The radiative-transfer model used is a stand-alone version of the ECMWF IFS ecRad model (Hogan and Bozzo, 2018), version 0.9.40, configured like in IFS cycle 43r1. Gaseous optical properties are computed by the Rapid Radiative Transfer Model – General Circulation Model (GCM) applications (RRTMG) (Mlawer et al., 1997). The cloud solver is the SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides (SPARTACUS) (Hogan et al., 2018). The LW and SW solvers are based on the Monte Carlo Independent Column Approximation (McICA; Pincus et al., 2003). Surface albedo is calculated by the CAMS reanalysis based on a snow-free surface albedo over land in the UV-visible (0.3–0.7 µm) and the near-infrared (0.7–5.0 µm) derived from a 5-year climatology by the Moderate Resolution Spectral Radiometer (MODIS) (Schaaf et al., 2002) and over ocean on a fit of aircraft measurements (Taylor et al., 1996). The albedo also includes the effect of snow cover and sea ice as simulated by the CAMS reanalysis. LW surface emissivity is computed by averaging the spectrally constant emissivity of four surface tiles in proportion to their simulated coverage of each grid box. Surface window emissivities used in that calculation are listed in Table 1. Outside the LW window region, the value for sea is used. Cloud vertical overlap is assumed to be exponential random. Scattering by clouds and aerosols in the LW spectrum is included. RF is integrated diurnally over six solar zenith angles, computed as a function of local latitude and day of the year, and symmetrically distributed around local noon. Radiative fluxes are calculated at 61 model half-levels, but for RF purposes only three levels are retained: surface, TOA, and tropopause. The tropopause level is identified daily according to its thermal definition, adopted by the World Meteorological Organization (WMO), where the tropopause is the lowest altitude at which lapse rate drops to 2 K km-1. In its standard version, ecRad uses fixed values for the effective radius of cloud liquid droplets and ice crystals at 10 and 50 µm, respectively. The calculations of radiative fluxes by the radiative-transfer code have been compared against globally averaged observational estimates (Kato et al., 2013) and found to be accurate within a few percent.

The distributions taken from the CAMS reanalysis as inputs to the CAMS radiative-transfer calculations are listed in Table 2. The distributions are used as the mean of four time steps (00:00, 06:00, 12:00, and 18:00 Z) for the reanalysis dated 00:00 Z daily. The distributions are used at the degraded horizontal resolution of 3.0∘×3.0∘, down from the original 0.75∘×0.75∘ resolution, to reduce computational cost. That decrease in resolution causes negligible (third decimal place) changes in globally averaged RF. Daily averaged concentrations of carbon dioxide and methane are taken from the data-assimilated, three-dimensional distributions obtained by CAMS Greenhouse Gases Fluxes (Chevallier et al., 2005; Bergamashi et al., 2013) for carbon dioxide and methane, respectively, with updates to both documented at https://atmosphere.copernicus.eu (last access: 14 July 2020). Nitrous oxide is set to its pre-industrial mixing ratio of 270 ppb (Myhre et al., 2013a). The inversion product versions used are v18r2 for carbon dioxide and v17r1 for methane. Figure 2 shows time series of global monthly total-column averages of carbon dioxide and methane concentrations. The annually averaged carbon dioxide concentration in 2017 was 404 ppm, up 8 % from 374 ppm in 2003. For methane, the concentration for year 2017 was 1804 ppb, up 4 % from 1730 ppb in 2003. Figure 2 also shows equivalent time series for background surface measurements by the NOAA Earth System Research Laboratory (downloaded from https://www.esrl.noaa.gov/gmd/ccgg/trends/global.html#global_data, last access: 14 July 2020) for carbon dioxide and by the Advanced Global Atmospheric Gases Experiment (AGAGE, downloaded from https://agage.mit.edu/data/agage-data, last access: 14 July 2020) for methane. Surface measurements are generally higher than the column averages, especially for methane that decreases with height by oxidation.

