2.3.1 Raw data extraction: from publications and national databases

GlobR2C2 (Global Recession Rates of Coastal Cliffs) database v1.0 was populated with data from two main types of published sources: published peer-reviewed English journal articles, and official but non-peer-reviewed studies arising from official organizations (e.g., the CEREMA French risk survey) in English, French or Spanish. Journal articles were selected when they reported quantified values of cliff recession rates and described the quantification method. The search was initiated with bibliographic web search engines (Web of Science, Google Scholar) and expanded using citations therein. We recognize that some references may have escaped our attention. We are keen to expand the database further with the contribution of the community. The version presented in this article is version 1.0. compiling references up to 2016.

2.3.2 Cliff and lithology description

The “cliff” and “lithology” entities contain information related to cliff morphology (i.e., height, length) and rock property (i.e., lithology, fracturing, weathering, folding, bedding).

Cliff geology may exhibit a very complex set of lithologic types, contact relationships, inherited tectonic structures and overprinted weathering. Authors often do not systematically report on these characteristics. Confronted with the heterogeneity of parameter presentation, we synthesized information in the following manner. A lithological name fills the “lithology” entity and a position field records rock position along the cliff (numbered from cliff toe to cliff top). Additional descriptions were copy/pasted in comment fields in order to preserve the original description. By comparison, rock state (weathering, folding, faulting, bedding etc.), is rarely mentioned. This could be because the cliffs do not present any such characteristics, or because authors did not think it was relevant and did not mention it. Moreover, parameters describing rock state are either complex, technically expensive to describe and quantify, or outside the authors' scientific field of expertise. They were characterized with a Boolean value (True/False) to be integrated in the database. “True” refers to the presence of fracturing/weathering mentioned in the paper. “False” means that authors either describe fracturing/weathering as non existent/negligible or it is not mentioned in the paper.

2.3.3 Cliff location

Cliff location is entered as geographic coordinates. Studied cliff site extent was digitized from publication information and mapped using Google Earth. A primary key links this geographic file to the database.

2.3.4 Measurement description

The measure entity contains the erosion rate values and measurement methodology (how erosion was measured, for how long, with what detection threshold). Erosion is generally provided as an erosion rate in meters per year, occasionally as finite retreat (in meters) or as minimum and maximum erosion rates or eroded volume (in cubic meters).

Cliff retreat measurement errors and time spans were also recorded. Measuring sea cliff erosion presents a wide range of techniques. Those techniques vary significantly in terms of the following: (i) accuracy, which range from field observation and “expert” estimates May and Hansom (2003) of volume loss to precise measurements using techniques such as lidar (Dewez et al., 2013); (ii) time period surveyed, which range from twenty minutes (Williams et al., 2018) to thousands of years (Choi et al., 2012; Hurst et al., 2017; Regard et al., 2012); and (iii) the spatial extent along the coast, which ranges from tens of meters (Letortu et al., 2015) to kilometers (Hapke et al., 2009). Moreover, these measurements can be divided into three classes of methods: one-dimensional (1-D), two-dimensional (2-D) or three-dimensional (3-D).

One-dimensional cliff retreat measurement techniques correspond to retreats calculated on single transects. Typically, they correspond to measurements made with peg transects that record the cliff toe retreat or transects on aerial photographs to quantify cliff-top retreat (Kostrzewski et al., 2015; Lee, 2008; Pye and Blott, 2015). Two-dimensional measurements are mostly based on aerial photograph comparison. They either quantify the area lost between two aerial photographs campaigns or average numerous transects (Costa et al., 2004; Letortu, 2013; Marques, 2006). Three-dimensional techniques record the evolution of the cliff face and quantify volumes (Letortu et al., 2015; Lim et al., 2005; Rosser et al., 2007). Initially, 3-D assessments were performed based on observable, large, rockfall scars or debris aprons, (May, 1971; Orviku et al., 2013; Teixeira, 2006) but now the two most commonly used methods are lidar and SfM.

2.3.5 CEREMA French national dataset

The French CEREMA institute published a systematic national coastal cliff recession inventory (Perherin et al., 2012) based on aerial photograph comparison every 200 m stretch of cliff along the entire French metropolitan coastline (1800 km of coastal rocky cliff, which corresponds to 465 (53 %) values in the database). This rich systematic dataset was obviously included in GlobR2C2 but with two caveats. On one hand, the CEREMA dataset introduces a strong spatial bias for French oceanographic and climatic conditions in the database observation records. This situation may risk polarizing the analytical results; however, this was recognized beforehand and specifically treated to prevent such bias (cf. Sect. 4.2.3). On the other hand, being a systematic study for every stretch of coastal cliff around the country makes it more robust to scientific and funding biases. Research funds are often sought for areas combining coastal threats with societal interest. Therefore, coasts with higher recession rates are more often sampled, while quiet stretches of coastlines remain in the shadows. Consequently, including this data provides a more representative set of values existing along coastlines. Little studied sectors of the CEREMA research are hard rock coastal stretches (e.g., hard proterozoic granites from French Brittany) and erosion rates lower than the study's detection threshold.

