The study was carried out using a computational modelling tool to support hydrological and hydrodynamics simulation scenarios, intending to give basic information about flood consequences over the urban systems. The result of the modelling process characterises the flood events, based on a design storm with a 25-year return period (RP). This RP was adopted due to the official Brazilian government requirements for flood control design. Departing from flood characterisation, and joining the socioeconomic information (obtained from the available census-2010), the UFRI can be built and used in the methodological framework proposed in this work. The detailed steps of this framework are described in the following sections.
2.2. Urban Flood Resilience Index—UFRI
To support the discussion about residual risk and compose the methodology proposed here, an index is developed to aid the planning and design of urban drainage solutions, adopting a methodology that departs from the basic concepts of risk management and evolves to consolidate a Resilience Index. At this point, it is important to highlight the understanding of resilience adopted in this study, broadly discussed in the introduction section.
The UFRI proposition makes it possible to build resilience maps and, consequently, to work to reduce risk consequences over time, especially regarding avoided losses. It is based on the index presented as S-FResI in Bertilsson et al. [
52], and was expanded in this work. The UFRI combines three sub-indexes, representing the three properties of resilience cited by Proag [
57]:
- (i)
absorptive capacity—the ability of the system to absorb the disruptive event, represented by the Sub-index of Risk to Resistance Capacity ().
- (ii)
adaptive capacity—the ability to adapt to the event, represented by the Sub-index of Risk to System Functional Capacity ().
- (iii)
restorative capacity—the ability of the system to recover, represented by the Sub-index of Risk to Material Recovery Capacity ().
Each sub-index considers hazard-related indicators, covering maximum flood depths, water flow velocities and flood permanence times, combined with related vulnerability indicators. The calculation of UFRI uses Equation (1); the hierarchical arrangement of the indicators and sub-indexes that compose the UFRI is shown in
Figure 3. The complete composition of the index is shown in
Figure 4. Each of the indicator formulations is presented below.
Parameters a, b and c are the weights associated with each sub-index. In the present study, the weighting process assumes equal values for all of them, since it is not the aim of this study to state the relative importance of each term in the resilience composition. In fact, defining this relative importance is something that may vary from case to case, and which should be a prerogative of decision makers.
2.2.1. Sub-Index of Risk to Resistance Capacity ()
The
represents resistance to damage, according to the degree of exposure of the population and the existing assets in the basin, i.e., the exposure of buildings and urban infrastructure to the potential damages of a given flood. Three indicators are used in its formulation: (i) the building exposure indicator; (ii) the urban infrastructure exposure; and (iii) the flood depth indicator. This sub-index is calculated using Equation (2).
—building exposure indicator.
The building exposure indirectly indicates the exposure of people. It is represented by built density area (
BD), in m²/ha. The higher the density, the more vertical the buildings, indicating a greater occupation, either residential or commercial. The values are normalised in a range between 0 and 1, with the highest exposure value (equal to 1) being attributed from the third quartile of built density distribution in the basin (and upwards), in order to avoid non-representative values of isolated high densities, which could distort the scale. This method was applied to the Canal do Mangue catchment, used as a case study, resulting in Equation (3).
—urban infrastructure exposure indicator.
This indicator represents an indirect measure of urban infrastructure exposure by road density (
RD), in m/ha. The greater the density of roads in a region, the greater the tendency for coverage of infrastructure services such as water supply, sanitation, public lighting, cable services, etc. The normalisation of the indicator was done similarly to
, with the highest exposure value being attributed to the third quartile of the sample and above. Values also vary between 0 and 1. The construction of the
to the Canal do Mangue catchment resulted in Equation (4).
—flood depth indicator.
This indicator computes the potential damage of the considered flood event, representing the potential hazard. The maximum flood depth
gives the value of the indicator, that is, depending on the maximum depths and the expected damages caused by these depths, a normalised value between 0 and 1 is attributed to the indicator through an exponential function. Thus, the greater the depth of flooding, the greater the potential damage to structures, goods and people exposed. A water depth of 1.30 m, which was chosen to represent very high potential damage (this would be the value that could cause integral losses inside a household), represents the highest value, while water depths bellow 0.15 m nullify the indicator. The normalised formulation can be seen in Equation (5).
2.2.2. Sub-Index of Risk to Material Recovery Capacity ()
This represents the socioeconomic part of the flood risk, through a “relative value” indicator relating the flood depth to the potential damage according to the income range of the population which is directly exposed to flood. Its formulation is presented in the form of Equation (6).
—relative value indicator.
