The Role of Bed Roughness in Wave Transformation Across Sloping Rock Shore Platforms

We present for the first time observations and model simulations of wave transformation across sloping (Type A) rock shore platforms. Pressure measurements of the water surface elevation using up to 15 sensors across five rock platforms with contrasting roughness, gradient, and wave climate represent the most extensive collected, both in terms of the range of environmental conditions, and the temporal and spatial resolution. Platforms are shown to dissipate both incident and infragravity wave energy as skewness and asymmetry develop and, in line with previous studies, surf zone wave heights are saturated and strongly tidally modulated. Overall, the observed properties of the waves and formulations derived from sandy beaches do not highlight any systematic interplatform variation, in spite of significant differences in platform roughness, suggesting that friction can be neglected when studying short wave transformation. Optimization of a numerical wave transformation model shows that the wave breaker criterion falls between the range of values reported for flat sandy beaches and those of steep coral fore reefs. However, the optimized drag coefficient shows significant scatter for the roughest sites and an alternative empirical drag model, based on the platform roughness, does not improve model performance. Thus, model results indicate that the parameterization of frictional drag using the bottom roughness length‐scale may be inappropriate for the roughest platforms. Based on these results, we examine the balance of wave breaking to frictional dissipation for rock platforms and find that friction is only significant for very rough, flat platforms during small wave conditions outside the surf zone.


Introduction
One of the longest standing debates in rocky coast geomorphology is whether subaerial weathering or wave processes dominate shore platform evolution (Kennedy et al., 2011), that is, the "wave versus weathering debate." One approach to help resolve this issue is through the measurement of surf zone hydrodynamics to quantify wave energy dissipation, wave forces, and wave-driven currents across shore platforms. For example, Stephenson and Kirk (2000) made wave height measurements across a quasihorizontal platform in New Zealand and found that despite the energetic offshore wave conditions, the amount of energy delivered to the platforms was very low with only 5-7% of the wave energy at the seaward edge of the platform reaching the cliff foot; they concluded that wave erosion was not effective in this area. The quantification of wave energy levels across the shore platform is also relevant in assessing the delivery of wave energy to the cliff toe (Naylor et al., 2010), and for determining the likelihood of large boulders being moved by waves across the platform (Nott, 2003).
Shore platforms are (quasi-) horizontal or gently sloping rock surfaces, generally centered around MSL and extending between spring high and spring low tidal level (Kennedy & Milkins, 2015). They are abundant along energetic rocky coasts and are often backed by eroding cliffs, sometimes with a beach deposit present at the cliff-platform junction. The development of shore platforms is intrinsically linked to coastal cliff erosion (Trenhaile, 1987), and they have been described as erosional stumps left behind by a retreating sea cliff (Pethick, 1984). Two shore platform types have been described (Sunamura, 1992): Type A platforms are characterized by a gently sloping (tanβ = 0.01-0.05) surface that extends beneath sea level without a marked break in slope and are usually found in large tidal environments (mean spring tide range > 2 m); Type B platforms are characterized by a (quasi-) horizontal surface fronted by a steep scarp (sometimes referred to as a low tide cliff) and typically occur in small tidal settings (mean spring tide range < 2 m).
Measurements have shown that shore platform gradient is positively correlated with tidal range (Trenhaile, 1999); however, it has recently been suggested that platform gradient may also be affected by the sea level history (Dickson & Pentney, 2012). The shore platform surface depends mainly on geological factors, such as lithology and the characteristics of the stratigraphic beds (thickness, strike, slip, etc.) and ranges from very smooth (similar to a sandy beach) to very rough (similar to a coral reef edge) (Trenhaile, 1987). Both the gradient and the roughness of shore platforms are expected to play key roles in driving nearshore dynamics through their effect on wave transformation processes, incident wave energy decay, wave setup, and infragravity wave generation.
Despite the recognized importance of wave processes in influencing shore platform dynamics and evolution (e.g., Dickson et al., 2013;Kennedy & Milkins, 2015), there is a paucity of appropriate process measurements made in these settings and even fewer studies in macrotidal environments. This represents a considerable time lag compared to nearshore research on sandy beaches, where wave data have been routinely collected since the 1980s (cf. Komar, 1998) and also compared to investigations of wave transformation process across coral reef platform (e.g., Brander et al., 2004;Lowe et al., 2005). The latter are rather similar to rocky shore platforms, both in terms of the gentle gradient (especially the Type B platforms) and the rough surface. Long-term evolution of platforms has been addressed by Dickson et al. (2013) who challenge simplified steady state equilibrium models that apply exponential decay, in wave height, and do not consider infragravity wave frequencies. This work links with that of Kennedy and Milkins (2015) who address beach accumulation on platforms as a possible negative feedback to reduce cliff retreat through increase wave dissipation.
A limited number of field data sets are available describing wave transformation across rocky shore platforms in microtidal settings. A common feature of these studies is the tidal modulation of the wave height and the depth limitation of the surf zone wave heights across the platform (Farrell et al., 2009;Marshall & Stephenson, 2011;Ogawa et al., 2011Ogawa et al., , 2015Ogawa et al., , 2016. The concept of a "saturated surf zone" (Thornton & Guza, 1982) is well demonstrated in each of these field investigations, and concurrent with the dissipation of short-wave energy is the increase in the infragravity wave height (Beetham & Kench, 2011;Ogawa et al., 2015). The latter finding is potentially a very important geomorphic process, especially during energetic wave conditions (storms), because it is these waves that may dominate the water motion at the landward edge of the shore platform and provide the main force for cliff erosion and cliff toe debris removal (Dickson et al., 2013).
