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Towards the end of June 2021, temperature records were broken by several degrees Celsius in several cities in the Pacific Northwest areas of the US and Canada, leading to spikes in sudden deaths and sharp increases in emergency calls and hospital visits for heat-related illnesses. Here we present a multi-model, multi-method attribution analysis to investigate the extent to which human-induced climate change has influenced the probability and intensity of extreme heat waves in this region. Based on observations, modelling and a classical statistical approach, the occurrence of a heat wave defined as the maximum daily temperature (TXx) observed in the area 45–52∘ N, 119–123∘ W, was found to be virtually impossible without human-caused climate change. The observed temperatures were so extreme that they lay far outside the range of historical temperature observations. This makes it hard to state with confidence how rare the event was. Using a statistical analysis that assumes that the heat wave is part of the same distribution as previous heat waves in this region led to a first-order estimation of the event frequency of the order of once in 1000 years under current climate conditions. Using this assumption and combining the results from the analysis of climate models and weather observations, we found that such a heat wave event would be at least 150 times less common without human-induced climate change. Also, this heat wave was about 2 ∘C hotter than a 1-in-1000-year heat wave would have been in 1850–1900, when global mean temperatures were 1.2 ∘C cooler than today. Looking into the future, in a world with 2 ∘C of global warming (0.8 ∘C warmer than today), a 1000-year event would be another degree hotter. Our results provide a strong warning: our rapidly warming climate is bringing us into uncharted territory with significant consequences for health, well-being and livelihoods. Adaptation and mitigation are urgently needed to prepare societies for a very different future.

This analysis estimates uncertainty in the NOAA global surface temperature (GST) version 5 (NOAAGlobalTemp v5) product, which consists of sea surface temperature (SST) from the Extended Reconstructed SST version 5 (ERSSTv5) and land surface air temperature (LSAT) from the Global Historical Climatology Network monthly version 4 (GHCNm v4). Total uncertainty in SST and LSAT consists of parametric and reconstruction uncertainties. The parametric uncertainty represents the dependence of SST/LSAT reconstructions on selecting 28 (6) internal parameters of SST (LSAT), and is estimated by a 1000-member ensemble from 1854 to 2016. The reconstruction uncertainty represents the residual error of using a limited number of 140 (65) modes for SST (LSAT). Uncertainty is quantified at the global scale as well as the local grid scale. Uncertainties in SST and LSAT at the local grid scale are larger in the earlier period (1880s–1910s) and during the two world wars due to sparse observations, then decrease in the modern period (1950s–2010s) due to increased data coverage. Uncertainties in SST and LSAT at the global scale are much smaller than those at the local grid scale due to error cancellations by averaging. Uncertainties are smaller in SST than in LSAT due to smaller SST variabilities. Comparisons show that GST and its uncertainty in NOAAGlobalTemp v5 are comparable to those in other internationally recognized GST products. The differences between NOAAGlobalTemp v5 and other GST products are within their uncertainties at the 95% confidence level.

Large temperature spatio-temporal gradients are a common feature of Mediterranean climates. The Portuguese complex topography and coastlines enhances such features, and in a small region large temperature gradients with high interannual variability is detected. In this study, the EURO-CORDEX high-resolution regional climate simulations (0.11° and 0.44° resolutions) are used to investigate the maximum and minimum temperature projections across the twenty-first century according to RCP4.5 and RCP8.5. An additional WRF simulation with even higher resolution (9 km) for RCP8.5 scenario is also examined. All simulations for the historical period (1971–2000) are evaluated against the available station observations and the EURO-CORDEX model results are ranked in order to build multi-model ensembles. In present climate models are able to reproduce the main topography/coast related temperature gradients. Although there are discernible differences between models, most present a cold bias. The multi-model ensembles improve the overall representation of the temperature. The ensembles project a significant increase of the maximum and minimum temperatures in all seasons and scenarios. Maximum increments of 8 °C in summer and autumn and between 2 and 4 °C in winter and spring are projected in RCP8.5. The temperature distributions for all models show a significant increase in the upper tails of the PDFs. In RCP8.5 more than half of the extended summer (MJJAS) has maximum temperatures exceeding the historical 90th percentile and, on average, 60 tropical nights are projected for the end of the century, whilst there are only 7 tropical nights in the historical period. Conversely, the number of cold days almost disappears. The yearly average number of heat waves increases by seven to ninefold by 2100 and the most frequent length rises from 5 to 22 days throughout the twenty-first century. 5% of the longest events will last for more than one month. The amplitude is overwhelming larger, reaching values which are not observed in the historical period. More than half of the heat waves will be stronger than the extreme heat wave of 2003 by the end of the century. The future heatwaves will also enclose larger areas, approximately 100 events in the 2071–2100 period (more than 3 per year) will cover the whole country. The RCP4.5 scenario has in general smaller magnitudes.

