Coral Reefs

, Volume 30, Supplement 1, pp 11–23 | Cite as

AUV-based bed roughness mapping over a tropical reef

Report

Abstract

Identifying fixed bed roughness scales of hydrodynamic relevance to waves and currents is challenging around coral reefs due to their highly inhomogeneous bathymetry. In order to characterize the spatial variability in reef roughness, a quantitative analysis of high-resolution sidescan sonar backscatter is performed for the identification of distinct substrates around a tropical reef and is related to echo sounder-based roughness measurements. Data were collected in the vicinity of the Kilo Nalu Observatory on the south shore of Oahu using sidescan sonar and a narrow beam echo sounder incorporated in a REMUS-100 (Remote Environmental Monitoring UnitS) autonomous underwater vehicle (AUV). With basic statistics and principal component analysis of variables derived from the backscatter data, it is possible to discriminate between areas of rough reef, bare reef, and rippled sand. Echo sounder-derived spectral analysis did not reveal dominant length scales. However, by combining the seabed classification obtained from sidescan measurements with echo sounder data, spectral root mean square (RMS) height values of approximately 3.3 cm and 7.3 cm are assigned to the bare reef and rough reef areas, respectively, for roughness with wavelengths between 0.2 and 6 m.

Keywords

Seabed roughness Sidescan sonar Substrate classification Autonomous underwater vehicle 

Introduction

The effects of seabed roughness on bed stress, \( \tau_{0} \), and turbulent boundary layers are normally represented through parameterizations that use a quadratic drag coefficient, CD, and a hydrodynamic roughness scale, z0 (Kundu 1990).

When the bottom boundary consists of homogeneous elements, the hydrodynamic roughness scale can be related to a roughness length, kb. For sand grains, for example, the roughness length is given by kb = 2.5D50, where D50 is the median grain diameter and is related to the hydrodynamic roughness by z0 = kb/30 (Nikuradse 1933). In the case of sand ripples, the hydrodynamic roughness is also a function of the ripple slope, \( \eta /\lambda \) where \( \eta \) is the ripple height, and \( \lambda \) is the ripple wavelength. Grant and Madsen (1982) gave the hydrodynamic roughness over ripples as
$$ z_{0} = k_{b} /30 \approx \eta^{2} /\lambda $$
Here, z0 is no longer uniquely determined by the roughness height, but also becomes a function of other parameters that reflect the bed geometry including horizontal element spacing (McLean et al. 1999).

Coral reef environments have complex bathymetry and a diversity of roughness scales that are closely connected to the heterogeneity of bottom types (i.e., sand, coral, pavement) that can be found within relatively short distances. For coral reef environments, there are currently no reliable parameterizations that can relate physical roughness scales to CD or z0 (Monismith 2007).

Sidescan sonar and multibeam echo sounders have been extensively used as tools for benthic habitat classification (e.g., Cochrane and Lafferty 2002; Bates and Oakley 2004; Blondel and Gómez-Sichi 2009, among many others). Automated seabed classification techniques change depending on the spatial scales of interest, instrumentation used, and geological and biological attributes of the seabed (Kenny et al. 2003). Some of these techniques include the use of fractal theory (Carmichael et al. 1996), neural network algorithms (Marsh and Brown 2009), texture analysis (Huvenne et al. 2002), canonical correspondence analysis (Henry et al. 2010), and cluster analysis (Preston 2009). In the context of tropical reef environments, Lucieer (2008) was able to classify the seabed into three main classes: reef, low reef, and sand, using an object-oriented technique (segmenting the acoustic data into objects of various sizes, based on their spectral and spatial characteristics) with 1-m resolution sidescan data. In the Seychelles, Collier and Humber (2007) used cluster analysis of sidescan data with a pixel resolution around 7 by 60 cm, to identify seven different bottom classes: fringing reef, pinnacle reef, patch reef, low-relief reef, sea grass, fine-grain sediment, and coarse-grain sediment. Unfortunately, none of these studies report actual physical roughness values that can be associated with the different bottom classes within the reef.

