Development of a tropical storm surge prediction system for Australia

Journal Pre-proof Development of a Tropical Storm Surge Prediction System for Australia

J. Freeman, M. Velic, F. Colberg, D. Greenslade, P. Divakaran, J. Kepert PII:

S0924-7963(20)30013-0

DOI:

https://doi.org/10.1016/j.jmarsys.2020.103317

Reference:

MARSYS 103317

To appear in:

Journal of Marine Systems

Received date:

13 May 2019

Revised date:

10 February 2020

Accepted date:

12 February 2020

Please cite this article as: J. Freeman, M. Velic, F. Colberg, et al., Development of a Tropical Storm Surge Prediction System for Australia, Journal of Marine Systems(2020), https://doi.org/10.1016/j.jmarsys.2020.103317

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© 2020 Published by Elsevier.

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Development of a Tropical Storm Surge Prediction System for Australia J. Freemana , M. Velica , F. Colberga , D. Greensladea , P. Divakarana , J. Keperta of Meteorology, Melbourne, Victoria, Australia

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a Bureau

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Abstract

The Australian tropical storm surge forecasting system is described, including

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the development of a tropical cyclone atmospheric forcing model and the config-

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uration of the ocean hydrodynamic model. The atmospheric model is developed as an asymmetric modified Rankine vortex and the resulting time dependent

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stress and pressure fields are applied to a shallow water hydrodynamic model. The system was benchmarked against seven contemporary tropical cyclones oc-

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curring within the northern Australian region between 2011–2017. The model storm surge response to the synthetic forcing was compared against tide gauge observations. For the seven test cases, the root mean square error for maximum

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sea level was 0.30 m, the mean absolute error was 0.21 m and the mean bias

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error was 0.11 m. For peak timings the the root mean square error of the model was 62 minutes, the mean absolute error was 48 minutes and the mean bias error was 8 minutes. Surface forcing fields were compared against observations for TC Yasi and found to be in general agreement.

1. Introduction Storm surges resulting from intense atmospheric forcing due to Tropical Cyclones (TC) have caused significant impacts on the Australian coastline, includ-

Email address: [email protected] (J. Freeman)

Preprint submitted to Elsevier

February 17, 2020

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ing the loss of lives, damage to infrastructure and negative effects on industries. Within the Australian region most TCs occur between November and April with an average of 11 TCs per year [9]. The forecasting of Tropical Cyclone induced storm surge is of vital importance for the safeguarding of Australian communities. Some of the earliest reports of storm surge due to TC interactions with

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the Australian coastline describe large impactful events. In 1899, TC Mahina

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crossed the Australian coast at Princess Charlotte Bay in Queensland and resulted in a storm surge estimated to be 12–14 metres [27] with at least 300

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known fatalities [41]. Further historical accounts document storm surges, resulting from TC events, ranging from 3.6 m at Mackay in January 1918, a 4.65

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m increase in the sea level over the normal tide level at Innisfail in March 1918

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with associated flooding of Mission Beach. In 1934 a tropical cyclone crossed the coast near Cape Tribulation with a reported 9.1 m storm surge at Bailey

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Creek. In January 1967, TC Dina developed in the central Coral Sea and tracked southwest before recurving just off the Queensland coast between Gladstone and Bundaberg. As it passed over Sandy Cape, a central pressure of 944.8 hPa was

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recorded and high water rose to 10 m above normal levels [4]

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Contemporary examples impacting Australian coastal communities include TC Yasi, which was one of the most powerful storms to cross the Queensland coastline. Yasi made landfall as a category 5 system during the 2011 TC season, and caused a storm surge greater than 5 metres at Cardwell. Inundation of the surrounding coastal regions occurred 6-9 hours later at high tide [34]. The economic impact of Yasi was estimated at $800M [33]. TC Debbie crossed the Queensland coast as a category 4 system on 28 March 2017 and resulted in a 2.6 metre storm surge at Laguna Quays. The operational forecasting of storm surge has been undertaken by many

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centres including the Met Office’s short-range storm surge ensemble prediction system for the UK [12], which has been operational since 2009, the Dutch Meteorological Institute’s medium-range system for the Dutch coast [7], which is based on the ECMWF atmospheric ensemble, and the Meteorological Service of Canada’s ensemble storm surge prediction system [2]. Examples of operational systems used to forecast the storm surge impacts

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specifically due to TCs include the Japan Meteorological Agency’s (JMA) depth

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averaged shallow water model which is forced by JMA’s dynamical mesoscale atmospheric model [19, 18, 17] and the U. S. National Weather Service runs

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the Sea, Lake and Overland Surges from Hurricanes (SLOSH) model [20] for a range of storm surge predictions and hazard assessments [13].

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JMA have been running numerical prediction models for TCs for the Japanese

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region since 1998 [19, 18]. The hydrodynamic model is based on the depth averaged shallow water equations and an adaptive mesh with a spatial resolution ranging from ∼1 km near the coast to 16 km over deep water. The domain

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covers 20◦ N–50◦ N and 117.5◦ E–150◦ E. The model is forced by surface winds and pressure from the JMA mesoscale atmospheric model on an ongoing basis

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providing 39-hour forecasts every 3 hours. When there is a TC in the Japan

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region, an additional 5 model runs are undertaken, forced with a simple parametric TC model merged into the atmospheric forcing. These 5 extra forecasts are based on TC tracks that are shifted from the official forecast track in position and propagation speed in order to take account of the forecast uncertainty. Gridded astronomical tides are added to the predicted storm surge to provide forecasts of total sea-level. Wave set-up is not currently included. JMA run a similar storm surge forecast for the Asian region over the domain 0 to 46◦ N and 95◦ E to 160◦ E at a spatial resolution of ∼3.7 km. The U.S. NWS uses the Sea, Lake and Overland Surges from Hurricanes

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(SLOSH) model [20] for a range of storm surge predictions and hazard assessments [13]. For real-time TC storm surge forecasts,it is applied in deterministic mode over 32 domains covering the U.S. East coast and offshore regions. The position of the forecast track determines which domains will be run. SLOSH forcing is provided by parametric TC information from the official forecast (location, radius-to-maximum-winds, pressure gradient). Using best track para-

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metric TC information for a set of 13 storms, SLOSH was found to be accurate

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to within 20% of the peak surge value [13].

