**2. FluBiDi mathematical model**

*Recent Advances in Flood Risk Management*

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,

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

**88**

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 [23]. Thus, the momentum equations are.

$$\frac{1}{8}\frac{\partial u}{\partial t} + \frac{n^2|u|u}{h^{\frac{4}{3}}} = -\frac{\partial h}{\partial \mathbf{x}} - \frac{\partial Z}{\partial \mathbf{x}} \tag{1}$$

$$\frac{1}{\text{g}} \frac{\partial \mathbf{v}}{\partial \mathbf{t}} + \frac{\text{n}^2 \text{w} \cup \text{w}}{\text{h}^{4/3}} = -\frac{\partial \mathbf{h}}{\partial \mathbf{y}} - \frac{\partial \mathbf{Z}}{\partial \mathbf{y}} \tag{2}$$

where X and Y are forces by mass unit at the x and y directions (m·s<sup>−</sup><sup>1</sup> ); u and v are the flow velocities in x and y directions, respectively (m·s<sup>−</sup><sup>2</sup> ); and x and y are horizontal and vertical directions in the Cartesian system. The Manning-Strickler equation for friction slopes was included for computing roughness coefficient. Z is the surface water level related to the land topography considering the rain contribution and infiltration losses.

Also, the governing mass continuity equation considers the rain contribution and infiltration losses, and if the inertia is not significant, it is given as.

$$\frac{\partial h}{\partial t} + \mathcal{U}\frac{\partial h\mu}{\partial \mathbf{x}} + \mathcal{U}\frac{\partial h\nu}{\partial y} = \left.\begin{array}{c} \mathbf{r} \ -f \end{array} \right. \tag{3}$$

The diffusive wave approximation neglects the local acceleration term and convective acceleration term in the momentum equations, and it is applicable in situations where Froude number is small [24]. Thus, FluBiDi defines the system considering dynamic, diffusive and kinematic wave properties for an overland flow in a basin.

The integral form of the shallow water equations to define schemes on different mesh types is considered for the numerical integration; thus, a finite volume method needs to be used for the governing Equations [23]. The surface integrals represent the conversion of the lineal integral into area integrals implying to contemplate the boundary of the region that involves some integrations (Green's theorem). Some schemes consider the homogeneous conservative part of the system and a discretisation of the non-conservative term with a "lateralisation" [25]. For that, it is necessary to take into account that the mesh could have known depth and velocity values and the border boundaries consider four points: one for the right side of the intercell (*R*) and another for the left side (*L*) and the other two for above and below the cell.

FluBiDi is born as a hydraulic mathematical model to simulate runoff based on rainfall, and, in almost all the similar models, it considers river basins exposed to high rainfalls that present an organised drainage net, increasing the water flow at the mainstream according to the amount and intensity of precipitation and the topography at the basin [26]. However, in very few cases, this situation is presented, although it is the best condition to calibrate the model. Ref. [27] indicated that the river gauge water level time series comparison is one of the best forms to test the model's performance. For FluBiDi, a river basin in the Tabasco state offered input and output discharges measured and the awareness of how it behaves becoming an excellent option to calibrate the model. FluBiDi version 1.6 offered utilities to achieve hazard maps using routines to simulate the hydraulic phenomena obtaining water levels, velocities and water extension. Surface water levels could be used as a variable at the boundary conditions in FluBiDi. This is an important contribution, since very few codes have the ability to delimit boundary conditions and most of them require the definition of input discharge and water level.

## **3. Model calibration**

Teapa River basin (TRB) together with Jalapa and Tacotalpa Rivers originate the La Sierra River with a basin (SRB) area of 1799.4 km2 . **Figure 1** shows the extension of the TRB. The TRB is an instrumented basin with hourly rainfall records, hourly water levels and flow gauging. Also, the TRB is subject to continuous historic floods being one of the most severe in 2007 with a Tr = 100 years. Particularly, at the Teapa station, the total drained area is 476 km2 , with records of average temperature of 25.9°C, with variations from 22.5° to 28.8°C during the year. The total annual average precipitation corresponds to 3133.4 mm, with average monthly variations of 105–520 mm [28, 29]. It is necessary to mention that the basin under study does not have any additional volume income to the precipitation; thus, the resulting flow corresponds only to the precipitation and the vegetation.

**91**

**3.1 Data**

**Figure 1.**

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

The natural vegetation consists of high evergreen forest and medium subperennifolia forest (limits with Chiapas) and grasslands and secondary subperennifolia

Many authors such as [27] identify as a common method to calibrate a flood model the use of historic flood records. In particular, if these records were acquired just after the event has passed, the accuracy of the model will be guaranteed. Thus, the main application of FluBiDi in TRB is the flood simulation by the estimation of the flow that drains at the outlet of the basin. To simulate flood, records include the period from November 19 to 24, 2015. In general, 2015 was classified around the country as the 12th year with more rainfall since 1941 with 872 mm of total cumulated rain. The reason for that was a series of cold fronts (CF) that hit the region in 2015 starting with the CF-7 (October 16–17) which left heavy punctual rains in Tabasco varying between 90 and 300 mm and generating in the SRB severe floods, the Teapa town being one of the places that remained uncommunicated with 1 m of water height. Then, the CF-8 (October 22–29) affected seriously the region by the day 25th with a cumulate precipitation of 160.7 mm, and this value increased with the arrival of the CF-14 (November 21–24) to 223.7 mm. In December 14–20, the CF-21 took place leaving rains around 125.4 mm in Macuspana by day 18th, but at the end of day 19th, rains were maintained around 120 mm in Puyacatengo. The heavy rains of the CF-21 caused that the La Sierra River to overflow and partially flood 13 communities, some of them, Teapa again, reaching in some cases a water height of 50 centimetres and affecting at least 350 families according to the Institute of Civil Protection of the Tabasco State [30]. There were also economic losses including flooded grasslands, and other losses were associated with low sales, absenteeism and delay of workers.

