Improvements and Operational Application of a Zero-Order Quick Assessment Model for Flood Damage: A Case Study in Italy

Flood damage assessment is an essential asset in flood risk management, and the literature brings several models, most based on damage curves. This kind of approach is essential and well established but not suitable for being applied in the immediate aftermaths of a flood. Herein, a new application of a zero-order model for the Po-Venetian plain area, which covers more than 20% of the Italian territory, is conceived and implemented. At first, a calibration of the model with damage data coming from past events in the region is carried out, showing that the calibration is site-specific. In particular, it is shown how the exponent in the power-law form of the model is the same as obtained in a previous work on another territory, while the intercept, defined as specific damage, varies. Then the algorithm is applied to the area affected during the flood that hit the Emilia-Romagna region (Northern Italy), in December 2020, for validation. Knowledge of the affected area comes from the quick assessment procedure commonly performed by the National Fire Corps in any significant flood, employing low-altitude all-weather helicopter GPS surveys. The paper shows that combining the model with such a rapid mapping technique leads to a near real-time estimation of damages in the aftermath of floods. The results are aimed at obtaining a first approximation figure. The estimation error shows this figure to be not far from those obtained with much more detailed approaches, requiring a much longer time for their setting. For that reason, the model results can contribute, among other things, by directing the immediate post-emergency management operations and promptly allocating financial resources for recovery.


Introduction
In the last decades, damage assessment has gained an essential role in the chain of flood risk evaluation. An assessment of expected damage is crucial in situations where structural or non-structural interventions are necessary to reduce the natural risk [1]. At the same time, rapid damage appraisal in the aftermath of floods is fundamental to support emergency management and address resources by identifying intervention priorities [2]. Flood damage data represent an essential source of knowledge for the scientific community to understand damage mechanisms and develop damage models [3]. Since flooding represented the third major cause of economic loss worldwide [4] between 2006 and 2015, European countries started to improve their damage data collection systems and damage modeling [5].
In Italy, since 2013, data are collected for the most intense events and are based on the self-declaration of citizens [6]. Forms filled in by citizens represent good pieces of information to analyze damage mechanisms, but they keep a subjective part on damage

Case Study
The flood originated from two subsequent events that hit Northern Italy at the end of 2020. In the Emilia-Romagna region, the descent of a deep depression wave caused the irruption of cold air and a sharp drop in temperatures in the first days of December. The polar currents caused abundant snowfalls down to lowland altitudes. From 4th to 8th December, hot and humid air flows fed intense and persistent rainfall on the whole region, giving rise to several successive thunderstorms, definitely unusual in the winter period in Italy.
The rapid increase in temperatures caused the partial melting of the snow that had fallen in the preceding days. This snowmelt heavily increased the runoff from the Apennine basins, generating floods with sequences of peaks close together on all watercourses [26]. The main focus of the analysis is the Panaro river, which is the last right tributary downstream of the Po River and which flows in the outskirts of the town of Modena (Figure 2).
The flood peak exceeded all historical records in the Panaro river plain sensors, causing a breach in the right bank levee, which occurred on the morning of 6 December by the village called Gaggio. An area of around 15 km 2 in Castelfranco Emilia and Nonantola was flooded, giving rise to severe damages. The flood then proceeded in a northeast direction during the morning.

