The COVID-19 pandemic is impacting human activities, and in turn energy use and carbon dioxide (CO2) emissions. Here we present daily estimates of country-level CO2 emissions for different sectors based on near-real-time activity data. The key result is an abrupt 8.8% decrease in global CO2 emissions (−1551 Mt CO2) in the first half of 2020 compared to the same period in 2019. The magnitude of this decrease is larger than during previous economic downturns or World War II. The timing of emissions decreases corresponds to lockdown measures in each country. By July 1st, the pandemic’s effects on global emissions diminished as lockdown restrictions relaxed and some economic activities restarted, especially in China and several European countries, but substantial differences persist between countries, with continuing emission declines in the U.S. where coronavirus cases are still increasing substantially.

We constructed a near-real-time daily CO2 emission dataset, the Carbon Monitor, to monitor the variations in CO2 emissions from fossil fuel combustion and cement production since January 1, 2019, at the national level, with near-global coverage on a daily basis and the potential to be frequently updated. Daily CO2 emissions are estimated from a diverse range of activity data, including the hourly to daily electrical power generation data of 31 countries, monthly production data and production indices of industry processes of 62 countries/regions, and daily mobility data and mobility indices for the ground transportation of 416 cities worldwide. Individual flight location data and monthly data were utilized for aviation and maritime transportation sector estimates. In addition, monthly fuel consumption data corrected for the daily air temperature of 206 countries were used to estimate the emissions from commercial and residential buildings. This Carbon Monitor dataset manifests the dynamic nature of CO2 emissions through daily, weekly and seasonal variations as influenced by workdays and holidays, as well as by the unfolding impacts of the COVID-19 pandemic. The Carbon Monitor near-real-time CO2 emission dataset shows a 8.8% decline in CO2 emissions globally from January 1st to June 30th in 2020 when compared with the same period in 2019 and detects a regrowth of CO2 emissions by late April, which is mainly attributed to the recovery of economic activities in China and a partial easing of lockdowns in other countries. This daily updated CO2 emission dataset could offer a range of opportunities for related scientific research and policy making.

A Correction to this paper has been published: https://doi.org/10.1038/s41467-020-20254-5

Motivated by the Cayley-Hamilton theorem, a novel adaptive procedure, called a Power Sparse Approximate Inverse (PSAI) procedure, is proposed that uses a different adaptive sparsity pattern selection approach to constructing a right preconditioner M for the large sparse linear system Ax = b. It determines the sparsity pattern of M dynamically and computes the n independent columns of M that is optimal in the Frobenius norm minimization, subject to the sparsity pattern of M. The PSAI procedure needs a matrix-vector product at each step and updates the solution of a small least squares problem cheaply. To control the sparsity of M and develop a practical PSAI algorithm, two dropping strategies are proposed. The PSAI algorithm can capture an effective approximate sparsity pattern of A −1 and compute a good sparse approximate inverse M efficiently. Numerical experiments are reported to verify the effectiveness of the PSAI algorithm. Numerical comparisons are made for the PSAI algorithm and the adaptive SPAI algorithm proposed by Grote and Huckle as well as for the PSAI algorithm and three static Sparse Approximate Inverse (SAI) algorithms. The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems. INVERSE PRECONDITIONING PROCEDURE 261 forms do, because they can express denser matrices than the total number of nonzero entries in their factors. However, factorized forms have their own drawbacks, and like ILU [7] they can fail due to breakdown during an incomplete factorization process. A comprehensive survey of sparse approximate inverse preconditioners, together with extensive numerical comparisons aimed at assessing the overall performance of the various methods, can be found in [46]. POWER SPARSE APPROXIMATEWe concentrate on the second kind of SAI preconditioners in this paper. A key issue is to determine the sparsity pattern of M effectively. The initial work is to prescribe it in advance [21][22][23].Once that is given, the computation of M is straightforward and one can solve n independent small least squares problems to get all the columns of M. This is called a static SAI procedure. M is required to be sparse as well as to approximate A −1 . Much work has been done in prescribing the sparsity pattern of M; e.g. [11,19,20,30,39,40,43]. The most common a priori pattern of M is simply that of A, and this is called the structure of 1-local matrix [22]. This choice can give good results for many problems but can also fail for many problems. One improvement is to use the sparsity structure of q-local matrix for q>1. However, M becomes denser quickly when q increases, even though q = 2 is often impractical [30].SAI techniques are based on the implicit assumption that the majority of the entries in A −1 are small, so that it is possible to find a sparse matrix M that is a good approximation to A −1 ....

