Near-reef and nearshore tropical cyclone wave climate in the Great Barrier Reef with and without reef structure

Coastal Engineering 157 (2020) 103652

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Coastal Engineering journal homepage: http://www.elsevier.com/locate/coastaleng

Near-reef and nearshore tropical cyclone wave climate in the Great Barrier Reef with and without reef structure David P. Callaghan a, *, Peter J. Mumby b, Matthew S. Mason a a b

School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia School of Biological Sciences, The University of Queensland, Brisbane, QLD, Australia

A R T I C L E I N F O

A B S T R A C T

Keywords: Tropical cyclones Wave climate Wave modelling Atmospheric boundary layer Great barrier reef Parametric wind fields Sparse storage technique Ecosystem function Coastal protection

The Great Barrier Reef (GBR) coral coverage is in rapid decline from severe and sustained pressures from lagoon water quality, crown-of-thorns starfish (COTS), coral bleaching, tropical cyclones, pollution and diseases. The two recent GBR coral bleaching events (2016–2017) lead to Great Barrier Reef Marine Park Authority (GBRMPA) shifting their focus from passive management to active intervention (Great Barrier Reef Blueprint for resilience by GBRMPA). These active interventions, potentially able to increase GBR resilience, as there are reefs that, due to their physical location relative to all other reefs, river and estuary entrances, ocean currents, have favourable coral growth conditions. To undertake such interventions, various information is required including tropical cyclone wave climates. This paper develops tropical cyclone wave climates for the entire GBR. These wave climates were developed by simulating several thousand synthetic cyclones derived from the “HadGEM” general circulation model with RCP8.5 climate change scenario. The synthetic cyclones adopted herein include the following climate changes assessed by comparing averages of key forcing parameters between 1950 to 1999 and 2050 to 2099. Their average arrival rate increases from 2.25 to 2.41 cyclones/year and their average maximum wind speed increases from 24 to 28 m/s. Their average radius to maximum winds remains constant at 51 km. Two key challenges were resolved, namely, long runtimes and large files (600 m grid increment covering 1800 km by 280 km). Runtimes were reduced by excluding cyclones where their wind speeds over the entire event never exceeded 10 m/s within GBR itself or within 100 km of the GBR over water. Maximum wave heights were compared with an extended fetch empirical expression, which was based on satellite data of tropical cyclones in open waters, when cyclones were outside the GBR lagoon. These comparisons indicate that predicted wave heights have a lower bias using default wave generation parameters when compared with the extended fetch empirical expression. Prediction uncertainty was estimated at no more than 10% from various cyclonic windfield models. The existing GBR reefs reduce nearshore wave or runup height by between 1.5 and 2 times compared to the no reef case. The reduction in wave or runup height was found to be minimal for 1 m sea level rise. These two findings indicate that there is more flooding potential from coral removal than SLR within the GBR lagoon.

1. Introduction As the name suggests, the Great Barrier Reef (GBR) offers protection from Pacific Ocean waves (Gallop et al., 2014; Jaffr�es and Heron, 2011) where lagoon waves measured by satellite altimeter data are largely dependent on local wind speed. Similar conclusions were drawn in (Callaghan et al., 2015) when estimating non-cyclonic wave climates. Waves would break on the seaward reefs initially and then further dissipate from bed friction, coral drag or additional breaking across reefs from irregular bathymetry. Combining this barrier to Pacific Ocean

waves with recent measurements of fringing reefs providing coastal protection (Beck et al., 2018; Ferrario et al., 2014), has led to sugges­ tions that the GBR is providing ecosystem functions of reduced wave height to Queensland coastal regions through reducing the nearshore wave climate. If cyclonic wave attenuation from the GBR is significant at reducing the nearshore wave height within the GBR lagoon, then shoreline management needs to adjust if this attenuation reduces with sea level rise. One way wave attenuation may remain unchanged is if vertical growth of coral keeps up with sea level rise. However, coral coverage is in rapid decline from severe and sustained pressures in the

* Corresponding author. E-mail addresses: [email protected], [email protected] (D.P. Callaghan). https://doi.org/10.1016/j.coastaleng.2020.103652 Received 18 March 2019; Received in revised form 13 January 2020; Accepted 19 January 2020 Available online 23 January 2020 0378-3839/© 2020 Elsevier B.V. All rights reserved.

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GBR. This decline is attributed to lagoon water quality, crown-of-thorns starfish (COTS), coral bleaching, tropical cyclones, pollution and dis­ eases (De’ath et al., 2012; Hughes et al., 2017; Hughes et al., 2019; Ortiz et al., 2018). It is expected that reductions in coral coverage may lead to water depths over reefs increasing, which would lead to a reduction in wave attenuation. The question is then, how these attenuated waves grow while propagating through the GBR lagoon (i.e., between offshore reefs forming this barrier and the coastline). The GBR lagoon varies in width from tens of kilometres to one hundred kilometres across. During cyclonic wave generation, the largest waves occur within a few radius of maximum winds (Young and Burchell, 1996; Young and Vinoth, 2013; Young, 2017) of the tropical cyclone. Hence, tropical cyclones that are smaller than the GBR lagoon width and slow moving can reach their maximum wave height. This would offset barrier reef wave attenuation. The GBR, the largest and most diverse coral reef on earth, is a challenging region for wave climate analysis. It is made up of around three thousand reefs of various morphologies and sizes, located between a few kilometres to 280 km offshore of the Queensland coast while extending over 1960 km alongshore (Fig. 1). Previous studies have done a compelling analysis of the impacts of historical cyclones on reefs (Puotinen et al., 2016). Here, we consider the impacts of the reefs on attenuating wave height and wave runup across the entire Great Barrier Reef Marine Park. Of the identified reefs, ca two third have surface areas that are greater than 0.36 km2 (Fig. 2). To model these reefs, grid in­ crements of the order a few hundred meters are required. This grid resolution would lead to very large computer memory usage and file storage requirements. Previous numerical modelling using a 2.5 km grid increment of the GBR by Young and Hardy (1993) obtained reasonable cyclonic wave predictions where wave height measurements were available (away from shallow areas). A similar numerical modelling outcome was achieved by Hardy et al. (2000) who used ca 1.5 km grid increment. These modelling efforts, combined with increases in computing capacity, indicate modelling cyclonic wave climate under climate change is potentially feasible by simulating several thousand synthetic cyclones derived from a general circulation model forced by particular climate change scenario. Emanuel et al. (2008) has, for example, developed several thousand synthetic cyclones for the GBR, which was successfully applied by Wolff et al. (2016) to characterize tropical cyclone clustering and its impact on coral cover within the GBR. This article uses Emanuel et al. (2008) synthetic tropical cyclones for estimating wave climate across the entire GBR. Wave climates will be estimated for three geometrical states of the reef; 1) existing state (Fig. 1), 2) with 1 m uniform sea level rise throughout the GBR and 3) with the entire reef removed back to the continental shelf. The third case, while not remotely possible, provides the wave climate in the

