**1. Introduction**

Floods are increasingly occurring around the world, and for some authors such as [1–3], climate change is one of the most important causes for them since it affects directly and indirectly the river network. Although the contribution of climate change is undeniable, also there is the human contribution to increase the frequency of floods. According to [4], human contribution includes its settlement in risk flooded zones, and, as consequence, cities with highly developed infrastructure and commodities could generate instability in the fluvial system due to the implementation of morphological adjustments in order to protect agriculture or cities on or around the floodplain [5, 6]. The different flood levels of damage along the

river are established according to the degree of the development of the region. A high-income region is more affected than a low-income region in terms of economic losses. However, low-income regions increase flood hazards since they have a poorly planned and managed infrastructure; thus, there is a growing population in a no suitable land such as floodplains and coastal and depressed inland areas, and economical losses are less than life losses [7]. When high- and low-income settlements are established in risk zones, some actions had been executed such as protective measurements as bank protection against migration, land protection constructing dam and levee systems and dredging [8]. However, these protective measures also have produced alterations in the channel and floodplain for a long time ago increasing the risk. Thus, it is necessary that flood control systems are matched with the river and floodplain changes and special care needs to be done to understand the causes and effects of the flood impact between natural and social environments in order to establish actions focused to minimise it [1, 7]. Ref. [9] considers that whether the purpose is the control of flood disasters, a flood risk management is clue, since it is the sum of actions to achieve the minimisation of the flood consequences. In general, [9] identifies two aspects that need to be addressed: the process of managing an existing flood risk and the planning of a system to reduce the flood risk. Generally, flood risk considered the probability of hazard (i.e. climatic change) and the exposure and vulnerability of the elements at risk (i.e. urbanised area) [1]. One way to predict flood hazards is as function of the computed probability of previous events known as return period (Tr). Flood hazards (exposure) represent *the exceedance probability of potentially damaging flood situations in a given area within a specified time period* [10]. In the case of vulnerability, it can be defined as *the potential for loss* [11], which could be associated in an urbanised system to the loss of the ecosystem services in the area. Although [12] pointed that urbanisation is not a synonym of an increment in flood vulnerability, some relationships could be expected. Urbanisation implies in some degree the presence of infrastructure, in particular against natural extreme events. An alternative is to consider both flood structural and nonstructural measurements as content.

In [13], the need for a quantitative but also a qualitative flood risk analysis was established. The first one provides information of the potential damage in terms of direct economic lost calculated using stage-damage functions (houses, industries and infrastructure), a situation that in the second case could not be achieved since it involves cultural, ecological and indirect economic damages [14]. One way to communicate both qualitative and quantitative hazard and the associated risk is through flood risk maps. For [15] there are flood hazard maps, which help to identify flooded areas with different probabilities, complemented by parameters indicating flood intensity, such as flood depth or flow velocity. Also, flood risk maps help to identify weak points of the flood defence system or indicate a need for action, even if the flood protection system adopted failure during the flood [9]. In fact, flood risk maps incorporate flood hazard information related to properties and population and their vulnerability to the hazard [1]. It is important to mention that many people have no other place to live, but they are habitual to frequent floods without representing any kind of lost. [16] pointed out that maybe due to the familiarity with flood or the lack of flooding experience, property owners in floodplains are not aware of the risk of living in a flood-prone area. The authors analysed the risk associated in terms of cost to protect their lives and properties. For that they mentioned that [17] were some of the first to manage the consumer perception of risk looking at the personal experience, history of past flooding, level of risk existing and how each individual responds to the risks. [16] stated that there is few information related to the effects of flooding risk on property values,

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*Flood Risk Assessment in Housing under an Urban Development Scheme Simulating Water Flow…*

the majority being focused to insurance by natural risk. They cited researches like [17–18] as the ones that use *property location vis-a-vis a floodplain* and the value of the property which reduces when it is in a flood-prone zone. However, in terms of economic aspects, it is only the responsibility of the house-owner and its perception of loss to have any insurance. This chapter looks at the property in terms of the economic loss as a function of the flood hazard zone location under three population growth rate scenarios at the north-east of the Valley of Mexico. The house prices were established according to the material used to build them and the impact when different flood intensity events (return periods) are applied. In order to achieve the flood risk map, a hazard map was created based on the identification of flood-prone areas and the impact in the implementation of a structural mitigation measure (hydraulic infrastructure) according to the hydrology, soil and climate, among other conditions of the study area. To identify the flood areas, the flood simulation was realised using the 2D mathematical model, FluBiDi (modelo de flujo didimencional), for different return periods previously calibrated using discharge data. The risk map contains the information about the consequences expected by the hazard (flood), specifically the influence of structural (channel rectification) and nonstructural mitigation measures (spatial econometric analysis

