The cloud-free global energy balance and inferred cloud radiative effects: an assessment based on direct observations and climate models

In the present study we assess the clear-sky radiation climatologies as simulated by a variety of GCMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5), which provided the basis for the most recent (5th) IPCC assessment report (IPCC 2013). They correspond to the 43 models listed in Table 1 of Wild et al. (2015), except for the following models which could not, or only partly, be considered in the present study due to incomplete clear-sky datasets: model versions CMCC-CESM, CMCC-CM, CMCC-CMS of the Centro Euro-Mediterraneo per I Cambiamenti Climatici (no surface shortwave and longwave clear-sky fluxes), CNRM-CM5 from the Centre National de Recherches Meteorologiques (wrong partitioning of shortwave clear-sky fluxes into downward and upward components over land), FGOALS-g2 from the Institute of Atmospheric Physics (corrupted surface downward clear-sky fluxes at poles, no surface shortwave clear-sky upward fluxes), and two versions of the Community Earth System Model, CESM1-CAM5 and CESM1-CAM5.1-FV2 (no surface clear-sky downward longwave fluxes). This leaves 38 and 37 CMIP5 models for the analysis of the shortwave and longwave clear-sky fluxes, respectively.

As in our previous studies (Wild et al. 2013, 2015) the model-calculated flux climatologies stem from the “historical all forcings” experiments, which aim at reproducing the evolution of climate over the twentieth century as realistically as possible, considering all major natural and anthropogenic radiative forcings. These include changes in atmospheric greenhouse gases, aerosol loadings (tropospheric and stratospheric volcanic), solar output, and land use. Most of the CMIP5 historic experiments cover the period from the mid nineteenth century up to 2005.

The GCM clear-sky fluxes are determined at every time-step irrespective of the presence of clouds. During cloudy conditions, clear-sky fluxes are calculated by removing the clouds in the radiative transfer calculations, but otherwise retaining the atmospheric input structure (e.g. profiles of water vapor, temperature, aerosols) that prevail during these cloudy conditions. This is also known as “Method II” according to Cess and Potter (1987) and Potter et al. (1992), whereas their definition of “Method I” refers to clear-sky climatologies which are only composed of truly cloud-free episodes. Clear-sky flux climatologies were established from the CMIP5 models as 5-year averages over the final complete years of their “historical all forcings” experiments, which correspond to the years 2000–2004. Since the year to year variations in the model-calculated clear-sky fluxes are small (the median annual variation at the various BSRN sites, defined as difference between the 5 and 95 percentiles, amounts to 2 Wm⁻²), a 5-year mean gives a representative depiction of the model clear-sky flux climatologies at the beginning of the 21th century. To derive a correction, which ensures an adequate comparison between model-calculated (according to Method II above) and observed (according to Method I) shortwave clear-sky flux climatologies, we additionally made use of the multi-century unforced control simulations of the CMIP5 models, as well as an in-house simulation with the model MPI-ESM-LR (see Sect. 4). The latter allowed to store and investigate the clear-sky fluxes at higher temporal resolution (daily data) than provided by the CMIP5 archive (only monthly data).

A detailed description of the models participating in CMIP5 is provided on the CMIP5 web-pages of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) (http://www-pcmdi.llnl.gov/). From most CMIP5 models multiple simulations of the historic experiments are available, which only differ in their initial conditions (ensemble experiments). However, the different ensemble members from a specific model hardly differ in terms of their clear-sky radiative flux climatologies (by less than 1 Wm⁻² on average), and the results presented in this study were found not to be sensitive to the choice of a particular ensemble member from a specific model. Therefore, results from only one ensemble realization of each model are presented in this study. This also avoids giving too much weight to specific models with large numbers of ensembles.

The observational reference data for the clear-sky fluxes at the Earth’s surface are derived from the records of the Baseline Surface Radiation Network (BSRN, Ohmura et al. 1998; Driemel et al. 2018). BSRN is a worldwide network of radiation sites measuring at highest possible accuracy with well-calibrated instruments and known accuracy, which can serve as anchor sites for a variety of applications. BSRN became operational in the early 1990s with a few sites and has gradually been growing to contain now more than 60 sites in different climate zones, which report their data to the BSRN Archive at the Alfred Wegener Institute (AWI) (http://www.bsrn.awi.de/). The BSRN data are recorded and stored at high temporal resolution (minute data), which is a prerequisite for the application of clear-sky detection algorithms as outlined below. BSRN sites are further requested to record shortwave radiation not only in terms of its total flux (measured with a pyranometer), but also separately in terms of the direct shortwave flux (measured with a pyrheliometer) and the diffuse shortwave flux (measured with a shaded pyranometer).

