The GBR is an offshore reef matrix that extends 2,300 km alongshore (Hopley et al. 2007), with more than 2,900 individual reefs (Hopley et al. 1989; Fig. 1). The average area of individual reefs is 6.9 km2, and the total reef area is 20,055 km2 (Hopley et al. 1989). In the north, reefs are predominantly two-dimensional (i.e., very narrow in the cross-shore direction) and create almost a complete barrier to incident waves (Young 1989). Further south, the reef matrix is more three-dimensional and porous, with porosity decreasing at the southern end. Wave propagation through the reef matrix is influenced by spectral modification of waves propagating across individual reefs, two-dimensional processes such as diffraction and refraction, and the porosity of the reef matrix (Young 1989). The wind and wave climate is strongly seasonal, with a summer-monsoonal climate. During April to September, waves are generated mainly by the persistent southeasterly winds, while during October to March, variable northerly winds dominate (Gourlay 1990).
Satellite altimeter data
Altimeter data were extracted from seven satellite missions: Topex-Poseidon, ERS1 and 2, GFO, Jason1 and 2, and Envisat. These data spanned September 1992 to May 2008, with a total of 5,205 passes over the GBR. Topex-Poseidon, Jason1, and Jason2 had a repeat cycle of 10 days, at 1,336 km altitude; ERS1, ERS2, and Envisat had a repeat cycle of 35 days at 800 km altitude; while GFO had a repeat cycle of 17 days at 800 km altitude. Only passes heading in a southwest–northeast orientation (descending) were used, because these are approximately perpendicular to the GBR matrix. In addition, only tracks with at least 30 repeat passes, and those that crossed the reef matrix at an angle of 70–110° (near perpendicular) compared to the local orientation of the matrix, were utilized. This resulted in 19 tracks with a total of 2,003 passes (Fig. 1). One H
s and wind speed 10 m above the sea surface derived from these passes were used.
Altimeters measure H
s within a circular footprint, the size of which varies with sea state, altimeter altitude, and pulse duration (Chelton et al. 1989). For example, the Topex–Poseidon footprint diameter increases from 8 km during calm sea, to 11 km for H
s of 15 m. Altimeters measure at 20 Hz and travel with a ground speed of around 6–7 km s−1. These measurements are usually averaged for oceanographic applications to 1 Hz to reduce noise. Therefore, depending on the sea state and the size of the footprint, a single 1 Hz-averaged measurement of H
s would typically be an average of 20 successive footprints over an area 10 km wide and 17 km long.
In close proximity to reefs and coasts, altimeter data frequently contain spikes. In previous studies, such errors have been removed by a combination of the application of land masks and automatic outlier removal algorithms (Young 1999; Zieger et al. 2009; Young et al. 2011). However, these techniques typically filter the data too aggressively, removing much valuable and reliable data close to reefs, which are required for the present research. Thus, the raw satellite altimeter passes were visually checked for obvious data errors and regions where data spikes were present were manually excluded, as was done by Young et al. (2013). In the present application, interest is in the attenuation of the altimeter-measured wave height across the reef matrix. As a result, the raw values of significant wave height provided by the respective satellite agencies were used rather than any post-processed calibrations (Zieger et al. 2009).
Bathymetry along the satellite passes was obtained from Project 3DGBR (Beaman 2010). This bathymetry has resolution of 0.001-arc degrees (100 m), with a horizontal datum of WGS84, and a vertical datum of mean sea level (MSL). It is a combination of multi-beam, single-beam, lidar, and satellite bathymetry collected between 1971 and 2010.
Hourly water levels relative to MSL at the same times and locations as the satellite passes were obtained from a numerical hydrodynamic hindcast (Haigh et al. 2014a, b). This hindcast utilized a depth-averaged tide and surge model, using the Danish Hydraulic Institute’s (DHI) Mike21 model. A flexible mesh was used with resolution of 20 km at the open boundaries around Australia, gradually increasing to a resolution of 10 km near the coast. The model was forced with meteorological fields obtained from the US National Center for Environmental Prediction’s (NCEP) global reanalysis (Kalnay et al. 1996; Kistler et al. 2001; Fig. 2).
