Study Locations
Two study locations in the USVI (Fig. 1) were selected for this research, as they had a diverse range of seafloor habitat types, bottom complexity, and bathymetric relief. The first location was relatively small (25 km2) and included the Buck Island Reef National Monument (BIRNM), north of St. Croix. The second location, situated due south of St. Thomas, was larger (120 km2) and included Flat Cay island and surrounding waters. These locations are of high interest to marine conservation managers because they include several federal and territorial marine protected areas, including Virgin Islands National Park (VINP), St. Thomas East End Reserve (STEER), and Cas Cay-Mangrove Lagoon Marine Reserve and Wildlife Sanctuary (CCMLMR). These areas provide a home to several species protected under the federal Endangered Species Act, including Hawksbill Turtles (Eretmochelys imbricata), Elkhorn Coral (Acropora palmata), and Staghorn Coral (Acropora cervicornis) (Pittman et al. 2008, NOAA OPR 2019). For these reasons, these locations have been studied intensively in the past, and as a result, they contain a variety of remotely sensed and in situ data sets that could help support the research described here. An additional benefit of the two locations is that the data for Buck Island were useful for testing (specifically, for comparisons of the output relative reflectance mosaics against in situ reflectance spectra), while Flat Cay was used to test if waveform metrics could be used to distinguish or characterize coral reef communities.
Data Collection
Bathymetric lidar data were collected by the USGS using the EAARL-B. The data were collected on 11 separate days between March 7 and March 21, 2014. The airborne data acquisition parameters are listed in Table 1. Processing of lidar point clouds and digital elevation models of the region was conducted by United States Geological Survey (USGS), as described in Fredericks et al. (2015).
Table 1 EAARL-B data collection parameters To process the lidar data, we adopted the definitions of lidar radiometric processing levels given in Kashani et al. (2015), wherein level 0 = raw intensity; level 1 = intensity correction (i.e., correction for range, angle of incidence); level 2 = intensity normalization (i.e., histogram normalization to match adjacent flight strips or data collected across different days, sites, following the level 1 processing); and level 3 = full, rigorous radiometric correction and calibration to obtain “true” surface reflectance (generally unattainable, due to lack of manufacturer-proprietary system information and full environmental characterization). With reference to these processing levels, seafloor relative reflectance, as defined in this study, is a level 2 product, whereas true reflectance corresponds to level 3.
The reference data for testing the seafloor relative reflectance mosaics consisted of underwater spectral reflectance measurements acquired from a small boat in July, 2012, at Buck Island (Fig. 2). These reference underwater spectral reflectance measurements (see Pe’eri et al. 2013, for details on data collection) were acquired for assessing the lidar-derived relative reflectance. While this fieldwork was performed specifically for this experiment, delays in fielding the EAARL-B led to the ~ 20-month gap between the field and airborne data collections. A consequence of the temporal offset between the field and airborne data collection is that some change in benthic habitat type occurred. Specifically, some of the seagrass bed boundaries were observed to have changed. These seagrass bed distribution changes were relatively easy to identify using our own aerial imagery collected with the EAARL-B lidar data, Google Earth imagery, and Esri World Imagery. Reference spectra collected in areas of seagrass bed migration were removed from the analysis, as well as a few additional spectra that were collected outside of the EAARL-B coverage extents, which were not precisely known at the time of the fieldwork. The number of remaining points (14) was fewer than desired but spanned a range of seafloor reflectance values and habitat types (including seagrass, coral, and sand) in the 1–10-m depth range (Fig. 3).