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

secondary forest, with some popal [28].

*Teapa River basin: Topographic relieve.*

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

**Figure 1.** *Teapa River basin: Topographic relieve.*

The natural vegetation consists of high evergreen forest and medium subperennifolia forest (limits with Chiapas) and grasslands and secondary subperennifolia secondary forest, with some popal [28].

### **3.1 Data**

*Recent Advances in Flood Risk Management*

\_\_\_ <sup>∂</sup>*<sup>h</sup>*

tion and infiltration losses.

and below the cell.

**3. Model calibration**

the surface water level related to the land topography considering the rain contribu-

Also, the governing mass continuity equation considers the rain contribution

<sup>∂</sup>*<sup>x</sup>* <sup>+</sup> *<sup>v</sup>* \_\_\_\_ <sup>∂</sup>*hv*

FluBiDi is born as a hydraulic mathematical model to simulate runoff based on rainfall, and, in almost all the similar models, it considers river basins exposed to high rainfalls that present an organised drainage net, increasing the water flow at the mainstream according to the amount and intensity of precipitation and the topography at the basin [26]. However, in very few cases, this situation is presented, although it is the best condition to calibrate the model. Ref. [27] indicated that the river gauge water level time series comparison is one of the best forms to test the model's performance. For FluBiDi, a river basin in the Tabasco state offered input and output discharges measured and the awareness of how it behaves becoming an excellent option to calibrate the model. FluBiDi version 1.6 offered utilities to achieve hazard maps using routines to simulate the hydraulic phenomena obtaining water levels, velocities and water extension. Surface water levels could be used as a variable at the boundary conditions in FluBiDi. This is an important contribution, since very few codes have the ability to delimit boundary conditions and most of

Teapa River basin (TRB) together with Jalapa and Tacotalpa Rivers originate the

of the TRB. The TRB is an instrumented basin with hourly rainfall records, hourly water levels and flow gauging. Also, the TRB is subject to continuous historic floods being one of the most severe in 2007 with a Tr = 100 years. Particularly, at the Teapa

of 25.9°C, with variations from 22.5° to 28.8°C during the year. The total annual average precipitation corresponds to 3133.4 mm, with average monthly variations of 105–520 mm [28, 29]. It is necessary to mention that the basin under study does not have any additional volume income to the precipitation; thus, the resulting flow

. **Figure 1** shows the extension

, with records of average temperature

them require the definition of input discharge and water level.

La Sierra River with a basin (SRB) area of 1799.4 km2

corresponds only to the precipitation and the vegetation.

station, the total drained area is 476 km2

The diffusive wave approximation neglects the local acceleration term and convective acceleration term in the momentum equations, and it is applicable in situations where Froude number is small [24]. Thus, FluBiDi defines the system considering dynamic, diffusive and kinematic wave properties for an overland flow in a basin. The integral form of the shallow water equations to define schemes on different mesh types is considered for the numerical integration; thus, a finite volume method needs to be used for the governing Equations [23]. The surface integrals represent the conversion of the lineal integral into area integrals implying to contemplate the boundary of the region that involves some integrations (Green's theorem). Some schemes consider the homogeneous conservative part of the system and a discretisation of the non-conservative term with a "lateralisation" [25]. For that, it is necessary to take into account that the mesh could have known depth and velocity values and the border boundaries consider four points: one for the right side of the intercell (*R*) and another for the left side (*L*) and the other two for above

<sup>∂</sup>*<sup>y</sup>* <sup>=</sup> *<sup>r</sup>* <sup>−</sup> *<sup>f</sup>* (3)

and infiltration losses, and if the inertia is not significant, it is given as.

