A modelling approach for estimating the frequency of sea level extremes and the impact of climate change in southeast Australia

Abstract

An efficient approach for evaluating storm tide return levels along the southeastern coastline of Australia under present and future climate conditions is described. Storm surge height probabilities for the present climate are estimated using hydrodynamic model simulations of surges identified in recent tide gauge records. Tides are then accounted for using a joint probability method. Storm tide height return levels obtained in this way are similar to those obtained from the direct analysis of tide gauge records. The impact of climate change on extreme sea levels is explored by adding a variety of estimates of mean sea level rise and by forcing the model with modified wind data. It is shown that climate change has the potential to reduce average recurrence intervals of present climate 1 in 100 year storm tide levels along much of the northern Bass Strait coast to between 1 and 2 years by the year 2070.

Appendix

The model used in this study is a two-dimensional hydrodynamic model called GCOM2D. The model solves the depth-averaged hydrodynamic equations for currents and sea levels on a regular Cartesian grid:

$$ \begin{gathered} \frac{\partial U}{\partial t} = fV - mg\frac{\partial \zeta }{\partial x} - \frac{m}{{\rho_{{{\upomega}}} }}\frac{\partial P}{\partial x} - m\left( {U\frac{\partial U}{\partial x} + V\frac{\partial U}{\partial y}} \right) + \frac{1}{{\rho_{{{\upomega}}} H}}\left( {\tau_{sx} - \tau_{bx} } \right) - \nu \nabla^{2} U, \\ \end{gathered} $$

(2)

$$ \begin{gathered} \frac{\partial V}{\partial t} = - fU - mg\frac{\partial \zeta }{\partial y} - \frac{m}{{\rho_{{{\upomega}}} }}\frac{\partial P}{\partial y} - m\left( {U\frac{\partial V}{\partial x} + V\frac{\partial V}{\partial y}} \right) + \frac{1}{{\rho_{{{\upomega}}} H}}\left( {\tau_{sy} - \tau_{by} } \right) - \nu \nabla^{2} V, \\ \end{gathered} $$

(3)

$$ \frac{\partial \zeta }{\partial t} = - m^{2} \left[ {\frac{\partial }{\partial x}\left( {\frac{UH}{m}} \right) + \frac{\partial }{\partial y}\left( {\frac{VH}{m}} \right)} \right]\,, $$

(4)

where U and V are the depth averaged currents in the x and y coordinate directions, respectively, H is the total depth, $\zeta$ is the surface elevation, f is the Coriolis parameter, g is the acceleration due to gravity, m is the map factor (a scaling which depends on the chosen map projection of the model grid), P is the atmospheric surface pressure, $\rho_{\text{w}}$ is the water density, $\nu$ is the coefficient of lateral eddy diffusion and has a value of 0.2, $\tau_{sx}$ and $\tau_{by}$, the bottom frictional stress in the x and y directions, respectively.

The surface wind stress components are computed using the quadratic relationship:

$$ \tau_{sx} = C_{\text{D}} \rho_{\text{a}} \left|{\mathbf{u_{a}} } \right|u_{\text{a}},\quad\tau_{sy} =C_{\text{D}} \rho_{\text{a}} \left| {\mathbf{u_{a}} }\right|v_{\text{a}} , $$

(5)

where $\left| {\mathbf{u_{a}} } \right| = \left( {u_{\text{a}}^{2} + v_{\text{a}}^{2} } \right)^{{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}$ u _a and v _a are the horizontal components of wind velocity at anemometer height, $\rho_{\text{a}}$ is the density of air and C _D is the drag coefficient based on Smith and Banke (1975) and expressed as follows:

$$ \begin{gathered} C_{\text{D}} = \left[ {0.63 + 0.066\left|{\mathbf{u_{a}} } \right|} \right] \times 10^{ - 3,}\quad\left| {\mathbf{u_{a}} } \right| < 25 {\text{ ms}}^{ -1} ; \hfill\\ C_{\text{D}} = \left[ {2.28 + 0.033\left( {\left|{\mathbf{u_{a}} } \right| - 25} \right)} \right] \times 10^{ -3,} \quad\left| {\mathbf{u_{a} }} \right| \ge {\text{ 25 ms}}^{ - 1} . \hfill\\ \end{gathered} $$

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The bottom stress is represented by a Manning’s n depth-dependent friction relation following Signell and Butman (1992):

$$ \tau_{\rm bx} = \rho_{\rm w} \frac{gn^{2}}{\left( {H + \zeta } \right)^{1/3}}\left(U^{2}+V^{2} \right)^{1/2} U,\quad \tau_{\rm by} = \rho_{\rm w} \frac{gn^{2}}{\left( {H + \zeta } \right)^{1/3}}\left( {U^{2} + V^{2}} \right)^{1/2}V, $$

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where n has the value 0.03 s m^1/3. This formulation ensures that the drag coefficient increases with decreasing water depth and is applied to water depths greater than 1 m. Equations 1–3 are solved on an Arakawa-C grid (Messinger and Arakawa 1976). The continuity equation and the gravity wave and Coriolis terms in the momentum equations are solved on the shortest time step, the ‘adjustment step’, using the forward-backward method. The non-linear advective terms are solved on an intermediate ‘advective time step’ using the two-time-level method of Miller and Pearce (1974). Finally, on the longest time step, the so-called physics step, the surface wind stress, bottom friction stress and atmospheric pressure gradient terms are solved using a backward-implicit method. This approach is efficient in oceanographic models with free surfaces because of the large disparity between advective speeds and gravity-wave phase speeds in deep water. Details of the solution procedure can be found in Hubbert et al. (1990).

The application of boundary conditions for water currents perpendicular to the lateral boundaries of all simulations (nested or stand alone) are as follows: On outflow boundaries, a radiation boundary condition, as described in Miller and Thorpe (1981) is applied to the velocity field to prevent the build up of wave energy within the numerical domain. On inflow boundaries, a zero-gradient condition is applied at velocity grid points.

The model simulations in this study are carried out solely with meteorological forcing since the tides are treated separately and so the water levels,$\zeta^{{}}$, on the lateral boundaries due to meteorological conditions are specified as the deviation of the surface pressure from a mean value $\bar{P} = 1013$ hPa according to

$$ \zeta^{\text{M}} = (\bar{P} - P)/\rho_{\text{w}} g $$

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