Kd490 → Secchi: the optical theory
This page explains the single relationship at the heart of the Submarius water-clarity model: the conversion from satellite-derived diffuse attenuation coefficient (Kd490) to Secchi disk depth (a proxy for “vertical visibility”).
What’s Kd490?
The diffuse attenuation coefficient at 490 nanometres measures how much downwelling blue-green light is absorbed and scattered per metre of water column. Higher Kd = more attenuation = less light getting through = lower visibility.
Units: m⁻¹ (per metre).
Typical values:
| Water type | Kd490 (m⁻¹) | Visual character |
|---|---|---|
| Open ocean (clear) | 0.02 – 0.05 | Deep blue, 30 m+ visibility |
| Coastal blue water | 0.05 – 0.15 | Blue-green, 10–25 m visibility |
| Coastal turbid | 0.15 – 0.5 | Green-grey, 3–10 m visibility |
| Estuarine / river-plume | 0.5 – 5+ | Brown-green, < 3 m visibility |
Satellites measure Kd490 by inverting the water-leaving radiance spectrum — essentially, by reading the colour of the water from above and modelling what attenuation would produce that colour.
Submarius pulls Kd490 from three independent sources (VIIRS-SNPP, NOAA’s VIIRS+OLCI multi-mission gap-filled product, GOES-16 ABI processed via ACOLITE) and fuses them via inverse-variance weighting in log-Kd space.
What’s Secchi depth?
The Secchi disk is a 30 cm white disk lowered into water until it disappears from view. The depth at which it disappears is the Secchi depth (Z_SD). It’s the oldest standardised measurement of water clarity and the one divers most intuitively recognise.
Roughly: Secchi depth in metres ≈ vertical visibility a diver experiences. Horizontal visibility is typically 1.5–2× Secchi depth in clear water.
The classical “1.7/Kd” rule
For decades the standard relationship was:
Z_SD ≈ 1.7 / Kd(490)
This worked tolerably well for moderate-clarity coastal water but broke at the extremes — too pessimistic for very clear blue water, too optimistic for very turbid coastal/estuarine water.
The Lee 2015 mechanistic model
Lee derived a new equation based on contrast detection by the human eye at the most transparent wavelength of the water type, rather than fixed 490 nm. The simplified form:
Z_SD ≈ 1 / Kd_tr × ln( r_t − r_w_pc × R_d_pc / N_c_pc)
where Kd_tr is Kd at the transparent-window wavelength (which shifts with water type — ~480 nm for clear blue ocean, ~550–580 nm for turbid coastal water).
The logarithmic ratio is empirically nearly constant across diverse water types: 2.38 ± 0.03.
So the practical simplification:
Z_SD ≈ 2.38 / Kd_tr
Validated against N = 338 globally distributed in-situ measurements spanning 1 m to 30 m+ visibility:
R² = 0.96, ~18% mean absolute error.
This is the strongest published physical relationship between satellite-observable optical properties and human-perceived underwater visibility. It’s the foundation Submarius builds on.
Wavelength shifts by water type
The “transparent window” — the wavelength at which water absorbs and scatters light least — shifts with water composition. From Lee 2015 Figure 4:
| Z_SD | Transparent wavelength | Perceived water colour |
|---|---|---|
| 5 m | 540 nm | Green-yellow |
| 10 m | 530 nm | Green |
| 20 m | 510 nm | Blue-green |
| 40 m | 480 nm | Blue |
Practical implication: Kd at 490 nm (what the satellite measures most directly) is most accurate for clear water. For coastal or turbid water, Kd(490) underestimates the relevant attenuation, and a naive 2.38/Kd(490) calculation will over-estimate visibility.
This is why Submarius uses an adaptive coefficient — Case-1 vs Case-2 — rather than a fixed value.
Case-1 vs Case-2 water
Oceanographers classify water into two broad optical types:
- Case-1 (open ocean, chlorophyll-dominated): the optical properties are determined primarily by phytoplankton. Lee’s coefficient ≈ 2.38.
- Case-2 (coastal, dominated by suspended sediment, CDOM, and river-borne material): the optical properties are dominated by inorganic particles and dissolved organics, not phytoplankton. The effective coefficient drops to ~1.5.
Most published consumer-facing visibility products use 2.38 everywhere and silently overestimate coastal turbidity by 30–50%.
Submarius computes a case-2 factor from:
- Coastline-geometry enclosure class (open / semi-open / enclosed)
- Distance to coast
- Satellite chlorophyll-a (elevated → bloom-influenced → leans Case-2)
- Active HAB flag
- Freshwater detection from coastline data
…then blends coefficients:
coeff = (1 − case2_factor) × 2.38 + case2_factor × 1.5
Z_SD = coeff / Kd
A Florida east-coast surf zone with Kd = 0.18 maps to Secchi ~8 m (realistic) instead of the ~12 m a Case-1-everywhere model would produce. The Bahamas deep with Kd = 0.04 maps correctly to ~60 m.
Where Kd490 falls short
The relationship has known limits. We don’t claim performance outside them:
- Optically shallow water. When the seafloor is bright (sand, coral rubble) and the water is shallow, satellite-observed colour is contaminated by bottom reflectance. Kd retrievals there are biased. Submarius corrects this with the bathymetric cap — see the model page.
- Adjacency effects within ~3 km of land. Land reflectance bleeds into nearby water pixels, inflating apparent clarity. Submarius downweights satellite Kd in shore-adjacent cells when Kd suggests clear water (high-Kd readings are honest; low-Kd readings are suspect).
- Severely turbid water (Kd > 1). Both the linear approximation and the Case-2 calibration weaken. Submarius reflects this in the uncertainty band.
- Subsurface features. Thermoclines, haloclines, and lensed plumes are invisible to surface satellites. The model can’t see them.
Citations and further reading
- Lee, Z. P. et al. (2015). Secchi disk depth: A new theory and mechanistic model for underwater visibility. Remote Sensing of Environment 169, 139–149. DOI
- IOCCG (2000). Remote sensing of ocean colour in coastal, and other optically-complex, waters. Reports of the International Ocean-Colour Coordinating Group, No. 3.
- Mobley, C. (1994). Light and Water: Radiative Transfer in Natural Waters. Academic Press. The textbook on the underlying physics.
The Submarius blog post how Kd490 satellite data predicts water clarity covers this material at lower technical density for a non-oceanographer audience.