A brief exploration of S-curves: forecasting global energy transition pathways

Thesis

A fast transition from fossil fuels to renewables is important to minimise further global warming, yet energy forecasts have systematically underestimated the technologies most critical to decarbonisation. This thesis asks: How can S-curves be used to better understand and forecast technological change? It comprises three papers that identify biases in standard S-curve estimation, develop a Bayesian forecasting framework grounded in empirical diffusion regularities, and apply the framework to assess the probability of energy transition scenarios in the IPCC AR6 report.

The first paper characterises the downward bias in S-curve asymptote estimates under standard fitting techniques. The bias can persist even when 30% of the curve is observed, and estimates exhibit high variance. We develop a parametric bootstrap debiasing method that leverages approximately unbiased growth and noise parameter estimates to correct the bias. Applied to electric vehicle and solar PV adoption data, the debiased estimates indicate continued sustained growth trajectories.

The second paper compiles 120 historical growth trajectories spanning centuries of technology adoption and shows that diffusion is systematically asymmetric. The Bertalanffy–Richards curve with β ≈ 2/3 provides superior out-of-sample fit, explaining nearly 95% of variance across technologies. These cross-technological regularities enable a technology-agnostic Bayesian forecasting framework whose distributional forecasts are well-calibrated. Applied to renewables, the framework forecasts that global solar PV will reach a median of roughly 80 PWh per year by 2050 (90% prediction interval 13–470 PWh), comparable to all the useful energy the world consumes today, surpassing nearly all IPCC AR6 scenarios and the International Energy Agency (IEA) net-zero by 2050 scenario. The wind forecast (median ∼ 5 PWh per year, 90% prediction interval 4–17 PWh) falls below many AR6 targets.

The third paper exploits a complementarity between empirically grounded forecasts and integrated assessment model (IAM) scenarios: scenarios explore what policy could achieve, while S-curve forecasts assess what historical diffusion trends suggest. The AR6 ensemble over-represents scenarios with low solar growth relative to our forecasts. Under trajectories consistent with observed diffusion patterns, warming at net-zero is likely limited to below 2◦C, with rapid electrification and a significant decline in fossil fuel share by 2050. The median net-zero year is 2068, with a 10% probability of reaching net-zero before 2050.

Taken together, the thesis demonstrates that technologies exhibit some remarkable regularities, and one can use S-curves to forecast them. Combining such forecasts with appropriate statistical methods provides a powerful empirical benchmark against which scenarios can be transparently evaluated.

Authors: Wagenvoort, BP

• DOI: 10.5287/ora-j0pdaqvj5
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: probabilistic forecasting; S-curves; technology diffusion; net-zero; energy transition
• Subjects: Energy transition; Time-series analysis; Environmental economics; Technological innovations