Physical and Oceanography Review

A glossary of the physical and oceanographic concepts used in the course, especially those that appear in Unit 1 (Moreton Bay shallow-water surge) and Units 8–10 (Great Barrier Reef thermistor-column capstone). Entries are alphabetical within each grouping.

Ocean structure and properties

Bathymetry. The shape of the ocean floor — the underwater analogue of topography. Encoded as a depth field H(x, y) in the shallow-water solver of Unit 1 and as the column depth H in the Unit 8 column model.

Deep reservoir. Idealisation of the ocean below the modelled column: a much larger volume of cold water whose temperature responds on timescales far longer than the modelled run. Used as a Dirichlet boundary T(-H, t) = T_{\text{deep}} in Unit 9.

Mixed layer. The near-surface region of the ocean kept nearly uniform in temperature, salinity, and density by wind-driven turbulent mixing and convective overturning. Depth ranges from a few metres (calm tropics) to hundreds of metres (stormy mid-latitudes). Modelled in Unit 8 §8.5 via large \kappa in the upper column.

Pycnocline. The depth at which density changes most rapidly. In tropical waters the density gradient is dominated by temperature, so the pycnocline coincides with the thermocline.

Stratification. Variation of seawater density with depth. Stable stratification (light water on top, dense water below) resists vertical mixing because buoyancy restores displaced parcels. In the GBR, surface heating produces strong stable stratification that suppresses upwelling outside of storm events.

Thermocline. The depth band over which temperature falls most steeply — typically 10–50 m in the GBR. Above: warm sun-heated water. Below: cold deep water. The transition is sharp because mixing across the thermocline is suppressed by stable stratification.

Heat and energy fluxes

Bulk formulas. Empirical relations that estimate air–sea heat / momentum / freshwater fluxes from easily measured quantities (wind speed, air temperature, humidity). The COARE 3.0 algorithm (Fairall et al. 2003) is the standard implementation. Used to set Q_{\text{np}}(t) in Unit 8 §8.4.

Degree-Heating-Weeks (DHW). NOAA Coral Reef Watch’s operational thermal-stress index: cumulative weekly sea-surface-temperature anomaly above the maximum-monthly-mean baseline. DHW > 4 °C·week signals significant bleaching risk; > 8 indicates mortality. Liu et al. 2014 is the canonical reference. A column model improves on DHW by resolving the vertical distribution of warm water.

Latent heat flux Q_{\text{lat}}. Heat carried away from the ocean by evaporation. Dominates the surface cooling budget in the tropics; proportional to wind speed and the saturation-vapour-pressure deficit.

Longwave radiation Q_{\text{LW}}. Infrared emission from the sea surface (\propto T^4 by Stefan–Boltzmann) minus downwelling longwave from the atmosphere. Net loss on most days; a strong night-time cooling term.

Sensible heat flux Q_{\text{sens}}. Heat conducted from the ocean to the (usually cooler) air. Small compared to latent heat in the tropics but signs and magnitudes flip during cold fronts.

Shortwave penetrating insolation Q_{\text{SW}}. Solar radiation that crosses the air–sea interface and is absorbed inside the water column, exponentially with depth. Modelled as a Beer–Lambert body source \mathcal{S}(z, t) in Unit 9 §9.5 rather than a boundary flux — the standard two-band Paulson–Simpson parameterisation.

Dynamics and transport

Advection. Transport of a quantity (heat, salt, tracer) by the bulk fluid motion: \mathbf{u}\!\cdot\!\nabla T. In the column model this reduces to w\, \partial_z T (Unit 8 §8.3).

Coriolis effect. Apparent deflection of fluid motion in a rotating reference frame, important at scales of \gtrsim 100 km and times of \gtrsim a few hours. Quantified by the Coriolis parameter f = 2\Omega \sin\phi, with \phi latitude. Deflects rightward in the Northern hemisphere, leftward in the Southern. Negligible on the Unit 1 surge scale (\sim 50 km, \sim 6 hours) but dominant in the full SWE system referenced in Unit 7 §7.2.

Diffusion / eddy diffusivity. Net transport of a quantity down its gradient by unresolved turbulent fluctuations. Modelled as a Fickian closure \partial_z(\kappa \,\partial_z T) with an effective eddy diffusivity \kappa \gg \kappa_{\text{molecular}}. Three standard closure choices (KPP, Mellor-Yamada, Pacanowski-Philander) are listed in Unit 8 §8.3.