A useful parameterization of the wave conditions in the surf zone is the ratio of wave height H to water depth h. For monochromatic waves, this parameter is referred to as the breaker index γ and its value ranges from about 0.7 to 1.2. For random waves, H/h must be defined in statistical terms and usually the root-mean-square wave height H rms or the significant wave height H s is used. For consistency, all H/h values quoted in this paper are H s /h, and values in the literature based on H rms have been converted to H s /h using H s = √2H rms . Original work on sandy beaches by Thornton and Guza (1982) suggested that H s /h is constant in the surf zone with an upper bound value of H s /h = 0.59, and this value has also been found in subsequent work (King et al., 1990;Wright et al., 1982). However, field and laboratory studies of wave transformation processes have also found that H s /h depends on wave steepness (Nairn et al., 1990), cross-shore position (Vincent, 1985), and beach gradient (Masselink & Hegge, 1995;Sallenger & Holman, 1985). In particular, the latter dependency on beach gradient is relevant for shore platforms: for example, assuming tanβ = 0 for a Type B platform and tanβ = 0.03 for a Type A platform results in a value for H s /h of 0.42 and 0.56, respectively, according to Sallenger and Holman (1985), and 0.5 and 0.65, respectively, according to Masselink and Hegge (1995). Based on field observations from three sandy beaches, Raubenheimer et al. (1996) proposed the following equation that predicts H s /h as a function of beach gradient tanβ, water depth h, and wave number k: where k is the local wave number given by 2π/L, and where the wavelength L is computed based on the wave period derived from the incident wave centroidal frequency. Care should be taken when comparing H s /h values between different studies due to the variety in methods used to derive H s from data (e.g., measurements based on wave staffs, pressure sensors, and current meters; use of different high-and low-frequency cutoffs, different methods for correcting for linear depth attenuation); for example, Raubenheimer et al. (1996) use a high-frequency cutoff of 0.18 Hz and do not correct the remaining water level signal for depth attenuation. Additionally, H s /h is also likely to depend on offshore bathymetry that is not accounted for in the simple tanβ/kh parameterization, for example, the presence of a sandbar.
Previous work on shore platforms has suggested values for H s /h of 0.59 (Farrell et al., 2009), 0.4 (Ogawa et al., 2011, and 0.4-0.6 (Ogawa et al., 2015; depending on platform gradient). It is noted that these H s /h values are upper bound values and not the result of least squares analysis between H s and h for saturated surf zone conditions, such as was carried out to derive equation (1). The notion of identifying an upper bound value for H s /h stems from wave transformation studies across coral reef platform where the aim is to identify the maximum wave condition that can occur for a given water depth over the reef (e.g., Hardy & Young, 1996;Nelson, 1994). The parameter H s /h is useful for making an assessment of wave conditions as a function of water depth. For example, if H s /h across a shore platform is 0.5 and the water depth h at the landward extent of the platform and at the base of the cliff is 2 m, then the waves impacting on the cliff are characterized by a significant wave height H s of 1 m. More specifically, however, H s /h is related to the rate of incident wave energy dissipation in the surf zone, which in turn controls radiation stress gradients, wave setup, and nearshore currents.
The ability to model the transformation of waves across the surf zone is clearly important, whether the surf zone is on a sandy beach or a rocky shore platform. Analytical and numerical models use the breaker index γ s as an essential tuning/calibration parameter for computing surf zone wave transformation and breakerinduced wave height decay (see section 2). It has been established that H s /h is strongly dependent on the bed gradient tanβ (Masselink & Hegge, 1995;Raubenheimer et al., 1996;Sallenger & Holman, 1985) and that steep surfaces are characterized by larger H s /h values than gently sloping surfaces. What is unknown, however, is whether the roughness of the surface over which the surf zone waves propagate plays a role in the wave transformation process and directly affects the value of γ s used in these models. According to Kobayashi and Wurjanto (1992), incident wave energy dissipation due to bottom friction is negligible in the surf zone of sandy beaches; however, Lowe et al. (2005) found that at the front of a coral reef, energy dissipation by bottom friction was comparable to that by wave breaking under modal wave conditions, and even exceeded breaking-induced dissipation under low wave conditions. These conflicting findings are easily explained by the vastly different bed roughness values between sandy beaches and coral reefs. In terms of bed roughness, shore platforms can range from beaches to coral reefs, with their surfaces ranging from extremely smooth to extremely rough, and with vertical variability varying from several millimeters to up to a meter.
The aim of this paper is to investigate whether wave transformation processes on shore platforms are different from that on sandy beaches due to differences in bed roughness. Specifically, we hypothesize that rough shore platforms enhance incident wave dissipation by friction (as opposed to breaking) and may influence energy transfer to the infragravity band by changing wave energy gradients in the surf zone and lowering incident band wave heights in the shoaling zone. The hypothesis will be tested by comparing H s /h, as well as the amount of infragravity wave energy across five different shore platforms representing a range of bed roughness values and gradients, and comparing these values with those obtained from a sandy beach.
The simple wave transformation model developed by Thornton and Guza (1983) will be used to help interpret and complement the field results and is introduced and discussed in section 2. The field sites and the methodology used to collect and analyze the data are described in section 3. The results obtained in the field and derived from a numerical model are presented in sections 4 and 5, respectively, and the implications are discussed in section 6.

