3D Grebe Floating Reed Nest: Blender Marsh, Raft Buoyancy and Incubation Energetics

Wading into the marsh...

Presets

Time and heave

Nest and clutch (restarts)

Weather and lake

Parents and rotting weed

3D view

Live readouts

Events

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Graphs

1. Temperature of the eggs and the nest cup against air; green line 36 C, red line 28 C (chilling)

2. Height of the egg-cup floor and of the rim above the water line; below zero is flooded

3. Heave: lake surface and nest base over the last 10 seconds, relative to the mean level

4. Embryo development and the sitting parent's energy reserve

Numerical checks

running...

How to use

The run starts by itself with a calm warm morning: two parents swap on the eggs, and the clock jumps ten minutes per second. Try: (1) choose Cold rainy week and watch the heap density climb in the readout and the cup freeboard shrink in graph 2. (2) Set Open-water fetch and Wind high, then watch graph 3: the nest base follows the water surface and the cup is washed when waves overtop it. (3) Raise Lake level by 40 cm with only 10 cm of anchor slack and see the tension build until the cup floods. (4) Untick Both parents share incubation and Cover the eggs to see the eggs cool in graph 1. (5) Use Time speed x1 to see the real-time heave and ripples.

The science

A raft that floats because its average density is below water. A grebe builds its nest from weed, reed stems and rotting plant matter heaped on the water and anchored to standing reeds. The heap is mostly air and wet fibre. Archimedes' principle gives the draft of a raft of mass M and waterline area A (a cylinder, diameter D):

d = M / (ρ_w A), M = m_dry(1 + w) + n m_egg + m_bird

Here w is the mass of absorbed water per kilogram of dry vegetation. For a uniform heap the draft is the fraction ρ_b/ρ_w of its height with ρ_b = ρ_dry(1 + w). Rain and wicking raise w (relaxation time of hours), decay removes dry mass, and the parents add fresh material, so the freeboard drifts over days. The nest is lost when the egg-cup floor (82% of the height) reaches the waterline: the spare buoyancy shown in the readout is ρ_w A (z_cup − d), the extra load that would just awash the cup.

Heave and waves. Vertical motion of the raft follows a damped oscillator driven by the local water level η(t):

(M + m_a) z'' = ρ_w g A s − M g − c z' − T_tether, s = clamp(η − z, 0, H), m_a = ρ_w D³/3

The undamped natural period is T = 2π√((M + m_a)/(ρ_w g A)), about 1.3 s for the default nest. The added mass of a heaving disc is a textbook value, not a fit to a real nest. Anchor strands act as a one-way spring: they are slack until the nest has risen by the slack length, then pull it down with stiffness 3.5 kN/m (a rising lake can then drown the cup). Wind waves use the fetch-limited deep-water fits H_s = 0.0016 U√(F/g) and T_p = 0.286 (gF/U²)^1/3 U/g, realised as two sine components with the right variance. The nest is assumed small against the wavelength (long-wave approximation).

Egg and nest thermodynamics. Two lumped nodes: eggs (heat capacity C_e = n m c, c = 3.3 kJ/kg K) and the nest cup material (C_c from its wet mass).

C_e T_e' = G_bp(T_bp − T_e) + G_ec(T_c − T_e) + G_ea(T_a − T_e) + G_f(T_w − T_e) C_c T_c' = G_ec(T_e − T_c) + G_cw(T_w − T_c) + G_ca(T_a − T_c) + P_mic

G_bp exists only while a parent sits (brood-patch temperature 38 C); a sitting parent also cuts the air conductances, and a layer of wet weed pulled over the eggs when they are left cuts them too. G_cw = k_bA/L conducts heat down to the lake through the freeboard thickness L — the lower the nest sits, the larger it gets, which is why a waterlogged nest chills its eggs. G_f is the flooding term from waves overtopping the cup. Rotting weed warms the cup with P_mic = p m_dry 2^{(T_c−20)/10} (Q₁₀ = 2, capped above 40 C, reduced in a waterlogged heap).

Incubation energetics. The sitting parent spends basal metabolism BMR = 3.79 M^0.723 W (non-passerine allometry, M in kg), extra heat when the air is below about 12 C, and 70% of the heat it delivers to the eggs. Off the nest it forages at three times BMR and gains a modest assimilated intake that you scale with food availability. Embryo development accumulates at (T_e − 24)/12 of the nominal rate (28 days at 36 C); a chilling load ∫ max(0, 30 − T_e) dt, hours of flooding and heat stress lower the hatching-success estimate.

Honest simplifications. (1) The nest is a vertical cylinder of uniform density, not a cone with a compacted base. (2) Added mass, damping ratio, conductances and all biological thresholds (28 C chilling, 160 C-hour tolerance, 4%/h flooding penalty) are plausible illustrative values, not measurements of one nest. (3) Parent behaviour is a simple schedule with two safety rules; real grebes also dive, turn the eggs and adjust cover to the weather. (4) Eggs are drawn 1.3 times larger than life so that they stay visible.

Checks run in the page. The settled draft equals Archimedes' value; the simulated heave period equals 2π/(ω₀√(1−ζ²)); a 40-minute bare cooling of the two-node model equals the exact matrix-exponential solution; at steady state under the brood patch the heat the parent delivers equals the conductive loss of the eggs; the wave height matches the fetch formula and splits its variance correctly between the two sine components.