In addition to the deterministic forecast, probabilistic forecasts are derived

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from the Probabilistic Storm Surge model (P-surge), which is comprised of an ensemble of SLOSH forecasts. The forcing for each ensemble member is created

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by modifying the official forecast TC position, size and intensity based on past

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errors [40].

Within the Bureau of Meteorology’s Tropical Cyclone Warning Centres in

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Queensland and the Northern Territory, the SEAtide system has provided operational storm surge forecasts [36]. SEAtide is a parametric modelling system, developed following the approach in Harper [15]. Geographical regions cover-

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ing the coastline of interest are established and many thousands of potential

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tropical cyclone scenarios are constructed in order to determine the storm tide response in each region as a function of the storm parameters. This information is then summarised into a further numerical parametric model for each region that enables rapid retrieval of response information. The system presented in this work provides the basis for the core components of the Australian tropical ensemble storm surge prediction system, which is one of three systems that comprise the Australian Storm Surge Forecasting system. The other components of the suite are the national storm surge system for forecasting anomalous sea levels due to mid-latitude storms and tropical lows [1],

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and an aggregate sea-level monitoring and alert system at tide gauge locations [39]. This work focuses on the atmospheric and ocean model development and verification of the storm surge forecasting system forced by best track models. The tropical storm surge forecasting system has been running operationally since October 2017 [14]. This system is triggered by tropical cyclone events occurring in the Australian region, defined by the World Meteorological Organ-

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isation as 90E to 160E in the Southern Hemisphere. For each tropical cyclone,

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an ensemble of storm characteristics is created following DeMaria et al. [8]. Each realisation represents a statistical perturbation of the official forecast track in

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order to quantify uncertainties in the tropical cyclones evolution. The ensemble of realisations represents the storm’s track, size, and intensity. Synthetic at-

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mospheric 10 metre wind stress and surface pressure fields are constructed for

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each ensemble member and these fields subsequently drive the hydrodynamic storm surge model. Descriptive statistics are then calculated from the ensemble

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of hydrodynamic models from which forecast guidance concerning the threat of storm surge is provided.

Here, we develop the Tropical Cyclone atmospheric forcing and ocean hy-

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drodynamic models which form the major components of the ensemble storm

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surge forecast system. We benchmark the model with seven contemporary tropical cyclones occurring in the Australian region and compare the model storm surge with coastal tide gauge observations. The benchmark cases were chosen according to the availability of quality controlled best track analysis data and, for some of the storms, the availability of tide gauge data at locations close to landfall of the storm. Each benchmark storm system was of varying intensity, track and duration, resulting in a range of coastal surge events from which the tropical Australian storm surge system was assessed.

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2. Surge Model The depth averaged momentum and continuity equations in cartesian coordinates for an incompressible fluid with the Bousinessq approximation are,

(1) (2)

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∂U τs − τb + U · ∇U + f × U = −g∇ (ζ − ζa ) + + A∇2 U ∂t ρ(h + ζ) ∂ζ + (h + ζ)∇ · U = 0 ∂t

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where U = (u, v) is the depth averaged velocity, Z

ζ

udz,

(3)

h

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1 U= h+ζ

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t is time, f is the upward pointing unit vector scaled by the Coriolis term, g is acceleration due to gravity, h is the water depth, ζ is the free surface height

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and ζa = −Pa /ρg is the surface elevation due to the inverse barometer effect where Pa is the atmospheric sea level pressure and ρ is density, τs and τb are the

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surface and bottom stress respectively and A = 5×10−5 m2 s−1 is the horizontal √ √ viscosity. The bottom quadratic stress is τb = (γ u2 + v 2 u, γ u2 + v 2 v) where

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γ = 10−3 is the bottom friction coefficient. At the domain boundaries the normal component of the depth averaged velocity is subject to the Flather [11] boundary condition whilst the sea level, ζ, is subject to a Chapman [5] boundary condition with zero external forcing. The initial condition is a zero surface level, ζ(x, y) = 0, and zero average velocity, U (x, y) = 0. The depth averaged equations in 1 and 2 are solved in a curvilinear coordinate system using the Regional Ocean Modeling System (ROMS) software [37]. For all model runs a 2 second time step is used and instantaneous average

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Figure 1: Tropical domain grid. The average grid resolution is 2.520 km with a minimum resolution of 1.878 km and coarsening to a resolution of 4.075 km over the deep ocean. The grid size is 465×3137 cells.

velocity and sea level anomaly fields are output at 10 minute intervals. The

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model grid is a coastline following curvilinear grid spanning 36.1◦ to 6.44◦ S and 105.08◦ to 162.2◦ E. The average grid resolution is 2.520 km with a finest resolu-

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tion of 1.878 km and coarsening to a resolution of 4.075 km over the deep ocean. The grid size is 465×3137 cells. The model bathymetry is interpolated from the

