Investigations Into the Application of Single-Beam Acoustic Backscatter for Describing Shallow Water Marine Habitats

Chapter 1 Producing thematic coral reef benthic habitat maps from single-beam acoustic backscatter has been hindered by uncertainties in interpreting the acoustic energy parameters E1 (~roughness) and E2 (~hardness), typically limiting such maps to sediment classification schemes. In this study acoustic interpretation was guided by high-resolution LIDAR (Light Detection And Ranging) bathymetry. Each acoustic record, acquired from a BioSonics DT-X echosounder and multiplexed 38 and 418 kHz transducers, was paired with a spatially-coincident value of a LIDAR-derived proxy for topographic complexity (Reef-Volume) and its membership to one of eight LIDAR-delineated benthic habitat classes. The discriminatory capabilities of the 38 and 418 kHz signals were generally similar. Individually, the E1 and E2 parameters of both frequencies differentiated between levels of LIDAR Reef-Volume and most benthic habitat classes, but could not unambiguously delineate benthic habitats. Plotted in E1:E2 Cartesian space, both frequencies formed two main groupings: uncolonized sand habitats and colonized reefal habitats. E1 and E2 were significantly correlated at both frequencies; positively over the sand habitats and negatively over the reefal habitats, where the scattering influence of epibenthic biota strengthened the E1:E2 interdependence. However, sufficient independence existed between E1 and E2 to clearly delineate habitats using the multi-echo E1/E2 Bottom Ratio method. The point-by-point calibration provided by the LIDAR data was essential for resolving the uncertainties surrounding the factors informing the acoustic parameters in a large, survey-scale dataset. The findings of this study indicate that properly interpreted single-beam acoustic data can be used to thematically categorize coral reef benthic habitats. Chapter 2 A large-scale acoustic survey was conducted in Apr-May 2008, with the objective of quantifying the abundance and distribution of seasonal drift macroalgae (DMA) in the Indian River Lagoon. Indian River was surveyed from the Sebastian Inlet to its northernmost extent in the Titusville area. Banana River was surveyed from its convergence with the Indian River northward to the Federal Manatee Zone near Cape Canaveral. The survey vessel was navigated along pre-planned lines running east-west and spaced 200 m apart. The river edges were surveyed to a minimum depth of approximately 1.3 m. Hydroacoustic data were collected with a BioSonics DT-X echosounder and two multi-plexed digital transducers operating at 38 and 418 kHz. The 38 and 418 kHz hydroacoustic data were processed with BioSonics Visual Bottom Typer (VBT) seabed classification software to obtain values of E1’ (time integral of the squared amplitude of the 1st part of the 1st echo waveform), E1 (2nd part of 1st echo), E2 (complete 2nd echo), and FD (fractal dimension characterizing the shape of the 1st echo). Following quality analysis, a training dataset was compiled from 131 hydroacoustic + video samples collected across the extent of the study area. The 38 and 418 kHz E1’, E1, E2, and FD datasets were merged and submitted to a series of three discriminant analyses (DA) to refine the training samples into three pure end-member categories; bare substrate, short SAV (typically Caluerpa prolifera, ~10cm or less), and DMA. The Fisher’s linear discriminant functions from the third and final descriptive DA were used to classify each of the 480,000+ hydroacoustic survey records as either bare, short SAV, or DMA. The classified survey records were then used to calculate the biomass of DMA as the product of average DMA cover for a block of ten records times the wet weight of DMA. The DMA biomass was found to be 69,859 metric tons (wet weight) within the 293.1 km2 study area. The acoustically-predicted mean percent cover of DMA was (i) significantly greater within the navigation channels (18.3%) than outside (12.2%), and (ii) significantly greater in the Indian River (12.9%) than in the Banana River (9.3%). The overall predictive accuracy of total SAV (i.e. short SAV plus DMA) was 78.9% (n=246) at three levels of cover (0-33, 33-66, and 66-100%). The Tau coefficient, a measure of the improvement of the classification scheme over random assignment, was 0.683 ± 0.076 (95% CI), i.e. the rate of misclassifications was 68.3% less than would be expected from random assignment of hydroacoustic records to total SAV cover. The incorporation of multi-plexed digital transducers in conjunction with new post-processing techniques realized the goal of establishing an accurate, efficient, and temporally consistent method for acoustically mapping DMA biomass. Chapter 3 This chapter presents the results of a large-scale hydroacoustic survey conducted in April-May 2008. The objective of this study was to map the distribution and vertical extent of muck in the Indian River Lagoon, utilizing the data collected during a seasonal drift macroalgae survey. Indian River was surveyed from the Sebastian Inlet to its northernmost extent in the Titusville area. Banana River was surveyed from its convergence with the Indian River northward to the Federal Manatee Zone near Cape Canaveral. The survey vessel was navigated along