Modeling Wave Transformation
The wave height across a mildly sloping nearshore, whether a beach or a shore platform, can be predicted using the wave height transformation model of Thornton and Guza (1983), which is an extension of the earlier model of Battjes and Janssen (1978). Assuming straight and parallel contours, the energy flux balance is Journal of Geophysical Research: Earth Surface

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where E is the energy density, C g is the wave group velocity, x is the cross-shore coordinate, hε b i is breaker dissipation, and hε f i is dissipation due to bed friction. The energy density and group velocity are calculated using the linear wave theory relationships: where ρ is the density of seawater, g is the gravitational acceleration, H rms is the root-mean-square wave height, k is the wave number corresponding to the peak frequency f p of the wave spectrum, and h is the local water depth. Thornton and Guza (1983) parameterize the rate of dissipation due to wave breaking as where B is an empirical breaker coefficient O(1) for the case of fully developed bores (Thornton & Guza, 1982) and γ is the critical wave breaking parameter. The rate of dissipation due to bottom friction is calculated by Thornton and Guza (1983) assuming quadratic bottom shear stress and parameterized as where C f is the bottom drag coefficient.
The energy flux balance equation (equation (2)) is solved by substitution of the breaking wave dissipation (equation (5)) and bottom friction dissipation (equation (6)) functions, and numerically integrating over the cross-shore spatial domain using a simple forward-stepping scheme, where Starting from the offshore boundary (Location 1), where H rms,1 and f p are known, the predicted quantities are obtained via equation (7). C g , 1 , 2 and E 1 are computed using linear theory (equations (3) and (4)) and the known values of H rms,1 , and h 1 and h 2 . The rates of breaking wave and frictional dissipation (equations (5) and (6)) are calculated, and E 2 and therefore H rms,2 are then predicted.
The breaker coefficient B is generally taken as a constant (B = 1; e.g., Lowe et al., 2005); therefore, the wave height transformation according to the Thornton and Guza (1982) model is only determined by the two "free" parameters γ and C f , which, respectively, control the rate of dissipation through breaking and bottom friction. It is informative to analyze the effect of these parameters on wave transformation over a plane-sloping bed. Figure 1 shows the results of a number of simulations using equation (7)  Wave energy dissipation by breaking, parameterized by γ, exerts a strong control on the wave height transformation. Increasing γ allows larger waves to propagate and shoal closer to the shoreline before breaking. This increases the rate of breaker dissipation across a narrow cross-shore region and causes larger values of the local wave height to water depth ratio H/h. Wave energy dissipation by bed friction is controlled by the bed roughness, parameterized by a drag coefficient C f . Increasing C f enhances energy dissipation and opposes the increase in wave height during the shoaling process. Energy dissipation due to friction is generally less than by wave breaking, even for the largest C f values and is mainly observed outside the surf zone. There is a weak influence of C f on the local H/h with the largest H/h values associated with the smoothest bed (smallest C f ). Overall, these model results suggest that γ exerts the primary control over wave height transformation across the nearshore in the surf zone across the typical geometry of Type A rock shore platform (1/50 slope) but that dissipation via bottom friction will cause a reduction in wave Journal of Geophysical Research: Earth Surface 10.1002/2017JF004277 Figure 1. Effect of varying γ and C f for wave transformation over a plane-sloping bed with tanβ = 0.02 according to Thornton and Guza (1982)  heights (or less shoaling) seaward of the surf zone. By optimizing predicted cross-shore variation in wave height with field observations, the values for the two parameters γ and C f can be obtained. In section 4, shoaling wave data will be used to optimize C f for the different field sites, whereas surf zone data will provide the means to optimize γ.  Table 1. Journal of Geophysical Research: Earth Surface 10.1002/2017JF004277 Figure 3 shows the cross-shore profiles of all sites and indicates that a range of platform morphologies are represented in the data. The Doolin platform is relatively narrow (x = 160 m), has the steepest gradient (tanβ = 0.031), and has a rather stepped morphology due to the limestone beds. The Freshwater West site was chosen to complement the four other deployments as it provided an ideal opportunity to measure two parallel sensor arrays, one across the relatively flat shore platform (FWR; tanβ = 0.018) and one across the flat sandy beach (FWB; tanβ = 0.011), to compare bed roughness effects on wave transformation processes under identical forcing. The Lilstock platform experiences the largest tide range (MSR = 10.7 m) and represents the widest platform (x = 325 m), while the Hartland Quay and Portwrinkle platforms are both relatively narrow (x = 140 m and x = 180 m, respectively) and steep (tanβ = 0.030 and tanβ = 0.028, respectively) platforms. All platforms have some degree of gravel-cobble beach deposit at their landward end, but these are particularly well developed at Hartland Quay and Lilstock. The roughness of the shore platform surfaces will be discussed in section 4.1, but it can already be observed in Figure 3 that the platforms at Portwrinkle and Lilstock represent the roughest and smoothest surfaces, respectively.

Morphological Data
Platform morphology was surveyed using RTK-GPS to obtain representative cross sections through the instrument arrays (cf. Figure 3). Survey points were taken at least every meter, capturing all significant irregularities and slope breaks. Cross-and alongshore platform variability was mapped at high-spatial resolution (3.1 mm at 10 m distance) using a Leica P20 terrestrial laser scanner. A 40 m wide strip of the platform was scanned using 6-12 scan positions centered around the instrument array. A digital elevation model (DEM) of the platforms was obtained by interpolating the high-resolution scan onto a regular 0.1 × 0.1 m grid.
The quantification of surface roughness is essential to determine the influence of the platform roughness on wave transformation processes. Two simple measures were used based on 1 × 1 m square tiles of the platform DEM. The first measure is, analogous to computing the height of wave ripples (Nielsen, 1992), four times the standard deviation associated within the square tiles (k σ = 4σ z ) and has units of m. Lowe et al. (2005) calculated k σ using observations of wave dissipation across a coral reef environment and found typical values of k σ = 0.16 m, which compared very well with measurements of the roughness. The second measure is the rugosity (k R ) defined as A r /A a ,À1 where A r is the actual surface area of the square tiles and A a is the geometric surface area (1 m 2 ). Rugosity is widely used in coral reef studies because it is relatively easy to determine in the field and k R = 0 (1) for a smooth (infinitely rough) surface. The estimates of the roughness parameters k σ and k R were alongshore averaged across the 40 m wide strip to obtain the cross-shore variability in bed roughness.

Hydrodynamic Data
Water levels were measured using a shore-normal array of up to 15 RBR solo D-Wave pressure transducers (PTs), individually housed within steel tubes and fixed to the bedrock with 10-15 m spacing. The PTs covered the full spring intertidal zone of the sites to capture shoaling, wave breaking, surf zone, and swash conditions, and the deployment strategy was kept consistent to aid comparison between sites. The field deployments lasted 8-13 tides with sensors sampling continuously at 8 Hz. Video cameras were used to log the periods of platform inundation during daylight hours. Individual image files were recorded at 4 Hz and used during subsequent processing to identify regions of breaking waves with reference to the pressure sensor locations.
A barometric pressure compensation (determined as the pressure recorded by the (exposed) sensors during each low tide) was used to convert absolute pressure recorded by the PTs to hydrostatic pressure. The dynamic pressure signal was corrected for depth attenuation using a local approximation approach (Nielsen, 1989), and the water depth (h) required for this approach was derived using a 10 min moving average filter.
All data analyses were conducted using 20 min data segments (N = 9,600); a compromise between limiting tidal nonstationarity in macrotidal settings and having sufficient data length to obtain representative statistical parameters. Spectra were computed using Welch's segment-averaging approach with 8 Hanning-tapered segments overlapped by 50%, proving 16 degrees of freedom. The spectral energy was partitioned into infragravity-and incident-wave energy, with the cutoff frequency separating these two frequency bands determined for each site and for each tide using the high tide wave spectrum from the seaward-most PT. If a spectral valley was present, the frequency associated with the minimum spectral energy was selected as the cutoff; in the absence of a clear spectral valley, a fixed cutoff value of 0.047 Hz was used. No high-frequency cutoff was applied. Using the array method of Gaillard et al. (1980), the wave spectra were redefined into incoming and outgoing components, from which the infragravity and incident wave heights (H s,inf and H s,inc ) were computed as 4 times the square root of the total spectral energy summed over the relative frequency bands. The spectral mean wave period was derived from the spectral moments (T spec = m À1 /m 0 ). Additional wave parameters computed for the 20 min data segments include the wave power or energy flux (P = EC g ) calculated according to linear wave theory (equations (3) and (4)); the wave skewness was calculated from the water surface elevation time series (skewness ¼ X n-n ð Þ 3 = σn 1:5 ) where n = water surface elevation, n = average water surface elevation, and σ = variance, while the asymmetry is the skewness of the derivative of the water surface.
To determine the contribution of wave breaking and bed friction to wave energy dissipation and assess the role of bed roughness in these processes, it is essential to know whether data are from the surf zone or the shoaling wave zone. Additionally, knowledge of the breaker wave height (H b ) and breaker depth (h b ) are important for normalizing the position of the data relative to the breakpoint. For each 20 min data Journal of Geophysical Research: Earth Surface 10.1002/2017JF004277 segment, the cross-shore variation in the wave height was used to identify H b and h b from the maximum wave height in the cross-shore array, with visual calibration performed through the video images whenever possible (Figure 4). If a clear spatial peak in the wave height was not discernible, usually because the surf zone extended beyond the seaward most pressure sensor (due to large wave heights and/or low tide level), that data segment was not used for determining the breaker conditions. Then, for every tide, the significant breaker height and the breaker depth were averaged using all data segments for which the breaker conditions could be determined. Due to the very strong tidal currents in the Bristol Channnel, the wave conditions at Lilstock exhibit a very pronounced diurnal inequality with the rising tide wave conditions much more energetic than the falling tide conditions; the falling tide data for Lilstock were removed from the analysis. Figure 5 presents the detrended DEMs of all study sites, including the sandy beach, and the alongshoreaveraged bed roughness parameters k σ and k R . The scaling for the DEMs is the same for all sites, and it is Figure 5. Detrended digital elevation models (DEMs) with PT locations (black circles) for all study sites with color scale running from À1 (dark blue) and +1 m (yellow). Offshore is at the top of the DEMs. The two lines to the right of the DEMs represent the cross-shore variation in the alongshore-averaged roughness based on standard deviation k σ and rugosity k R .

