Impact of highest maximum sustained wind speed and its duration on storm surges and hydrodynamics along Krishna–Godavari coast

Abstract

The storm surge and hydrodynamics along the Krishna–Godavari (K–G) basin are examined based on numerical experiments designed from assessing the landfalling cyclones in Bay of Bengal (BoB) over the past 38 years with respect to its highest maximum sustained wind speed and its duration. The model is validated with the observed water levels at the tide gauge stations at Visakhapatnam during 2013 Helen and 2014 Hudhud. Effect of gradual and rapid intensification of cyclones on the peak water levels and depth average currents are examined and the vulnerable locations are identified. The duration of intensification of a rapidly intensifying cyclone over the continental shelf contributed to about 10–18% increase in the peak water levels, whereas for the gradually intensifying cyclone the effect is trivial. The inclusion of the wave-setup increased the peak water levels up to 39% compared to those without wave-setup. In the deep water region, only rapidly intensifying cyclones affected the peak MWEs. Intensification over the continental slope region significantly increases the currents along the shelf region and coast. The effect on peak maximum depth averaged current extends up to 400 km from the landfall location. Thus, it is necessary to consider the effect of various combinations of the highest cyclone intensity and duration of intensification for identifying the worst scenarios for impact assessment of coastal processes and sediment transport. The study is quite useful in improving the storm surge prediction, in preparedness, risk evaluation, and vulnerability assessment of the coastal regions in the present changing climate.

Appendix

The generalized wave continuity equation is

$$\frac{{\partial^{2} \zeta }}{{\partial t^{2} }} + \tau_{0} \frac{\partial \zeta }{{\partial t}} + S_{p} \frac{{\partial \tilde{J}_{\lambda } }}{\partial \lambda } + \frac{{\partial \tilde{J}_{\phi } }}{\partial \phi } - S_{p} {\text{UH}}\frac{{\partial \tau_{0} }}{\partial \lambda } - {\text{VH}}\frac{{\partial \tau_{0} }}{\partial \phi } = 0$$

(8)

where

$$\tilde{J}_{\lambda } = S_{p} Q_{\lambda } \frac{\partial U}{{\partial \lambda }} - Q_{\phi } \frac{\partial U}{{\partial \phi }} + fQ_{\phi } - \frac{g}{2}S_{p} \frac{{\partial \zeta^{2} }}{\partial \lambda } - gS_{p} H\frac{\partial }{\partial \lambda }\left[ {\frac{{P_{s} }}{{g\rho_{0} }} - \alpha \eta } \right] + \frac{{\tau_{s\lambda ,winds} + \tau_{s\lambda ,waves} - \tau_{b\lambda } }}{{\rho_{0} }} + \left( {M_{\lambda } - D_{\lambda } } \right) + U\frac{\partial \zeta }{{\partial t}} + \tau_{0} Q_{\lambda } - gS_{p} H\frac{\partial \zeta }{{\partial \lambda }}$$

$$\tilde{J}_{\phi } = S_{p} Q_{\lambda } \frac{\partial V}{{\partial \lambda }} - Q_{\phi } \frac{\partial V}{{\partial \phi }} + fQ_{\lambda } - \frac{g}{2}\frac{{\partial \zeta^{2} }}{\partial \phi } - gH\frac{\partial }{\partial \phi }\left[ {\frac{{P_{s} }}{{g\rho_{0} }} - \alpha \eta } \right] + \frac{{\tau_{s\lambda ,winds} + \tau_{s\lambda ,waves} - \tau_{b\phi } }}{{\rho_{0} }} + \left( {M_{\phi } - D_{\phi } } \right) + V\frac{\partial \zeta }{{\partial t}} + \tau_{0} Q_{\phi } - gH\frac{\partial \zeta }{{\partial \phi }}$$

The vertically integrated momentum equations are

$$\frac{\partial U}{{\partial t}} + S_{p} U\frac{\partial U}{{\partial \lambda }} + V{ }\frac{\partial U}{{\partial \phi }} - fV = - gS_{p} \frac{\partial }{\partial \lambda }\left[ {\frac{{p_{s} }}{{g\rho_{0} }} + \zeta - \alpha \eta } \right] + \frac{{\tau_{s\lambda ,winds} + \tau_{s\lambda ,waves} - \tau_{b\lambda } }}{{\rho_{0} H}} + \frac{{M_{\lambda } - D_{\lambda } }}{H}$$

