Photorealistic water rendering: lakes and oceans

Question: Day Hike is a first-person co-op hiking game in Babylon.js 9.18, set on a coast and forest like Washington's Olympic Peninsula. Its water is a flat plane with one scrolling normal map, and it does not look real. We want photorealistic water of two kinds, rendered in real time in a browser: a still forest lake, murky with algae at its margin and insects over it, and an ocean coast with waves that are large and concave where real ones would be, small where real ones would be, and white where they break. How does real water of both kinds behave, what do shipped games do about it, and what can a browser afford on WebGPU and on WebGL2? The water system is meant to be reused, in later maps and in other games, so the survey covers water at arm's length as well as from a kilometre away.

Short answer: most of what makes water read as real is cheap, and most of it is about light, not waves. Water is a window at your feet and a mirror 20 m away, and the water itself is dark, so across a lake or a sea what is seen is the sky and the far shore upside down. A sheltered lake mirrors its trees; a rough sea never mirrors its coast, and shows sky from 20 to 30° up. A brown forest lake lets red through least badly (measured attenuation about 1.1, 1.5 and 3.5 per metre for red, green and blue at a Secchi depth of 1.8 m), so its bed is an amber rim a few metres wide round a black mirror. On the Olympic Peninsula only the lowland lakes with marsh at an end are murky, at 1.5 to 3.8 m of Secchi depth; the high lakes are clear to the bed at 5 to 11 m, so one lake material has to span both, with its attenuation as the setting. "Algae around the sides" is floating mats of filamentous algae in the shallows. Insect swarms hold station over a marker, do not flock, and vanish above 3 m/s of wind; a swarm is nearly silent, and the whine is one mosquito at the ear.

At the coast, the sea is never small (a median of 2 m at 11 s offshore, 3 m in January), waves arrive in sets, turn to the beach, and grow before they break in water about 1.3 times their height. Whether a wave spills or plunges is set by the beach's slope. The game's sea bed, at 1:67, spills in every sea. The concave wave belongs on a steep face, and this coast has them: the pebble beaches between its headlands stand at 1:9 to 1:17. Foam in the surf decays over about 20 s, longer than the gap between waves, so the inner surf stays white through a set.

Games solved the open sea years ago with an FFT of a wave spectrum, at 0.1 to 2 ms on desktop GPUs. At the shore, shipped engines shrink waves where nature grows them. The concave breaker has shipped in four places as one technique: a small baked texture of the wave's cross-section over time, swept along the shore. Nobody publishes its cost, which is the cost of a mesh fine enough to draw the lip, and nobody has drawn one in a browser. In a browser the FFT costs about 0.7 ms a cascade as WebGL2 fragment passes on an Apple M5, and under 1 ms for three small cascades in WebGPU compute; with the simulation in compute, drawing the water costs more than simulating it. For a still lake the mirror is the picture, every published reflection method is weakest there, and no one has published what a mirrored render costs in a browser.

The game is public at game-dayhike and playable at games.csarko.sh/dayhike. Its renderer's two paths are described in WebGPU and WebGL2: what changes and what does not, and its material plugins in Babylon.js material plugins: hooks and traps. Numbers given without a source are our own arithmetic from the sources beside them: Fresnel's equations, the wave dispersion relation, and the published buoy, lidar and survey data.

Day Hike's world is a procedural coast and forest modelled on Washington's Olympic Peninsula: the Pacific west of the start, sand bays between headlands, sea stacks, a highway along the shore, and a trail that climbs a peak. The player is on foot at eye height; there are no boats and no swimming, so water is always looked at from land, from a few metres to a few kilometres away.

Three properties of the renderer bound every option in section 9. No material can read the scene's depth or its colour: the game has no depth pass, no pre-pass and no mirror or refraction target. Every custom shader is a GLSL plugin on a PBR material, translated to WGSL ahead of time for WebGPU, so each new material variant is a shader to record and ship. And the frame is limited by the GPU: about 20 ms on an Apple M4 at 1080p on the high tier, which leaves water perhaps 1 to 2 ms there and well under 1 ms on the low tier.

Three properties of the world matter as much as the renderer:

• No player can reach the sea. An invisible wall runs along the highway, which lies between the forest and the beach. The nearest a player gets to the waterline is about 62 m on a headland and up to 141 m in a bay. The surf is seen from the road, from the trail and from the summit, never from the wet sand. That is a fact of this map and not of the water system: later maps, and other games built on it, will put a player at the waterline, so nothing below is ruled out because of the distance.
• There is no lake. The largest inland water is the pond above. A lake 50 to 300 m across is a new stage in the terrain function, which changes the world every player must agree on; and on a hillside of gradient 0.25, a level rim 300 m across stands about 38 m proud of the slope on one side, so it has to sit in flatter ground or a cut.
• The sea bed is nearly flat. It falls 1.5 m in 100 m (1:67) for the first 530 m, so the sea is under 1 m deep for its first 65 m. Section 3.3 shows what kind of wave that makes.

2.1 Fresnel reflection: clear at your feet, a mirror at a distance

A flat water surface reflects about 2 % of the light that meets it head on, and the fraction rises with the angle from the vertical, slowly at first and steeply near grazing [1]. From the Fresnel equations with a refractive index of 1.333, for an eye 1.7 m above flat water:

The whole change from window to mirror happens between 2 and 20 m from a standing walker. The common shortcut, Schlick's approximation, reads 22 % low at 53° and 14 % high at 80° for water, so it makes the middle distance slightly more mirror-like than it is; the exact curve fits in a one-dimensional lookup.

Water itself is dark. Section 2.3 puts the light that comes back out of a forest lake at under 1 % of what went in, and out of green coastal water at 1 to 4 %. So the reflection wins long before it reaches 50 %: across a lake or a sea, what is seen is mostly the sky and the far shore, upside down. Looking down beside your feet, it is the bed and the water's own colour.

2.2 Wind sets the roughness

Cox and Munk measured the slopes of the sea surface from photographs of sun glitter. For a clean surface the mean square slope grows linearly with the wind speed U in m/s: 0.003 + 0.00512 U in total, a little more along the wind than across it [2]. That is a root-mean-square slope of about 5° at 1 m/s, 10° at 5 m/s and 13° at 10 m/s. An oil slick cuts the mean square slope by a factor of two to three, to 0.008 + 0.00156 U [3]. The slopes that make glitter belong mostly to capillary waves, not to the larger gravity waves [4]: they are millimetres to centimetres long, the slowest of them 1.7 cm long and moving at 0.23 m/s [5]. Beyond a few metres they are smaller than a pixel, so a renderer has to carry them as a roughness, not as geometry.

The Beaufort scale gives the same ladder in words: a mirror under 0.3 m/s, "ripples with appearance of scales" to 1.5 m/s, glassy wavelets that do not break to 3.3 m/s, and the first scattered white horses from 3.4 m/s [6]. In a laboratory the first wavelets grew once the friction velocity passed about 2 cm/s, and the wind at which they become visible depends on the water's temperature [7].

Three consequences for the picture follow from the geometry of a tilted facet, and the classic observers of light on water report all three.

• Reflections stretch vertically, never sideways. Every point of light becomes "an oblong spot with its long axis in the vertical plane containing the eye and light-source" [8]. The ratio of its width to its length is the sine of the angle at which the eye looks along the water [9]: about 1 to 12 for water 20 m away and 1 to 59 at 100 m. A lamp on the far shore, or a low moon, is a long streak pointing at the viewer, and the sun's glitter is a narrow column when the sun is low and a broad patch at the feet when it is high. On flat water the glitter vanishes into a single image of the sun [4].
• A rough sea is darker than the sky above the horizon. "Our gaze falls on the slopes of the distant wavelets", so the far sea shows "the colour of the sky at a height of 20° to 30°" and not the pale sky at the horizon [8]. Summing Fresnel reflection over Cox and Munk's slopes gives the same answer in numbers: water 100 m away reflects 90 % when flat but about 42 % in a 5 m/s wind. A glassy sea is paler and merges with the sky.
• A rough sea does not mirror the coast. "The first 25° or 35° of the sky above the horizon are, in reality, hardly visible in the reflection", which "explains why one never sees trees, dunes, etc., on the coast reflected in the sea; they are not high enough" [8]. A sheltered lake is the opposite case. There "the regular reflection" plays "a much more prominent part than in the case of the sea", and the image is the landscape itself seen "from a point as far below the surface of the water as our eye is above it", so the undersides of branches show in it [8].

Shelter decides which of the two a lake is. Behind a line of trees the wind's grip on the water recovers only after 40 to 60 tree heights, and an aerial photograph of a forest lake shows the water flat for about three tree heights from the upwind shore [10]. With 30 to 50 m conifers, a lake a few hundred metres across is sheltered over its whole surface. In light air it is a patchwork: glassy where the trees shelter it or a film of pollen or organic matter damps the ripples, ruffled and darker where a gust touches down. A natural slick in Cox and Munk's own data had about a fifth of the roughness of clean water in the same wind [3]. Above about 3 m/s on open water, foam and debris gather into lines along the wind, 1 to 300 m apart [11].

2.3 Water colour and murk: absorption by depth

Pure water absorbs red light 50 to 100 times more strongly than blue: 0.0092 per metre at 450 nm against 0.34 per metre at 650 nm [12]. That is why clear water is blue. Everything else in natural water shifts the balance. Plankton absorbs blue and red and leaves green. Dissolved organic matter from soils and rotting plants absorbs blue most and falls away toward the red, so water rich in it is yellow, brown or the colour of tea [13]. Sediment scatters at every wavelength and makes water pale and opaque.

How fast light dies with depth is the diffuse attenuation coefficient, Kd, in units of per metre. Measured in lakes with a spectrometer, and estimated for the coast from the measured chlorophyll:

The lake values are read from the published curves and are good to about 15 %. The coast's row is a floor: it counts plankton alone, and the water beside the beach also carries sediment and river colour (section 4.3).

In brown water the order of the channels turns over. Red goes least fast, so the water transmits red-brown, and "the very rapid attenuation of irradiance with depth" between 400 and 500 nm leaves little blue below 1.5 to 2 m [14].

Seen from above, a bed at depth H shows through with its brightness pulled toward the deep water's own by exp(−2 Kd H), the light having gone down and come back [17]. In the humic lake above that leaves a pale bed 30 cm down at half its red, two fifths of its green and an eighth of its blue, which is amber; at 1 m it has a tenth of its red, a twentieth of its green and no blue. The bed is a warm rim a few metres wide, and beyond it the lake is a dark mirror. Over the same pale sand in the sea, the filter is green.

The water body itself returns very little. Its reflectance just under the surface is a fraction of the ratio of backscattering to absorption, the fraction rising from about 0.35 with the sun overhead to about 0.5 with a low sun, and about 0.54 of that gets out through the surface [14]. For brown lake water that comes to well under 1 % of the light that went in.