Platform Roughness
Journal of Geophysical Research: Earth Surface 10.1002/2017JF004277 evident that the surfaces of the shore platforms are highly variable, with Portwrinkle clearly the roughest platform and Lilstock the smoothest. The sandy beach at Freshwater West represents, not surprisingly, by far the smoothest surface. In addition to providing useful insight to the main roughness elements, the DEMs also highlight the geological bedding, which is almost shore-perpendicular at Hartland Quay, oblique to the shore at Freshwater West, almost shore parallel at Doolin and Lilstock, and complex at Portwrinkle. Faults also contribute to roughness (e.g., Hartland Quay, and Portwrinkle).
The visual difference in platform roughness is well quantified by the alongshore-averaged roughness parameters plotted in Figure 5. The roughest platform (Portwrinkle) has typical values for k σ and k R of 0.3 m and 0.2, respectively, the smoothest platform (Lilstock) has values 0.1 m and 0.05, respectively, and the sandy beach 0.01 m and 0.01, respectively. For all sites, the bed roughness parameters do not vary much across the profile and can be characterized by a single value (cross-platform average): variability between the sites is generally greater than variability within the sites. It is noted that the values of the roughness parameters k R and especially k σ increase with the grid size of the DEM. A grid size of 1 m was adopted for all sites; therefore, the roughness values are directly comparable with each other but not necessarily with that of other studies.

Wave Conditions
Considerable variability in the forcing wave conditions was experienced during all field experiments, with offshore significant breaker heights ranging from 0.5 m to 3 m ( Figure 6). At all sites, energetic conditions with breaker heights exceeding 1.5 m occurred for multiple tidal cycles, and breaker conditions were generally less energetic than the offshore wave conditions. The largest breaking waves were encountered at Freshwater West (H b = 1.8-2.4 m) and the calmest conditions occurred at Portwrinkle (H b = 0.7-1.0 m).

Incident Wave Height
During all tides and at all sites, the cross-shore variability in the incident wave height measured by the PT array displayed the well-established "saturated" signature in the surf zone with H s,inc decreasing with decreasing h (Figure 7). Outside the surf zone, H s,inc increases up to the breakpoint due to wave shoaling for most data runs. The ratio H s,inc /h generally increases in the landward direction, both inside and outside the surf zone, in line with predictions according to the Thornton and Guza (1983) model (cf. Figure 1).
The H s,inc /h values for all data are distributed into class bins and plotted versus the normalized platform/beach slope (tanβ/kh) and compared to equation (1) in Figure 8. Although the trends in the field data are similar to those predicted by equation (1), the observed H s,inc /h values are consistently higher than predicted. This is attributed to differences in the way the raw pressure data were processed: Raubenheimer et al. (1996) removed frequencies >0.18 Hz from the analysis and did not correct the pressure signal for depth attenuation (an approach that was considered inappropriate for the range of wave periods represented in the current data set and one that would have led to a systematic underprediction of the data collected under relatively short-period wave conditions). Application of the 0.18 Hz filter by Raubenheimer et al. (1996) (1) for the seaward most data segments (smallest values of tanβ/kh) and less than the predictions for the landward most data segments (largest values of tanβ/kh).  Raubenheimer et al. (1996) represented by equation (1).

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Wave Shape
Transformation in waveshape is explored in Figure 9, where wave skewness (A skew ) and wave asymmetry (A asym ), computed using the Hilbert transform (cf. Ruessink et al., 2012), are plotted against the normalized surf zone position (h/h b ) for each 20 min data burst. For three of the sites (DOL, FWR, and FWB), the skewness increases steadily up to the breakpoint (h/h b = 1) and then decreases toward the shoreline. At HLQ and PTW, the peak in skewness occurs around the midsurf zone position (h/h b = 0.4-0.6), after which A skew remains constant, whereas at LST, skewness is more or less constant across the entire surf zone. The trends in the wave asymmetry is much more consistent across all sites and A asym becomes increasingly negative (more asymmetric) toward the shore.
The Ursell number (Ur), calculated following Doering and Bowen (1995), gives an indication of the nonlinearity of the waves across the platform at each site, where larger Ur values represent stronger nonlinear effects: with a w = 0.5H s . Figure 10 shows the wave skewness and wave asymmetry as a function of the Ursell number. For DOL, FWR, and FWB, the skewness values increase from close to zero for low Ursell values (Ur < 0.4) and peak at A skew = 1-1.5 around Ur = 1-2. For LST, HLQ, and PTW there is no clear maximum in skewness and A skew remains more or less constant at A skew = 0.5-1 for Ur > 2. Wave asymmetry is near zero for Ur < 0.5 and becomes increasingly negative (increasingly asymmetric in shape) with increasing Ur values, reaching maximum values near the shoreline (A asym < À0.5).
Our results are compared with the predictions of Ruessink et al. (2012): where and P 1 = 0, P 2 = 0.857 ± 0.016, P 3 = 0.471 ± 0.025, P 4 = 0.297 ± 0.021, P 5 = 0.815 ± 0.055, P 6 = 0.672 ± 0.073, (Figure 10). Skewness at DOL, FWR, and FWB is consistently underpredicted, whereas at LST, HLQ, and PTW there is a reasonable fit for Ur < 2 but also underprediction for greater Ur values. The asymmetry observations at DOL, FWR, and FWB match the Ruessink et al. (2012) predictions quite well across the full range of Ur values, but at LST, HLQ, and PTW the A asym values are underpredicted for Ur > 1. In summary, in comparison with the predictions of Ruessink et al. (2012), which were derived from data collected on sandy beaches, the waves propagating across the shore platforms appear to have been more skewed at DOL, FWR, and FWB indicating enhanced shoaling, and less asymmetric at LST, HLQ, and PTW suggestive of not fully developed asymmetric bores.