<sup>∂</sup>*<sup>t</sup>* <sup>+</sup> *<sup>u</sup>*\_\_\_\_ <sup>∂</sup>*hu*

**90**

Many authors such as [27] identify as a common method to calibrate a flood model the use of historic flood records. In particular, if these records were acquired just after the event has passed, the accuracy of the model will be guaranteed. Thus, the main application of FluBiDi in TRB is the flood simulation by the estimation of the flow that drains at the outlet of the basin. To simulate flood, records include the period from November 19 to 24, 2015. In general, 2015 was classified around the country as the 12th year with more rainfall since 1941 with 872 mm of total cumulated rain. The reason for that was a series of cold fronts (CF) that hit the region in 2015 starting with the CF-7 (October 16–17) which left heavy punctual rains in Tabasco varying between 90 and 300 mm and generating in the SRB severe floods, the Teapa town being one of the places that remained uncommunicated with 1 m of water height. Then, the CF-8 (October 22–29) affected seriously the region by the day 25th with a cumulate precipitation of 160.7 mm, and this value increased with the arrival of the CF-14 (November 21–24) to 223.7 mm. In December 14–20, the CF-21 took place leaving rains around 125.4 mm in Macuspana by day 18th, but at the end of day 19th, rains were maintained around 120 mm in Puyacatengo. The heavy rains of the CF-21 caused that the La Sierra River to overflow and partially flood 13 communities, some of them, Teapa again, reaching in some cases a water height of 50 centimetres and affecting at least 350 families according to the Institute of Civil Protection of the Tabasco State [30]. There were also economic losses including flooded grasslands, and other losses were associated with low sales, absenteeism and delay of workers.

#### *3.1.1 Meteorology and hydrometric stations*

Meteorological data was obtained from nine weather stations located in the area (see **Figure 5**): Puyacatengo, Teapa, El Refugio, Francisco I. Madero, Chapultenango, Tapilula, El Escalón, Arroyo Grande and Oxolotan [31]. Data are provided in the latency of 10 min/hourly/daily rainfall (mm), 10 min/hourly and daily temperature (°C), hourly/daily relative humidity (%), average daily wind speed (m·s<sup>−</sup><sup>1</sup> ) and sunshine hours, among others. Also some daily evaporation records were obtained, but once they were compared with the effective precipitation, they have turned out to be negligible. These records could be used as an input to the model in order to simulate the event. In addition, the Teapa hydrometric station provides every 10 min continuous water level records obtained with an electronic system for real-time measurements and with quotation in the reference level bank of the hydrometric station. Daily water velocity using a hydraulic windlass method was acquired at 8 a.m. for each subsection in which the total section is divided using the divided channel method (DCM) [32].

It is important to know the spatial and temporal distribution of precipitation; thus, data for the nine weather stations were firstly grouped from 10 min to hourly rainfall values. **Figure 2** presents the analysis of spatial precipitation records for some hours, as well as the cumulative representation for the total modelling period of 6 days (144 hours).

The importance of the spatial-temporal analysis of precipitation can be observed since in the weather station (Chapultenango) rained the same or more that the cumulate rain for the total period of 7 days. In Chapultenango (see **Figure 4e, f**), the maximum rainfall value was around 250 mm for 1 h that corresponded to the maximum 24 h cumulative rainfall continuous value on November 23, whereas in the Teapa weather station, the maximum cumulated rainfall in 24 h was approximately 180 mm with less than 100 mm in 1 h.

**Figure 3** shows the comparison of records for water surface level and water elevation discharge curves. **Figure 5a** presents the relationship between the real-time water level measurements and the daily gauge in the period under study; the error was less than 2%. **Figure 5b** indicates the water level related to the discharge is 330 times, which is used to carry out an adjustment to a quadratic polynomial function. This polynomial function provides the final discharge (Q ) to the automatised water level measurements (without outliers present within the circle in **Figure 5b**). This provides from November 18 to 26, 2015, a total of 190 values of estimated discharges for 190 water surface elevations measured.

After reviewing the quality of rainfall information, it was considered that data ensure greater consistency to feed the mathematical model.

#### *3.1.2 Topographic and thematic data*

To apply the mathematical model, it is required to generate a mesh that represents the elevations and other topographic features (surface drainage system, slope and orientation) accurately. In this case, the digital elevation model (DEM) was obtained from the National Institute of Statistical and Geography (INEGI) Mexican Elevation Continuum [33]. Derived from the DEM (with a 30-m cell size), a mesh of 100 m per 100 m was resized in order to fulfil with the restriction for the modelled time required. Thus, for the new mesh, an interpolation technique was used where the main variable is the size against the calculation time. The merge of 100 m size is fed to the model in order to process it and recalculate variables such as slope, aspect, flow direction and basin limits.

A compendium of thematic maps, topography, climatology, edaphology, physiography, geology, hydrology, land use and vegetation, potential land use

**93**

**Figure 2.**

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

and communication channels, were obtained from [33]. These maps and other information available from documents were integrated in a geographic information system (GIS), according to its continuous or discrete nature. In the case

*Spatial analysis of precipitation from November 22 to 23, 2015.*

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

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

#### **Figure 2.**

*Recent Advances in Flood Risk Management*

of 6 days (144 hours).

180 mm with less than 100 mm in 1 h.

for 190 water surface elevations measured.

*3.1.2 Topographic and thematic data*

aspect, flow direction and basin limits.

ensure greater consistency to feed the mathematical model.

