Numerical & Computational Oceanography

Regional Ocean Modeling System

Terrain-following sigma-coordinate model widely used for regional and coastal simulations. Supports baroclinic dynamics, nested domains, tidal forcing, and biogeochemical coupling. Applied for Gulf of Mexico circulation, tidal mixing, and sediment transport studies.

Finite Volume Community Ocean Model

Unstructured triangular-grid finite-volume model ideal for estuaries, tidal inlets, and complex coastal geometry. Handles wetting/drying of intertidal flats and incorporates atmosphere-wave-ocean coupling for realistic coastal simulations.

Advanced Circulation Model

High-resolution unstructured-grid model for storm surge, tidal circulation, and coastal flooding. The gold standard for hurricane impact assessment along the Gulf and Atlantic coasts, supporting FEMA flood maps and emergency preparedness planning.

Semi-implicit Cross-scale Hydroscience Integrated System

Next-generation hybrid V-grid model (unstructured horizontal + terrain-following/z-level vertical) supporting fully baroclinic dynamics, atmosphere-ocean-wave-sediment coupling, and seamless cross-scale simulations from rivers to ocean basins.

Global & Basin-Scale Ocean Models

Isopycnal-coordinate models used for global ocean reanalysis and forecasting. HYCOM (Hybrid Coordinate Ocean Model) and MOM6 provide open-boundary conditions for regional models and long-term climate simulations with high fidelity in deep-ocean layer representation.

Spectral Wave Models

Third-generation spectral wave models simulating wind-wave generation, propagation, and dissipation. WAVEWATCH III for oceanic scales; SWAN for nearshore wave transformation, shoaling, refraction, and diffraction in coastal zones.

Watershed & Riverine Models

Hydrological and hydraulic models for watershed runoff, riverine floodplain inundation, and land-ocean connectivity. Coupled with ADCIRC for compound flooding scenarios integrating riverine discharge, tidal forcing, and storm surge contributions.

Momentum Equations (Horizontal)

The horizontal momentum equations governing large-scale ocean circulation, incorporating the Coriolis force, pressure gradient force, and turbulent friction terms.

where \( f = 2\Omega\sin\phi \) is the Coriolis parameter, \( \rho_0 \) is a reference density, and \( \mathcal{F} \) represents turbulent friction/mixing terms.

Hydrostatic Equation

Fundamental vertical force balance in the ocean under the hydrostatic approximation, valid for large horizontal-to-vertical scale ratios typical in ocean basins and continental shelves.

This approximation eliminates solving the vertical momentum equation, dramatically reducing computation cost in large-scale ocean models.

Continuity Equation (Mass Conservation)

Mass conservation for an incompressible Boussinesq fluid, ensuring the divergence of the velocity field is zero throughout the ocean volume.

In Boussinesq models, density variations are only retained in the buoyancy term; the full mass conservation uses incompressibility.

Temperature & Salinity Conservation

Advection-diffusion equations for potential temperature and salinity, the two fundamental tracers determining seawater density and driving thermohaline circulation.

\( \kappa_T \) and \( \kappa_S \) are turbulent diffusivities; \( Q_T \) and \( Q_S \) represent surface heat flux and freshwater forcing respectively.

Seawater Equation of State (TEOS-10)

The nonlinear thermodynamic relationship between seawater density, temperature, salinity, and pressure — the closure equation for all ocean models.

\( \alpha \) = thermal expansion coefficient, \( \beta \) = haline contraction coefficient. The Gibbs SeaWater (gsw) Python library implements full TEOS-10.

Advection-Diffusion Equation

General transport equation for any scalar tracer (dissolved oxygen, nutrients, sediment, dye) capturing both advective transport by currents and turbulent mixing.

\( K \) is the turbulent eddy diffusivity; \( S_C \) is a source/sink term. This equation governs water quality and biogeochemical modeling in coastal systems.

Laplace & Poisson Equations

Used for the pressure solver in incompressible flow, stream-function computation, and as the classic teaching example in finite-difference methods for numerical oceanography.

Solved numerically via Gauss-Seidel iteration or direct matrix methods. The 2-D heat equation solver is a foundational code exercise in computational ocean science.

Navier-Stokes Equations (Full)

The complete momentum balance for a viscous fluid. Ocean models derive from the Reynolds-averaged Navier-Stokes (RANS) equations with turbulence closure schemes (k-ε, Mellor-Yamada, KPP).

In ocean modeling, the Coriolis force \( -2\boldsymbol{\Omega}\times\mathbf{u} \) is added to the right-hand side to account for Earth's rotation.

Mississippi Sound Hydrodynamics & Water Quality

Coupled hydrodynamic–water quality modeling of the Mississippi Sound using FVCOM and CE-QUAL-ICM. Investigating freshwater discharge influence on harmful algal bloom dynamics, seasonal hypoxia, and salinity stratification variability. NSF-funded doctoral research at Mississippi State University.

Floodplain Connectivity — Lower Mississippi Alluvial Valley

HEC-RAS and SWAT-coupled floodplain inundation modeling to quantify hydrological connectivity in the Lower Mississippi Alluvial Valley. Assessed habitat restoration scenarios for bottomland hardwood ecosystems and migration corridors for fish and waterfowl.

ROMS Simulation: Mesoscale Eddies & Loop Current

Regional ROMS simulation of Gulf of Mexico seasonal circulation, focusing on Loop Current dynamics, mesoscale eddy formation, and sea surface temperature anomalies. Validated against satellite altimetry (CMEMS) and HYCOM reanalysis products.

Sea Surface Temperature Trend Analysis

Long-term SST trend analysis for the Bay of Bengal using AVHRR, MODIS, and in-situ CTD observations. Identified warming signatures (>10°C seasonal anomalies) linked to altered monsoon-driven circulation and implications for tropical cyclone intensification.

Python Computational Oceanography Tutorials

Open-source educational materials for computational oceanography: 2-D Laplace heat equation solver (Gauss-Seidel), advection schemes stability analysis, tidal harmonic analysis with t_tide, HYCOM API data access workflows, and xarray-based ocean climatology processing. Published on GitHub and Medium.

Coupled Hydrodynamic–Water Quality Modeling of Mississippi Sound

Manuscript describing FVCOM-based simulation of coastal circulation and dissolved oxygen dynamics in the Mississippi Sound under varying freshwater discharge and wind forcing regimes. Target journal: Estuarine, Coastal and Shelf Science.

Hydrological Connectivity in the Lower Mississippi Alluvial Valley

Floodplain inundation frequency and habitat connectivity analysis using HEC-RAS coupled with multi-temporal remote sensing, informing conservation planning for migratory fish corridors and waterbird breeding habitat in the LMAV.