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

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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.

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  • Bernier NB, Thompson KR (2006) Predicting the frequency of storm surges and extreme sea levels in the northwest Atlantic. J Geophys Res 111:C10009. doi:10.1029/2005JC003168

  • Bernier NB, Thompson KR, Ou J, Ritchie H (2007) Mapping the return periods of extreme sea levels: allowing for short sea level records, seasonality, and climate change. Glob Planet Chang 57:139–150. doi:10.1016/j.gloplacha.2006.11.027

    Article  Google Scholar 

  • Black KP, Hatton DN, Colman R (1990) Prediction of extreme sea levels in northern Port Phillip Bay and the possible effect of a rise in mean sea level. Report to the Board of Works, Victorian Institute of Marine Science, Melbourne, Australia

  • Church JA, Hunter JR, McInnes KL, White NJ (2006) Sea-level rise around the Australian coastline and the changing frequency of extreme sea-level events. Aust Meteorol Mag 55:253–260

    Google Scholar 

  • Coles SG (2001) An introduction to statistical modeling of extreme values. Springer, London

    Google Scholar 

  • CSIRO and Bureau of Meteorology (2007) Climate change in Australia. Technical report, CSIRO and Bureau of Meteorology, Australia, 140 pp. Available at

  • Flather RA, Williams JA (2000) Climate change effects on storm surges: methodologies and results. In: Climate scenarios for water-related and coastal impacts. ECLAT-2 Workshop Report 3, KNMI, The Netherlands

  • Foreman GG (1977) Manual for tidal heights analysis and prediction, Pacific Marine Science Report 77-10. Institute of Ocean Sciences, Victoria, Canada, 98 pp

  • Godin G (1972) The analysis of tides. University of Toronto Press, Toronto

    Google Scholar 

  • Horsburgh KJ, Wilson C (2007) Tide-surge interaction and its role in the distribution of surge residuals in the North Sea. J Geophys Res 112:C08003. doi:10.1029/2006JC004033

  • Hubbert GD, McInnes KL (1999) A storm surge inundation model for coastal planning and impact studies. J Coast Res 15:168–185

    Google Scholar 

  • Hubbert GD, Leslie LM, Manton MJ (1990) A storm surge model for the Australian region. Q J R Meteorol Soc 116:1005–1020

    Article  Google Scholar 

  • Hunter J (2009) Estimating sea-level extremes under conditions of uncertain sea-level rise. Clim Chang (submitted)

  • IPCC (2001) Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK and New York, USA, 881 pp

  • IPCC (2007) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK and New York, USA, 996 pp

  • Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Leetmaa A, Reynolds B, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–471

    Article  Google Scholar 

  • Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25:1287–1304

    Article  Google Scholar 

  • Lionello P, Elvini E, Nizzero A (2003) Ocean waves and storm surges in the Adriatic Sea: intercomparison between the present and the doubled CO2 climate scenarios. Clim Res 23:217–231

    Article  Google Scholar 

  • Lowe JA, Gregory JM, Flather RA (2001) Changes in the occurrence of storm surges around the United Kingdom under a future climate scenario using a dynamic storm surge model driven by the Hadley Centre climate models. Clim Dyn 18(3–4):179–188

    Article  Google Scholar 

  • McGranahan G, Balk D, Anderson B (2007) The rising tide: assessing the risks of climate change and human settlements in low elevation coastal zones. Environ Urban 19(1):17–37

    Article  Google Scholar 

  • McInnes KL, Hubbert GD (2003) A numerical modeling study of storm surges in Bass Strait. Aust Meteorol Mag 52:143–156

    Google Scholar 

  • McInnes KL, Walsh KJE, Hubbert GD, Beer T (2003) Impact of sea-level rise and storm surges on a coastal community. Nat Hazards 30(2):187–207

    Article  Google Scholar 

  • McInnes KL, Macadam I, Hubbert GD, Abbs DJ, Bathols JA (2005) Climate change in Eastern Victoria Stage 2 report: the effect of climate change on storm surges. Report to the Gippsland Coastal Board, CSIRO Marine and Atmospheric Research, Aspendale, Victoria, Australia, 37 pp. Available at

  • McInnes KL, O’Grady JG, Hubbert GD (2009) Modelling sea level extremes from surges and wave setup for climate change assessments in southern Australia. J Coast Res (accepted)

