Global warming contributes to changes in local temperature and precipitation distributions. These shifts alter key statistical properties such as the mean, variance, and frequency of severe climate events, making accurate predictions more complex. In this study, we analyze temperature and precipitation data from the National Oceanic and Atmospheric Administration's (NOAA) Twentieth Century Reanalysis Project, covering the period from 1950 to 2015 across the continental United States. We employ the expected shortfall (ES) regression method to examine trends in temperature and precipitation relative to time and El Ni & ntilde;o-Southern Oscillation (ENSO). Unlike quantile regression, which focuses on specific conditional quantiles such as the median, ES provides insights into averages beyond a certain quantile, offering a more comprehensive description of the tails. Our findings reveal notable differences between ES and mean and quantile regression results, highlighting distinct spatial and temporal trends on interannual-to-decadal time scales. Specifi-cally, ES regression captures significant temperature increases over the decadal time scale, especially in the upper tails, across the southern and central United States, which supports the disappearance of "global warming hole" over the recent decades. Additionally, ENSO events, particularly El Ni & ntilde;o, are found to intensify cooling effects in the Gulf Coast region during the winter, particularly for upper tails. The findings demonstrate the usefulness of expected shortfall regression in estimating temperature and precipitation distributions and characterizing changes in the tails.

Observed distributions of atmospheric temperature are non-Gaussian. Therefore, moments beyond variance are necessary in determining the frequency of extreme temperature events. Here we propose a simple kinematic model for atmospheric mid-latitude temperature variability based on symmetric advection from a non-symmetric background temperature profile. We then use this model to derive analytical expressions for the higher order moments of temperature distributions. Our results show that nonzero skewness and kurtosis arise due to the nonlinearity of the time-mean meridional temperature profile. The analytical model matches an idealized Held-Suarez atmospheric model, indicating nonlinearity of time-mean temperature in latitude is the dominant contribution to nonzero skewness and kurtosis in synoptic temperature variations. Model analysis further shows decrease in higher order moments due to climate change come roughly equally from changes in mixing length and changes in the background temperature profiles.

Ensembles of General Circulation Models (GCMs) are the primary tools for investigating climate sensitivity, projecting future climate states, and quantifying uncertainty. GCM ensembles are subject to substantial uncertainty due to model inadequacies, resolution limits, internal variability, and inter-model variability, meaning rigorous climate risk assessments and informed decision-making require reliable and accurate uncertainty quantification (UQ). We introduce conformal ensembles (CE), a new approach to climate UQ that quantifies and constrains projection uncertainty with conformal prediction sets and observational data. CE seamlessly integrates climate model ensembles and observational data across a range of scales to generate statistically rigorous, easy-to-interpret uncertainty estimates. CE can be applied to any climatic variable using any ensemble analysis method and outperforms existing inter-model variability methods in uncertainty quantification across all time horizons and most spatial locations under SSP2-4.5. CE is also computationally efficient, requires minimal assumptions, and is highly robust to the conformity measure. Experiments show that it is effective when conditioning future projections on historical reanalysis data compared with standard ensemble averaging approaches, yielding more physically consistent projections.

Efforts to diagnose the risks of a changing climate often rely on downscaled and bias-corrected climate information, making it important to understand the uncertainties and potential biases of this approach. Here, we perform a variance decomposition to partition uncertainty in global climate projections and quantify the relative importance of downscaling and bias-correction. We analyze simple climate metrics such as annual temperature and precipitation averages, as well as several indices of climate extremes. We find that downscaling and bias-correction often contribute substantial uncertainty to local decision-relevant climate outcomes, though our results are strongly heterogeneous across space, time, and climate metrics. Our results can provide guidance to impact modelers and decision-makers regarding the uncertainties associated with downscaling and bias-correction when performing local-scale analyses, as neglecting to account for these uncertainties may risk overconfidence relative to the full range of possible climate futures.

Large climate model ensembles are the primary tool for robustly projecting future climate states and quantifying projection uncertainty. Despite significant advancements in climate modeling over the past few decades, overall projection certainty has not commensurately decreased with steadily improving model skill. We introduce conformal ensembling, a new approach to uncertainty quantification in climate projections based on conformal inference to reduce projection uncertainty. Unlike traditional methods, conformal ensembling seamlessly integrates climate model ensembles and observational data across a range of scales to generate statistically rigorous, easy-to-interpret uncertainty estimates. It can be applied to any climatic variable using any ensemble analysis method and outperforms existing inter-model variability methods in uncertainty quantification across all time horizons and most spatial locations under SSP2-4.5. Conformal ensembling is also computationally efficient, requires minimal assumptions, and is highly robust to the conformity measure. Experiments show that it is effective when conditioning future projections on historical reanalysis data compared with standard ensemble averaging approaches, yielding more physically consistent projections.