Case Study
The flood originated from two subsequent events that hit Northern Italy at the end of 2020. In the Emilia-Romagna region, the descent of a deep depression wave caused the irruption of cold air and a sharp drop in temperatures in the first days of December. The polar currents caused abundant snowfalls down to lowland altitudes. From 4th to 8th December, hot and humid air flows fed intense and persistent rainfall on the whole region, giving rise to several successive thunderstorms, definitely unusual in the winter period in Italy.
The rapid increase in temperatures caused the partial melting of the snow that had fallen in the preceding days. This snowmelt heavily increased the runoff from the Apennine basins, generating floods with sequences of peaks close together on all watercourses [26]. The main focus of the analysis is the Panaro river, which is the last right tributary downstream of the Po River and which flows in the outskirts of the town of Modena ( Figure 2). The Governor of the Region asked the national Government for the proclamation of a state of emergency (https://www.protezionecivile.gov.it/it/dipartimento/amministrazione-trasparente/interventi-straordinari-e-di-emergenza, last access on 20 January 2022) . The state of emergency is the measure through which the Government deals with extraordinary events by allocating an adequate amount of money for the emergency management and teams for rescue intervention and first aid to the population. This enabled the damage self-declarations procedure carried out by citizens. As we can observe in Figure 3, the territory was completely flooded, both in the rural part of the town and in the The flood peak exceeded all historical records in the Panaro river plain sensors, causing a breach in the right bank levee, which occurred on the morning of 6 December by the village called Gaggio. An area of around 15 km 2 in Castelfranco Emilia and Nonantola was flooded, giving rise to severe damages. The flood then proceeded in a northeast direction during the morning.
The Governor of the Region asked the national Government for the proclamation of a state of emergency (https://www.protezionecivile.gov.it/it/dipartimento/amministrazionetrasparente/interventi-straordinari-e-di-emergenza, last access on 20 January 2022). The state of emergency is the measure through which the Government deals with extraordinary events by allocating an adequate amount of money for the emergency management and teams for rescue intervention and first aid to the population. This enabled the damage self-declarations procedure carried out by citizens. As we can observe in Figure 3, the territory was completely flooded, both in the rural part of the town and in the city center. The Governor of the Region asked the national Government for the proclamation of a state of emergency (https://www.protezionecivile.gov.it/it/dipartimento/amministrazione-trasparente/interventi-straordinari-e-di-emergenza, last access on 20 January 2022) . The state of emergency is the measure through which the Government deals with extraordinary events by allocating an adequate amount of money for the emergency management and teams for rescue intervention and first aid to the population. This enabled the damage self-declarations procedure carried out by citizens. As we can observe in Figure 3, the territory was completely flooded, both in the rural part of the town and in the city center. Moreover, intense activities are carried out over the flooded territories to map the flood's perimeter and take notes of the damages reported by citizens. Indeed, people Moreover, intense activities are carried out over the flooded territories to map the flood's perimeter and take notes of the damages reported by citizens. Indeed, people affected by the flood can ask for economic compensation damages to private houses, public goods, and economic activities by filling in forms collected in the aftermath of the flood, which are then processed and stored by the region [22].
In the specific case under investigation, information regarding the flood extension and local water elevation was quickly collected by different actors in the aftermath of the event. All available data have been integrated with further investigations to obtain the detailed flood mapping necessary to run the zero-order damage model. Moreover, citizens' claims for damage refunds were made available by the Emilia-Romagna Regional Authority. Table 1 shows the number of available data, including both damages to primary dwellings and holiday houses. It is worth noting that they refer only to damages produced by the levee breach. Other minor damages, mainly due to stagnation, were observed in the town of Modena but are not treated in this paper.

Model
The "zero-order" damage model is a regression model in the form where D is the total damage to residential buildings in the area under investigation, in currency units, F a is the residential flooded area footprint (m 2 ), s a "specific damage" parameter denoting the damage (also in currency units) corresponding to the unit surface of buildings, and m an exponent of the power-law 9, derived by the regression analysis. It can be observed that the model allows estimating damage to residential buildings with just a few pieces of information: the only variable requested for damage calculation is indeed the residential flooded area F a , which can be obtained by combining national statistical data once the total flooded surface envelope S 0 is known. "Zero-order" means indeed that the model does not account for the flood water elevation. The dependence of damage on the surface has been proven to be meaningful in many applications [27]. Height is also important but is here neglected in the top-down approach, which needs to be applied within a time window where this piece of information cannot be available. The model was initially calibrated and validated on a set of 3729 citizens' claims collected after 8 different national emergency states in Southern Italy. Given that significant differences exist between the physical and the socio-economic context of the area under investigation and South Italy [28], the implementation of the model required a new calibration for its application over the case study.
This new application allows us to underline some points on the definition of a homogenous area concept: in fact, here we introduce a new dataset for calibration and validation that, even though it is in Italy, refers to a completely different context. It is important to understand how a homogeneous area can be identified to properly apply the model. How the socio-economic variables, together with the morphologic ones, affect the equation's parameters is still under investigation and will be the topic of the next work.

