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Abstract Earth’s energy imbalance (EEI) is a fundamental metric of global Earth system change, quantifying the cumulative impact of natural and anthropogenic radiative forcings and feedback. To date, the most precise measurements of EEI change are obtained through radiometric observations at the top of the atmosphere (TOA), while the quantification of EEI absolute magnitude is facilitated through heat inventory analysis, where ~ 90% of heat uptake manifests as an increase in ocean heat content (OHC). Various international groups provide OHC datasets derived from in situ and satellite observations, as well as from reanalyses ingesting many available observations. The WCRP formed the GEWEX-EEI Assessment Working Group to better understand discrepancies, uncertainties and reconcile current knowledge of EEI magnitude, variability and trends. Here, 21 OHC datasets and ocean heat uptake (OHU) rates are intercompared, providing OHU estimates ranging between 0.40 ± 0.12 and 0.96 ± 0.08 W m⁻²(2005–2019), a spread that is slightly reduced when unequal ocean sampling is accounted for, and that is largely attributable to differing source data, mapping methods and quality control procedures. The rate of increase in OHU varies substantially between − 0.03 ± 0.13 (reanalysis product) and 1.1 ± 0.6 W m⁻² dec⁻¹(satellite product). Products that either more regularly observe (satellites) or fill in situ data-sparse regions based on additional physical knowledge (some reanalysis and hybrid products) tend to track radiometric EEI variability better than purely in situ-based OHC products. This paper also examines zonal trends in TOA radiative fluxes and the impact of data gaps on trend estimates. The GEWEX-EEI community aims to refine their assessment studies, to forge a path toward best practices, e.g., in uncertainty quantification, and to formulate recommendations for future activities. 

Abstract Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-level spectrum from smeared detector-level data. For computational and practical reasons, these spaces are typically discretized using histograms, and the smearing is modeled through a response matrix corresponding to a discretized smearing kernel of the particle detector. This response matrix depends on the unknown shape of the true spectrum, leading to a fundamental systematic uncertainty in the unfolding problem. To handle the ill-posed nature of the problem, common approaches regularize the problem either directly via methods such as Tikhonov regularization, or implicitly by using wide-bins in the true space that match the resolution of the detector. Unfortunately, both of these methods lead to a non-trivial bias in the unfolded estimator, thereby hampering frequentist coverage guarantees for confidence intervals constructed from these methods. We propose two new approaches to addressing the bias in the wide-bin setting through methods called One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB intervals are a bin-wise modification of an existing guaranteed-coverage procedure, while the PO intervals are based on a decision-theoretic view of the problem. Importantly, both approaches provide well-calibrated frequentist confidence intervals even in constrained and rank-deficient settings. These methods are built upon a more general answer to the wide-bin bias problem, involving unfolding with fine bins first, followed by constructing confidence intervals for linear functionals of the fine-bin counts. We test and compare these methods to other available methodologies in a wide-bin deconvolution example and a realistic particle physics simulation of unfolding a steeply falling particle spectrum. 

Abstract Atmospheric aerosols influence the Earth’s climate, primarily by affecting cloud formation and scattering visible radiation. However, aerosol-related physical processes in climate simulations are highly uncertain. Constraining these processes could help improve model-based climate predictions. We propose a scalable statistical framework for constraining the parameters of expensive climate models by comparing model outputs with observations. Using the C3.AI Suite, a cloud computing platform, we use a perturbed parameter ensemble of the UKESM1 climate model to efficiently train a surrogate model. A method for estimating a data-driven model discrepancy term is described. The strict bounds method is applied to quantify parametric uncertainty in a principled way. We demonstrate the scalability of this framework with 2 weeks’ worth of simulated aerosol optical depth data over the South Atlantic and Central African region, written from the model every 3 hr and matched in time to twice-daily MODIS satellite observations. When constraining the model using real satellite observations, we establish constraints on combinations of two model parameters using much higher time-resolution outputs from the climate model than previous studies. This result suggests that within the limits imposed by an imperfect climate model, potentially very powerful constraints may be achieved when our framework is scaled to the analysis of more observations and for longer time periods.