Industry: Environmental Product: ModelRisk Application: Climate change impact analysis
A coastal city with $43bn of exposed assets across five districts wants to know what climate change will cost it in flood damage by 2050. The consultancy runs its best-estimate scenario — central warming, central sea-level rise, central surge — and reports an expected annual damage of $9.3bn. City planners take that figure into the capital programme and size the flood defences against it.
The problem is that a single year of climate damage is nothing like its average. Run 2050 eighty thousand times in ModelRisk — drawing a warming level from a scenario-weighted mixture, mapping it through the storm-tide hazard, and pushing that through a convex depth-damage curve for each district — and the expected annual damage is $9.55bn, close to the central case. But the median year costs only $8.31bn, while the P90 is $19.66bn, the P95 is $22.60bn, and the P99 is $27.90bn. There is a 92% chance of exceeding a $1bn loss in any single year, and roughly one year in a hundred wipes out two-thirds of the entire asset base. Defences scaled to the $9.3bn average are, by construction, overwhelmed in exactly the years that matter.
Flood damage is convex in hazard: a water level a metre over a defence crest does far more than twice the damage of half a metre over, because depth-damage curves steepen and more assets come into play at once. Run a convex function at the average hazard and you get a number well below the average of the function — the central-case $9.3bn systematically understates the expected damage, and says nothing at all about the tail where the convexity bites hardest.
The second trap is to treat the five districts as independent and let their damages average away. They do not, because a flood is a city-wide event. The model draws one warming level per simulated year — the shared common factor — and that single draw raises sea level and surge intensity for every district simultaneously. A hot-tail year floods the port, downtown, the residential south and the transport corridor together. Holding back only a small idiosyncratic term for local defence condition, the model preserves this co-movement: the Spearman correlation between the port and downtown district damages is 0.95 under the shared hazard, against 0.00 when the hazard is shuffled to break the link. That correlation is what builds the fat aggregate tail; independence would have smeared the catastrophe years into a comfortable, and wrong, bell curve.
Because warming is the common factor, the emissions pathway does not just nudge the average — it relocates the entire damage distribution.
Under a low-emissions future the expected annual damage is $5.53bn with a P95 of $16.85bn and an 81% chance of breaching $1bn in a year. Under middle-of-the-road emissions that rises to a $9.22bn mean, a $21.06bn P95 and a 96% breach probability. Under high emissions the mean reaches $15.00bn, the P95 $26.23bn, and the city breaches $1bn in essentially every year (100%). The gap between the curves is the value of mitigation, expressed in the currency planners understand — avoided damage — and it is far larger than any single central-case number conveyed.
Sweeping each lever across its range, the warming level dominates at ±$5.61bn of expected annual damage around the baseline. The two physical responses to warming follow — defence crest height at ±$3.91bn (a reminder that the city's own engineering, not just the climate, sets the loss) and storm-surge intensification at ±$3.70bn — while the sea-level-rise response contributes ±$1.82bn. The ranking is a budgeting instruction: warming is exogenous and must be planned around, but crest height is the largest controllable driver, so raising defences competes directly with the hazard itself.
For sizing reserves and reinsurance, planners need the exceedance curve, not a single expected value.
At the $1bn loss level the probability of a breach in any year runs from 81% under low emissions to 100% under high emissions. Read at higher loss levels, the two curves fan apart: the high-emissions world keeps a meaningful probability of multi-billion-dollar years long after the low-emissions curve has fallen away. This is the curve a city sizes a catastrophe reserve against — and it makes plain that the reserve adequate for a low-emissions future is far too small for a high-emissions one.
A year of climate impact is not its average, it is a convex, correlated distribution with a heavy tail. ModelRisk is what lets a city plan against the loss years instead of against the loss it expects in a typical year.