Calibration Area
The calibration area was defined looking for homogeneity for two factors: the first concerns the morphologic context where the flood occurs, the second deals with the social and economic fabric of the flooded areas. For example, we might consider a lowland environment, characterized by large extensions of flooded areas, relatively low water velocity values, and high residence times; alternatively, we could be facing a more typically mountainous environment, with narrower valleys, high slopes, high flow speeds, high potential momentum exchange with exposed assets, and typically shorter residence times. Regarding social and economic texture, we need to consider, for example, that agricultural zones with a dispersed urban texture are quite different from a typical urban environment with high population, and commercial and infrastructural density [29]. Indeed, the specific damage parameter s accounts for all these aspects, and its rating strongly depends on the spatial scale at which the calibration is performed.
The case study covers a small portion of the Po Valley, which can be considered typical of the physical and socio-economic context of the whole Po-Venetian plain region. The model was then calibrated and validated at the scale of the whole plain.
The Po-Venetian plain is the most extensive floodplain in Italy, covering an area of 42,000 km 2 within the Po River watershed. The Po is the longest Italian river with a length of over 650 km; its watershed is 75,000 km 2 and covers most of Northern Italy [30]. In the national framework, it represents the highest concentration of inhabitants and economic activities. The plain covers just one-eighth of the national territory and hosts nearly 15 million inhabitants, equal to over a quarter of the Italian population. The demographic density, 355 inhabitants per square kilometers, is almost double the national average. Though agriculture remains a strategic asset in the territory, the importance of economic activities emerges even more clearly as we consider on the national scale that 40% of employees in industry and 33% of employees in the tertiary sector work in this area [31]. Municipalities in the plain settle mostly at low elevations and in a quite similar morphological context. The built environment [32] follows main road infrastructures and river lines as a nearly continuous sequence, as easily seen in any satellite image of Northern Italy taken at night. The Po Valley, as a whole, is also typically a specific flood-prone area protected by hundreds of kilometers of embankment lines [33]. Disastrous floods mainly occur as a result of the overtopping of the embankments [34] due to breaches caused, e.g., by the action of burrowing animals [35] or seepage and piping problems [36]. Together with the analysis of long records of floods on the Po River [37], these considerations support the assumption that the flood type as damage forcing agent is reasonably uniform on the Po-Venetian plain.

Calibration Data
Damage data are not always made available by regional authorities for research purposes. For this work, we obtained data related to 21 floods that occurred in the latest years in the Po-Venetian area.
Damage claims are available for 406 municipalities that were strongly damaged by some past flood events [22]. Of these municipalities, around 60% show an average altitude of less than 350 m a.s.l. We limited the calibration and validation dataset to this subset to be sure to deal with a typical plain environment, such as the one characterizing the case study area. Moreover, municipalities with a few claims (1-2 units) have been excluded as they are less meaningful for the model calibration. The final dataset is then composed of data from 187 municipalities, shown in Figure 4, located in the regions Emilia-Romagna, Lombardia, and Veneto, and corresponding to 7907 single damage claims (i.e., damage to an individual residential building), collected after the declaration of 11 national states of emergency. The total dataset has been divided into two datasets to calibrate and validate the model with a random choice: actually, damage data collected in the same region were used in part for the calibration, in part for the validation phase. In particular, 113 municipalities have been considered for model calibration (corresponding to 4453 damage claims), while 74 municipalities for validation (3454 claims).

Definition of the Residential Flooded area
As already discussed, the only variable requested by the model for damage assessment is the residential flooded area 9 m 2 ). This variable is an indicator of the overall building footprint surface within the event flooded perimeter and can be obtained from national statistical data once the total flooded surface envelope is known. Indeed, the Italian National Statistics Institute (ISTAT) (http://dati.istat.it/, last access on 20 January 2022) provides different data about the housing stock such as surface, number of floors, construction typology, materials, etc. Such data are aggregated at the resolution of the

