In this thesis, we conduct research toward understanding coupled physics-biology processes in ocean straits. Our focus is on new analytical studies and higher-order simulations of idealized dynamics that are relevant to generic biological processes. The details of coupled physics-biology models are reviewed and an in-depth global equilibrium and local stability analysis of a Nutrient-Phytoplankton-Zooplankton (NPZ) model is performed. This analysis includes parameter studies and methods to evaluate parameter sensitivity, especially in the case where some system parameters are unknown. As an initial step toward investigating the interaction between physics and biology in ocean straits, we develop and verify a new coupled physics-biology model for two-dimensional idealized physical processes including tides and apply it to the San Bernardino Strait in the Philippine Archipelago. This two-dimensional numerical model is created on a structured grid using operator splitting and masking. This model is able to accurately represent biology for various physical flows, including advection-dominated flows over discontinuities, by using the Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical model is verified against a Discontinuous-Galerkin (DG) numerical scheme on an unstructured grid. Several simulations of tidal flow are completed using bathymetry and flow magnitudes com- parable to those found in the San Bernardino Strait with different sets of parameters, tidal periods, and levels of diffusion. Results are discussed and compared to those of a three-dimensional modeling system. New results include: new methods for analyzing stability, the robust two-dimensional model designed to best represent advection-dominant flows with minimal numerical diffusion and computational time, and a novel technique to initialize three-dimensional biology fields using satellite data. Additionally, application of the two-dimensional model with tidal forcing to the San Bernardino Strait reveals that flow frequencies have strong influence on biology, as very fast oscillations act to stabilize biology in the water column, while slower frequencies provide sufficient transport for increased biological activity.

In this work we derive an exact, closed set of evolution equations for general continuous stochastic fields described by a Stochastic Partial Differential Equation (SPDE). By hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component, we derive a system of field equations consisting of a Partial Differential Equation (PDE) for the mean field, a family of PDEs for the orthonormal basis that describe the stochastic subspace where the stochasticity `lives’ as well as a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new evolution equations are derived directly from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of the solution. If additional restrictions are assumed on the form of the representation, we recover both the Proper Orthogonal Decomposition equations and the generalized Polynomial Chaos equations. We apply this novel methodology to two cases of two-dimensional viscous fluid flows described by the NavierStokes equations and we compare our results with Monte Carlo simulations.

Error Subspace Statistical Estimation (ESSE), an uncertainty prediction and data assimilation methodology employed for real-time ocean forecasts, is based on a characterization and prediction of the largest uncertainties. This is carried out by evolving an error subspace of variable size. We use an ensemble of stochastic model simulations, initialized based on an estimate of the dominant initial uncertainties, to predict the error subspace of the model fields. The dominant error covariance (generated via an SVD of the ensemble-generated error covariance matrix) is used for data assimilation. The resulting ocean fields are provided as the input to acoustic modeling, allowing for the prediction and study of the spatiotemporal variations in acoustic propagation and their uncertainties. The ESSE procedure is a classic case of Many Task Computing: These codes are managed based on dynamic workflows for the: (i) perturbation of the initial mean state, (ii) subsequent ensemble of stochastic PE model runs, (iii) continuous generation of the covariance matrix, (iv) successive computations of the SVD of the ensemble spread until a convergence criterion is satisfied, and (v) data assimilation. Its ensemble nature makes it a many task data intensive application and its dynamic workflow gives it heterogeneity. Subsequent acoustics propagation modeling involves a very large ensemble of short-in-duration acoustics runs.

This paper presents a rigorous, yet practical, method of multigrid data assimilation into regional structured-grid tidal models. The new inverse tidal nesting scheme, with nesting across multiple grids, is designed to provide a fit of the tidal dynamics to data in areas with highly complex bathymetry and coastline geometry. In these areas, computational constraints make it impractical to fully resolve local topographic and coastal features around all of the observation sites in a stand-alone computation. The proposed strategy consists of increasing the model resolution in multiple limited area domains around the observation locations where a representativeness error is detected in order to improve the representation of the measurements with respect to the dynamics. Multiple high-resolution nested domains are set up and data assimilation is carried out using these embedded nested computations. Every nested domain is coupled to the outer domain through the open boundary conditions (OBCs). Data inversion is carried out in a control space of the outer domain model. A level of generality is retained throughout the presentation with respect to the choice of the control space; however, a specific example of using the outer domain OBCs as the control space is provided, with other sensible choices discussed. In the forward scheme, the computations in the nested domains do not affect the solution in the outer domain. The subsequent inverse computations utilize the observation-minus-model residuals of the forward computations across these multiple nested domains in order to obtain the optimal values of parameters in the control space of the outer domain model. The inversion is carried out by propagating the uncertainty from the control space to model tidal fields at observation locations in the outer and in the nested domains using efficient low-rank error covariance representations. Subsequently, an analysis increment in the control space of the outer domain model is computed and the multigrid system is steered optimally towards observations while preserving a perfect dynamical balance. The method is illustrated using a real-world application in the context of the Philippines Strait Dynamics experiment.

We present the spatial and temporal variability of the acoustic field in Dabob Bay during the PLUSNet07 Exercise. The study uses a 4-D data-assimilative numerical ocean model to provide input to an acoustic propagation model. The ocean physics models (primitive-equations and tidal models), with CTD data assimilation, provided ocean predictions in the region. The output ocean forecasts had a 300m and 1-5m resolution in the horizontal and vertical directions, at 3-hour time intervals within a 15-day period. This environmental data, as the input to acoustic modeling, allowed for the prediction and study of the temporal variations of the acoustic field, as well as the varying spatial structures of the field. Using a one-way coupled-normal-mode code, along- and across-sections in the Dabob Bay acoustic field structures at 100, 400, and 900 Hz were forecasted and described twice-daily, for various source depths. Interesting propagation effects, such as acoustic fluctuations with respect to the source depth and frequency as a result of the regional ocean variability, wind forcing, and tidal effects are discussed. The novelty of this work lies in the possibility of accurate acoustic TL prediction in the littoral region by physically coupling the real-time ocean prediction system to real-time acoustic modeling.