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Geoscience Australia 500 metre bathymetric dataset [42] onto the ROMS model grid using a bilinear interpolation method. The land-sea mask was generated using the zero contour level of the interpolated bathymetry and manually post processed to remove single cell land points, isolated wet cells and single cell channels and bays. The model domain and bathymetry is shown in Figure 1. Wetting and drying of wet cells is activated with a critical depth of 0.1 m. The sea level at coastal cells is defined as,

ζsl = ζ + ζsu ,

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(4)

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where ζsu is the contribution to the sea level due to wave setup. Astronomical tides are linearly added for operational forecasts but are not considered here. The wave setup component of the sea level is given by [28]

ζsu = 0.07936Hs S

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2πHs gTp2

− 14 ,

(5)

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where Hs is significant wave height, Tp is peak period, g is acceleration due to

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gravity and S is the bathymetric slope. S is determined from the interpolated bathymetry as,

(6)

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tan(S) = k∇hk,

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Significant wave height and peak period is given by the AUSWAVE-R model [3]. AUSWAVE-R is a regional WAVEWATCH III forecast model spanning

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the region 60◦ -12◦ N, 69◦ E-180◦ E with a 0.1◦ resolution. The AUSWAVE-R model is forced by NWP winds and produces 3 day wave forecast fields at 1

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hour temporal resolution. To determine the wave setup at coastal locations, the AUSWAVE-R Hs and Tp fields are spatially interpolated onto the ROMS model

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grid using a natural neighbour interpolation method and we linearly interpolate

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the Hs and Tp fields in time to match the ocean model output timesteps.

3. Atmospheric Model Atmospheric forcing for the surge model run is determined from the Bureau of Meteorology’s archive of best track tropical cyclone data which contains tropical cyclone locations and intensities at hourly intervals for storms occurring within the Australian region. For each historical storm scenario a modified Rankine vortex is generated which includes storm forward motion induced asymmetry and an inflow angle correction to the gradient wind field. The velocity profile of the modified Rankine vortex is calculated through the

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radial integration of the axisymmetric vorticity, ωa , [24]

V (r) =

1 r

Z

r

sωa (s)ds.

(7)

0

The vorticity is defined as the piecewise function

  −1−α   r cω m rm

r > rm ,

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r ≤ rm (8)

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ωa (r) =

    ωm

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where rm is the radius to maximum winds in metres, ωm is the maximum vorticity in seconds−1 , α is a decay rate constant with 0 < α < 1 and c =

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(1 − α)/2.

V (r) =

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Substitution of equation 8 into to equation 7 gives,  R  1 r    r 0 sωa (s)ds

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    1 R rm sω (s)ds + a r 0

r ≤ rm (9) 1 r

Rr rmax

sωa (s)ds

r > rm ,

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from which the axisymmetric radial velocity is,

V (r) =

   rωm    2    r2 ω   m2r m −

r ≤ rm (10)   1−α  r r(1−α) 1 − rm 2 rm ωm c

r > rm

To enforce continuity of vorticity across rm a blending function is applied to equation 8 in accordance with Kepert [24]. The vorticity is modified by multiplication with a polynomial blending function, centred about rm , prior to

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evaluating the integral in equation 9,  ωa (r) = wωm + [1 − w(r)] cωm

r rm

−1−α (11)

where w is the blending function,

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si ≤ −1

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(1+si )5 (128−325si +345s2i −175s3i +35s4i ) 256

−1 < si < 1

(12)

si ≥ 1

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    1        w(r) = w(si ) = 1 −          0

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si is the scaled radial distance,

r − ri Lb

(13)

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si =

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and the blending distance, Lb , is centred on rm . We use a blending distance of Lb = 15 km. Application of the blending function results in an underestimation

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of Vm after integration. To recover the prescribed Vm we estimate the initial maximum vorticity, ωm , as,

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ωm =

aVm rm

(14)

where a is set to an initial value of 2.06 (which is 3% larger than the value in equation 10). We then integrate the blended vorticity equation (equation 8 with the blending function defined in equation 11) and iteratively update the value of the coefficient a = Vm /Vm∗ , where Vm∗ is the current estimate of the maximum velocity, until the term a equals 1.

ωm =

Vm Vm∗

10



Vm rm

 (15)

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During each iteration we also update the value for the vortex decay parameter, α. Calculation of the vortex decay parameter is constrained by the the available radial velocity data present in the best track data. In cases where only Vm and rm are present, α is determined using the climatological relationship [25],

(16)

of

α = 0.1147 + 0.0055Vm − 0.001(φ − 25)

where φ is latitide in degrees. When Vm , rm and the velocity at another radius

α=



Vm v1



rm r1



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log

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are present we determine α as the ratio of logarithms,



(17)

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log

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For all other cases we perfrom a least squares fit to the data, n P

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where,

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α=

(log Vm ) xi − xi yi

i=1

n P

i=1

,

 xi = log

(18)

x2i

ri rm



yi = log (vi ) .

(19) (20)

The vortex described by equation 10 is axisymmetric. In general the gradient wind field of a tropical cyclone will be asymmetric due to the forward motion of the storm. We introduce storm asymmetry by radially modifying the velocity distribution to include the forward velocity of the storm,

V (r, θ) = V (r) + δf m Vf m sin(θ)

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(21)

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where θ is the angle relative to the storm direction, δf m is the fraction of forward motion and is in the range 0.5–1.0, and Vf m is the storm forward motion velocity. For southern hemisphere storms, Vm is nominally located 90◦ anticlockwise to the storm direction vector. However, the location of Vm can be anywhere from 65◦ to 114◦ [15]. In the subsequent model we locate the storm maximum velocity at 65◦ anticlockwise from the storm direction and set δf m = 0.5. The storm

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forward motion velocity is calculated using a forward difference of best track

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fix data where the distance covered by the storm over the time period between consecutive fixes is determined by the Haversine formula. Setting Vf m to zero

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reduces the vortex to the axisymmetric structure.