2.4 The shore's edge: wet sand, foam and caustics

Wet sand. Beach sand measured as it dried reflects, when saturated, about 0.40 of what it does dry, "with little apparent color change". The change comes in two steps: the first few percent of moisture take off 15 %, sand between 5 and 25 % moisture hardly differs, and the last step to saturation does the rest, so that "only a distinction between a dry and a wet surface is practical" [18]. Three states are enough: dry, damp at about 0.7, soaked at 0.4. The gloss comes on top. Water lying on sand is a true mirror, unlike the sea beside it: "a streak of wet sand, in which reflections of certain parts of the sky are smooth and perfect" [8]. From 10 to 30 m away a walker sees it at 80 to 87° from the vertical, where it reflects 35 to 70 % of the sky.

Foam. Foam is white because light scatters among its bubbles with almost no absorption. Fresh, thick whitecaps reflect about 40 % in the visible, up to about 55 % at the moment of breaking; thin or aged foam about 18 %; and the figure falls to 3 to 10 % within about 10 s [19]. Averaged over its life a whitecap reflects about 22 % [20]. Bubbles below the surface do not look white. They brighten the water's own colour, which near this coast is green [19]: the pale green glow behind a breaking wave.

Caustics. The bright moving net on a shallow bed is sunlight focused by the crests of ripples [21]. A crest focuses at about four times its radius of curvature, so centimetre ripples draw the net on a bed 10 to 50 cm down and metre waves on a bed of several metres. From land it shows only in clear shallows over a pale bed, in sun, within a few metres of the walker. In brown water it is gone with the bed.

2.5 Night and the headlamp

A full moon gives 0.05 to 0.3 lux against the sun's 32,000 to 100,000 [22]. At night the water body returns nothing, and a lake shows only as the sky's reflection and the shore's silhouette in it.

A lamp worn on the head is a special case, because the light source sits at the eye. A facet returns the lamp to the eye only if it faces the eye, which at a distance d needs a tilt of atan(d / 1.7): 30° at 1 m, 60° at 3 m. Ripples tilt 4 to 10°. So the lamp's sparkle is confined to a patch almost under the walker, and farther out the water throws the beam away and looks black. What does come back from out there is whatever stands steep: rain rings, foam, wet stones, floating leaves. Near the feet, 98 % of the beam enters the water. In clear shallows it lights the bed; in brown water it lights an amber haze that ends within a metre, and the haze glows back at the eye because the lamp is beside it.

3.1 The waves that arrive

The nearest long record is the buoy off Cape Elizabeth, 131 m of water, west of the Olympic coast [23]. From its hourly records for 2015 to 2024:

Two things stand out. The sea here is never small: a calm summer day still carries a metre of swell. And the peak period is far longer than the mean period, which means two seas at once: long swell from distant storms, with a shorter wind sea riding on it.

Wave heights in a random sea follow a Rayleigh distribution, so about one wave in seven is higher than the significant height and the largest of a hundred is about 1.5 times it [24]. They also arrive in groups. Surfers' "sets" are real: successive wave heights are correlated, more so the narrower the swell's spectrum, and rip currents pulse with them for 30 s to a minute at a time [25].

3.2 Coming in: waves slow, shorten, grow and turn

In deep water a wave's length is 1.56 T² metres for a period of T seconds and its speed is 1.56 T m/s. Once the water is shallower than half a wavelength the wave feels the bed: it slows, shortens and, after a slight dip, grows, keeping its period [26]. From the dispersion relation:

Close to shore every long wave travels at nearly the same speed, the square root of g times the depth, whatever its period; crests bunch up; and long swell grows much more than short waves before it breaks. The shape changes too: crests sharpen and troughs flatten.

Where a crest meets the depth contours at an angle, the end in shallower water moves slower and the crest turns toward the shore (Snell's law applied to wave speed) [26]. A 12 s swell that leaves deep water at 45° to the contours is within 10° of parallel to them at 2 m depth; a 6 s wind wave is still at 19°. So swell lines arrive nearly parallel to the beach, and short chop arrives visibly askew.

Where the bed is not uniform, the same bending sorts the waves along the shore. Wave energy "is focused on the headlands" and "dispersed in the bays" [27]. How much depends on how spread the sea is: over a shoal in the laboratory a single-direction swell grew to nearly 2.5 times its height, and a sea with a realistic spread of directions to 1.1 to 1.4 times [28].

Behind a headland or a stack, waves leak sideways into the shadow. On the line straight behind the tip a single wave train keeps half its height, and a spread sea about 70 % [27]. Deeper in, what survives depends on wavelength. From the classical solution for a wall's end, 200 m behind the tip and 100 m into the shadow, a 4 s chop of 25 m wavelength keeps 14 % of its height and a 14 s swell of 150 m wavelength keeps 30 %. So the lee of a headland has lost its chop and still heaves with a low, clean swell. A stack narrower than a wavelength barely shadows the swell at all: "wave energy spreads behind the entire pile" [27].

Local wind adds chop wherever it blows, and fetch limits it. By the engineering manual's growth law an 8 m/s wind raises waves 3 cm high and 0.2 m long over 50 m of water, 12 cm and 1.4 m over a kilometre [29]. Without wind, ripples die by viscosity: a 1 cm ripple in about a second, a 10 cm one in a minute and a half.

3.3 Breaking waves: spilling or plunging, and where

A wave breaks when its height reaches a fraction of the depth under it. The classical value is 0.78, and it rises with the beach's slope toward twice that [30]. So waves break in water about 1.3 times as deep as they are high: a 2 m swell in 2.5 m of water.

What kind of breaker it makes is set by the beach's slope against the wave's steepness, the Iribarren number: the slope divided by the square root of the offshore height over the deep-water wavelength.

For this coast's seas, on the slopes of section 4:

The flat sand spills in every sea, and so does the game's sea bed. The steep faces plunge. A steep face only sees unbroken waves when the tide is high enough to cover the flat in front of it, and a big sea breaks far out whatever lies inshore, so the real coast shows both at once: lines of spilling white water out over the sand, and a concave wave dumping on the pebbles at high tide. Wind shifts the balance: "onshore winds cause waves to break in deeper depths and spill, whereas offshore winds cause waves to break in shallower depths and plunge" [30].

The plunging wave, measured [32], [33], [34]:

• The lip leaves the crest at 1.3 to 1.5 times the wave's speed, more in shallow water, and falls nearly as a thrown object does.
• The tube under it, when the lip touches down, is 1.7 to 3.2 times as long as it is wide, 2.55 on average, and stretches to as much as 5 within half a second. Its shape varies as much from wave to wave as from beach to beach: steeper beds make rounder tubes, but slope explains only about a fifth of the variation.
• Between the plunge and the splash ahead of it there is a gap that lasts 1 to 4 s, and then a dense mat of foam behind a rolling bore.

Along a crest, breaking starts at one point and runs sideways. Surfers measure the angle: at about 50° the break runs along the crest at a pace a surfer can follow, and at 0° the whole crest falls at once [35].

3.4 The surf zone and the swash

Once broken, waves are held to a fraction of the depth: their root-mean-square height is 0.42 of it [30]. So bores shrink steadily toward the shore, and near the beach they all move at about the square root of g times the depth, 3 m/s in a metre of water. Where a bar lies offshore, "the wave may cease breaking, re-form, and break again on the shore" [30], which is what makes separate lines of white water with darker water between. South-west Washington's beaches have two or three bars, their crests 200 to 1,000 m out and mostly less than 5 m down [36]; the one profile measured off the Olympic coast's sand shows one.

At the beach a bore collapses into "a thin wedge of water whose tip propagates up the beach face" [37]. The uprush is faster and shorter than the backwash [38]. On pebbles, much of the uprush sinks in, so the backwash is weak. On a flat sand beach in a large swell the waterline does not follow each wave: on the Oregon coast almost all of the run-up's movement was at periods of minutes, about 230 s at its peak [39]. The beach floods and drains slowly while small bores ride over it.

Rip currents are where the white water has a gap. They run at 0.3 to 0.6 m/s, up to 2.4 m/s, are 5 to 90 m wide, and show as "darker, narrow gaps" with foam streaming seaward [25]. In a bay between headlands they leave along the rocks.

Against rock the rules change. A steep wave that meets a wall without trapping air throws a jet up at "eight to ten times" the wave's speed, and "sea sprays rising several tens of meters" are seen at cliffs in storms [40]. Over the surf itself hangs a haze of salt. At one Californian pier the plume stood 20 to 30 m deep and carried downwind for kilometres [41].

3.5 Sea foam: how long it lasts

Two things follow. Foam outlives the wave that made it, so within a set the surf zone does not clear between waves; it clears in the lull between sets. And the inner surf is a nearly continuous cover that each bore renews, not separate patches on clear water.

3.6 The sound of surf

Surf is loud and low. Measured on the Baltic, its level rose from 60 dB(A) under waves 0.4 m high to 78 dB(A) under waves of 2 m, and "the energy of the spectra is shifted toward lower frequencies when waves change from spilling to plunging" [49]. The hiss is bubbles: one of radius 1 mm rings at about 3.3 kHz, and the pitch falls as the size grows.

A plunging wave has a sound of its own. Recorded from a cliff, every band rose by 5 to 12 dB as a wave broke, most of all at 50 Hz, and plunging waves had "a distinctive 'whoomphing' or bellowing sound that is absent when waves are merely spilling", with peaks at 34, 48 and 78 Hz from the air trapped in the tube [50].

On a pebble beach the backwash rattles. The pitch is set by the size of the stones: under water, about 4 kHz for 2 cm stones and 1 kHz for 7.5 cm [51].

Surf carries inland as a rumble that rises and falls with the sets. A long beach is a line of sound, which fades more slowly with distance than a single source does, and air and forest take the high frequencies first.

4.1 Two kinds of beach, each with two slopes

The National Park Service mapped 174 beaches on the Olympic coast. Sand beaches are the commonest and cover more ground than every other kind together; cobble beaches cover 0.03 % of the strip [52]. The sand is fine, 0.20 to 0.25 mm on six of seven beaches sampled, and the service classes those beaches as intermediate, neither flat and dissipative nor steep and reflective [53]. The long flat beaches of south-west Washington, which are often pictured as "the Washington coast", are a different coast.

The slopes from lidar and from the beach surveys are our own reductions of the published data. One published table of slopes for these beaches was set aside, because the profiles it rests on fall 9 to 12 m where the largest tide is about 4 m.

The mean tide range at La Push is 1.96 m and the range between the daily extremes is 2.60 m [58]. On the flat sand that moves the waterline 200 to 300 m twice a day; on a pebble face, about 30 m. The beaches also move with the seasons. At Kalaloch the shoreline shifted about 50 m over a year; at Rialto about 10 m, and its face kept its slope [55].