Ekman pumping. Vertical velocity induced by the curl of the surface wind stress in the rotating ocean: positive (upwelling) under cyclonic stress, negative (downwelling) under anticyclonic. The mechanism by which the Unit 9 wind-stress envelope \tau(t) drives the column’s w(z, t).

Eddy. A coherent circular flow structure with horizontal scales from \sim 1 km (submesoscale) to \sim 100 km (mesoscale). Carries heat, salt, and biology far from its generation point. Eddies are unresolved by the workshop shallow-water solver, which is one reason its eddy diffusivity \kappa has to absorb their mixing.

Internal waves. Waves propagating along density interfaces (typically the thermocline). Driven by tides, winds, and topographic interactions. They contribute to vertical mixing when they break, providing one of the background-\kappa contributions in KPP-style closures.

Upwelling / downwelling. Vertical movement of water columns: upwelling brings cold, nutrient-rich deep water up (w > 0); downwelling pushes warm surface water down (w < 0). The first cooling hypothesis in the capstone scenario.

Coastal and reef-specific terms

AIMS. The Australian Institute of Marine Science — the federal research agency that monitors the Great Barrier Reef. Supplies the operational moorings the capstone is loosely modelled on (Davies Reef tower at 18°49'31''S, 147°38'50''E).

Great Barrier Reef (GBR). The world’s largest coral reef ecosystem, \sim 2300 km along the Queensland coast. The capstone is set on the central GBR off Townsville.

Moreton Bay. A shallow, semi-enclosed bay east of Brisbane in south-east Queensland, bounded by the mainland, Moreton Island, and North Stradbroke Island. Setting for the Unit 1 surge example.

Pile Light. The historic light station at the entrance of the Brisbane River into Moreton Bay; in Unit 1 it marks the river-mouth region that anchors the surge model’s boundary condition (the G1 gauge itself sits mid-bay at Mud Island).

Shallow-water equations (SWE). A depth-integrated reduction of the 3-D Navier–Stokes equations valid when horizontal length-scales greatly exceed water depth. The 2-D unknowns are surface elevation \eta and depth-averaged horizontal velocity \mathbf{u}_h. Cover the Unit 1 surge problem in linearised form; the full nonlinear system is sketched in Unit 7 §7.2 (where it serves as a worked PINN-failure example, not a fully-solved benchmark).

Storm surge. An anomalously high water level driven by strong onshore winds, low atmospheric pressure, or river discharge. The Unit 1 example is a freshwater-driven analogue — same shallow-water physics, different forcing.

Sea-Surface Temperature (SST). Temperature in the top \sim 1 m of the ocean, measured by satellite or in-situ. The quantity most operational coral-bleaching products (NOAA Coral Reef Watch) use because it’s available globally. SST misses subsurface structure — exactly what the column model resolves.

Tide gauge. A fixed instrument measuring sea-surface elevation at a single point, typically once per minute. The four Moreton Bay gauges (G1–G4) in Unit 1 are tide gauges in the modelled sense, providing the boundary-data record from which the source ψ(t) is recovered.

Tikhonov regularisation. A general inverse-problem technique: add a penalty \lambda\,\|L\theta\|^2 (typically on the smoothness or magnitude of the unknown) to the data-fitting loss to stabilise an otherwise ill-posed inversion. Used in both Unit 1 (adjoint inverse) and Unit 9 (PINN inverse). Detail in Unit 1 §1.2 and Unit 7 §7.5.

Physical constants and standard values

Symbol	Value	Meaning
g	9.81\,\text{m/s}^2	gravitational acceleration
\rho_0	1025\,\text{kg/m}^3	reference seawater density
c_p	3990\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}	specific heat of seawater
\sigma_{\text{SB}}	5.67\times 10^{-8}\,\text{W}\,\text{m}^{-2}\,\text{K}^{-4}	Stefan–Boltzmann constant
L_v	2.45\times 10^{6}\,\text{J}\,\text{kg}^{-1}	latent heat of vapourisation
\alpha_T	\sim 2\times 10^{-4}\,\text{K}^{-1}	thermal expansion coefficient
\kappa_{\text{molecular}}	1.4\times 10^{-7}\,\text{m}^2\,\text{s}^{-1}	molecular thermal diffusivity (water)
\kappa_{\text{turbulent}}	10^{-5}–10^{-3}\,\text{m}^2\,\text{s}^{-1}	typical effective eddy diffusivity