Industry: Government and Public Sector
Product: ModelRisk
Application: Infrastructure planning

A Water Scheme Sized for 628 ML/Day Has a 47% Chance of Running Out

The business case for the new regional water scheme rested on a single number. At the agency's 1.35% long-run demand-growth assumption, peak demand 30 years out projected to 628 ML/day — comfortably inside the proposed 640 ML/day design capacity. On paper the scheme was right-sized with headroom to spare, and the deterministic plan never breached capacity within the planning horizon. Then the planners rebuilt the demand forecast in ModelRisk and the picture inverted: 47% of simulated futures exceeded the 640 ML/day capacity before the design year, with the median breach arriving in year 22. The single-line forecast had hidden a near-coin-flip risk of building a scheme that runs out of water inside its design life.

Why a point estimate is the wrong tool for capacity sizing

Capacity decisions are bets on a long-horizon demand path, and the deterministic plan compounds one growth rate forward for 30 years. That is not a forecast — it is the centre of a forecast, with all the dispersion stripped out. The real question a capacity planner faces is not "what is the expected demand in year 30?" but "across the plausible range of growth futures, how often does this much capacity run out, and when?" Only a distribution answers that, and only the distribution tells you how much extra capacity buys how much extra security.

Where the demand path actually lives

Demand is modelled as a 30-year compounding path starting from today's 420 ML/day. The engine of the uncertainty is a shared long-run growth regime: a single Normal draw per trial (mean 1.35%/yr, standard deviation 0.7 percentage points) that sets the drift for every year of that trial's path. On top of the regime sits small independent annual noise (2% per-year usage wobble from weather, tariffs and conservation campaigns) that does not persist.

That shared regime is the modelling decision that matters. Population and economic activity in a region are persistent — a high-growth decade tends to stay high-growth — so a planner cannot treat each year's growth as an independent draw. If you do, the 30 annual shocks average out and the year-30 forecast collapses toward its mean (the central-limit trap). With the shared regime in place, the year-10 and year-30 demand within a path correlate at 0.83, and the spread of year-30 peak demand is 2.1× wider than the naive independent-year model produces. That extra spread is the entire risk story.

The resulting year-30 peak demand runs mean 642 ML/day, P10 463, P50 625, and P90 843 ML/day — a fan that quietly straddles the 640 ML/day design line the deterministic plan sat just beneath.

The deterministic dashed line tracks neatly below capacity to the design year. The P10–P90 band tells the real story: the upper half of the cone crosses the capacity line years before the horizon ends.

When the scheme runs out of headroom

Of the futures that breach the 640 ML/day capacity, the first-breach year is itself a distribution. The earliest simulated breach lands in year 8; the P10 is year 16, the median year 22. In other words, when this scheme fails to keep up, it does not fail gracefully at the very end of its life — a meaningful slice of futures exhausts its headroom less than two-thirds of the way through the horizon, while the city is still mid-build-out on everything that depends on it.

Right-sizing: how much capacity buys how much security

The decision is not "640 or not" — it is a sizing dial. Sweeping the design capacity from 600 to 900 ML/day and reading off the breach probability turns the abstract trade-off into a procurement curve.

At the proposed 640 ML/day, the breach probability is 47%. Stepping up: 720 ML/day → 28%, 800 ML/day → 15%, and reaching the agency's 10% "one-in-ten-horizons" service standard requires roughly 844 ML/day — about a third more capacity than the original business case. The curve also shows diminishing returns above ~850 ML/day, where each additional 50 ML/day shaves only a couple of points off the breach probability. That is the inflection a procurement committee needs to argue about, and it does not exist on a single-point forecast.

What actually drives the year-30 peak

A tornado on the P90 year-30 peak demand ranks the inputs the sizing decision depends on.

The two halves of the growth regime dominate: the long-run growth-rate mean moves the P90 demand by ±112 ML/day across its plausible range, and the uncertainty about that rate (the regime standard deviation) moves it by almost as much, ±100 ML/day. Starting-demand metering error (±39 ML/day) and annual weather/tariff noise (±21 ML/day) are second-order. The lesson for the agency is concrete: a year of demographic study to tighten the growth-rate estimate shifts the sizing decision far more than refining any operational input — because it is the spread of the regime, not the annual wobble, that determines how much capacity the scheme needs.

What the model changed

• The design capacity was revised upward from 640 to roughly 845 ML/day to meet the 10% service standard, with the breach-probability curve — not a single forecast — as the justification put to the funding board.
• A staged-augmentation option was costed instead of building the full capacity on day one: build to 720 ML/day, hold a pre-approved expansion to 850 ML/day, and trigger it on observed demand. The exceedance-year distribution (P10 breach in year 16) set the earliest date the trigger could realistically be needed and therefore the lead-time the option had to preserve.
• Demographic data collection was funded ahead of detailed design, because the tornado showed growth-regime uncertainty — not operational inputs — was the largest single mover of the sizing decision.

ModelRisk Functionality Used

• Compounding demand paths with a shared growth regime — one Normal draw per trial propagated across all 30 years, reproducing the 0.83 year-10/year-30 demand correlation that a naive independent-year model washes out (and the 2.1× wider tail it produces).
• Capacity-sweep simulation — re-evaluating the breach probability across 31 candidate capacities to draw the right-sizing curve and locate the 844 ML/day point that meets the 10% service standard.
• First-exceedance timing — extracting the distribution of the year capacity is first breached (earliest year 8, median year 22) to set the lead-time for a staged-augmentation trigger.
• Tornado sensitivity — ranking the four sizing drivers and identifying growth-regime uncertainty (±100 ML/day) as a top-two mover, redirecting the pre-design budget toward demographic study.

For infrastructure capacity, the design figure is not a number — it is a tail probability. ModelRisk turns "the forecast says we're fine" into "we're fine 53% of the time, and here is what it costs to be fine 90% of the time."