To examine the relations between physical and hydrodynamic roughness over coral reefs, Nunes and Pawlak (2008) obtained boat- and diver-based roughness measurements over a section of the coral reef around the Kilo Nalu Observatory, Oahu, Hawaii. In their observations, the bed was characterized by a rough spectral distribution of length scales between 0.3 and 10 m with a characteristic spectral slope of −3.0 ± 0.7 (i.e., average slope of the power spectral curve in the logarithmic space). The roughness amplitude also showed high-spatial variability on scales of 50–100 m. These roughness estimates were compared qualitatively with sidescan sonar data, collected from an autonomous underwater vehicle (AUV).

Expanding on the findings of Nunes and Pawlak (2008), we present a series of observations that quantitatively compare higher-resolution sidescan and physical roughness measurements over the coral reef in the vicinity of Kilo Nalu. The observations are obtained using a REMUS-100 (Remote Environmental Monitoring UnitS, Hydroid, Inc) AUV with a customized narrow beam echo sounder.

The use of AUVs for seabed mapping has expanded in recent years (e.g., Grasmueck et al. 2006; Shcherbina et al. 2008; Williams et al. 2010). AUVs are particularly well suited to obtain high-resolution sidescan data and fixed bed roughness measurements in environments such as coral reefs, where roughness scales can change abruptly over short distances. These types of vehicles provide a sampling platform that can cover long distances at a constant speed and are more stable than boats due to the reduced influence of surface waves. By cruising at a smaller, constant elevation over the seabed, the acoustic footprint of the echo sounder is also kept constant, improving the overall quality of the data collected.

Our immediate goal is to implement and test a simple methodology for seabed classification in tropical reef environments using the backscatter data from the AUV sidescan sonar, and then, using bottom range measurements from the narrow-beam echo sounder, to assign characteristic RMS (root mean square) height values to different bottom types identified.

Methodology

Study area

The study area is located offshore of Honolulu, Hawaii, at the Kilo Nalu Observatory (KNO; www.soest.hawaii.edu/OE/KiloNalu) (Pawlak et al. 2009). Figure 1 shows the location of the study site including the AUV track for a survey carried out in December 2009. Markers KN1 and KN2 denote the position of two upward-looking 1.2-MHz acoustic Doppler current profilers (ADCP, RD Instruments) cabled to KNO. The survey area covers approximately 800 × 500 m, ranging in depth from 8 to 35 m. The survey area was rotated by 30 degrees to align it roughly with the bathymetric contours. The wave environment at the study site is seasonal (Pawlak et al. 2009) with wave heights reaching up to 3 m in summer months. The offshore slope of the study area is relatively steep, ranging from 0 to 40 m depths within 1 km. This steep slope suggests that local bathymetry accounts for most of the wave transformation processes, in contrast to broad-shelf continental regions.
Fig. 1

Study area. The blue line shows the track followed by the AUV during the survey. KN1 and KN2 mark the location of two moored ADCPs that are part of the Kilo Nalu Observatory. The green squares mark the location of the photographs shown in Fig. 2

The seabed in the south shore of Oahu consists mainly of Holocene limestone reef, with large areas covered by live coral mixed with patches of carbonate sands (Ferrall 1976). At KNO, the reef is comprised of encrusting algae and corals with sparser coverage by branching and lobate corals (Porites lobata and Pocillopora meandrina) over very rough fossil reef from the shoreline out to approximately 12 m depth. Farther offshore, a band of relatively flat reef deepens to approximately 15 m where dense coverage by branching corals extends out to about 20 m depth. Seaward of 20 m depth, coral coverage is sparse (Pawlak et al. 2009).

For the present study, we separate the substrate into three main classes, which focus on varying roughness characteristics:
  1. (a)

    Rough reef: branching corals and rough fossil reef;

     
  2. (b)

    Bare reef or hard ground: low reef, often covered with a thin layer of carbonate sands;

     
  3. (c)

    Rippled sand: carbonate sands deep enough to support ripple formation.