We integrate equation 8 a total of 9 times for each best track fix, with each

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velocity profile describing the north, north east, east, south east, south, south

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west, west and north west sectors. The best track velocity data is modified according to equation 21 and we use the median radius of the best track sector data to determine the radius of the 64 kt, 48 kt and 34 kt winds. A lower bound

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of 0.1 m s−1 for Vm is imposed. An additional velocity profile is calculated for Vm and inserted at 65◦ anticlockwise from the storm direction. The gradient

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wind between calculated profiles is determined using a linear interpolation and

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the velocities are converted into velocity vector components via,

π  u = −f sin − θ V (r, θ) 2  π v = f cos − θ V (r, θ) 2

(22) (23)

where f = 2Ω sin(φ) is the Coriolis term, Ω is the Earth’s angular velocity in metres per second and φ is the latitude of the storm centre in radians. The modification of the gradient winds through the introduction of the storm’s forward motion velocity results in the previously symmetric radial veloc12

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ity profile becoming asymmetric. Friction causes the wind field to spiral towards the centre, rather than be circular. The inflow angle is [30],

(24)

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      r ≤ rm 10 1 + rrm          β = 20 + 25 r − 1 rm ≤ r < 1.2rm rm          25 r ≥ 1.2rm

and the angle correction is applied by rotating the gradient wind vectors inward

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by β.

The conversion of gradient winds to wind stress follows Large and Pond [26]

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with the drag coefficient, Cd , capped for wind speeds greater than 23.23 m s−1

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[32],

(25)

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    1.2 V (r, θ) < 10.92 m s−1        3 Cd 10 = 0.49 + 0.065V (r, θ) 10.92 m s−1 ≤ V (r, θ) < 23.23 m s−1          2.0 V (r, θ) ≥ 23.23 m s−1

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Atmospheric pressure is derived from the gradient wind equation,  Zr  2 V (s) PA (r) = Pc + ρ + f V (s) ds s

(26)

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where Pc is the minimum central pressure in hPa, and ρ = 1.15 kg m3 is density. We ignore the difference between 10 m and gradient winds for this calculation. The central pressure of the storm is calculated using the wind-pressure relationship of Knaff et al. [25] with the latitudinal corrections suggested by Courtney and Knaff [6]. For each of the computed radial velocity profiles we integrate

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Figure 2: THe seven best track cases for TC Anthony (January 2011), Yasi (February 2011), Ita (April 2014), Lam (February 2015), Marcia (February 2015), Olwyn (March 2015) and Debbie (March 2017).

equation 26 and the pressure between profiles is linearly interpolated.

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The stress and pressure forcing fields are generated on a 0.025◦ resolution grid using all available best track data and these fields are interpolated onto the

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model grid at runtime using a cubic interpolation method. The forcing fields

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are linearly interpolated in time during the model run.

4. Results

The seven best track cases represent contemporary tropical cyclone systems occuring in the tropical Australian basins between 2011–2017. These systems are TC Anthony (January 2011), Yasi (February 2011), Ita (April 2014), Lam (February 2015), Marcia (February 2015), Olwyn (March 2015) and Debbie (March 2017) and the strom track for each tropical cyclone is given in Figure 2. For each benchmark best track case, atmospheric pressure and surface stress forcing fields are determined using the method given in Section 3. The derived 14

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atmospheric forcing fields are then applied to the surge model given in Section 2. For each case, the model surge, ζ, wave setup up, ζsu , and sea level, ζsl = ζ +ζsu , is compared with the residual centred tide gauge observations at select locations. The residual centered data was calculated by subtracting the predicted harmonic tide signal. Comparisons between the tide gauge observation and the model are performed at the closest model grid point to the gauge location, which ranges

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from 150 m at Bowen up to a distance of 5.5 km at Port Alma.

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Here, we present the results for TC Yasi in detail. Summary results for the the maximum sea level, max(ζsl ), and the difference between the model

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maximum and the observation maximum at various locations are given in Table 1.

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The root mean squared (RMS) error of the model minus observations for sea

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level is 0.30 m, the mean absolute error (MAE), X |model − observation| n

(27)

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MAE =

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was 0.21 m, and the mean bias error (MBE), X model − observation n

(28)

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MBE =

is 0.11 m.

