Offshore incident waves

The offshore wave climate of the GBR consists largely of southeasterly swell generated in the Coral Sea (Fig. 1), and occasionally, cyclone-generated waves during December to April (summer; Hopley et al. 2007). Mean, peak wave period (T p ) is generally between 8 and 9 s offshore of the GBR, and from the forereef (around the 100 m contour) decreases to between 6 and 7 s, likely due to the local generation of wind waves (Fig. 6a). The mean incident wave direction is southeasterly (Fig. 6b). Therefore, the offshore wave height relevant to the wave attenuation along a given satellite pass may be quite different to the offshore wave height extracted from the pass itself. That is, the waves measured by the altimeter seaward of the GBR may not propagate along the altimeter track. Rather, waves measured by the altimeter landward of the GBR matrix could have propagated from a seaward point to the southeast. However, if it can be assumed that the wave field seaward of the GBR does not change significantly; then, the discrepancy in direction of the satellite track and offshore waves will not introduce significant error. To investigate whether this is the case, numerical model-derived H s along the 2,000 and 100 m depth contours offshore of the GBR matrix were analysed. For most of the 2,000 m contour, mean H s varied between 1.6 and 1.8 m; and SD was between 0.7 and 0.75 m. From 12 to 14°S mean H s100 decreased from 1.7 to 1.2 m (Fig. 6c), and SD decreased from 0.7 to 0.5 m (Fig. 6d). From 14 to 15°S, mean H s100 increased from 1.2 to 1.7 and SD also increased from 0.5 to 0.7. From 15°S, there was a decrease in mean H s100 to 1.5–1.6 m and SD was between 0.65 and 0.7 m. South of 21°S, mean H s100 increased to 1.75 m.

Fig. 6 a Mean T p from the model; b mean H s from the WAVEWATCH III hindcast (colour) and mean incident wave direction (arrows); c H s along the 100 and 2,000 m contours (H s100 and H s2000 ); and d standard deviation between 1992 and 2008 Full size image

The abrupt decrease in mean H s100 and H s2000 around 14 to 15°S is due to a change in the local orientation of the coast and the reef matrix. For most of the GBR, the mainland and the reef matrix faces the northeast. However, from 14 to 15°S (Princess Charlotte Bay, Fig. 1), the orientation becomes more northerly, so is largely sheltered from the incident southeasterly waves (Fig. 6b). In this area, the forereef is very steep and the 100 m and 2,000 m contours lie up to 8 km apart, compared with up to 500 km in the central GBR (Fig. 1). Therefore, the sheltering effect of the coastal orientation is evident in incident H s along the 100 and 2,000 m contours. No satellite tracks were analysed from this section of coast due to the large discrepancy between the orientation of the coast and reef matrix with altimeter passes (Fig. 1). However, for the remainder of the GBR matrix, within 1° latitude (~111 km) regions, mean incident H s2000 varied by <2 cm, and mean H s100 by <5 cm. Therefore, assuming that the measured offshore incident H s from the satellite tracks represents the wave conditions seaward of the GBR which would propagate across the reef matrix, is likely to result in errors of H s of only a few cm.

Porosity of the reef matrix

There is a trend of increasing reef matrix porosity from north to south (Fig. 7a). In the north, porosity averages approximately 0.6 (i.e., 60 % porous) where the shelf is narrower than 8 km. From 15°S as the shelf widens, porosity starts to increase, and in the central GBR is mostly between 0.7 and 0.95. In the south, the shelf is up to 300 km wide, and there is an extensive lagoon that is more than 200 km wide in the far south. This lagoon leads to high porosities of generally more than 0.8. The trend of porosity is similar to the much lower resolution (1° latitude) estimate of the area of shelf to reef calculated by Hopley et al. (1989; Fig. 7a), but here calculated at much higher resolution. The porosity index indirectly reflects the geomorphology of individual reefs. For example, according to Hopley et al. (1989), north of 16°S, planar reefs are common and associated with extensive reef flats and a lack of lagoons, leading to lower porosity in the north. Crescentic reefs dominate the central GBR between 14 and 22°S, with an open back reef area and lagoons, reflected in the increasing porosity index in the area. Lagoonal reefs are mainly restricted to south of 19°S, and in combination with the wide shelf and extensive lagoons, leads to the highest porosity index in the southern GBR.