This represents the economic recovery capacity of a region against the damages of a given flood event. The indicator is calculated using the relationship between potential economic losses and the capacity to replace these losses, represented by the difference between the total income and the average expenditure of a family. In this way,
is intended to represent a socioeconomic variable, equalised according to the relationship between the potential loss caused by the flooding event and the economic class of the exposed population, assessing not an absolute loss, but rather, the ability to recover from the damage suffered.
is given by Equation (7).
where
: Cost of damage to a building
: Cost of damage to building contents
: Total area built in the analysis unit
: Building susceptibility indicator
: Total Income of the population in the analysed region
: Average replacement capacity of the population in the analysed region
The whole formulation of this indicator can be found in Rezende et al. (2018) [
50] and is based in Salgado (1995) [
58].
—building susceptibility sub-indicator.
The indicator of the susceptibility of buildings is represented by the average height of the buildings in the analysed region. Buildings with one floor are more susceptible to flooding damages than multi-floors buildings. This indicator is used as a correction factor to the , which is based on flood depth-damage curves.
—social vulnerability indicator.
This indicator represents the portion of a region’s social vulnerability related to the percentage of people who are potentially the most vulnerable to flood events, from a physical point of view. It is related with people vulnerability to the hazard, represented by the velocity factor indicator (the product of flow velocity and water depth) and how rapid velocities can drag a person with the flow [
59].
is given by Equation (8).
where
: indicator of vulnerable persons
: indicator of non-vulnerable persons
: velocity factor indicator for vulnerable people
: velocity factor indicator for non-vulnerable people
The whole formulation of this indicator can be found in Rezende et al. (2018) [
50].
and—vulnerability of people sub-indicators.
represents the direct proportion of the population that is younger than 15 and older 60 years of age, in relation to the total population. It represents people who are more prone to flooding consequences. is the complement of the .
—velocity factor sub-indicator.
The velocity factor (VF) directly indicates the potential to drag people away during a flood event. The normalisation of
considers previous studies on the stability of people when exposed to water [
60]. Based on this study, two risk classifications of the loss of stability were developed for vulnerable and non-vulnerable groups, as shown in
Table 1.
The normalised formulations of
and
are given by Equations (9) and (10).
2.2.3. Sub-Index of Risk to System Functional Capacity ()
This represents the system’s ability to continue providing part of its services during a flood event. This subscript considers the mobility risk indicator, represented by the relationship between road hierarchy and non-attendance by rail transport with the flooding event. This sub-index indicates the impact of the flood on traffic and people. It also assesses the impact on rescue access through the analysis of flooding of fire department resources and their surroundings, indicating potential difficulties in carrying out emergency actions. The general formulation is given by Equation (11).
—aid access difficulty indicator.
This indirectly represents the difficulty of a given region to receive help from a specialised aid team. In the present study, due to ready access to data, the Fire Department of Rio de Janeiro in the Canal do Mangue catchment was used. Each facility was associated with an influence area, which can be penalised when the flood reaches the position where the Fire Department is installed. The penalisation considers the flood depth, representing the difficulty or even the impossibility of exiting the building.
—mobility risk indicator.
The mobility risk indicator represents how much the transportation system is affected by a flood event, assessing the potential impact on the traffic of cars and people mobility. For this, it uses a road hierarchy indicator and a non-compliance indicator for rail transport, relating them to a permanence factor of flooding, as a hazard indicator.
is given by Equation (12).
—road hierarchy sub-indicator.
This indicator is given by the highest route hierarchy within the analysis area, according to the values presented in
Table 2. The information of this hierarchy comes from CET-Rio, an organ of the Municipal Transport Department of Rio de Janeiro City.
—non-rail transport service sub-indicator.
This evaluates the lack of availability of subways or train stations in a radius of 1000 m and 500 m, indicating the places with the highest coverage of transport services, which would indirectly present better possibilities for mobility during flooding events.
is given by the complement of the rail system offer indicator
, ranked according to the classification presented in
Table 3.
—permanence factor sub-indicator.
is the hazard indicator relative to the permanence of flooding. This indicator indirectly assesses the stormwater network’s ability to drain floods, evaluating the time that urban areas stay flooded. It considers three classes: (i) water depths between 10 cm and 25 cm (T1); (ii) between 25 cm and 50 cm (T2); and (iii) above 50 cm (T3). Each class is normalised according to a maximum time for which the maximum impact of flooding could be reached. The definition of the maximum hazard time for each class considers the relative impact for the urban system. Thus, for class T1, areas flooded for three hours would have a high impact on the mobility of people, restricting their movements and increasing the possibility of transmission of waterborne diseases. For class T2, with floods of up to 50 cm, sidewalks are surpassed and traffic can be affected, assuming that a 60-min period of flooding is sufficient to result in a high negative impact. For class T3, a period of 30 min could have a significant impact on traffic, with total disruption, in case of floods exceeding 50 cm in depth.
is calculated by Equation (13).