Timing comparisons of the model’s maximum sea level against the tide gauge observation for locations with a surge signal gave a root mean squared error of 62 minutes, a mean absolute error of 48 minutes and a mean bias error of 8 minutes, and the surge maximum time for the benchmark cases is given in Table 2. 4.1. TC Yasi The best track data for TC Yasi, shown in Figure 3, consisted of 72 hourly position fixes commencing with a Category 3 storm located south of the Solomon 15

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Observation Maximum (m)

Model Maximum (m)

Model - Observation (m)

Bowen

0.96

0.84

-0.12

Laguna Quays

0.86

1.67

0.81

Shute Harbour

0.51

0.92

0.41

Dalrymple Bay

0.43

0.84

0.41

Cardwell

5.14

5.04

Clump Point

2.74

2.32

Townsville

2.25

Cape Ferguson

1.85

Mourilyan

1.10

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Yasi

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Anthony

-0.10 -0.42 -0.23

1.97

0.12

1.33

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2.02

0.23

Cooktown

1.10

1.55

0.45

Cairns

0.58

0.48

-0.10

0.52

0.57

0.05

0.26

0.44

0.18

Groote Eylandt

0.79

0.69

-0.10

Mornington Island

0.66

0.50

-0.16

0.51

0.44

-0.07

0.30

0.33

0.03

Port Alma

1.88

1.91

0.03

Rosslyn Bay

0.53

1.24

0.71

Urangan

0.42

0.62

0.20

Gladstone

0.41

0.94

0.53

Dalrymple Bay

0.32

0.53

0.21

Point Murat

1.07

0.92

-0.15

Geraldton

0.31

0.23

-0.08

Laguna Quays

2.47

2.93

0.46

Shute Harbour

1.21 16

1.23

0.02

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Ita

Cardwell Clump Point

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Weipa

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Lam

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Thursday Island Marcia

Olwyn

Debbie

Table 1: Model maximum sea level comparison with tide gauge observations for the seven best track storms.

Observation Maximum Time

Model Maximum Time

Laguna Quays

2011-01-30 09:55

2011-01-30 10:50

55

Shute Harbour

2011-01-30 09:55

2011-01-30 11:10

75

Bowen

2011-01-30 11:45

2011-01-30 12:10

25

Cardwell

2011-02-02 15:15

2011-02-02 15:20

5

Clump Point

2011-02-02 14:15

2011-02-02 14:00

-15

Townsville

2011-02-02 15:25

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Model - Observation (minutes)

2011-02-02 16:10

45

Mourilyan

2011-02-02 13:55

2011-02-02 13:40

-15

Mourilyan

2011-02-02 16:45

2011-02-02 16:20

-25

Cape Ferguson

2011-02-02 15:05

2011-02-02 15:50

45

2015-02-20 05:30

2015-02-20 04:30

-60

2015-02-20 04:30

2015-02-20 05:20

50

2015-03-12 17:30

2015-03-12 16:20

-70

Laguna Quays

2017-3-28 03:35

2017-3-28 03:10

-25

Shute Harbour

2017-3-28 04:55

2017-3-28 02:10

-165

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Anthony

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Yasi

Port Alma

Olwyn

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Gladstone

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Marcia

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Point Murat Debbie

Table 2: Model maximum sea level timings and tide gauge maximum sea level timings for best track storm cases exhibiting a surge signal. The difference is model - observation, where negative values indicate that the model peak occured earlier than the observation and positive values indicate that the model peak time was later than the observed maximum.

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Islands over the Coral Sea on January 31, 2011. The system accelerated in a west-southwest direction and intensified to a Category 4 storm as it moved towards the Queensland coast. On February 3, TC Yasi made landfall near Mission Beach as a Category 5 storm. TC Yasi represented one of the strongest and most devastating tropical cyclone events to impact the Queensland coast. The storm surge response to this event was recorded at 5.3 m at Cardwell,

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located just south of the landfall. Inundation along coastal regions between

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Carins and Townsville was also experienced during high tide.

Comparison of the synthetic vortex model for TC Yasi with surface and

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satellite observations of this event are presented in Figures 4 through Figure 7. Figure 4a shows the ASCAT [10] surface winds for 1 February 2011. Velocity

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data from the ASCAT platform represents the equivalent neutral wind speeds at

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10 meters above the water surface, derived from surface roughness (wind stress) and is roughly equivalent to an 8–10 minute mean surface wind [35]. The model

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vortex for TC Yasi at 1 February 2011 at 11:00 UTC is given in Figure 4b. The storm asymmetry is apparent in the ASCAT observations with large wind velocities located in the south-west qudrant of the wind field. In comparison,

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storm.

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the model vortex exhibits a slight asymmetric structure in this quadrant of the

The model windfield was interpolated onto the ASCAT observation over a region about the storm centre, spanning 148.125◦ E - 155.875◦ E and 21.875◦ S to 12.125◦ S and the RMS difference between these fields was 4.57 ms−1 . The difference between the ASCAT observation and the model vortex is shown in Figure 5. A comparison of two surface atmospheric pressure observations and the model pressure at Clump Point and at -14.788◦ S, 153.576◦ E in the Coral Sea is given in Figure 6. The model vortex exhibits a lower background atmospheric

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Figure 3: TC Yasi storm track.

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Figure 4: (a) TC Yasi, ASCAT 10 metre wind vectors and velocity magnitude for 1 February 2011 and (b) TC Yasi, model atmospheric 10 metre wind vectors and velocity magnitude for 1 February 2011 at 11:00 UTC.

surface pressure when compared with the observations, due to the specification of a background environmental pressure value derived from climatology [6]. The

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minimum pressure of the observation in 6a was 941 hPa and model gave a minimum pressure of 945 hPa, representing a difference of 4 hPa. Closer to landfall

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of the storm, the surface pressure comparison at Clunp Point is shown in Figure 6b. The observed minimum pressure at this location was 930 hPa and the model

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vortex minimum pressure was 937, giving a difference of 7 hPa. In both cases, the model vortex shows comparable timing with the observations. The windspeed observations at four weather stations, whose locations are shown in Figure 7a, is compared with the model vortex windspeed in Figure 7b. The observation locations are all south of the storm track, with the closest observation point located at Orpheus Island. The windspeed comparison for locations further from the storm landfall location near Cardwell show reasonable timings, with the model peak windspeed occurring later than the observations. In the three cases where observations are available near the model peak wind-

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Figure 5: (a) TC Yasi, Difference between ASCAT 10 metre wind velocity magnitude for 1 February 2011 and model atmospheric 10 metre wind velocity magnitude for 1 February 2011 at 11:00 UTC.