4.2 Stacks, fog and cold water

The Coast Pilot lists the heights of the stacks and islands. Most are 20 to 70 m; the tallest, Jagged Island, is 98 m. The large ones are flat-topped with vertical sides and carry grass or trees; many bare ones are white with guano; pinnacles run to about 48 m tall and 18 m thick [59]. The park counts 228 stacks in its strip, most of them rooted in rock platforms that dry at low tide [52].

Summer is the fog season. At sea, fog cuts visibility below 0.9 km on 3 to 10 days a month [59]; at Quillayute airport, 5 km inland, heavy fog is recorded on about 42 days a year, most of them from August to October [60].

The water is cold all year. At La Push it is 11.4 °C in summer, about 3 °C colder than at the buoy offshore, because summer winds draw deep water up along the shore; the warmest month at the beach is September [58].

4.3 How clear the sea is: nobody has measured it at the shore

We found no record of Secchi depth, or of any light measurement in the water, for the surf or the first few kilometres of this coast. The marine sanctuary's own review lists turbidity among the gaps in its data [61]. What exists is farther out. On the shelf in June 2003, 7 to 40 km offshore, the median chlorophyll at the surface was 7.5 µg/L and a tenth of the stations passed 16.5 µg/L [62]. From space, the diffuse attenuation at 490 nm within 10 km of shore runs at 0.5 to 1.2 per metre in summer and 0.24 to 0.31 per metre on the clear days of winter [63]; near shore a satellite's figure is a guide, not a measurement.

Both say the same thing. In summer the sea off this coast is green and dim, with perhaps 1 to 4 m of visibility into it, not blue and not clear.

5.1 Which lake is murky, measured

The Olympic Peninsula has three kinds of lake, and only one is murky.

So a murky lake is a lowland one, with wetland at its margin and conifers to the bank, and a lake high on a mountain is clear to its bed. A world with both needs both pictures. Sections 5.2 to 5.4 are about the first, and section 5.5 about the second.

Crocker Lake, in the third class, was surveyed in detail in 1998 [68]. It covers 31 ha and is 4.0 m deep at most. Its water was "very muddy brown" and its Secchi depth about 1.5 m. Ten metres from the shore it is 0.9 m deep. Within that strip the bed is mostly silt, with sand, a little gravel and sunken wood. Plants grow no deeper than 2 m. The survey found waterweed "very dense in shallows", yellow pond-lily "in large patches" and already dying back in early September, cat-tail, bulrush and pondweeds.

With a Secchi depth of 1.5 to 1.8 m, section 2.3's humic lake is the match: the bed shows through the first few decimetres of water, is dim at 1 m and gone by about 1.5 m. On Crocker's slope that is a band 5 to 15 m wide along the shore.

5.2 What "algae around the sides" is

A lake's margin is zoned by depth. Plants that stand out of the water grow where it is less than about 1.2 to 1.5 m deep; floating-leaved plants grow in "protected areas where there is little wave action"; submerged plants reach as far out as the light does, and where the water is unclear all summer they "will be restricted to shallow areas near shore" [69]. In a brown lake the whole planted band is a few metres to a few tens of metres wide.

Four different things get called algae, and they look nothing alike:

The first is what a walker means by algae around the sides: bright to yellow-green woolly rafts in the warm shallows, caught among stems and against logs. The mats rise "when bubbles, generated by its own photosynthesis or respiration, or created by decay of its tissues, get trapped in the mats and make them buoyant" [73], so they are studded with bubbles, and an old yellowing mat floats as well as a fresh one. Beside it, in its seasons, lie the rest of the surface's litter: pollen as "yellow-green dust on the lake in early summer", foam on "windward shores, coves and in eddies", and the cast skins of hatching insects as a dark cloud with an oily sheen [71]. All of it is matt. None of it reflects like water, which is why it reads so strongly on a dark mirror.

5.3 Insects: who, where, when, and how they move

Two results decide how a swarm should be built. A swarm is not a flock: its members do not line up with each other, so the flocking rules games use for birds would make it look wrong. Each insect is pulled toward the swarm's centre and jitters. And a swarm belongs to a place: "moving the landmark leads to an overall displacement of the swarm" [77].

Swarms are a calm-evening sight. Midge flight fell off above about 2.5 m/s of wind and stopped above 3 m/s [80]. In Washington and Oregon the mosquito months are July to September [81].

5.4 Sound: the whine is one insect at the ear

A female mosquito's wings beat at about 475 Hz [82]; males beat higher, and raise their pitch further when they swarm. Midges are lower: in one species about 240 Hz for females and 434 Hz for males [83]. But a swarm is nearly silent. About 70 swarming males measured 20 dB at 0.9 m from the swarm's centre [84], which is a whisper at arm's length. The sound everyone knows is a single insect within a few tens of centimetres of one ear: it swells, shifts from ear to ear and fades, with almost no change of pitch, because at half a metre a second the Doppler shift is a fraction of a percent.

So the sound of insects at a lake is a quiet bed and, over it, single passes close to the head. Around it sits the rest of the pond: on the Olympic Peninsula, the Pacific chorus frog, whose calls carry energy from about 1.0 to 4.5 kHz and run from an hour before sunset past midnight, February to May [85].

5.5 The clear lake, high on the mountain

Eight subalpine lakes in Olympic National Park, 1,224 to 1,589 m up, were measured in September 2010 [64]. In seven the Secchi disc was still visible on the bed, at depths of 4.6 to 10.9 m. Their dissolved organic carbon was 0.12 to 0.65 mg/L and their chlorophyll at most 0.32 µg/L: no stain and almost no algae. The eighth, fed by a snowfield, had a Secchi depth of 1.4 m with as little carbon and chlorophyll as the rest.

What changes in the picture follows from section 2.

• The bed is the subject near the bank. With the attenuation of section 2.3's very clear lake (about 0.2, 0.12 and 0.2 per metre), a bed 2 m down keeps a little under half its red and blue and three fifths of its green, and at 5 m a seventh of its red and blue and three tenths of its green. The shallows are the colour of their stones, the deeper water green to blue-green, and the shape of the basin can be read from the bank.
• Refraction and caustics show. The bed appears raised, at three quarters of its depth when seen from straight above and less when seen at a slant, and it swims with the ripples. In sun the net of caustics lies on it. Neither shows in brown water.
• The mirror is the same. Fresnel reflection does not depend on what is under the surface, so from 10 m out the lake still shows the sky and the far slope. Where it mirrors something dark, the bed shows through instead.
• The margin is bare. Without nutrients there are no algal mats or scum, and the cover is what falls in: needles, pollen in early summer, sunken wood.

6.1 Offshore is solved: FFT ocean waves

The open sea converged years ago on one recipe. A statistical wave spectrum fills a grid of frequencies; an inverse FFT turns it into a tileable patch of heights and horizontal displacements, which sharpen the crests [86]. One patch either repeats visibly or lacks detail, so several patches of different sizes are summed: four cascades from about 5 m to 1 km in War Thunder [87], one to three bands of 64 to 256 texels a side in Unity's HDRP [88], eight cascades of 512 texels in Crest [89]. The mesh is a set of camera-centred rings or a quadtree, with a flat skirt to the horizon.

6.2 Near shore, engines do the opposite of nature

Real waves grow as the water shallows (section 3.2). Shipped engines shrink them. Crest multiplies each wave by the depth over half its wavelength, fading it to nothing at the waterline, and its source says so plainly: "i model 'Deep' water, but then simply ramp down waves in non-deep water with a linear multiplier" [91]. Unreal's water has a "wave attenuation water depth" that does the same [92]. It ships because offshore waves must not run through a beach, and this is the cheapest way to stop them. Crest's manual is frank about the rest: "Modelling realistic shoreline waves efficiently is a challenging open problem" [93].

What engines add on top, from least to most physical:

• Wave trains that follow the shore. War Thunder bakes depth, distance to shore and the direction to shore into one texture of 4k by 4k texels for a map 65 km across, then runs waves whose phase is the distance to shore, scaled by depth, with the tops pushed forward to steepen the face, a sawtooth driving the foam, and the wet sand shaded as the water rolls back [87]. Unity's "shore wave" decal has the same parts, with a breaking range and a share of skipped waves to make sets [94]. Crests drawn this way follow the coastline's outline, not the paths real waves take: round a stack they radiate outward instead of wrapping.
• Shelter computed from the terrain. War Thunder also bakes an "openness" value for each texel by looking upwind for land, and scales both the ocean's and the shore's waves by it, so the lee of an island is calmer without anyone painting it [87]. It is the only shipped method we found that works shelter out from the terrain.
• A shallow-water simulation near the shore. Crest 5 blends a height-and-velocity grid in by depth: below a minimum depth the shape comes from the simulation alone [95]. Such a simulation does shoal, steepen, turn to the bed and run up the beach. It has no dispersion, and as a height field it cannot curl. It is also cheap where it has been measured: Tencent's water system reports 0.13 ms for a grid of 512 cells a side with its foam on an RTX 3080, and 0.5 ms on a PlayStation 5 with four steps a frame, at one cell a metre [96]. The same talk lists shoreline waves by simulation as future work. What a grid cannot do is reach: at cells of 0.25 to 1 m, 512 cells cover 130 to 500 m of shore.

6.3 The plunging breaker is one technique, and it is baked

Horizon Forbidden West draws a true plunging breaker along a long coastline, and it is not simulated. The observation it rests on is that the curling part of a wave "looks a lot like it's a constant shape translating along the wavefront", so one animated cross-section serves every wave [97]. A simulated breaker "needed so much cleanup" that the studio used a hand-animated curve instead, stored as one texture: across the wave in one axis, time in the other, with the inside of the tube kept "because you can look into the tube". Artists draw where the wavefronts are and where each reaches its breaking moment; a compute shader bends the water's vertices to the cross-section at each wavefront. One artist laid out every wave in the game. The limits are named in the talk: "the triangle density wasn't high enough", and foam kept per vertex pops on the wave's face. No cost is given.

Three more parties have published the same construction:

Unity's sample shows two limits of the approach. The texture is sampled by arc length along the curled surface, so the stretched lip keeps its share of samples; but the engine's normal is built from a height gradient and clamped to point upward, so the underside of the lip is lit as if it faced the sky [88]. Hellblade II shows a use worth noting: the same wave data that moves the mesh tells the sound whether the wave is "coming in or going out" at the spot where the player stands, and changes the ground's material underfoot as the water arrives [100].

None of the four gives a cost, because the cost is not the texture's. It is the cost of a mesh fine enough to draw a lip, which these engines get from hardware tessellation. Unity reports its whole water system at "approximately 4ms on the GPU on the latest generations" of console, most of it "due to the important number of vertices required to get nice waves" [102]. An older answer to the same need suits a game whose player never leaves the land: Killzone 3 played back an ocean mesh animated ahead of time, 20,000 to 30,000 polygons, its triangles scattered "with the density based on the distance to where the player could walk" [103].