Based on historical aerial photograph archives, CEREMA acknowledges that the quality of photographs limits the detectable cliff recession to rates higher than 10 cm yr⁻¹. Below this value, they deem recession rates as undetermined. We chose to record those undetermined values in the database but not to use them in the statistical analysis. We discuss this decision in discussion section.

2.3.6 Tides

The tidal range describes the variation in the height of the water surface. One consequence is that the cliff and platform undergo cyclic wetting and drying that weakens and erodes the constituting rocks (Kanyaya and Trenhaile, 2005). Rather than referring to difficult to use tidal records from tide gages, tidal modeling was performed with FES 2012 software (Carrère et al., 2012). This model gives all the constituents of the harmonic tide analysis. For our analysis, eight harmonics were considered: M2, N2, K2, S2, P1, K1, O1 and N2_2. These harmonics represent the diurnal and semi-diurnal main components of the tide harmonic model. The model produces a time series between given start and stop dates of sea level within a regular grid of 0.25^∘. Tidal characteristics were retrieved for each study location for two entire years, from which the mean amplitude over two cycles was extracted (i.e., height difference between successive high and low tides).

Table 1Field estimates of uniaxial compressive strength (Hoek and Brown, 1997) associated with the Hoek and Brown term in the database and the corresponding lithologies in the database.

^* Point load tests on rocks with a uniaxial compressive strength below 25 MPa are likely to yield highly ambiguous results.

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2.3.7 Waves

Wave properties were extracted from the ERA-interim reanalysis dataset (Dee et al., 2011). This gridded data has a pixel size of 0.75^∘. Temporally, data spacing is 6 h during the 1979–2016 period. Wave assault was characterized both in terms of mean agitation and extreme events. Three mean parameters characterize wave assailing force: significant wave height of combined swell and wind, wave period and wave direction. For swell characteristics, mean significant wave height and wave period characterize the average sea agitation. The wave direction value records the most frequent wave direction for the duration of the reanalysis period (1979–2016).

Anticipating that mean sea state values may be deceptive metrics, a record of extreme events was also described. Those events were characterized by the 95th percentile of wave significant height as suggested by Castelle et al. (2015). To complete this quantile value, the number of storms experienced at each cliff site was calculated between 1979 and 2016.

2.3.8 Climate

Climatic information was extracted from Climate Research Unit data between 1961 and 1990 (Mitchell and Jones, 2005). The grid size is 0.5^∘, at monthly time steps. Chosen parameters likely to influence erosion rate are mean annual rainfall, mean monthly temperatures and the number of freezing days (number of days per year below 0 ^∘C). We did not find a global climatic dataset reporting time series of rainfall and temperatures spanning the durations covered by the articles contained in GlobR2C2.

2.3.9 Cliff height

Cliff height often appeared to be missing. Filling this value is not straightforward because cliff height can be strongly variable along the surveyed cliff. Nevertheless, in order to provide a robust estimate, a mean cliff height was extracted from the 7.5 arcsec spatial-resolution GMTED2010 data global DEM (Danielson and Gesch, 2011). Cliff height extraction consisted of computing a buffer around the cliff extension shapefile, in which the mean value of the non-zero pixels (corresponding to the sea) was computed. To assess the accuracy of these cliff height estimates, they were compared against those rare values presented in publications. The estimations were found to be close to values given in publications with a root mean square error of 19 m at global scale. We deem it sufficient for a first attempt at the global scale, and probably not greatly different from the cliff height accuracy seen in the publications.

2.4.1 Integration of punctual records

We mentioned earlier that measurement techniques were either 1-D, 2-D or 3-D. These methods do not reflect the exact same processes and a choice was made to force all measurements to homogeneously report 2-D type measurements. The 3-D measurements in cubic meters per year were divided by cliff face surface in a cliff top equivalent retreat in meters per year. One-dimensional measurements do not average information laterally. Cliff retreat is stochastic in time and space and 1-D measurements profiles may happen to quantify erosion on a particulary high or low erosion transect. Therefore, erosion rates of the transect measurements were averaged for a unique study, cliff and period of time in order to limit the risk of over- or under-representation.