*3.1.1 Meteorology and hydrometric stations*

Meteorological data was obtained from nine weather stations located in the area (see **Figure 5**): Puyacatengo, Teapa, El Refugio, Francisco I. Madero, Chapultenango, Tapilula, El Escalón, Arroyo Grande and Oxolotan [31]. Data are provided in the latency of 10 min/hourly/daily rainfall (mm), 10 min/hourly and daily temperature

sunshine hours, among others. Also some daily evaporation records were obtained, but once they were compared with the effective precipitation, they have turned out to be negligible. These records could be used as an input to the model in order to simulate the event. In addition, the Teapa hydrometric station provides every 10 min continuous water level records obtained with an electronic system for real-time measurements and with quotation in the reference level bank of the hydrometric station. Daily water velocity using a hydraulic windlass method was acquired at 8 a.m. for each subsection in which the total section is divided using the divided channel method (DCM) [32]. It is important to know the spatial and temporal distribution of precipitation; thus, data for the nine weather stations were firstly grouped from 10 min to hourly rainfall values. **Figure 2** presents the analysis of spatial precipitation records for some hours, as well as the cumulative representation for the total modelling period

The importance of the spatial-temporal analysis of precipitation can be observed

since in the weather station (Chapultenango) rained the same or more that the cumulate rain for the total period of 7 days. In Chapultenango (see **Figure 4e, f**), the maximum rainfall value was around 250 mm for 1 h that corresponded to the maximum 24 h cumulative rainfall continuous value on November 23, whereas in the Teapa weather station, the maximum cumulated rainfall in 24 h was approximately

**Figure 3** shows the comparison of records for water surface level and water elevation discharge curves. **Figure 5a** presents the relationship between the real-time water level measurements and the daily gauge in the period under study; the error was less than 2%. **Figure 5b** indicates the water level related to the discharge is 330 times, which is used to carry out an adjustment to a quadratic polynomial function. This polynomial function provides the final discharge (Q ) to the automatised water level measurements (without outliers present within the circle in **Figure 5b**). This provides from November 18 to 26, 2015, a total of 190 values of estimated discharges

After reviewing the quality of rainfall information, it was considered that data

To apply the mathematical model, it is required to generate a mesh that represents the elevations and other topographic features (surface drainage system, slope and orientation) accurately. In this case, the digital elevation model (DEM) was obtained from the National Institute of Statistical and Geography (INEGI) Mexican Elevation Continuum [33]. Derived from the DEM (with a 30-m cell size), a mesh of 100 m per 100 m was resized in order to fulfil with the restriction for the modelled time required. Thus, for the new mesh, an interpolation technique was used where the main variable is the size against the calculation time. The merge of 100 m size is fed to the model in order to process it and recalculate variables such as slope,

A compendium of thematic maps, topography, climatology, edaphology, physiography, geology, hydrology, land use and vegetation, potential land use

) and

(°C), hourly/daily relative humidity (%), average daily wind speed (m·s<sup>−</sup><sup>1</sup>

**92**

*Spatial analysis of precipitation from November 22 to 23, 2015.*

and communication channels, were obtained from [33]. These maps and other information available from documents were integrated in a geographic information system (GIS), according to its continuous or discrete nature. In the case

**Figure 3.**

*Water surface level and gauged records at the Teapa hydrometric station.*

**Figure 4.** *FluBiDi results calibrated. Red points mean data measured are wrong.*

#### **Figure 5.** *Study area in the Texcoco ex-lake at the ZMCM.*

of the land use map, it is very important for mathematical modelling since it is the base information for the mesh of the Manning roughness coefficient "n". It is necessary to mention that this coefficient can vary according to the time of the year; that is, for modelling in October–November, soil moisture increases to saturation; thus, the roughness coefficient also increases in a proportion of 0.03 and 0.05.

**95**

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

FluBiDi is configured to report flow depth and velocity data every hour, in order to compare results from the mathematical model with the correspondent real-time value measured at the hydrometric station. As response of the dynamic character of floods and the influence of water displacement downstream, FluBiDi provides flow equations in two horizontal dimensions, so water velocities correspond to its average value in vertical. For the simulation in the TRB, FluBiDi considers the contribution of water mass generated in the rainfall period that varies in time and space. Therefore, different hietograms are defined in different areas of the study domain. In the simulation of precipitation processes, it may be necessary to consider the infiltration of water in the no-saturate soil. Modelling infiltration is especially important to the transformation of rainfall into runoff. As it was mentioned, a mesh of the roughness coefficient of Manning "n" was obtained with the same resolution of grid from the DEM (100 m

estimated directly from the reading of water levels related to the volumetric discharge.

FluBiDi is a mathematical model created to be used in real basins that is the case

reporting data at each hour with an interval of 5 seconds for the calculation time step, estimating that 24 hours of rea.l time are mathematically processed in approximately 1 hour. In the model, it was the key to assess the maximum water level at the precise time when it is presented looking at the flood prevention. For this reason, in this calibration real precipitation data were used at the peak hours registered. Results are presented in **Figure 4** for November 24 at 6:00 am: an average volumet-

·s<sup>−</sup><sup>1</sup>

depth from 37.54masl head measured and 37.62masl head simulated.

median value of 34.766 in data measured and 34.764 in simulated was achieved, and a standard deviation of 0.64 and 0.66, respectively. The linear correlation is r = 0.87. The maximum water level has a difference around 8 cm of a total 4 m of water

In **Figure 6a** around November 24 and 25, there are two outliers that indicate the presence of a daily discharge relatively similar to the one observed on the 23rd. However, in **Figure 6b**, a water level increment similar to the one presented on November 23 was not reported. Therefore, as the volumetric rain coincides on the day of the maximum discharge and there are no other increases in subsequent water level days, it is considered that the gauge discharges may have an error in their methodology. If there is no rain, the discharge then maintains lower, and there is no