Adjustment of radiative fluxes to account for changes in stratospheric temperatures uses the fixed dynamical heating (FDH) method (Ramaswamy et al., 2001). Convergence is reached when globally averaged changes in heating rate, RF, and stratospheric temperature become less than 0.05 K d-1, 0.05 W m-2, and 0.01 K, respectively. The maximum number of iterations is also set to 200. Once stratospheric adjustment is complete, the sum of the SW + LW radiative fluxes at the tropopause equals that at the top of the atmosphere. Methane RF is given in the LW and SW parts of the spectrum, although it is now known that ecRad – similar to many other radiative-transfer codes used in global models – is unlikely to properly handle methane absorption bands in the SW part of the spectrum because it does not have sufficient spectral resolution. Therefore, the CAMS products likely underestimate methane RF in the SW spectrum, and that underestimate affects its stratospheric adjustment. The SW contribution may be of the order of 15 % of total methane RF (Etminan et al., 2016).

To obtain aerosol RF, it is necessary to distinguish between aerosols of natural origin and aerosols of anthropogenic origin. The ECMWF IFS does not keep track of the aerosol origin mainly to keep computational cost reasonable but also due to the following reasons.

Aerosol origin is not always given in emission inventories.

The first update is the replacement of continental-wide anthropogenic fractions used over land surfaces by a fully gridded dataset that includes seasonal variations. Over land, identification of component aerosol optical depths (AODs) starts with removing the contribution of mineral dust aerosols from total AOD. The remaining non-dust AOD, τnon-dust, is then distributed between anthropogenic and fine-mode natural components, referred to as τanth and τfine-mode, respectively, as follows: 1τanth=fanth⋅τnon-dust,2τfine-natural=1-fanth⋅τnon-dust, where fanth is the anthropogenic fraction of the non-dust AOD. In Bellouin et al. (2013), fanth was prescribed over broad regions on an annual basis. Here, fanth is given by monthly distributions on a 1∘×1∘ grid. This new dataset derives from an analysis of AeroCom 2 numerical models (Kinne et al., 2013). Its annual average is shown in Fig. 3. Anthropogenic fractions show a north–south gradient, as expected from the location of population and industrial activities. Anthropogenic fractions are larger than 0.8 over most industrialised regions of North America, Europe, and Asia. The largest fractions are located over China, where more than 90 % of non-dust AOD is attributed to anthropogenic aerosols. In the Southern Hemisphere, anthropogenic fractions are typically smaller than 0.7 on an annual average. In terms of seasonality, anthropogenic fractions remain larger than 0.7 throughout the year in the Northern Hemisphere, with a peak in winter when energy consumption is high. In the Southern Hemisphere, seasonality is driven by biomass-burning aerosols, which are considered purely anthropogenic in the CAMS Climate Forcing estimates. Anthropogenic fractions therefore peak in late boreal summer in South America and southern Africa.

The second change concerns the fine-mode fraction (FMF) of marine AOD at 0.55 µm, which gives the fraction of marine AOD that is exerted by marine particles with radii smaller than 0.5 µm. In Bellouin et al. (2013), this fraction was set to a fixed value of 0.3. Here, this fraction is determined by a gridded dataset that includes monthly variations. The dataset is obtained by applying the method of Yu et al. (2009) to daily MODIS Collection 6 aerosol retrievals of AOD and FMF. First, the marine aerosol background is isolated by selecting only ocean-based scenes where total AOD at 0.55 µm is between 0.03 and 0.10. Then, an AOD-weighted averaged FMF is computed. The analysis has been applied to retrievals from MODIS instruments on both the Terra (dataset covering 2001–2015) and Aqua (dataset covering 2003–2015) platforms. Both instruments yield very similar marine FMF distributions, and the distributions used here are the multi-annual monthly averages of the two instruments. Figure 4 shows the marine FMF derived from MODIS/Terra for the months of January and July. It suggests that marine FMF varies over a wide range of values. Regions of high wind speeds, around 40–50∘ in both hemispheres, are associated with large FMFs, indicating that the marine aerosol size distribution includes a sizable fraction of smaller particles there. There are indications of contamination by fine-mode anthropogenic and mineral dust aerosols in coastal areas, but the impact on speciated AODs is small because the aerosol identification algorithm uses broad FMF categories rather than absolute values. Indeed, anthropogenic AOD decreases only slightly in the roaring forties in the Southern Ocean and tends to increase slightly in the northern Atlantic and Pacific oceans. On a global average, the change in anthropogenic AOD due to the improved specification of marine FMF is +0.001 (+1.4 %). Bellouin et al. (2013) estimated the relative uncertainty in τanth at 18 %. The updates to land-based anthropogenic fractions and marine FMF described here are not expected to reduce their large contribution to that uncertainty.