We use a methodological framework exploiting the power of large ensembles to evaluate how well ten coupled climate models represent the internal variability and response to external forcings in observed historical surface temperatures. This evaluation framework allows us to directly attribute discrepancies between models and observations to biases in the simulated internal variability or forced response, without relying on assumptions to separate these signals in observations. The largest discrepancies result from the overestimated forced warming in some models during recent decades. In contrast, models do not systematically over- or underestimate internal variability in global mean temperature. On regional scales, all models misrepresent surface temperature variability over the Southern Ocean, while overestimating variability over land-surface areas, such as the Amazon and South Asia, and high-latitude oceans. Our evaluation shows that MPI-GE, followed by GFDL-ESM2M and CESM-LE offer the best global and regional representation of both the internal variability and forced response in observed historical temperatures.

Heat waves such as the one in Europe 2003 have severe consequences for the economy, society, and ecosystems. It is unclear whether temperatures could have exceeded these anomalies even without further climate change. Developing storylines and quantifying the highest possible temperature levels is challenging given the lack of a long homogeneous time series and methodological framework to assess them. Here, we address this challenge by analyzing summer temperatures in a nearly 5000-yr preindustrial climate model simulation, performed with the Community Earth System Model CESM1. To assess how anomalous temperatures could get, we compare storylines generated by three different methods: 1) a return-level estimate, deduced from a generalized extreme value distribution; 2) a regression model, based on dynamic and thermodynamic heat wave drivers; and 3) a novel ensemble boosting method, generating large samples of reinitialized extreme heat waves in the long climate simulation. All methods provide consistent temperature estimates, suggesting that historical exceptional heat waves such as those in Chicago in 1995, Europe in 2003, and Russia in 2010 could have been substantially exceeded even in the absence of further global warming. These estimated unseen heat waves are caused by the same drivers as moderate observed events, but with more anomalous patterns. Moreover, altered contributions of circulation and soil moisture to temperature anomalies include amplified feedbacks in the surface energy budget. The methodological framework of combining different storyline approaches of heat waves with magnitudes beyond the observational record may ultimately contribute to adaptation and to the stress testing of ecosystems or socioeconomic systems to increase resilience to extreme climate stressors.

Equilibrium climate sensitivity—which remains the largest uncertainty in climate projections—is constrained to a ‘likely’ range of 2.2–3.4 K by taking into account the variability of global temperature about long-term historical warming. Narrowing down long-term global warming estimates Equilibrium climate sensitivity (ECS) is the long-term change in global mean surface temperature predicted to occur in response to an instantaneous doubling of atmospheric carbon dioxide concentrations. It is an inherently artificial metric, but is nonetheless an important tool when comparing climate models, and a key point of policy discussion. The seemingly intractable range of ECS estimates complicates policy making because the response of the real climate system to the lowest and highest predicted temperature change would translate into radically different policy options. Peter Cox and colleagues now constrain climate models by their ability to simulate observed variations in climate, and conclude that ECS has a central estimate of 2.8 degrees Celsius (°C), which sits towards the middle to lower end of current estimates, and a range of 2.2–3.4 °C. Importantly, their approach allows them to almost exclude ECS estimates above 4.5 °C or below 1.5 °C. Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO 2 ) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO 2 . Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the ‘likely’ range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5–4.5 degrees Celsius for more than 25 years 1 . The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC ‘likely’ range) of 2.2–3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship 2 between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming 3 , which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.

Preparing for climate change requires an understanding of the degree to which global warming has regional implications. Here we document a strong relationship between the magnitude and extent of warming and explain its origin using a simple model based on binomial statistics. Applied to HadCRUT5 instrumental observations, the model shows that 96% of interannual variability in the proportion of regions experiencing anomalous warmth over the last century can be explained on the basis of the magnitude of global mean surface temperature (GMST) anomalies. The model performs similarly well when applied to a variety of unforced and forced model simulations and represents a general thermodynamic link between global and local warming on annual timescales. Our model predicts that, independent of the baseline that is chosen, 95% of the globe is expected to experience above‐average annual temperatures at 0.7°C of GMST warming, and 99% at 1.0°C of warming. Plain Language Summary Whereas many studies focus on global mean surface temperature (GMST), it is also critical to understand the spatial patterns of this warming in preparing for a warmer world. Using a simple statistical model, we describe a strong relationship between GMST and the spatial extent of above‐average temperature anomalies each year. This relationship is shown to hold across various model simulations and historical temperature data, capturing both annual and decadal trends. We can use our model alongside projections to gain insight into the extent of warming variations. For instance, 1°C GMST warming from a given baseline climate generally corresponds to a world in which 99% of places across the globe will be anomalously warm every year. Key Points A simple statistical model relates the proportion of Earth's area that is anomalously warm to global mean surface temperature (GMST) The model predicts 96% of the interannual variance in the proportion of anomalous warmth between 1900 and 2021 on the basis of GMST 1.0°C of GMST warming corresponds to 99% of the globe being anomalously warm, independent of baseline