Definition of the Residential Flooded Area
As already discussed, the only variable requested by the model for damage assessment is the residential flooded area F a 9 m 2 ). This variable is an indicator of the overall building footprint surface within the event flooded perimeter and can be obtained from national statistical data once the total flooded surface envelope S 0 is known. Indeed, the Italian National Statistics Institute (ISTAT) (http://dati.istat.it/, last access on 20 January 2022) provides different data about the housing stock such as surface, number of floors, construction typology, materials, etc. Such data are aggregated at the resolution of the "census areas", polygons from an irregular adaptative mesh covering the whole country (for a total of 402,678 census areas), with an average size of 0.8 km 2 . The dimension decreases with the increase in the complexity of the urban texture [38]. In an urban environment, the size of a census area can reach that of a single block. Census data were published every ten years after the general national census in 1991, and in this paper, we stick to data published in 2011 since they are the most recent available, and the most suitable to deal with events that occurred after 2013. Indeed, the national statistical system is currently transitioning towards a new "permanent" model with the resolution of the data at the scale of a single building, but data are not available yet. The use of building census data in natural risk reduction policies is not new. For example, it is used for seismic vulnerability distribution assessment at the national scale [39]. We then cropped the census areas mesh (available in the ISTAT national geodatabase) with the total flooded surface S 0 , thus obtaining an estimate of F a by simple GIS operations.
The total flooded area S 0 was derived by combining several pieces of information. First, we analyzed satellite data. In the aftermath of major floods, delineation of flooded areas is usually performed by multispectral satellite data, SAR (Synthetic Aperture Radar) images, or a combination of both [40]. In our case, the Italian Civil Protection is an authorized user of the Copernicus Emergency Management Service Mapping (CEMS) [23], whose Rapid Mapping service provides on demand a pre-event [41] and three post-event maps of the affected area, for emergencies arising from natural or anthropogenic disasters anywhere in the world. The service was activated 9 h after the breach had started with the following tag of the Emergency Management Service, Rapid Mapping activation: "EMSR487: Flood in Emilia-Romagna Region, Italy" ( Figure 5). https://www.protezionecivile.it/it/dipartimento/amministrazione-trasparente/interventistraordinari-e-di-emergenza/emergenze-il-rischio-meteo-idro, last access on 20 January 2022). Many of these cases involved multiple flood events. From these data, it is clear that activations only take place on major events for which strategic support is required for the emergency and rescue organization. These conditions are not always the case. On the other hand, damage due to hydrogeological emergencies is increasing due to climate change [42], and it is crucial to be able to systematically have a rapid estimate of the damage to understand the intensity of the impact, starting with the assessment of flooded area boundaries. It should also be remembered that satellite assessments, however accurate, involve approximations due to the delay with which the satellite visits the disaster site, compared to the actual event time. CEMS largely corrects these aspects by integrating more surveys, even from the ground. The fact remains that it is convenient to have a flexible and timely parallel procedure, suitable for localized events and with low residence times, available even in the case of the non-activation of CEMS. For this reason, the Italian National Fire Corp has developed a rapid assessment procedure of flooded areas. The widespread diffusion of the Corps assets throughout the territory allows immediate activation due to the direct and trusting attitude citizens naturally have with the Fire Brigade in any calamity. The Fire Corps, using a geographic information system (GIS), creates, manages, and analyzes data related to floods, integrating location data (where things are) with all types of In Italy, during 2020, there were 5 CEMS activations due to floods. In the same period, 12 national emergency states were declared by the Government in Italy due to meteorological and hydrological factors (Data from the government site https://www.protezionecivile. it/it/dipartimento/amministrazione-trasparente/interventi-straordinari-e-di-emergenza/ emergenze-il-rischio-meteo-idro, last access on 20 January 2022). Many of these cases involved multiple flood events. From these data, it is clear that activations only take place on major events for which strategic support is required for the emergency and rescue organization. These conditions are not always the case. On the other hand, damage due to hydrogeological emergencies is increasing due to climate change [42], and it is crucial to be able to systematically have a rapid estimate of the damage to understand the intensity of the impact, starting with the assessment of flooded area boundaries.
It should also be remembered that satellite assessments, however accurate, involve approximations due to the delay with which the satellite visits the disaster site, compared to the actual event time. CEMS largely corrects these aspects by integrating more surveys, even from the ground. The fact remains that it is convenient to have a flexible and timely parallel procedure, suitable for localized events and with low residence times, available even in the case of the non-activation of CEMS. For this reason, the Italian National Fire Corp has developed a rapid assessment procedure of flooded areas. The widespread diffusion of the Corps assets throughout the territory allows immediate activation due to the direct and trusting attitude citizens naturally have with the Fire Brigade in any calamity. The Fire Corps, using a geographic information system (GIS), creates, manages, and analyzes data related to floods, integrating location data (where things are) with all types of descriptive information (water depth, building damages, search and rescue operations, etc.). This provides a foundation for mapping and analysis to understand flood patterns, citizens' needs, and future planning. The benefits include improved communication and efficiency as well as better management and decision making. The report of substantial flooding of the territory also triggers the take-off of an all-weather helicopter that moves to the disaster site. Once the edge of the flooded area is reached, the helicopter follows its entire length. A GPS device records the track, which is immediately made available via radio. This procedure can be repeated several times during the same event, also providing indications of the dynamics of the flood.
A further class of data reinforces this assessment. Every intervention that the fire brigade teams carry out on the territory is georeferenced with a GPS point. During a flood, the calls are generally many dozen; they counted 640 interventions in three days in this specific case. This punctual information can provide some advice on the intensity of the event and confirm the quality of the assessment. Examples of the raw data directly from GPS tracks and the final result after data processing are respectively reported in Figures 5 and 6.  Once the flooded area has been delimited, after a comparison among Copernicus data, Fire Corps mapping, and local verification, we can assess the total flooded buildings' footprint area by elaborating on statistical data referring to the census areas included in . In detail, for the analysis, we refer to three census variables that are (m 2 ), the Once the flooded area S 0 has been delimited, after a comparison among Copernicus data, Fire Corps mapping, and local verification, we can assess the total flooded buildings' footprint area F a by elaborating on statistical data referring to the census areas included in S 0 . In detail, for the analysis, we refer to three census variables that are S r (m 2 ), the surface area of dwellings occupied by at least one resident person, N b (-), the number of residential buildings occupied by at least one resident person, and the group of variables R i (-), the number of dwellings with i-storeys.
For each census area included in the flooded perimeter, we evaluated the total surface S s (m 2 ). The average surface of a floor M f s (m 2 ) was then evaluated (for every census area) as the ratio between the surface area of dwellings occupied by at least one resident person S r and the total number of floors.
where n is the maximum number of floors. We thus obtained the total footprint area A r (m 2 ) of residential buildings in each section by multiplying the average surface by the total number of dwellings N b (-). By assuming that each building has just one flooded floor, i.e., the maximum water level on the ground less than 2.50-3.00 m, A r is actually an estimation of F a .
For the section only partially included in the flooded area, we estimated the surface of the flooded building F a proportionally for the partially flooded surface F s .