Radiative effect and forcing of aerosol–radiation interactions are computed by radiative-transfer calculations that combine the speciated AODs derived above with prescriptions of aerosol size distribution and single-scattering albedo. The methods are as described in Sect. 4 of Bellouin et al. (2013) with one exception: the prescription of single-scattering albedo has been updated from a few continental-wide numbers to gridded monthly climatologies. This updated dataset introduces two major improvements compared to Bellouin et al. (2013). First, the new dataset provides the monthly cycle of fine-mode absorption. Second, the dataset is provided on a finer, 1∘×1∘ grid. The method used to produce the dataset is described in Kinne et al. (2013). First, distributions of fine-mode extinction and absorption AODs are obtained from a selection of global aerosol numerical models that participated in the AeroCom simulations using a common set of aerosol and precursor emissions for present-day conditions (Kinne et al., 2006). To include an observational constraint, those modelled distributions are then merged with retrievals of aerosol single-scattering albedo (SSA) for the period 1996–2011 at more than 300 AERONET sites. The merging is based on a subjective assessment of the quality of the measurements at each of the AERONET sites used, along with their ability to represent aerosols in a wider region around the site location. The main impact of merging observed SSAs is to make aerosols in Africa and South Asia more absorbing than numerical models predicted. The distribution of annual and column-averaged aerosol SSA is shown in Fig. 5. The dataset represents the local maximum of absorption over California and the change in absorption as biomass-burning aerosols age during transport, which is visible over the south-eastern Atlantic. Over Asia, Europe, and South America, absorption is also larger near source regions, with less absorption elsewhere.

It is worth noting that the SSA distribution characterises absorption of fine-mode aerosols but is used to provide the absorption of anthropogenic aerosols, which is not fully consistent. The inconsistency is, however, mitigated by two factors. First, fine-mode aerosols are the main proxy for anthropogenic aerosols in the Bellouin et al. (2013) algorithm that identifies aerosol origin, and their distributions are broadly similar. Second, regions where natural aerosols such as marine and mineral dust may contaminate the fine-mode AOD often correspond to minima in anthropogenic AOD.

Like in Bellouin et al. (2013), the RF of aerosol–radiation interactions (RFari) is estimated in clear-sky (cloud-free sky) then scaled by the complement of the cloud fraction in each grid box to represent all-sky conditions, thus assuming that cloudy-sky aerosol–radiation interactions are zero. Experimental estimates of cloudy-sky RF have been done but are based on a simplified account of cloud albedo, which limits their usefulness. For the year 2003, globally averaged above-cloud anthropogenic and mineral dust AODs weighted by cloud fraction are 0.005 and 0.003, respectively, or 8 % of their clear-sky counterparts. Above-cloud marine and fine-mode natural AODs are negligible. Above-cloud anthropogenic aerosols exert a positive radiative effect because of their absorbing nature and the high reflectance of clouds. Those radiative effects commonly reach +5 to +10 W m-2 locally during the biomass-burning season that lasts from late August to October over the south-eastern Atlantic stratocumulus deck. However, this only translates into a cloudy-sky anthropogenic RFari of +0.01 W m-2, in agreement with AeroCom-based estimates, which span the range +0.01±0.1 W m-2 (Myhre et al., 2019). Studies based on the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) estimate that all-sky radiative effects of present-day above-cloud aerosols range between 0.1 and 0.7 W m-2 on an annual average over 60∘ S to 60∘ N (Oikawa et al., 2018; Kacenelenbogen et al., 2019), but only a fraction of that radiative effect contributes to RFari because of compensations from pre-industrial biomass-burning aerosols. Neglecting above-cloud aerosols therefore introduces a small uncertainty into the global average but leads to larger errors regionally and seasonally.

