Analysis of Sample Frames and Subsampling Methods for Reef Fish Surveys

Introduction: The National Oceanic and Atmospheric Administration’s Biogeography Branch has conducted surveys of reef fish in the Caribbean since 1999. Surveys were initially undertaken to identify essential fish habitat, but later were used to characterize and monitor reef fish populations and benthic communities over time. The Branch’s goals are to develop knowledge and products on the distribution and ecology of living marine resources and provide resource managers, scientists and the public with an improved ecosystem basis for making decisions. The Biogeography Branch monitors reef fishes and benthic communities in three study areas: (1) St. John, USVI, (2) Buck Island, St. Croix, USVI, and (3) La Parguera, Puerto Rico. In addition, the Branch has characterized the reef fish and benthic communities in the Flower Garden Banks National Marine Sanctuary, Gray’s Reef National Marine Sanctuary and around the island of Vieques, Puerto Rico. Reef fish data are collected using a stratified random sampling design and stringent measurement protocols. Over time, the sampling design has changed in order to meet different management objectives (i.e. identification of essential fish habitat vs. monitoring), but the designs have always remained: • Probabilistic – to allow inferences to a larger targeted population, • Objective – to satisfy management objectives, and • Stratified – to reduce sampling costs and obtain population estimates for strata. There are two aspects of the sampling design which are now under consideration and are the focus of this report: first, the application of a sample frame, identified as a set of points or grid elements from which a sample is selected; and second, the application of subsampling in a two-stage sampling design. To evaluate these considerations, the pros and cons of implementing a sampling frame and subsampling are discussed. Particular attention is paid to the impacts of each design on accuracy (bias), feasibility and sampling cost (precision). Further, this report presents an analysis of data to determine the optimal number of subsamples to collect if subsampling were used. (PDF contains 19 pages)

On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.