Precise and high-resolution carbon dioxide (CO 2 ) emission data is of great importance in achieving carbon neutrality around the world. Here we present for the first time the near-real-time Global Gridded Daily CO 2 Emissions Dataset (GRACED) from fossil fuel and cement production with a global spatial resolution of 0.1° by 0.1° and a temporal resolution of 1 day. Gridded fossil emissions are computed for different sectors based on the daily national CO 2 emissions from near-real-time dataset (Carbon Monitor), the spatial patterns of point source emission dataset Global Energy Infrastructure Emissions Database (GID), Emission Database for Global Atmospheric Research (EDGAR), and spatiotemporal patters of satellite nitrogen dioxide (NO 2 ) retrievals. Our study on the global CO 2 emissions responds to the growing and urgent need for high-quality, fine-grained, near-real-time CO 2 emissions estimates to support global emissions monitoring across various spatial scales. We show the spatial patterns of emission changes for power, industry, residential consumption, ground transportation, domestic and international aviation, and international shipping sectors from January 1, 2019, to December 31, 2020. This gives thorough insights into the relative contributions from each sector. Furthermore, it provides the most up-to-date and fine-grained overview of where and when fossil CO 2 emissions have decreased and rebounded in response to emergencies (e.g., coronavirus disease 2019 [COVID-19]) and other disturbances of human activities of any previously published dataset. As the world recovers from the pandemic and decarbonizes its energy systems, regular updates of this dataset will enable policymakers to more closely monitor the effectiveness of climate and energy policies and quickly adapt.

Day-to-day changes in CO2 emissions from human activities, in particular fossil-fuel combustion and cement production, reflect a complex balance of influences from seasonality, working days, weather and, most recently, the COVID-19 pandemic. Here, we provide a daily CO2 emissions dataset for the whole year of 2020, calculated from inventory and near-real-time activity data. We find a global reduction of 6.3% (2,232 MtCO2) in CO2 emissions compared with 2019. The drop in daily emissions during the first part of the year resulted from reduced global economic activity due to the pandemic lockdowns, including a large decrease in emissions from the transportation sector. However, daily CO2 emissions gradually recovered towards 2019 levels from late April with the partial reopening of economic activity. Subsequent waves of lockdowns in late 2020 continued to cause smaller CO2 reductions, primarily in western countries. The extraordinary fall in emissions during 2020 is similar in magnitude to the sustained annual emissions reductions necessary to limit global warming at 1.5 °C. This underscores the magnitude and speed at which the energy transition needs to advance.

The global animal food chain has a large contribution to the global anthropogenic greenhouse gas (GHG) emissions, but its share and sources vary highly across the world. However, the assessment of GHG emissions from livestock production is subject to various uncertainties, which have not yet been well quantified at large spatial scale. We assessed the uncertainties in the relations between animal production (milk, meat, egg) and the CO 2 , CH 4 , and N 2 O emissions in Africa, Latin America and the European Union, using the MITERRA-Global model. The uncertainties in model inputs were derived from time series of statistical data, literature review or expert knowledge. These model inputs and parameters were further divided into nine groups based on type of data and affected greenhouse gas. The final model output uncertainty and the uncertainty contribution of each group of model inputs to the uncertainty were quantified using a Monte Carlo approach, taking into account their spatial and cross-correlation. GHG emissions and their uncertainties were determined per livestock sector, per product and per emission source category. Results show large variation in the GHG emissions and their uncertainties for different continents, livestock sectors products or source categories. The uncertainty of total GHG emissions from livestock sectors is higher in Africa and Latin America than in the European Union. The uncertainty of CH 4 emission is lower than that for N 2 O and CO 2 . Livestock parameters, CH 4 emission factors and N emission factors contribute most to the uncertainty in the total model output. The reliability of GHG emissions from livestock sectors is relatively high (low uncertainty) at continental level, but could be lower at country level.

also an acute need to act quickly to avoid and/or adapt to climate-related challenges already being felt.However, the Global North should recognize Global South countries for the strides they have taken, particularly given that the Global North's historic and current emissions form the bulk of atmospheric GHG concentrations. Countries in the Global North should further acknowledge the deep historical economic inequities that contribute to the differentiated implementation of climate solutions. They must recommit to the 'common but differentiated responsibilities' principle formalized in the United Nations Framework Convention on Climate Change in 1992 and, while acknowledging existing progress, provide tangible financial support for further advancing climate solutions.Climate change affects us all. Partnerships at local, regional and international scales are key to the successful implementation of climate solutions, and the strongest partnerships are those built on mutual respect and shared goals 25 . To achieve the ambitious 1.5 °C warming target, we will need all hands working together in an equitable way. Only through true partnership between the Global North and Global South, and shared recognition of advances made in countries around the world, can we ever hope to advance climate action.