Bulk Statistics
For overall comparison between the sites, midsurf zone position bulk parameters (total wave signals, averaged over all PTs where h/h b = 0.45 to 0.55) for H s,inc /h, A skew , A asym , and %Ig are presented in Figure 13 with their corresponding 95% confidence intervals. Across all of the parameters and sites, there are a number of statistically significant differences (indicated by nonoverlapping CI's), but few clear trends exist for any one location and there are no sites that consistently score highest/lowest. In terms of similarity, the data can be grouped as follows: (1) DOL and FWR have the highest H s,inc /h and %Ig values and are the most nonlinear (both in terms of skewness and asymmetry; (2) LST, HLQ, and PTW are characterized by the lowest H s,inc /h and %Ig values and are the least nonlinear; and (3) FWB falls very much between these two groups in all aspects, except for H s,inc /h, where it is characterized by the lowest value, although this could be due to a limited number of measurements from the inner-surf zone region. The link between the bulk parameters and platform roughness will be addressed within the discussion.
A strong association appears to be present between the proportion of infragravity energy (%Ig) and the wave asymmetry (A asym ). DOL and FWR have the largest %Ig compared to the other sites and are characterized by the most asymmetric (pitched forward) waveform; the sites with the least asymmetric surf zone waves (LST, HLQ, and PTW) were characterized by the lowest %Ig values. Greater values of A asym suggest enhanced bore development and more intense short-wave dissipation.

Numerical Model
The purpose of the energy flux model (equation (2)) is to support the field observations by exploring the parameter space of γ and C f relative to platform roughness. The model is initialized at the seaward boundary (x = 0 m) using observations from the most offshore PT. A normalized cross-shore grid spacing of Δx 0 ¼ Δx= Δx is the dimensional grid size, is used and the profile smoothed with a 6 m moving average filter (determined using a convergence test) to minimize small-scale steps in the bathymetry caused by the geometry of individual rock elements. First, the model is calibrated for the free parameters γ and C f which control the dissipation by wave breaking and friction, respectively.
Seaward of the surf zone, the dissipation of short wave energy is dominated by bottom friction and is therefore principally controlled by the bed roughness; this zone can therefore be used to calibrate C f . Data from four tides from each field site (excluding FWB where the PT array was too short to permit reliable model optimization) were used to calibrate the model, totalling approximately 750 model simulations. To calibrate C f , we only used data recorded from seaward of the surf zone. A strict a priori assumption of the breaker criterion γ (H s,inc /h) for the region seaward of the surf zone was determined by a visual inspection of the data bursts from each tide (typically H s,inc /h = 0.28-0.42) as described in section 3.3, identifying those PTs which were very clearly located seaward of the surf zone and where dissipation must be solely due to bottom friction. The model was run for each of these tides over a range of C f and with γ set to 0.42, a typical value from the existing literature (e.g., Thornton & Guza, 1983). The optimum value for C f was determined by minimizing error estimates between the observed and modeled wave heights across the region seaward of the surf zone.
To quantify the model error, the absolute root-mean-square error ϵ abs and relative bias ϵ bias were computed by comparing the incident wave height H s,inc obtained from the measurements (M) with the computed H s (C) at each PT location (i) and for each 10 min burst (t), and where |À| indicates the modulus and hÀi the mean, respectively:  Values of ϵ abs and ϵ bias tending to zero indicate higher model performance. The most offshore PT was excluded from the calibration, since data from this location are used as the seaward boundary forcing for the model and are thus not independent. This calibration was repeated for all field sites and the optimum C f for each site was determined by minimizing the rms and bias errors for every burst within each tide and computing the mean C f by averaging the rms and bias errors ( Figure 14). DOL, HLQ, and PTW display parabolic curves of the distribution of the rms error for C f , with the optimum C f indicated by the minima. However, for FWR and LST the error curves asymptotically tend toward zero, indicating an effective model C f of zero. The distribution of the bias displays a similar pattern across the field sites and indicates that the shoaling wave heights at FWR and LST are underpredicted, which explains why the optimization is driving C f toward zero at these sites.
Inside the surf zone, however, wave energy is dissipated by both bottom friction and wave breaking. The model was calibrated for γ by optimizing model performance for PTs determined to be within the surf zone, with C f set to the value determined above for the region seaward of the surf zone. As for C f above, the optimum γ for each field site was determined as the mean γ of the combined rms and bias errors for each tide (Figure 15). The results for the calibration of γ display clear parabolic curves for the rms errors at all sites except PTW, which tends to increase toward larger values of γ, and the results are consistent between rms and bias errors.
Example model outputs for each platform are compared to field observations in Figure 16. Absolute rootmean-square errors for H s are O(10 À2 )m based on the four calibration tides at all platforms, and qualitatively, the model performance is very good at all cross-shore locations, except at the very shallow landward-most PT at DOL and FWR, which experience significant wave reflection, wave setup and nonlinear processes not included in the simple model, and the midsurf zone region at PTW. Rates of wave energy dissipation are also well predicted and reveal that frictional dissipation appears to be negligible at all sites except PTW. At PTW, frictional dissipation is observed to increase moving landward from the shoaling wave to surf zone, presumably as wave orbital velocities increase under the breaking waves, but breaker dissipation remains the dominant in the surf zone. It is noteworthy that there are several large spikes of predicted dissipation (i.e., at DOL and PTW) that are not observed in the field observations. These result from instantaneous model dissipation over step changes in profile bathymetry to which the waves observed in the field do not appear to immediately respond and it results in the overall model error being greatest for PTW. A landward increase in H s,inc /h (typically 0.4-1.0) is observed for both the field and model data. This is consistent with the observations of Ogawa et al. (2011) and is the expected model behavior when wave breaking is the dominant mode of dissipation (Figure 1). It is well predicted by the model at all sites except HLQ, which displays a consistent overprediction at the landward end of the platform; it is unclear why this is the case.
The dissipation parameters determined via the optimization of the energy flux model, averaged over the four tides at each field site, are presented in Table 2. The combined estimates of γ and C f from the model provide an indication of the relative importance of short-wave dissipation by bottom friction and by wave breaking over the rock platforms. The optimized γ s range from 0.51 at DOL to 0.93 at PTW, which extends from the upper range typically reported from sandy beaches (~0.5-0.64) to significantly higher values. The optimized C f is highly variable, ranging from O(10 À4 ) at FWR and LST to O(10 À1 ) at PTW. Qualitatively, the C f values for LST (smoothest) and PTW (roughest) are consistent with the observed platform roughness length-scales k σ and k R , but it is unclear why it is so low for FWR, the second roughest site. The mean ratio of frictional to breaker dissipation hε f /ε b i at the midsurf zone position (0.45 ≥ h/h b ≥ 0.55) for all tides examined is typically <0.15 (Table 2); only at PTW does friction dominate where hε f /ε b i = 3.82.