absence of wave height reductions from the GBR. These three cyclonic wave climates will provide a first order estimate of the shoreline pro­ tection provided by the reef under cyclonic conditions. The article is arranged into two main sections. The first of these two major sections is section 2 which presents the modelling approach, its limitations and sensitivity testing. The second of these two major sec­ tions is section 3 which presents wave climates for three scenarios ob­ tained using the modelling approach of section 2. These two sections are arranged in a self-contained manner for easy of reading. A summary, including a brief discussion is communicated in section 4. The particular contents of Section 2 are: model type, cyclonic winds, bathymetry, reef locations and sizes, methods to handle lengthy simulation periods and large storage requirements. Winds sensitivity testing is included by comparing wave climate predictions between different parametric wind models and atmospheric boundary layer approaches. Wave height gen­ eration is tested by comparing predictions with satellite-derived maximum cyclonic wave height. These tests providing a measure of prediction accuracy and uncertainty. The particular contents of Section 3 are: three cyclonic wave climates are presented and discussed for existing reef geometries for with and without sea level rise, and a bare sloping continental shelf (e.g., as if the reef never existed). The three wave climates described above are available for download at https://doi.org/10.14264/uql.2019.169, in self describing netCDF and geographical information system shapefile format. 2. Wave-modelling approach Sections 2.1 through to 2.5 presents the modelling approach, with sensitives of several modelling choices tested herein. The wave climate information being sort are near to but offshore of reefs through the GBR and for along the Queensland Coastline but within the GBR Lagoon. The first objective provides reef managers with the cyclonic wave climate for each reef. The second objective facilitate estimation of shoreline wave climate. In this article, we use changes in wave runup and Gourlay number as an initial assessment for changes from sea level rise. Conse­ quently, our modelling approach focuses on cyclonic wave climate estimation in 20 m water depth. When developing our modelling approach, including tides and storm surge dynamics was considered. The tidal range varies throughout the GBR with 6 m ranges near the shoreline to a few centimetres at the barrier reefs (Callaghan et al., 2007). Similarly, storm surges can be several metres at the shoreline decreasing to a few centimetres offshore at the barrier reefs. Our past experience of tidal and storm surge modelling of the GBR indicated that the computation time required for their inclusion when running enough synthetic cyclones to assess wave attenuation from the more than 3000 Fig. 1. Mean sea level (MSL) water depth through the Great Barrier Reef and Capri­ corn Bunker Group, Queensland, Australia. Left most panel, the entire reef system extending alongshore from south of the Capricorn Bunker Group and north of Torres Strait (ca 1960 km/1060 NM) and crossshore from the shoreline to offshore of the outer barrier (ca continental shelf, between 30 and 280 km offshore). Right three panels zoom in on the northern, central and southern regions, all using the colour scale shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

2

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Fig. 2. Distribution of nominal reef area within the Great Barrier Reef, obtained from Great Barrier Reef Marine Park Authority (Anonymous, 2019). Number of model grids shown in brackets is based on a 600 m grid increment.

reefs making up the GBR would take many years using high performance computing. When excluding tides and storm surges, the modelling approach can use all synthetic cyclones within a few days, thereby have many more predictions to form the wave climate. When including tides and storm surges, the additional computational demand limits the number of synthetic cyclones. Consequently, it was concluded that limitations introduced excluding tides and storm surges was less than including them. Nevertheless, users of these wave climates should note they have been estimated without tide and storm surge. This means that the dataset available online from this modelling is limited to off-reef and offshore of coastlines. The modelling approach, now being limited to wave estimates offreefs and offshore of coastlines, allows sharpening of our modelling focus onto cyclonic wave generation and wave attenuation by barrier reefs and reefs within the GBR lagoon. This can be achieved by using the computationally less demanding wave action equations compared to cases where on-reef wave climates are being estimated where the significantly more demanding momentum equations are often needed. While predictions are off-reef, there is an additional limitation in that wave breaking within the model selected will be different from more rigorous approaches. At off-reef locations, this difference is manifest in the reef lee region as underestimates (estimated at less than 0.5 m wave height differences). This limitation was accepted over the more rigorous approaches which would have led to a much reduce set of synthetic cyclones predictions for estimate the wave climate. The GBR extents along a north-west to south-east axes, over 14.5� latitude. Wave action equation models using spherical regular grids are limited to non-rotated grids. For the GBR, that includes many more spherical grid points compared to a Cartesian grid aligned with the GBR. This raises the question, are there limitation in using rotated Cartesian grids compared with using spherical coordinates. There will be differ­ ences in propagation path between these two coordinate systems. These differences grow with propagation distance. The GBR lagoon varies between a few kilometres to approximately 100 km and at 100 km, the propagation path error is 85 m (maximum difference between a great circle (spherical coordinates) and Cartesian paths. This error was accepted and the much faster grid aligned Cartesian grids adopted. Finally, the modelling approach is tested for sensitivity to assumed wind fields and adopted bathymetry (section 2.3) and was compared to an extended fetch tropical cyclone empirical wave model (section 2.5). These together provide an accuracy indication of this modelling approach.