Model Calibration on the Po-Venetian Floodplain HA
As previously explained, the "zero-order" damage model has been calibrated and validated on two different randomly generated damage datasets chosen in the homogeneous area (HA) of the Po-Venetian floodplain. The damage is then expressed by the formula We show the results of the calibration/validation process in Figure 7, where each point represents a single municipality with the aggregated conventional surface F a and the related claimed damage D. The orange line represents the regression line, built on calibration data, on the log-log plane.
We note the "quasi-linear" relationship due to the power-law exponent being close to one. On the other side, the coefficient of the same power-law indicates the specific damage in the order of 110 EUR/m 2 . The correlation coefficient of the regression is R 2 = 0.70. The error distribution analysis is shown in Figure 8. We observe that half of the data stand in the +/−50% relative error range.
The same can be observed in the graph in Figure 9 where the distribution of observed versus estimated damages is shown. The green line is the best agreement and points represent the values for those municipalities considered in the validation phase. We observed during the validation that points far from the line are those with a few claims. = 110.47 . (5 We show the results of the calibration/validation process in Figure 7, where each point represents a single municipality with the aggregated conventional surface and the related claimed damage D. The orange line represents the regression line, built on calibration data, on the log-log plane. We note the "quasi-linear" relationship due to the power-law exponent being clos to one. On the other side, the coefficient of the same power-law indicates the specific dam age in the order of 110 EUR/m 2 . The correlation coefficient of the regression is = 0.70 The error distribution analysis is shown in Figure 8. We observe that half of the data stand in the +/−50% relative error range.  We note the "quasi-linear" relationship due to the power-law exponent being to one. On the other side, the coefficient of the same power-law indicates the specific age in the order of 110 EUR/m 2 . The correlation coefficient of the regression is = The error distribution analysis is shown in Figure 8. We observe that half of the data s in the +/−50% relative error range. ing to the error classes (x-axis). The red line represents the cumulative error.
The same can be observed in the graph in Figure 9 where the distribution of observed versus estimated damages is shown. The green line is the best agreement and points rep resent the values for those municipalities considered in the validation phase. We observed during the validation that points far from the line are those with a few claims.

