intensity only, generally referring to a specific (extreme or historical) flood scenario or fixed hydrological events with selected return periods. Accordingly, the same flooding hazard indicator and classification are used regardless of the exceedance probability of the potentially hazardous flood event. Fewer methods (i.e., the 22 listed in Table 2 out of 72 total, approximately 3 out of 10) combine flooding intensity and flood exceedance probability. For example, Aronica, Candela, et al. (2012) used distinct hazard level classifications for hydrologic events of different return periods so that, for a given flooding magnitude, the hazard level is higher for more frequent flood events. Therefore, including flooding probability in hazard assessment enables different consideration of a potentially damaging situation (i.e., more tolerable or less tolerable) depending on its probability of occurrence. Methods that use intensity-probability matrices are based on a similar concept and are very popular (e.g., LAWA, 2006; PLUIES, 2003; Stephenson, 2002) due to the simplicity of visualisation and application. An alternative effective method of combining inundation intensity and probability is based on defining the hazard classes through conditions set on flooding hazard indexes calculated for flood scenarios of different return periods (Adige River Basin Authority, 2005). Accordingly, a univocal hazard level can be attributed to a fixed location while starting from flood events of different return periods.

Tables 1 and 2 show that various flooding hazard indicators are currently used in the literature and in practical applications by scientists and practitioners. The most used is flood depth, followed by flow velocity, because these parameters reasonably have the greatest influence on flooding consequences (e.g., Merz et al., 2007). Indeed, flood depth is involved in defining flood hazard in almost all cases in Tables 1 and 2 (except items 18 and 30 in Table 1), either alone as representative itself of flood hazard (in approximately 18% of cases), or in combination with flow velocity or other relevant flooding parameters. Meaningful indexes representative of inundation intensity are obtained by combining flood depth and flow velocity. Among these, the most used is the product of flood depth and flow velocity, which is involved in almost 30% of the flood hazard assessment methods considered. Other basic hydraulic quantities are sometimes used as flood hazard indicators, namely energy head (e.g., Kramer et al., 2016) and total flow momentum, expressed as hydrostatically equivalent total depth (Aureli et al., 2008). Besides flood depth and flow velocity, other flooding quantities are rarely considered in flooding hazard assessment, despite their potential impact on the safety of people and the resilience of buildings and infrastructure. These quantities are mainly flooding arrival time (Pieterse et al., 2009), flooding duration (e.g., Mani et al., 2014; Ongdas et al., 2020; Tingsanchali & Promping, 2022), and other factors, such as turbidity (e.g., DEFRA Environment Agency, 2006b). The possible transport of floating objects (e.g., large wood debris) or pollutants is normally disregarded. National authorities in charge of soil defence from flooding and water resource management often identify distinct riverine hazard zones on the basis of the areas that are prone to flooding as a result of flood events of selected return periods (e.g., FEMA, 2021; Po River Basin Authority, 1999). According to this approach, flooding hazard is expressed by means of selected classes of inundation probability or, equivalently, through the probability of exceedance of a selected threshold flood depth (Efstratiadis et al., 2022).

Quantitative flood hazard classifications are commonly tailored to specific elements at risk, such as people (e.g., DEFRA Environment Agency, 2006b; Liu et al., 2021; Xia et al., 2011), vehicles (e.g., Shand et al., 2011; Xia et al., 2011), or buildings (e.g., de Bruijn et al., 2015; Krieger et al., 2017; Maijala, 2001), sometimes accompanied by a qualitative description of the hazardous implications expected (e.g., García-Martínez & López, 2005; Priest et al., 2009; Wade et al., 2005) and by recommendations on planning limitations and protection measures (e.g., Beffa, 2000). Garrote et al. (2020) even proposed a specific hazard ranking for cultural heritage sites. The graphical hazard classification by ACER (1988) changes depending on the jeopardised element (people, houses, vehicles, etc.). The hazard classification for people by Cox et al. (2010) is differentiated according to age (infants, children, adults), while the hazard categories defined by Kramer et al. (2016) for vehicles differ for passenger cars and emergency vehicles. It is indeed reasonable that the hazard level, which provides a concise interpretation of the flooding information in terms of potential hazard, is tailored to the exposed element. For instance, a given flooding intensity (expressed, e.g., in terms of water depth) can be very hazardous for a person and much less damaging for a building. On the other hand, other methods provide a general evaluation of the flooding hazard in an anthropised area (e.g., an urban area, as in Cançado et al., 2008 and in Tingsanchali & Promping, 2022), with no reference to specific elements at risk (e.g., Smith et al., 2014). Most of the methods considered in this review (about 1 out of 2) belong to this category. Hazard classes can be defined either mathematically (e.g., DEFRA Environment Agency, 2006b; Khaing et al., 2019; Mani et al., 2014; Patra et al., 2019) or graphically (e.g., ACER, 1988; Aronica, Candela, et al., 2012; Ministerio de Medio Ambiente, 1996) through conditions set on relevant flooding variables.