the RCP8.5 climate change scenario. While there are other RCPs avail­ able, RCP8.5 was selected as the worst possible scenario available. This conservative approach is consistent with engineering associated with safety and when planning using uncertain knowledge of the future. The synthetic database contains 6000 storms (tracks, radii to maximum winds, and maximum winds, Fig. 3), 40 events in each year from 1950 to 2099, 150 years in total, that are tracking near or through the GBR. During the 20th century (1950–1999), mean annual arrival rate (Fig. 3) was 2.25 TC/year with these rates varying from a low of 1.22 to a high of 3.75 TC/year. In the 21st century mean annual arrival rate was 2.33 TC/year with a range of 1.31–3.74 TC/year. For return period estima­ tion (see section 3, equation (2)), stationary conditions were adopted with an annual arrival rate of 2.3 TC/year. The wave modelling applied Simulating WAves Nearshore, version 4120 (Booij et al., 1999; Holthuijsen, 2007; Ris et al., 1999) or SWAN, which has been successfully applied in tropical cyclone estimates (Cheung et al., 2003; Huang et al., 2013; Liu et al., 2010), with extensive testing by Zijlema et al. (2012) for very high wind speeds. This wave model was applied using the non-stationary formulation, with half hour time increment and three iterations per time step, adopted from testing using a small, medium and large synthetic cyclone. To that end, direc­ tional resolution of 10� and 40 frequency bins between 0.05 Hz and 1 Hz was adopted. The 3rd generation wind generation model default pa­ rameters were adopted after simulations of TC Ita indicated that the default drag coefficient (CD) yielded peak significant wave heights within the scatter expected from Young’s estimates (Young, 1988, 2017; Young and Vinoth, 2013), determined from satellite observations, when TC Ita was in the Coral Sea and well away from the GBR. However, CD varies with wind speed under these settings and even go negative be­ tween 60 m/s and 70 m/s, which leads to unstable and non-physical wave predictions. CD variation was therefore kept except a limit was included to ensure CD � 5 � 10 4. This threshold was obtained from data trends in Zijlema et al. (2012). It could be that these very strong wind speeds actually break down waves, however, there is an absence of data above 60 m/s,.e.g, Holthuijsen et al. (2012) and hence, this limit needs to be kept in mind when applying predictions reported here. During testing, the integrating scheme designed to reduce the garden-sprinkler effect often failed. Consequently, the first order up­ wind scheme was applied. The wave model used two regular grids (Fig. 4) rotated to be aligned with the Queensland coastline with an outer grid extending well into the Coral Sea and the inner grid focusing on the GBR. The outer grid increment was 6 km (3.2 nm) in both alongshore and cross-shore di­ rections. The extent of this grid encompasses the relevant (for GBR) wave fetches within Coral Sea for every tropical cyclone simulated. This distance was tested by simulating the largest cyclone in the database and ensuring it captured the maximum wave height and spatial variation as reported by Young (2017). This outer grid was used to estimate the inner

2.1. Wave model forcing, specifications and grids Emanuel et al. (2008) estimated synthetic tropical cyclones using several general circulation models (GCM) and representative concen­ tration pathways (RCP). This work has selected the HadGEM GCM and 3

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Fig. 3. Emanuel et al. (2008) synthetic tropical cyclone database for the Great Barrier Reef. Top panel, annual arrival rate, middle left and right panels, histograms of radius to maximum winds and maximum wind speeds, bottom left panel, joint histogram and bottom right panel, tropical cyclone tracks (land shaded grey and GBR reefs contained within orange polygon). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

grid boundary conditions. The inner model covered the longshore extent where �5 m/s winds occurred and spanned the maximum east and west extents of the GBR. The adopted inner grid spacing of 600 m (0.32 nm) results in 32% of reefs being less than one grid cell in area (i.e., they are sub-grid reefs), 29% of reefs are modelled with between 1 and 5 grid cells and 39% of reefs being modelled by more than 5 grid cells (Fig. 2). This grid offers a factor 6 increase in modelling resolution to that used in the previous modelling of this region by Hardy et al. (2000). Testing finer resolutions resulted in model simulations failing due hardware limitations, indicating the 600 m was already near the computational capacity currently available. A rotated regular grid was used to minimise the numerical effort. The regular grid approach was adopted over the flexible mesh as its extents can be dynamically changed to suit tropical cyclone wind field extents,

whereas, that ability was not readily achievable using a flexible mesh. As will be explained further in this section, grid extents were varied for each segment being simulated to decrease calculation times. The rotated regular grid further ruled out using spherical coordinates and conse­ quently, Universal Transverse Mercator 55 South coordinate system was adopted to locate depth information on a two-dimensional Cartesian coordinate system. While this introduces errors in wave predictions (e. g., great circles being curves in Cartesian coordinates), those are accepted and are second order given cyclonic waves are generated within a much smaller region of the lagoon and Coral Sea compared to the overall length of the wave model where these deviations would become large (see section 2). Of the 6000 synthetic cyclones generated by Emanuel et al. (2008), 3406 impact GBR grid with at least 10 m/s wind speed within the model 4

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Fig. 4. Two examples for wind wave model grids applied for two tropical cyclones, with the gold outer grid (6 km or 3.2 nm grid increment) and the purple inner grid (0.6 km or 0.32 nm). The orange polygon is the area of interest (GBR). The red circles are radii to maximum winds. See Fig. 3 for land and sea extents. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