Equations (14)–(16) show the normalisation of each term of the
. The weights considered in this study aimed to prioritise the impact of higher water levels, considering the following values:
a = 0.10;
b = 0.22; and
c = 0.68. These weights were originally proposed in the work of Zonensein [
49].
with,
: total duration of floods with water depths between 10 cm and 25 cm
: total duration of floods with water depths between 25 cm and 50 cm
: total duration of floods with water depths greater than 50 cm
2.3. A New Methodological Framework to Measure Urban Flood Resilience
This item presents in an organised and reproducible way for the logical sequence of the necessary procedures to apply the tools to evaluate urban flood resilience, considering the new framework proposed in this paper. It aims to provide a quick guide to facilitate the application of this methodology in other basins.
The existing tools already provide useful information for applications, for example, in mapping the results of specific sets of flood control interventions. However, a systemic overview and the proper organisation of these tools are essential to promote a systemic approach to the process of FRM. Therefore, the project should be oriented according to a risk logic, and not only “damages and losses reduction” internalising the residual risk from potential future uncertainties.
To provide a comprehensive view of the proposed framework, a flowchart of the necessary steps to assess the flood resilience in urban basins using the UFRI is presented in
Figure 5. The following steps describe the development of the resilience assessment proposed in this paper, according to the criterion of future scenarios assessment, based on the use of a flood modelling process and UFRI mapping.
1. Watershed delimitation
Once the urban system to be evaluated has been established, the river basins that contribute to the system must be physically defined.
2. Delimitation of the modelling domain
In this phase, the areas that will be considered for the detailed hydrodynamic modelling process should be delimitated. If the modelling domain does not cover the whole basin, the boundary conditions must be defined.
3. Delimitation of the interest domain
The domain of interest must cover the entire threatened urban system. This step is very important and should be done with caution, since an incorrect definition of the limits of the domain of interest can exclude strategic or vulnerable areas from the analysis, thereby distorting the results.
4. Determination of the modelling system
The application of the method proposed in this paper allows a resilience evaluation to be performed in a concentrated way for the entire basin, providing a single value of resilience for the whole system. However, the use of UFRI necessitates defining the hydrodynamic modelling tool’s needs. It should be able to simulate flooding events considering the flow occurring both in the main channels and on the urban plains, providing results of flooding in the whole urban space. For a better evaluation of the system, the use of two-dimensional or quasi-2D modelling systems is recommended.
5. Definition of the modelling scenarios
The number of modelling scenarios will depend on the number of interventions sets to be evaluated. Each scenario should represent, in current and future situations, the drainage system conditions, the urban characteristics of the basin, and the hydrological events. The intersection of these conditions determines the final scenarios to be simulated.
6. Hydrological modelling
This step aims to estimate the design storms, as well as inflows to the modelling domain, which will be used in the hydrodynamic modelling phase. The scale of evaluation, concerning critical events to the urban watershed, should define the storm events.
7. Hydrodynamic modelling
Once the modelling tool and the simulation scenarios have been set, the database for hydrodynamic modelling is created, considering the boundary conditions imposed by possible downstream restrictions and flood hydrographs from upstream reaches. This step results in the responses of the hazard-related parcels of flood events (water depths, flow velocities and flooding permanence) for each of the simulation scenarios.
8. Socioeconomic and environmental information survey
This step can be carried out soon after the definition of the watershed area (step 1) or even after the delimitation of the domain of interest (step 3), in order to reduce the amount of information to be assessed, by limiting the survey area to that which will realistically be evaluated. Commonly, several government agencies provide necessary information for this study step, such as income distribution, population and built density, land use, road hierarchy, public services coverage, etc.
9. Constitution of independent indicators
Some of the proposed indicators that compose the UFRI depend only on social, economic and/or environmental information, and do not suffer from variations in flood dynamics. Such indicators are elaborated from the mapping of the socioeconomic and environmental information in the area of interest, comprising part of the vulnerability of the region. If future scenarios include land use changes or the implementation of adaptive measures in the urban system to increase resilience to floods, these indicators may also need to be revised.
10. Constitution of the dependent indicators
Beyond the flood hazard indicators themselves, which refer to the maximum flooding depth, maximum flow velocity and flooding permanence, there is also a series of socioeconomic indicators that vary according to the flooding response. Thus, these flood-dependent indicators, representing both the hazards and the associated vulnerability, are composed after running the simulation scenarios, which will provide the information necessary to complement the calculations.