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Figure 6: TC Yasi, surface pressure observations and model.

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Figure 7: TC Yasi windspeed observation (a) locations and (b) comparison between observations and model.

speed, the synthetic vortex exhibits lower windspeeds, ranging from a maximum

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windspeed difference of 15 m s−1 at Davies Reef to 10 m s−1 at Hardy Reed. The underestimation of the peak values and delay in the timing of the peak

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may be due to the insufficient asymmetry in the modelled vortex. This could be addressed by modifying the value of δf m in equation 21. This is not done

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here but left for further investigation. See section 5 for further discussion. The velocity structure for TC Yasi derived from the best track data for 2 February 2011 at 00:40 UTC is given in Figure 8a. The storm forward motion at this time was 11 m s−1 as the system moved towards the Queensland coast resulting in an asymmetric vortex structure. Large velocities are seen in the south western quadrant of the vortex with onshore winds of up to 60 m s−1 . The synthetic vortex structure exhibited sustained surface stresses of 8.52 N m−2 for over 10 hours prior to landfall and the minimum central pressure of the system during this time was 934 hPa.

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As TC Yasi progressed towards Queensland, the storm motion was almost orthogonal to the coast and this generated a strong north westerly system of ocean currents across the whole model domain as shown in Figure 8b with a subdomain given in Figure 9. The large surge response near Cardwell is a result of local coastal geometry with the interplay of strong ocean currents due to sustained intense surface forcing and flow blocking due to Hinchinbrook Island,

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resulting in an accumulation of fluid in the region which significantly increased

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the coastal sea levels. Figure 9a and 9b show the sea level and currents at 14:00 UTC and 14:50 UTC respectively for 11 February 2011. These snapshots are

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prior to the peak surge values and show the northward movement of water along the coastline and the strong onshore current directions resulting from the TC

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system moving directly over this area.

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Coastal cells south of landfall exhibited sea level values ranging from 4.5–5.0 m. The largest maximum sea level values were near Cardwell with locations

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further south showing sea levels between 2.0–3.0 m. South of Townsville, the storm induced surge was between 1.0 and 2.0 m. For locations north of the track, the sea level response was reduced, due to the smaller surface stresses in the

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northern section of the storm and the winds directed away from the coastline.

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Correspondingly, the maximum sea level values experienced in this part of the domain were less than 2.0 m. Tide gauge data for Cardwell, Clump Point, Cape Ferguson, Mourilyan and Townsville exhibited a storm surge response to TC Yasi, with the largest responses at locations south of the storm centre. The Cardwell tide gauge, given in Figure 10a, recorded a large storm surge anomaly with an observed maximum sea level of 5.135 m. The surge model performed well, returning a maximum surge of 5.04 m, which includes a wave setup component of 0.56 m, 5 minutes after the time of the observed maximum.

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The best track data shows the storm making landfall near Clump Point. The surge model gave a maximum sea level of 2.32 m compared with an observation value of 2.74 m. The model peak surge timing is 25 minutes earlier than the observed maximum and the wave setup contribution for this location was 0.58 m (Figure 10b). Inspection of model cells within 25 km of the observation location show that the maximum sea levels south of Clump Point increased by up to 3.0

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metres.

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The maximum sea level observed at Cape Ferguson was 1.85 m with the model returning a maximum value of 1.97 m (Figure 10c). The wave setup

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component for Cape Ferguson was 0.56 m and the model peak timing was 45 minutes earlier than observed maximum. At this location, the observation time

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series shows a sustained sea level of ∼1.7 m over 3 hours whilst the model

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returned sea levels around ∼1.9 m over the same duration. Comparison of observed peak surge levels and timings at Mourilyan, given

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in Figure 10d, showed that the surge model successfully reproduced the double peak sea level structure seen in the observations and slightly overestimated the maximum sea level by 0.23 m. The second peak in the model sea level response

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was the result of a wave being reflected by Hinchinbrook Island and propagating

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northward along the coast. The model peak timing is compared for both of the local maxima values in Figure 10d and is within 15 minutes and 25 minutes of the observed maximum values. The wave setup contribution to the sea level for Mourilyan was 0.80 m which may be the contributing factor in the slight over estimation of surge levels at this location. For times near landfall of TC Yasi, the AUSWAVE-R data gave significant wave heights up to 12 m and peak periods up to 16 s. Coastal cells about Mourilyan were exposed to the full extent of the wave fields, unlike locations further south where the wave dynamics were disrupted by the presence of coastal island features.

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At Townsville, about 1500 km south of landfall, the surge model returned a maximum value of 2.02 m whilst the observed maximum was 2.25 m (see Figure 10e). The model peak timing is within 45 minutes of the observed maximum values and the wave setup component for this location was 0.28 m. Across the five observation locations, the RMS error of the model surge maximum minus the observation was 0.24 m, the MAE was 0.22 m and the

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MBE was -0.08 m.