Analysis of Field Data
Field data collected from five sloping (Type A) rock shore platforms (Sunamura, 1992) and one intertidal beach were used to study wave transformation processes across the intertidal surfaces and specifically address the role of surface roughness on wave transformation. Due to the different lithology and bedding types, the five shore platforms represent a range in surface gradient and roughness. The platforms at Freshwater West (FWR) and Lilstock (LST) are relatively gently sloping (tanβ = 0.018 and 0.021, respectively) and the steeper platforms are present at Portwrinkle (PTW), Hartland Quay (HLQ), and Doolin (DOL) (tanβ = 0.028, 0.30, and 0.31, respectively). LST represents the smoothest surface (k R = 0.015) and the roughest platform is at PTW (k R = 0.090). The beach site FRB is characterized by the gentlest gradient (tanβ = 0.011) and the smoothest surface (k R = 0.002). During the fieldwork the different sites experienced varying wave and tidal conditions, with PTW and FWR representing the smallest and largest waves (H b = 0.7-1.0 m and H b = 1.7-2.5 m, respectively), and DOL and LST experiencing the smallest and largest tides (MSR = 4.2 m and MSR = 10.7 m, respectively). A large number of pressure sensors (12-15) were deployed in a single Table 2 Summary of Platform Gradient (tanβ), Roughness Length-Scale (k σ ), and Empirical Drag Coefficient (C f,Nielsen ; equation (17)), and Numerical Model Short-Wave Dissipation Parameters, Averaged Over Four Tidal Cycles for All Field Sites Note. Model parameters are the following: Optimized drag coefficient (C f ), rms and significant breaker criterion (γ), ratio of frictional to breaker dissipation (hε f /ε b i), and wave height to water depth ratio (H s,inc /h).

Journal of Geophysical Research: Earth Surface
10.1002/2017JF004277 transect across each shore platform and data were collected over 8-13 tides. This data set represents the most extensive ever collected on rocky shore platforms, both in terms of the range of environmental conditions experienced, and the duration and spatial resolution of the measurements. It also represents the only wave transformation data set so far collected on Type A platforms, as all previous studies have been conducted on subhorizontal Type B platforms.
In agreement with all previous studies of wave transformation across shore platforms, wave energy is strongly tidally modulated and is depth limited (i.e., saturated) across the inner part of the intertidal region (e.g., Farrell et al., 2009;Marshall & Stephenson, 2011;Ogawa et al., 2011). Additionally, the relative contribution of infragravity energy to the total wave energy content in the surf zone increases in a landward direction (cf. Beetham & Kench, 2011;Ogawa et al., 2015). We also demonstrate that the absolute infragravity energy level, quantified by the incoming infragravity wave height, decreases in the landward direction. The intertidal shore platforms, therefore, represent effective dissipaters of both incident and infragravity energy. As the waves propagate and dissipate across the platform, there are also systematic changes in the waveshape: wave skewness increases up to the seaward extend of the surf zone and then decreases (DOL, FWR, and FWB) or stays more or less constant (HLQ, LST, and PTW), and at all sites the wave asymmetry becomes increasingly negative in the landward direction indicating the presence of turbulent and forward pitching bores, indicative of continuous wave breaking.
The local wave height to water depth ratios H s,inc /h calculated here over the shore platforms compare favorably with those reported where wave breaking is the dominant form of dissipation over sandy beaches (Raubenheimer et al., 1996), near-horizontal rock platforms (Ogawa et al., 2011) and the fore reef of coral reefs (Vetter et al., 2010). Significantly, the consistent landward increase in H s,inc /h indicates that dissipation by wave breaking is a continuous process across the platforms, confirmed by the observed landward increase in negative wave asymmetry and that at any cross-shore location there is a combination of breaking and broken waves. This contrasts to observations across similarly rough (or rougher) coral reefs platforms, where the initial peak in H s,inc /h observed as waves break on the steep fore reef is followed by a decrease in H s,inc /h as energy dissipation becomes dominated by frictional drag with no breaking over the subhorizontal reef flat (Lowe et al., 2005;Rogers et al., 2016;Vetter et al., 2010). This difference occurs because the shore platforms studied here have relatively steep and near-constant planar slopes, whereas on coral reefs there is a clear distinction between the steeply sloping fore reef and the subhorizontal reef platform. As such, the morphology of coral reefs is rather similar to that of Type B shore platforms; therefore, care should be taken in extrapolating the present findings derived from Type A platforms to Type B platforms.
The aim of this paper is to investigate whether wave transformation processes on shore platforms are different from that on sandy beaches due to differences in bed roughness. The approach has been to compare observed data trends in terms of relative wave height (H s,inc /h), wave skewness (A skew ), wave asymmetry (A asym ), and incoming infragravity wave height (H s,inf ) between the different platforms and with expressions related to these parameters from the literature derived from sandy beaches. The systematic landward increase in H s,inc /h was linked to the normalized slope tanβ/kh using equation (1) based on Raubenheimer et al. (1996), which combines the nondimensional water depth kh with the bed gradient tanβ and which provides a good description of the data (accounting for underprediction due to the difference in data filtering prior to analysis; cf. section 4.3). The dependence of H s,inc /h on tanβ is also evident when comparing across the different platform sites, with the steeper platforms DOL, HLQ, and PTW displaying larger surf zone values of H s /h than the flatter platforms LST and FWR and particularly the beach FWB. This is consistent with studies on sandy beaches (e.g., Masselink & Hegge, 1995;Sallenger & Holman, 1985). No obvious control of the platform roughness on H s,inc /h could be discerned. The development of wave nonlinearity (skewness and asymmetry) was compared with formulations (equations (9)-(12)) suggested by Ruessink et al. (2012). The qualitative trends in the data, as a function of the Ursell Number (Ur; equation (8)), are well represented by these equations, specifically the increase then decrease in wave skewness, which peaks at Ur = 1-2, and the progressive increase in negative wave asymmetry with decreasing Ur. The most pitched-forward surf zone waves (most negative A asym ) and the highest skewness values were observed at the sites which experienced the most energetic wave conditions (DOL, FWR, and FWB), and no obvious influence of platform roughness on waveshape was observed. When compared with sandy beaches, the spatial trends in waveshape are similar, which would suggest that the role of roughness is not significant.

