MY SIMULATOR

Turtle Nest Tide Lab

Will the sea reach the eggs before they hatch?

INTERACTIVE 3D

Incubation day 0.0Sea level 0.00 mRun-up reach 0.00 mMean hatch success 100%FPS 0

Sea Turtle Nest Tide Lab: Storm Surge, Wave Run-up and Hatching Success

Four marked nests sit at different heights on a beach. Over a 55-day incubation the tide, a storm surge and wave run-up wet the sand; eggs drown if the chamber stays saturated, and a nest washes out if swash reaches it. Click the beach to move the selected nest, then press Start season.

Scenario

Nests ready

Cross-shore profile (live)

Water level and nest heights (m above mean sea level)

1 · Sea

Tide η = SLR + A cos(2πt/12.42 h), A modulated by a 14.8-day spring-neap cycle, plus a Gaussian surge (10 h width).

2 · Waves and storm

Wave setup and run-up from the Stockdon et al. (2006) formula for the beach slope.

3 · Beach

Foreshore slope and berm crest height set the profile; the dune toe sits 25 m behind the berm crest.

Experiments (measured vs predicted)

Run an experiment. They run on copies and do not disturb the live season.

Independent numerical checks

Also run outside the browser: node src/check.js.

The science

Water level. Mean water level η(t) = SLR + A(t) cos(2π t / 12.42 h) + S g(t) with spring-neap modulation A(t) = A₀[1 + m cos(2π t / 14.77 d)] and a Gaussian storm surge g(t) = exp[−½((t − t_s)/10 h)²]. Waves grow in the storm as H₀(t) = H_s + ΔH g(t).

Wave setup and run-up. For deep-water wave height H₀ and period T, with deep-water wavelength L₀ = gT²/2π and foreshore slope β, Stockdon et al. (2006) give set-up ⟨η⟩ = 0.35 β √(H₀L₀) and swash S = √(H₀L₀(0.563β² + 0.004)); the 2 % exceedance run-up is R_2% = 1.1(⟨η⟩ + S/2). The empirical formula was fitted on natural beaches and is a statistical estimate, not a hydrodynamic solution.

Eggs. The egg chamber centre sits 0.55 m below the nest surface (typical green-turtle value; species differ). The chamber is saturated whenever η + setup ≥ z_nest − 0.55; wash-over exposure accumulates each hour weighted by the share of waves whose run-up reaches the nest, p = exp[−3.912((z_nest − η)/R_2%)²] (Rayleigh run-up maxima scaled so that R_2% is exceeded by 2 % of waves; p = 1 when the mean sea level itself reaches the nest). Hatch success is exp(−H_sat/τ_s) · exp(−H_wash/τ_w) with τ_s = 60 h and τ_w = 12 h. These two tolerance times are illustrative assumptions: field studies show success falling steeply with hours of inundation, but the exact numbers vary by species, stage and sand. Embryos are most sensitive in late incubation (not modelled).

Tide-only closed form. With no waves, surge or neap modulation the fraction of time the chamber is under water is (1/π) arccos[(z_e − SLR)/A] (0 when z_e − SLR > A, 1 when below −A); the checks and the first experiment use it.

Not modelled: beach erosion or accretion during the storm, groundwater lag and salinity, rainfall, shading and sand temperature (so no sex ratio here — see the sibling heat-diffusion labs), predators, nest relocation, real tide tables. Hatchlings are drawn 6× larger so you can see them; their number is the surviving share of an illustrative clutch of 100 eggs.