In general terms, FluBiDi is a distributed 2D physical-based model for forecasting runoff developed by [19] and complemented by [20] the Institute of Engineering of National Autonomous University of Mexico (UNAM, in Spanish). Firstly, FluBiDi seeks to establish runoff for any site within a basin under study and determines the contribution volume of this site to the total basin runoff (including local rain). Secondly, FluBiDi provides an interpretation closer to reality since it incorporates several variables and parameters of the hydrologic cycle and basin characteristics based on the physical principles that scale changes are possible using parametric values [20]. As a 2D (dimensional) model, it represents floodplain flow as a two-dimensional field with the assumption that the third dimension (water depth) is shallow in comparison to the other two dimensions as [21, 22] noticed. FluBiDi, as most approaches solve the 2D shallow water equations, represents mass and momentum conservation in a plane and can be obtained by depth-averaging the Navier–Stokes equations. These equations are founded of the motion of viscous fluids involving parametrisation at a macroscale from the basic microscale equation in the vertical direction under the assumptions of hydrostatic pressure distribution and uniform velocity profiles. The development of the equations could be found at

*DOI: http://dx.doi.org/10.5772/intechopen.82719*

of properties at risk).

**2. FluBiDi mathematical model**

[23]. Thus, the momentum equations are.

*g* ∂*u*\_\_\_ ∂*t*

> *g* \_\_\_ ∂*v* <sup>∂</sup>*<sup>t</sup>* <sup>+</sup> *<sup>n</sup>*<sup>2</sup> \_\_\_\_\_ <sup>|</sup>*v*|*<sup>v</sup>*

v are the flow velocities in x and y directions, respectively (m·s<sup>−</sup><sup>2</sup>

<sup>+</sup> *<sup>n</sup>*<sup>2</sup> \_\_\_\_\_ <sup>|</sup>*u*|*<sup>u</sup> h* \_\_ 4 3

where X and Y are forces by mass unit at the x and y directions (m·s<sup>−</sup><sup>1</sup>

=−\_\_\_ <sup>∂</sup>*<sup>h</sup>* <sup>∂</sup>*<sup>x</sup>* <sup>−</sup> \_\_\_ <sup>∂</sup>*<sup>Z</sup>*

*<sup>h</sup>*4/3 =−\_\_\_ <sup>∂</sup>*<sup>h</sup>*

horizontal and vertical directions in the Cartesian system. The Manning-Strickler equation for friction slopes was included for computing roughness coefficient. Z is

<sup>∂</sup>*<sup>y</sup>* <sup>−</sup> \_\_\_ <sup>∂</sup>*<sup>Z</sup>*

<sup>∂</sup>*<sup>x</sup>* (1)

<sup>∂</sup>*<sup>y</sup>* (2)

); u and

); and x and y are

\_\_1

\_\_1

*Flood Risk Assessment in Housing under an Urban Development Scheme Simulating Water Flow… DOI: http://dx.doi.org/10.5772/intechopen.82719*

the majority being focused to insurance by natural risk. They cited researches like [17–18] as the ones that use *property location vis-a-vis a floodplain* and the value of the property which reduces when it is in a flood-prone zone. However, in terms of economic aspects, it is only the responsibility of the house-owner and its perception of loss to have any insurance. This chapter looks at the property in terms of the economic loss as a function of the flood hazard zone location under three population growth rate scenarios at the north-east of the Valley of Mexico. The house prices were established according to the material used to build them and the impact when different flood intensity events (return periods) are applied. In order to achieve the flood risk map, a hazard map was created based on the identification of flood-prone areas and the impact in the implementation of a structural mitigation measure (hydraulic infrastructure) according to the hydrology, soil and climate, among other conditions of the study area. To identify the flood areas, the flood simulation was realised using the 2D mathematical model, FluBiDi (modelo de flujo didimencional), for different return periods previously calibrated using discharge data. The risk map contains the information about the consequences expected by the hazard (flood), specifically the influence of structural (channel rectification) and nonstructural mitigation measures (spatial econometric analysis of properties at risk).