10.1002/2017JF004277
Following the work of Inch et al. (2017), the total infragravity wave height (H inf ), where 0 < h/hb < 0.33, was related to a wave power parameter (H o 2 T p ). With the exception of DOL for some tides, the observed values of H inf are consistently overpredicted by the formulation of Inch et al. (2017). We attribute this to enhanced friction imparted on the infragravity wave motion by the rough platform surfaces, leading to suppressed infragravity wave energy in the (inner) surf zone. This suggestion is supported by McCall et al. (2017) who used the current data set and the XBeach numerical model to investigate the relationship between the drag coefficient (used for parameterizing friction for steady currents and infragravity wave motion) and the platform roughness. They found that if a smoothed rock platform profile was used, the drag coefficient required to provide the best agreement between observed and modeled infragravity wave energy levels increased with platform roughness.
In a final attempt to identify a demonstrable influence of platform roughness on wave transformation parameters, average values for a range of variables were computed for each of the platforms. The "independent" variables selected are wave power (H b 2 T; averaged over all tides with data), platform gradient (tanβ) and platform roughness (k σ and k R ), and are listed in Table 1. The "dependent" variables are relative wave height (H s,inc /h), percentage incoming infragravity wave height (%H s,inf ), wave skewness (A skew ), and wave asymmetry (A asym ). The dependent variables were averaged for each of the sites, but only for data from the midsurf zone position (h/h b = 0.45-0.55), and are shown in Figure 13. A correlation matrix was constructed (not shown), and only four correlations were statistically significant at a level higher than 0.1. Strong correlations were obtained between the different wave parameters: wave skewness was correlated with the breaking wave power (r = 0.88; p = 0.02), whereas wave asymmetry was correlated with the percentage of incoming infragravity energy (r = À0.85; p = 0.03). Finally, a weak correlation was found between the bed gradient and the relative wave height (r = 0.72; p = 0.10), supporting previous work on sandy beaches (e.g., Raubenheimer et al., 1996). Most importantly, none of the dependent variables are correlated to the platform roughness.

Numerical Modeling
The simple numerical model of Thornton and Guza (1983) was used to support the field observations and investigate the dissipation of the incident wave energy across the platforms by wave breaking and bottom friction, parameterized by γ s and C f , respectively. The optimized values for the model breaker criteria γ s (0.51-0.93, Table 2) are larger than the observed bulk midsurf zone values of H s,inc /h (Figure 13a) for all sites except DOL but encouragingly fall between the range of values reported in the literature for sandy beaches (0.4-0.59) (Raubenheimer et al., 1996;Sallenger & Holman, 1985;Thornton & Guza, 1983) and coral reefs (0.59-1.15) (Lowe et al., 2005;Péquignet et al., 2011;Vetter et al., 2010). The result of the calibration for C f is less clear, since, although the optimum value of C f at LST (0.005), DOL (0.05), HLQ (0.049), and PTW (0.34) reflects the increasing hydraulic roughness of these platforms, the range of C f spans 2 orders of magnitude. C f was also estimated from the data for the tides used in the model calibration by regressing the measured rate of dissipation equation (2) across all adjacent PT pairs in the region seaward of the breakers against equation (6), where C f is the regression coefficient (e.g., Wright et al., 1982). A large amount of scatter was observed in the data that was attributed to strongly shoaling waves, but statistically significant (p < 0.05) estimates of C f ≈ 0.1 were obtained for DOL, LST, and PTW, which fall within the range of values obtained from the model calibration. While this large range leads us to question how representative the calibrated values of C f are, it is encouraging that except for LST (where C f is very small), the values fall within the region between sandy beaches (0.01, e.g., Thornton & Guza, 1983) and coral reefs (0.16, 0.22, and 1.8, Falter et al., 2004;Lowe et al., 2005;Monismith et al., 2015); therefore, we also compare our calibrated values of C f with the empirical wave friction model of Nielsen (1992) to gain further insight. Nielsen (1992) predicts the wave friction factor f w for rough turbulent boundary layers as a function of the ratio of the near-bed horizontal wave orbital amplitude A b to the hydraulic roughness length-scale k w (e.g., Jonsson, 1966;Madsen, 1994;Swart, 1974) f w ¼ exp 5:5 A b k w À0:2 À 6:3 The value of k w is usually specified as a function of the grain diameter D, where k w = 2D (Nielsen, 1992). To be consistent with the definition in equation (17), D ≈ 2σ r , where σ r is the roughness amplitude and k w = 4σ r Journal of Geophysical Research: Earth Surface 10.1002/2017JF004277 (e.g., Lowe et al., 2005). Applying equation (17) to the roughness estimated using the terrestrial laser scanner, k w ≡ k σ ( Figure 5 and Table 1), allows a comparison with the predicted drag coefficient C f derived from the numerical model through the relationship f w = 2C f . The mean drag coefficients computed over the four model optimization tides for all of the platforms using equation (17) are O(10 À2 ) with the smallest value associated with the smoothest platform (LST, 0.0225) and the largest with the roughest (PTW, 0.069).
Comparing these empirical estimates with those determined via the numerical model optimization shows that the trends in C f are well replicated when FWR is excluded and that for our middle range of platforms DOL and HLQ (tanβ~0.03, k σ~0 .02), the empirical and numerical estimates are in close agreement. For the roughest platform PTW, C f is underpredicted, but Nielsen (1992) notes that f w and C f are very similar for friction coefficients >0.05, so by ignoring the phase lag between the flow velocity and bed sheer stress, we could assume that f w = C f at PTW, which would increase the empirically derived C f toward that derived from the model calibration.
After optimization of the numerical model, typical rms errors between predicted and observed H s are consistently small (3-10 cm) and the distribution of wave energy dissipation is generally well replicated ( Figure 16). The model results indicate that breaking wave dissipation dominates across all platforms except PTW and, in line with the field observations, do not show any systematic variations in the wave height decay between sites that can be linked to platform roughness. The predicted H s,inc /h compare well with the observations at the majority of the platform sites, in particular DOL, LST, and PTW, which all display the strong landward increase in H s,inc /h associated with the increasing proportion of broken wave bores toward the shoreline. This suggests that the Rayleigh distribution inherent in the model formulation (equation (5) and Figure 1) can be used to successfully parameterize the wave height dissipation by wave breaking across the majority of the rock platforms studied.
The results of the numerical model generally agree well with the field observations (i.e., Figure 16) and the range of computed H s,inc /h fall within the expected range between sandy beaches and coral reefs; however, there are concerns about the calibration of C f that question the suitability of the model. This is highlighted by the very high optimized C f for PTW (0.34), the roughest platform, and the very low optimized C f for FWR (0.005), also a very rough site. In the present study, both C f and γ are independently calibrated, while in studies of wave propagation over reefs it is common to fix one of the dissipation parameters and calibrate for the other (e.g., Lowe et al., 2005;Péquignet et al., 2011). When the optimized C f is replaced by Nielsen's (1992) empirical estimate (or the data-derived values) and the model is recalibrated for γ, larger rms errors for H s, inc are obtained (not shown). Certainly, for the roughest platforms PTW and FWR, the ratio A b /k w in equation (17) for the incident-wave frequencies approaches unity, which means that the wave orbital length-scale is similar to the roughness length scale (Madsen, 1994). This may imply that the numerical model used here incorrectly parameterizes the physics of wave-roughness interaction across a very rough rock platform and suggests an alternative parameterization may be required. One approach could be to specify a relative roughness linked to the large-scale morphology of individual platform roughness elements. These are often of a similar height or diameter to the surf zone water depth and directly affect the passage of waves, which must flow around and over such structures. A parameterization similar to that of flow through canopies, where f w ∝ α w , may be more appropriate, where α w is the ratio of the flow in the canopy to that just above the canopy, which is shown to depend on the ratio of the spacing of the canopy elements to A b (e.g., Huang et al., 2012;Lowe et al., 2007;Monismith et al., 2015). Therefore, for very rough rock platforms, frictional drag may scale with the ratio of the rock element spacing to A b ; however, this requires further investigation by field observation and higher-order numerical modeling, since Rogers et al. (2016) do correlate f w to A b /k w across an exceptionally rough coral reef.