Predicting sea surface temperature (SST) within the El Ni\~no-Southern Oscillation (ENSO) region has been extensively studied due to its significant influence on global temperature and precipitation patterns. Statistical models such as linear inverse model (LIM), analog forecasting (AF), and recurrent neural network (RNN) have been widely used for ENSO prediction, offering flexibility and relatively low computational expense compared to large dynamic models. However, these models have limitations in capturing spatial patterns in SST variability or relying on linear dynamics. Here we present a modified Convolutional Gated Recurrent Unit (ConvGRU) network for the ENSO region spatio-temporal sequence prediction problem, along with the Ni\~no 3.4 index prediction as a down stream task. The proposed ConvGRU network, with an encoder-decoder sequence-to-sequence structure, takes historical SST maps of the Pacific region as input and generates future SST maps for subsequent months within the ENSO region. To evaluate the performance of the ConvGRU network, we trained and tested it using data from multiple large climate models. The results demonstrate that the ConvGRU network significantly improves the predictability of the Ni\~no 3.4 index compared to LIM, AF, and RNN. This improvement is evidenced by extended useful prediction range, higher Pearson correlation, and lower root-mean-square error. The proposed model holds promise for improving our understanding and predicting capabilities of the ENSO phenomenon and can be broadly applicable to other weather and climate prediction scenarios with spatial patterns and teleconnections.

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from rescaling low-resolution climate models. We propose a statistical approach, called NN-GPR, using Gaussian process regression (GPR) with an infinitely wide deep neural network based covariance function. NN-GPR requires no assumptions about the relationships between models, no interpolation to a common grid, no stationarity assumptions, and automatically downscales as part of its prediction algorithm. Model experiments show that NN-GPR can be highly skillful at surface temperature and precipitation forecasting by preserving geospatial signals at multiple scales and capturing inter-annual variability. Our projections particularly show improved accuracy and uncertainty quantification skill in regions of high variability, which allows us to cheaply assess tail behavior at a 0.44$^\circ$/50 km spatial resolution without a regional climate model (RCM). Evaluations on reanalysis data and SSP245 forced climate models show that NN-GPR produces similar, overall climatologies to the model ensemble while better capturing fine scale spatial patterns. Finally, we compare NN-GPR's regional predictions against two RCMs and show that NN-GPR can rival the performance of RCMs using only global model data as input.

Climate conditions affect winter heating demand in areas that experience harsh winters. Skillful energy demand prediction provides useful information that may be a helpful component in ensuring a reliable energy supply, protecting vulnerable populations from cold weather, and reducing excess energy waste. Here, we develop a statistical model that predicts winter seasonal energy consumption over the United Kingdom using a multiple linear regression technique based on multiple sources of climate information from the previous fall season. We take the autumn conditions of Arctic sea-ice concentration, stratospheric circulation, and sea-surface temperature as predictors, which all influence North Atlantic oscillation (NAO) variability as reported in a previous study. The model predicts winter seasonal gas and electricity consumption two months in advance with a statistically significant correlation between the predicted and observed time series. To extend the analysis beyond the relatively short time scale of gas and electricity data availability, we also analyze predictability of an energy demand proxy, heating degree days (HDDs), for which the model also demonstrates skill. The predictability of energy consumption can be attributed to the predictability of the NAO and the significant correlation of energy consumption with surface air temperature, dew point depression, and wind speed. We further found skillful prediction of these surface climate variables and HDDs over many areas where the NAO is influential, implying the predictability of energy demand in these regions. The simple statistical model demonstrates the usefulness of fall climate observations for predicting winter season energy demand prediction with a wide range of potential applications across energy-related sectors.