The algorithm that estimates the RF of aerosol–cloud interactions (RFaci) is the same as that used in Bellouin et al. (2013). It is based on satellite-derived cloud susceptibilities to aerosol changes, which are given seasonally and regionally. Statistics of satellite retrievals of liquid clouds are poor at high latitudes (Grosvenor et al., 2018), so cloud susceptibilities are not available poleward of 60∘ and RFaci is not estimated there. Aerosol changes are obtained by the anthropogenic AOD derived in Sect. 2.2. The cloud susceptibilities are applied to low-level (warm) clouds only.

The three-dimensional distributions of carbon dioxide and methane derived for present-day (PD) strongly benefit from data assimilation of surface measurements and satellite retrievals, which partly offset the biases of the chemistry model. That, however, creates the difficulty that estimating PI concentrations by running the chemistry model with PI emissions would be biased with respect to the data-assimilated, present-day distributions. Instead, daily PI mixing ratios of carbon dioxide and methane are scaled from daily CAMS Greenhouse Gas Flux mixing ratios in each grid box and at each model level using the following equation:

3[X]PI=[X]PD⋅[X]PI,surfaceAR5[X]PD,surface, where [X] denotes the mixing ratio of carbon dioxide or methane, and angle brackets denote annual averaging. All variables are taken from the CAMS Greenhouse Gas Flux inversions, except for PI surface mixing ratios, [X]PI,surfaceAR5, which come from footnote a of Table 8.2 of Myhre et al. (2013a), 278 ppm for carbon dioxide and 772 ppb for methane. The scaling factors are calculated at the surface because this is the level where PI concentrations are given in Myhre et al. (2013a): the whole profile is scaled like the surface level, which is justified by the relatively well-mixed nature of both gases. By construction, the scaled PI distribution has the same global, annual average value at the surface as given in Myhre et al. (2013a) but inherits the horizontal, vertical, and temporal variabilities of the PD distribution. Using this scaling method replicates the PD amplitude of the seasonal cycle of carbon dioxide and methane concentrations. For carbon dioxide, there is a suggestion from modelling studies that the amplitude of the seasonal cycle may have increased since PI (Lindsay et al., 2014). Replicating the PD amplitude would therefore cause a small underestimate of the forcing.

Like carbon dioxide and methane, ozone distributions in the CAMS reanalysis are strongly affected by data assimilation of ozone profiles and total and partial columns (Inness et al., 2015). Consequently, it is also not advisable to simply simulate PI ozone concentrations by running the chemistry model with PI emissions, as that would introduce biases between a data-assimilated PD and a free-running PI. Instead, daily PI ozone mixing ratios are scaled in each grid box and at each model level from daily CAMS reanalysis mixing ratios as follows: 4[O3]PI=[O3]PD⋅[O3]PICMIP6[O3]PDCMIP6, where [O3] denotes ozone mixing ratios and angle brackets denote monthly averaging. [O3]PDCMIP6 and [O3]PICMIP6 are taken from the three-dimensional CMIP6 input4MIPs ozone concentration dataset of Hegglin et al. (2016), briefly described by Checa-Garcia et al. (2018), for the years 2008–2012 for PD and 1850–1899 for PI. The Hegglin et al. (2016) dataset was obtained by merging 10-year running-averaged simulated ozone distributions by the Canadian Middle Atmosphere Model (CMAM) and the Whole Atmosphere Chemistry Climate Model (WACCM), both driven by CMIP5 historical emissions (Lamarque et al., 2010). The models resolve the chemistry and dynamics of the troposphere and stratosphere, allowing for mutual influence. Historical stratospheric ozone reflects the effects of long-lived greenhouse gases such as carbon dioxide, nitrous oxide, and methane in a physically and chemically consistent way. The interannual variability, including the Quasi-Biennial Oscillation, is included. The CMAM pre-industrial control configuration uses precursor and greenhouse gas emissions for the year 1850 in a 40-year simulation, with the last 10 years used to create the mean ozone field. The WACCM pre-industrial control configuration averages precursor and greenhouse gas emissions over the 1850–1859 period. The reference spectral and total irradiances are derived from averages over the period 1834–1867 (solar cycles 8–10), but the 11-year solar cycle is not considered.