The availability of both direct and diffuse measurements is indispensable for the detection of cloud-free conditions, as clouds substantially modify the ratio between these two components. The Long and Ackerman (2000) clear-sky detection algorithm for shortwave radiation that we apply in this study makes use of this behaviour, as well as of the high temporal resolution of the data. Specifically, this algorithm analyses the magnitude and variability of the minute time-series of total (global) and diffuse shortwave irradiance periods to infer clear (i.e. cloudless) sky episodes. The identified clear-sky data at minute resolution are then used on a daily basis to empirically fit functions using the cosine of the solar zenith angle as the independent variable for days that exhibit the minimum amount of clear-sky times across the necessary range of solar zenith angles as defined by Long and Ackerman (2000). The fit coefficients are interpolated through time for days that cannot be adequately fitted, and then the coefficients (fitted or interpolated) are used to calculate continuous estimates of the clear-sky downward total, diffuse and direct shortwave radiation. The methodology requires some modification for climates such as the tropical western Pacific characterized by persistent cloudiness as detailed in Long and Gaustad (2004). As shown in Long and Ackerman (2000), the uncertainty of the clear-sky estimates due to interpolation is about of the same magnitude as the total shortwave measurements themselves for the instantaneous values. The long-term averaging of these values as used in the present study significantly decreases the uncertainties. Following the procedure as described above, clear-sky climatologies of surface downward shortwave radiation were produced at 53 BSRN sites which provide multiyear shortwave records that allow to establish climatologies (Table 1) (Hakuba et al. 2017). The periods covered by these reference climatologies do not necessarily exactly match the ones of the model climatologies (which is not a strict requirement due to the non-deterministic nature of the modelling setups), yet both observational and model climatologies can be considered as representative of the beginning of the 21th century.

The clear-sky detection algorithm for the longwave radiation is based on Long and Turner (2008), and takes into account the temporal variability of downward longwave radiation, as well as the difference between the measured ambient air temperature and effective sky brightness temperature calculated from the longwave measurements. The detected “effective” clear-sky data are used along with the previously detected shortwave clear-sky data to fit functions using collocated air temperature and humidity measurements as the independent variable in the formulation developed by Brutsaert (1975). These longwave detected periods are labelled “effective” clear-sky because the broadband downwelling longwave is insensitive to high, cold, thin clouds, thus the detected clear-sky times represent primarily periods with no low- and mid-level clouds. Similar to the shortwave clear-sky method, the fit coefficients are interpolated through time and used to produce continuous estimations of clear-sky longwave fluxes. Following this procedure, the data availability allowed the construction of clear-sky climatologies of surface downward longwave radiation at 31 BSRN sites (Table 1).

The TOA clear-sky references referred to in this study are obtained from the satellite-based Energy Balanced and Filled (EBAF) dataset from the Clouds and the Earth’s Radiant Energy System (CERES, Wielicki et al. 1996) program, CERES-EBAF Edition 4.0 (Loeb et al. 2018).

Our best estimates of the global mean downward surface shortwave and longwave clear-sky radiation of 247 and 314 Wm⁻², respectively, as derived in the above sections can then be combined with additional estimates of the TOA clear-sky fluxes and surface radiative properties, to allow for a quantitative diagram of the global mean energy balance under cloud-free conditions (Fig. 1). Note that the clear-sky flux magnitudes in this diagram are representative for an atmospheric structure corresponding to all-sky conditions but with clouds removed. This view thus corresponds to the climate model-type representation of clear-sky fluxes (Method II according to Cess and Potter 1987), and enables a direct comparison with the clear-sky budgets obtained from GCM output. It further allows the isolation and quantification of the effects of clouds on the global mean Earth radiation budget, by comparing the all-sky fluxes with the clear-sky fluxes merely obtained by removing the clouds, but with otherwise identical atmospheric conditions.