Most of the hazard assessment methods reviewed (approximately 86% of the total) are applied indifferently to flooding phenomena, regardless of their causes, and hence their use can be found in multiple contexts in the literature. For example, the flood hazard classification methods by ACER (1988) and DEFRA Environment Agency (2006b) have been applied to riverine and coastal flooding, as well as to levee breach flooding; the method by Loat (2010) has been applied to both flooding and landslides. On the other hand, some methods have been specifically proposed for a certain flood disaster, such as dam-break (e.g., Ministerio de Medio Ambiente, 1996; Patra et al., 2019) or debris flow (e.g., Loat & Petrascheck, 2008; Rickenmann, 2005). In this case, specific flood intensity parameters and hazard categorizations suitable for the particular hazardous process are used (e.g., Aronica, Biondi, et al., 2012).

Finally, Table 3 shows that the approach used to derive most of the quantitative methods considered (about 61%) is heuristic — that is, the selection of the hazard indicator and the classification adopted are not soundly motivated theoretically or empirically; rather they are based on the expert judgement of the practitioner/modeller or, more simply, on previous studies (Rufat et al., 2015). The remaining methods derive from the analysis of experimental data (in approximately 31% of cases), conceptual models (in approximately 3% of cases), or mixed approaches (in approximately 5% of cases; see items 18 and 31 in Table 1, or items 14 and 15 in Table 2).

4 CONCLUSIONS

Flood hazard assessment is a key step in flood risk analysis, which in turn translates into emergency planning, flood risk management strategies, and mitigation and protection measures to improve the resilience of communities living in flood-prone areas. This justifies the great attention paid to this topic in the past decades.

A comprehensive literature review of the quantitative methods currently used by scientists and practitioners for flood hazard assessment is presented in this article. Such methods are typically based on the quantitative categorisation of a suitable flood hazard index, defined as a combination of relevant flooding parameters. Hydrodynamic numerical modelling of the flooding process is required to calculate the flood hazard index and determine the flood hazard level (based on the associated classification). Basic details on quantitative methods proposed in scientific studies or adopted by government agencies were reported in summary tables, indicating the mode of expression for flood hazard (flood intensity only, or flood intensity in combination with flood probability), the methodological approach (conceptual, empirical, or heuristic), the exposed elements considered (people, vehicles, buildings, etc.), and the contexts of application (riverine flooding, dam-break or levee breach flooding, flooding in coastal or urban areas, debris flow, etc.).

This review aims to help modellers and practitioners select the most appropriate flood hazard assessment method for the specific needs and the application of interest, as well as identify references where relevant application examples and case studies can be found. A flood hazard analysis based on thorough knowledge of the features of existing flood hazard methods can support more informed assessments, consequently more effective decision-making.

Aspects that are worth improving and represent future challenges in flood hazard assessment analysis were discussed in detail. These range from the representativeness of the flood hazard indicator depending on the flooding cause and the stage of the flood event, to the standardisation and validation of the flood hazard classification methods, as well as the mapping of flood hazard uncertainty. The effective communication of the outcomes of a flood hazard analysis increases public awareness of the potential harm of flooding, thereby reducing its negative impact in terms of loss of life, economic and social damage, and loss of cultural and environmental heritage.

The comprehensive analysis of the current quantitative flood hazard assessment methods might encourage new contributions for improved hazard evaluation in flood risk mapping.