11. Calculation of flood risk sub-indexes
After the construction of all the independent and dependent indicators, it is possible to calculate the subindexes of flood risk, which are divided into the three groups that relate to the resilience of a system: (i) capacity to resist; (ii) ability to recover; and (iii) ability to maintain operations, that is, the ability to remain functional.
12. Mapping the urban flood resilience index
From the flood risk sub-indexes, the Urban Flood Resilience Index can be mapped in the domain of interest for each simulation scenario, considering the return period of the storm and the conditions of the drainage system and the urban patterns. In this step, the partial UFRI maps, which represent resilience to floods, are drawn from a static point of view, as a direct response to a given set of hydrological events.
13. Evaluation of the urban resilience
Flood resilience must assume a multi-temporal characteristic, in which the response of the urban system involves the occurrence of several possible events, internalising the residual risk to the risk evaluation and management process, either by incorporating future scenarios with changes in the variables of hazard or vulnerability, or by the evaluation of hydrological events superior to the design storm. In this paper, one evaluation method is addressed, named here future scenarios criterion. In this evaluation approach, the occurrence of an intense hydrological event (with a pre-defined return period) in an adverse future scenario is considered, comparing the consequent UFRI results with the current scenario. From the mapping of the UFRI in each scenario (current and future) for the reference events, the average values of the UFRI in the urban system are calculated. The average UFRI results for each scenario are embedded in a resilience scale calculus, which will provide a numerical value to support the evaluation of the performance of urban interventions for flood mitigation, considering potential future stresses to the system. The next item provides more details about this proposed method.
2.4. Future Scenarios Criterion
Male [
61] defines resilient infrastructures as “those systems of assets that will be able to survive and perform well in an increasingly uncertain future”. Considering this statement, the methodology proposed by Miguez & Vérol [
28], which considers the analysis of future scenarios, is applied to assess the resilience of urban drainage systems to floods. In this method, the flood resilience of a basin is measured on a scale that evaluates the efficiency of a set of urban interventions to mitigate floods and the associated loss of efficiency when facing a future scenario of changes in land use patterns or climate conditions, based on the decrease of flood risk protection. To complete this analysis, the future risk of doing nothing is also estimated and compared with the behaviour of a set of future interventions. The method is better explained on the following.
In addition to the probability of occurrence of events of greater magnitude than that of the design event, when the actions to reduce flood risks are defined, there are uncertainties regarding the potential disturbance in the current hydrological patterns related to the climate change. Most studies comprising future assessments of the urban system operations consider the impacts of climate change using the
Representative Concentration Pathway RCP-4.5 scenario, which represents a medium impact scenario, with a temperature increase between 0.9 and 2.0 °C for the year of 2040 [
62]. When considering the end of the century, this increase may reach up to 6 °C [
63].
Considering that the variation found in precipitation rates has an approximately linear behaviour in relation to the atmospheric temperature variation [
64], estimates of the possible impacts of global climate change on intense rainfall regimes indicate a probability of increases of between 8% and 24% in precipitation volume.
In the case of coastal cities, there are also predictions of changes in mean sea levels (MSL), which could have significant impacts on the drainage systems of these regions. Global projections estimate potential increases of MSL of between 0.26 m and 0.55 m by the year 2100 in an optimistic scenario, and of between 0.45 m and 0.82 m in a more pessimistic one [
65]. For Brazil, it is estimated that the MSL could behave similarly to these estimates [
66], with a minimum increase of about 0.50 m [
67]. Such changes will stress the operations of drainage networks based on the current criteria of hydrological and hydraulic standards, which do not consider the potential impacts of climate change.
The method to estimate flood resilience (FResI) proposed by Miguez [
28] is here adapted for use with the UFRI as input, allowing assessments to be made of urban flood resilience considering the capacity to absorb potential future impacts. The original formulation used the FRI, that computes flood characteristics and possible consequences, using flood depths, flow velocities, flooding duration, affected dwellings, income, sanitation conditions and road hierarchies. The original FResI calculated a mean value of resilience to the entire watershed, comparing the variation of a
flood risk index over time, assuming one current and one future condition [
28], and considering that resilience was greater as the risk was lower—resilience was considered to work against risk materialisation.