2.4.2 Field unit conversion

Original data may be provided in different ways (for example the time span between two measurements may be given by a duration or by start and end dates). As often as possible this information is summarized in a single duration field with a homogeneous unit. The following are the operations performed:

• To obtain a duration in years, the fields measure duration (year), measure beginning and measure ending (date) were merged together.

• Retreat (m) and eroded volume (m³) were converted to retreat rate (m yr⁻¹).

• The mean cliff height was either obtained from a cliff height mean field or as the mean between height min, height max (m).

• The error (m yr⁻¹) was a compilation of the error value and error type.

2.4.3 Average site climate

Some explanatory variables were strongly correlated with each other (e.g., wave period vs. wave significant height). This redundant information may lead to spurious correlation. Therefore, new synthetic variables combine existing variables:

Figure 4Cliff site locations (red dots) and number of studies contained in the GlobR2C2 database by country (published before 2016).

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• Monthly mean temperatures were converted to mean annual temperature and amplitude.

• Deep water swell energy flux was computed using swell period and significant height

  $$\begin{array}{}\text{(1)}& E_f={\displaystyle \frac{\mathrm{1}}{\mathrm{8}}}\mathit{\rho }g{H}_{\mathrm{s}}^{\mathrm{2}}{C}_g\text{with}{C}_{\mathrm{g}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}g{\displaystyle \frac{T}{\mathrm{2}\mathit{\pi }}},\end{array}$$

  where ρ is water density, H_s (m) is significant wave height, C_g (m s⁻¹) is wave group velocity and T (s⁻¹) is wave period.

• Swell incidence angle with respect to the cliff (angle between 0 and 90^∘).

Figure 5Time line of cliff erosion publications recorded in GlobR2C2 differentiated by measurement method.

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2.4.4 Rock resistance inference

The database, filled with information from publications, results in more than 40 distinct lithological descriptions. We first grouped lithology into 9 groups with a similar classification to that of Woodroffe (2002) for historical comparison. But lithology alone does not govern rock mass mechanical properties. Tectonic inheritance, deformation, fracturing and weathering weaken the rock masses. Consequently, the rock constituting the cliffs are divided by rock mass strength criteria. Following the practical examples from Hoek and Brown (1997), we propose to further aggregate Hoek and Brown's macroscopic rock mass strength categories into three categories. Hoek and Brown (1997) describe field estimates of rock strength and experimental uniaxial compressive strength. They describe seven grades of rock resistance, from extremely weak to extremely strong. Table 1 in this study describes field estimates, resistance terms, compressive strength and provides examples of such materials. This table is associated with our Hoek and Brown classification and the relative lithologies found in the database.

Figure 6Cliff recession rates differentiated using the Hoek and Brown rock mass strength criterion, which merges lithological descriptions and the fracturing/weathering state of the cliff rock.

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Aggregation criteria are based on the fields lithology name, weathering, fracturing and comments, in which all published details on rock strength, structural geology, weathering were preserved. Rocks were classed into three resistance classes termed hard, medium and weak. One may note that a similar approach, but with only two classes, was adopted by the EUROSION project consortium (Doody and Office for Official Publications of the European Communities, 2004). The hard rock class clusters granite, gneiss and limestones together. Weak rocks are mainly poorly consolidated rocks (weakly cemented sandstones, glacial tills and glacial sands) or strongly weathered rocks. Weak rocks also noticeably include well studied chalk cliffs. Medium resistant rocks correspond to claystone shales and siltstones.

Figure 7Erosion rate versus marine forcings (wave energy flux (W), tidal range (m) and number of storms) for each one of the Hoek and Brown rock resistance class. Lines beneath the scatterplots represent moving median per bin and the numbers are the Spearman correlation coefficients, which were only reported when the p value was significant.

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3.4.1 Erosion vs. rock mass properties

One of the first influential factors often pointed to in literature is rock resistance (Benumof et al., 2000; Bezerra et al., 2011; Costa et al., 2004; May and Heeps, 1985). Figure 6 shows the erosion rate distributions for the three rock resistance classes based on Hoek and Brown criterion. Three distinct behaviors can be seen. Hard rock (341 observations) erodes at a median rate of 2.9 cm yr⁻¹ with a median absolute deviation (MAD) of 3.4 cm yr⁻¹. Medium resistance rock coasts (63 observations) erode at a median value of around 10 cm yr⁻¹, with a MAD of 7.8 cm yr⁻¹. Due to the small number of observation of medium resistance rocks, this resistance class should be considered carefully. Finally, weak rocks (403 observations) erode at a median value of 23 cm yr⁻¹ and reach rates higher than 10 m yr⁻¹ with a MAD of 25 cm yr⁻¹.