As shown, the model adequately predicts the discharge and water levels obtained from the precipitation recorded in the Teapa hydrometric station. This offers a very good agreement between FluBiDi and the measured values which guarantee an

Results from the calibration of FluBiDi were very satisfactory giving guarantee

of the reliability of the model to be used with confidence in other basins with similar characteristics, even if it is ungauged at the output basin and without water depth references in the inundated zones. [27] mentioned three aspects that need to

·s<sup>−</sup><sup>1</sup>

was obtained using FluBiDi, and the value obtained from

and a volumetric flow rate of 400 m3

; this implies a relative error (RE) of 5%. A

that corresponds to the one

·s<sup>−</sup><sup>1</sup>

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

per 100 m side). The base flow was estimated in 40 m3

of the TRB with a drained area of 476 km<sup>2</sup>

·s<sup>−</sup><sup>1</sup>

transfer from another side because of the type of basin.

**4. Application of model on an ungauged basin**

*3.1.3 FluBiDi requirements*

**3.2 Results**

ric discharge of 423 m3

the hydrometric station was 400 m3

efficient rainfall-runoff relationship.

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

### *3.1.3 FluBiDi requirements*

*Recent Advances in Flood Risk Management*

*Water surface level and gauged records at the Teapa hydrometric station.*

*FluBiDi results calibrated. Red points mean data measured are wrong.*

of the land use map, it is very important for mathematical modelling since it is the base information for the mesh of the Manning roughness coefficient "n". It is necessary to mention that this coefficient can vary according to the time of the year; that is, for modelling in October–November, soil moisture increases to saturation; thus, the roughness coefficient also increases in a proportion of 0.03

**Figure 3.**

**Figure 4.**

**94**

and 0.05.

**Figure 5.**

*Study area in the Texcoco ex-lake at the ZMCM.*

FluBiDi is configured to report flow depth and velocity data every hour, in order to compare results from the mathematical model with the correspondent real-time value measured at the hydrometric station. As response of the dynamic character of floods and the influence of water displacement downstream, FluBiDi provides flow equations in two horizontal dimensions, so water velocities correspond to its average value in vertical. For the simulation in the TRB, FluBiDi considers the contribution of water mass generated in the rainfall period that varies in time and space. Therefore, different hietograms are defined in different areas of the study domain. In the simulation of precipitation processes, it may be necessary to consider the infiltration of water in the no-saturate soil. Modelling infiltration is especially important to the transformation of rainfall into runoff. As it was mentioned, a mesh of the roughness coefficient of Manning "n" was obtained with the same resolution of grid from the DEM (100 m per 100 m side). The base flow was estimated in 40 m3 ·s<sup>−</sup><sup>1</sup> that corresponds to the one estimated directly from the reading of water levels related to the volumetric discharge.

### **3.2 Results**

FluBiDi is a mathematical model created to be used in real basins that is the case of the TRB with a drained area of 476 km<sup>2</sup> and a volumetric flow rate of 400 m3 ·s<sup>−</sup><sup>1</sup> reporting data at each hour with an interval of 5 seconds for the calculation time step, estimating that 24 hours of rea.l time are mathematically processed in approximately 1 hour. In the model, it was the key to assess the maximum water level at the precise time when it is presented looking at the flood prevention. For this reason, in this calibration real precipitation data were used at the peak hours registered. Results are presented in **Figure 4** for November 24 at 6:00 am: an average volumetric discharge of 423 m3 ·s<sup>−</sup><sup>1</sup> was obtained using FluBiDi, and the value obtained from the hydrometric station was 400 m3 ·s<sup>−</sup><sup>1</sup> ; this implies a relative error (RE) of 5%. A median value of 34.766 in data measured and 34.764 in simulated was achieved, and a standard deviation of 0.64 and 0.66, respectively. The linear correlation is r = 0.87. The maximum water level has a difference around 8 cm of a total 4 m of water depth from 37.54masl head measured and 37.62masl head simulated.

In **Figure 6a** around November 24 and 25, there are two outliers that indicate the presence of a daily discharge relatively similar to the one observed on the 23rd. However, in **Figure 6b**, a water level increment similar to the one presented on November 23 was not reported. Therefore, as the volumetric rain coincides on the day of the maximum discharge and there are no other increases in subsequent water level days, it is considered that the gauge discharges may have an error in their methodology. If there is no rain, the discharge then maintains lower, and there is no transfer from another side because of the type of basin.

As shown, the model adequately predicts the discharge and water levels obtained from the precipitation recorded in the Teapa hydrometric station. This offers a very good agreement between FluBiDi and the measured values which guarantee an efficient rainfall-runoff relationship.

### **4. Application of model on an ungauged basin**

Results from the calibration of FluBiDi were very satisfactory giving guarantee of the reliability of the model to be used with confidence in other basins with similar characteristics, even if it is ungauged at the output basin and without water depth references in the inundated zones. [27] mentioned three aspects that need to

**Figure 6.**

*Mass curves for station in 1988 and 2011. Source: [35].*

be addressed by the model to simulate large events: *the interchange of flow between the channel and floodplain, floodplain storage capacity and flow resistance across the floodplain* due to soil and vegetation conditions.

