Required observable	Representation	Invalid when
Static surface and bathymetry; only bottom visibility, refraction, attenuation, or caustics matter	Static bathymetry plus optical transport	Surface motion, waterline motion, or interaction is required
Prescribed coast-following crests; no flow or interaction claim	Coast SDF plus prescribed shoreline phase	Diffraction, run-up, bulk flow, or changing wet/dry topology matters
Few coherent waves; no local disturbance	Parametric displaced surface	Broad stochastic bands or dense interaction dominate
Bounded weak waves and local impulses	Linear heightfield	Breaking, bulk flow, or wet/dry topology matters
Fixed bathymetry; phase-averaged shoaling/refraction	Wave action or rays	Diffraction, interference, or instantaneous crest parity matters
Fixed bathymetry; linear diffraction/interference	Frequency-domain mild slope	Breaking, run-up, moving bed, or live broad spectra matter
Long waves over permanently wet variable depth	Linear elevation/discharge shallow water	Wet/dry fronts, bores, or finite-amplitude flow matter
Run-up, bores, depth-averaged wakes, or changing wet topology	Positivity-preserving nonlinear shallow water	Dispersive or three-dimensional breaking is required
Overturning, entrained air, jets, or three-dimensional vortices	External free-surface/particle/VOF solver	A single-valued or depth-averaged model is sufficient
Body motion affects water and water reaction affects the body	Selected water solver plus the two-way coupling branch	One-way visual following or a prescribed wake is sufficient

Route broad homogeneous wind sea or swell to $threejs-spectral-ocean. Normal- only detail is a display optimization, not another physical owner.

Record domain size, smallest resolved wavelength, interaction radius, bathymetric variation, phase/error tolerance, conservation needs, wet/dry topology, and sustained budget. Hybridize only across an explicit spatial or frequency handoff.

Complete when: every required observable has exactly one valid owner and every rejected representation has a stated validity or measured cost reason.

2. Freeze coordinates, state, and ownership

Use metres and seconds in a stable physics frame:

z_b(x,z) = upward-positive bed elevation
eta(x,z,t) = free-surface elevation
h = max(eta-z_b,0)

phi > 0 on land
phi = 0 at the authored still-water coast
phi < 0 in water.

Declare the water datum, gravity, bed and coast-distance sources, valid mask, cell footprint, reconstruction/filter, boundary labels, obstacle representation, current, and clock. Horizontal coast distance is not vertical water depth.

Assign exactly one owner to water state, geometry, offshore forcing, foam, exposed-bed wetness, caustics, opaque refraction inputs, and final output. Every boundary is periodic, reflecting/wall, absorbing/radiation, prescribed inflow, or outflow with a named mathematical treatment.

For each water boundary, declare producer, consumer, and state owner; units and stable physics frame/origin; sample instant or application interval, clock, cadence, and sample phase; support/filter; validity, staleness, and error; and state/resource versions. Distinguish rates from interval-integrated mass, momentum, or energy. Name forcing, reaction, geometry, and presentation ownership and their order. A clock discontinuity, rebase, representation or owner change, or incompatible version resets every dependent solver, foam, wetness, query, and temporal state. Invoke $threejs-choose-skills when a multi-system route still needs ownership selection.

Complete when: bed, coast, datum, state, boundary, clock, and output ownership agree at every sample; the SDF zero contour and z_b=eta_0 contour meet their declared gate.

3. Implement the selected branch

Read only the linked heading span: start at the heading and stop before the next heading at the same or higher level.

Selected representation	Required reference spans
Static surface and bathymetry	Domain data and invariants, then the required optical spans below
Parametric displaced surface	Exact parametric waves and Physics-horizontal queries
Bounded linear heightfield	Bounded linear heightfield
Prescribed coast-following phase	Domain data and invariants and Prescribed shoreline phase
Wave action or rays	Domain data and invariants and Depth-aware wave action and rays
Frequency-domain mild slope	Domain data and invariants and Mild-slope branch
Fixed-wet linear shallow water	Domain data and invariants and Fixed-wet linear shallow water
Nonlinear wet/dry shallow water	Domain data and invariants and Nonlinear shallow water with wet/dry fronts
External solver	Use the External solver adapter contract below; load only shared spans needed by its published channels

Load these additional spans only when the named concern is selected:

offshore coupling: Offshore/nearshore handoff;
breaking, foam, or exposed-bed wetness: Breaking, foam, and wetness;
sparse execution: Sparse active tiles;
live-grid CPU queries: Live GPU-grid query contract;
receiver caustics: Receiver-space caustics;
refraction or interface reflection: Refraction and Fresnel;
absorption or scattering: Beer-Lambert transport;
coastal optical/lifecycle integration: Optics and presentation;
GPU implementation: WebGPU implementation.

