The algorithm to produce the Clouds and the Earth’s Radiant Energy System (CERES) Edition 4.0 (Ed4) Energy Balanced and Filled (EBAF)-surface data product is explained. The algorithm forces computed top-of-atmosphere (TOA) irradiances to match with Ed4 EBAF-TOA irradiances by adjusting surface, cloud, and atmospheric properties. Surface irradiances are subsequently adjusted using radiative kernels. The adjustment process is composed of two parts: bias correction and Lagrange multiplier. The bias in temperature and specific humidity between 200 and 500 hPa used for the irradiance computation is corrected based on observations by Atmospheric Infrared Sounder (AIRS). Similarly, the bias in the cloud fraction is corrected based on observations by Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and CloudSat. Remaining errors in surface, cloud, and atmospheric properties are corrected in the Lagrange multiplier process. Ed4 global annual mean (January 2005 through December 2014) surface net shortwave (SW) and longwave (LW) irradiances increase by 1.3 W m−2 and decrease by 0.2 W m−2, respectively, compared to EBAF Edition 2.8 (Ed2.8) counterparts (the previous version), resulting in an increase in net SW + LW surface irradiance of 1.1 W m−2. The uncertainty in surface irradiances over ocean, land, and polar regions at various spatial scales are estimated. The uncertainties in all-sky global annual mean upward and downward shortwave irradiance are 3 and 4 W m−2, respectively, and the uncertainties in upward and downward longwave irradiance are 3 and 6 W m−2, respectively. With an assumption of all errors being independent, the uncertainty in the global annual mean surface LW + SW net irradiance is 8 W m−2.

The estimate of surface irradiance on a global scale is possible through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input. Computed top-of-atmosphere (TOA) irradiances, however, do not necessarily agree with observation-based values, for example, from the Clouds and the Earth’s Radiant Energy System (CERES). This paper presents a method to determine surface irradiances using observational constraints of TOA irradiance from CERES. A Lagrange multiplier procedure is used to objectively adjust inputs based on their uncertainties such that the computed TOA irradiance is consistent with CERES-derived irradiance to within the uncertainty. These input adjustments are then used to determine surface irradiance adjustments. Observations by the Atmospheric Infrared Sounder (AIRS), Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), CloudSat, and Moderate Resolution Imaging Spectroradiometer (MODIS) that are a part of the NASA A-Train constellation provide the uncertainty estimates. A comparison with surface observations from a number of sites shows that the bias [root-mean-square (RMS) difference] between computed and observed monthly mean irradiances calculated with 10 years of data is 4.7 (13.3) W m−2 for downward shortwave and −2.5 (7.1) W m−2 for downward longwave irradiances over ocean and −1.7 (7.8) W m−2 for downward shortwave and −1.0 (7.6) W m−2 for downward longwave irradiances over land. The bias and RMS error for the downward longwave and shortwave irradiances over ocean are decreased from those without constraint. Similarly, the bias and RMS error for downward longwave over land improves, although the constraint does not improve downward shortwave over land. This study demonstrates how synergetic use of multiple instruments (CERES, MODIS, CALIPSO, CloudSat, AIRS, and geostationary satellites) improves the accuracy of surface irradiance computations.

Earth's Energy Imbalance (EEI) is a relatively small (presently ∼0.3%) difference between global mean solar radiation absorbed and thermal infrared radiation emitted to space. EEI is set by natural and anthropogenic climate forcings and the climate system's response to those forcings. It is also influenced by internal variations within the climate system. Most of EEI warms the ocean; the remainder heats the land, melts ice, and warms the atmosphere. We show that independent satellite and in situ observations each yield statistically indistinguishable decadal increases in EEI from mid‐2005 to mid‐2019 of 0.50 ± 0.47 W m⁻² decade⁻¹ (5%–95% confidence interval). This trend is primarily due to an increase in absorbed solar radiation associated with decreased reflection by clouds and sea‐ice and a decrease in outgoing longwave radiation (OLR) due to increases in trace gases and water vapor. These changes combined exceed a positive trend in OLR due to increasing global mean temperatures.