#### **4.1 Characteristics of the river basin**

The study zone is located within the Valley of Mexico metropolitan area (zona metropolitana del Valle de México, ZMCM) at the west part corresponding to the Mexico State. The area involves the plain of the last ex-Lake of Texcoco, the largest one of an interconnected lake system during the prehispanic era. In **Figure 5**, the area of 92 km2 can be shown with an average slope of 1% formed by an anthropic watershed defined by highways in the upper zone (the total contribution zone is 1020 km2 ). The study area is located in the subbasin "p" of Lakes of Texcoco and Zumpango of the hydrological region Panuco No. 26, and it corresponds to an endorheic basin without exit to the sea. Thus, all the rainfall becomes runoff and generates the lakes.

The Valley of Mexico is surrounded by mountains on all four sides creating a basin with only one small opening at the north. There main types of climate in the study area are subhumid temperate and dry temperate and both semi-cold semi-dry with rain in summer. The dry season is subdivided into two: dry hot (between March and May), with predominance of dry tropical air and high temperature, and dry cold (from November to February) characterised by polar-type air with low moisture content and temperature. The region receives anticyclonic systems, producing weak winds [34]. The expansion of Mexico City implicated the drying of the lakes and the expansion of the urban sprawl towards the lowlands. Thus, floods are a constant problem with inundated plains and urban settlements in a constant flood risk. In 2015, there were approximately 60,000 homes susceptible to flooding; these homes are dispersed in the grey and green area (**Figure 5b**).

#### **4.2 Data**

In this case, the incoming flow to the system could be assigned to hydrograms coming from the upper part of the whole basin where some hydrometric stations are presented. The model was fed with eight hydrograms located each one in the river cut at the desire study area; they correspond to the vehicular bridges to cross the Texcoco-Tepepan highway over the riverbeds. Additionally, [35] provides local precipitation from four climatological stations (7, 25, 29 and 35) (**Figure 6**) located in the periphery but representative of the study area.

**97**

**Figure 7.**

*Hp acumulada considerada en la modelación.*

depth occurred.

**4.3 FluBiDi application**

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

In 1988, there is a spatial difference in the rain observing between day 4 and 5 a cumulative rain of 24 h around of 90 mm in station 25, whereas in 2011 the spatial rain was almost homogeneous and of lower 24 h rain accumulating with 65 mm and with a mayor period of arriving. As result, it was determined that the rain is distributed in a homogeneous manner within the study basin, additionally to the size of the basin and the geomorphological characteristics. Therefore, a single station was proposed, which is the one that contributes with the hietogram fed to FluBiDi under a concentrated model of rain. Other consideration was to pose a hypothetical and very unfavourable event considering 5 consecutive rainy days. To this rain event, a statistical analysis was applied to four Tr = 20, 50, 100 and 200 years. Additionally, historical events were considered: Derby 1988 and Arlene 2011. Results are shown in **Figure 7**, a recurrence of less than 20 years for the 5 continuous days of rain, which

As well as in the TRB calibration (Section 3), thematic data was available as well as topography and land use since it is a swamp area with some human settlements, soil and vegetation which are easily determined, but the hydrogeological conditions become very complex. The topographic information consisted in LIDAR (light detection and ranging) scale 1:10,000 with a grid resolution of 5 m per size [33]. The mesh generated from it to feed the model was integrated by 1900 rows per 1020 columns to cover all the study zone with a resolution of 10 mX10 m in order to

Unlike the TRB, for this case there was no information that allows a quantita-

The discharge from the eight streams coming from the upper part of the basin was represented with its correspondent histogram and feed to the model as initial condition. At this point, the structural measure was incorporated to the flood

tive calibration. However, a qualitative calibration was carried out based on historical information of the rainfall generated by the remnants of the hurricane Derby in September, 1988, and the TS Arlene on late June and early July 2011. Both remnants left prolonged rainfall over much south central Mexico wherein Mexico City is affected by subsequent flooding damaging hundreds of homes and several roads. This information was compared with flood maps from INEGI showing the areas that could be inundated for the study area [33]. Additionally, there was social information extracted from newspapers related to the water

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

is the case of interest in areas with little slope.

consider 1 sec as time interval to run the FluBiDi model.

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

In 1988, there is a spatial difference in the rain observing between day 4 and 5 a cumulative rain of 24 h around of 90 mm in station 25, whereas in 2011 the spatial rain was almost homogeneous and of lower 24 h rain accumulating with 65 mm and with a mayor period of arriving. As result, it was determined that the rain is distributed in a homogeneous manner within the study basin, additionally to the size of the basin and the geomorphological characteristics. Therefore, a single station was proposed, which is the one that contributes with the hietogram fed to FluBiDi under a concentrated model of rain. Other consideration was to pose a hypothetical and very unfavourable event considering 5 consecutive rainy days. To this rain event, a statistical analysis was applied to four Tr = 20, 50, 100 and 200 years. Additionally, historical events were considered: Derby 1988 and Arlene 2011. Results are shown in **Figure 7**, a recurrence of less than 20 years for the 5 continuous days of rain, which is the case of interest in areas with little slope.

