Abstract Climate change projections depend on future climatic conditions and a historical reference period. A key uncertainty in estimating precipitation projections stems from the uncertain net contribution of internal variability to the value of precipitation averaged over the reference period, \: ₁. Here we derive equations that, when used with observational data, climate model output, and Bayes’ Theorem, can estimate this contribution. The resulting estimate depends on how accurately the ensemble mean is assumed to simulate externally forced change (EFC). Solutions are obtained for cases where the ensemble mean is perfectly accurate, and where it under- or overestimates EFC. The method is applied in a Case Study on precipitation change in south-east Australia. If the ensemble accurately simulates EFC from 1900–1999 to 2000–2021 then the CMIP5-based estimate of \: ₁ has a mean of -31. 2 mm, which is -8. 1% of the 2000–2021 multi-model mean precipitation. As this value is larger in magnitude than the projected drying over the entire 21st century under the RCP4. 5 scenario, precipitation will most likely increase relative to 2000–2021, if the EFC is accurately simulated. This contrasts sharply with widespread expectations. The expected change in precipitation relative to 2000–2021 remains positive through to the mid-21st century even if the ensemble mean EFC is inaccurate, provided that the magnitude of the simulated EFC exceeds 50% of its real-world counterpart. These results have significant implications for people who produce, communicate or use projections. Constraining \: ₁ impacts estimates of future change via a process called “ reversion to the mean ”.
Scott B. Power (2026) studied this question.