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Broadband (spectrally‐integrated) radiation calculations are dominated by the expense of spectral integration, and many applications require fast parameterizations for computing radiative flux. Here we describe a novel approach using a linear weighted sum of monochromatic calculations at a small set of optimally‐chosen frequencies. The empirically‐optimized quadrature method is used to compute atmospheric boundary fluxes, net flux profiles throughout the atmosphere, heating rate profiles, and top‐of‐the‐atmosphere forcing by CO2, in the longwave for clear skies. We evaluate the method against two modern correlated k‐distribution models and find that we can achieve comparable errors with 32 spectral points. We also examine the effect of minimizing different cost functions, and find that in order to accurately represent heating rates and CO2 forcing, these quantities must be included in the cost function. Plain Language Summary: Quantifying the way radiation flows through the atmosphere is computationally expensive, and most applications require fast approximation. In this paper, we develop an empirically‐optimized quadrature method that can compute quantities of interest in climate science and weather prediction such as radiative flux throughout the atmosphere, heating rates, and forcing by carbon dioxide. The method uses a simple optimization algorithm, combined with a linear model, to achieve accuracy and computational cost of similar order of magnitude to the modern correlated k‐distribution models. Depending on the focus of the application, the algorithm can easily be adapted to prioritize desired quantities. Key Points: Spectrally integrated radiative quantities can be estimated from a small weighted set of monochromatic calculationsTradeoffs between computational cost and accuracy are commensurate with correlated k‐distribution modelsOptimization priorities can be tailored to a specific applications [ABSTRACT FROM AUTHOR]

Atmospheric inversions provide estimates of carbon dioxide (CO2) fluxes between the surface and atmosphere based on atmospheric CO2 concentration observations. The number of CO2 observations is projected to increase severalfold in the next decades from expanding in situ networks and next‐generation CO2‐observing satellites, providing both an opportunity and a challenge for inversions. This study introduces the TRACE Regional Atmosphere–Carbon Ensemble (TRACE) system, which employ an ensemble‐based simultaneous state and parameter estimation (ESSPE) approach to enable the assimilation of large volumes of observations for constraining CO2 flux parameters. TRACE uses an online full‐physics mesoscale atmospheric model and assimilates observations serially in a coupled atmosphere–carbon ensemble Kalman filter. The data assimilation system was tested in a series of observing system simulation experiments using in situ observations for a regional domain over North America in summer. Under ideal conditions with known prior flux parameter error covariances, TRACE reduced the error in domain‐integrated monthly CO2 fluxes by about 97% relative to the prior flux errors. In a more realistic scenario with unknown prior flux error statistics, the corresponding relative error reductions ranged from 80.6% to 88.5% depending on the specification of prior flux parameter error correlations. For regionally integrated fluxes on a spatial scale of 106 km2, the sum of absolute errors was reduced by 34.5%–50.9% relative to the prior flux errors. Moreover, TRACE produced posterior uncertainty estimates that were consistent with the true errors. These initial experiments show that the ESSPE approach in TRACE provides a promising method for advancing CO2 inversion techniques. Plain Language Summary: To gain a better understanding of the main drivers behind atmospheric carbon dioxide (CO2) variations and trends, it is essential to accurately quantify CO2 exchanges—also known as fluxes—between the atmosphere and other components of the Earth system. It is generally not possible to directly measure surface CO2 fluxes at regional scales; however, fluxes can be inferred from a network of atmospheric CO2 concentration observations combined with atmospheric modeling and inversion methods, which seek to find the most likely fluxes given prior knowledge and observational evidence. This paper presents a new regional inversion framework called TRACE Regional Atmosphere–Carbon Ensemble (TRACE) for deriving CO2 fluxes at high resolution in space and time. One of the major innovations in TRACE is the ensemble‐based dual state and parameter estimation approach, which makes it computationally feasible to ingest large volumes of observations into the system. A series of experiments were carried out in a domain over North America to test the new framework in a controlled setting. In the experiments, we used synthetic tower observations of atmospheric CO2 concentrations to constrain parameters controlling terrestrial biogenic and oceanic CO2 fluxes. The results show that TRACE is capable of accurately estimating both the magnitude and spatial pattern of regional CO2 fluxes. Key Points: An ensemble‐based simultaneous state and parameter estimation approach is introduced for regional CO2 flux inversionsThe new dual‐state TRACE Regional Atmosphere–Carbon Ensemble (TRACE) framework provides a flexible platform for conducting coupled atmosphere–carbon data assimilationControlled experiments show that TRACE is effective at constraining regional CO2 fluxes using in situ CO2 concentration observations [ABSTRACT FROM AUTHOR]