As well as in the TRB calibration (Section 3), thematic data was available as well as topography and land use since it is a swamp area with some human settlements, soil and vegetation which are easily determined, but the hydrogeological conditions become very complex. The topographic information consisted in LIDAR (light detection and ranging) scale 1:10,000 with a grid resolution of 5 m per size [33]. The mesh generated from it to feed the model was integrated by 1900 rows per 1020 columns to cover all the study zone with a resolution of 10 mX10 m in order to consider 1 sec as time interval to run the FluBiDi model.

Unlike the TRB, for this case there was no information that allows a quantitative calibration. However, a qualitative calibration was carried out based on historical information of the rainfall generated by the remnants of the hurricane Derby in September, 1988, and the TS Arlene on late June and early July 2011. Both remnants left prolonged rainfall over much south central Mexico wherein Mexico City is affected by subsequent flooding damaging hundreds of homes and several roads. This information was compared with flood maps from INEGI showing the areas that could be inundated for the study area [33]. Additionally, there was social information extracted from newspapers related to the water depth occurred.

#### **4.3 FluBiDi application**

*Recent Advances in Flood Risk Management*

*floodplain* due to soil and vegetation conditions.

**4.1 Characteristics of the river basin**

*Mass curves for station in 1988 and 2011. Source: [35].*

area of 92 km2

generates the lakes.

green area (**Figure 5b**).

**4.2 Data**

1020 km2

**Figure 6.**

be addressed by the model to simulate large events: *the interchange of flow between the channel and floodplain, floodplain storage capacity and flow resistance across the* 

The study zone is located within the Valley of Mexico metropolitan area (zona metropolitana del Valle de México, ZMCM) at the west part corresponding to the Mexico State. The area involves the plain of the last ex-Lake of Texcoco, the largest one of an interconnected lake system during the prehispanic era. In **Figure 5**, the

watershed defined by highways in the upper zone (the total contribution zone is

Zumpango of the hydrological region Panuco No. 26, and it corresponds to an endorheic basin without exit to the sea. Thus, all the rainfall becomes runoff and

can be shown with an average slope of 1% formed by an anthropic

). The study area is located in the subbasin "p" of Lakes of Texcoco and

The Valley of Mexico is surrounded by mountains on all four sides creating a basin with only one small opening at the north. There main types of climate in the study area are subhumid temperate and dry temperate and both semi-cold semi-dry with rain in summer. The dry season is subdivided into two: dry hot (between March and May), with predominance of dry tropical air and high temperature, and dry cold (from November to February) characterised by polar-type air with low moisture content and temperature. The region receives anticyclonic systems, producing weak winds [34]. The expansion of Mexico City implicated the drying of the lakes and the expansion of the urban sprawl towards the lowlands. Thus, floods are a constant problem with inundated plains and urban settlements in a constant flood risk. In 2015, there were approximately 60,000 homes susceptible to flooding; these homes are dispersed in the grey and

In this case, the incoming flow to the system could be assigned to hydrograms coming from the upper part of the whole basin where some hydrometric stations are presented. The model was fed with eight hydrograms located each one in the river cut at the desire study area; they correspond to the vehicular bridges to cross the Texcoco-Tepepan highway over the riverbeds. Additionally, [35] provides local precipitation from four climatological stations (7, 25, 29 and 35) (**Figure 6**) located

in the periphery but representative of the study area.

**96**

The discharge from the eight streams coming from the upper part of the basin was represented with its correspondent histogram and feed to the model as initial condition. At this point, the structural measure was incorporated to the flood

**Figure 7.** *Hp acumulada considerada en la modelación.*

simulation process. This structural measure of mitigation is based on rectified and lining of the riverbed to have a perfect geometry. Thus, the flood simulation was done under two conditions (**Figure 8**): (a) with the current hydraulic infrastructure and (b) with the rectification of channels. Results were used to carry out the risk assessment under a scenario of urban growth in 20 and 50 years from 2015.

The FluBiDi model was run 10 times: 5 with current conditions and 5 with mitigation measure, from which the water depths and velocity values were obtained to (1) current conditions, (2) Tr = 20 years, (3) Tr = 50 years, (4) Tr = 100 years and (5) Tr = 200 years making each of the cells an area of interest and also to the historical condition for the remnants of the hurricanes Derby and Arlene. The urban growth is evaluated through the number of houses settled in the area; thus, in 2015 it was of 18,569, and its expected increment was favoured by the possible construction at the east of the new international airport of Mexico City. The number of houses expected to increase is of 52,800 in a 20-year planning horizon and up to 158,500 homes in 50 years.

#### **4.4 Results**

For each cell, it is possible to generate a limnigram as shown in the example of **Figure 9a** for a site in an area susceptible to flooding, but it is not the lowest, and some runoff is expected. **Figure 9b** shows the results of the model for the current infrastructure conditions, as well as the mitigation measures proposed for the four Tr analysed and the Arlene event in 2011.

Based on the hypothetical event and taking as reference Tr = 50 years, the maximum value under current conditions is 2232.1 masl passing with the mitigation measures at 2231.84 m. The major difference is that the inundated area takes at least 1 1/2 day to become flooded. Also, it is observed for Arlene that as a result of the mitigation work, the maximum flood levels decrease 28 cm (from 2232 to 2231.72) having the maximum value in 2 days later (from 2.3 to 4.3).