In research, breaking has been added to a shallow-water simulation by launching sheets of connected particles from steep wave fronts, so that the top outruns the base and the sheet overturns; 160,000 to 200,000 cells ran at 40 to 75 frames a second on a 2007 desktop processor [104].

Nothing shipped chooses the breaker's type from the beach's slope. Where waves plunge is an artist's decision everywhere we looked.

6.4 Foam rendering, five ways

Unity's foam then ages: a lifetime value erodes a foam texture from solid white into lace, with sharp edges on fresh foam and soft ones on old [88]. Crest adds a second, bluish layer of bubbles under the surface [107]. Crest's foam buffer costs 0.16 ms in the high setting above [89]. Sea of Thieves blurs its foam buffer with feedback "to simulate the foam dispersing" [108].

6.5 Shading the water

Every modern system reads the scene's colour and depth behind the water, bends the lookup by the surface normal, and darkens it with distance through the water [88], [109]. For reflections the usual answer is screen-space reflection over a sky or probe fallback (section 7.1). Light through a wave's crest is a shape trick everywhere. Sea of Thieves blends toward a brighter colour by "a combination of view angle, sun direction and a wave peak mask" made from the horizontal displacement [108]; none of these is a volume integral. Skull and Bones sets the water's colour from three amounts, as oceanographers do: living plankton, which turns water green; sediment, which makes it opaque; and dissolved "yellow matter", which returns a "reddy brown" [101].

The piece most often missing is the distant glitter. Wave slopes smaller than a pixel either alias into random sparkle or average away into a mirror with a pinpoint sun. The fix is to turn the lost slope variance into roughness, which LEAN mapping does with two filterable textures of slope moments, shown on a two-layer ocean [110], and which Bruneton, Neyret and Holzschuch built into an ocean that moves from geometry to normals to roughness with distance [111]. Far Cry 5 builds a "variance based" smoothness buffer in screen space and calls it "very important for filtering lighting" [90]. For a walker looking across kilometres of sea toward a low sun, this decides whether the sea reads as water.

7.1 Water reflections are the hard part, and the studios say so

On a still lake the mirror image is the picture (section 2.1), and every published method is weakest exactly there.

Far Cry 5 left the mirrored render for screen space over an environment map, and says why: it was "difficult to maintain", "often it didn't match up with what was rendered in the main view", and it allowed only one water height [115]. Its whole water system, lakes and rivers, costs 1.9 ms on a platform the slide does not name [90]. Avatar: Frontiers of Pandora traces rays for water as a reflection layer of its own, 2.1 to 3.0 ms at quarter resolution, and still warns that the join between the screen-space result and the coarser traced world shows on "low roughness reflections such as mirror and still water", so that "artists need to avoid those kind of reflective surfaces" [116].

We found no first-hand account of the water in Red Dead Redemption 2, The Witcher 3, Death Stranding or Alan Wake 2's lake beyond a line on how its transparency is sorted.

7.2 Murk, the edge and what floats

Murk in shipped engines is a fog inside the water with a colour and a density for each water body. CryEngine's water volume has a fog density, a fog colour and a switch for shadows on the fog [117]; Unreal's single-layer water has absorption and scattering coefficients for each colour channel and reads the scene's depth and colour behind the surface [109]. Neither gives the density a physical unit, which is where section 2.3's measured coefficients can stand in.

For the contact line, The Last of Us Part II paints a texture of distance from every shore and object, turns it into travelling ripples with a sine, and gets the normal from the difference between the texture and a shifted copy of itself. One such texture covered 150 m at 1024 px. Where ripples from two edges meet they interfere as real ones do, because the waves are summed [118].

Algae has shipped as part of the water's own material. Far Cry 5's water carries an algae tiling, an intensity and a falloff from the shoreline, drawn in the same pass as foam [90]. CryEngine's water shader has a decal slot, and its manual's example is an algae surface [119]. The Last of Us Part II's water buffers held foam, churn and an algae normal side by side [118]. Floating leaves in Ghost of Tsushima are particles: they "land on water surfaces and flow with the current", tens of thousands on screen at once [120]. We found no account of duckweed or lily pads in a named game.

7.3 Insects and their sound

No published source gives the number of insects a game draws or the distance at which they appear; those numbers have to come from the animals (section 5.3). What games do publish is how small creatures react. In Ghost of Tsushima the frogs, crabs and birds are particles that spawn animated meshes, and they scatter because each character carries a faint sphere of wind that the particles can sense [120].

In audio middleware the pattern for scattered small sounds is one emitter that spawns sounds at random positions between a minimum and a maximum distance from itself, at random intervals, with random pitch and volume and a cap on voices [121].

In a browser the pieces are the Web Audio panner and oscillator. A panner in its HRTF mode is the costly one: "very expensive", in the words of a browser audio engineer, where the equal-power mode is "rather cheap" [122]. Chrome runs two convolutions for a still source and four while it moves, since each step of position starts a cross-fade of about 45 ms [123]. An oscillator's frequency can change at every sample [124], so a whine can be made with no recording at all. No measurement of a panner's cost in milliseconds was found.

8.1 What the two APIs allow

Day Hike draws with WebGPU on its high tier, in Chrome and Edge on macOS and Windows, and with WebGL2 everywhere else, which includes every Mac in Safari and every phone.

Almost everything water needs has a WebGL2 form, at a higher cost. What has none is compute, atomics and random-access writes.

8.2 What Babylon.js 9.18 gives

The engine has every building block and no ocean. Its WaterMaterial is not a PBR material, so none of the game's material plugins can attach to it, the fog among them; it renders the scene three times a frame, its waves are one sine along each axis, and its Fresnel term cannot reach full reflection at grazing angles. The engine's WebGPU ocean is a demonstration outside the package [128]: three cascades of 256 texels at 250, 17 and 5 m, a JONSWAP spectrum, fold-driven foam that accumulates, and a clipmap mesh. By our count of its source it issues about 230 compute dispatches a frame, because its FFT is one dispatch for each stage of each of four fields in each cascade.

Two details of the engine bear on reflections. Its planar mirror renders an explicit list of meshes, with a refresh rate, a blur and cheaper stand-in materials available, which are the levers for making a mirror affordable. And its clip plane is a discard in the fragment shader, so every material drawn into a mirror compiles a new variant; three.js and PlayCanvas clip with an oblique projection instead, which needs no shader change [129], [130]. That method moves the near plane onto the clip plane "at absolutely no performance cost", but it has "a severe impact on depthbuffer precision" [131], so nothing drawn into such a mirror may read depth from the depth buffer. The engine's newest release, 9.28, has neither an oblique mirror nor hardware clip distances, and no ocean. Since 7.21 a material plugin can be written in WGSL as well as GLSL [132].

8.3 What others have built on the web

None of these seven states a frame time. Three newer projects do.

8.4 Measured costs of water in a browser

The browser figures below come from single authors' repositories a few weeks old, and nobody has reproduced them. They are enough to size an experiment and not enough to skip it.

Four things follow.

• On WebGL2 the FFT is the cost. Three cascades of 256 texels take over 2 ms on a chip newer than any the medium tier is meant for. One cascade fits; so does a sea computed ahead of time. Tessendorf's notes give the way to make one loop: round every wave's frequency down to a multiple of 2π over the loop's length [86]. The rounding is coarsest for the longest waves. In a 20 s loop a swell 200 m long travels 43 % too slowly, and in a 100 s loop 9 % too slowly, so a loop suits wind chop, and swell is better carried by a few analytic waves that need no loop.
• On WebGPU the simulation is cheap and the drawing is not. Every source that separates the two found the shading and the vertex work as dear as the simulation or dearer. Moving the wave textures from 32-bit to 16-bit floats saved one author 1.27 ms of drawing and almost nothing of simulation [140].
• How the FFT is dispatched matters more than its size. The native figure above runs each direction of the transform as one dispatch that works in place. No one has published the cost of three cascades of 256 texels in WebGPU compute on Apple silicon.
• Nobody draws a plunging breaker in a browser. The one project that tried reports two failures, "a folded strip formed a bright cylindrical tube, while a reduced fold formed a long horizontal shelf", and keeps a patch that only rounds the crest [138]. Particle fluids do run: about 100,000 particles on a laptop's integrated GPU and 300,000 on "decent GPUs", by their author's account, in a tank and not at a shore [142].

We found no measured cost, in any browser engine on named hardware, for a mirrored second render of a scene or for a copy of the scene's colour taken in the middle of a frame.

8.5 Measuring it ourselves

Two traps wait for whoever measures. Chrome rounds WebGPU's timestamp queries to steps of 65,536 ns unless its developer features are switched on [143], and a water pass of 0.1 to 0.8 ms is only 2 to 12 such steps. And on WebGL2 over Metal, timer queries do not add up: one project's sections summed to 12.6 ms inside a frame of 2.3 ms, and the queries themselves cost 2 to 7 % of the frame rate [137]. Paired frame times with the feature on and off are the measure to trust there.

Costs are the published ones from sections 6 to 8, on the hardware their sources name. "Not measured" means no source gave a figure. None of these has been measured in Day Hike.

9.1 The sea's surface

9.2 Waves at the shore, and the breaker

9.3 Foam

9.4 Reflection

9.5 Colour, murk and the bed

9.6 The mesh

The sea's rings have cells of 8 m near the camera. Waves shorter than about 16 m cannot be drawn on them. Every system in section 8 uses cells of 0.25 to 1 m near the viewer, and a player at the waterline needs the same. Two densities have to be met at once: fine cells round the camera, wherever it stands, and fine cells along the break line, where a plunging lip is drawn, however far off the camera is. Killzone 3's mesh, dense where the player could walk, is the pattern for the second.

9.7 The lake's margin and its cover

A clear lake and a murky one are the same material with different attenuation. What moves is where the effort goes: on a clear lake, to the bed, its refraction and its caustics; on a murky one, to the cover and the margin.

9.8 Insects

9.9 Sound

Recordings that may ship in a public game are few. The US National Park Service's sound gallery is in the public domain and holds a recording of surf from Olympic National Park [144]. On Freesound, recordings of a mosquito at the microphone and of Pacific chorus frogs in Washington are offered under Creative Commons 0 [145], [146]. The well-known bird archives license for non-commercial use or under share-alike terms, which would bind the game's own audio.

What follows is what this survey looked for and did not find. Each is either a measurement to make in the game or a number to choose by eye.

In the renderer

• The cost of three FFT cascades of 256 texels in WebGPU compute on Apple silicon, or on an integrated GPU.
• The cost of a mirrored second render in any browser engine, and of a copy of the scene's colour taken in the middle of a frame.
• The cost of the mesh that a plunging breaker needs. No shipped use of the technique gives a figure.
• Whether a baked field of wave travel time gives crests that read as real round a headland. We found no game that does it.
• What an HRTF panner costs for each source, in milliseconds, in Chrome and in Safari.