Implications for Wave Dissipation Over Rock Platforms
Under the conditions during which we collected our data, there does not appear to be a significant impact of roughness on wave energy dissipation; however, there may be conditions when bed friction becomes important (e.g., Lowe et al., 2005). While we have some concerns about the applicability of several of the model results, there is sufficient confidence, inspired by the good fit in Figure 16 and the skillful quantification of H s,inc /h across our middle range of sites, to use the model to investigate the importance of frictional dissipation across a shore platform.

10.1002/2017JF004277
Wave energy dissipation by bed friction ε f was integrated across the intertidal region of a Type A shore platform for varying wave conditions, bed gradients, and C f values. Two of these parameters were fixed at the mean observed values and a number of simulations were run by varying the remaining input parameters ( Figure 17). The relative importance of frictional dissipation increases with decreasing wave height and bed gradient, and increasing bed roughness. The absolute values for the wave dissipation by friction increase with increasing wave height and bed roughness, and decreasing bed gradient. These results indicate that frictional dissipation is only significant on platforms that are very rough (C f > 0.1), low gradient (tanβ < 0.02) and/or subjected to small wave conditions (H o < 0.5 m), where friction may account for~20% of the total wave energy dissipation. However, under small waves, the absolute amount of energy dissipated is very small (<1 kW m À2 ), so across these very rough flat platforms the total amount of frictional dissipation scales with H o . This implies that over the majority of Type A rock shore platforms short-wave breaking is the dominant source of dissipation and the effects of bottom friction are small (<10% of the total), so can probably be disregarded in wave energy balance models. Further analysis using models with more physical processes (e.g., phase-resolving or surf-beat models) is required to similarly investigate the sensitivity of nearshore currents and infragravity waves to the bed roughness of the platforms.
Finally, we briefly revisit the morphological implications of our findings to discuss the role of wave action in the evolution of rocky coasts. Type A shore platforms primarily dissipate energy by wave breaking, which drives mean near-bed currents through the generation of radiation stress gradients (Longuet-Higgins & Stewart, 1962). These currents will impart a drag force onto the rock surface, acting to cause direct platform erosion (e.g., through hydraulic plucking of weathered, fractured rock), and abrasion by the transport of loose materials across its surface (Sunamura, 1992). Wave dissipation by bed friction is of secondary importance, and it is only important where the turbulence associated with the broken waves reaches the bed at the shallow landward extreme of the platform that wave forces have a direct effect on platform erosion. This conjures up an image of a wide turbulent surf zone, effective at dissipating wave energy, but only able to leverage this energy for doing geomorphological work within a narrow shallow-water region. This narrow turbulent region, comprising of the swash and inner surf zone, migrates twice-daily across the platform due to the tide, and it is in this zone where most of the geomorphic work is considered being done. Considering platforms such as DOL with slab-like steps in the upper profile, we may expect slabs to be loosened by direct wave forcing and then removed by the mean wave-generated near-bed currents (Stephenson & Naylor, 2011). Conversely, at HLQ wave-generated currents are probably focused into the channels formed by the crossshore orientation of the bedding planes, directly eroding rock fragments and causing abrasion. Lastly, it appears to be the gradient of the Type A platform that determines the delivery of wave energy, and hence potential for cliff toe erosion (Naylor et al., 2010), by controlling the cross-shore distribution of the rate of wave breaking dissipation. We thereby suggest that for the purposes of determining the role of waves in cliff erosion and rocky shore evolution, the majority of Type A shore platforms may be modeled in a similar manner to a sandy beach.

Conclusions
Here we present for the first time a comprehensive analysis of wave transformation across sloping (Type A) rock shore platforms. Observations from five platforms, all with contrasting surface roughness, gradient, and wave climate, represent the most extensive ever collected on rock shore platforms and demonstrate that frictional dissipation by platform roughness is of secondary importance compared to wave breaking dissipation. This is similar to observations on smooth sandy beaches but is in contrast to rough coral reef platforms where friction has been observed to dominate. Rock platforms are shown to dissipate both incident and infragravity wave energy and, in line with previous studies, surf zone wave heights are saturated and strongly tidally modulated. Waves develop skewness and asymmetry across the platforms, and the relative wave height to water depth ratio scales with platform gradient. Overall, comparisons between the observed properties of the waves and formulations derived from sandy beaches have not highlighted any systematic variations between the sites that can be attributed to (differences in) platform roughness.
Optimization of a simple numerical wave transformation model provides further exploration of the frictional and wave breaking parameter space. The breaker criterion falls between the range of values reported for flat sandy beaches and steep coral fore reefs, lending further support to the control by platform gradient; however, the optimized drag coefficient for frictional wave dissipation is significantly scattered for the roughest sites. Further exploration using an empirical drag coefficient does not improve performance and suggests that high-order numerical wave models are required to successfully parameterize frictional dissipation over the roughest platforms. Model simulations using a range of average data from our most typical platforms indicate that friction accounts for~10% of the total intertidal short-wave dissipation under modal wave conditions, only becoming significant (~20%) across very rough, flat platforms, under small wave conditions. Overall, observational and modeling results suggest that frictional dissipation of short-wave energy can probably be neglected for the majority of Type A rock platforms, particularly inside the surf zone, which can be treated similarly to sandy beaches when assessing wave energy delivery to the landward end of the platforms.