window (GBR plus 100 km offshore), excluding wind speed changes from cyclone propagation speed. The grid extents for both outer and inner grid vary for each TC segment simulated (Fig. 4), to cover wind speeds exceeding 5 m/s (i.e., to include higher speeds when translational speeds are included). First, the inner grid extents are determined (purple rectangle, Fig. 4) and then the outer model extents are determined by enclosing an additional 100 km in the longshore directions and to the offshore extents of outer window (blue rectangle, Fig. 4). All grids are collocated on the main calculation grid. This approach achieves signif­ icant decreases in simulation effort, albeit coming at the cost of bespoke coding to manage the large number of simulations (managing this manually was assessed as unfeasible from the likelihood of human errors and the time involved). Computational effort was further reduced by excluding periods within each event when events tracked away from GBR and thereby having maximum wind speed on the grid below 5 m/s. The excluded periods where re-included if the period was less than 20 h. Each segment was further divided up into 24-h simulations, to reduce computational effort as cyclone footprints are small compared to their travelled distance over several days. When events re-entered GBR or swapping between 24-h simulations, those nonstationary simulations where initialized using a stationary simulation. Testing was undertaken for the number of iterations required for the wave model to converge to within 0.1 m of the fully converged significant wave heights (of many metres). By reducing this requirement simulation speed is increased by ca tenfold, and when this approach was compared to several particular TC’s, run to full accuracy, errors in significant wave height were of order 0.01 m, indicating bulk energy was correct even if its distribution in frequency and direction was questionable. The information being obtained from simulations were the maximum wave height over the entire tropical cyclone and corre­ sponding wave period and direction for that maximum, in each wave propagation direction sector of Northerly, North-easterly, through to North-westerly (eight in all). Additionally, the overall maximum wave height and corresponding wave period and direction was recorded. These results were recorded for wave heights exceeding 5 cm (these simulations were run without background waves, as storms were syn­ thetic). Temporal information was recorded for the entire outer grid, however, this was infeasible for the inner grid and consequently, tem­ poral results were limited to reef regions, which equated to 12.5% of the inner grid. To enable this limited output, a sparse approach was used where files contained the indices of grid cells being saved followed by information at these cells. Indices were calculated as

index ¼ i þ ðj

1ÞNi

(1)

where i and j are matrix location (i,j) and Ni is the matrix size in i. To further assist in reducing storage usage, files were zipped and 16-byte integers used to store output (providing 0.001 m and 0.001 s resolu­ tion for significant wave height and peak period). With these three techniques implemented, the combined storage capacity for all simula­ tions was 140 GB. Without these techniques, storage was estimated at 4 TB. 2.2. Wave model bathymetries used to estimate wave climates The outer and inner grid water depth (Fig. 1) was developed to ensure reasonable estimates were obtained within the shallow regions along the Queensland coastline. This is particularly important given the aim of estimating nearshore wave climates. To achieve this goal, the following bathymetry datasets were adopted. Starting from lowest res­ olution, “etopo1” 1 min grid (Amante and Eakins, 2009); “gbr100 m” 100 m grid (Beaman, 2018b), “gbr30 m” 30 m grid (Beaman, 2010, 2018a, 2018b); satellite derived bathymetry for Capricorn Bunker Group 15 m grid (Roelfsema et al., 2018); satellite derived bathymetry, using the same approach as Roelfsema et al. (2018), for the Northern Group 15 m grid covering all reefs between 14� 230 S or 100 km north of Cooktown to 17� 530 S or 100 km south of Cairns, (pers. comm. Roelf­ sema, 2016); and reefs impacted by Tropical Cyclone Ita 30 m grid (pers. comm. Gonzalez-Rivero, 2014). The bathymetry was developed by removing data points of lower resolution when they overlapped with higher resolution data. The various model cells points were allocated a depth using the following approach: for MSL depth greater than 10 m, the cell was assigned the average of all depths available in that cell; and for MSL depth less than 10 m, the cell was assigned the minimum depth of all depths available in that cell. The first approach for deeper grids follows normal modelling practice. The second approach adopted ensured shallow reef regions were included. This approach overcame �nase Zanopol et al. (2014) the need to use obstacles, for example, as Ta did for wind farms, to model sub-grid sized reefs. While the obstacle approach represents a refinement over adopted approach, it requires significantly more assumptions (wave transition coefficients for all wave directions). 2.3. Statistical simulations and wave model sensitivities The wave model was applied to estimate the maximum wave height 5

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Table 1). The atmospheric boundary layer model followed Kepert (2001). In all cases, translation speed wind field corrections are included, adopting 50% contribution consistent with data from Lin and Chavas (2012). To test wave climate sensitivity to the applied para­ metric wind field, the gradient wind fields were also estimated using Holland et al. (2010) (H10, Table 1) and Emanuel and Rotunno (2011) (ER11, Table 1), both with Kepert (2001) boundary layer. McConochie et al. (2004) and Vickery et al. (2009) provide alterative models for including surface friction (i.e., translating from gradient winds to winds 10 m above the sea level and changing inflow angles) to Kepert (2001). These models would yield differences in wave prediction, however such differences are considered secondary compared with the following four significant limitations in estimating cyclonic wind waves: approxima­ tions employed by either Sobey et al. (1977), McConochie et al. (2004) or Vickery et al. (2009) compared to the Kepert (2001) boundary model; data uncertainty for inflow angle (Uhlhorn et al., 2007), translation speed impacts in the boundary layer wind speeds (Lin and Chavas, 2012) and typical wave model accuracy (e.g., Callaghan et al., 2015). The more recent semi-empirical model by Snaiki and Wu (2018) has not been included as the synthetic tropical cyclone data is missing information required to apply this model. To assess wave predictions, the differences between models are assessed around each reef within the GBR labelled “near-reef”, and along the Queensland coast at the 20 m mean sea depth contour, labelled “nearshore”. The impact on wave heights from including surface fric­ tion, i.e., comparing statistical simulations Gradient and Standard (Table 1), was that they were reduced by an average of ca 3% for nearreef and 7% for nearshore locations (left panels of Fig. 5) with particular reefs and nearshore locations having increased wave heights attributed to changes in inflow direction leading to fetch increases. Using Holland et al. (2010) gradient wind parametric model (H10, Table 1) increased wave heights, on average, by ca 5% for near-reefs and 4% for nearshore locations (centre panels of Fig. 5) over the reference model (Standard, Table 1). Similarly, waves heights increased, compared to this reference model, by an average ca 10% for Emanuel and Rotunno (2011) (ER11, Table 1) gradient winds (right panels of Fig. 5). The wave model mean water depth at each cell was, as indicated above, set using: for depth greater than 10 m, the cell was assigned the average of all depths available in that cell; and for depth less than 10 m, the cell was assigned the minimum depth of all depths available in that cell. Using this minimum water depth ensured shallow regions of reefs were included for capturing depth-limited wave breaking dissipation. To understand the implications of this modelling approach, statistical simulation BathChk (Table 1) was completed using mean water depth in all wave model cells (Fig. 6). The impact on nearshore wave climate at 20 m water depth was minimal in both qualitative and quantitative aspects (limited scatter with a 5% increase in 1% exceedance significant wave height, right panel of Fig. 6). However, significant changes occur with near-reef wave climate (left panel of Fig. 6), indicating that depth limited wave breaking is a significant physical process within the GBR, particularly when reefs are located within the wave shadow of other reefs. It also indicates that these assumptions on water depth over reefs are overpowered by cyclonic wave generation within the GBR lagoon when considering nearshore waves.