Figure 6 shows the monthly cross sections of the PD-to-PI ratios used to scale CAMS reanalysis ozone mixing ratios following the equation above. The ratios exhibit a strong hemispheric contrast. In the Northern Hemisphere, ratios are typically larger than 1.5 throughout the year and can be around 2 in the lower troposphere above polluted regions. In the Southern Hemisphere, ratios are closer to 1.2 and are below 1 in the upper tropospheric Antarctic ozone hole, where the ozone layer has been diminished since PI conditions. Figure 6 also compares surface ozone volume mixing ratios in the Hegglin et al. (2016) dataset for the year 1850 to those resulting from scaling CAMS reanalysis ozone concentrations, averaged over the period 2003–2016. CAMS PI surface ozone is about 1.7 larger than in the Hegglin et al. (2016) dataset. The global distribution of PI ozone concentrations is poorly known due to a lack of measurements in different regions of the world, but ACCMIP models (Young et al., 2013) and the isotopic analysis of Yeung et al. (2019) suggest that the PI ozone levels in the Northern Hemisphere were of the order of 20 to 30 ppbv in the Northern Hemisphere and 10 to 25 ppbv in the Southern Hemisphere. CAMS estimates are higher, probably because of overestimations of surface ozone in the CAMS reanalysis, especially in the Tropics and Northern Hemisphere (Inness et al., 2019), which propagate to the PI estimates. Although it will be good to reduce those biases in future versions of the dataset, the fact that both PI and PD ozone concentrations are similarly biased should not have a large impact on tropospheric ozone RF, which mostly depends on the PI to PD increment in ozone concentrations.

The anthropogenic AOD (Sect. 2.2), which is then used to estimate RFari and RFaci, is defined with respect to PD natural aerosols, which is a different reference to PI (1750) so a correction is required (Bellouin et al., 2008). That correction factor is taken from Bellouin et al. (2013) and is equal to 0.8; i.e. RFari and RFaci defined with respect to PI are 80 % of RFari and RFaci defined with respect to PD natural aerosols.

All experiments in this section are performed using the CAMS reanalysis dataset for the year 2003. Greenhouse gas concentrations for carbon dioxide, methane, and nitrous oxide but also for CFC-11, CFC-12, HCFC-22, and CCl4 from 2003 and 1850 are taken from the Representative Concentration Pathways (RCP) historical dataset (Meinshausen et al., 2011). Although these forcings do not comprise the totality of anthropogenic greenhouse gas RF, 98 % of the well-mixed greenhouse gas RF is included from these species according to Table 8.2 of Myhre et al. (2013a), which is for the year 2011.

In addition to the parametric uncertainty discussed in Sect. 4.1, there is parametric uncertainty from the base climate state unrelated to any climatological averaging. Meteorological reanalysis is not perfect since limited and spatially incomplete observations are used to drive an atmospheric model (Dee et al., 2011). Additionally, the SW, and to a lesser extent LW, transmission and reflectivity of the atmosphere is heavily dependent on aerosol optical properties, which are not well constrained from observations (Regayre et al., 2018; Johnson et al., 2018).

To quantify those uncertainties, a 240-member perturbed parameter ensemble (PPE) is built by sampling uncertainty in 24 input variables, including aerosol and greenhouse gas emission and composition parameters, using a Latin hypercube approach (Lee et al., 2011) according to assumed prior distributions (Table 6). For each sample set, a pair of 2003 and 1850 simulations is performed, using the 2003 reanalysis data as before. Prior distributions of each parameter are informed from literature ranges and other modelling studies. In many cases the prior distributions in Table 6 differ from those used in referenced studies. Our prior distributions are informed by the references but are adapted to account for known information about the default parameter combinations used in ecRad, which produce a 2003 IRF estimate that is well within the expected range (see Sect. 4.1.1). For example, the geometric standard deviation of the sulfate size distribution is modified from the prior used in Lee at al. (2013) of 1.2–1.8 to account for the fact that the IFS by default uses a relatively small size distribution mean radius of 35 nm with a larger geometric standard deviation of 2.0 than used in Lee et al. (2013). The prior for mean sulfate size distribution used in the PPE admits values that are mostly larger than 35 nm, so the geometric standard deviation is reduced to compensate.