This work documents version two of the Department of Energy's Energy Exascale Earth System Model (E3SM). E3SMv2 is a significant evolution from its predecessor E3SMv1, resulting in a model that is nearly twice as fast and with a simulated climate that is improved in many metrics. We describe the physical climate model in its lower horizontal resolution configuration consisting of 110 km atmosphere, 165 km land, 0.5° river routing model, and an ocean and sea ice with mesh spacing varying between 60 km in the mid‐latitudes and 30 km at the equator and poles. The model performance is evaluated with Coupled Model Intercomparison Project Phase 6 Diagnosis, Evaluation, and Characterization of Klima simulations augmented with historical simulations as well as simulations to evaluate impacts of different forcing agents. The simulated climate has many realistic features of the climate system, with notable improvements in clouds and precipitation compared to E3SMv1. E3SMv1 suffered from an excessively high equilibrium climate sensitivity (ECS) of 5.3 K. In E3SMv2, ECS is reduced to 4.0 K which is now within the plausible range based on a recent World Climate Research Program assessment. However, a number of important biases remain including a weak Atlantic Meridional Overturning Circulation, deficiencies in the characteristics and spectral distribution of tropical atmospheric variability, and a significant underestimation of the observed warming in the second half of the historical period. An analysis of single‐forcing simulations indicates that correcting the historical temperature bias would require a substantial reduction in the magnitude of the aerosol‐related forcing. Plain Language Summary: The U.S. Department of Energy recently released version two of its Energy Exascale Earth System Model (E3SM). E3SMv2 experienced a significant evolution in many of its model components (most notably the atmosphere and sea ice models), and its supporting software infrastructure. In this work, we document the computational performance of E3SMv2 and analyze its ability to reproduce the observed climate. To accomplish this, we utilize the standard Diagnosis and Evaluation and Characterization of Klima experiments augmented with historical simulations for the period 1850–2015. We find that E3SMv2 is nearly twice as fast as its predecessor and more accurately reproduces the observed climate in a number of metrics, most notably clouds and precipitation. We also find that the model's simulated response to increasing carbon dioxide (the equilibrium climate sensitivity) is much more realistic. Unfortunately, E3SMv2 underestimates the global mean surface temperature compared to observations during the second half of historical period. Using sensitivity experiments, where forcing agents (carbon dioxide, aerosols) are selectively disabled in the model, we determine that correcting this problem would require a strong reduction in the impact of aerosols. Key Points: E3SMv2 is nearly twice as fast as E3SMv1 with a simulated climate that is improved in many metrics (e.g., precipitation and clouds)Climate sensitivity is substantially lower with a more plausible equilibrium climate sensitivity of 4.0 K (compared to an unlikely value of 5.3 K in E3SMv1)E3SMv2 underestimates the warming in the late historical period due to excessive aerosol‐related forcing [ABSTRACT FROM AUTHOR]

The ocean reduces human impacts on global climate by absorbing and sequestering CO2 from the atmosphere. To quantify global, time‐resolved air‐sea CO2 fluxes, surface ocean pCO2 is needed. A common approach for estimating full‐coverage pCO2 is to train a machine learning algorithm on sparse in situ pCO2 data and associated physical and biogeochemical observations. Though these associated variables have understood relationships to pCO2, it is often unclear how they drive pCO2 outputs. Here, we make two advances that enhance connections between physical understanding and reconstructed pCO2. First, we apply pre‐processing to the pCO2 data to remove the direct effect of temperature. This enhances the biogeochemical/physical component of pCO2 in the target variable and reduces the complexity that the machine learning must disentangle. Second, we demonstrate that the resulting algorithm has physically understandable connections between input data and the output biogeochemical/physical component of pCO2. The final pCO2 reconstruction agrees modestly better with independent data than most other approaches. Uncertainties in the reconstructed pCO2 and impacts on the estimated CO2 fluxes are quantified. Uncertainty in piston velocity drives substantial flux uncertainties in some regions, but does not