The 3D version tracks four global area fractions (snow / bare ice / pond / water) with empirical rate constants, then paints them onto a grid by a fixed, pre-sorted elevation rank — cells never exchange anything, so "low ground" is really just a static percentile assignment decided once at the start. This 2D version is a genuinely different, independently-computed model: every one of its 1,936 cells (a 44×44 grid) keeps its own snow depth, ice thickness and pond depth, stepped from a real surface energy balance in physical units:
Q_abs = S·(1 − α) − Q_loss (W/m², per cell, per-cell α)
E_melt = Q_abs · 86.4 · η · Δt (kJ/m², η = melt efficiency)
Δdepth = E_melt · 100 / (ρ · L_f) (cm, L_f = 334 kJ/kg latent heat)
Snow (ρ≈330 kg/m³) is consumed before ice (ρ≈900 kg/m³) — the same absorbed energy melts roughly 2.7× more snow depth than ice depth, because snow is the less dense phase. Meltwater produced is added, density-converted to liquid-water depth, to that cell's own standing pond — ice thickness is tracked per cell, so melt-through to open water happens locally, wherever a cell's ice has actually run out, not from a global depth threshold applied everywhere at once.
Standing water then genuinely moves: every step it is routed between neighboring cells along the hydraulic-head gradient (elevation + local pond depth), one exact unit at a time, so it can never be created or destroyed — only redistributed toward topographic lows, which is where real Arctic melt ponds are observed to form. The "Total meltwater volume" readout is exactly that conserved quantity (it only falls when drainage removes it through the ice, never through the routing step itself).
- Incoming shortwave — solar forcing at the surface; higher values feed every step of the loop for every cell.
- Initial snow depth — a deeper snowpack delays bare-ice exposure per cell.
- Meltwater drainage — models ice permeability: a per-cell exponential loss of standing pond depth through brine channels/seal holes.
This is the same positive-feedback mechanism sea-ice models parameterize (absorbed energy → phase change → lower albedo → more absorbed energy), but reached here through per-cell thermodynamics and real mass-conserving lateral flow instead of the 3D version's global rate constants and static topography paint.