  • Messinger F. Arakawa A (1976) Numerical methods used in atmospheric models. GARP publication series no. 17, WMO/ICSU Joint Organizing Committee, Geneva, Switzerland, 64 pp

  • Miller MJ, Pearce RP (1974) Numerical model of a cumulonimbus. Q J R Meteorol Soc 100:133–154

    Article  Google Scholar 

  • Miller MJ, Thorpe AJ (1981) Radiation conditions for the lateral boundaries of limited-area numerical models. Q J R Meteorol Soc 107:615–628

    Article  Google Scholar 

  • Mitrovica JX (2003) Recent controversies in predicting post-glacial sea-level change. Quat Sci Rev 22(2–4):127–133. doi:10.1016/S0277-3791(02)00225-1

    Article  Google Scholar 

  • Nakićenović N, Swart R (eds) (2000) Special Report on Emissions Scenarios, a Special Report of Working Group III of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK and New York, USA, 599 pp

  • Pugh DT, Vassie JM (1980) Applications of the joint probability method for extreme sea level computations. Proc Inst Civil Eng Part 2 69:959–975

    Google Scholar 

  • Signell RP, Butman B (1992) Modeling tidal exchange and dispersion in Boston Harbor. J Geophys Res 97:15591–15606

    Article  Google Scholar 

  • Smith SD, Banke EG (1975) Variation of the sea surface drag coefficient with wind speed. Q J R Meteorol Soc 101:665–673

    Article  Google Scholar 

  • Tawn JA, Vassie JM (1989) Extreme sea levels: the joint probabilities method revisited and revised. Proc Inst Civil Eng Part 2 87:429–442

    Google Scholar 

  • Tawn JA, Vassie JM (1990) Spatial transfer of extreme sea level data for use in the revised joint probability method. Proc Inst Civil Eng Part 2 89:433–438

    Google Scholar 

  • Wealands S, Grayson, RB, McMaster M, Tan KS, Provis D (2002) Representing terrain accurately for flood modelling in large coastal lagoons: a case study of the Gippsland Lakes. In: Proceedings of the 27th Hydrology and Water Resources Symposium, Melbourne, Australia, 20–23 May 2002

  • Woth K (2005) North Sea storm surge statistics based on projections in a warmer climate: how important are the driving GCM and the chosen emission scenario? Geophys Res Lett 32:L22708. doi:10.1029/2005GL023762

  • Woth K, Weisse R, von Storch H (2006) Climate change and North Sea storm surge extremes: an ensemble study of storm surge extremes expected in a changed climate projected by four different Regional Climate Models. Ocean Dyn 56:3–15. doi:10.1007/s10236-005-0024-3

    Article  Google Scholar 

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The authors would like to acknowledge Rodger Grayson and Kim Seong Tan of the University of Melbourne for kindly making available tide gauge data within the Gippsland Lakes, the Port of Melbourne Corporation for tide gauge data at Port Franklin and Port Welshpool, Melbourne Water Corporation for tide gauge data at St. Kilda and Frankston and Mr. Paul Davill of the National Tidal Centre of the Australian Bureau of Meteorology for providing tide gauge data from other locations and assisting in the processing of tide gauge data supplied by other agencies. They would also like to thank Mr. Ray Rice of Cardno Lawson and Treloar Pty Ltd and Graeme Ball of the Bureau of Meteorology for providing wind data from the Kingfish B Oil Platform. This work was funded by the Gippsland Coastal Board through a grant from the Australian Department of Environment and Heritage, the Antarctic Climate and Ecosystem CRC, the Australian Department of Climate Change and the CSIRO Climate Adaptation National Research Flagship through the Australian Climate Change Science Program and the Victorian Department of Sustainability and Environment. The authors are also grateful to Mr. Bill Mitchell of the National Tidal Centre of the Bureau of Meteorology and Dr. Mark Hemer and Dr. Tom Beer from the Centre for Australian Weather and Climate Research, a partnership between CSIRO and the Bureau of Meteorology, for useful discussions on the material presented in this manuscript.

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Correspondence to K. L. McInnes.



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:

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

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:

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

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:

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

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

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

where n has the value 0.03 s m1/3. This formulation ensures that the drag coefficient increases with decreasing water depth and is applied to water depths greater than 1 m. Equations 13 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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McInnes, K.L., Macadam, I., Hubbert, G.D. et al. A modelling approach for estimating the frequency of sea level extremes and the impact of climate change in southeast Australia. Nat Hazards 51, 115–137 (2009).

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