In the world

• How clear the sea is within a few kilometres of the Olympic coast, and in its surf.
• The slope of the sand flat below Rialto's pebble face, and the size of the pebbles.
• How long foam lasts once it is left on the wet sand, and how thick the sheet of water is that carries it there.
• How high spray rises at a natural stack. The sources say "several tens of meters" and give no measurement.
• The distance at which the published levels of surf sound were taken, and any spectrum of pebbles rattling as heard in air.
• When mosquitoes and biting flies are worst on the Olympic Peninsula. The park's own pages do not mention them.
• How the water is drawn in Red Dead Redemption 2, The Witcher 3, Death Stranding, Ghost of Tsushima and Avatar: Frontiers of Pandora's sea. We found no first-hand account of any.

Read only in part

Some papers were read as abstracts, because their publishers refuse automated reading: Koepke's and Schenck's in section 2.4, Kahma and Donelan's in 2.2, Ruggiero's run-up paper in 3.4, and Callaghan's and Monahan's whitecap lifetimes in 3.5. Two talks that bear on the breaker were not readable at all: Guerrilla's 2024 follow-up on simulated rolling waves, and Sledgehammer's on the sea of Call of Duty: WWII.

Three questions in this survey were about the world and not the renderer. We have answered them, and each answer changes which of section 9's options are worth their cost.

1. The water is built as if the player can reach it. Nobody reaches Day Hike's beach today, but the water is a system to be reused, in later maps and in other games, where the player will stand in the swash. So the last 20 m of the beach are in scope: the swash sheet and its mirror on the wet sand, foam thinning to lace, refraction of the bed, a fine mesh at the waterline, and with them a shallow-water simulation. What reads from a distance is wanted as well: sets, break lines that follow the bed, foam that lives 20 s, glitter and sound.
2. The coast gets a steep beach. On a bed of 1:67 every wave spills, whatever its size. A concave wave belongs on a face of about 1:12 reached by unbroken swell, so the world gains a pebble pocket beach between two headlands, as this coast has. The flat sand bays stay, and keep their lines of spilling white water.
3. Lakes sit low and high. A lowland lake with marsh at an end is murky, with algae at its margin; a lake high on the mountain is clear to its bed. One lake material serves both, with the measured attenuation of section 2.3 as its setting. Either needs a basin the terrain does not make today, in ground flat enough to hold a level rim.

The sea bed and the lakes are part of the world every player must agree on, so the second and third change the world, and are best made together.

Two more questions follow from section 8 and wait for a measurement: whether materials gain a way to read the scene's depth and colour, which refraction and reflections by marching need; and whether the water's shader is written in WGSL beside the GLSL the other tiers use, which would spare it the translation that every other material goes through.