After a surface/optics branch, apply the matching bullets in surface acceptance. After a coastal branch, apply the matching bullets in coastal acceptance.

Parametric surface

Evaluate one displacement map, both analytic tangents, the horizontal Jacobian, and the upward cross-product normal. Physics-horizontal queries invert the horizontal map.

Branch complete when: parameter and physics-horizontal samples have unambiguous semantics; analytic tangents/normals match finite differences; the minimum Jacobian is positive or every fold is classified invalid; and query residuals meet their gate.

Bounded linear heightfield

Use ping-ponged height/vertical-velocity state, fixed dt, dimensioned sources, an explicit boundary condition, and this dispatch order:

event gather -> propagate -> swap -> derivatives -> optical auxiliaries.

Before accepting this branch, import the bounded-heightfield dispersion comparator and call boundedHeightfieldDispersion() with the selected c, dt, dx, dz, kx, and kz. It predicts the undamped (gamma=0) discrete phase; compare that prediction with the measured analytic-mode phase. Measure amplitude error independently for the actual damping and source configuration. The helper rejects nonfinite arithmetic, excludes marginal CFL equality, and separates global stability from represented-mode admission; DC phase fields are explicitly unavailable, not fake numeric measurements.

Branch complete when: the CFL margin is positive; analytic-mode phase and amplitude errors, boundary reflection, mean drift, precision error, and finite-value scan pass; overlapping events have no write race; and every consumer reads derivatives from the new state.

Prescribed coast-following phase

Derive crest phase from coast distance or a converged eikonal travel-time field. The phase branch owns crest placement and a prescribed wash mask only; it makes no flow, momentum, or wave-energy claim.

Branch complete when: crest direction, spacing, and speed; coastwise continuity; eikonal residual and unreachable classification; medial-axis coast ownership; and fragment-footprint filtering all pass their gates, with the no-flow/no-energy claim explicit.

Wave action or rays

Transport dimensioned action/energy by frequency and direction. Keep current, intrinsic frequency, group velocity, quadrature, dissipation, and a separately owned display phase explicit. Rays make no diffraction/interference claim.

Branch complete when: dispersion/group velocity, phase-loop or curl, action/energy balance, shoaling/refraction, regularization, and handoff reflection pass over the represented band.

Mild slope

Solve complex phase/amplitude for fixed, slowly varying bathymetry with radiation/open boundaries. Prefer an offline solution when sources and bathymetry are stationary.

Branch complete when: manufactured or independent-reference convergence, phase/amplitude interpolation, boundary reflection, and stored-field invalidation pass.

Fixed-wet linear shallow water

Evolve surface perturbation and depth-integrated discharge with compatible discrete divergence/gradient or one finite-volume flux.

Branch complete when: permanently wet state is enforced; mass and declared energy behavior close; dispersion and boundary reflection pass; and no wet/dry, bore, or finite-amplitude claim is made.

Nonlinear wet/dry shallow water

Evolve conservative depth and momentum with one canonical face flux, well-balanced bathymetry, positivity-preserving update, dry-cell division policy, fixed stable step, and conservative source accounting.

Branch complete when: depth stays nonnegative without unreported clamping; lake at rest remains stationary; mass closes against boundary/source fluxes; dry cells stay finite; shoreline/run-up and grid/timestep/dry-threshold convergence pass; and boundary reflection is within gate.

External solver

Consume its versioned surface, velocity, wet/dry, material, and presentation state through an explicit adapter. Keep external process/queue/fence latency and unavailable channels visible.

Branch complete when: units, frame, clock, interpolation, error, lifecycle, failure/recovery, and presentation ownership are proven; the render frame does not synchronously read back or advance the external solve.

Two-way body coupling

When body motion must affect water and water must react on the body, use one declared coupling interval:

predict body state
-> sample the same previous/current water bracket at body support points
-> scatter displacement or impulse to water conservatively
-> advance water once
-> reduce reaction force, torque, and interface work over the same support
-> correct body state
-> commit both versions together.

Use one physics frame, units, sample identity, and support/Jacobian convention. Keep collision and render LOD out of the coupling support. Classify the method as explicit loose coupling or bounded residual iteration; strong added-mass or stiff feedback requires the iterative branch or an external coupled solver.

