Date —Air 0 °CIce h 0 mCover A 0 %Albedo 0Ocean 0 °C—FPS 0

Drag to orbit, wheel or pinch to zoom, or use the camera buttons. White slabs are floes (thickness and freeboard follow the model), blue discs are melt ponds, glowing dots are mixed-layer water motion (illustrative). The buoy is a weather and ice-mass-balance station.

Sea Ice Floes: Stefan Growth, Melt Ponds and the Ice-Albedo Loop

Run the Arctic year: ice grows by conduction in winter, ponds form in summer, and open water absorbs the sun that the ice used to reflect.

Climate

Ice and ocean

Time

Live readouts

Thickness and snow

Cover, albedo and absorbed sunlight

Experiments

Each button runs 4 model years headless from your current settings and reports the 4th September minimum cover, the April thickness and the largest pond fraction.

Independent numerical checks

Controls

Drag or one finger: orbit; wheel or pinch: zoom. Camera buttons jump to a high view, the waterline, under the ice or top-down.
Presets set several sliders together. Sliders act immediately; changing latitude, initial thickness or pressing Reset restarts the model from 1 October.
Time scale is model days per real second. Pause freezes the model; the camera stays free.

The science

Insolation and climate. Daily-mean top-of-atmosphere sunlight: Q = (S₀/π)(h₀ sinφ sinδ + cosφ cosδ sin h₀), cos h₀ = −tanφ tanδ, declination δ = 23.44° sin(2π(d−81)/365). At the surface: SW = 0.70 (1 − 0.4 c) Q. Air temperature is a seasonal cosine (mean −17 °C at 80 °N, amplitude 17 K, minus 0.7 K per degree of latitude) plus your warming offset. These are typical round numbers, not a reanalysis.

Surface balance (zero-layer ice). With ice-base temperature T_f = −1.8 °C and effective thickness h_eff = h + (k_i/k_s) h_s: (1 − α)SW + K_B(T_a − T_s) − L₀(1 − 0.75 c) + (k_i/h_eff)(T_f − T_s) = 0. K_B = 12 W m⁻² K⁻¹ lumps turbulent and linearised longwave exchange; L₀ = 90 W m⁻² is the extra longwave deficit under clear sky, reduced by 75 % of cloud cover. If T_s would exceed 0 °C it is held at 0 °C and the excess flux melts snow first, then ice.

Growth and melt at the base. ρ_i L_f dh/dt = k_i(T_f − T_s)/h_eff − F_w, with ρ_i = 917, L_f = 3.34×10⁵ J/kg, k_i = 2.1 W m⁻¹ K⁻¹. For a fixed T_s and F_w = 0 this integrates to Stefan's law h² = h₀² + 2 k_i (T_f − T_s) t /(ρ_i L_f): thin ice grows fast, thick ice slowly.

Albedo and melt ponds. Bare ice α = 0.08 + 0.52 tanh(h/0.5 m); dry snow 0.84, wet snow 0.68 (surface within 2 K of melting); pond 0.30; open water 0.07. Pond meltwater depth W follows 60 % of the surface melt and drains or refreezes with a 6-day time constant when it is cold; pond fraction f_p = 0.45 (1 − e^{−W/0.06 m}), on snow-free ice only.

Open water and floe edges. The mixed layer (depth H) warms by sunlight on open water and loses heat to the ice base: ρ_w c_w H dT/dt = (1 − A)[(1 − 0.07)SW + K_B(T_a − T) − L₀(1 − 0.75c)] − A·25(T − T_f). Lateral melt speed m = 1.6×10⁻⁶ (T − T_f)^1.36 m/s (Maykut and Perovich 1987 form) acts on the floe perimeter, dA/dt = −4 A m / D, and the heat it uses, ρ_i L_f h ΔA, is taken from the mixed layer. When the layer would drop below T_f, the deficit freezes new 0.2 m ice (frazil), raising A. Together this is the ice-albedo feedback: less ice means more absorbed sunlight, a warmer layer and more lateral melt.

Freeboard. Archimedes with the snow load: fb = h − (ρ_i h + ρ_s h_s)/ρ_w; the 3D floes are drawn at exactly this height.

Simplifications: one mean thickness for the whole pack, no ice drift, ridging or export, no thickness categories or internal brine pockets, no ocean heat advection, no wind forcing, constants typical rather than fitted. Use the sweeps for relative sensitivities, not forecasts. The glowing under-ice dots are illustrative. Assets built with Blender; scene by Three.js.