Climate change and anthropogenic pressures transform ecosystems and jeopardize the services they provide, especially in coral reefs (Vergés et al., 2014; Hughes et al., 2017; Pecl et al., 2017). Coral reefs are affected from the physiological to ecosystem levels (Pendleton et al., 2016; Richmond et al., 2018) by increasing sea surface temperatures (SST), ocean acidification, and typhoons, along with a plethora of additional anthropogenic threats (Wilkinson, 1999; Hoegh-Guldberg et al., 2007; Carpenter et al., 2008; Carilli et al., 2009; Rogers et al., 2014; Darling et al., 2019; Ribas-Deulofeu et al., 2021). Reefs must show increasing capacities to resist and recover from stressors in order to persist (Hughes et al., 2003, 2010, 2011). In this context, structural complexity has been identified as a critical factor to understand reef resilience abilities (Graham et al., 2015; Maynard et al., 2017). A growing body of literature on reef rugosity has highlighted the losses in reefs’ structural complexities together with an erosion of resilience capacities (Syms and Jones, 2000; Chong-Seng et al., 2012; Graham and Nash, 2013; González-Rivero et al., 2014; Rogers et al., 2014). Mechanical damages and reduced growth rates of corals have led to a consequential loss in reef structural complexity over the past decades (Young et al., 2012; Bozec et al., 2015; Hoegh-Guldberg et al., 2017; Mollica et al., 2018).

Measurements of reef structural complexity were first performed by Risk in the 1970s (Risk, 1972), and were later adapted by Luckhurst and Luckhurst (1978) into the “rugosity index,” also referred to as the chain method, which measures the difference between the distance covered by a fine-link chain closely laid over a substrate and its known linear distance. Since then, the rugosity parameter has remained the most widely used measure of reef structural complexity, and multiple methods to estimate it have been proposed (e.g., Polunin and Roberts, 1993; Dustan et al., 2013; Young et al., 2017; Lazarus and Belmaker, 2021). In the 1990s, the visual rugosity index emerged to estimate larger scales of rugosity (Polunin and Roberts, 1993). This proposed index was based on a six-point scale ranging from zero—no vertical relief observed along the transect—to five—an exceptionally complex substrate relief with numerous caves and overhangs characterizing the transect (Polunin and Roberts, 1993; Wilson et al., 2007).

Since then, improvements in underwater techniques and other technological advances have allowed researchers to develop new methods and metrics to assess reef rugosity more accurately (Figueira et al., 2015; Ferrari et al., 2016; Young et al., 2017; Lazarus and Belmaker, 2021). Yet, even with enhanced tridimensional models, most of the recent studies have used linear-rugosity (chain method) or fractal dimensions to quantify reef rugosity (Ferrari et al., 2016; Young et al., 2017; Magel et al., 2019). In addition, most recent methods have been impeded by either their restricted resolution (e.g., satellite imagery) or their operational capacities in underwater ecosystems (e.g., Structure from Motion (SfM) photogrammetry), reducing the range of reefs in which researchers could implement them (Friedman et al., 2012; Knudby et al., 2014; Burns et al., 2015; Figueira et al., 2015; Ferrari et al., 2016; Yanovski et al., 2017). On the other hand, despite the broad acceptance of the traditional chain method, its in situ deployment remains laborious, time consuming, and inaccurate compared to techniques such as SfM photogrammetry (Risk, 1972; Luckhurst and Luckhurst, 1978; Knudby and LeDrew, 2007). In parallel, visual estimations of habitat complexity (Polunin and Roberts, 1993) have been widely used and praised for their correlations with the fish communities (Wilson et al., 2007). However, visual census approaches show limited relationships with benthic composition and yield observer bias, making the studies that use them difficult to replicate (Bayley et al., 2019). The more recent development of the Digital Reef Rugosity (DRR) method by Dustan et al. (2013) offers a good compromise between data resolution and field implementation difficulties. Yet, as suggested by the authors themselves, other statistics on depth profiles might yield better rugosity estimations than what they proposed (Dustan et al., 2013). Consequently, none of the existing methods or metrics led to a consensus on how reef rugosity should be measured or estimated (Knudby and LeDrew, 2007; Graham and Nash, 2013; Yanovski et al., 2017; Lazarus and Belmaker, 2021).