1. [1]
   C. Mobley, "The level sea surface," Ocean Optics Web Book, May 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://www.oceanopticsbook.info/view/surfaces/the-level-sea-surface
2. [2]
   C. Mobley, "Cox-Munk sea surface slope statistics," Ocean Optics Web Book, May 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://www.oceanopticsbook.info/view/surfaces/cox-munk-sea-surface-slope-statistics
3. [3]
   C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Amer., vol. 44, no. 11, pp. 838-850, Nov. 1954. Accessed: Sep. 29, 2026. [Online]. Available: https://userpages.umbc.edu/~martins/phys650/Cox%20and%20Munk%20Glint%20paper.pdf
4. [4]
   D. K. Lynch, D. S. P. Dearborn, and J. A. Lock, "Glitter and glints on water," Appl. Opt., vol. 50, no. 28, pp. F39-F49, 2011. Accessed: Sep. 29, 2026. [Online]. Available: https://csuohio.elsevierpure.com/ws/portalfiles/portal/39955766/Glitter%20and%20Glints%20on%20Water.pdf
5. [5]
   Wikipedia contributors, "Capillary wave," Wikipedia. Accessed: Sep. 29, 2026. [Online]. Available: https://en.wikipedia.org/wiki/Capillary_wave
6. [6]
   Wikipedia contributors, "Beaufort scale," Wikipedia. Accessed: Sep. 29, 2026. [Online]. Available: https://en.wikipedia.org/wiki/Beaufort_scale
7. [7]
   K. K. Kahma and M. A. Donelan, "A laboratory study of the minimum wind speed for wind wave generation," J. Fluid Mech., vol. 192, pp. 339-364, 1988. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.1017/S0022112088001892
8. [8]
   M. Minnaert, The Nature of Light and Colour in the Open Air. New York, NY, USA: Dover, 1954. Accessed: Sep. 29, 2026. [Online]. Available: https://archive.org/details/minnaert-light-and-color-in-nature
9. [9]
   J. A. Shaw, "Glittering light on water," Opt. Photon. News, vol. 10, no. 3, pp. 43-45, Mar. 1999. Accessed: Sep. 29, 2026. [Online]. Available: https://psl.noaa.gov/outreach/education/science/glitter/
10. [10]
    C. D. Markfort, E. L. Resseger, W. Zhang, F. Porté-Agel, and H. G. Stefan, "Wind sheltering of small lakes by complex terrain," presented at the 20th Symp. Boundary Layers and Turbulence, Boston, MA, USA, Jul. 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://ams.confex.com/ams/20BLT18AirSea/webprogram/Manuscript/Paper209465/Wakes_extended_abstract_070912_CMarkfort.pdf
11. [11]
    Wikipedia contributors, "Langmuir circulation," Wikipedia. Accessed: Sep. 29, 2026. [Online]. Available: https://en.wikipedia.org/wiki/Langmuir_circulation
12. [12]
    R. M. Pope and E. S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements," data file, Oregon Medical Laser Center, 1997. Accessed: Sep. 29, 2026. [Online]. Available: https://omlc.org/spectra/water/data/pope97.txt
13. [13]
    E. Boss, "Colored dissolved organic matter," Ocean Optics Web Book, Jan. 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://www.oceanopticsbook.info/view/optical-constituents-of-the-ocean/colored-dissolved-organic-matter
14. [14]
    H. Arst et al., "Optical properties of boreal lake waters in Finland and Estonia," Boreal Environ. Res., vol. 13, pp. 133-158, 2008. Accessed: Sep. 29, 2026. [Online]. Available: https://www.borenv.net/BER/archive/pdfs/ber13/ber13-133.pdf
15. [15]
    F. Henderikx Freitas, G. S. Saldías, M. Goñi, R. K. Shearman, and A. E. White, "Temporal and spatial dynamics of physical and biological properties along the Endurance Array of the California Current ecosystem," Oceanography, vol. 31, no. 1, pp. 80-89, 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://par.nsf.gov/servlets/purl/10078647
16. [16]
    A. Morel, H. Claustre, D. Antoine, and B. Gentili, "Natural variability of bio-optical properties in Case 1 waters: attenuation and reflectance within the visible and near-UV spectral domains, as observed in South Pacific and Mediterranean waters," Biogeosciences, vol. 4, no. 5, pp. 913-925, Oct. 2007. Accessed: Sep. 29, 2026. [Online]. Available: https://bg.copernicus.org/articles/4/913/2007/bg-4-913-2007.pdf
17. [17]
    M. L. Zoffoli, R. Frouin, and M. Kampel, "Water column correction for coral reef studies by remote sensing," Sensors, vol. 14, no. 9, pp. 16881-16931, 2014. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC4208206/
18. [18]
    C. Nolet, A. Poortinga, P. Roosjen, H. Bartholomeus, and G. Ruessink, "Measuring and modeling the effect of surface moisture on the spectral reflectance of coastal beach sand," PLoS ONE, vol. 9, no. 11, Art. no. e112151, Nov. 2014. Accessed: Sep. 29, 2026. [Online]. Available: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0112151
19. [19]
    H. M. Dierssen, "Hyperspectral measurements, parameterizations, and atmospheric correction of whitecaps and foam from visible to shortwave infrared for ocean color remote sensing," Front. Earth Sci., vol. 7, Art. no. 14, Feb. 2019. Accessed: Sep. 29, 2026. [Online]. Available: https://www.frontiersin.org/articles/10.3389/feart.2019.00014/full
20. [20]
    P. Koepke, "Effective reflectance of oceanic whitecaps," Appl. Opt., vol. 23, no. 11, pp. 1816-1824, 1984. Accessed: Sep. 29, 2026. [Online]. Available: https://opg.optica.org/abstract.cfm?URI=ao-23-11-1816
21. [21]
    H. Schenck, "On the focusing of sunlight by ocean waves," J. Opt. Soc. Amer., vol. 47, no. 7, pp. 653-657, 1957. Accessed: Sep. 29, 2026. [Online]. Available: https://opg.optica.org/abstract.cfm?URI=josa-47-7-653
22. [22]
    Wikipedia contributors, "Lux," Wikipedia. Accessed: Sep. 29, 2026. [Online]. Available: https://en.wikipedia.org/wiki/Lux
23. [23]
    National Data Buoy Center, "Station 46041, Cape Elizabeth: historical standard meteorological data, 2015 to 2024," NOAA. Accessed: Sep. 29, 2026. [Online]. Available: https://www.ndbc.noaa.gov/station_page.php?station=46041
24. [24]
    Coastal Wiki contributors, "Statistical description of wave parameters," Coastal Wiki, Flanders Marine Institute. Accessed: Sep. 29, 2026. [Online]. Available: https://www.coastalwiki.org/wiki/Statistical_description_of_wave_parameters
25. [25]
    U.S. National Weather Service, "Rip current science," NOAA. Accessed: Sep. 29, 2026. [Online]. Available: https://www.weather.gov/safety/ripcurrent-science
26. [26]
    Coastal Wiki contributors, "Shallow-water wave theory," Coastal Wiki, Flanders Marine Institute. Accessed: Sep. 29, 2026. [Online]. Available: https://www.coastalwiki.org/wiki/Shallow-water_wave_theory
27. [27]
    J. Bosboom and M. J. F. Stive, Coastal Dynamics. Delft, The Netherlands: TU Delft OPEN Books, 2023. Accessed: Sep. 29, 2026. [Online]. Available: https://books.open.tudelft.nl/home/catalog/book/202
28. [28]
    U.S. Army Corps of Engineers, "Estimation of nearshore waves," in Coastal Engineering Manual, EM 1110-2-1100, pt. II, ch. 3, Apr. 2002. Accessed: Sep. 29, 2026. [Online]. Available: https://coastalengineeringmanual.tpub.com/Part-II-Chap3/
29. [29]
    U.S. Army Corps of Engineers, "Meteorology and wave climate," in Coastal Engineering Manual, EM 1110-2-1100, pt. II, ch. 2, Jul. 2003. Accessed: Sep. 29, 2026. [Online]. Available: https://coastalengineeringmanual.tpub.com/Part-II-Chap2/
30. [30]
    U.S. Army Corps of Engineers, "Surf zone hydrodynamics," in Coastal Engineering Manual, EM 1110-2-1100, pt. II, ch. 4, Jul. 2003. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20250824030847/http://www-f1.ijs.si/~rudi/sola/surf-zone.pdf
31. [31]
    J. A. Battjes, "Surf similarity," in Proc. 14th Int. Conf. Coastal Eng., Copenhagen, Denmark, 1974, pp. 466-480. Accessed: Sep. 29, 2026. [Online]. Available: https://journals.tdl.org/icce/index.php/icce/article/download/2921/2586
32. [32]
    M. A. Erinin, X. Liu, S. D. Wang, and J. H. Duncan, "Plunging breakers. Part 1. Analysis of an ensemble of wave profiles," arXiv:2210.01925, 2022. Accessed: Sep. 29, 2026. [Online]. Available: https://arxiv.org/pdf/2210.01925
33. [33]
    A. O'Dea, K. Brodie, and S. Elgar, "Field observations of the evolution of plunging-wave shapes," Geophys. Res. Lett., vol. 48, no. 16, 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20231210110208/https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021GL093664
34. [34]
    C. A. Benbow, "A temporal and spatial analysis of wave-generated foam patterns in the surf zone," M.S. thesis, Naval Postgraduate School, Monterey, CA, USA, Dec. 2015. Accessed: Sep. 29, 2026. [Online]. Available: https://calhoun.nps.edu/handle/10945/47904
35. [35]
    B. E. Scarfe, T. R. Healy, and H. G. Rennie, "Research-based surfing literature for coastal management and the science of surfing: a review," J. Coastal Res., vol. 25, no. 3, pp. 539-557, May 2009. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.2112/07-0958.1
36. [36]
    D. R. Di Leonardo and P. Ruggiero, "Regional scale sandbar variability: observations from the U.S. Pacific Northwest," Cont. Shelf Res., vol. 95, pp. 74-88, 2015. Accessed: Sep. 29, 2026. [Online]. Available: https://ir.library.oregonstate.edu/downloads/s7526f101
37. [37]
    M. Brocchini and T. E. Baldock, "Recent advances in modeling swash zone dynamics: influence of surf-swash interaction on nearshore hydrodynamics and morphodynamics," Rev. Geophys., vol. 46, no. 3, 2008. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20250801190206/https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2006RG000215
38. [38]
    Coastal Wiki contributors, "Swash zone dynamics," Coastal Wiki, Flanders Marine Institute. Accessed: Sep. 29, 2026. [Online]. Available: https://www.coastalwiki.org/wiki/Swash_zone_dynamics
39. [39]
    P. Ruggiero, R. A. Holman, and R. A. Beach, "Wave run-up on a high-energy dissipative beach," J. Geophys. Res., vol. 109, no. C6, Jun. 2004. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.1029/2003JC002160
40. [40]
    Y. Watanabe and D. M. Ingram, "Size distributions of sprays produced by violent wave impacts on vertical sea walls," Proc. Roy. Soc. A, vol. 472, no. 2194, Art. no. 20160423, Oct. 2016. Accessed: Sep. 29, 2026. [Online]. Available: https://eprints.lib.hokudai.ac.jp/repo/huscap/all/67295/RSPA_dropstats_f_YW_DMI.pdf
41. [41]
    A. M. J. van Eijk et al., "Sea-spray aerosol particles generated in the surf zone," J. Geophys. Res., vol. 116, no. D19, 2011. Accessed: Sep. 29, 2026. [Online]. Available: https://publications.tno.nl/publication/34612105/cBMaXz/pub441903.pdf
42. [42]
    A. H. Callaghan, G. B. Deane, M. D. Stokes, and B. Ward, "Observed variation in the decay time of oceanic whitecap foam," J. Geophys. Res., vol. 117, no. C9, 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.1029/2012JC008147
43. [43]
    E. C. Monahan and C. R. Zietlow, "Laboratory comparisons of fresh-water and salt-water whitecaps," J. Geophys. Res., vol. 74, no. 28, pp. 6961-6966, Dec. 1969. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.1029/JC074i028p06961
44. [44]
    A. Callaghan, G. de Leeuw, L. Cohen, and C. D. O'Dowd, "Relationship of oceanic whitecap coverage to wind speed and wind history," Geophys. Res. Lett., vol. 35, no. 23, Art. no. L23609, Dec. 2008. Accessed: Sep. 29, 2026. [Online]. Available: https://publications.tno.nl/publication/34634744/GrDGh7/2008-U-P0367.pdf
45. [45]
    M. F. M. A. Albert, M. D. Anguelova, A. M. M. Manders, M. Schaap, and G. de Leeuw, "Parameterization of oceanic whitecap fraction based on satellite observations," Atmos. Chem. Phys., vol. 16, no. 21, pp. 13725-13751, Nov. 2016. Accessed: Sep. 29, 2026. [Online]. Available: https://acp.copernicus.org/articles/16/13725/2016/acp-16-13725-2016.pdf
46. [46]
    G. Sinnett, "The nearshore heat budget," Ph.D. dissertation, Univ. California San Diego, La Jolla, CA, USA, 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://escholarship.org/uc/item/7nt521mv
47. [47]
    J. MacMahan, "Increased aerodynamic roughness owing to surfzone foam," J. Phys. Oceanogr., vol. 47, no. 8, pp. 2115-2122, 2017. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20250612005904/https://journals.ametsoc.org/view/journals/phoc/47/8/jpo-d-17-0054.1.xml
48. [48]