and corresponding wave period and direction for each of the synthetic tropical cyclones. These predictions were then used to estimate wave climate statistics. To test the sensitivities of these wave climate esti­ mates, a number of statistical simulations were undertake (Table 1) and compared. These sensitivity test focus on wind forcing of the wave model (Gradient, Standard, H10, and ER11, Table 1) and bathymetry applied (Standard cf BathChk). These sensitivities tests quantify model related differences from various approaches applied are assessed in this section. The assessment of the coastal protection functions of coral reefs along the Queensland coasts comes from comparisons between Stan­ dard, NoGBR and SLR statistical simulations. As we have done here, it is common to quantify the coastal protection functions of coral reefs by estimating the reef-associated attenuation of wave energy at the coast (Arkema et al., 2015; Baldock et al., 2015; Beck et al., 2018; Sheppard et al., 2005). Our two counterfactuals give complementary insights into the importance of the GBR. First, an assumption of a 1 m increase in net depth (SLR cf Standard) is a generic means of estimating the conse­ quences of a loss of current coral structure, as has been applied globally (Beck et al., 2018). The rationale here is that many coral structures stand approximately 1 m above the substrate yet these are easily lost after cyclones or major coral bleaching events (Done, 1992). This counter­ factual therefore provides a sense of the short-term impact of a loss of live coral on ecosystem functioning. The second, more dramatic, coun­ terfactual in which reef structures are removed (NoGBR cf Standard), provides a measure of the existence value of the GBR for coastal pro­ tection. As stated earlier, we do not imply that this function will be lost. However, it is possible that persistent losses of calcifying corals and algae under climate change and ocean acidification (Kennedy et al., 2013) could lead to long-term erosion of reef structures and exacerbate the effects of sea-level rise on net increases in depth (Perry et al., 2018). Future studies will explore these more realistic scenarios in more detail. While we present these three scenarios in this section, wave climate predictions for Standard, SLR and NoGBR are presented in section 3. In all, these seven statistical simulations represent approximately five million computing hours on a high performance computer. The additional model arrangements for these seven statistical simulations are provided in the remainder of this section. Gradient wind fields were estimated using Emanuel (2004) and applied to the wave model directly (Gradient, Table 1) and including an atmospheric boundary layer, bring in surface friction effects (Standard, Table 1 Summary of wave model statistical simulations. Each of the seven simulations involves simulation of 3406 synthetic tropical cyclones that affect the GBR reefs and Queensland shoreline. The balance of wave model specifications is provided through the text in this section. Statistical Simulation

Code

Changes in model specification

Gradient

A

Standard

B

H10

C

ER11

D

BathChk

E

NoGBR

F

SLR

G

Model configuration from section 2.1 and bathymetry from section 2.2 Emanuel (2004) gradient winds Gradient model with Kepert (2001) atmospheric boundary winds Model configuration from section 2.1 and bathymetry from section 2.2, Holland et al. (2010) gradient winds with Kepert (2001) atmospheric boundary winds Model configuration from section 2.1 and bathymetry from section 2.2, Emanuel and Rotunno (2011) gradient winds with Kepert (2001) atmospheric boundary winds Standard model with all cells assigned mean of measured water depths within each cell (see section 2.2) Standard model with no reef structures, continental shelf retained (see Fig. 7 and section 2.4) Standard model with 1 m sea level rise

2.4. The ‘no reef’ bathymetry The ‘no reef’ bathymetry (Fig. 7) used for statistical simulation NoGBR (Table 1) was determine by estimating the continental shelf geometry through the following. First, working with original bathyme­ try information (see section 2.2), depth measurements within the polygons defining reefs, after they were offset outwards by 2 km, were removed. The remaining data were used to estimate grid depths. Cells with no data were assigned values obtained by smoothing the linearly interpolated values from surrounding cells with data. The smoothing kept cells containing data fixed. It also kept interpolated cells with bed

Online (https://doi.org/10.14264/uql.2019.169) wave climate predictions are available are B, F or G. Other simulations are available on request from the lead author. 6

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Fig. 5. Comparisons of 1% exceedance significant wave height (Hs,1%) for all synthetic cyclones simulated (i.e., 3406 events). Left panels, prediction differences between Gradient & Standard (of Table 1), from including/excluding atmospheric boundary layer. Centre panels, prediction differences between Standard & H10 (of Table 1), from changing gradient winds to Holland et al. (2010). Right panels, prediction differences between Standard & ER11 (of Table 1) from changing gradient winds to Emanuel and Rotunno (2011). Top panels, maximum near-reef wave height at each reef identified by the Great Barrier Reef Marine Park Authority (Anonymous, 2019). Bottom panels, nearshore wave height at 600 m increments (grid resolution). The line of best fit (yellow line) that passes through the origin is shown in the title along with 95% confidence limits and coefficient of determination (R2). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 6. Comparisons of 1% exceedance significant wave height (Hs,1%, of all synthetic cyclones simu­ lated) for adopted cell depths (Standard of Table 1) to using mean depth for all cells (BathChk of Table 1). Left panel, maximum near-reef wave height at each reef identified by the Great Barrier Reef Marine Park Authority (Anonymous, 2019). Right panel, near­ shore wave height at 600 m increments (grid resolu­ tion). The line of best fit (yellow line) that passes through the origin is shown in the title along with 95% confidence limits and coefficient of determina­ tion (R2). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

gradient greater than 5% constant). For reefs on the outer continental shelf, a threshold of 70 m was used to limit changes from smoothing (see for example, cross-section 11, Fig. 7). This approach was obtained by trial-and-error. As there are no data available to check if the ‘no reef’ bathymetry is appropriate, it should be seen as no more than what the

continental shelf may have been. The resulting wave climate is then the likely upper limit on changes to nearshore waves offered by offshore GBR reefs. The final situation being evaluated are changes in wave or runup height reductions with sea level rise. This statistical simulation (SLR, 7