The currently most accurate estimates for the global mean clear-sky fluxes at the TOA as presented in Fig. 1 can be obtained from the CERES EBAF dataset. We use here data from its latest Edition 4.0 (Loeb et al. 2018), where the global annual mean estimates for the reflected shortwave clear-sky and outgoing longwave clear-sky fluxes amount to 53 and 268 Wm⁻², respectively. These values, however, are aggregated only from cloud-free scenes, and thus, similarly to the BSRN shortwave clear-sky climatologies discussed previously, may slightly differ from the computation of clear-sky TOA fluxes in climate models (c.f. Sect. 4.2). The effect of sampling over all types of atmospheric conditions as in climate models, rather than only over truly cloud-free conditions in the calculation of the global mean clear-sky fluxes have been estimated by Kato et al. (2013) using the CERES EBAF framework. For the global mean shortwave reflected and outgoing longwave radiation at the TOA, Kato et al. (2013) estimate this sampling effect at 0.24 and − 1.25 Wm⁻², respectively (their Table 2). This signifies, that considering not just the (slightly drier) atmospheres as under true clear-sky conditions, but all atmospheric conditions (with somewhat more water vapor content) in the calculation of the clear-sky fluxes, results in a slightly lower outgoing clear-sky longwave and slightly higher reflected clear-sky shortwave radiation at the TOA, as one would expect. To keep the clear-sky energy balance diagram consistent with the GCM definition of clear-sky fluxes (Method II), we therefore slightly adjusted the CERES TOA global mean values for Fig. 1 with the abovementioned corrections of 0.24 and − 1.25 Wm⁻² in the shortwave and longwave, respectively. With these corrections, rounded to integers, the global mean clear-sky TOA shortwave reflected radiation remains at 53 Wm⁻², while the outgoing longwave radiation is slightly reduced to 267 Wm⁻² (Fig. 1). The associated uncertainties of these estimates amount to ± 2 and ± 3 Wm⁻², respectively (Fig. 1) (Loeb et al. 2009). Combined with a global mean TOA insolation of 340 Wm⁻² (solar constant divided by four to obtain the average TOA insolation on a square meter on the Earth’s sphere), the total amount of shortwave absorption under cloud-free conditions becomes 287 Wm⁻². Note that the cloud-free energy balance in the diagram shown in Fig. 1 is not the balance that Earth would achieve in equilibrium when no clouds could form. As mentioned above the diagram is rather representative for the GCM-type of clear-sky fluxes determined by removing the clouds but otherwise retaining the entire atmospheric structure. As a consequence, unlike in the all-sky case, the TOA budget is far from being balanced between shortwave clear-sky absorption (287 Wm⁻²) and longwave clear-sky emission (267 Wm⁻²). In the all-sky budget (Fig. 14 left, reproduced from Wild et al. 2015) the difference between these two quantities is largely remediated by the global net cloud radiative effect.

Open image in new window

In our representation of the clear-sky energy balance we further retain the same radiative properties for the surface emission and surface albedo as in the discussion of the all-sky budget in Wild et al. (2015), to be consistent. Using thus the global surface albedo of 13.5% from Wild et al. (2015) and the best estimate of 247 Wm⁻² for the global mean clear-sky shortwave downward radiation (Sect. 4.3), the global mean clear-sky surface shortwave absorption and reflection become 214 and 33 Wm⁻², respectively (Fig. 1). A detailed description of the derivation of the surface albedo value can be found in Wild et al. (2015). Strictly speaking, the surface albedo under clear-skies slightly differs from the one under all-sky conditions, because the incident radiation under clear-skies is more directional particularly over ocean. According to the dataset of CERES EBAF surface, this effect is, however, small on a global mean basis, at 0.3% (Kato et al. 2018, as can be derived from their Table 5). This corresponds to a change in surface shortwave reflection of only 0.7 Wm⁻², so that the magnitude of this flux rounded to integer remains at 33 Wm⁻² as given in Fig. 1.