     
Examples of these classes are shown in Fig. 2 corresponding to the locations marked in Fig. 1.
Fig. 2

Photographs illustrating the different bottom classes of interest during this study: a Rough reef, b Bare reef, c Rippled sand (abandoned stormwater pipe is visible in the background). The approximate location of these photographs is shown in Fig. 1

Instrumentation

A REMUS-100 AUV equipped with a 900-kHz acoustic sidescan system (Marine Sonic Technology, Ltd) was used to survey the study area. The sidescan sonar records acoustic intensity reflected from the seabed on either side of the vehicle. The AUV was programmed to maintain an altitude of 3 m above the bottom at a cruise velocity of 1.3 m/s, which rendered sonar coverage of about 60 m in the cross-track direction. The resulting spatial resolution of the acoustic data was approximately 6 cm in the cross-track direction and 12 cm in the along-track direction. Because sidescan records only backscatter intensity, no direct information regarding bottom range is obtained. To this end, the AUV was outfitted with a narrow beam (2.5° beam width) echo sounder (Imagenex Technology Corp.) with a range resolution close to 1 cm, and a sampling frequency that varied between 9 and 18 Hz, which results in along-track resolution between 7 and 14 cm. The cross-track resolution was determined by the sidescan sampling scheme, which was designed with a spacing of 45–15 m for consecutive transect legs (see Fig. 1) in order to maximize coverage. Note also that the echo sounder measurements are obtained directly under the vehicle (nadir), where sidescan data are degraded by acoustic backscatter from the water column.

Results

Sidescan backscatter measurements

The analysis of sidescan data for seabed classification made in this study follows a similar process as that used by Preston (2009) for ship-mounted multibeam data. Using software developed by the Hawaii Mapping Research Group (HMRG) at the University of Hawaii, sidescan data were processed to eliminate intensity returns from the water column, which in effect removes data near the nadir of the vehicle. A high-pass filter was then used to smooth changes in backscatter intensity due to small variations in the vehicle’s attitude (pitch, roll, yaw). This preliminary process significantly reduces the effects of instrument and survey variations, thus isolating the effects of the seabed on backscatter amplitude. The data set was then interpolated to a 5-cm by 5-cm georeferenced grid. Figure 3 shows a subset of the sidescan sonar data from our survey before and after the processing was applied. In the processed data (Fig. 3b), it is easier to visually identify different types of bottom substrates, such as bare and rough reef, as areas with smoother and rougher texture, respectively. Sidescan data are sufficiently resolved to enable identification of moored KNO instrumentation in close-up views.
Fig. 3

Sample sidescan backscatter intensity data: a Unfiltered data; b Filtered, georeferenced data processed using HMRG software

For large data sets where visual identification is not practical, quantitative examination of variations in bottom class can be carried out using principal component analysis (PCA) (i.e., Preston 2009), which determines relationships between a set of variables that best account for variability in a data set. Several variables derived from the acoustic intensity of bottom return were examined for use in the PCA analysis. Maximum variability was accounted for with the first two principal components using a variable set comprised of variance, skewness, entropy, power spectral slope, and anisotropy calculated on the georeferenced data. These variables were calculated in boxes of 6 m by 6 m, without overlap, covering the complete acoustic data. Since the overarching goal of our research is concerned with effects of rough, heterogeneous seabeds on waves and currents, the size of these boxes was chosen to be as small as possible, in order to best resolve the variability in bottom type, but with the constraint that in each box there should be enough acoustic intensity values to allow for robust statistics to be calculated over scales comparable with typical wave orbital amplitudes (~1–3 m). One of the consequences of the boxing process is the loss of data near the edges and nadir sections of the imaged region. This loss, however, is minimized by the overlap in coverage that results from the 15/45-m line spacing in the survey pattern (see Fig. 1).

To illustrate the data processing method, Fig. 4 shows an example of the calculation of variance, skewness, and entropy calculated for the backscatter intensity data in Fig. 3b. To maximize data coverage, we defined a coordinate system with the x-axis oriented in the cross-shore direction and approximately parallel to the survey tracks. The georeferenced sidescan data were then rotated clockwise into this coordinate frame. In general, higher variances in sidescan backscatter intensity (Fig. 3a) were observed in regions with rough reef formations, and low variances corresponded to areas covered by bare reef. It must be noted that backscatter amplitudes (and thus variance) can depend on instrument range and beam and grazing angle to the seabed (Preston 2009). Even though the AUV provides a very stable platform, these three variables are not constant during a survey, changing with vehicle attitude and speed. Because of this, variance alone is not used to separate different bottom types. Since large acoustic shadows are often observed in the rough reef–covered areas, these areas can have low variance but are well described by the skewness. High positive values of skewness in the sidescan data (Fig. 4b) indicate that the probability distribution of backscatter intensity within a particular box has a large number of low values related to shadows projected by coral heads or some other large feature.
Fig. 4