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Fig. 7. The three left most panels, starting from the far left and working towards the right, existing reef bathymetry (used in statistical simulations Gradient, Standard, H10, ER11 and SLR, colour bar to the right), no reef bathymetry (NoGBR, colour bar to the left) and the difference between them (colour bar to the right). The three right most panels, cross-sections showing existing reef (orange) and no reef (NoGBR, combination of blue and orange lines) with the gold dots indicating identified locations that are reefs. Cross-sections titles (1 through to 12) relate to cross-sections similarly numbered on the two left most panels. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1) used the same bathymetry as statistical simulation Standard (Table 1) with the water depth uniformity increased by 1 m while holding reef crest elevations constant, i.e., the worst-case scenario. 2.5. Prediction evaluations against an extended fetch empirical wave model Wave modelling predictions for statistical simulation Standard (Table 1), comprising of 3406 cyclones, were visually checked for consistent wind fields and significant wave heights over the outer model domain, ensuring simulations had run as intended. These checks indi­ cated all 3406 simulations were successfully completed with no apparent numerical issues (e.g., unstable or missing predictions). Approximately 10% of simulations (343 simulations) were randomly selected, with the maximum significant wave heights over deep water when systems were sufficiently far from either the wave model bound­ aries or GBR were compared to extended fetch tropical cyclone empir­ ical wave model (Young and Vinoth, 2013; Young, 2017). The maximum significant wave heights generated using Young’s model were generally higher than those generated by the wave model with the deviation increasing with increasing wave height (Fig. 8). The maximum wind speeds which generated these large waves and for which there was the relatively large differences were generally over 60 m/s. When the wave predictions were generally greater than those derived using Young’s methodology, the cyclones were tracking towards the south-east and away from the GBR. The extended fetch wave model has been developed using tropical

Fig. 8. Comparing process-based wave model SWAN with the empirical extended fetch wave model by Young and colleagues (Young and Vinoth, 2013; Young, 2017).

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Fig. 9. The GBR tropical cyclone significant wave height (Hs) climate, for statistical simulations Standard (top panels, Table 1) and NoGBR (bottom panels) for 5% (left most panel), 25%, 50%, 75%, 95% and 99% (right most panel) percentiles (or exceedances of 95%, 75, 50%, 25%, 5% and 1%). Model grids and GBR limits shown by Fig. 4. The relevant colour bar is located to the right of each map, with the minimum being zero for all maps and maximum varying (0.8 m for 5% to 9 m for 99% percentiles). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 10. The GBR tropical cyclone significant wave height (Hs) climate, for statistical simulations Standard (three lest most panels, Table 1) and NoGBR (three right most panels) for 10, 50 and 100 year return period. Model grids and GBR limits shown by Fig. 4. The relevant colour bar is located to the right of each map, with the minimum being zero for all maps and maximum varying (4.5 m for 10 y to 8 m for 100 y return period). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

cyclones with maximum wind speeds between 20 m/s and 60 m/s. The default parameter wave generation model yields predictions on average 12% less than this model, which at this stage is considered acceptable given the following. First, the wave height sensitivities between various parametric wind field models and reef bathymetries. Second, the reduce dissipation (or increasing wind-wave growth parameters) in the wave model to bring these predictions into alignment, is unlikely to materially change the qualitative assessment of relative reef exposure or changes in nearshore wave climate. These qualitative and quantitative checks, therefore, confirmed that the wave model was providing sensible pre­ dictions and was fit-for-purpose.

(Langford, 2006) is 1.1%, which is less than model sensitivity and deep-water accuracy (sections 2.3 and 2.5). The return periods are estimated as follows. First, defining χ as the annual arrival rate (see section 2) of n synthetic cyclones, then the period covered by the syn­ thetic events is n=λ or 6000/2.3–2609 years. Adopting natural proba­ bility estimators (Coles, 2001) for y1 � :::yj ::: � yn , yields Prfyj g ¼ j � 1 n=λ. The annualised return period then is TR ðjÞ ¼

1

1 e

Prfjg

:

(2)

Finally, the annualised return period of interest are obtained through linear interpolation. Spatial cyclonic wave climate (Figs. 9 and 10) confirm previous findings that the outer reefs systematically dissipate large Pacific Ocean waves (Fig. 11). This indicates that there will be reefs that are protected by virtue of their location. For brevity, spatial information of the 1 m sea level rise case has not been shown as at the scale of the GBR, increases are indistinguishable from the existing cyclonic wave climate (top panel of Fig. 9 or left panels of Fig. 10). Comparing the maximum near-reef wave height for existing and 1 m sea level rise (SLR, Table 1) in­ dicates an increase of 14% for near-reef waves up to 4 m significant and a 3% increase above this wave height. The cyclonic wave climate varies along the Queensland coastline with lagoon wave heights increasing as lagoon widths increase. This result confirms pervious finds that lagoon waves include local generation (The modelling approach, see section 2, excludes tide and surges, amongst other things, which introduces ac­ curacy limitations on these predictions.). The southern reef has higher near-reef waves as they have fetches extending into the Pacific Ocean. These extended fetches offset the reduced exposure from reduced

