From rain gauge to flood map: pick a return period, change the land use and the defences, and watch the expected annual damage.
The science
Return period. Annual-maximum storm depth is modelled by a Gumbel (EV1) law: PT = μ + σ KT, KT = −(√6/π)[γ + ln ln(T/(T−1))] with μ = 65 mm, σ = 20 mm for a 6 h storm (model values, [перевірити за джерелом]). A T-year event has a 1/T chance in any year, not a fixed schedule; the chance of at least one in n years is 1 − (1 − 1/T)n.
Runoff. SCS curve number: S = 25400/CN − 254, Ia = 0.2 S, Q = (P − Ia)² / (P − Ia + S) applied to the cumulative rain; basin CN is the area-weighted mix of forest 55, farmland 70 and urban 90 [перевірити за джерелом]. The hyetograph is an alternating-block profile from P(t) ∝ t0.4.
Routing. The SCS triangular unit hydrograph has qp = 0.208 A / Tp (m³/s per mm, A in km²) with Tp = Δt/2 + 0.6 Tc, convolved with the excess rain. 45 % of the basin drains into a level-pool reservoir (A dL/dt = I − O, spillway O = 1.7 L H3/2); the rest joins below the dam after a 1 h travel lag. Retention ponds are modelled as a peak shave with the stored volume released after the event.
River stage. Manning: Q = (1/n) A R2/3 S1/2 for a trapezoid channel (b = 35 m, banks 1.8 m high, n = 0.035, S = 0.002) plus a rough floodplain strip (n = 0.06, 80 m effective width) once the banks overtop. The stage is the same height above the bed along the river (uniform-flow assumption).
Hazard map. The water level at every river reach is spread over the terrain by a connected flood fill (a cell floods if its ground, plus the levee on the protected bank, is below the local level and it touches flooded water). Depth is level minus ground. A depth-damage curve 1 − e−d/0.8 times the asset value gives the damage for each return period; EAD = ∑ ½(Di + Di+1)(pi − pi+1) over p = 1/T (trapezoid, with the largest-event damage held for p → 0).
Simplifications. Lumped basin, 1-D uniform-flow river with a static (bathtub-like) floodplain: no 2-D flow, no dynamic wave attenuation, no soil moisture or snow, no dam breach (overtopping is flagged), no storm surge, one asset-value table. Everything is a model value for planning exercises, not a forecast or a design tool. Only buildings and infrastructure counts are reported.
Blender-modelled terrain and buildings, Three.js r160. Educational model values.