pre-planned lines running east-west and spaced 200 m apart, except for when muck was indicated by the oscilloscope display, at which point a meandering path was adopted to demarcate the horizontal extent of muck. Hydroacoustic data were collected with a BioSonics DT-X echosounder and two multi-plexed digital transducers operating at 38 and 420 kHz. The vertical extent of muck was derived from the 38 kHz hydroacoustic signal, which was processed with Visual Analyzer, a fish-finding software package produced by BioSonics Inc. The software was adapted to integrate echo energy below the water-sediment interface, and a set of post-processing algorithms were developed to translate the sub-bottom echo energy profile into continuous scale estimates of muck thickness. In this manner 500,000+ 38 kHz pings were translated into 88,927 geo-located estimates of muck layer thickness, down to a minimum bottom depth of 1 m. Ground-truthing was conducted in July 2008 at twenty sites within the Indian River. The predictions of muck layer thickness were found to be accurate over the ground-truthed range of 0-3m (r2 = 0.882, SE=0.52m). The vertical distribution of acoustically-predicted muck demonstrated the tendency for muck to accumulate in deeper areas of the lagoon. For the case of Indian River (excluding navigation channels), muck was not detected in depths shallower than 1.4m and rare in the range of 1.4-2.2 m (only 3.6% of records had a predicted muck thickness greater than 0.5 m). The frequency of muck plateaued between 2.2-3.4 m (9.6%) before making a sharp rise to 82% in the range of 4-5 m. As expected, the mean muck layer thickness was significantly greater within the navigation channels (0.56 m) than outside of them (0.08 m). A significant latitudinal trend of muck thickness was detected within the Indian River navigation channels. The mean muck thickness decreased from 1.38 m at its northernmost origins to 0.83 m in the Titusville area before plateauing at approximately 0.4 m for the remainder of segments. Outside of the main ICW channels, 23 individual muck deposits were identified; 22 in the Indian River and 1 in the Banana River. Factors in descending order of co-occurrence were proximity to causeways or jetties, riverbed depressions, and proximity to shore and drainage channels. In conclusion, this study establishes that a single-beam acoustic survey is a cost-effective and accurate alternative for mapping the distribution and vertical extent of muck deposits in the shallow-water environment of the Indian River Lagoon. Moreover, the temporal consistency afforded by a digital transducer allows for direct and meaningful comparisons between successive surveys. Chapter 4 A thematic map of benthic habitat was produced for a coral reef in the Republic of Palau, utilizing hydroacoustic data acquired with a BioSonics DT-X echosounder and a single-beam 418 kHz digital transducer. This paper describes and assesses a supervised classification scheme that used a series of three discriminant analyses (DA) to refine training samples into end-member structural and biological elements, utilizing E1′ (leading edge of 1st echo), E1 (trailing edge of 1st echo), E2 (complete 2nd echo), fractal dimension (1st echo shape), and depth as predictor variables. Hydroacoustic training samples were assigned to one of six predefined groups based on the plurality of benthic elements (sand, sparse SAV, rubble, pavement, rugose hardbottom, branching coral), visually estimated from spatially co-located ground-truthing videos. Records that classified incorrectly or failed to exceed a minimum probability of group membership were removed from the training dataset until only ‘pure’ end-member records remained. This refinement of ‘mixed’ training samples circumvented the dilemma typically imposed by the benthic heterogeneity of coral reefs, i.e. to either train the acoustic ground discrimination system (AGDS) on homogeneous benthos and leave the heterogeneous benthos un-classified, or attempt to capture the many ‘mixed’ classes and overwhelm the discriminatory capability of the AGDS. This was made possible by a conjunction of narrow beamwidth (6.4o) and shallow depth (1.2 to 17.5 m), which produced a sonar footprint small enough to resolve most of the microscale features used to define benthic groups. Survey data classified from the 3rd-Pass training DA were found to (i) conform to visually-apparent contours of satellite imagery, (ii) agree with the structural and biological delineations of a benthic habitat map created from visual interpretation of 2004 IKONOS imagery, and (iii) yield values of benthic cover that agreed closely with independent, contemporaneous video transects. The methodology was proven on a coral reef environment for which high quality satellite imagery existed, as an example of the potential for single-beam systems to thematically map coral reefs in deep or turbid settings where optical methods are unsatisfactory. Chapter 5 Beginning In the winter of 2003-2004, several episodes of red drift macroalgae blooms resulted in massive amounts of macroalgae washing ashore the beaches of Sanibel Island, Bonita Springs, and Ft Meyer Florida. A study conducted after the first event supported a link to increasing land-based nutrient enrichment. A large-scale program was initiated in May 2008, with the