Pond storage. The pond volume V(h) and area A(h) come from the terrain height grid: V(h) = sum over cells of max(0, h − z) ΔxΔy. The level h obeys dV/dt = Q_in − Q_weir − Q_seep − E·A, solved with a backward-Euler step and bisection (stable at any time step).

Spill. Over the crest the flow is a broad-crested weir, Q = C_w W H^3/2 with C_w ≈ 1.6 m^1/2/s (typical 1.5-1.7). Raising the dam by one log lifts the crest 0.08 m; the steady spill head H = (Q/(C_wW))^2/3 does not depend on the crest height (checked).

Seepage. Water leaks through the sticks like groundwater under a dam (Dupuit-Darcy): Q_s = K (1 − seal) W (H² − h_T²)/(2T). K = 0.02 m/s is an illustrative value; mud plaster reduces it, flood flow and time erode the plaster.

Catchment. Inflow = baseflow + rain (3 mm/h × runoff 0.15 × 6 km²) + snow-melt (degree-day: 4 mm SWE per °C per day, 50 % runoff). Snow falls when it is cold. All catchment numbers are illustrative.

Beaver energy. Kleiber’s law, BMR = 70 M^0.75 kcal/day (20 kg → 662 kcal/day), times an activity factor (rest 1.2, walking 1.9, swimming 2.3, hauling 2.6) and a cold penalty in cold water. Food energy per branch/berry is game-scaled, not a measured value. Carrying capacity 16 kg and the gnawing times are game choices; speeds are about 2x real to keep the game playable.

Ecology. Trees regrow logistically (r = 0.25/day), trout, deer and waterfowl grow logistically toward a capacity set by pond area, depth, dissolved oxygen (Elmore-Hayes saturation polynomial) and riparian trees. These are toy ecosystem models, not field data.

Simplifications. One uniform pond level, no ice, no flow field; the waterfall and spray are visual. A year lasts 120 days. Not a design tool for real dams.