Example of statistical features calculated on the data subset shown in Fig. 3. The data reference frame has been rotated clockwise and divided into 6 × 6 m boxes. All variables have been normalized by their maximum value within the subset. a Variance; b Skewness; c Entropy

Entropy is a statistical measure of randomness that can be used to characterize the texture of the input data. Here, we use the entropy (H) defined as:
$$ H = - \sum\limits_{i = 0}^{L - 1} {p(z_{i} )\log_{2} p(z_{i} )} $$
where p(z) is the histogram of the intensity levels in a region, and L is the number of possible intensity levels (Gonzalez et al. 2003). Figure 4c shows the entropy calculation over the sample data subset. Higher entropy values over the rough reef areas reflect the more heterogeneous nature of this type of substrate, while values of entropy over bare reef patches are much lower due to the generally smoother bed.

Surface vessel-based echo sounder-based observations by Nunes and Pawlak (2008), obtained in the same region as the observations presented here, pointed to spectral slope as a potential variable to characterize bottom roughness in areas where no specific length scales could be easily identified. We calculate the power spectral density of acoustic intensity for each box in the data set following standard spectral analysis procedures (i.e., Bendat and Piersol 1971). Spatial series segments of 6 m length in the along-track direction were detrended, with segments then divided into 120-pixel blocks without overlap. Spectra are calculated for each block and averaged over the box. Finally, the spectral slope is calculated in the logarithmic domain using a least squares fit in the wavenumber band between 1/30 and 1/150 cm−1.

For illustration, the spectra calculated in two different boxes, one with rough reef (Fig. 5a) and one with bare reef (Fig. 5c), are shown in Figs. 5b, d, respectively. The high/low variances observed over the rough/bare reef areas (Fig. 4a) are reflected in the fact that the most energetic spectrum corresponds to the rough reef–covered box (spectral slope = −1.73), while the least energetic corresponds to the bare reef box (spectral slope = −0.89). In general, over the rough reef and bare reef areas, the spectral analysis reveals no outstanding length scales. While these types of spectral slopes are consistent over the surveyed area, in instances where a box contains a few large features, such as a single coral head, the spectral calculation alone is not useful to separate rough reef and bare reef, as the assumption of stationarity in the data cannot be made.
Fig. 5

Estimation of mean along-track spectral slope. a Backscatter intensity over rough reef; b Corresponding mean power spectra; c Backscatter intensity over sand ripples and its mean power spectra d. The dashed lines represent the 95% confidence intervals. The red line represents the least square fit in the wavenumber band between 1/30 and 1/150 cm−1

To investigate the directionality in the seabed substrate, we estimate an anisotropy index based on the 2D spectrum (Jackson and Richardson 2007) of the intensity counts within each box (Fig. 6). We use principal component analysis to find the main axes of variability of the 2D spectra (dashed and solid black lines in Fig. 6) and define the anisotropy index as:
$$ AI = 1 - {\frac{{L_{\min } }}{{L_{\text{maj}} }}} $$
where Lmin and Lmaj are the principle axes of the variability. These axes can be interpreted as the semiminor and semimajor axes of an elliptical fit to the 2D spectrum. The maximum anisotropy (AI = 1) occurs when the length of minor semiaxis is zero, when all the variability is concentrated in one direction, while the minimum anisotropy (AI = 0) occurs when both variability axes are equal. Figure 6 shows an example of this calculation for two boxes. The rough reef box (Fig. 6a) has a very low anisotropy index since both the major and minor semiaxes (red and blue lines in Fig. 6b) have approximately the same length. On the other hand, the box that contains sand ripples (Fig. 6c) has a very high anisotropy index, with the semimajor axis (oriented along the ripple crests) much larger than the semiminor axis.
Fig. 6

Estimation of seabed directionality. a Backscatter intensity over rough reef; b Corresponding 2D power spectra; c Backscatter intensity over sand ripples and its 2D power spectra d. The red and blue lines in (e) and (d) represent the principal axes of sidescan backscatter variance