Implementation of the Model in Emilia-Romagna December 2020 Flood
The flooded surface , at its maximum extension, was estimated around 13 km 2 by the Fire Corps assessment. Further surveys on the ground were performed later on by the municipality that confirmed the estimate. Such an area involves two municipalities Castelfranco Emilia and Nonantola. For them, we evaluated the flooded residential area (through the method previously described) and finally the expected damage with Equa tion (5).
Results in terms of the flooded area , estimated damage D, observed damage and global relative estimation errors are summarized in Table 2. It must be noted tha Castelfranco Emilia was flooded just over a single census area. The town of Nonantola instead was significantly hit by the event giving rise to a higher characteristic surface area .

Implementation of the Model in Emilia-Romagna December 2020 Flood
The flooded surface S 0 , at its maximum extension, was estimated around 13 km 2 by the Fire Corps assessment. Further surveys on the ground were performed later on by the municipality that confirmed the estimate. Such an area involves two municipalities, Castelfranco Emilia and Nonantola. For them, we evaluated the flooded residential area (through the method previously described) and finally the expected damage with Equation (5).
Results in terms of the flooded area F a , estimated damage D, observed damage D 0 and global relative estimation errors are summarized in Table 2. It must be noted that Castelfranco Emilia was flooded just over a single census area. The town of Nonantola instead was significantly hit by the event giving rise to a higher characteristic surface area F a .

Comparison between HA
The first level of reasoning must be devoted to comparing the models derived for the Po-Venetian plan and for the South of Italy that, as previously discussed, can be considered homogeneous areas for flood damage model estimation.
The Po-Venetian plain covers 64,662 km 2 , while the HA considered in the previous work deals with 84,339 km 2 . These areas are the mosaics of respectively 3 and 5 regions for which more than one national state of emergency has been declared for flood events in the last decade in several municipalities. Although the surface areas of the two HA are substantially close to each other (21.5% and 28.0% of the entire national territory), the two samples are different regarding climatic, demographic, social, and economic characteristics. In essence, all the elements that lead to the production of flood damage are inherently different.
We compare the two case study areas' climates, to underline that the features of the two territories, even though they are in the same country, are completely different. The comparison is carried out by following the usual scheme proposed by W. Köppen [43], adding a few brief notes on the rainfall and temperature regime [44]. As far as the Po-Venetian plain is concerned, we can observe both "sub-continental temperate" and mainly the "continental temperate" "Cf" types. The mean annual temperature ranges between 9.5 • C and 25 • C. The rainfall trend presents a remarkable variability in Italy [45]. The precipitation regime in the HA shows two maximum rain periods in spring and autumn and two minimum periods in summer and winter. Generally, the autumn maximum is prevalent, and severe flood events usually occur in this period [46].
In the Southern Italy HA, we observe a "subtropical temperate" (Cs) in the Ionic, Mediterranean, and Sicily Island coastal strip, marked by quite limited and very irregular rainfall. The mean annual temperature is higher than 17 • C. On the Tyrrhenian side down to Calabria and Apulia, we find the "hot temperate" type, usually characterized by summer droughts (Csa). The mean annual temperature ranges from 14.5 to 16.9 • C. Mainly, the Mediterranean precipitation regime is typical of nearly the whole of Southern Italy, which presents a maximum winter rainfall and a minimum summer rainfall: it affects Sicily, Calabria, and parts of Apulia. Rainfall is more abundant along the Tyrrhenian side, which is open to the west's perturbations, rather than on the Adriatic-Ionian coast. Over the whole of the Southern Italy HA, heavy convective thunderstorms often induce flooding, one of the natural disasters most responsible for damage to the built environment, infrastructures, and loss of lives [47].
The difference between the two HAs under demographic, social, and economic characters is summarized in Table 3: the duality of the Italian macro regions under different points of view is clear, starting, for example, from the productivity per capita values [28]. All data are derived by the National Institute of Statistics data warehouse [48]. Since the analyses are conducted on recent events (in fact, the damage self-declaration's collection in Italy has started with uniform national criteria only in 2013), we here refer to 2011 census data. However, it is also worth noticing that the built environment is developing slowly in Italy, and the built heritage is mainly old [49]. We can observe how the two areas are in fact pretty different from both climatic and demographic points of view.  Figure 10 compares the empirical curves derived by the model calibration for the two case studies. The power-law parameters are presented in the following Table 4. It is worth observing that the exponent deriving from the power-law regression is the same, m = 0.96, for the two case studies. The degree of data dispersion is also absolutely comparable. We can deduce that the quasi-linearity hypothesized for the model between the characteristic surface and the damage constitutes a reasonably robust assumption, independent of the territorial context considered.