The ground truth for the reef cover characterization consisted of generating 100-m2 photo mosaics of coral reef communities around Flat Cay. Underwater video footage of 9 sites, ranging in depth from ~ 2 to ~ 17 m, was collected by swimming in a lawnmower pattern along transects placed on the seafloor between September 4 and 9, 2016. Overlapping still frames were extracted from the video and stitched together into a single composite image using texture based video mosaic (Rzhanov et al. 2006; Gu and Rzhanov 2006). To create a species map for each dive site, each mosaic was georeferenced and viewed on a high-resolution computer screen. Corals and macroalgae were identified and manually segmented down to the lowest possible taxonomic level, typically genus or species. Adobe Photoshop’s Magic Wand tool was used to isolate each coral head and patch of macroalgae and mask them with a species-specific color. These masks were used to calculate percent cover. To account for difficulties in identification to species level (especially among octocoral genera) and the effects of less-abundant species, we created five functional groups. Hard corals were divided into “domed” and “branched” groups based on colony growth form in order to represent the varied habitat types they provide and expected differences in response to lidar signals. The domed coral group includes boulder, brain, hill, pillar, and star corals, while the branched coral group includes finger, fire, and staghorn corals. The remaining three groups comprise the octocorals, sponges, and macroalgae turf (mostly genus Dictyota).
Signal Processing
The bathymetric lidar equation, which is given in various forms in the published literature (e.g., Wang and Philpot 2002; Tuell and Park 2004; Collin et al. 2008; Narayanan et al. 2009; Tuell and Carr 2013), relates the received optical power for a laser return pulse to parameters related to the lidar system, the acquisition geometry, and the environment. While various formulations differ slightly, a general form is as follows:
$$ {P}_R=\frac{P_T\eta \rho {F}_p{A}_r{\cos}^2\theta }{\pi {\left({n}_wH+D\right)}^2}{e}^{-2n\left(\mathrm{s},{\omega}_0,\theta \right) KD\sec \phi } $$
(1)
where PR is the received optical power; PT is the transmitted power; η is the system optical efficiency factor; ρ is the reflectance of bottom; Fp is the loss due to insufficient FOV; Ar is the effective area of the receiver optics; θ is the off-nadir transmit angle; nw is the refractive index of the water; H is the altitude of the lidar above the water; D is the water depth; n(s, ω0, θ) is the pulse stretching factor; s is the scattering coefficient; ω0 is the single scattering albedo; K is the diffuse attenuation coefficient of the water; and ϕ is the off-nadir angle of the lidar beam after refraction at the air-water interface. Note that the term D sec ϕ is the slant range of the laser pulse from the water surface to seafloor. For all wavelength-dependent parameters, such as ρ, K, and ω0, it is understood that the wavelength, λ, at which the parameter is evaluated is that of the lidar system, which is 532 nm for nearly all current bathymetric lidar systems (Guenther 2007).
Typically, it is not possible to directly solve Eq. 1 for ρ, the reflectivity of the seafloor at the laser wavelength (532 nm), due to unknown lidar system parameters (e.g., PT, η, FP) and environmental parameters (e.g., s, ω0, θ, K, n). It is for this reason that most studies of topo-bathymetric lidar reflectance mapping, including this one, aim to produce relative reflectance, rather than “true” or “absolute” seafloor reflectance. In this work, a data-driven approach was taken to derive corrections to lidar bottom intensity (i.e., the data itself was used to drive the determination of correction coefficients) to obtain seafloor relative reflectance. The full, end-to-end workflow for generating the relative reflectance mosaics is depicted in Fig. 4. It is important to note that this workflow was designed to be applied to very large data sets, covering up to hundreds of square kilometers of the seafloor and encompassing tens of millions of lidar points collected over a period of several days to weeks. Therefore, key considerations in developing the workflow included the following: (1) reducing human operator time, (2) reducing computer processing time, and (3) reducing seamline artifacts at the junctions of flight lines and acquisition dates.