Figure 10Ranges of erosion rates within different lithology. Comparison between the study by Woodroffe 2002 and this study.

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Macroscopic rock mass strength classes, although possibly crude, exhibit the ordered behavior expected from the literature: weak rocks erode faster than medium strength rocks, and medium strength rocks erode faster than hard rocks. Central erosion rate values increase by a factor of 2 to 3 from one class to the next.

These values are in agreement with Woodroffe's work (2002); however, even if those distributions are distinct, they are broadly spread and multimodal.

4.2.1 Erosion rates, study duration and stochastic behavior

Statistical exploratory data analysis is a way to dissolve local particularity into a global analysis. Nonetheless, including every quantitative study implies mixing rates measured via different methods, accuracy, and spatial and temporal extents, which could be a source of bias. Erosion is stochastic: the occurrence of a big rare event would influence the actual figure of the observed retreat rate. Rohmer and Dewez (2013) for instance, describe statistical indicators for testing the outlier nature of very large rockfalls, with methods borrowed from hydrology, seismology and financial statistics. These indicators were applied to a chalk cliff site in Normandy (northern France) in Dewez et al. (2013). During the 2.5 year terrestrial lidar monitoring period, a massive 70 000 m³ rockfall caused a local cliff top retreat of more than 19 m (Dewez et al., 2013). That is more than one hundred years' worth of average retreat in one event. Consequently, the estimated annual cliff recession rate rose from 13 to 0.94 m yr⁻¹, a 7-fold increase, just by including this random and definitely unrepresentative event (Dewez et al., 2013). Further examples of this can be seen in other studies covering the same site. Costa et al. (2004) estimated the recession rate to be ca. 15 cm yr⁻¹ in 29 years from aerial photos; whilst Regard et al. (2012), using millennial recession rates from ¹⁰Be accumulated in flint stones exposed in the chalk coastal platform, obtained 11 to 13 cm yr⁻¹ over 3000 years.

GlobR2C2 addresses the concern of non-representative erosion values by compiling all studies available online, and retaining information from all sites and survey periods. Therefore, the actual dispersion of recession rate values is preserved, which allows for the recognition outlying values (Fig. 11).

4.2.2 Forcing proxies

While publication-derived cliff recession rates and cliff conditions could be forced into a coherent database framework, environmental forcings were so scarcely and heterogeneously documented that the same rationalization process was not possible on the basis of publication alone. Instead, publicly available global climatic and sea condition databases were used. These databases present the advantage of being spatially and temporally continuous thanks to reanalyzed climate and sea state models. Their principal limitation is their coarse-grained definition compared to site specificities. Nevertheless, they document external forcings (i) in a uniform fashion (regular spatial and temporal sampling steps), (ii) for the entire globe and (iii) reflect forcing condition for durations spanning several decades. Consequently, even if regional or continental datasets offer higher resolution information in space or time, the global extent ensures that all cliff sites worldwide are uniformly documented.

4.2.3 Literature biases as future tracks to improve cliff evolution understanding

GlobR2C2's worldwide compilation shows that research in this domain is very active. A large body of quantitative data already exist. However, even if data coverage is somewhat global, publications have been found to focus primarily on a few western countries. This finding also reflects the strategy of literature search adopted: only international and national literature published in English, French or Spanish were compiled. Due to the language barrier, we are aware that studies in Russian, German or Japanese, among other languages, were unwillingly omitted.

Spatially, our search strategy did not flag scientific literature on the evolution of African and South American cliffs. Cliff recession studies appears to be focused on the richest areas where economically valuable coastal assets are exposed to losses. This geographic distribution induces an overrepresentation of temperate climates and a limited presence of some extreme climates or wave conditions like equatorial or polar regions. These underrepresented extrema could be the key to understanding the effects of climate and wave conditions on cliff erosion.

Figure 11Survey time vs. erosion rate by groups of measurement techniques.