Since the original publication of this paper, the authors have found an error in their code, which has now been corrected, resulting in a slight change to the results but not in the key outcomes of the study.As described in the Methods subsection 'Future RSLC estimates based on two previous studies,' two different approaches were used to obtain the projections of future relative sea-level change.In the method by Vega-Westhoff et al. (Earth's Future 7, 677-690, 2019), two scenarios that account for the dynamics of ice-sheet melting, labelled as 2 °C+ and 5 °C+ in the paper, are not considered.To circumvent this, the authors imputed the results for 2 °C and 5 °C again, in place of what would have been 2 °C+ and 5 °C+.However, in the initial code used, this imputation was forgotten and NAs ("not available" data) were inadvertently used to produce the results.This caused the rest of the computations, which looked at what specific warming level would cause the higher frequency (a 100-fold change) in extreme sea levels to be triggered, to return NAs.These results were interpreted as the outcome that none of the warming levels considered triggered that specific change in frequency.Note that this is a valid result for some of the gauges used but not for all that were labelled and counted as such in the original results.The authors have now changed the code in the repository and inserted a few lines to perform the imputation described correctly.Owing to this, Figure 1, Table 1 and Extended Data Figure 3 (originals available below in Supplementary information for transparency) were revised to reflect the change in data, as well as the corresponding text that discusses the results in the main article.

Simulation models of multi‐sector systems are increasingly used to understand societal resilience to climate and economic shocks and change. However, multi‐sector systems are also subject to numerous uncertainties that prevent the direct application of simulation models for prediction and planning, particularly when extrapolating past behavior to a nonstationary future. Recent studies have developed a combination of methods to characterize, attribute, and quantify these uncertainties for both single‐ and multi‐sector systems. Here, we review challenges and complications to the idealized goal of fully quantifying all uncertainties in a multi‐sector model and their interactions with policy design as they emerge at different stages of analysis: (a) inference and model calibration; (b) projecting future outcomes; and (c) scenario discovery and identification of risk regimes. We also identify potential methods and research opportunities to help navigate the tradeoffs inherent in uncertainty analyses for complex systems. During this discussion, we provide a classification of uncertainty types and discuss model coupling frameworks to support interdisciplinary collaboration on multi‐sector dynamics (MSD) research. Finally, we conclude with recommendations for best practices to ensure that MSD research can be properly contextualized with respect to the underlying uncertainties.

The Paris agreement focused global climate mitigation policy on limiting global warming to 1.5 or 2 °C above pre-industrial levels. Consequently, projections of hazards and risk are increasingly framed in terms of global warming levels rather than emission scenarios. Here, we use a multimethod approach to describe changes in extreme sea levels driven by changes in mean sea level associated with a wide range of global warming levels, from 1.5 to 5 °C, and for a large number of locations, providing uniform coverage over most of the world’s coastlines. We estimate that by 2100 ~50% of the 7,000+ locations considered will experience the present-day 100-yr extreme-sea-level event at least once a year, even under 1.5 °C of warming, and often well before the end of the century. The tropics appear more sensitive than the Northern high latitudes, where some locations do not see this frequency change even for the highest global warming levels. Combining previous estimates in a multimethod approach, extreme sea levels are assessed under global warming levels of 1.5–5 °C at over 7,000 coastal sites worldwide. By 2100 or before, about 50% of locations exhibit present-day 100-year extreme sea levels at least once per year, even at 1.5 °C of warming.

Efforts to understand and quantify how a changing climate can impact agriculture often rely on bias-corrected and downscaled climate information, making it important to quantify potential biases of this approach. Here, we use a multi-model ensemble of statistically bias-corrected and downscaled climate models, as well as the corresponding parent models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), to drive a statistical panel model of U.S. maize yields that incorporates season-wide measures of temperature and precipitation. We analyze uncertainty in annual yield hindcasts, finding that the CMIP5 models considerably overestimate historical yield variability while the bias-corrected and downscaled versions underestimate the largest weather-induced yield declines. We also find large differences in projected yields and other decision-relevant metrics throughout this century, leaving stakeholders with modeling choices that require navigating trade-offs in resolution, historical accuracy, and projection confidence. Historical annual maize yields in the U.S. are overestimated by CMIP5 models and underestimated by bias-corrected and downscaled models due to differences in temperature and precipitation hindcasts, according to a multi-model ensemble comparison.

The current uncertainty surrounding the Earth's equilibrium climate sensitivity is an important driver for climate hazard projections. While the implications for projected global temperature changes have been extensively studied, the impacts on sea level projections have been relatively unexplored. Here we analyze the relationship between the climate sensitivity and sea level projections, with a particular focus on the high‐impact upper tail. We utilize a Bayesian calibration of key climate and sea level parameters using historical observations and the reduced‐complexity Earth system model, Hector‐BRICK. This methodology allows us to focus on plausible realizations of the climate system in a probabilistic framework. We analyze the effects of high‐end climate sensitivity (above 5 K) on projections and spatial patterns of sea level change. The sea level projections hinge critically on the upper tail of the climate sensitivity, especially for the highly decision‐relevant upper tail. Results have important implications for timing of threshold exceedances and regional variability.