In this section, tropopause IRF is calculated on level 29, and a 3hr_21hr time-stepping methodology is used. The distribution of the global mean tropopause IRF for the year 2003 in the 240-member PPE using ecRad is shown in Fig. 9. The distribution of RF is positively skewed and well-represented by a lognormal distribution (red curve in Fig. 9). This contrasts with the anthropogenic forcing assessment in the IPCC AR5, which shows a mild negative skew (Myhre et al., 2013a), mostly due to the influence of the asymmetric uncertainty in AR5-assessed aerosol forcing. It should be noted, however, that the two different methods of arriving at distributions of radiative forcing are not equivalent and have different approaches to quantify sources of uncertainty.

The mean (5 %–95 %) IRF from the 240-member ensemble is 2.44 (1.67 to 3.42) W m-2, which is slightly stronger than the 2.33 W m-2 arising from using default ecRad parameters (Sect. 4.1.1). The mean (5 %–95 %) IRF from the lognormal curve fit is 2.44 (1.67 to 3.40) W m-2. Due to the good agreement between the sample and distribution fit, the mean and uncertainty range from the lognormal curve fit to the PPE are used in our overall uncertainty assessment for computational ease.

The individual sources of uncertainty from Sect. 4.1 and 4.2 are combined to produce an overall uncertainty estimate (Table 7). To produce the combined uncertainty, each individual source of uncertainty is assumed to be uncorrelated with the others. A million Monte Carlo samples were drawn from each distribution, corresponding to the individual sources of uncertainty listed in Table 7. This approach is taken as it is not straightforward to add non-symmetric uncertainties in quadrature. The combined uncertainty in IRF represents a range of 64 % to 143 % of the mean. This range is used to evaluate the RF uncertainty of the CAMS RF estimates, assuming that the uncertainty range calculated for the IRF in 2003 applies to all years.

Figure 10 shows RF time series and average distributions over the CAMS reanalysis period 2003–2017. Over that period, RF of carbon dioxide and methane have increased by 26 % and 6 %, respectively, because their atmospheric concentrations have increased. Ozone and aerosol radiative forcing do not show significant trends over the period. In terms of distributions, carbon dioxide and methane RF peak in the Tropics and have a good degree of symmetry between the two hemispheres. Tropospheric ozone RF is also maximum in the Tropics but is larger in the Northern Hemisphere, where tropospheric pollution is larger, than in the Southern Hemisphere. Stratospheric ozone RF peaks at high latitudes. It is positive in the high latitudes of the Northern Hemisphere because of influences from the troposphere (see Sect. 5.3) and negative in the high latitudes of the Southern Hemisphere because of stratospheric ozone depletion, in good agreement with Checa-Garcia et al. (2018). RFari follows the distribution of anthropogenic aerosols, which are located over and downwind of polluted and wildfire regions. RFari is negative over most of the globe, except small areas of high-albedo desert regions where anthropogenic absorption switches the sign to positive. Recall that above-cloud RFari is neglected in those calculations, so areas of positive RF from biomass-burning aerosols overlying clouds (e.g. Zuidema et al., 2016) are not represented. RFaci is also heterogeneously distributed, with large RF exerted by aerosol perturbations to mid-latitude Northern Hemisphere clouds and stratocumulus decks.

Clouds exert a sizable modulation of RF. Figure 11 shows the RF time series and average distributions in cloud-free conditions. This is estimated by setting cloud amounts to zero in radiative-transfer calculations but keeping other variables, in particular water vapour, fixed. Results suggest that RF would generally be stronger, in terms of absolute magnitude, in the absence of clouds. Alternatively, the results can be formulated as clouds masking a fraction of cloud-free RF. Clouds mask 14 % of carbon dioxide and methane RF. That estimate is similar to the previous estimate of 13 % for carbon dioxide by Myhre et al. (1998) but smaller than the estimate of 29 % given for methane by Minschwaner et al. (1998). Clouds mask 17 % of tropospheric ozone RF and switch the sign of global-mean stratospheric ozone RF, which, however, remains weak. Clouds mask at least 70 % of RFari, this value being a lower bound because the CAMS estimate excludes a small contribution from above-cloud aerosol absorption. Interestingly, the net effect of clouds is to weaken total aerosol RF since RFaci is weaker than the fraction of RFari masked by clouds. Clouds have little effect on trends.

