Sea Turtle Nest Heat

What is modelled

Heat flows through sand by diffusion. The surface temperature has a daily cycle and a slow seasonal swing; each wave is damped and delayed as it travels down. The nest temperature sets how fast the embryos develop, and the average temperature in the middle third of development decides the sex: a warm clutch gives more females.

Equations

• Diffusion ∂T/∂t = α ∂2T/∂z2, solved with explicit finite differences (α r = 0.29 at the largest diffusivity).
• Damped wave T(z,t) = Tm + A e−z/d cos(ωt − z/d), damping depth d = √(2α/ω).
• Development rate r(T) = Q10(T−30)/10 / 55 d with Q₁₀ = 2.5, plus metabolic heating ΔT = ΔTmax p2 as development p advances.
• Female share f = E[ 1 / (1 + exp(−(Tmid + δ − Tpiv) / w)) ] averaged over the clutch spread δ.

Checks run in the page

• The seasonal amplitude and lag at the nest depth match the analytic wave.
• The daily wave at a 10 cm probe matches its damped amplitude.
• The day-by-day development integrator matches the closed form, and the cycle mean is the mean sand temperature.
• A Monte Carlo of 40,000 eggs matches the Gauss-Hermite average of the logistic curve.

Honest simplifications

The sand is a uniform, dry-or-wet medium with one diffusivity, there is no rain, shading or evaporation, the forcing is two clean sine waves, and the sex-ratio curve and development numbers are illustrative values of the right size, not fitted to a population.

• Press Shallow nest, 25 cm and see more of the daily swing reach the eggs.
• Press Hot beach, warming and read how far the female share climbs.
• Press Wet sand, fast heat: the damping depths grow with the square root of the diffusivity.