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Abstract:

The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot temperatures can become. Generalized Extreme Value theory provides a data-driven estimate of extreme thresholds; however, upper bounds may be exceeded by future events, which undermines attribution and planning for heatwave impacts. Here, we show how the occurrence and relative probability of observed yet unprecedented events that exceed a priori upper bound estimates, so-called “impossible” temperatures, has changed over time. We find that many unprecedented events are actually within data-driven upper bounds, but only when using modern spatial statistical methods. Furthermore, there are clear connections between anthropogenic forcing and the “impossibility” of the most extreme temperatures. Robust understanding of heatwave thresholds provides critical information about future record-breaking events and how their extremity relates to historical measurements

Abstract:

An anomalous signal-to-noise ratio (also called the signal-to-noise paradox) present in climate models has been widely reported, affecting predictions and projections from seasonal to centennial timescales and encompassing prediction skill from internal processes and external climate forcing. An anomalous signal-to-noise ratio describes a situation where the mean of a forecast ensemble correlates better with the corresponding verification than with its individual ensemble members. This situation has severe implications for climate science, meaning that large ensembles might be required to extract prediction signals. Although a number of possible physical mechanisms for this paradox have been proposed, none has been universally accepted. From a statistical point of view, an anomalous signal-to-noise ratio indicates that forecast ensemble members are not statistically interchangeable with the verification, and an apparent paradox arises only if such an interchangeability is assumed. It will be demonstrated in this study that an anomalous signal-to-noise ratio is a consequence of the relative magnitudes of the variance of the observations, the ensemble mean, and the error of the ensemble mean. By analysing the geometric triangle formed by these three quantities, and given that for typical seasonal forecasting systems both the correlation and the forecast signal are relatively small, it is concluded that an anomalous signal-to-noise ratio should, in fact, be expected in such circumstances.