Figure 12 shows the time evolution, average distribution, and rate of change of total RF over the period 2003–2017. Here, the rate of change is calculated as the change in total RF from one year to the next. Total RF is obtained by adding the CAMS estimates of the RF of carbon dioxide, methane, ozone, and aerosols. Total RF is estimated at +1.17 W m-2 in 2003 and has increased to +1.77 W m-2 in 2017. The fact that total RF has become more positive over the period indicates driving of further increases in surface temperatures. Total RF is positive over most of the globe, with peaks in the Tropics, where carbon dioxide, methane, and tropospheric ozone RF peak. RF is also large at high latitudes of the Northern Hemisphere for two reasons. First, this is where both tropospheric and stratospheric ozone contribute large positive RF. Second, this is where RFaci is not estimated because the satellite retrievals on which the estimate relies are biased due to large solar zenith angles (see Sect. 2.3). There are a few regions where aerosol RF more than offsets the RF of the other forcing agents, leading to a negative total RF. This happens in the North Pacific and over China but also off the coast of biomass-burning regions in West Africa and the Maritime Continent, although neglecting above-cloud RFari may exaggerate the offset. Rates of change in total RF have varied over the period but generally remained between 20 and 70 mW m-2 yr-1. The years 2012, 2014, and 2015 have slower rates, less than 10 mW m-2 yr-1 because of a slowdown in methane RF increase and a large aerosol RF, respectively. The years 2013 and 2017 have rates above 90 mW m-2 yr-1 because of a weaker aerosol RF combined, for 2017, with a strong methane forcing. Note that Fig. 12 and its analysis does not account for the contribution of, and changes in, radiative-forcing agents that are not estimated in CAMS, notably nitrous oxide and halocarbons, surface albedo and land use changes, and solar and volcanic RF.

Our more consistent treatment of forcing agents led to CAMS Climate Forcing estimates and uncertainties within previously assessed ranges but with noticeable differences for aerosols. In CAMS, the 1σ uncertainty range for carbon dioxide and methane forcing is estimated at 13 %, slightly larger than the 10 % uncertainty generally assumed in IPCC Assessment Reports. The uncertainty ranges for ozone and aerosols are larger, at 50 % for tropospheric ozone, 100 % for stratospheric ozone, and 38 % for total aerosol radiative forcing. The IPCC AR5 provides estimates for the year 2011, so they are compared to the same year from the CAMS dataset (Table 8). CAMS best estimates are close to those made at the time of the AR5, with the exception of RFari and RFaci, which are 60 % stronger in CAMS than in AR5, although these are still within assessed uncertainty ranges. RFari and RFaci are also consistent with the recent assessment by Bellouin et al. (2020a). CAMS uncertainty ranges are wider (although not greatly so) than assessed in AR5 because we have assessed a much more comprehensive set of uncertainty sources than AR5.

The CAMS estimates of RF by carbon dioxide and methane are based on the three-dimensional distributions of CAMS greenhouse gas flux inversions. Most previous estimates are either based on radiative-transfer calculations that assume a uniform mixing ratio of these gases or use simplified expressions, especially those by Myhre et al. (1998), obtained by fitting the calculations of radiative-transfer models of varying spectral resolution. Figure 13 compares the CAMS estimates to calculations using the same methods and input datasets, except that carbon dioxide and methane are now prescribed uniformly as measured by the ESRL and AGAGE networks (see Sect. 2.1 and Fig. 2). The year 2017 is not included in that comparison because calculations with uniform concentrations have only been done for the period 2003–2016. Pre-industrial concentrations are set to 278 ppm for carbon dioxide and 722 ppb for methane, like in Sect. 3.1. Also included in the comparison are estimates from the simplified expressions in Table 3 of Myhre et al. (1998), calculated using annually averaged mass-weighted atmospheric concentrations from the CAMS greenhouse gas flux inversions. Calculations assume the same pre-industrial concentrations as above and in addition assume a pre-industrial concentration of 270 ppb for nitrous oxide (again from Table 8.2 of Myhre et al., 2013a), which is a required input for the methane forcing calculation.