Historical temperature measurements are the basis of global climate datasets like HadCRUT4. This dataset contains many missing values, particularly for periods before the mid-twentieth century, although recent years are also incomplete. Here we demonstrate that artificial intelligence can skilfully fill these observational gaps when combined with numerical climate model data. We show that recently developed image inpainting techniques perform accurate monthly reconstructions via transfer learning using either 20CR (Twentieth-Century Reanalysis) or the CMIP5 (Coupled Model Intercomparison Project Phase 5) experiments. The resulting global annual mean temperature time series exhibit high Pearson correlation coefficients (≥0.9941) and low root mean squared errors (≤0.0547 °C) as compared with the original data. These techniques also provide advantages relative to state-of-the-art kriging interpolation and principal component analysis-based infilling. When applied to HadCRUT4, our method restores a missing spatial pattern of the documented El Niño from July 1877. With respect to the global mean temperature time series, a HadCRUT4 reconstruction by our method points to a cooler nineteenth century, a less apparent hiatus in the twenty-first century, an even warmer 2016 being the warmest year on record and a stronger global trend between 1850 and 2018 relative to previous estimates. We propose image inpainting as an approach to reconstruct missing climate information and thereby reduce uncertainties and biases in climate records.An artificial intelligence-based method may infill gaps in historical temperature data more effectively than conventional techniques. Application of this method reveals a stronger global warming trend between 1850 and 2018 than estimated previously.

Lake ecosystems are jeopardized by the impacts of climate change on ice seasonality and water temperatures. Yet historical simulations have not been used to formally attribute changes in lake ice and temperature to anthropogenic drivers. In addition, future projections of these properties are limited to individual lakes or global simulations from single lake models. Here we uncover the human imprint on lakes worldwide using hindcasts and projections from five lake models. Reanalysed trends in lake temperature and ice cover in recent decades are extremely unlikely to be explained by pre-industrial climate variability alone. Ice-cover trends in reanalysis are consistent with lake model simulations under historical conditions, providing attribution of lake changes to anthropogenic climate change. Moreover, lake temperature, ice thickness and duration scale robustly with global mean air temperature across future climate scenarios (+0.9 °C °C air –1 , –0.033 m °C air –1 and –9.7 d °C air –1 , respectively). These impacts would profoundly alter the functioning of lake ecosystems and the services they provide. Anthropogenic climate change is impacting the temperature and ice cover of lakes across the globe, according to an attribution analysis based on hindcasts and projections from lake models.

Dengue is a mosquito-borne viral disease that occurs mainly in the tropics and subtropics but has a high potential to spread to new areas. Dengue infections are climate sensitive, so it is important to better understand how changing climate factors affect the potential for geographic spread and future dengue epidemics. Vectorial capacity (VC) describes a vector's propensity to transmit dengue taking into account human, virus, and vector interactions. VC is highly temperature dependent, but most dengue models only take mean temperature values into account. Recent evidence shows that diurnal temperature range (DTR) plays an important role in influencing the behavior of the primary dengue vector Aedes aegypti. In this study, we used relative VC to estimate dengue epidemic potential (DEP) based on the temperature and DTR dependence of the parameters of A. aegypti. We found a strong temperature dependence of DEP; it peaked at a mean temperature of 29.3°C when DTR was 0°C and at 20°C when DTR was 20°C. Increasing average temperatures up to 29°C led to an increased DEP, but temperatures above 29°C reduced DEP. In tropical areas where the mean temperatures are close to 29°C, a small DTR increased DEP while a large DTR reduced it. In cold to temperate or extremely hot climates where the mean temperatures are far from 29°C, increasing DTR was associated with increasing DEP. Incorporating these findings using historical and predicted temperature and DTR over a two hundred year period (1901-2099), we found an increasing trend of global DEP in temperate regions. Small increases in DEP were observed over the last 100 years and large increases are expected by the end of this century in temperate Northern Hemisphere regions using climate change projections. These findings illustrate the importance of including DTR when mapping DEP based on VC.