Challenge A · Water clarity
Locate the euphotic boundary
Current euphotic depth
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Light at probe depth
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Concept: Clear water carries useful light deeper than turbid water; both follow an exponential model.
The maths
Water: I(z)/I₀ = exp(−kz).
Euphotic depth: zₑ = ln(100)/k, at 1% light.
Two-depth measurement: I(z₂)/I(z₁) = exp[−k(z₂ − z₁)].
Inverse coefficient: k = −ln[I(z₂)/I(z₁)]/(z₂ − z₁).
Spectroscopy: A = εcl; c = A/(εl).
Dilution: D = Vfinal/Valiquot; cdiluted = cstock/D.
k: m⁻¹; z and zₑ: m; ε: L/(mol·cm); c: mol/L; l: cm; A: dimensionless.
Assumption: each medium has one constant attenuation coefficient at one optical band, without multi-component spectra. The cuvette is homogeneous and follows the linear Beer–Lambert law.
Live quantitative models
Depth and calibration
Light fraction against depth · logarithmic intensity axis
Absorbance against concentration · linear window
Current model
Clear-water reference
Turbid-water reference
Observation / sample ●
Investigation controls