INTERACTIVE MODEL · FIELD NOTE · OCEANOGRAPHY

The Water Column Light Bench

A live model accompanying “Twenty One Percent of the Ocean Got Darker”

Read the full field note · Our calculation

Everything in the ocean darkening result runs through one coefficient. Set it yourself below and watch what it does to the depth of the lit layer. Then take a white disk down a rope and find out how badly you can estimate the same coefficient by eye.

I(z) = I₀ · exp(−K_d · z) z_1% = ln(100) / K_d = 4.60517 / K_d

Model 1. The water column

The left panel is a slice of ocean 250 metres deep. Each horizontal strip is shaded by how much surface light survives to that depth, computed from the equation above and nothing else. The hard rule is the one percent level, the conventional floor of the euphotic zone. Move the coefficient and the rule moves.

Attenuation K_d(490) 0.040 per metre Probe depth 50 m Water preset open ocean Surface shimmer on

1% depth: 115.1 m 10% depth: 57.6 m light at probe: 13.534% Secchi you would read: 42.5 m

The strips are a direct rendering of exp(−K_dz), so the picture is the equation. Nothing here is a measurement: it is the textbook model with your number in it.

Model 2. A white plate on a rope

A Secchi disk is a white plate lowered on a marked line until you cannot see it any more. The depth at which it vanishes converts to an attenuation coefficient by the Poole and Atkins relation, K_d = 1.7 / Z. Below, the disk's contrast against the background falls off at 2.3 K_d per metre, which is the rate that puts the two percent visibility threshold exactly at 1.7 / K_d. The water sample is randomised and its true coefficient is hidden until you commit to a reading.

Lower the disk to 6 m Trend year 2003 Shoaling band 10 to 50 m

Commit or resample

your reading: not committed your K_d estimate: – true K_d: hidden error: –

Lower the disk until the plate is gone, then press “It vanished”. Judging the moment is the whole skill, and the whole problem.

Contrast threshold fixed at 2%, conversion constant fixed at 1.7. Published constants run from 1.4 to 2.0, so even a perfect reading carries a spread of about 43% in the euphotic depth it implies.

Twenty years of it

The year slider applies the paper's reported shoaling linearly across the study window, 2003 to 2022. Pick a band and drag the year: the ledger below is the club's own arithmetic on Davies and Smyth's reported areas, scaled to the year you have reached. The paper reports areas and shoaling depths; it does not report a volume, and this one is ours.

years elapsed: 0 shoaling in this band: 0.0 m global lit volume lost: 0 km³ share of ocean volume: 0.0000%

Full window total: 3,747,102 km³
Rate: 197,216 km³ per year
In Lake Superiors: 0 of 310
As an even layer: 0.00 m over the whole ocean

Bands charged at 30 m, 75 m and 100 m over areas of 35,953,713, 23,056,910 and 9,392,219 km². Ocean volume taken as 1.335 × 10⁹ km³. Straight-line interpolation across 19 elapsed years is an assumption, not a finding.

What to take away from pushing the sliders

Two things tend to land harder here than they do in prose. The first is that the one percent rule moves fast at the clear end and barely at all at the murky end, which is the inverse square in the derivative made visible. The second is how coarse a Secchi reading is: even committing carefully, most people land several metres off, and several metres of Secchi error is tens of metres of euphotic depth.

Neither model reproduces the paper. Davies and Smyth worked with twenty annual satellite composites, an ARIMA filter and quantile regression, against a light threshold taken from copepod behaviour rather than the one percent convention. What you have here is the physics underneath their result, with the arithmetic left where you can check it.