(9)

$$\frac{\partial V}{{\partial t}} + S_{p} U\frac{\partial V}{{\partial \lambda }} + V{ }\frac{\partial V}{{\partial \phi }} - fU = - g\frac{\partial }{\partial \phi }\left[ {\frac{{p_{s} }}{{g\rho_{0} }} + \zeta - \alpha \eta } \right] + \frac{{\tau_{s\phi ,winds} + \tau_{s\phi ,waves} - \tau_{b\phi } }}{{\rho_{0} H}} + \frac{{M_{\phi } - D_{\phi } }}{H}$$

(10)

where t = time, H = ζ + h = the total water depth, ζ = the deviation of the water surface from the mean water level, h = bathymetric depth; $\lambda$ = degrees longitude (east of Greenwich is positive) and $\phi$ = degrees latitude (north of equator is positive). $S_{p} = \cos \phi_{0} /\phi$, is a spherical co-ordinate conversion factor and $\phi_{0}$ is a reference latitude. U, V = the depth-averaged horizontal velocities in x- and y-directions, respectively, $Q_{\lambda } = UH,$ and $Q_{\phi } = VH,$ are fluxes per unit width in x- and y-directions, respectively, $f = 2{\Omega } sin\phi$ = the Coriolis parameter, ${\Omega }$ = the angular speed of the earth, P_s = the atmospheric pressure at free surface, g = acceleration due to gravity, $\eta$ = the Newtonian equilibrium tidal potential, $\alpha$ = the effective earth elasticity factor, $\rho_{0}$ = the reference density of water, $\tau_{s, winds} ,\tau_{s, waves }$ = the applied free surface stress due to winds and waves, respectively, $\tau_{b} =$ bottom stress, $M_{\lambda } ,M_{\phi }$ are lateral stress gradients, $D_{\lambda } ,D_{\phi }$ are momentum dispersion terms.

$\tau_{0}$ is a numerical parameter that optimizes the phase propagation properties (Kolar et al. 1994; Atkinson et al. 2004).

The SWAN governing action balance equation is

$$\begin{gathered} \frac{\partial N}{{\partial t}} + \frac{\partial }{\partial \lambda }\left[ {\left( {c_{\lambda } + U} \right)N} \right] + cos^{ - 1} \phi \frac{\partial }{\partial \phi }\left[ {\left( {c_{\phi } + V} \right)N{ }cos\phi } \right] + \frac{\partial }{\partial \theta }\left[ {c_{\theta } N} \right] \hfill \\ \;\;\; + \frac{\partial }{\partial \sigma }\left[ {c_{\sigma } N} \right] = \frac{{S_{tot} }}{\sigma } \hfill \\ \end{gathered}$$

(11)

where $c_{\lambda } ,c_{\phi }$ are the group velocities; U, V are the ambient current; $c_{\theta } ,c_{\sigma }$ are the propagation velocities in $\theta$- and $\sigma$- spaces; $S_{tot}$ is wave growth by wind action lost due to white capping, surf breaking and bottom friction and action exchanged between spectral components due to nonlinear effects in deep and shallow water.

The radiation stress gradients are computed by

$$\tau_{{sx,waves{ }}} = - \frac{{\partial S_{xx} }}{\partial x} - \frac{{\partial S_{xy} }}{\partial y}$$

(12)

$$\tau_{{sy,waves{ }}} = - \frac{{\partial S_{xy} }}{\partial x} - \frac{{\partial S_{yy} }}{\partial y}$$

(13)

where S_xx, S_xy, and S_yy are the wave radiation stresses (Longuet-Higgins and Stewart 1964; Battjes 1972) and are given as:

$$S_{xx} = \rho_{0} g\iint {\left( {\left( {n{ }cos^{2} \theta + n - \frac{1}{2}} \right)\sigma N} \right)d\sigma d\theta }$$

(14)

$$S_{xy} = \rho_{0} g\iint {\left( {n{ }sin\theta cos\theta \sigma N} \right)d\sigma d\theta }$$

(15)

$$S_{yy} = \rho_{0} g\iint {\left( {\left( {n{ }sin^{2} \theta + n - \frac{1}{2}} \right)\sigma N} \right)d\sigma d\theta }$$

(16)

where n is the ratio of group velocity to phase velocity.