Figure 7a shows the mosaic of sidescan backscatter intensity and the corresponding statistical variables obtained by applying the procedure described earlier to the entire survey data set. In order to avoid artifacts introduced by the creation of a mosaic, such as averaging over overlapped sections, 120-m-long along-track subsets of data were analyzed individually and then organized into a single matrix, demeaned, and normalized by their standard deviation to prepare for input to the PCA routine. Data along the edges and nadir of each image were kept only if their box contained more than 95% valid data.
Fig. 7

Normalized demeaned statistical variables used in the PCA. a Mosaic image of sidescan backscatter collected in the KNO vicinity; b Variance; c Skewness; d Entropy; e Power spectral slope; f Anisotropy

Some seabed characteristics can be immediately identified by visual inspection of the mosaic. Regions with rougher texture in the middle and northern section (shallower part) of the study area are associated with rough reef covered areas; the smoother texture sections of the image correspond to areas covered by either bare reef or sand. A large sand ripple field near the western boundary can be identified from close-up views of the mosaic. An abandoned stormwater pipe that runs in the southwest direction from the northeast boundary of the surveyed region is also evident. The rough reef areas coincide with high variance, high entropy, and steep spectral slopes (Fig. 7b, d, and e, respectively); the ripple fields are registered as areas with high anisotropy (Fig. 7f) and also steep spectral slopes (Fig. 7e) due to the presence of a pronounced spectral peak located toward the lower wavenumbers of the fit window. Note that since spectral slope values are negative, the steeper slopes correspond to the lower (blue) values.

The first two components of the PCA using these variables capture most of the variability in the data set. These two components, PC1 and PC2, account for 51 and 23% of the variability, respectively, while the next two components account for only 16 and 6%. Figure 8 shows the relative contribution of each variable to each statistical mode. The dominant variables for PC1 are variance and entropy, while PC2 is controlled by anisotropy and to a smaller degree by spectral slope. It must be noted that the sign of these contributions is arbitrary and is indicative only of the relations between the variables. For example, within PC1, entropy varies proportionally to variance, skewness, and anisotropy and inversely to spectral slope.
Fig. 8

Relative contribution of each sidescan-derived variable for the first two principal components. a PC1 explains 51% of the variability of sidescan backscatter intensity; b PC2 explains 23%

Figure 9 shows the reconstruction of the original data field using each of the first two components. A preliminary visual inspection suggests that using the spatial pattern for PC1 (Fig. 9a), it is possible to discriminate between bare and rough reef covered areas and that PC2 can be used to identify areas covered by sand ripples. It is more difficult to make a physical interpretation of PC3, 4, and 5 (not shown) since their contributions are less significant to the data variance and spatial patterns are not distinct.
Fig. 9

Spatial distribution of sidescan-derived PC coefficients. a PC1 coefficients; b PC2 coefficients

Verification of PCA-based seabed classification

To assess the validity of the PCA-based classification of bare reef, rough reef, and sand ripples for our surveyed area, we inspected a random subset of the data covering 20% of the surveyed area. For each selected subset, we visually identified 6-m2 boxes as bare reef, rough reef, rippled sand, or mixed substrate. Figure 10a shows a histogram of the PC1 values that correspond with the visual classification. Histogram peaks corresponding to bare reef and rough reef classes in Fig. 10a occur at about PC1 = −1.4 and PC1 = 2.7, respectively. Choosing a threshold PC value to separate different bottom types will introduce errors that are proportional to the overlapped area between the different curves in the histogram. The tradeoff between accuracy in seabed classification and area included in the classification is quantified in Fig. 10b–d. The pink lines in Fig. 10b represent the fraction of PC-classified boxes that are correctly identified as rough reef, while the black lines represent the fraction of all rough reef boxes that are included in the classification. As the PC1 threshold value increases from −3 to 3.5, our classification accuracy increases from close to 30% to around 90%, but the fraction of rough reef boxes included decreases to near 10% as rough reef boxes with low PC1 values are excluded. Analogous information is shown for bare reef and sand ripples (using a PC2 threshold for the latter). Using a threshold value of PC2 < −2 to identify sand ripple boxes, our PC1-based rough reef and bare reef classification is further improved, albeit by a small percentage, by excluding those boxes identified as ripples from the PC1 predictions (solid lines in Fig. 10b–c).
Fig. 10