    A. H. Callaghan, G. B. Deane, and M. D. Stokes, "A comparison of laboratory and field measurements of whitecap foam evolution from breaking waves," J. Geophys. Res. Oceans, vol. 129, no. 1, Jan. 2024. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20250613093633/https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023JC020193
49. [49]
    K. Bolin, "Wind turbine noise and natural sounds: masking, propagation and modeling," Ph.D. dissertation, KTH Roy. Inst. Technol., Stockholm, Sweden, 2009. Accessed: Sep. 29, 2026. [Online]. Available: https://kth.diva-portal.org/smash/get/diva2:217217/FULLTEXT01.pdf
50. [50]
    C. Dallas and C. Tollefsen, "Physical mechanisms underlying the acoustic signature of breaking waves," Can. Acoust., vol. 43, no. 3, 2015. Accessed: Sep. 29, 2026. [Online]. Available: https://jcaa.caa-aca.ca/index.php/jcaa/article/download/2779/2502/3433
51. [51]
    T. Petrut, T. Geay, C. Gervaise, P. Belleudy, and S. Zanker, "Passive acoustic measurement of bedload grain size distribution using self-generated noise," Hydrol. Earth Syst. Sci., vol. 22, no. 1, pp. 767-787, Jan. 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://hess.copernicus.org/articles/22/767/2018/hess-22-767-2018.pdf
52. [52]
    J. Riedel, S. Sarrantonio, and S. Dorsch, "Geomorphology of coastal Olympic National Park," Nat. Park Service, Fort Collins, CO, USA, Natural Resource Rep. NPS/NCCN/NRR-2021/2260, 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://npshistory.com/publications/olym/nrr-2021-2260.pdf
53. [53]
    S. C. Fradkin and J. R. Boetsch, "Intertidal monitoring in the North Coast and Cascades Network: sand beach monitoring 2010 annual report," Nat. Park Service, Fort Collins, CO, USA, Natural Resource Tech. Rep. NPS/NCCN/NRTR-2012/592, 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://irma.nps.gov/DataStore/DownloadFile/449854
54. [54]
    A. S. Farris and K. M. Weber, "Beach foreshore slope for the West Coast of the United States," ver. 1.1, U.S. Geological Survey data release, Sep. 2024. Accessed: Sep. 29, 2026. [Online]. Available: https://www.sciencebase.gov/catalog/item/65a0296bd34e5af967a3841d
55. [55]
    I. Miller, "Shoreline survey data collected at Rialto and Kalaloch Beaches, Washington State, 2018-2019," PANGAEA, 2019. Accessed: Sep. 29, 2026. [Online]. Available: https://doi.org/10.1594/PANGAEA.902570
56. [56]
    P. Ruggiero, J. Wood, G. Kaminsky, and H. Baron, "2012-2013 Olympic Peninsula open coast beach data collection, analysis, and archiving," Oregon State Univ. and Washington State Dept. Ecology, Jul. 2013. Accessed: Sep. 29, 2026. [Online]. Available: https://ecology.wa.gov/getattachment/4abb6c89-b344-490c-85e0-5194165997a6/ECY_NearshoreBathymetry_QuinaultQuileute.pdf
57. [57]
    P. Ruggiero et al., "Beach morphology monitoring in the Columbia River littoral cell: 1997-2005," U.S. Geological Survey, Reston, VA, USA, Data Series 260, 2007. Accessed: Sep. 29, 2026. [Online]. Available: https://pubs.usgs.gov/ds/2007/260/ds260.pdf
58. [58]
    NOAA Center for Operational Oceanographic Products and Services, "Station 9442396, La Push, Quillayute River, WA: datums and water temperature," NOAA. Accessed: Sep. 29, 2026. [Online]. Available: https://tidesandcurrents.noaa.gov/datums.html?id=9442396
59. [59]
    NOAA Office of Coast Survey, United States Coast Pilot 10: Oregon, Washington, Hawaii and Pacific Islands, 2026 ed., ch. 6. Accessed: Sep. 29, 2026. [Online]. Available: https://nauticalcharts.noaa.gov/publications/coast-pilot/files/cp10/CPB10_WEB.pdf
60. [60]
    N. Bond, "Early autumn fog in WA," Office of the Washington State Climatologist, Oct. 2, 2013. Accessed: Sep. 29, 2026. [Online]. Available: https://climate.uw.edu/2013/10/02/early-autumn-fog-in-wa/
61. [61]
    Office of National Marine Sanctuaries, "Olympic Coast National Marine Sanctuary condition report: 2008-2019," NOAA, Silver Spring, MD, USA, 2022. Accessed: Sep. 29, 2026. [Online]. Available: https://sanctuaries.noaa.gov/media/docs/2008-2019-ocnms-condition-report.pdf
62. [62]
    Washington State Dept. Ecology, "Condition of coastal waters of Washington State, 2000-2003: a statistical summary," Olympia, WA, USA, Pub. 07-03-051, Dec. 2007. Accessed: Sep. 29, 2026. [Online]. Available: https://apps.ecology.wa.gov/publications/documents/0703051.pdf
63. [63]
    NASA Ocean Biology Processing Group, "MODIS-Aqua monthly diffuse attenuation coefficient at 490 nm, 4 km," dataset erdMH1kd490mday, NOAA CoastWatch West Coast Node. Accessed: Sep. 29, 2026. [Online]. Available: https://coastwatch.pfeg.noaa.gov/erddap/griddap/erdMH1kd490mday.html
64. [64]
    S. C. Fradkin, W. Baccus, R. Glesne, C. Welch, B. Samora, and R. Lofgren, "Mountain lake study sites in the North Coast and Cascades Network: version 1.1," Nat. Park Service, Fort Collins, CO, USA, Natural Resource Data Series NPS/NCCN/NRDS-2012/364.1, 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://irma.nps.gov/DataStore/DownloadFile/456731
65. [65]
    S. C. Fradkin et al., "Large lowland lakes monitoring protocol: North Coast and Cascades Network," Nat. Park Service, Apr. 2013. Accessed: Sep. 29, 2026. [Online]. Available: https://irma.nps.gov/DataStore/DownloadFile/467558
66. [66]
    G. Thomason and M. Dawson, "Final report for Jefferson County lakes monitoring water quality assessment," Jefferson County Public Health, Port Townsend, WA, USA, Feb. 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://www.co.jefferson.wa.us/Archive/ViewFile/Item/755
67. [67]
    G. C. Bortleson and N. P. Dion, "Preferred and observed conditions for sockeye salmon in Ozette Lake and its tributaries, Clallam County, Washington," U.S. Geological Survey, Tacoma, WA, USA, Water-Resources Investigations 78-64, 1979. Accessed: Sep. 29, 2026. [Online]. Available: https://pubs.usgs.gov/wri/1978/0064/report.pdf
68. [68]
    Washington State Dept. Ecology, "Water quality assessments of selected lakes within Washington State, 1998," Olympia, WA, USA, Pub. 00-03-039, Dec. 2000. Accessed: Sep. 29, 2026. [Online]. Available: https://apps.ecology.wa.gov/publications/documents/0003039.pdf
69. [69]
    Minnesota Dept. Natural Resources, "Where aquatic plants grow." Accessed: Sep. 29, 2026. [Online]. Available: https://www.dnr.state.mn.us/shorelandmgmt/apg/wheregrow.html
70. [70]
    Texas A&M AgriLife Extension, "Filamentous algae," AquaPlant. Accessed: Sep. 29, 2026. [Online]. Available: https://aquaplant.tamu.edu/plant-identification/alphabetical-index/filamentous-algae/
71. [71]
    Maine Dept. Environmental Protection, "Lakes: why does the water look like that?" Accessed: Sep. 29, 2026. [Online]. Available: https://www.maine.gov/dep/water/lakes/surface.html
72. [72]
    Washington State Dept. Health, "Blue-green algae." Accessed: Sep. 29, 2026. [Online]. Available: https://doh.wa.gov/community-and-environment/contaminants/blue-green-algae
73. [73]
    Missouri Dept. Conservation, "Filamentous green algae," field guide. Accessed: Sep. 29, 2026. [Online]. Available: https://mdc.mo.gov/discover-nature/field-guide/filamentous-green-algae
74. [74]
    F. van Breugel, J. Riffell, A. Fairhall, and M. H. Dickinson, "Mosquitoes use vision to associate odor plumes with thermal targets," Curr. Biol., vol. 25, no. 16, pp. 2123-2129, Aug. 2015. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC4546539/
75. [75]
    S. Butail, N. C. Manoukis, M. Diallo, J. M. C. Ribeiro, and D. A. Paley, "The dance of male Anopheles gambiae in wild mating swarms," J. Med. Entomol., vol. 50, no. 3, pp. 552-559, 2013. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC4780853/
76. [76]
    N. C. Manoukis et al., "Structure and dynamics of male swarms of Anopheles gambiae," J. Med. Entomol., vol. 46, no. 2, pp. 227-235, 2009. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC2680012/
77. [77]
    A. Attanasi et al., "Collective behaviour without collective order in wild swarms of midges," PLoS Comput. Biol., vol. 10, no. 7, Art. no. e1003697, Jul. 2014. Accessed: Sep. 29, 2026. [Online]. Available: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003697
78. [78]
    J. G. Puckett, D. H. Kelley, and N. T. Ouellette, "Searching for effective forces in laboratory insect swarms," Sci. Rep., vol. 4, Art. no. 4766, Apr. 2014. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC3996478/
79. [79]
    P. Pellitteri, "Deer flies and horse flies," Univ. Wisconsin-Madison Extension, rev. Apr. 27, 2004. Accessed: Sep. 29, 2026. [Online]. Available: https://hort.extension.wisc.edu/articles/deer-flies-and-horse-flies/
80. [80]
    L. Vebrová, A. van Nieuwenhuijzen, V. Kolář, and D. S. Boukal, "Seasonality and weather conditions jointly drive flight activity patterns of aquatic and terrestrial chironomids," BMC Ecol., vol. 18, Art. no. 19, Jun. 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC6006739/
81. [81]
    J. Snyder, "Mosquitoes," PNW Pest Press, no. 12, Pacific Northwest School IPM Consortium, Spring 2014. Accessed: Sep. 29, 2026. [Online]. Available: https://wpcdn.web.wsu.edu/wp-puyallup/uploads/sites/415/2014/12/PNW_PPMosquito_Spring2014.pdf
82. [82]
    T. Nakata, P. Simões, S. M. Walker, I. J. Russell, and R. J. Bomphrey, "Auditory sensory range of male mosquitoes for detection of female flight sound," J. Roy. Soc. Interface, vol. 19, no. 193, Art. no. 20220285, Aug. 2022. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC9399701/
83. [83]
    Wikipedia contributors, "Chironomus annularius," Wikipedia. Accessed: Sep. 29, 2026. [Online]. Available: https://en.wikipedia.org/wiki/Chironomus_annularius
84. [84]
    L. Feugère, G. Gibson, N. C. Manoukis, and O. Roux, "Mosquito sound communication: are male swarms loud enough to attract females?" J. Roy. Soc. Interface, vol. 18, no. 177, Art. no. 20210121, Apr. 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC8086941/
85. [85]
    D. V. Nelson, H. Klinck, A. Carbaugh-Rutland, C. L. Mathis, A. T. Morzillo, and T. S. Garcia, "Calling at the highway: the spatiotemporal constraint of road noise on Pacific chorus frog communication," Ecol. Evol., vol. 7, no. 1, pp. 429-440, Jan. 2017. Accessed: Sep. 29, 2026. [Online]. Available: https://pmc.ncbi.nlm.nih.gov/articles/PMC5216672/
86. [86]
    J. Tessendorf, "Simulating ocean water," SIGGRAPH course notes, 2004. Accessed: Sep. 29, 2026. [Online]. Available: https://jtessen.people.clemson.edu/reports/papers_files/coursenotes2004.pdf
87. [87]
    T. Tcheblokov, "Ocean simulation and rendering in War Thunder," presented at China Game Developers Conf., Shanghai, China, 2015. Accessed: Sep. 29, 2026. [Online]. Available: https://developer.download.nvidia.com/assets/gameworks/downloads/regular/events/cgdc15/CGDC2015_ocean_simulation_en.pdf
88. [88]
    Unity Technologies, "High Definition Render Pipeline: water system source," Graphics, GitHub repository, master. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/Unity-Technologies/Graphics/tree/master/Packages/com.unity.render-pipelines.high-definition/Runtime/Water
89. [89]
    H. Bowles and T. Read-Cutting, "Multi-resolution water rendering in Crest," presented at SIGGRAPH Advances in Real-Time Rendering in Games, Los Angeles, CA, USA, Jul. 2019. Accessed: Sep. 29, 2026. [Online]. Available: https://advances.realtimerendering.com/s2019/CrestSIGGRAPH2019-Final-for_web.pptx
90. [90]
    B. Grujic and C. Cutocheras, "Water rendering in Far Cry 5," presented at Game Developers Conf., San Francisco, CA, USA, Mar. 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://media.gdcvault.com/gdc2018/presentations/Grujic_Branislav_WaterRenderingFarCry5.pdf
91. [91]
    Wave Harmonic, "GerstnerShared.hlsl," crest, GitHub repository, master. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/wave-harmonic/crest/blob/master/crest/Assets/Crest/Crest/Shaders/OceanInputs/GerstnerShared.hlsl
92. [92]
    Epic Games, "Water body actors in Unreal Engine," Unreal Engine 5 documentation. Accessed: Sep. 29, 2026. [Online]. Available: https://dev.epicgames.com/documentation/en-us/unreal-engine/water-body-actors-in-unreal-engine
93. [93]
    Wave Harmonic, "Shallows and shorelines," Crest Ocean System documentation. Accessed: Sep. 29, 2026. [Online]. Available: https://crest.readthedocs.io/en/latest/user/shallows-and-shorelines.html