5. Discussion

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Comparison of the seven best track case studies with tide gauge observations

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gave a root mean squared error for maximum sea level of 0.30 m, a mean absolute error of 0.21 m and a mean bias error of 0.11 m. Timing comparison of the

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model’s maximum sea level against the tide gauge observation for locations with a surge signal gave a root mean squared error of 62 minutes, a mean absolute

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error of 48 minutes and a mean bias error of 8 minutes. For the strongest category storm systems, the Category 5 TC events of Yasi

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and Marcia, the root mean squared error of the coastal sea level surge maximums range from 0.24 m for Yasi and up to 0.42 m for Marcia. Further, the system

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demonstrated agreement for the lower intensity tropical cyclones with RMS errors ranging from 0.11 m for Lam, up to 0.50 m for Anthony. The no surge signal results for TC Anthony are also in agreement with the observations for this event, indicating that the model configuration is sufficiently representing the characteristics of the atmospheric forcing due to TC winds and pressure as well as the ocean response to forcing across the range of storm intensities. The strongest storms modelled were TC Yasi and Marcia, which both made landfall as Category 5 systems. For TC Yasi, the model showed good agreement with the tide gauge observations across all comparison locations. At Cardwell,

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(a) TC Yasi track, 10 metre wind vectors and surface pressure contours

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(b) TC Yasi track, ocean sea level and currents. Figure 8: TC Yasi atmospheric forcing and ocean response for 2 February 2011 at 15:00:00 UTC.

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(a) 2 February 2011 at 14:00 UTC.

(b) 2 February 2011 at 14:50 UTC

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Figure 9: TC Yasi ocean sea leavel and currents.

the closest observation location to landfall, the model gave a maximum seal level

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of 5.04 m with the observation data measuring a maximum sea level of 5.14 m. The modeled maximum was within 5 minutes of the observed peak. For all

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observation locations, the system was within 0.41 m of the observed maximum

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sea level. For TC Marcia, the largest surge was 1.88 m observed at Port Alma and the model returned a maximum surge response of 1.91 m with the model peak timing occurring 60 minutes earlier than the observed peak. Across all observation locations for TC Marcia, the model returned a RMS error of 0.42 m. The Category 4 systems of TCs Ita, Lam and Debbie also compared well with the tide gauge observations. The RMS error for these systems was 0.25 m, 0.12 m and 0.32 m respectively. For TC Ita, the model overestimated the surge response at Cooktown by 0.45 m with the observation locations further south of landfall showing a small surge response as the system decayed in intensity. For 28

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Figure 10: TC Yasi surge, wave setup, total sea level and observations.

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TC Lam, no tide gauge observations were available close to the landfall location, which made verification of the systems performance difficult. Comparison of the model and observations at the three available observation locations gave a RMS error of 0.11 m. However, at each of these locations the surge response was negligible. Model results for TC Debbie at Laguna Quays and Shute Harbour compared well with the observations, with the model surge maximum being

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within 0.46 m and 0.01 m, respectively. At Laguna Quays, the tide gauge closest

For this storm, the RMS error was 0.32 m.

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to landfall, the model peak timing was within 25 minutes of the observed peak.

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The model RMS error for the Category 3 storm TC Olwyn was 0.12 m. As with TC Lam, no tide gauge observations were available at the model maximum

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surge location in Exmouth Gulf. The closest observation to the model maximum

observed maximum.

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was at Point Murat and the model surge maximum was within 0.16 m of the

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The Category 2 system of TC Anthony returned a model RMS error of 0.50 m across the 4 observation comparison locations, with the model returning a maximum surge at Bowen that was 0.12 m less than the observed maximum.

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At observation locations south of landfall, the model overestimated the surge

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response. Factors which contribute to this result include a misalignment of the surface forcing winds due to uncertainties in the inflow angle, the location of the maximum winds and the forward motion contribution to the vortex asymmetry. Optimisation of these parameters would improve the surge results against the observations and would potentially reduce the errors for other locations south of landfall as well. Additionally, the surge peak timings will also be influenced by adjusting the strength and direction of the surface stresses. The test cases show that the largest surge responses occur around the location of storm landfall, and fall away to lower surge heights at locations at a

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greater distance from the land crossing site. This characteristic is further constrained by the intensity and size of the tropical cyclone. For example, TC Yasi, which was the largest and strongest of the systems considered in this study gave comparable surge results to the available tide gauge data. However, for smaller and less intense TC systems whilst demonstrating accuracy at landfall, the surge error against the tide gauge observation increases at locations further away from

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the landfall site. This is due to the atmospheric forcing. For small TCs with low

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to moderate intensities, the spatial extent of the high velocity vortex region is limited, and under the model presented here, the atmospheric velocities beyond

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the outer radius of the storm converge to a modest wind speed. This delivers a lower stress forcing to ocean regions that are further away from the storm

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centre, and results in smaller surge values at these locations. Blending of the

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synthetic vortex fields with a background atmospheric field, derived from numerical weather prediction forecasts or climatology, may improve these results.

the TC.

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In any case, the primary region of interest is coastal locations near landfall of

In general, the performance of the system across the seven benchmark best

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track cases demonstrates accuracy at coastal locations about the landfall loca-

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tion of the TC. Under the operational implementation of the surge forecasting system, an ensemble of surge models is run, with each member model being forced by a unique TC realisation. These TC instances are generated as a statistical perturbation of the official TC forecast track and includes variations in TC track location, spatial size and intensity [8]. The ensemble approach aims to mitigate the inherent uncertainties in forecasting TC characteristics and results in an ensemble of coastal surge results from which forecast guidance concerning the likelihood of a surge event is produced. The sparse tide gauge coverage over the vast Australian coastline makes

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direct comparison of the model sea levels at landfall difficult for several of the systems modelled here. For example, the model response for TC Lam suggested a maximum coastal surge of 2.5 m, whilst TC Olwyn returned a maximum sea level that was greater than 3.0 m. Unfortunately, at both of these maximum value locations no observation data was available for comparison. The location of the tide gauge network is another factor in the model error estimates. In

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general, tide gauge observations are in sheltered locations and may not include

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a wave setup component. In addition, gauges may be located in areas with complex coastlines or bathymetry which are not well resolved by the model.