Visual verification of PCA-based bottom classification. a Histogram of visually identified bottom classes versus PC1 values. bd Fraction of PC-classified boxes that are accurately identified (pink lines), and fraction of total class boxes included in the classification by the PCA (black lines), for rough reef, bare reef, and sand ripples, respectively. The dashed lines in (b) and (c) represent the reduction in accuracy that results from including sand ripples that can be identified from PC2 into the PC1 classification

Choosing appropriate thresholds for seabed classification will depend on the application or particular process that is of interest. We find that a good compromise between accuracy in the classification and area included can be achieved by choosing a value of PC1 > 1 (80% accuracy, 80% included) for the rough reef class, a PC1 < −0.6 (78% accuracy, 78% included) for bare reef, and PC2 < −2 (75% accuracy, 70% included) for sand ripples in the vicinity of Kilo Nalu. The areas between those values remain unclassified (28% of the total area) and include mixed boxes that had similar proportions of bare reef, rough reef, and sand ripples. The result of this classification is shown in Fig. 11. For the given thresholds, we classify 26% of the survey area as rough reef, 42% as bare reef, and 4% as rippled sand.
Fig. 11

PCA-based classification of seabed types near the Kilo Nalu Observatory. The green squares show the location of the photographs shown in Fig. 2

Echo sounder-based roughness measurements

Using the narrow beam echo sounder mounted on the REMUS-100 AUV, we are able to directly measure range to the bottom with an average horizontal resolution of 10 cm. The spatial series of bottom range was corrected to account for variations in vehicle pitch, roll, and yaw. Measurements corresponding to sharp changes in any of those variables were rejected.

The bottom range series is divided into 12 m segments with 50% overlap, and power spectral density is calculated following standard procedures (Bendat and Piersol 1971). We calculate a root mean square (RMS) height as \( {\text{RMS}} = \sqrt {\int {S \cdot dk} } , \) where S is the power spectral density, and k is the wavenumber.

Figure 12a shows the spectral RMS height calculated from the spatial series of bottom range. The similarities between the sidescan PC1 pattern and RMS spatial distribution are qualitatively apparent. Maximum RMS height values generally coincide with the areas identified as rough reef from sidescan observations, while lower values of RMS height are observed around the bare reef covered areas.
Fig. 12

a RMS height measurements obtained from the narrow beam echo sounder; b sidescan PC1 coefficients interpolated onto the AUV track; c RMS altitude versus sidescan PC1 magnitude

From the hydrodynamic point of view, we are interested in relating different types of seabeds with a measured RMS height. The altitude measurements are obtained directly at the vehicle’s nadir, however, where sidescan quality is poor. In order to compare the sidescan PCA-based bottom identification and the echo sounder roughness measurements, the sidescan PC1 coefficients are interpolated to the vehicle echo sounder track using the nearest neighboring values (Fig. 11b). A least squares fit of interpolated PC1 values to the RMS height yields an r2 = 0.52 (Fig. 11c). It should be noted that there is no reason to expect a linear relationship between RMS height and PC1. The relatively high r2 value, however, reflects the relation between bed type and roughness, even with the expected errors introduced by the georeferencing and the interpolation of the sidescan data.

Using the thresholds discussed in the previous sections to separate between bare reef, sand ripples, and rough reef, we find average RMS values of 7.3 cm ± 1.4 cm(mean ± SD) for rough reef–covered areas, 3.3 cm ± 1 cm for the bare reef areas and 2.5 cm ± 0.3 cm for the rippled sand areas. This latter value requires careful interpretation. First, because of the anisotropy associated with the ripples, the RMS value is dependent on the sample path orientation relative to the ripples. The AUV path is not consistent relative to the ripples, however, and is generally not perpendicular to the ripple crests. More significantly, ripples contribute less than 2% of the overall distance sampled by the echo sounder, so RMS statistics are not as robust relative to the broader bare reef coverage. The ripple RMS values fall within the bare reef RMS error bands but are lower than the average bare reef values, which suggest that RMS variations for bare reef areas are likely dominated by contributions at wavenumbers below ripple scales.