Due to the friendly output format from FluBiDi, results from the 10 mathematical simulations provided the envelope of maximum values of water depths for each cell and are presented in a map. Thus, one possible hazard scenario could be analysed throughout **Figure 10A** showing the current topographic conditions and **Figure 10B** considering the structural mitigation measure. Also, this kind of map was obtained for maximum velocities in each cell.

Comparing both maps, it was observed that the mitigation work effectively reduces those zones with higher elevations of water depth, although for lower elevation zones, water depths remain similar under both conditions. Channel rectification reduces that the river overspill; however, as this is a zone susceptible to inundation, it is impossible to eliminate the flood risk completely since there is the impact of the

**99**

**Figure 10.**

**Figure 9.**

*Example of limnigrams for each cell.*

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

local rain. Thus, an important extension of the floodplain remains inundated although with a minor water depth as well as a small number of vulnerable houses; as long as people know there is an inundated zone, construction housing is limited. This situation leaves the necessity to improve water management in the study zone, and one option is to add a regulation associated to the amount of houses projected where the construction based on the hazard maps is allowed or not. In particular, for 50-year growth projection, the percentage of increment is 8.51 times the houses in 2015. Both measures, structural and nonstructural, were assessed in order to have a risk map. [7] mentioned that it is highly recommendable to use a nonstructural measure than a structural one. However, as it was observed here, the combination of both measures

*Hazard flood maps considering as hydraulic infrastructure: (A) current conditions and (B) structural measure.*

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

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

**Figure 9.** *Example of limnigrams for each cell.*

*Recent Advances in Flood Risk Management*

158,500 homes in 50 years.

Tr analysed and the Arlene event in 2011.

having the maximum value in 2 days later (from 2.3 to 4.3).

was obtained for maximum velocities in each cell.

*Hydraulic infrastructure considered in the flood simulation using FluBiDi.*

**4.4 Results**

simulation process. This structural measure of mitigation is based on rectified and lining of the riverbed to have a perfect geometry. Thus, the flood simulation was done under two conditions (**Figure 8**): (a) with the current hydraulic infrastructure and (b) with the rectification of channels. Results were used to carry out the risk assessment under a scenario of urban growth in 20 and 50 years from 2015. The FluBiDi model was run 10 times: 5 with current conditions and 5 with mitigation measure, from which the water depths and velocity values were obtained to (1) current conditions, (2) Tr = 20 years, (3) Tr = 50 years, (4) Tr = 100 years and (5) Tr = 200 years making each of the cells an area of interest and also to the historical condition for the remnants of the hurricanes Derby and Arlene. The urban growth is evaluated through the number of houses settled in the area; thus, in 2015 it was of 18,569, and its expected increment was favoured by the possible construction at the east of the new international airport of Mexico City. The number of houses expected to increase is of 52,800 in a 20-year planning horizon and up to

For each cell, it is possible to generate a limnigram as shown in the example of **Figure 9a** for a site in an area susceptible to flooding, but it is not the lowest, and some runoff is expected. **Figure 9b** shows the results of the model for the current infrastructure conditions, as well as the mitigation measures proposed for the four

Based on the hypothetical event and taking as reference Tr = 50 years, the maximum value under current conditions is 2232.1 masl passing with the mitigation measures at 2231.84 m. The major difference is that the inundated area takes at least 1 1/2 day to become flooded. Also, it is observed for Arlene that as a result of the mitigation work, the maximum flood levels decrease 28 cm (from 2232 to 2231.72)

Due to the friendly output format from FluBiDi, results from the 10 mathemati-

cal simulations provided the envelope of maximum values of water depths for each cell and are presented in a map. Thus, one possible hazard scenario could be analysed throughout **Figure 10A** showing the current topographic conditions and **Figure 10B** considering the structural mitigation measure. Also, this kind of map

Comparing both maps, it was observed that the mitigation work effectively reduces those zones with higher elevations of water depth, although for lower elevation zones, water depths remain similar under both conditions. Channel rectification reduces that the river overspill; however, as this is a zone susceptible to inundation, it is impossible to eliminate the flood risk completely since there is the impact of the

**98**

**Figure 8.**

**Figure 10.**

*Hazard flood maps considering as hydraulic infrastructure: (A) current conditions and (B) structural measure.*

local rain. Thus, an important extension of the floodplain remains inundated although with a minor water depth as well as a small number of vulnerable houses; as long as people know there is an inundated zone, construction housing is limited. This situation leaves the necessity to improve water management in the study zone, and one option is to add a regulation associated to the amount of houses projected where the construction based on the hazard maps is allowed or not. In particular, for 50-year growth projection, the percentage of increment is 8.51 times the houses in 2015. Both measures, structural and nonstructural, were assessed in order to have a risk map. [7] mentioned that it is highly recommendable to use a nonstructural measure than a structural one. However, as it was observed here, the combination of both measures

improves results reducing considerably the probability of flood. Also, as [7] indicated, one finds that a better understanding of the system is crucial, since as a susceptible area to floods, it cannot be ignored and expected that there is no any flood risk. On the contrary it will continue but at different degree.