94. [94]
    Unity Technologies, "Deform a water surface," High Definition Render Pipeline 17.0 manual. Accessed: Sep. 29, 2026. [Online]. Available: https://docs.unity3d.com/Packages/com.unity.render-pipelines.high-definition@17.0/manual/water-deform-a-water-surface.html
95. [95]
    Wave Harmonic, "Shallow water simulation," Crest 5 documentation. Accessed: Sep. 29, 2026. [Online]. Available: https://docs.crest.waveharmonic.com/Components/Inputs/ShallowWaterSimulation.html
96. [96]
    Z. Mao and K. Wu, "Open-world water rendering and real-time simulation," presented at Game Developers Conf., San Francisco, CA, USA, Mar. 2023. Accessed: Sep. 29, 2026. [Online]. Available: https://media.gdcvault.com/gdc2023/Slides/Open-World+Water+Rendering+and+Real-Time+Simulation_Mao_Zhenyu%26Wu_Kui.pdf
97. [97]
    H. Malan, "Rendering water in Horizon Forbidden West," presented at SIGGRAPH Advances in Real-Time Rendering in Games, Vancouver, BC, Canada, Aug. 2022. Accessed: Sep. 29, 2026. [Online]. Available: https://advances.realtimerendering.com/s2022/SIGGRAPH2022-Advances-Water-Malan.pptx
98. [98]
    Unity Technologies, "High Definition Render Pipeline: water samples, rolling wave," Graphics, GitHub repository, master. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/Unity-Technologies/Graphics/tree/master/Packages/com.unity.render-pipelines.high-definition/Samples~/WaterSamples
99. [99]
    Imaginary Blend, "Fluid Flux documentation," Jan. 10, 2025. Accessed: Sep. 29, 2026. [Online]. Available: https://imaginaryblend.com/2025/01/10/fluid-flux-documentation/
100. [100]
     J. Linneman, A. Battaglia, and W. Judd, "The making of Senua's Saga: Hellblade 2, the Ninja Theory interview," Eurogamer, Aug. 8, 2024. Accessed: Sep. 29, 2026. [Online]. Available: https://www.eurogamer.net/digitalfoundry-2024-the-big-senuas-saga-hellblade-2-tech-interview
101. [101]
     K. Kirkpatrick, "Making waves for Skull and Bones: advancements in water tech," presented at Game Developers Conf., San Francisco, CA, USA, Mar. 2023. Accessed: Sep. 29, 2026. [Online]. Available: https://www.gdcvault.com/play/1029230
102. [102]
     A. de Tocqueville, "The new Water System in Unity 2022 LTS and 2023.1," Unity Blog, Jun. 28, 2023. Accessed: Sep. 29, 2026. [Online]. Available: https://unity.com/blog/engine-platform/new-hdrp-water-system-in-2022-lts-and-2023-1
103. [103]
     SideFX, "Guerrilla Games: Killzone 3," customer story, Apr. 27, 2011. Accessed: Sep. 29, 2026. [Online]. Available: https://www.sidefx.com/community/guerrilla-games-killzone-3/
104. [104]
     N. Thürey, M. Müller-Fischer, S. Schirm, and M. Gross, "Real-time breaking waves for shallow water simulations," in Proc. Pacific Graphics, Maui, HI, USA, Oct. 2007, pp. 39-46. Accessed: Sep. 29, 2026. [Online]. Available: https://graphics.ethz.ch/Downloads/Publications/Papers/2007/Thue07b/Thue07b.pdf
105. [105]
     Wave Harmonic, "UpdateFoam.compute," crest, GitHub repository, master. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/wave-harmonic/crest/blob/master/crest/Assets/Crest/Crest/Shaders/Resources/UpdateFoam.compute
106. [106]
     J. Dupuy and E. Bruneton, "Real-time animation and rendering of ocean whitecaps," in SIGGRAPH Asia Tech. Briefs, Singapore, Nov. 2012. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20240415195251/https://inria.hal.science/hal-00967078/document
107. [107]
     H. Bowles, D. Zimmermann, C. Noris, and B. Wang, "Crest: novel ocean rendering techniques in an open source framework," presented at SIGGRAPH Advances in Real-Time Rendering in Games, Los Angeles, CA, USA, Aug. 2017. Accessed: Sep. 29, 2026. [Online]. Available: https://advances.realtimerendering.com/s2017/Ocean_SIGGRAPH17_Final.pptx
108. [108]
     N. Ang, A. Catling, F. C. Ciardi, and V. Kozin, "The technical art of Sea of Thieves," in ACM SIGGRAPH Talks, Vancouver, BC, Canada, Aug. 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://history.siggraph.org/wp-content/uploads/2022/09/2018-Talks-Ang_The-Technical-Art-of-Sea-of-Thieves.pdf
109. [109]
     Epic Games, "Single layer water shading model in Unreal Engine," Unreal Engine 5 documentation. Accessed: Sep. 29, 2026. [Online]. Available: https://dev.epicgames.com/documentation/en-us/unreal-engine/single-layer-water-shading-model-in-unreal-engine
110. [110]
     M. Olano and D. Baker, "LEAN mapping," in Proc. ACM SIGGRAPH Symp. Interactive 3D Graph. Games, Washington, DC, USA, 2010. Accessed: Sep. 29, 2026. [Online]. Available: https://www.csee.umbc.edu/~olano/papers/lean/lean.pdf
111. [111]
     E. Bruneton, F. Neyret, and N. Holzschuch, "Real-time realistic ocean lighting using seamless transitions from geometry to BRDF," Comput. Graph. Forum, vol. 29, no. 2, pp. 487-496, May 2010. Accessed: Sep. 29, 2026. [Online]. Available: https://web.archive.org/web/20240417164935/https://inria.hal.science/inria-00443630/document
112. [112]
     Epic Games, "Planar reflections in Unreal Engine," Unreal Engine 5 documentation. Accessed: Sep. 29, 2026. [Online]. Available: https://dev.epicgames.com/documentation/en-us/unreal-engine/planar-reflections-in-unreal-engine
113. [113]
     A. Cichocki, "Optimized pixel-projected reflections for planar reflectors," presented at SIGGRAPH Advances in Real-Time Rendering in Games, Los Angeles, CA, USA, Aug. 2017. Accessed: Sep. 29, 2026. [Online]. Available: https://advances.realtimerendering.com/s2017/PixelProjectedReflectionsAC_v_1.92_withNotes.pdf
114. [114]
     R. Génin, "Screen space planar reflections in Ghost Recon Wildlands," Aug. 8, 2017. Accessed: Sep. 29, 2026. [Online]. Available: https://remi-genin.github.io/posts/screen-space-planar-reflections-in-ghost-recon-wildlands/
115. [115]
     S. McAuley, "The challenges of rendering an open world in Far Cry 5," presented at SIGGRAPH Advances in Real-Time Rendering in Games, Vancouver, BC, Canada, Aug. 2018. Accessed: Sep. 29, 2026. [Online]. Available: https://advances.realtimerendering.com/s2018/The%20Challenges%20of%20Rendering%20an%20Open%20World%20in%20Far%20Cry%205%20(With%20Notes).pdf
116. [116]
     Q. Kuenlin, "Raytracing in Snowdrop: an optimized raytracing pipeline for consoles," presented at Game Developers Conf., San Francisco, CA, USA, Mar. 2024. Accessed: Sep. 29, 2026. [Online]. Available: https://media.gdcvault.com/gdc2024/Slides/GDC+slide+presentations/Kuenlib_Quentin_Raytracing_In_Snowdrop.pdf
117. [117]
     Crytek, "Water volume," CRYENGINE V manual. Accessed: Sep. 29, 2026. [Online]. Available: https://www.cryengine.com/docs/static/engines/cryengine-5/categories/23756816/pages/36869912
118. [118]
     W. Ikeda, "Creative and experimental VFX in The Last of Us Part II," presented at Game Developers Conf., Jul. 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://media.gdcvault.com/GDC+2021/GDC21_Creative+and+Experimental+VFX+in+The+Last+of+Us+Part+II.pdf
119. [119]
     Crytek, "WaterVolume shader," CRYENGINE V manual. Accessed: Sep. 29, 2026. [Online]. Available: https://www.cryengine.com/docs/static/engines/cryengine-5/categories/23756816/pages/29449415
120. [120]
     M. Vainio, "How stunning visual effects bring Ghost of Tsushima to life," PlayStation Blog, Jan. 12, 2021. Accessed: Sep. 29, 2026. [Online]. Available: https://blog.playstation.com/2021/01/12/how-stunning-visual-effects-bring-ghost-of-tsushima-to-life/
121. [121]
     Firelight Technologies, "Instrument reference: scatterer instrument," FMOD Studio 2.03 user manual. Accessed: Sep. 29, 2026. [Online]. Available: https://d1s9dnlmdewoh1.cloudfront.net/2.03/studio/instrument-reference.html
122. [122]
     P. Adenot, "Web Audio API performance and debugging notes." Accessed: Sep. 29, 2026. [Online]. Available: https://padenot.github.io/web-audio-perf/
123. [123]
     Chromium Authors, "hrtf_panner.cc," Chromium, GitHub repository, main. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/chromium/chromium/blob/main/third_party/blink/renderer/platform/audio/hrtf_panner.cc
124. [124]
     MDN contributors, "OscillatorNode: frequency property," MDN Web Docs, Mozilla. Accessed: Sep. 29, 2026. [Online]. Available: https://developer.mozilla.org/en-US/docs/Web/API/OscillatorNode/frequency
125. [125]
     W3C GPU for the Web Working Group, "WebGPU," specification source, GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/gpuweb/gpuweb/blob/main/spec/index.bs
126. [126]
     B. Houston, "EXT_color_buffer_float," Web3D Survey, WebGL2 extensions. Accessed: Sep. 29, 2026. [Online]. Available: https://web3dsurvey.com/webgl2/extensions/EXT_color_buffer_float
127. [127]
     B. Houston, "OES_texture_float_linear," Web3D Survey, WebGL2 extensions. Accessed: Sep. 29, 2026. [Online]. Available: https://web3dsurvey.com/webgl2/extensions/OES_texture_float_linear
128. [128]
     E. Popov, "OceanDemo," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/Popov72/OceanDemo
129. [129]
     three.js Authors, "Water.js," three.js, GitHub repository, dev. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/mrdoob/three.js/blob/dev/examples/jsm/objects/Water.js
130. [130]
     PlayCanvas, "water.mjs," PlayCanvas engine, GitHub repository, main. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/playcanvas/engine/blob/main/scripts/esm/water.mjs
131. [131]
     E. Lengyel, "Oblique view frustum depth projection and clipping," J. Game Develop., vol. 1, no. 2, pp. 5-16, Mar. 2005. Accessed: Sep. 29, 2026. [Online]. Available: https://terathon.com/lengyel/Lengyel-Oblique.pdf
132. [132]
     Babylon.js Authors, "Material plugins," Babylon.js Documentation, GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/BabylonJS/Documentation/blob/master/content/features/featuresDeepDive/materials/using/materialPlugins.md
133. [133]
     B. Paleologue, "Ocean simulation with FFT and WebGPU," Mar. 20, 2024. Accessed: Sep. 29, 2026. [Online]. Available: https://barthpaleologue.github.io/Blog/posts/ocean-simulation-webgpu/
134. [134]
     owenyuwono, "poseidon," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/owenyuwono/poseidon
135. [135]
     squall01337, "abyssal-ocean," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/squall01337/abyssal-ocean
136. [136]
     reed-soul, "SeedOcean," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/reed-soul/SeedOcean
137. [137]
     booherbg, "clean-room-fft-ocean: performance notes," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/booherbg/clean-room-fft-ocean/blob/HEAD/docs/perf.md
138. [138]
     siliconjungle, "inkwell-webgpu-water," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/siliconjungle/inkwell-webgpu-water
139. [139]
     SamG-Coder, "coastal-simulation-cuda-webshader," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/SamG-Coder/coastal-simulation-cuda-webshader
140. [140]
     R. Ryan, "Ocean rendering, part 2: profiling and optimization," Mar. 22, 2026. Accessed: Sep. 29, 2026. [Online]. Available: https://rtryan98.github.io/2026/03/22/ocean-rendering-part-2.html
141. [141]
     ColinLeung-NiloCat, "UnityURP-MobileScreenSpacePlanarReflection," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/ColinLeung-NiloCat/UnityURP-MobileScreenSpacePlanarReflection
142. [142]
     matsuoka-601, "WebGPU-Ocean," GitHub repository. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/matsuoka-601/WebGPU-Ocean
143. [143]
     Dawn Authors, "Constants.h," Dawn, GitHub repository, main. Accessed: Sep. 29, 2026. [Online]. Available: https://github.com/google/dawn/blob/main/src/dawn/common/Constants.h
144. [144]
     U.S. National Park Service, "Sound gallery," Natural Sounds. Accessed: Sep. 29, 2026. [Online]. Available: https://www.nps.gov/subjects/sound/gallery.htm
145. [145]
     bruno.auzet, "real mosquito," Freesound, Creative Commons 0. Accessed: Sep. 29, 2026. [Online]. Available: https://freesound.org/people/bruno.auzet/sounds/742549/
146. [146]
     onionaire, "frog clip 1 - 04.02.24," Freesound, Creative Commons 0. Accessed: Sep. 29, 2026. [Online]. Available: https://freesound.org/people/onionaire/sounds/852296/