[1] One year of instantaneous top‐of‐atmosphere (TOA) and surface shortwave and longwave irradiances are computed using cloud and aerosol properties derived from instruments on the A‐Train Constellation: the Cloud‐Aerosol Lidar with Orthogonal Polarization (CALIOP) on the Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite, the CloudSat Cloud Profiling Radar (CPR), and the Aqua Moderate Resolution Imaging Spectrometer (MODIS). When modeled irradiances are compared with those computed with cloud properties derived from MODIS radiances by a Clouds and the Earth's Radiant Energy System (CERES) cloud algorithm, the global and annual mean of modeled instantaneous TOA irradiances decreases by 12.5 W m⁻² (5.0%) for reflected shortwave and 2.5 W m⁻² (1.1%) for longwave irradiances. As a result, the global annual mean of instantaneous TOA irradiances agrees better with CERES‐derived irradiances to within 0.5W m⁻² (out of 237.8 W m⁻²) for reflected shortwave and 2.6W m⁻² (out of 240.1 W m⁻²) for longwave irradiances. In addition, the global annual mean of instantaneous surface downward longwave irradiances increases by 3.6 W m⁻² (1.0%) when CALIOP‐ and CPR‐derived cloud properties are used. The global annual mean of instantaneous surface downward shortwave irradiances also increases by 8.6 W m⁻² (1.6%), indicating that the net surface irradiance increases when CALIOP‐ and CPR‐derived cloud properties are used. Increasing the surface downward longwave irradiance is caused by larger cloud fractions (the global annual mean by 0.11, 0.04 excluding clouds with optical thickness less than 0.3) and lower cloud base heights (the global annual mean by 1.6 km). The increase of the surface downward longwave irradiance in the Arctic exceeds 10 W m⁻² (∼4%) in winter because CALIOP and CPR detect more clouds in comparison with the cloud detection by the CERES cloud algorithm during polar night. The global annual mean surface downward longwave irradiance of 345.4 W m⁻² is estimated by combining the modeled instantaneous surface longwave irradiance computed with CALIOP and CPR cloud profiles with the global annual mean longwave irradiance from the CERES product (AVG), which includes the diurnal variation of the irradiance. The estimated bias error is −1.5 W m⁻² and the uncertainty is 6.9 W m⁻². The uncertainty is predominately caused by the near‐surface temperature and column water vapor amount uncertainties.

Differences of modeled surface upward and downward longwave and shortwave irradiances are calculated using modeled irradiance computed with active sensor-derived and passive sensor-derived cloud and aerosol properties. The irradiance differences are calculated for various temporal and spatial scales, monthly gridded, monthly zonal, monthly global, and annual global. Using the irradiance differences, the uncertainty of surface irradiances is estimated. The uncertainty (1σ) of the annual global surface downward longwave and shortwave is, respectively, 7 W m⁻² (out of 345 W m⁻²) and 4 W m⁻² (out of 192 W m⁻²), after known bias errors are removed. Similarly, the uncertainty of the annual global surface upward longwave and shortwave is, respectively, 3 W m⁻² (out of 398 W m⁻²) and 3 W m⁻² (out of 23 W m⁻²). The uncertainty is for modeled irradiances computed using cloud properties derived from imagers on a sun-synchronous orbit that covers the globe every day (e.g., moderate-resolution imaging spectrometer) or modeled irradiances computed for nadir view only active sensors on a sun-synchronous orbit such as Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation and CloudSat. If we assume that longwave and shortwave uncertainties are independent of each other, but up- and downward components are correlated with each other, the uncertainty in global annual mean net surface irradiance is 12 W m⁻². One-sigma uncertainty bounds of the satellite-based net surface irradiance are 106 W m⁻² and 130 W m⁻².