Branch complete when: equal-and-opposite impulse, force, torque, displaced volume, and interface-work residuals meet their gates; stationary buoyancy, translation/rotation, grid/timestep, and iteration controls converge; and no render-frame readback advances or corrects either state.

4. Derive shared surface state once

Geometry, tangents, normal, velocity, shadows, foam source, refraction, and temporal consumers derive from the selected state version. A handoff has one geometry owner at every location. Coherent surfaces use matched amplitude and differentiate the blend, including weight gradients; power windows apply only to independent or orthogonal bands.

Build one foam source from the strongest represented cause: modeled breaking loss, calibrated shock/entropy loss, exact compression/Jacobian, or prescribed crest arrival. Store either transported coverage or conserved areal density and use its matching equation. One dissipation partition drives one history.

Exactly one exposed-bed receiver owns wetness. Inundation or a declared prescribed wash mask sets it wet; drying is timestep-correct. Wetness changes receiver material response, not water mass or shoreline geometry.

For sparse coastal execution, activate from causal influence and interaction support rather than visibility alone. Fill halos and boundaries before whole-tile stencils; preserve one face flux across neighbors; account for activation/deactivation state and error.

Complete when: one state version explains every geometric and optical consumer, foam and wetness each have one owner and reset rule, sparse inactive regions have an explicit model, and no displayed seam has two surfaces.

5. Evaluate optical transport

The opaque color/depth input excludes water. Reconstruct and validate the refracted ray before using its length. Classify the incident side, use exact dielectric Fresnel near total internal reflection, and apply Beer-Lambert extinction in metres:

sigma_t = sigma_a + sigma_s
T = exp(-sigma_t pathLengthMeters)

L_water = F L_reflection
        + (1-F) etaRadiance [T L_background + (1-T) omega_0 L_source].

Use the reference's explicit physical-versus-reduced radiance convention for etaRadiance; Fresnel power transmission is not automatically a cross-index radiance conversion. For positive extinction divide scattering by the actual extinction, with a separate zero branch, and evaluate short optical depths stably. Caustics replace the corresponding direct-light transport instead of adding it again. Foam replaces a bounded fraction of this response. A specular BRDF owns sun glint unless another explicitly budgeted lobe replaces it.

Caustics deposit surface-cell power in receiver space using the determinant of the receiver map. Track invalid/TIR samples, power before and after deposition, regularization, filtering, and clamp.

Complete when: Fresnel/TIR classification, refracted-ray residual, path-length validity, absorption/scattering partition, caustic receiver placement, energy ledger, and final/no-optics/no-caustics/no-foam views pass.

6. Integrate GPU state and lifecycle

Run await renderer.init() and require renderer.backend.isWebGPUBackend === true before allocating or submitting compute/storage work. Simulation textures use NoColorSpace, explicit precision, no generated mips, and integer loads for stencils. Each whole-grid producer/consumer dependency crosses a dispatch boundary. renderer.computeAsync(...) is initialization-safe; its resolved promise is not GPU-completion evidence. Keep simulation resolution independent of viewport resolution.

Use an opaque pass excluding water, then explicitly budget the water/composite work that consumes it. Do not sample an attachment while writing it or label multiple traversals as one pass. Use one RenderPipeline and output transform. If renderOutput(...) owns conversion, set pipeline.outputColorTransform = false. After replacing pipeline.outputNode, set pipeline.needsUpdate = true. Presentation consumes immutable previous/current state with stable identity. Resize, representation, cadence, active-domain, datum, origin, source, and solver-version changes migrate compatible state or reset every dependent history. Dispose resources and listeners with their owner.

Complete when: the initialized native-WebGPU backend/capabilities, dispatch and allocation inventory, peak live bytes, precision comparison, warm sustained timings, and rebuild/dispose plateau are recorded; no frame-critical readback or double output transform remains.

7. Final falsification

Inspect the applicable diagnostics, not only the final image:

bathymetry, coast distance/frame, wet mask, boundaries, state, derivatives;
phase/action/discharge, energy or mass residuals, reflection, wet/dry state;
foam source/transport/reaction and wetness history;
refraction validity, Fresnel/TIR, extinction terms, caustic deposition;
final and disabled-effect captures at fixed cameras and multiple times.

Complete when: every selected branch criterion passes, every omitted phenomenon is outside the claim, every handoff has one producer and consumer, every resource has an owner and reset/dispose rule, and one causal water state reaches one final output transform.

threejs-water-optics

Water Optics

1. Gate the water model