Industry: Environmental Product: ModelRisk Application: Quantifying uncertainty in renewable energy adoption
A national energy-policy advisory group built its 2040 strategy on a single adoption curve: the renewable share of generation would climb from today's 22% along a tidy s-curve and reach about 69% by 2040, comfortably clearing the legislated 60% target. That one curve underpinned grid-investment sequencing, fossil-retirement schedules and the emissions trajectory submitted to parliament. The problem is that adoption of a generation technology across a whole market is not a curve -- it is a fan. How high the share ultimately settles, how steep the climb is, and when it inflects all depend on a carbon-price and technology-cost regime nobody can pin to a point.
The team rebuilt the forecast in ModelRisk as a logistic uptake model with an uncertain ceiling, growth rate and inflection year, plus a persistent policy/LCOE regime that shifts the whole trajectory. The first output was not a date and not a single share -- it was the distribution below, and a probability the single curve could never produce.
The deterministic plan put the 2040 share at 68.6%. The simulation agreed on the centre -- simulated P50 = 66.6% -- but opened a band the single curve hid: P10 = 54.6% to P90 = 78.6%. And against the 60% legislated target, that band carries a verdict the point estimate suppressed: there is only a 75.3% probability the target is met by 2040 -- a one-in-four chance of a public miss.
A logistic adoption curve has three parameters, and a deterministic forecast freezes all three. The ultimate achievable share L is capped by grid-firming and dispatchability limits, not by ambition. The steepness k sets how fast the market converts once it tips. The inflection year t0 sets when that tipping happens. Pick central values for all three and you get one smooth s-curve that looks authoritative and hides every risk. In reality the three are coupled by a single force: a supportive decade -- rising carbon prices, falling solar and storage costs, stable subsidy regimes -- steepens k and pulls t0 forward together, while a stalled-policy decade flattens and delays both. The model draws that persistent regime once per path and lets it move k and t0 coherently, so multi-year share keeps its spread instead of averaging back to the mean. The check confirms the coupling: the regime correlates +0.42 with the 2040 share, and steepness k correlates -0.26 with the inflection year -- supportive decades go faster and earlier.
Plotting the 2040 share distribution against the 60% line turns a planning assumption into a probability.
With a median of 66.6% and a P10 of 54.6%, a meaningful slice of the distribution sits below the line: the probability of meeting the 60% target is 75.3%. The deterministic 68.6% looked safely clear -- but it could not say how often the target is missed, and it is the 24.7% miss probability, not the central case, that should size the policy contingency and the fossil-retirement hedge.
The sequencing question is timing: by which year is the target more likely than not to have been met? Sweeping the cumulative probability that the share has reached 60% by each year answers it directly.
The probability of having met the target reaches 50% only at 2038, and by 2040 it stands at 75.3% -- it never reaches certainty within the horizon. In 24.7% of paths the share is still short of 60% at 2040. That late, uncertain crossing is what argues for front-loading the policy levers that steepen the curve rather than assuming the legislated date takes care of itself.
If the band on the 2040 share is what creates policy risk, the follow-up is which input drives that band. The tornado ranks the one-at-a-time P10-to-P90 swing of each input on the 2040 share.
The ultimate achievable share L moves the 2040 outcome by 19.4 percentage points across its range -- the largest single driver -- ahead of the adoption steepness k at 10.5 points and the persistent policy/LCOE regime at 10.4 points, with the inflection year at 9.3 points. The re-ranking is the actionable finding: the most valuable thing the advisory group can do to narrow the forecast is to resolve how high the grid can ultimately absorb renewables -- the firming and dispatchability ceiling -- rather than refining the early-adoption timing the deterministic model fixated on.
For a generation technology, market adoption is not a curve, it is a fan -- and the decision that matters, whether the legislated target will actually be met, lives in the one-in-four miss probability the single s-curve was never able to show.