The input to the relative reflectance mapping process depicted in Fig. 4 consisted of georeferenced EAARL-B lidar point clouds created with the USGS ALPS software. (Readers interested in the details of this step and the algorithms implemented in ALPS are referred to Nagle and Wright et al. (2016).) Importantly for this work, each bottom return lidar point in each point cloud had an intensity value, I, which was taken to be the peak amplitude of the detected bottom return and, in turn, proportional to the received optical power. The first step in our procedure was to perform pre-processing or cleaning of the lidar data set, which entailed removing areas of land, as well as obvious noise points. The next step was to apply intensity corrections, corresponding to level 1 processing, as defined in Kashani et al. (2015). Corrections were applied for the following: (1) depth (or, perhaps more precisely stated, for the range-dependent attenuation of radiant flux in the water column) and (2) angle of incidence.
The depth correction was obtained by first considering a simplified form of the bathymetric lidar equation (Eq. 1), adapted from Guenther (1985):
$$ {P}_R={P}_T W\rho {e}^{-2 KD\sec \phi } $$
(2)
The form of the lidar equation given in Eq. 2 is based on the simplifying assumptions that (a) the above-water flying height is relatively large compared to the depth, (b) pulse stretching can be neglected, and (c) other unknown parameters in Eq. 1 can be assumed constant and combined into a constant system-loss term, W. From Eq. 2 (and with the further assumptions that the transmit power and system losses are constant throughout the data collection), it can be seen that the natural log of the bottom reflectance is linearly related to depth (or to slant range through the water column), with linear parameters that are functions of the diffuse attenuation coefficient and seabed reflectance. As the goal of the depth correction was to remove the depth dependence to obtain better estimates of ρ, we performed a linear regression of uncorrected intensities on depth for areas of constant bottom type and water clarity. The linear transformation parameters were then used in the correction to remove the depth dependence. Figure 5 shows a heatmap created using points from entire day of data collection with the resulting linear best-fit line. The color scale can be interpreted as “hotter” regions being those of high point concentration. This type of heatmap was found very beneficial in this study for visualizing trends in large volumes of data.
Using the parameters of the linear fit depicted in Fig. 5, the depth correction is given by the following:
$$ {I}^{\prime }=\frac{\ln (I)}{aD\sec \phi +b} $$
(3)
where I′ is the corrected intensity, I is the input (uncorrected) intensity, a and b are the coefficients of the linear fit described above, D is water depth, and ϕ is the off-nadir angle of the laser beam in the water. As before, the product D sec ϕ is the slant range of the laser pulse from the water surface to seafloor.
The next step in the process was the incidence angle correction. This correction is extremely important, since, unlike other bathymetric lidar systems, such as the Optech CZMIL (Feygels et al. 2013) and SHOALS (Collin et al. 2008), the EAARL-B does not attempt to maintain a constant off-nadir transmit pulse angle but instead scans back and forth across the field of view, passing nearly through nadir. This created a pronounced reduction in intensity towards the outer edges of the swath.
The incidence angle correction was computed in a data-driven approach, similar to the depth correction. The form of the incidence angle correction, based on the Phong reflectance model (Phong 1975; Jutzi and Gross 2009; Hasegawa 2006) is:
$$ {I}^{\prime \prime }=\frac{I^{\prime }}{\alpha {\cos}^{\beta}\theta } $$
(4)
In a manner similar to the depth correction, the parameters α and β (which relate to the specular or non-Lambertian nature of the seafloor) were determined empirically through a curve-fitting procedure (Fig. 6).
An underlying assumption in the correction procedures described above is that the points used to derive the correction parameters had the same “true” reflectance; hence, it was important that the subsets of points used as input were collected from a homogeneous bottom type. When and where possible, homogeneous regions were identified with the aid of imagery and/or existing habitat maps. For the EAARL-B deep receiver channel, an initial approximation of correction parameters was made using all of the points calculated for given day. Then, the resulting point cloud was used to assist in delineation of uniform bottom type, typically sand. The points of uniform bottom were then used to determine final correction parameters.
Continuing with the workflow depicted in Fig. 4, a normalization step was next performed, corresponding to level 2 processing, as defined in Kashani et al. (2015). This step consisted of first matching points from overlapping point clouds within 1 m of each other. The distributions of the corrected intensities of the matched points were analyzed, and a linear transformation (shifting and scaling of the intensities) was performed on the second point cloud, such that its mean and standard deviation were made to equal that of the first point cloud.
