About Floodline

Floodline is a California flood-defense simulation built on real water-system physics — levees, weirs, pump stations, and reservoir releases. Six historical scenarios span the 1986 Yuba flood to the 2017 Oroville spillway crisis. $2 indie release on itch.io and Steam.

How to play

Each scenario starts with an inflow forecast and current system state. Choose levee inspections, pump activation, gate operations, and (in some scenarios) controlled-flooding releases. Score points for protected area, lose for inundation. Real CA water hydrology.

Frequently asked questions

How the model works — the real hydrology

Floodline routes water with the local-inertial shallow-water scheme of Bates, Horritt & Fewtrell (2010) — the solver inside LISFLOOD-FP and most modern 2D flood-inundation models — on a 40 m grid, in SI units, with Manning's roughness per land cover. It is not a full Saint-Venant / HEC-RAS 2D solver (the convective acceleration term is dropped, so it does not resolve supercritical shocks), but momentum, depth-dependent conveyance, backwater and wave propagation are all real. Everything below is exactly what the code does.

Momentum: unit discharge across each cell face

Each cell holds a water depth h above its bed z (terrain plus any structure). Between every pair of neighbouring cells the solver carries a unit discharge q (m²/s) that persists from step to step — this is the momentum. Each sub-step it is updated with

q⁺ = [ θ·q + ½(1−θ)(q₋ + q₊) − g·h_f·Δt·∂η/∂x ] / [ 1 + g·Δt·n²·|q| / h_f^7/3 ]

• η = z + h is the water-surface elevation; its gradient across the face drives the flow.
• h_f, the face flow depth, is max(η_i, η_j) − max(z_i, z_j) — so a levee crest higher than the water surface on both sides carries no flow at all, and overtopping depth is what governs flow once it does.
• n is Manning's roughness, averaged across the face: river 0.035, dredged channel 0.025, concrete spillway 0.015, floodplain 0.05, pavement 0.02, built-up town 0.10. Conveyance scales as h^5/3/n, which is why a 3 m flood wave moves an order of magnitude faster than a 10 cm sheet of runoff and why cutting a channel drains a bowl.
• The friction term is semi-implicit (it divides rather than subtracts), which keeps the scheme stable on steep dry hillslopes, and the θ = 0.85 q-centred average of de Almeida et al. (2012) damps grid-scale checkerboarding.

Continuity & conservation

Depths update from the face discharges: Δh = Δt/Δx · (Σ q_in − Σ q_out). Before that, a donor limiter scales every outgoing face of any cell whose scheduled export exceeds what it holds, so depths never go negative and total volume is conserved to floating-point precision — water enters only as rain, inflow or surge and leaves only through infiltration, pumps and the outlet. The time step obeys the CFL condition Δt ≤ 0.7·Δx / √(g·h_max) by sub-stepping whenever the deepest water demands it.

Sources, sinks & boundaries

• Time compression: one game-second is 150 real seconds, so a 180 s scenario is a 7½-hour storm and a flood wave crosses the 7 km valley in a visible half-minute.
• Rain is added as depth every step: (mm/hr ÷ 3.6·10⁶) × real seconds elapsed.
• Off-map watershed runoff: rational-method Q = C·i·A with C = 0.45 over a virtual basin watershedRatio× the visible map (5× by default), lagged through a linear reservoir with a one-hour time constant — the delayed limb of the hydrograph.
• River inflow enters through the channel cells in the top two rows of the map at 1 000 m³/s per scenario inflow unit; Cedar Rapids peaks near 2 600 m³/s, close to the 4 000 m³/s the Cedar River actually delivered in June 2008 scaled to this channel.
• Infiltration is a Green-Ampt-style sink limited by antecedent saturation: taken = min(depth, rate·(1 − saturation)), with rate ≈ 14 mm/hr loam, 29 sand, 5 clay. Pre-wet soil (high AMC in historical scenarios) absorbs far less, so rain wins during a storm.
• Pumps are rated at 45 m³/s (a large municipal flood station), drawn from a 5×5 footprint in proportion to depth; siphons pass 8 m³/s over 3×3 once primed by 10 cm of standing water.
• Downstream boundary: the outlet row is a free outfall discharging at Manning normal depth on the local bed slope. Bowl maps below sea level (Katrina) close the outlet — the only ways out are over the levee or through a pump.
• Storm surge is a stage boundary: the lake rows are held at a prescribed water-surface elevation through the surge hydrograph, and the inertial solver decides what overtops.

Levee stress & overtopping

Levees do not fail on a simple height check — they accumulate stress while overtopped. When any neighbour's water surface exceeds the levee crest, stress builds as stress += dt · rate · (1 + 3·overtopping depth), where rate = 1.0 (0.5 if reinforced), so deeper overtopping fails a levee faster. A breach fires when stress crosses 5 (10 if reinforced); the crest drops 0.5 m and the solver's momentum equation produces the resulting breach wave. When not overtopped, stress relaxes at −0.5·dt. Sandbags erode under real flow velocity (> 1 m/s), not static head. Damage follows HAZUS-style depth–damage curves.

Scenarios are calibrated against published USGS, DWR and USACE post-event reports, but the model stays first-order: treat it as an intuition-builder for routing, storage and levee risk, not as a certified flood forecast.

Built by a practicing water-resources engineer. For the professional versions of this math, see the free open-channel & hydrology calculators at pe-calc.com, or HydroComplete for stormwater design software.

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