In this section, we discuss the model-based PR and intensity changes and synthesize them with the observation-based results already obtained in Section 3.
Model-specific bias-corrected temperature thresholds used to calculate PR are decided as per Section 2.1 using observed return times found in Table 1. For the Siberian region, the ERA5 analysis, which was available for analysis immediately after the event, was used to determine the return time, for which we took the rounded best estimate value of 130 years. For Verkhoyansk, the analysis from the Climate Explorer method was used to determine the return time. Here the best estimate was indeterminate and so the well-defined rounded lower bound of 140 years was used.
For both event definitions, we calculated the PR and intensity values of the event in the observations and the models, using only models that passed the evaluation (Section 4). Model results were synthesized with one another and then with the combined observational results to give an overarching attribution statement, following the same methodology as in Philip et al. (2020a, 2020b) and summarized briefly here. The synthesis confidence limits represent contributions arising in the model results from two sources: finite sampling of ‘weather noise’ within each model and from biases between models, which is here called ‘model spread’ (part of the model uncertainty).
First, the observations were combined by averaging the best estimate, lower and upper bounds, as the natural variability is strongly correlated (both are based on the same observations over 1979–2020). The difference is added as representation uncertainty (white extensions on light blue bars, Fig. 4).
Second, the models were combined by computing a weighted average (using inverse model total variances), as the natural variability in the models, in contrast to the observations, is uncorrelated. However, due to the model spread being larger than expected from variability due to sampling of weather noise alone, a model spread term was added to each model in addition to the weighted average (white extensions on the light red bars, Figs. S5, S6), to account for systematic model errors. For the PR in the Verkhoyansk analysis, we can run into the problem that the 2020 event is often above the upper bound of the probability distribution in 1900. The upper bound is due to the negative shape parameter of the GEV distributions (that always occur for daily heat wave analyses). The value for 2020 being above this upper bound formally means that the event would have been impossible in that climate. This is indicated by ‘inf’ values for the PR (Table S4). The results including this value are not mathematically well defined and so are intended merely to indicate the possibility that the event was physically impossible in a 1900 climate. However, this does depend on the assumptions made in the analysis.
Third, the synthesized results of observations and models are consistent and are therefore combined into a single result in two ways: (i) the model uncertainties beyond the model spread were neglected and the weighted average of models and observations computed (magenta bar, Fig. 4); (ii) as model bias can be larger than model sampling uncertainties, the more conservative estimate of an unweighted average of observations and models was computed (white box around the magenta bar, Fig. 4).
Event in the climate of 2020
The synthesis of 50 ‘good’ models combined with observations shows with confidence that PR for the 6-month prolonged heat in Siberia is large (Fig. 4 (a)), with a lower bound of almost 500 and best estimate around 90,000, making the event virtually impossible in a 1900 climate. All ‘good’ models had lower bounds of the PR estimates well above 1, i.e. there is an agreement that the event probability has increased due to rising regional temperatures. Furthermore, there is a large degree of consistency between observational and model analyses for both PR and changes in intensity. Therefore, we are confident of the overall result. The average of the best estimates of the two observations has a larger shift in intensity (around 3.5 °C) than the model average best estimate (around 2.5 °C), although the longer observational dataset (GISTEMP; 2.9 °C) is closer to the models, and the two observational values are well within each other’s uncertainty estimates (Fig. 4 (c)), so there is no evidence of a recent acceleration of the trend beyond natural variability.
An event like the extreme temperature of 20 June 2020 at Verkhoyansk station has synthesis best estimate PR of 200 million, while still including the possibility of PR < 1 (Table 3, Fig. 4 (b)). The precise value (or even the order of magnitude) of this best estimate is not to be taken seriously given that it incorporates diverging values. Additionally, there is less agreement between models and observations, the latter having an infinite best estimate and upper bound PR and lower bound of 4.5.
These differences are due to the very large uncertainties involved, illustrated by the very wide observational and model 95% confidence intervals. The observational analysis is based on a smaller dataset (a series of length O(100)) than the models (ensembles), and PR estimates will be subject to greater sampling uncertainty, particularly the upper bound of the bootstrapped fitting procedure. This issue, explored recently by Paciorek et al. (2018), provides evidence that our observational confidence intervals for PR may be overestimated. Nevertheless, we do not see a practical alternative means of estimating the confidence intervals in this method, which is based on historical series and transient simulations with potentially strongly correlated estimates of past and present probability distributions.
While the Verkhoyansk PR results are of low confidence, encompassing the possibility of ‘no change’, the synthesized results for the change in intensity do confidently show a positive anthropogenic shift in temperature. The model synthesis intensity change 1.7 °C (0.5–2.9 °C) is consistent with the intensity change from observations of 1.3 °C (0.6–3.0 °C), and the model + observed synthesis value is 1.5 °C (0.8–2.5 °C). We can also see from Fig. S6 and Table S4 that it is mainly the added, conservative model spread component of uncertainty that takes model PR < 1 in most cases and that most individual models in fact confidently give PR > 1. Considering both this and the intensity results therefore increases the confidence that the true value of the PR is indeed above 1.
The weighting used to add model uncertainty in the synthesis makes it possible that models with very large PR are down-weighted unnecessarily by the synthesis algorithm, which assumes log-normal distributions, so that we could expect larger values to be closer to the truth. Removing the weighting for model uncertainty gives a PR > 4600 (using all good models) so that the good models on their own are confident of a very large PR value for June TXx at Verkhoyansk. We conclude that the presence of the upper bound in the station analysis exposes weaknesses in our synthesis methods that make the results even more uncertain than the algorithm itself indicates.
A parallel analysis of 7 SMILE large ensembles was also conducted using a different method to the covariate approach (see SI). Instead, the large ensemble values at 2018–2022 could be used directly in the parametric fit and compared with the same from an earlier epoch (1950–1954). Due to the shorter experiment length, the epoch in the 1950s was chosen as a baseline climate in place of the 1900 baseline used for the rest of the analysis.
The SMILE results, synthesized over the 7 models with the same method above, give a Siberian region PR (2020 to the 1950 baseline) with best estimate (95% confidence limits) of 2000 (700–10,000). For Verkhoyansk, the analysis gives 3.3 (>1.4) although 5 out of the 6 models with results have lower bounds less than unity. For complete results for the individual SMILE models, see Tables S5, S6 and Fig. S7.
These values for both the Siberian region and Verkhoyansk would be even larger still if the analysis could be conducted to the same 1900 baseline as the models using the covariate approach. Using this different method of analysis, we would draw very similar conclusions regarding the change in the likelihood of the regional Siberian heat, and so this provides semi-independent evidence for the near impossibility of this event in the natural world.
Event in the climate of 2050
The best estimate synthesis PR increases by year 2050, compared to 2020, by another 3 to 4 orders of magnitude, although the lower bound of the PR is less than that for 2020 (see Fig. S8). Given that the probabilities of occurrence in the climate of 1900 are extremely small, the uncertainties in PR are so large (due to division by almost zero) that the precise figures are not well defined. What is clear is that the PR will have increased further in 2050. The synthesis change of intensity for 2050 is 4.9 °C (2.4 to 7.3 °C) which is an increase in best estimates of around 1.9 °C over the next 30 years. In other words, a hot spell with a 140-year return time in 2050 would be expected to be about 2 °C warmer than today.
The PR values for 2050 are an order of magnitude or more larger again, at 60,000 (20,000–300,000), repeating the picture of a dramatically increasing probability of occurrence with projected regional temperature rises.