Next, the level 2 intensities were interpolated to a regular grid. Although any of a number of interpolation algorithms could have been used in this step, based on experimentation, we used inverse distance weighting (IDW), which was found to reduce seamline artifacts between adjacent flight lines and to generally create a more uniform representation of regions in which the angle of incidence correction has been either over- or under-applied, while also keeping processing times within practical limits.
Next, a second histogram normalization was performed, such that the level 2 intensity rasters could be combined for multiple flight lines and days, while minimizing seamlines. This was achieved using custom software developed as part of this research. This software applies semi-automated histogram scaling and shifting to adjust the contrast and brightness across adjacent rasters using a graphical user interface (GUI). Overlapping gridded data were adjusted by the user until overlapping regions visually matched. The output relative reflectance mosaic was generated in Esri ASCII raster format, with values linearly scaled to the 0–255 range (i.e., 8-bit rasters), for compatibility with other coastal GIS data layers. The resulting relative reflectance mosaics were then assessed visually and through quantitative comparison with the reference spectra acquired in the Buck Island site.
The final signal processing step was to generate additional features (metrics) that relate to the shape of the identified bottom return in the EAARL-B lidar waveform. The specific waveform features generated in this study and further described in Parrish et al. (2014) were as follows: (1) standard deviation (a measure of the width or “spread” of the bottom return pulse), (2) area under the curve (a measure of the total energy returned from the bottom), and (3) skewness (a measure of the asymmetry of the bottom return waveform). The key idea underlying the use of these features is that coral, seagrass, or other cover types are theorized to modify the shape of the bottom return waveform; hence, these features that relate to the bottom return waveform shape could be useful predictors of cover type. Further description of and justification for the use of these types of shape-based waveform features for seabed habitat analysis is provided by Collin et al. (2008). The three features are computed as described in Parrish et al. (2014):
$$ A={\sum}_{n=0}^{N-1}y\left[n\right] $$
(5)
$$ \overline{n}=\frac{\sum_{n=0}^{N-1}n\cdotp y\left[n\right]}{A} $$
(6)
$$ \sigma =\sqrt{\frac{\sum_{n=0}^{N-1}{\left(n-\overline{n}\right)}^2\cdotp y\left[n\right]}{A}} $$
(7)
$$ \gamma =\frac{\sqrt{A}\ \left({\sum}_{n=0}^{N-1}{\left(n-\overline{n}\right)}^3\cdotp y\left[n\right]\right)}{{\left({\sum}_{n=0}^{N-1}{\left(n-\overline{n}\right)}^2\cdotp y\left[n\right]\right)}^{3/2}} $$
(8)
where N is the length, in samples, of the subset of the full waveform identified as the bottom return by the ALPS software, y[n] is the digitized bottom return waveform; n = 0, 1, 2, …, N − 1 is the waveform sample number, A is the area under the curve, \( \overline{n} \) is the bottom return waveform mean, σ is the standard deviation (width metric for the bottom return), and γ is the skewness (asymmetry metric for the bottom return).
Using the underwater image mosaics generated from the in situ (diver) data, we performed linear regressions to assess the associates between the percent cover of each of these groups (along with a combined hard coral group) and the lidar waveform metrics. Three of the nine sites were below a depth of 10 meters and were excluded from this analysis, for two key reasons. First, the manner by which the waveform metrics were interpolated to into GIS-compatible formats meant that the increasing footprint size of the lidar waveform with increasing depth was not represented, so the waveform metrics include higher amounts of error at greater depths. Second, the deeper sites were dominated by soft corals and experienced greater amounts of surge—the constant motion of the soft corals within the video meant that the percent cover metrics calculated from those photo mosaics were less accurate, as the same moving soft corals may appear in multiple locations or be excluded entirely.