Coral reef rugosity is based essentially on the physical characteristics of the inhabiting organisms, and this structure can be measured from the micro scale (from millimeters to decimeters) to the macro scale (e.g., based on larger organisms such as massive Porites colonies, which can reach over a meter in scale) (Graham and Nash, 2013; Darling et al., 2017). In addition, the geological context of the studied reef also contributes to its rugosity, especially to its macro-rugosity (Kleypas et al., 2001; Graham and Nash, 2013; Darling et al., 2017). Numerous fish and other mobile reef organisms have been shown to prefer specific structural scales (Chong-Seng et al., 2012; Graham and Nash, 2013; Richardson et al., 2017). In the Indo-Pacific, studies showed that micro-rugosity, such as that provided by branching corals, tends to favor smaller fishes, such as Pomacentridae, as it offers them many potential refuges (e.g., Wilson et al., 2008; Graham and Nash, 2013), while large and medium-sized fishes show stronger relationships with macro-rugosity (Wilson et al., 2008; Dustan et al., 2013). Consequently, it is crucial to quantify the contributions of the different scales of rugosity to the overall reef rugosity, along with the contributions from biotic (reef organisms) and abiotic (geological features) parameters, since reef organisms constitute the primary targets of management strategies (Harborne et al., 2012; Graham et al., 2015; Darling et al., 2017). The chain method and SfM photogrammetry describe the finer scale of habitat variability (Knudby and LeDrew, 2007; Dustan et al., 2013; Magel et al., 2019) and most remote-sensing methods describe larger scale factors such as bathymetric variations (Purkis et al., 2008; Friedman et al., 2012; Dustan et al., 2013; Graham and Nash, 2013). Missing finer- or broader-scale rugosities may result in only a partial understanding of the relationship between structural complexity and reef composition and, ultimately, lead to inadequate reef management strategies (Friedman et al., 2012; Graham et al., 2015; Maynard et al., 2017).

Consequently, in this study, we propose a framework that combines fine-scale depth profiles with fast computations to accurately quantify reef rugosity, but more importantly to measure the relative contributions of fine and coarse rugosities (decimeter to meters) into the overall rugosity of the reef ecosystems. We present nine theoretical cases to demonstrate our method. We further tested the feasibility and performance of our method on 50 fine-scale depth profiles from South Taiwan coral reefs.

Reef rugosity estimations were based on high-resolution depth profiles from theoretical and in situ line-transects. Our calculations (Supplementary File 1) used the roughness index Rq, developed for engineering purposes to estimate the surface roughness profile of materials (Posey, 1946). Rq (also called R.M.S. in certain studies) represents the Root Mean Squared deviation from the assessed surface profile. To discriminate between the contributions of fine and coarse scales of rugosity on the total rugosity profile, we adapted the Rq index (Equation 1) as followed:

with l = transectlength;andm=ln; in this study, l = 20m.

Rugosity profiles were then plotted along with a first-degree polynomial function to represent the total rugosity of each transect (fine and coarse scales rugosity, Rq₁). Successive estimations of Rq were performed from the first order of polynomial up to the twelfth order. As the orders of polynomials increased, the fit we obtained improved, and thus the remaining rugosity decreased, allowing us to move along a continuum from coarse to fine scale rugosity. Rq₁ represents the overall rugosity of our line-transects, while Rq₁₂ corresponds to the fine scale rugosity contribution. To estimate the proportion of coarse scale rugosity in our transects, we subtracted the fine scale rugosity Rq₁₂ from the overall rugosity Rq₁ of the transect. From here on, we refer to the contribution of coarse scale rugosity to the transects as Rq₁–Rq₁₂.

To compare our method with commonly used rugosity methods, we computed the expected rugosity of our transects with the chain method. Our “virtual chain index” (Equation 2) was calculated as followed:

with virtual chain link size corresponding to the depth profile resolution of the transects, since m=ln.