3. Tropical cyclone wave climates The statistical simulations are used to estimate exceedance statistics of all cyclones modelled and for particular return periods, assuming quasi-stationary cyclone arrival rate (that is, the averaged arrive rate over the period simulated). Exceedance statistics are determined by ranking maximum wave heights as x1 � :::xi ::: � xN , assigning percen­ � � 1 tiles of 100 i N 2 , and linear interpolating percentiles of interest. Ex­ ceedance levels are 100% less its percentile. A review of literature around estimating percentiles reveals an extensive array of suggestions with, for example, Langford (2006) providing 15 different methods. Testing shows that differences vanish for large N compared with the percentile being calculated. For the 99% (or 1% exceedance), this in­ volves interpolating between 98.99% and 99.02% for i of 3372 and 3373 respectively, and for statistical simulation Standard (Table 1), the mean absolute relative error between different definitions of percentiles 10

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frequency of cyclones propagating through the southern region (when compared with the northern region, which experiences almost twice as many). The outer reef barrier system is very effective at resetting the wave height from many metres in the Pacific Ocean basin to less than a metre just within the lagoon where the barrier is nearly continuous north of central GBR. South of central GBR, the barrier is formed from a series of reefs, acting together to dissipate ocean waves to less than a metre. Nevertheless, there are isolated locations were lagoon wave climate is enhanced by exposure to Pacific Ocean fetches. The 1% exceedance maximum near-reef significant wave height varies from 1 m to 10.5 m throughout the reef. This range comes from reefs protecting other reefs. Wave shadows are generated by reefs for a particular wave direction. While this concept is well established (Gallop et al., 2014), the question of whether reef’s location, relative to other reefs, can lead to a reduced cyclonic wave climate, i.e., from many different wave heights, directions and periods, is less obvious. These statistical simulations include many different sea states and hence, it is concluded that there are reefs that are sheltered by different reefs under different waves, leading them to have less cyclonic wave exposure. The maximum near-reef significant wave height using the reefs identified by the Great Barrier Reef Marine Park Authority (Anonymous, 2019) indicate that 25% of reefs are exposed to maximum near-reef significant wave height maxfHs;1% g � 2:2 m and maxfHs;1% g � 4:7 m: One conse­ quent of wave attenuation from reefs within the GBR is that there is a range of wave exposure across the more than three thousands reefs forming the GBR. This variation in wave exposure leads to variation of corals species (Roelfsema et al., 2018). That variation adds to the resilience of the GBR. The 1 m sea level rise, applied instantaneously, statistical simulation (SLR, Table 1) changes these divisions to maxfHs;1% g � 2:5 m and maxfHs;1% g � 4:8 m: The existing (statistical simulation Standard) nearshore 100-year return period wave exposure, measured as significant wave height at the 20 m depth contour (Fig. 12 top panel), generally increases from a low between Lockhart River and Bamage (Hs ~ 3.5 m) to a sustained high between Townsville and Agnes Waters (Hs ~ 5 m). The 10-year return period, however, has a more uniform wave height (Hs ~ 2 m) across the entire GBR. The existing wave exposure has local effects with either the 10-year or 100-year quantities dipping locally (for example, Airlie Beach has wave heights dropping from ca 5 m–2 m). These local effects are from reefs or islands located offshore of the 20 m depth contour located nearest to the Queensland coast. The 2% exceedance runup height, R2%, used for flood evaluation, was estimated using Nielsen and Hanslow (1991). pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2% � ln 50 � 0:6 tanβF Ho;rms Lo (3) using βF ¼ 0:2 (beach face slope, value selected as an upper limit within the GBR), and where Ho;rms is the deep water root mean square wave height (taken here as Hs/1.4 by assuming Rayleigh distributed wave height) and Lo is the deep water wavelength, here based on peak wave period. It is noted that there are many runup height predictors, each with their own justifying data sets. The point of this analysis is not an extensive review of runup height approaches, but of the potential reduction of runup height by GBR. A comparison of Nielsen and Hans­ low (1991) and Stockdon et al. (2006) and for the beach face slope selected yields pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2% e0:24 Ho;rms Lo (4) for Nielsen and Hanslow (1991) and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2% e0:20 Ho;rms Lo

Fig. 11. Cyclonic wave transmission coefficient K ( ¼ Hs,Standard/Hs,NoGBR) from GBR reefs related wave attenuation for 5%, 25%, 50%, 75%, 95% and 99% percentiles and 10, 50 and 100 year return period. Model grids and GBR limits shown by Fig. 4.

(5)

for Stockdon et al. (2006), illustrating that while the magnitude changes (in this case by 18%), the qualitative nature of runup height being e pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ho;rms Lo is maintained. That is, while the magnitude is up for 11

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Fig. 12. 10-year (thin lines) and 100-year (thick lines) return period significant wave height (top panel, Hs), Gourlay number (middle panel, wHs Ts p ) and 2% exceedance runup height (bottom panel), along the Queensland coast, for statistical simulations Standard (red), NoGBR (green) and SLR (blue, Table 1). See Fig. 1 for location of towns shown. Near-shore waves are taken at the 20 m depth contour.

refinement (better data on beach face slopes and runup height formu­ lation), the conclusions drawn regarding runup height reductions are qualitatively reliable. The existing runup heights are typically between 4 and 6 m for the 100-year return period and less than 4 m for the 10-year return period (Fig. 12 bottom panel) and has a similar spatial distribu­ tion as wave height. However, the interaction between wave height and period, has led to spatial drops in runup height being less pronounced cf wave height. One significant difference between wave and runup height is the rapid changes in runup height occurring over a few kilometres, within the southern GBR cf the smooth spatial variations seen in the northern GBR. As the wave height shows smooth spatial variation throughout the GBR, these rapid variations are from wave period vari­ ations. The differences between regions north and south of 480 km

(distance from Elliott Heads, Fig. 12) is fetch length, which becomes more constrained by outer reefs north of this point. In particular, with Pacific Ocean fetches featuring less and less for wave generation be­ tween Yeppoon and Mackay. These estimates indicate that north of Mackay, cyclonic waves are generated in the lagoon (with the exception of a few gaps in the outer reef system). The difference between statistical simulation NoGBR less Standard, provides a measure of the current wave or runup height reduction (Fig. 12) provided by the reef for cyclonic conditions. The barrier reef reduces nearshore wave heights, at the 100-year return period, by a factor 1.53 [1.04; 2.20], with 95% confidence range provided in the square brackets. A similar protection is afforded at the 10-year return period with a reduction factor of 1.62 [1.06; 2.32]. This reduction 12