Three-dimensional distributions yield a slightly larger RF than uniform distributions, but the differences are only within 1 % to 2 %. Such small differences agree with past studies done on methane RF (Freckleton et al., 1998; Minschwaner et al., 1998), although they did not include shortwave effects and so obtained a different sign for the difference. Differences are likely due to saturation of RF as concentrations increase: RF has a logarithmic dependence on concentrations for carbon dioxide and a square-root dependence for methane, and concentrations are effectively lower in the three-dimensional case (Fig. 2). The increase in RF is contributed by land surfaces, where distributions depart most from uniformity because of local anthropogenic and natural sources. Three-dimensional distributions yield a stronger carbon dioxide RF but a weaker methane RF than simplified expressions, but again differences are small compared to overall uncertainties.

Although we presented tropospheric and stratospheric ozone forcing separately in Sect. 5.1, based on our tropopause definition, we recognise that there is some artificiality in the separation. Although stratospheric ozone change is primarily driven by ozone-depleting substances (ODS), modelling studies indicate a compensatory increase in stratospheric ozone due to emissions of gases conventionally regarded as tropospheric ozone precursors (carbon monoxide, methane and nitrous oxides). Similarly, ODS affect tropospheric ozone, mostly via changes in stratosphere-troposphere exchange. Søvde et al. (2011, 2012), for 1850–2000, and Shindell et al. (2013b), for 1850–2005, estimate that the precursors offset about 35 %–40 % of the negative stratospheric RF due to ODS, while about 15 % of the positive tropospheric ozone forcing due to precursors is offset by ODS. For the total ozone RF, ODS offset about half of the positive forcing due to the precursors.

In that context, it is interesting to look at total ozone RF, the sum of tropospheric and stratospheric ozone RFs. Figure 14 shows time series and distributions of total ozone RF for the period 2003–2017. After an increase from 2003 to 2005, dominated by an increase in tropospheric ozone concentrations, total ozone RF has been stable around 0.32 W m-2. In terms of distribution, ozone RF is positive over most of the globe, with a maximum in the tropical Northern Hemisphere. The high latitudes of the Southern Hemisphere are, however, associated with a negative ozone RF, due to stratospheric ozone depletion.

Because aerosols have short residence times in the troposphere, on the order of 1 week, distributions of trends in their concentrations and radiative forcing are driven by changes in aerosol primary and precursor emissions, which are themselves driven by air quality policy and economic decisions, at least over industrial regions. Figure 15 shows deseasonalised trends in anthropogenic AOD as estimated by the aerosol origin identification algorithm described in Sect. 3.3 applied to the CAMS reanalysis for the period 2003–2017. Although globally averaged anthropogenic AOD shows essentially no trend over the period, this hides very large regional trends. According to the CAMS reanalysis, total AOD has decreased over the eastern United States, Europe, South America, and China and increased over India and Siberia (Rémy et al., 2019). As shown in Fig. 15, the aerosol origin identification algorithm attributes those trends to anthropogenic aerosols, except for the Siberian trends, despite the Siberian trends being most probably caused by an increase in wildfires in the region. Decreasing aerosol amounts in China after about 2010 are confirmed by analyses of satellite aerosol retrievals and ground-based sun photometers (Filonchyk et al., 2019) and air quality monitoring (Zheng et al., 2018). Both studies detect the start of the decrease in 2013 and attribute it to the implementation of China's Clean Air Action. Over South America, Aragão et al. (2018) report a decrease in deforestation rates over 2003–2015, which is expected to be associated with a decreasing trend in biomass-burning aerosol emissions. Over India, analyses of ground-based remote sensing measurements confirm the increasing trend and attribute it to an increase in anthropogenic emissions (Babu et al., 2013; Satheesh et al., 2017). Figure 15 also shows wide oceanic regions, especially in the southern Pacific and Southern Ocean, associated with small but statistically significant positive trends. Those trends may not be real, as they are smaller than the 0.001 yr-1 drift in AOD that may affect the MODIS Collection 6.1 retrievals (Levy et al., 2018) that are assimilated in the CAMS reanalysis. Those trends could also reveal shortcomings of the aerosol identification algorithm or be real trends caused by biomass-burning aerosols transported from the Maritime Continent, South America, and Africa. The confidence in those trends and in the associated RFari and RFaci in these regions is therefore low.