primary goal of further defining the possible roles and sources of nutrient enrichment with respect to nuisance macroalgae blooms. This study reports the results of the hydroacoustic mapping component of this program. The goal of this study was to identify areas of substrate suitable for supporting a macroalgae bloom. Areas within San Carlos Bay and offshore Sanibel Island, FL were hydroacoustically surveyed from nearshore to about 11 km offshore during the periods of October 6-10, 2008 and May 10-22, 2009. The hydroacoustic data was acquired with a BioSonics DT-X echosounder and a multiplexed single-beam digital transducers operating at 38 and 418 kHz. Eleven acoustic parameters derived from the 38 and 418 kHz signals were utilized to classify the survey data into 5 ascending categories of visually-apparent seabed roughness. Classes 1 and 2 were both primarily constituted of unconsolidated silt and sand-sized sediments, unsuitable for a bloom. Class 3 is a marginal substrate for a bloom, consisting of packed sand and large intact shell debris. Classes 4 and 5 offer the best attachment sites for a bloom, consisting of consolidated shell hash, live hardbottom, and submerged aquatic vegetation. The majority (~ 80%) of acoustic classifications were of soft bottom sediments (classes 1-2), but there were two significant expanses of rough seabed suitable for macroalgae attachment. These two areas covered a total of 19 km2, within which ~ 56% of the hydroacoustic records classified as “rough” (classes 3-5). The first was a large area of seagrass beds and live hardbottom in the mouth of San Carlos Bay, where large amounts of macroalgae were variably present during the April-May 2009 surveys. The second was offshore Lighthouse Point, near the mouth of San Carlos Bay, situated near a large sand spit that extended from the beach to approximately 6 km offshore. Along the west side of the sand spit there were substantial areas of moderate to high bottom roughness, mostly in the form of consolidated shell hash. The average depths of these two acoustically-rough areas were only 5.0 and 4.0 m, so sufficient irradiance to initiate a bloom could be assumed. These textured and shallow areas on or near the mouth of San Carlos Bay are presumably potential sources for macroalgae attachment and growth, which could easily be transported onto the beaches under some storm conditions given the close proximity to the shoreline. In contrast, the areas in open Gulf of Mexico waters were classified predominantly as soft sediments with low bottom roughness. The site offshore Redfish Pass had a moderate (~22%) proportion of “rough” classifications out to 5km offshore, but from 5-10km offshore the bottom classified as \u3e95% soft sediments. The other two Gulf of Mexico sites classified as \u3e95% soft sediments from nearshore to 11 km offshore. Independent, concurrent video transects indicated there were small areas with large amounts of shell and live hard bottom that occurred sporadically greater than 10km offshore, but all things considered the open Gulf waters around Sanibel Island may not be a major source of drift macroalgae. Chapter 6 This study presents the results of methods developed for acoustic remote sensing of Acropora cervicornis, a threatened species of scleractinian sporadically occurring on the nearshore hardbottom of Southeast Florida. The objective was to develop techniques for mapping isolated Acropora patches on a scale larger than what is feasible using on-the-ground methods. A time-series of A. cervicornis cover could inform resource managers about the fate of such patches, e.g. do they appear and vanish, creep by extension from a central point, or leap by colony fragmentation. The main challenge to acoustically mapping A. cervicornis was distinguishing it from gorgonians occupying the same habitat. Hydroacoustic surveys were conducted in October 2009 at two nearshore sites in Broward County, FL utilizing a BioSonics DT-X echosounder and multiplexed single-beam digital transducers operating at frequencies of 38 and 418 kHz. NCRI scientists have monitored the spatial extent and percent cover of A. cervicornis within these sites, providing an ideal background against which to calibrate the hydroacoustic predictions. Two approaches were evaluated. The first approach utilized BioSonics EcoSAV post-processing software, designed to predict areal cover and canopy height of submerged aquatic vegetation using a series of heuristic pattern-recognition algorithms. Anchored over A. cervicornis, the 38 and 418 kHz signals performed similarly well. Anchored over gorgonians, the 38 kHz signal detected the canopy roughly half as frequently as the 418 kHz signal. Undifferentiated 418 kHz EcoSAV cover was allocated to either A. cervicornis or gorgonians exploiting this frequency-dependent detection. The second approach utilized the acoustic energy (E0, E1′, E1, and E2) and shape (fractal dimension) parameters obtained from BioSonics Visual Bottom Typer software. A dual-frequency training dataset was used to classify records as sand, bare pavement, gorgonians, or A. cervicornis. Both approaches yielded promising results, based on a number of metrics, unambiguously demonstrating that single-beam AGDS are capable of reliably detecting A. cervicornis and gorgonians under controlled conditions