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Furthermore, studies focus on fast eroding coasts because they represent bigger risks and also due to of methodological limitation. Indeed, the French CEREMA study provides the majority of the erosion values for hard rocks (265 values from 343, 77 %) and medium rocks (47 values from 66, 71 %). Without this systematic study soft rock represents 75 % of measured cliff retreat. This fact biased the analysis by mostly documenting erosion distribution in higher values. The weight of this bias can be appreciated thanks to the French CEREMA study. This study contains null erosion values for coastal sectors where the cliff was not seen to recess in a detectable manner on historical photographs. However, this detection threshold is deemed to be of the order of 10 cm yr⁻¹ (Perherin et al., 2012), which is rather high. Therefore, null recession could reflect erosion situations anywhere on the spectrum from 0 to 10 cm yr⁻¹. These null values represent 67 % of the studies of rocky coasts, which means that slowly eroding rocky coasts are common and ignoring this information can affect conclusions. In order to check the importance of the bias induced by those values, we explored two extreme cases. The erosion value was set to either a small value of 1 mm yr⁻¹ or to the detection threshold of 10 cm yr⁻¹. Table 2 shows the influence of the null value on the distribution of the erosion rate for the three Hoek and Brown rock strength classes. While the median and quantile absolute values are affected by the value attributed to null observations, the expected order of rock sensitivity to erosion is maintained. Weak rocks erode at higher rates than medium and hard rock. Therefore, we trust this result. Further, the dependency relationships flagged earlier remain. A weak positive correlation still exists between frost day frequency, and a maximum tidal efficiency for the tidal range between 1 and 3 m still is observed.

4.2.4 Cliff retreat vs. platform evolution and rock coast erosion

The cliff retreat rates discussed here cannot capture the overall rock coast erosion complexity. In particular, it is obvious that the rock shore platform coevolves with the cliff (Moses and Robinson, 2011; Sunamura, 1992; de Lange and Moon, 2005). Sunamura (1992) proposes that the shore platform erodes vertically at a rate proportional to its dip and cliff retreat. The processes driving this vertical erosion are numerous (cf. Introduction). It has also been proposed that the shore platform width reflects the total cliff retreat since the Holocene transgression; thus, it also reflects the average rock coast erosion since then (Regard et al., 2012). Applied to our findings, these ideas imply that harder rocks, leading to slower cliff retreat, come with steeper platform slopes.

On the one hand, platform width may be a powerful proxy for long-term cliff retreat. However, this analysis is not currently possible due to the fact the seaward platform boundary is not obvious (Kennedy, 2015), and there is also a lack of worldwide information on rock shore platform widths. On the other hand, this idea is debated, because it implicitly favors the static model for the evolution of shore platforms instead of the equilibrium model (Dickson et al., 2013; Moon and de Lange, 2008; Stephenson, 2008; de Lange and Moon, 2005).

Beyond its width, the rock platform behavior encompasses the dynamics of the scree apron lying on it and possibly shielding it from sea action (Regard et al., 2013). Indeed, cliff collapse is the only stage within the platform/cliff erosion cycle leading to apparent retreat. This transitory character could lead to long-term cliff retreat rate under- or over-estimation. Working with an important dataset, like the one presented here, averages data variability, ensuring the extrema are not overrepresented (cf. Sect. 4.2.1).

4.2.5 Toward a new rocky coast cliff research agenda

Table 2Distribution characteristics of cliff erosion rates (in m yr⁻¹) compiled from publications in GlobR2C2 and differentiated by Hoek and Brown rock resistance types. The different lines in the table reflect how the characteristic distribution values change when the erosion rate value given to cliff instances where erosion rates were smaller than the detection threshold in the CEREMA study are changed (n instances for N total observations). Null values were handled in three different ways: (i) insignificant rates were removed from the distribution computation; (ii) null values were used and assigned an arbitrary low erosion rate of 0.001 m yr⁻¹; and (iii) null values were used and assigned an arbitrary rate of 0.1 m yr⁻¹.

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This bibliographic synthesis has highlighted the strengths and weaknesses of the current rocky coast research efforts. The trend over the last three decades has gone towards increasing the quality and the resolution of cliff recession data and documenting a growing number of sites, which is positive. However, what this study highlights is the lack of a description of critically useful parameters to aid in understanding cliff evolution dynamics, which includes the following: (i) cliff height; (ii) finer rock mass characteristics descriptions, in particular weakening phenomena such as weathering and fracturing; and (iii) foreshore descriptions, in particular the type (sand beach/pebble beach/rock platform) and geometry (elevation, slope, width) of the foreshore. Moreover, the geographical distribution of the sites studied highlights a major gap in knowledge regarding extreme climates (tropical, equatorial and glacial), slowly retreating cliffs and medium resistance rock types. We also found that literature concerned with cliff retreat was not simultaneously trying to link shore platform processes to cliff retreat or to how local variations specifically affected cliff retreat.