Po-Venetian Plain
Southern Italy Exponent (-) 0.96 0.96 Coefficient (EUR/m 2 ) 110.47 532.14 The same calibration process leads to a specific damage estimate for the Po-Venetian floodplain, nearly equal to one-fifth of that obtained for Southern Italian regions. The following considerations can explain this fact. In Northern Italy, multi-story buildings are much more diffuse than single-floor houses. ISTAT data are reported in Figure 11. We observe how one-story buildings are around 9% of the total in the Po-Venetian plain and nearly 30% in the Southern Italy region. This fact, for a given flood event, is assumed to increase the intensity of the damage.  The same calibration process leads to a specific damage estimate for the Po-Venetian floodplain, nearly equal to one-fifth of that obtained for Southern Italian regions. The following considerations can explain this fact.
In Northern Italy, multi-story buildings are much more diffuse than single-floor houses. ISTAT data are reported in Figure 11. We observe how one-story buildings are around 9% of the total in the Po-Venetian plain and nearly 30% in the Southern Italy region. This fact, for a given flood event, is assumed to increase the intensity of the damage.
Water 2022, 14, x FOR PEER REVIEW 14 of 19 Figure 11. Characteristics of buildings for Po-Venetian floodplain and Southern Italy, obtained from the ISTAT data [31], reworked by the authors.
A first screening has been performed for both HAs' calibrations to consider just direct inundation from floodplain events. However, the characteristics of flood processes are pretty different in the two HAs. Po-Venetian plain flood processes are typical of extensive plain contexts, with inundation processes very different from those of the Southern Italy Figure 11. Characteristics of buildings for Po-Venetian floodplain and Southern Italy, obtained from the ISTAT data [31], reworked by the authors.
A first screening has been performed for both HAs' calibrations to consider just direct inundation from floodplain events. However, the characteristics of flood processes are pretty different in the two HAs. Po-Venetian plain flood processes are typical of extensive plain contexts, with inundation processes very different from those of the Southern Italy basins' typical Apennine and coastal environment valleys. Coastal convective thunderstorms determine most floods in Southern Italy. As noticed before, Mediterranean coastal regions are frequently affected by heavy precipitation events that produce flash floods and landslides [50]. As well as convective rainfall events, most flood processes in the Po-Venetian plain are connected to mesoscale stratiform precipitation patterns, especially relevant for flooding when associated with orographic forcing [51]. This peculiarity, together with the typically flat Padanian landscape, gives rise to different damage-generating phenomena.
A further observation stands in the social vulnerability to natural hazards in Italy [52,53]. There is a significant gap between vulnerability in the North of Italy, which is significantly lower than in the South. Although the gap decreases in time [54], the difference remains unfortunately high, enough to explain at least a part of the corresponding gap in specific damage.