Multi-texture image segmentation

Visual perception of images is closely related to the recognition of the different texture areas within an image. Identifying the boundaries of these regions is an important step in image analysis and image understanding. This thesis presents supervised and unsupervised methods which allow an efficient segmentation of the texture regions within multi-texture images. The features used by the methods are based on a measure of the fractal dimension of surfaces in several directions, which allows the transformation of the image into a set of feature images, however no direct measurement of the fractal dimension is made. Using this set of features, supervised and unsupervised, statistical processing schemes are presented which produce low classification error rates. Natural texture images are examined with particular application to the analysis of sonar images of the seabed. A number of processes based on fractal models for texture synthesis are also presented. These are used to produce realistic images of natural textures, again with particular reference to sonar images of the seabed, and which show the importance of phase and directionality in our perception of texture. A further extension is shown to give possible uses for image coding and object identification

FEMDA: a unified framework for discriminant analysis

Although linear and quadratic discriminant analysis are widely recognized classical methods, they can encounter significant challenges when dealing with non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new approach, the model considered is an arbitrary Elliptically Symmetrical (ES) distribution per cluster with its own arbitrary scale parameter. This flexible model allows for potentially diverse and independent samples that may not follow identical distributions. By deriving a new decision rule, we demonstrate that maximum-likelihood parameter estimation and classification are simple, efficient, and robust compared to state-of-the-art methods

Statistical eigen-inference from large Wishart matrices

We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of the population covariance matrix are unknown and focus on inferential procedures that are based on the sample eigenvalues alone (i.e., "eigen-inference"). Results found in the literature establish the asymptotic normality of the fluctuation in the trace of powers of the sample covariance matrix. We develop concrete algorithms for analytically computing the limiting quantities and the covariance of the fluctuations. We exploit the asymptotic normality of the trace of powers of the sample covariance matrix to develop eigenvalue-based procedures for testing and estimation. Specifically, we formulate a simple test of hypotheses for the population eigenvalues and a technique for estimating the population eigenvalues in settings where the cumulative distribution function of the (nonrandom) population eigenvalues has a staircase structure. Monte Carlo simulations are used to demonstrate the superiority of the proposed methodologies over classical techniques and the robustness of the proposed techniques in high-dimensional, (relatively) small sample size settings. The improved performance results from the fact that the proposed inference procedures are "global" (in a sense that we describe) and exploit "global" information thereby overcoming the inherent biases that cripple classical inference procedures which are "local" and rely on "local" information.Comment: Published in at http://dx.doi.org/10.1214/07-AOS583 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models

This chapter gives a survey on the use of statistical designs for what-if analysis in simula- tion, including sensitivity analysis, optimization, and validation/verification. Sensitivity analysis is divided into two phases. The first phase is a pilot stage, which consists of screening or searching for the important factors among (say) hundreds of potentially important factors. A novel screening technique is presented, namely sequential bifurcation. The second phase uses regression analysis to approximate the input/output transformation that is implied by the simulation model; the resulting regression model is also known as a metamodel or a response surface. Regression analysis gives better results when the simu- lation experiment is well designed, using either classical statistical designs (such as frac- tional factorials) or optimal designs (such as pioneered by Fedorov, Kiefer, and Wolfo- witz). To optimize the simulated system, the analysts may apply Response Surface Metho- dology (RSM); RSM combines regression analysis, statistical designs, and steepest-ascent hill-climbing. To validate a simulation model, again regression analysis and statistical designs may be applied. Several numerical examples and case-studies illustrate how statisti- cal techniques can reduce the ad hoc character of simulation; that is, these statistical techniques can make simulation studies give more general results, in less time. Appendix 1 summarizes confidence intervals for expected values, proportions, and quantiles, in termi- nating and steady-state simulations. Appendix 2 gives details on four variance reduction techniques, namely common pseudorandom numbers, antithetic numbers, control variates or regression sampling, and importance sampling. Appendix 3 describes jackknifing, which may give robust confidence intervals.least squares;distribution-free;non-parametric;stopping rule;run-length;Von Neumann;median;seed;likelihood ratio