Fig. 7 a Porosity index every 10 km alongshore between the coast and 100 m contour; b wave transmission coefficient calculated as in Nelson and Lesleighter (1985) at the 40 m contour; and c mean (star and lines) and standard deviation (bar) of submergence to mean sea level at the edge of the reef matrix (reef crest) Full size image

Reef submergence

The depth of submergence of the reef matrix along each of the altimeter tracks is shown in Fig. 7c. Although successive altimeter passes are nominally along the same track, the exact tracks vary within several km, reflected in the standard deviation of bathymetry. The mean depth of reef submergence varied between 15 and 45 m, with significant variability between passes and no clear trend along the length of the GBR. It is not surprising that there is no apparent trend in submergence along the length of the GBR.

Coral reefs tend to grow up to the low tide level, and hence, one would initially expect a similar depth of submergence at all locations. This relationship is reflected in the positive correspondence between tidal range, and the variation of reef submergence (represented by standard deviation). However, the correlation coefficient (r) is relatively low at 0.22 and is not statistically significant, with a probability value (p) of 0.37 (Fig. 8a).

Fig. 8 Relationship between a mean spring tidal range and standard deviation (SD) of reef crest submergence to MSL; and b porosity and wave transmission (K T ) matrix to lee. r is the correlation coefficient and p is the probability value Full size image

Wave transmission

Reef geomorphology has a strong influence on wave attenuation and the development of locally generated wind waves. This is demonstrated in Fig. 9 which shows the mean values of H s averaged over all passes along tracks 1, 6, and 14 in the northern, central, and southern GBR, respectively (see Fig. 1 for track locations). In the northern GBR (Fig. 9a), waves attenuated by an average of 0.7 m at the reef matrix edge, then generally decreased in height in the lee of the matrix, with a slight increase in height towards the coast likely due to shoaling. In the central GBR where the shelf is wider, waves break at the edge of the reef matrix, then decrease further in height due to friction over the reef matrix. The region in the lee of the reef matrix is deeper and wider than in the north, allowing local generation of wind waves, and possibly wave penetration through spaces in the reef matrix (Fig. 9b). In the southern GBR, there are multiple lagoons between reefs, where there was local generation of wind waves (Fig. 9c).

Fig. 9 Mean bathymetry (black) and mean H s (blue) along tracks as a function of distance from the offshore H s extraction location along tracks a 1, b 6, and c 14. Grey dotted lines show standard deviation Full size image

The wave transmission coefficient (K T ) represents the percentage of H s transmitted between two locations (Nelson and Lesleighter 1985; Lugo-Fernández et al. 1998) given by:

$$ K_{\text{T}} = \frac{{H_{1} }}{{H_{2} }} $$ (1)

where H 1 is significant wave height further offshore; and H 2 is further landward. There was significant scatter in K T for each of the tracks (Fig. 7b). Although the porosity index (Fig. 7a) increases from north to south along the GBR, there is no clear similar trend when considering K T (offshore to matrix). There was no statistically significant relationship between the mean porosity of the reef matrix and mean K T (offshore to lee), with a p value of 0.73 (Fig. 8b). That is, the data do not clearly show that a more porous reef matrix allows significantly larger amounts of wave energy to penetrate the matrix.

There is, however, an increasing trend from north to south in K T (matrix to lee of matrix). On all tracks, there was an abrupt reduction in mean H s over the edge of the reef matrix of between 0.5 and 1.2 m, followed by further reduction in H s as waves travelled over the matrix and into the lee (Fig. 10). There was an increase in H s in the lee of the matrix due to local wind-wave generation, which occurs mainly from track 6 southwards. This was reflected in K T (matrix to in the lee of matrix), which was often greater than 1, and up to 1.6 in the southern GBR (Fig. 7b). These values of K T (matrix to in the lee of matrix) greater than 1 reflect the process of local generation of wind waves in the GBR lagoon, where H s increases between offshore and the lagoon.

Fig. 10 Mean values of H s along all tracks from north to south (top to bottom of plot). The track number is shown on the right. Distance onshore is from the offshore point seaward of the reef matrix for each altimeter pass Full size image

Incident H s , wind, and submergence

Figure 11 assesses (1) H s over the reef matrix as a function of offshore incident wave height and the depth of reef matrix submergence (Fig. 11a), and (2) H s in the lee of the reef matrix as a function of wind speed and H s over the reef matrix (Fig. 11b). The depth of reef matrix submergence ranged from 40 to 0.5 m, and offshore incident H s ranged from 0.2 to 4.5 m (Fig. 11a). For depth of reef submergence greater than approximately 7 m, H s over the reef matrix was strongly dependent on incident offshore H s rather than the depth of crest submergence. However, at submergence of <7 m, where more wave breaking and friction decay could be expected, H s was no longer a function of depth of submergence.

Fig. 11 a H s in the lee of the reef matrix as a function of depth of submergence of the crest and incident H s ; and b H s in the lee of the matrix as a function of H s at the matrix and wind speed Full size image