The aFResI proposed in this paper is given directly by the resilience index and not with the application of a flood risk index, as proposed in the original paper. The adapted method uses the same mathematical construction, but it has incorporated a weight system to the two parcels that compose the aFResI,
the loss of efficiency of the solution in a future situation (P1) and
the efficiency of the solution in the future situation (P2), presented in the form of Equation (17).
aFResI = adapted resilience index, with values between 0 e 1
P1 = parcel 1, which measures the loss of efficiency of the solution proposed in a future situation when compared to the present.
P2 = parcel 2, which measures the efficiency of the solution in the future situation, relating the behaviour of the system with and without the proposed set of measures in the future, subjected to the stressing conditions considered.
e = parcels weights
The parcel 1 (P1) is calculated by the subtraction of value 1 (100% of efficiency maintained) from the project UFRI in the present situation minus the project UFRI in the future situation divided by project UFRI in the present situation. Equation (18) presents the components of P1.
Parcel 2 (P2) represents UFRI considering a future with the implementation of the proposed project compared with doing nothing. It is calculated by the relationship between UFRI with project minus UFRI for doing nothing (no actions), both in the future situation, divided by UFRI with the project implementation in the future situation. P2 is calculated by Equation (19).
The future scenario examined in this study considers a medium impact scenario of climate change, with an increase of 0.50m on MSL and a 16% increment in precipitation intensity.
2.6. Simulation Scenarios
The use of simulation scenarios can provide useful responses to basin to pre-defined storm events, considering possible alternatives to flood risk control by introducing interventions in the drainage system or by adapting urban configuration.
In this way, the present research considers the hypothesis that an urban system supported by smaller stormwater detention measures, distributed on the watershed, could offer greater resilience to flooding than that presented by systems with large and concentrated flood control structures. The evaluation of this hypothesis was carried out with the use of the proposed method and the simulation of one baseline situation and two project alternatives, with both being supported by mathematical modelling. The proposed method aims to support decision-making process, providing a tool to evaluate and compare multiple design approaches and different sets of interventions. Therefore, the proposed index was constructed to incorporate not only drainage system aspects, but also socioeconomic variables. This characteristic allows evaluations to be carried out of both interventions directly in the drainage network (flood control measures) and adaptation strategies to the urban environment, attempting to identify for vulnerability reductions.
In this paper, due to the case study comprises an already highly urbanised area, only flood control measures were considered in FSC application. This is therefore not a limitation of the proposal. Data availability, characteristics of the study area and modeller decisions will define the analysis aspect. The case study is used as an example to confirm the usability of the tool and the proposed framework. Therefore, the proposed scenarios aim to analyse the response of the drainage system to hydrological events simulating present and future conditions, considering the “doing nothing” alternative and two different design alternatives to the drainage system: C0—without interventions; C1—with concentrated interventions; C2—with distributed interventions.
The first condition without interventions (C0) aims to provide a baseline, allowing later comparisons with the project alternatives. It considers the hydraulic conditions of the urban drainage system without any measures being taken.
Then, the mathematical model is adapted to introduce large stormwater detention tanks (C1) to store part of the discharge of the main channels, reducing the peak flow. This alternative aims to reduce the hydraulic overload in some channel reaches with low flow capacity.
Finally, the model is adapted to introduce smaller detention structures (C2), which are distributed throughout the basin. These structures are located at the bottom of hillsides and on urban occupied plains, prioritising public spaces such as squares, gardens and parking lots, integrating drainage solutions into the urban open space system.
The evaluation of a more distributed set of interventions assumes a global tendency of urban stormwater management which tries to deal with flood events in a more sustainable way. As concluded by Zhang et al. [
48], “the combination of conventional and decentralised stormwater management systems, which not only protect environmental quality but also promote water and energy savings, will prove to be the most practical solution for most cities in the future”. Therefore, the case study contributes to reinforcing the advantages of adopting distributed measures to face stormwater issues.
The simulation scenarios include a combination of hydrological events with urban system conditions. The hydrological scenarios can represent probabilities of occurrence (return periods) or future changes in climate behaviour. The urban system conditions can represent land uses and adaptations measures in drainage networks.
A climate scenario with MSL elevation and an increase in the rainfall volume reproduces the potential adversity in the Future Scenarios Criterion (FSC), which was applied in this study. This configuration aims to test the behaviour of the drainage system with the two proposed alternatives of intervention in a possible scenario of climate change. Note that this choice reflects a possible future stressing factor to the watershed, considering that it already presents dense occupation and problems related with unplanned land use and uncontrolled urban growth, including the presence of slums in the hilly areas.
The application of the FSC for the analysis of the urban flood resilience in this study considers the rainfall event with a 25-year RP, regarding the Brazilian national standards used for major drainage network assessments [
70]. This configuration produces six simulation scenarios, as shown in
Figure 7.