In addition, to mimic diving conditions, two observers used videos to visually categorize the structural complexity of our in situ transects using the six-point scale proposed by Polunin and Roberts (1993). Zero, the first level, corresponded to no vertical relief observed along the transect. Levels one and two corresponded to sites with low structural complexity, and sparse and widespread relief, respectively. Level three was for moderately complex sites, while level four was for very complex sites with numerous caves and fissures. Finally, level five corresponded to sites with exceptional complexity, including numerous caves and overhangs (Polunin and Roberts, 1993; Wilson et al., 2007).

The visual rugosity index has been estimated for the 50 in situ transects by two observers. The observers only agreed on rugosity estimations for 16 of these transects. For most transects (22 out of 50), their rugosity estimations only differed by 1 level (e.g., 4 of the 5 transects from Chufengbi were ranked level 1 by one observer and level 2 by the other). For 12 of the 50 transects, the estimations differed by at least 2 levels (e.g., WLT2 to WLT4 were ranked level 3 by one observer and level 1 by the other). The greatest difference between the observers was 3 levels.

There was variability in the chain index and Rq indices among transects that had equal visual rugosity index scores. For example, the chain indices of the six transects ranked level 3 by both observers (DBS1, HBH1, HBH4, JLS4, JLS5, and LK2) ranged from 1.27 to 1.51. Similarly, for these transects, Rq₁ ranged from 0.24 to 0.99, Rq₁–Rq₁₂ ranged from 0.06 to 0.73, and Rq₁₂ ranged from 0.18 to 0.26.

Similarly to Wilson et al. (2007) and Young et al. (2017), we found an important observer bias in the qualitative rugosity estimation methods such as the visual rugosity index proposed by Polunin and Roberts (1993). Using visual indices to estimate reef rugosity is neither costly nor time intensive, but this method is subject to observer bias (Young et al., 2017; Bayley et al., 2019). Our study stresses the need to move away from visual estimations of reef rugosity if we want to accurately estimate the role of a reef’s complexity in its resilience capacities and relationship to the benthic and fish communities, and adequately track changes in this parameter over time or geographic ranges.

Chain and rugosity estimations from our theoretical and in situ transects suggested that the chain index poorly accounts for coarse scale rugosity (Table 2). This is a known consequence of the size of the chain link (Knudby and LeDrew, 2007; Friedman et al., 2012)—in our “virtual chain” case, the chain link corresponds to the resolution of the considered transect, which is comprised in our dataset between 12.5 and 19.4 cm. The inaccurate estimations of coarse scale rugosity by the chain method could be detrimental to specific reef organisms, such as large fishes (Wilson et al., 2008; Dustan et al., 2013; Graham and Nash, 2013). We recommend using Rq indices to better estimate reef rugosity and the relationship between rugosity and reef resilience capacity in the face of disturbances.

Using a single rugosity index to estimate reef structural complexity could lead to transects with different rugosity patterns and sources being assigned equal rugosity scores. This is true for the chain index (Knudby and LeDrew, 2007) and the rugosity indices presented in the present study. Indeed, when a single Rq level is considered, transects with different rugosity patterns could yield the same Rq scores for a given polynomial order. Instead of looking at a single Rq level, we recommend looking at three key Rq levels simultaneously: Rq₁, which illustrates the overall rugosity of the surveyed profiles; Rq₁₂, which represents the fine scale rugosity of the profiles; and Rq₁–Rq₁₂, an estimate of a profile’s coarse scale rugosity.

