Flood hazard assessment for the coastal urban floodplain using 1D/2D coupled hydrodynamic model

Abstract

In the current study, the one-dimensional/two-dimensional (1D/2D) coupled hydrodynamic model is used for the development of flood hazard maps for the frequently flooded coastal urban floodplain of the Surat city, India. The releases from the Ukai dam and tidal levels at the Arabian Sea are considered as upstream and downstream boundary conditions, respectively. The floodplain roughness was estimated using the existing land use land cover (LULC) classification, and the performance of the developed coupled hydrodynamic model was evaluated against the past flood data of year 2006 and 2013. The flood frequency analysis was carried out for peak inflow into the Ukai reservoir, and subsequently, the design flood hydrographs for different return periods have been developed. Finally, the simulated model output has been used to develop multi-parameter flood hazard maps defining the stability of people, vehicles, and buildings. More than 80% of the entire coastal urban floodplain of the Surat city is submerged during 100-year return period flood, with West and North zone of the city being the worst affected regions. Out of the total flooded area, nearly 20% area is under significant hazard for adults. The 27% area offers instability hazard to large four-wheel drive vehicles, whereas 14% area is affected with moderate to high hazard for buildings. The instability index for specific vehicle types is dominated by floating of small and large cars over 90% of the flooded area. Further, the combined hazard maps revealed that 14% of the flooded area is under very severe hazard category, posing a threat to the stability of people, vehicles, and buildings. The developed hazard maps will work as an effective non-structural measure for local administrative agencies to minimize the losses and better future planning.

Appendices

Appendix 1

The Saint–Venant equation represented by conservation of mass and momentum equation as

Continuity equation (mass):

$$\frac{\partial Q}{{\partial x}} + \frac{\partial A}{{\partial t}} = q$$

(5)

Momentum equation:

$$\frac{\partial Q}{{\partial t}} + \frac{{\partial \left( {\alpha \frac{{Q^{2} }}{A}} \right)}}{\partial x} + gA\frac{\partial h}{{\partial x}} + \frac{gQ\left| Q \right|}{{C^{2} AR}} = 0$$

(6)

Here, Q = discharge along the channel (m³/s), A = cross-sectional flow area (m²), q = lateral inflow (m²/s), t = time (sec) and x = distance (m), $\alpha$ = momentum distribution coefficient, g = acceleration due to gravity (m/s²), h = free surface elevation (m), C = Chezy’s resistance coefficient (m^1/2/s), R = hydraulic radius (m)

The equations are numerically solved by implicit finite difference (six-point Abbot) scheme (Abbott and Ionescu 1967).

Appendix 2

The simplified form of depth-averaged Navier Stokes equations as

$$\frac{\partial \zeta }{{\partial t}} + \frac{\partial p}{{\partial x}} + \frac{\partial q}{{\partial y}} = \frac{\partial d}{{\partial t}}$$

(7)

$$\frac{\partial p}{{\partial t}} + \frac{\partial }{\partial x} \left( {\frac{{p^{2} }}{h}} \right) + \frac{\partial }{\partial y} \left( \frac{pq}{h} \right) + gh\frac{\partial \zeta }{{\partial x}} + \frac{{gp\sqrt {p^{2} + q^{2} } }}{{C^{2} .h^{2} }} - \frac{1}{{\rho_{w} }} + \left[ {\frac{\partial }{\partial x}\left( {h\tau_{xx} } \right) + \frac{\partial }{\partial y} \left( {h\tau_{xy} } \right)} \right] - \Omega q - fVV_{x} + \frac{h}{\rho w} \frac{\partial }{\partial x} \left( {p_{a} } \right) = 0$$

(8)

$$\frac{\partial q}{{\partial t}} + \frac{\partial }{\partial y} \left( {\frac{{q^{2} }}{h}} \right) + \frac{\partial }{\partial x} \left( \frac{pq}{h} \right) + gh\frac{\partial \zeta }{{\partial y}} + \frac{{gq\sqrt {p^{2} + q^{2} } }}{{C^{2} .h^{2} }} - \frac{1}{{\rho_{w} }} + \left[ {\frac{\partial }{\partial y}\left( {h\tau_{yy} } \right) + \frac{\partial }{\partial x} \left( {h\tau_{xy} } \right)} \right] + \Omega q - fVV_{y} + \frac{h}{\rho w} \frac{\partial }{\partial y} \left( {p_{a} } \right) = 0$$

(9)

Here, h = water, d = time varying depth (m), $\upzeta$ = surface elevation (m), p, q = flux densities in x and y direction (m³/s/m), C = Chezy’s constant (m^1/2/s), g = acceleration due to gravity (m/s²), f = wind friction factor, V, Vx, Vy = wind speed and its component in x and y direction (m/s), Ω = Coriolis parameter, latitude dependent (s⁻¹), P_a = atmospheric pressure (kg/m/s²), ρw = density of water (kg/m³), t = time (s), τ_xx, τ_xy, τ_yy = component of effective stress (N/m²).

Appendix 3

Statistical performance indices, root mean square error (RMSE) is defined as

$${\text{RMSE}} = \left[ {\frac{{\mathop \sum \nolimits_{i = 0}^{n} \left( {y_{o} - y_{s} } \right)^{2} }}{N}} \right]^{\frac{1}{2}}$$

(10)

Here, ${y}_{o}$ = observed value of the variable, ${y}_{s}$ = simulated value of the variable

The RMSE is a measure of scatter of the residuals, and an RMSE value close to zero represents the good performance of the model.