Discussion of the Results
The validated model has been applied to the two municipalities most affected by the flood, Nonantola, and Castelfranco Emilia, both located in the region Emilia-Romagna in the province of Modena. The main characteristics of the two municipalities are reported in Table 5. The surface of Castelfranco Emilia is almost twice the area of Nonantola, and the same can be said for the number of inhabitants. For this reason, the number of residential buildings is higher in the larger municipality, even though the degree of urbanization is lower. Indeed, Nonantola is a small town with suburbs, while Castelfranco Emilia as a whole, can be seen as a rural area. The entire surface of the two municipalities is included in the delimitation of the medium flood hazard zone identified within the context of the Flood Directive, corresponding to return periods between 500 (low hazard) and 200 years (medium hazard). The "high hazard" zone (20-50 years return period) is instead limited to 8% of the municipality area in Castelfranco and 15% in Nonantola. In the specific case study, inundation was due to a levee failure during a lower return period rainfall event even though the ground effects were coherent with the hazard level considered in the mapping.
From the map of Figure 12, we observe that the municipal territory of Castelfranco Emilia was flooded just for a small portion of the total area. Moreover, residential buildings in the flooded area were few and dispersed, and the flood-invested area was mainly crops. From Table 2, we can observe that the model underestimates the observed damage with a relatively high error. Actually, the observed damage is made by the sum of only 16 damage claims, two orders of magnitude less than those of Nonantola, thus decreasing the reliability of the model estimation.
to 8% of the municipality area in Castelfranco and 15% in Nonantola. In the specific case study, inundation was due to a levee failure during a lower return period rainfall event even though the ground effects were coherent with the hazard level considered in the mapping.
From the map of Figure 12, we observe that the municipal territory of Castelfranco Emilia was flooded just for a small portion of the total area. Moreover, residential buildings in the flooded area were few and dispersed, and the flood-invested area was mainly crops. From Table 2, we can observe that the model underestimates the observed damage with a relatively high error. Actually, the observed damage is made by the sum of only 16 damage claims, two orders of magnitude less than those of Nonantola, thus decreasing the reliability of the model estimation. The town of Nonantola and its urban settlement were strongly damaged. The model estimation is much more significant in claims availability, leading to a lower estimation error. In Figure 13, we show the difference between the observed and the estimated values, and the comparison with the calibration dataset. The town of Nonantola and its urban settlement were strongly damaged. The model estimation is much more significant in claims availability, leading to a lower estimation error. In Figure 13, we show the difference between the observed and the estimated values, and the comparison with the calibration dataset. As in our previous work on South Italy, we can observe that the order of magnitude is the same between the observed and estimated damage (at least for the most significant case), which, even though it may seem to be a rather rough estimate, is in line with results obtained by more sophisticated damage models, which required a level of analysis and an amount of time unsuitable for application in the flood's aftermath [25]. This is undoubtedly an encouraging result that further corroborates our intention to implement the model as a quick tool to obtain a first-order estimation of damages. As in our previous work on South Italy, we can observe that the order of magnitude is the same between the observed and estimated damage (at least for the most significant case), which, even though it may seem to be a rather rough estimate, is in line with results obtained by more sophisticated damage models, which required a level of analysis and an amount of time unsuitable for application in the flood's aftermath [25]. This is undoubtedly an encouraging result that further corroborates our intention to implement the model as a quick tool to obtain a first-order estimation of damages.

Conclusions
We have presented here a procedure for a quick estimate of the damage in the aftermath of a flood event. Private asset damage is considered, while that related to productive activities will be treated in a forthcoming paper. We have discussed the whole assessment cycle, starting from outlining the inundated area down to the economic estimate of the loss. The quick assessment of the flooded area boundaries is performed by low-altitude GPS surveys performed by all-weather capability helicopters. This kind of survey is a standard practice of the Italian National Fire Corps in any significant flood event. GPS tracks once processed and analysed, allow a detailed reconstruction of the flooded perimeter. Sometimes multiple surveys are performed, leading to a view on the inundation process dynamics. This kind of data, integrated into the zero-order flood damage model, allows a near real-time estimation of damages. Such information can contribute, among other things, to addressing the immediate post-emergency management operations and helps policymakers to correctly and promptly allocate financial resources. In the chaos of the postevent, the priorities are to recover the injured, take care of the displaced, and re-establish essential services. There is no time (and frequently no way) for a detailed field damage survey. Even though the methodology may appear quite rough, the results, considering the aims of the model, seem to be promising. However, a direct comparison between the zero-order and the traditional damage curve approach could be interesting and will be carried out in the future.
The "zero-order" method was introduced in a previous paper with a successful application in Southern Italy. With the present work, the model is implemented on the Po-Venetian plain area, which covers more than 20% of the Italian territory and presents completely different characteristics from climate, morphologic, demographic, social, and economic points of view. Comparing the two case studies confirms that the "zero-order" approach can lead to the first estimate of damages, at least in the order of magnitude. The results are obtained by calibrating a single parameter, given by the specific damage per unit flooded area. In particular, the paper shows how a single calibration can account for estimates on areas of the order of thousands of square kilometers. The calibration process requires a previous detailed analysis at the regional scale to obtain homogeneous areas that can be treated as a unique environment for quick damage estimation.  Data Availability Statement: Dataset related to this article was kindly provided by Regional Authorities, the Fire Corps, and the National Civil Protection Department, and are available with their permission.