Our constrained multivariate analysis highlighted interesting relationships between certain rugosity levels and the main benthic contributors of the transects examined. Indeed, we observed that transects with higher coarse than fine scale rugosity contribution had a larger contribution of macro-algae, but did not necessarily present higher overall rugosity, which is consistent with the expectations in the literature (Chong-Seng et al., 2012), as macro-algae often provide a more flexible structure of the habitat and reduced the fine scale rugosity via space competition between coral and macro-algae (McCook et al., 2001; Chong-Seng et al., 2012). On the other hand, it was surprising that tabulate corals had a negative score on the first RDA axis; this might be caused by our fine scale rugosity size class. Indeed, in our dataset the average interval between two measurements was 15.73 ± 1.50 cm, therefore, our depth profiles might have only recorded the general morphology of the tabulate corals and not its smallest structural variations on their surface (≤ centimeter scale). However, it could also be a consequence of the low abundance of tabulate corals throughout KNP, as highlighted by Ribas-Deulofeu et al. (2021) (average tabulate coral cover in 2015: 2.55 ± 2.01%).

PCA analyses allowed us to visually identify transects with similar patterns of overall, coarse and fine scale rugosity altogether, as they were plotted close together in our multivariate representations (Figures 7, 8), giving us a relative ranking for the transects based on our three major rugosity levels. Eventually, those visualizations could be used to identify clusters of transects or sites that are particularly consequential for specific reef organisms or management strategies (as illustrated for our study case by dashed circles on Figures 7, 8). However, the interpretation of those results and their transcriptions into management strategies will have to be adapted to the studied depth profile resolution and the captured size ranges. For example, with the resolution of our dataset (decimeter to meter), if managers are seeking areas that will be more favorable to larger herbivorous fishes, then they should prioritize transects and sites with higher coarse scale rugosity (Wilson et al., 2008; Dustan et al., 2013), which in our case means the transects in the upper right-hand side of the PCA visualizations—i.e., JLS1, JLS4 or JLS5 (illustrated by the yellow dashed circle A in Figures 7, 8). Alternatively, if managers are seeking to restore or maintain global structural reef complexity, then transects aggregating on the left side of our PCA (illustrated by the gray dashed circle C in Figures 7, 8) could represent high-priority areas for their management strategy, as these transects globally present a low structural complexity at both fine and coarse scales, due to either specific environmental conditions or harmful anthropogenic activities. The lower left-hand sides of our Figures 7, 8 represent transects with higher fine scale rugosity, which are more favorable to small reef-associated organisms such as damselfishes (blue dashed B circle in Figures 7, 8; Wilson et al., 2008; Graham and Nash, 2013; Rogers et al., 2014). Transects in the black dashed D circle have good overall rugosity with good contributions from both coarse and fine scale rugosity, which could be favorable to both larger and smaller reef organisms (Figures 7, 8). In addition, tb-RDA analysis (Figure 8) allows us to identify the functional groups responsible for the key levels of rugosity that managers might seek to improve. Going a step further, linking our Rq indices with the benthic composition of the surveyed transects can allow reef managers to identify the proportion of the overall rugosity they can manage. Indeed, specific management strategies will influence different types of reef organisms and are unlikely to modify the abiotic components of reef rugosity, such as the bathymetric gradient or the geological features of the surveyed locations. Consequently, relative contribution of fine and coarse scale rugosity provided by inhabiting organisms will better inform reef managers of the extent to which they can improve the rugosity of their targeted reefs.

Our indices allow the distinction of rugosity at a variety of scales. However, size ranges captured by them are constrained by the resolution of the depth profiles, which can be adjusted according to the targeted ecological process. For example, an interest in coral recruitment will probably need a resolution from the millimeter to the decimeter, defining the limits of the fine and coarse rugosities, respectively. In contrast and following the same definition, decimeter to kilometer scales will better respond to the requirements in seascape ecology. In our case, a resolution from the decimeter to the meter better fitted with our focus on benthic community dynamics, which can be translated by the increase/decrease of benthic taxa’s covers and link to our Rq indices via constrained redundancy analysis.

Despite certain similarities between our Rq indices and fractal dimension approaches, such as reflecting rugosity contributions across different scales (Young et al., 2017), the use of polynomial functions in our indices does not allow for a pre-set of size categories for each Rq, but only a post-calculation of the size ranges captured by them. This could constitute the main weakness of our approach and should be the object of further developments to address it. Yet, the strengths of our approach remain in its wide application to various purposes, along with its relative simplicity in both application and computation [in comparison with other approaches (e.g., fractal dimension)].