The RMS height values reported here are calculated over the 0.2–6 m−1 bandwidth. These limits are set by our interest in RMS height scales calculated over scales comparable with the typical near-bed wave orbital amplitude in the area. Integrating over wider bands will increase the magnitude of the RMS height. As reported by Nunes and Pawlak (2008), no dominant length scales were revealed by the spectral analysis except in rippled areas (average wavelength of 75–100 cm). Finally, spectral (and thus RMS height) estimations calculated over the more limited wavenumber bands: 0.66–6, 0.5–2, and 0.2–0.5 m−1 and (not shown here) indicate that the rough reefs have greater variance (more energetic spectra) in all the wavenumber bands measurable by our methods.

Changes in vehicle altitude related to surface wave motions or to vehicle adjustments with bathymetric changes inevitably introduce variations in the bottom range data. Since we are interested in small-scale roughness (wavelengths < 6 m), these motions, which occur at low frequencies, only introduce low-wavenumber biases into the spatial series, which do not affect our analysis. Typical surface wave periods of 10 s, for example, will introduce variations with scales of O(10 m) at the typical survey velocities. Vehicle adjustments to changes in bottom bathymetry occur on similar timescales.

Discussion

One of the many challenging aspects in identifying length scales of hydrodynamic relevance around tropical coral reefs is associated with the highly inhomogeneous bathymetry. In this type of environment, roughness length scales can vary over relatively short distances, so our capacity to understand seabed roughness effects on waves and currents over coral reefs is limited by a lack of detailed seabed information.

Using an AUV, we obtained measurements at a horizontal resolution of ~5 cm for the sidescan backscatter data, and ~10 cm for the echo sounder data. Compared with boat-derived roughness measurements (Nunes and Pawlak 2008), the use of an AUV for this task improves the quality and resolution of the data obtained by increasing platform stability and by maintaining a near-constant acoustic footprint for the echo sounder-based roughness measurements. This enabled a quantitative comparison between bottom classes identified from the sidescan sonar data, and RMS height measured with the narrow beam echo sounder.

To identify different bottom types near Kilo Nalu, we use principal component analysis to reduce the sidescan backscatter information to essentially two statistical modes (PC1 and PC2) that account for 74% of the total variance. The spatial patterns for PC1 and PC2 reflect the spatial patterns of bare reef, rough reef, and sand ripples observed over the surveyed area. Visual verification of these similarities indicates that using this technique for automatic detection of seabed type, we can separate these bottom classes with a degree of certainty that varies according to the choice of a PC threshold value. In our case, we set this threshold value to PC1 > 1 for rough reef (80% accuracy), PC1 < −0.6 for bare reef (75% accuracy), and PC2 < −2 for sand ripples (75% accuracy). The extent to which the PC modes are site-specific has not been established. We can expect that the relationships between variables (variance vs. entropy, etc) will hold in general for these bed classes, although relative values would vary. In addition, the presence of other bed classes (i.e., sea grasses) could complicate the interpretation of the PC modes. A similar but more comprehensive approach has been used in the past to discriminate bottom types using sidescan and multibeam echo sounder data (e.g., Collier and Humber 2007; Preston 2009), although not at the high resolution, we present here.

Errors in seabed classification using this methodology may come from multiple sources, including instrument/platform performance, human error in the visual classification of the sidescan images, the choice of a box size for the subdivision of the sidescan images, and the processing of sidescan data that is required in order to obtain properly georeferenced information.

Although the validity in using spectral estimates alone for characterizing broad-banded roughness is questionable because phase information is lost (i.e., different signals can have similar power spectra Rajagopalan 2010), the RMS height is still a robust estimate of the energy content within a given wavenumber band. While the echo sounder-derived bottom range spectra over the study area did not reveal any conspicuous length scales, using the sidescan-based bottom classification, we are able to assign estimates of physical roughness to the bare reef and rough reef areas using mean RMS values of 3.3 and 7.3 cm, respectively. The highest RMS values over the survey area correspond to rough reef areas found in the shallower (<10 m) part of the surveyed area, consistent with findings by Nunes and Pawlak (2008). One of the main limitations derived from this combined approach is the difference in the areas ensonified by the sidescan and narrow beam echo sounder, as the latter points directly to the bed below the AUV where sidescan backscatter data are not reliable. However, this can be resolved by programming repeated AUV surveys over the same region with narrower separation between consecutive navigation legs.