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translates into enhanced inundation protection (bottom panel of Fig. 12) in that potential for wave runup flooding are reduced by a factor 2 (10year: 2.12 [1.12; 3.32] and 100-year 1.92 [1.08; 2.96], respectively). The nature of these cyclonic waves, in terms of cross-shore beach erosion, where beach profile shape changes from accretive to erosive, were assessed using the Gourlay number (Baldock et al., 2017; Gourlay, 1968, 1980; Wright and Short, 1984). The Gourlay number is defined here as G¼

Hs ws Tp

Barrier Reef Marine Park Authority was estimated at various exceedance thresholds, with the 1% maximum near-reef significant wave height at each reef indicating that there are a wide range of reef exposures from ca 1 m–10.5 m. These estimations further indicate that there is an ecosystem function provided by GBR to itself through providing reefs with variable exposure to waves, leading to a range of coral species. The ecosystem functioning loss under climate change was estimated using a worst-case scenario in which all reefs have no vertical growth under 1 m sea level change. Under this change, waves below ca 4 m significant, increased on average, by 14% with lesser increases for larger wave heights. The existing reduction in wave or runup heights (a measure of shoreline protection) from the GBR has been estimated by comparing existing reef with an idealised no reef scenario. These differences indi­ cate that GBR reduce wave forcing from between a factor 1.5 to 2, depending on how it is assessed (nearshore wave or runup height) and return period selected (10- and 100-year). It was found that changes in nearshore cyclonic wave or runup heights at either 10- or 100-year re­ turn period was at most, increased by five percent under sea level rise. The beach erosion from cross-shore processes was included and it was interesting to find that presence or absence of reefs is unlikely to change beach shapes (similar Gourlay numbers) but would lead to wider surf zones from increased nearshore wave height. Nevertheless, the ecosystem function is provided by reducing the active beach width and there-by limiting landward erosion under cyclonic conditions. It was again found that there was limited reduction in this function with 1 m sea level rise. While these findings are counter to those of reduced coastal pro­ tection from fringing reefs (Beck et al., 2018; Ferrario et al., 2014) under sea level rise, the difference is that there is relatively few fringing reefs within the GBR available to provide wave attenuation without subse­ quent wave generation. That is, the outer barrier, while effectively dissipating Pacific Ocean wave energy, the lagoon fetches are long enough that there is enough distance for cyclonic winds to re-establish cyclonic wave heights.

(6)

where Hs is the near-shore significant wave height with corresponding peak wave period, Tp and ws is the sediment settling velocity. For this regional analysis, settling velocity was taken as 0.1 m/s based on settling measurements of GBR coral sand (Gunnell, 1986). The Gourlay number for existing reef and no reef structure indicates nominal changes and hence, it is expected that shifts in beach shapes may well be marginal (Gourlay numbers similar for statistical simulation Standard and NoGBR, middle panel of Fig. 12). While the change in shapes under cyclonic conditions is unlikely to change, the active zone (significant sediment transport) will widen as larger waves breaking further offshore are predicted. The reef structure, does provide a reduced amount of longshore variability in cross-shore changes. The longshore sediment transport changes, however, suffer too much uncertainty in their esti­ mates with such limited data, to make any comments either way. The 10 and 100-year nearshore wave climate, as measured using significant wave height and 2% exceedance runup height, are qualita­ tively similar for with and without 1 m SLR (statistical simulations Standard and SLR Fig. 12). Their quantitative differences are wave heights increase by a factor 1.03 [1.01; 1.08] for 10-year and 1.03 [1.01; 1.05] for 100-year return period respectively. The quantitative differ­ ences are similar for runup height (10-year of 1.04 [0.84; 1.24] and 100year of 1.03 [0.94; 1.12]) albeit with larger confidence limits for vari­ ations introduced through wave period and direction changes. While this analysis focuses on cyclonic waves, it is expected, given these cyclonic wave estimates, that reefs are unlikely to influence everyday nearshore waves. However, their ability to block Pacific Ocean gener­ ated waves may impact on the reefs themselves as shallow reefs will experience increased Pacific Ocean waves during sea level rise. That is, while there is limited signal at the shoreline, there is expected increased exposure around outer reefs from sea level rise for everyday waves. Wave climates presented in this section can be freely downloaded from https://doi.org/10.14264/uql.2019.169, in self-describing netCDF and geographical information system shapefile format.

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement David P. Callaghan: Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization, Data curation. Peter J. Mumby: Conceptualiza­ tion, Formal analysis, Resources, Data curation, Writing - review & editing, Project administration, Funding acquisition. Matthew S. Mason: Methodology, Software, Validation.

4. Summary The tropical cyclonic wave climates have been estimated (presented herein and available online) using Emanuel et al. (2008) estimated synthetic tropical cyclones, Emanuel (2004) gradient winds and Kepert (2001) atmospheric boundary layer, the simulating waves nearshore wave model (Booij et al., 1999; Holthuijsen, 2007; Ris et al., 1999) with a 600 m grid increment. Seven statistical simulations where used to estimate prediction uncertainties, the ecosystem functions related to reducing wave or runup heights, from existing GBR and possible reduction under 1 m sea level rise. Wave prediction uncertainty from wind forcing approaches ranged from 7% to þ10% and from water depth approaches up to 21%. The cyclonic wave climate generally increased from north to south, even though the cyclonic exposure reduces from north to south (number of synthetic tropical cyclones in the southern region is approximately half that of the northern region). This was seen to be related to the in­ crease in lagoon width from north to south and then the incorporation of Pacific Ocean fetches within the southern region. The cyclonic wave climate for each reef identified by the Great

Acknowledgments Shoreline data was provided by Queensland Government, reef out­ lines was provided by the Great Barrier Reef Part Authority, Common­ wealth of Australia. The high performance computing was supported by Queensland Cyber Infrastructure Foundation and The University of Queensland. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.coastaleng.2020.103652.

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