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The contribution of wave setup to total coastal sea-level is more significant in areas of steep continental shelves compared to broad shallow shelves [21].

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In the Tropical regions that are of interest here, Australia’s continental shelf is

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relatively broad, e.g., around the Great Barrier Reef (northeast coast) and the north-west shelf (see Figure 1). This means that wave setup is going to be most

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important around the southern coast of Queensland. Within the ocean model formulation, the stress forcing on the depth averaged ocean model is applied as the difference between the surface atmospheric

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forcing stress, τs , and the bottom stress, τb , where the stress components are √ √ given by τb = (γ u2 + v 2 u, γ u2 + v 2 v). The bottom stress drag coefficient, γ, has a constant value of 10−3 across the entire ocean grid domain in this work. However, changes in bottom topography due to localised bathymetric gradient changes and the presence of reefs may be realised within the model through the implementation of a spatially varying bottom stress drag coefficient. This modification will effect the depth averaged ocean currents with stronger currents occurring in regions characteristic of smaller drag coefficients and weaker currents in areas of higher drag, such as the Great Barrier Reef and through island chains with surrounding steep bathymetry.

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The strength and direction of the ocean currents calculated from the application of the synthetic vortex TC stress fields plays an important role in the resulting sea level increases at the coast line, potentially affecting the magnitude and timing of the surge response. The generation of synthetic atmospheric stress and pressure fields contains several variables that are only loosely constrained. Whilst no optimisation or tuning of these parameters was undertaken

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in this work there are a number of options for further refining this component

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of the system. Variables of influence within the atmospheric model include the wind stress drag parameterisation, the inflow angle correction and the forward

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motion dynamics.

The wind stress parameterisation, given in equation 25, follows Large and

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Pond (1981) with the drag coefficient limited for wind speeds greater than 23.23

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m s−1 . However, Powell et al. [32] show that the Large and Pond (1981) formulation is valid up to gradient wind speeds of 35 m s−1 . Recent studies have strengthened the case for the stress drag coefficient increasing linearly until ap-

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et al. [38] gives,

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proximately 30 m s−1 [38]. Modifying equation 25 in accordance with Soloviev

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    1.2 V (r, θ) < 10.92 m s−1        3 Cd 10 = 0.49 + 0.065V (r, θ) 10.92 m s−1 ≤ V (r, θ) < 33.0 m s−1          2.635 V (r, θ) ≥ 33.0 m s−1

(29)

The application of Equation 29 resulted in the generation of higher stresses in high velocity areas of the TC system, which is subsequently manifested as larger coastal sea level values and stronger ocean currents for the higher category cyclone systems. For some slow moving systems that undergo rapid inten-

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sification, the updated drag parameterisation in Equation 29 may provide an improved approximation to the surface forcing than the relationship given in equation 25. The influence of the stress formulation is countermeasured by the forward motion fraction, δf m . Reducing the amount of storm forward motion, which is essentially a crude approximation to the frictional characteristics present in

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the boundary layer between the atmosphere and ocean interface, reduces the

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stress magnitudes even in the case where the upper limit of the drag coefficient is limited as wind speeds approach large velocities. Wind field asymmetry is

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introduced through the forward motion coefficient, δf m , in equation 21 which is added to the direction of maximum winds. Harper and Holland [16] note

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that this is the least satisfactory aspect of the current empirical approaches to

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modelling the cyclone surface wind field. Storm asymmetry would be better described by more sophisticated approaches (for example [22, 29]) or through

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direct numerical simulation.

The inflow velocity angle of the synthetic storms has a minor influence on the maximum sea level but strongly influences the surge maximum timing. For

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the TC Yasi case, the directional adjustment of the velocity field (equation

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24) improved the peak timing comparisons at all tide gauge locations. The inward rotation of the velocity vectors by 20◦ –25◦ for r > rm resulted in the surface stress forcing becoming more orthogonally aligned with the coastline when compared with models that exclude this factor. Further complications arise when the storm tracks follow the coastline or the system moves over land areas, as was the case for TCs Ita and Marcia. For tropical cyclones moving over land, the wind field weakens due to increased surface roughness and the inflow angle is rotated even further toward the storm centre [31, 23]. The atmospheric model presented currently lacks the ability to accu-

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rately model the stress field when the TC system is over land areas. For systems that move along the coastline, the gradient wind fields are further complicated due to the discontinuity in the boundary layer characteristics between land and ocean. Whilst numerical weather prediction systems deliver a potential solution to this challenge, the computational cost currently remains too high to run an ensemble of dynamic TC models that cover the uncertainties present in forecast

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TC track location, size and intensity.

6. Conclusion

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Here, we presented the atmospheric and ocean model configurations that

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comprise the two major components of the Australian tropical storm surge forecasting system. The components were benchmarked against seven contemporary

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tropical cyclones occurring in the Australian basin. The modelled storm surge response is in good agreement with tide gauge observations and verifies the

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Highlights • A new operational storm surge prediction system was developed for Australia. • We describe the tropical cyclone model that matches storm observations.

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• The modelled storm surge compares well with tide gauge observations. • Modelling of seven tropical cyclone events gave maximum sea levels within

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30 cm of observations.

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