Each 0.5 m cell of the 24 m floe patch keeps a snow depth hs, an ice thickness H and a pond depth d. The net flux that melts it is
F = max(0, κ·S(t)·(1 − α) − 20 W/m²)
S(t) = S_peak·sin(π(0.15 + 0.7 t/100 d))
snow: dh_s = F·Δt / (ρ_s L_f) ρ_s = 300 kg/m³
ice: dH = F·Δt / (ρ_i L_f) ρ_i = 917 kg/m³, L_f = 3.34·10⁵ J/kg
α_pond(d) = 0.20 + (0.55 − 0.20)·e^(−d/0.15 m)
Albedos: snow 0.84, bare ice 0.55, open ocean 0.06. Snow goes first (its latent-heat budget is spent before the ice surface sees any melt); meltwater, converted by density ratio, joins one pool of volume V that fills the snow-free relief up to a common level w (mean of max(0, w − si) = V). Seepage through the ice drains V at rate k (slider). A cell whose ice is gone becomes open water and the pond water above it is lost to the sea. The deeper a pond, the lower its albedo, the faster it melts: the ice-albedo feedback.
Simplifications, stated plainly: κ = 0.7 lumps conduction, transmission and turbulent losses into one number; there is no refreezing, no diurnal cycle, no ice motion and the floe sits at its freeboard (only the relief differences from melt are kept); one common pond level stands in for lateral flow; the surrounding camp, the margin slab and the distant floes are static scenery and their freeboard is exaggerated for readability; pond-albedo constants are illustrative values within the observed range, not a fit to a particular floe. Sea-ice models (for example CICE) treat these processes with far more detail.
- Peak shortwave — the midsummer daily-mean solar input; the season ramps up and down around it.
- Snow depth — more snow delays bare ice and pond formation (wind drifts it into the low spots).
- Drainage — high values keep ponds shallow and bright; low values let them deepen and melt through.
The striped stake plants a 10 cm-banded gauge on the surface; the yellow-capped bands show how far the surface has lowered or the snow has melted.