increase globally integrated estimates of uncertainty in CO2 fluxes from observation‐based products. Our reconstructed CO2 fluxes show larger interannual variability than smoother neural network approaches, but a lesser trend since 2005. We estimate an air‐sea flux of −1.8 PgC/yr (anthropogenic flux of −2.3 ± 0.5 PgC/yr) for 1990–2019, agreeing with other data products and the Global Carbon Budget 2020 (−2.3 ± 0.4 PgC/yr). Plain Language Summary: The ocean absorbs carbon dioxide from the atmosphere, moderating the human impact on Earth's climate. To quantify how much carbon dioxide is removed from the atmosphere each year, we must know how much gas is exchanged at each location across the ocean over time. The observations necessary to quantify this gas exchange are very sparse and require gap‐filling in both space and time. Because of the heterogeneity of this gas exchange, complex relationships between the ocean observations with near global coverage and ocean carbon are determined using machine learning algorithms and other statistical techniques. A concern is that these statistical algorithms do not require inputs to be linked to outputs in a manner consistent with ocean carbon cycle process understanding. Here, we develop a novel machine learning approach that starts by removing known physical signals from the data to create a cleaner signal for the computer algorithm to learn. Additional analysis demonstrates appropriate mechanistic links between algorithm inputs and outputs. Key Points: A new approach for pCO2 reconstruction applies pre‐processing to remove the direct effect of temperature, simplifying the target variable for machine learningReconstructed pCO2 captures independent data more closely than most existing productsEstimated ocean carbon uptake has a trend since 2005 (−0.05 PgC/yr2) that is on the lower end of previous observation‐based estimates [ABSTRACT FROM AUTHOR]

Empirical studies have shown that plant photosynthetic responses to environmental change can vary over time due to acclimation, but acclimation responses are often not included in Earth System Models. Photosynthetic least cost theory can be used to develop models of photosynthetic acclimation that are simple and testable. The theory is based on the idea that plants will acclimate to minimize the ratio of carbon costs to photosynthetic assimilation rate (Prentice et al., 2014, https://doi.org/10.1111/ele.12211). Formulations of this theory have been developed for C3 plants, but not C4 plants, which account for over 20% of global photosynthesis and are over‐represented among widely grown crops. Here, we use photosynthetic least cost theory to derive a model for C4 photosynthetic acclimation to above‐ground abiotic conditions. We then compare our model's responses to a similar model of C3 photosynthetic acclimation and find that C4 photosynthesis has the highest simulated advantage over C3 photosynthesis in hot, dry, and low CO2 environments. We find that this advantage predicts C4 abundance globally, but that the shallower CO2 response of C4 as compared to C3 photosynthesis will reduce C4 plant competitiveness under future conditions, despite higher temperatures. We also show that an acclimated model predicts similar or faster rates of C4 under all conditions than a model that does not consider acclimation, suggesting that Earth System Models (ESMs) are underestimating future C4 carbon uptake by not including acclimation. Our model is designed for easy incorporation into such ESMs. Plain Language Summary: Plants change their rate of photosynthesis in response to their environment. Their photosynthetic rates can change minute to minute based on the quick changes in their environment, but they can also change over much longer timescales as the plants become accustomed to a new environmental condition. Long‐term (days to weeks) regulation of photosynthesis is termed acclimation. When we predict how plants will behave in the future, we must take acclimation into account so that we can more accurately predict the future carbon, water, and nutrient cycles. Previous studies have developed mathematical models of photosynthetic acclimation for some, but not all, plants. One understudied group of plants that lacked an acclimation model were the C4 species, a subtype of plants often found in deserts and other arid environments, but one that also includes important agricultural crops such as maize. In this study, we develop a theoretical model of photosynthetic acclimation for C4 species and show that the model yields expected results based on where C4 plants currently grow. Our model can improve the predictions of carbon, water, and nutrient cycling in larger Earth System Models. Key Points: A parameter‐sparse model of C4 photosynthetic acclimation to changes in environmental conditions based on photosynthetic least cost theoryIncluding acclimation will improve simulations of C4 carbon assimilation and water/nutrient‐use efficiencies under present/future conditionsIn simulated competition experiments with a similar C3 model, C4 photosynthesis becomes less advantageous under increased carbon dioxide [ABSTRACT FROM AUTHOR]