As an initial step in characterizing roughness, we have reported direct measurements of a vertical length scale as RMS height. For some bed types, hydrodynamic roughness is often related to bedform steepness, which effectively introduces a horizontal length scale. Determination of hydrodynamically relevant horizontal scales is not straightforward for inhomogeneous roughness like that over reefs. For the reef data considered here, we can, however, provide an estimate of the steepness of the bottom relief as \( \Updelta z/\Updelta x \), where \( \Updelta z \) is the height difference between two consecutive echo sounder measurements, and \( \Updelta x \) is the horizontal distance between the measurements. We consider data only where \( \Updelta x \) values are 7–12 cm to avoid aliasing. Figure 13 shows the absolute value of steepness averaged over the same 12 m segments where RMS height is calculated (Fig. 12a). It is clear that higher steepness values correlate well with higher RMS heights over the rough reef areas and that low steepness does it with low RMS heights over bare reef regions. If we follow the argument used for rippled beds, where the hydrodynamic roughness is proportional to the steepness times the roughness element height (Grant and Madsen 1982), predicted roughness values are 2 cm for rough reef, 0.5 cm for bare reef, and 0.4 cm for rippled sand. It is not clear; however, whether the ripple roughness model should apply for a highly irregular reef surface where bed height varies across a range of horizontal scales, and subsequently, bedform slopes will be highly variable. Further study of hydrodynamics over these surfaces is needed in order to address this issue.
Fig. 13

Absolute value of bedform steepness \( \left( {\Updelta z/\Updelta x} \right) \) averaged over the same 12 m segments where RMS height is calculated

Hearn (2008, 2010) emphasizes the importance of the surface area and height of roughness elements in controlling friction within a reef and describes other possible approaches for identifying characteristic lengths including relating rugosity measurements to fractal dimensional scales. Reef rugosity is measured using a chain of length, L fit to the surface of the reef between two points separated by a distance, x. The rugosity is then the dimensionless ratio of the two lengths, L/x. Expanding this concept to three-dimensional surfaces Purkis and Kohler (2008), used LIDAR data from the Puerto Rico shelf to show that rugosity can be expressed in terms of fractal dimension. From multibeam data from Navassa Island near Haiti Zawada et al. (2010), used fractal roughness as a proxy for topographic complexity, showing that no natural separation exists between small- and large-scale variability in topography over the entire reef. There are no current methods that are able to relate these measurements to hydrodynamic roughness, however.

Given the variability observed in roughness scales (and bottom types), it should be noted that it remains unclear how far upstream or downstream they affect the combined wave-current structure. Since it is likely that isolated bottom features would have a different effect than larger coral patches on the circulation in the near-shore, statistical techniques like clustering analysis (Hoppner et al. 1999) that reflect geometrical shapes, densities of individual clusters and the spatial relations, and distances among them, are good candidates for extending our initial analysis. The technique of separating bottom classes using a fixed principal component value can be considered as a hard clustering technique, in that it separates bottom areas discretely into a particular bottom class (cluster). In coral reef environments, where sand, coral, and pavement are often found intermingled, fuzzy clustering techniques that allow elements to belong to different clusters simultaneously, with different degrees of membership, might be more appropriate for seabed classification.

Notes

Acknowledgments

The authors thank Judith Wells, Jonathan Fram, and Kumar Rajagopalan for their helpful suggestions during our weekly meetings. We are indebted to Roy Wilkens and Roger Davis for providing the sidescan preprocessing software and for their assistance in its use. We are also thankful to Jennifer Patterson, Chris Colgrove, Kimball Millikan, and Brian McLaughlin for their support during field operations and to Alyssa Glass for her help with the visual verification of sidescan data. This work was carried out with funding from the Office of Naval Research Coastal Geosciences Program (Grants N00014-07-1-1182 and N00014-10-1-0414).

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Ocean and Resources Engineering, School of Ocean and Earth Science and TechnologyUniversity of Hawaii at ManoaHonoluluUSA

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