Tides are mixed with both diurnal and semidiurnal components, except in Broad Sound (Fig. 2) where they are diurnal only (Hopley et al. 2007). Reefs may be exposed at low spring tides, while at high tide can be submerged by several metres (Symonds et al. 1995). North of 18°S, mean spring tidal range is <2 m, then starts to increase around Townsville to 2.5 m (Fig. 2). From here, tidal range increases to more than 6 m in the vicinity of Broad Sound. South of 23°S, tidal range decreases. This has implications for the spatial variability in the depth of reef submergence.
The dominant wave direction (southeasterly) and the satellite tracks (southwest–northeast) have different orientations. Therefore, the analysis undertaken here would be much simpler if it were possible to assume that deep water wave heights were relatively spatially invariant along the length of the GBR matrix. To investigate whether this assumption could be made, wave data were extracted along the 100 and 2,000 m contours from a 30-yr wave hindcast using WAVEWATCH III (Tolman 1991, 2009). The model covered the period from 1979 to 2009 (Durrant et al. 2014) and was forced with Climate Forecast System Reanalysis surface winds (CFSR; Saha et al. 2010). The model was run on a 0.4 by 0.4° global grid, with a series of nested grids of 10 arc min down to 4 arc min (~7 km) around the Australian coast (Fig. 3). These grids were two way-nested following Tolman (2008), resulting in a completely self-consistent means of locally increasing resolution, providing data of significantly higher quality and resolution than was previously available. The mean and standard deviation of Hs were calculated for the full 30 years covered by this hindcast. A comparison between offshore H
s measured by the altimeters and the model was in good agreement with close to a 1:1 correlation (Fig. 4). There was only a slight bias by the model of 0.22 m.
A typical barrier reef consists of a forereef sloping up to the reef crest; a lagoon; and a reef flat (Lowe et al. 2005). Individual reefs at the edge of the GBR shelf tend to have steep offshore-facing edges, so waves have little interaction with the seabed even a few 100 m from the forereef (Hopley et al. 2007). Most waves break over the reef crest, then can subsequently reform where there is a lagoon (Gourlay 1990), and break closer to shore (Fig. 5b).
Wave attenuation was estimated over the segment of reef matrix that was closest to the coast by extracting Hs measured by satellite altimeters, at three locations along each satellite pass:
offshore where depth seaward of the reef matrix first exceeded 100 m to MSL;
within the reef matrix at the subsequent satellite measurement after the offshore location;
lee of the reef matrix at the furthest measurement landward of the reef matrix where the depth becomes less than 40 m (Fig. 5).
Linear regression showed that distance across the reef matrix between the extraction points offshore and in the lee of the matrix did not have a statistically significant influence on the magnitude of wave attenuation.
Porosity index of the reef matrix
The porosity of the reef matrix was represented by a ‘porosity index’. This index was generated based on the volume of water compared to the volume of reef above the 40 m depth contour (Fig. 5b), between the forereef (100 m depth) and the lee of the reef. A range of depths were tested from 0 to 100 m with respect to MSL. Sensitivity testing showed that using 40 m gave the greatest range of porosities across different sections of reef, and is also a level which distinguishes between individual reefs, the regions between reefs, and the GBR lagoons in the lee of the reef matrix. In addition, this corresponds to the approximate depth where waves start to ‘feel the bottom’. The mean incident wave period in the GBR region from the hindcast was 8.1 s, with standard deviation of 1.4 s. According to linear wave theory (Dean and Dalrymple 1991), the corresponding deep water wave length for an 8 s wave is around 100 m; waves start to ‘feel the bottom’ when water depth is half the wave length, which is 50 m depth for a wave with 100 m wave length.
A porosity index of 0 indicates that the entire volume above 40 m was reefs or seabed (i.e., 0 % porous), while 1 specifies that there were no reefs or seabed above 40 m depth (i.e., 100 % porous). This index was calculated for the length of the GBR, in cells that were 10 km wide (corresponding to the approximate width of the satellite footprints), extending from the coast to the 100-m contour. The index was developed to understand mean wave attenuation over the GBR.
Future research is planned to understand more about the permeability of the reef matrix, which will be determined not just by the porosity index, but likely also the angle of incident wave approach, and the effectiveness of the individual reef geomorphology at dissipating waves, which depends in part on reef slope and spatial continuity.