The amount of shortwave radiation absorbed within the cloud-free atmosphere can then be determined as residual between the cloud-free absorption of shortwave radiation in the total (TOA) climate system (287 Wm⁻²) and at the surface (214 Wm⁻²), and thus amounts to 73 Wm⁻². The 73 Wm⁻² of atmospheric shortwave clear-sky absorption closely match our previous estimates of this quantity which we obtained more than a decade ago based on older models and their biases against much fewer direct clear-sky observation (Wild et al. 2006). Two decades ago we estimated the global mean clear-sky atmospheric absorption similarly at 72 Wm⁻², not derived from clear-sky climatologies as they were not available at the time, but from a stand-alone evaluation of the radiation codes under cloud-free conditions used in the ECHAM3 and ECHAM4 climate models (Wild et al. 1998). Also, from the completely independently derived CERES-EBAF Ed.4. satellite-derived dataset, the very same global mean atmospheric shortwave clear-sky absorption of 73 Wm⁻² has been determined (Kato et al. 2018) as in the present study. Further, in another independent approach, Kim and Ramanathan (2008) obtained a closely matching estimate of 72 Wm⁻² for this quantity, by integrating global satellite-derived data sets for aerosols, water vapor and total ozone with a Monte Carlo Aerosol-Cloud-Radiation (MACR) model.

This indicates that the estimate of the global mean shortwave absorption in the cloud-free atmosphere, somewhat above 70 Wm⁻², seems to be fairly robust. Thus, about 21% of the incoming shortwave radiation at the TOA, or about 30% of the total amount of shortwave radiation absorbed by Earth may be absorbed in the cloud-free atmosphere.

The 73 Wm⁻² derived here for the global mean clear-sky shortwave atmospheric absorption are distinctly higher than some of the earlier estimates, and many of the simulated values of this quantity in GCMs, particularly in older models. This fits to the evidence for a lack of shortwave atmospheric absorption in many of the GCM radiation codes compared to line-by-line reference codes in radiation code intercomparison projects spanning more than two decades (Fouquart et al. 1991; Barker et al. 2003; Oreopoulos et al. 2012). The situation in GCMs has somewhat improved over the years. While the global mean clear-sky shortwave atmospheric absorption in some of the GCMs of the early 1990s did not even reach 60 Wm⁻² (Wild et al. 1998), this quantity was gradually enhanced in subsequent GCM generations, to 67 and 69 Wm⁻² in terms of multi-model means in the AMIPII and CMIP3 model intercomparison projects, respectively (Wild et al. 2006), and finally to 71 Wm⁻² in the CMIP5 multi-model mean (Table 1). This development is in line with the notion of an overall improvement in the performance of more recent GCM radiation codes in the context of the Continual Intercomparison of Radiation Codes (CIRC) compared to earlier assessments (Oreopoulos et al. 2012). Increasing water vapor absorption, due to the improved description of the shortwave continuum absorption in the near-infrared windows and revised spectroscopic absorption coefficients, may favour this development (Radel et al. 2015; Paynter and Ramaswamy 2012, 2014; Kim and Ramanathan 2008). A more accurate description of the aerosol radiative properties in the GCM radiative transfer calculations may further contribute to the enhanced shortwave absorption (Ackerman et al. 2003; Kim and Ramanathan 2008). Note that now about half of the CMIP5 models calculate a clear-sky atmospheric absorption that exceeds 70 Wm⁻² (Fig. 2 middle panel), and are thus in close agreement with the best estimate supported here. Yet there are still a number of CMIP5 models with a substantially lower clear-sky atmospheric absorption (Fig. 2 middle panel). This low absorption in some of these models may rather point to an inadequate implementation of known radiation physics in their radiation codes than to remaining genuine uncertainties in the representation of aerosols and the water vapor continuum.

In the longwave part of the cloud-free global energy balance diagram in Fig. 1, the surface fluxes consist of the downward longwave clear-sky radiation of 314 Wm⁻² (Sect. 5.3), and the upward longwave clear-sky surface radiation of 398 Wm⁻². This latter flux remains essentially the same as in the all-sky diagram (Fig. 14 left), since in the clear-sky we keep the surface and atmospheric properties identical to the all-sky except for the clouds as pointed out earlier, and the emission in the clear-sky thus comes from the surface with the same temperature as the all-sky. For a discussion of the justification of the 398 Wm⁻² for the all/clear-sky longwave surface upward radiation the reader is referred to Wild et al. (2015). To be precise, there would still be a slight difference between the clear-sky and all-sky surface upward longwave radiation even under otherwise identical surface and atmospheric conditions. This is due to the fact the surface upward longwave flux contains not only the longwave emission from the Earth’s surface, but added to this also a small contribution of the upward reflected fraction of downward longwave radiation. This reflection is neglected when the Earth’s surface is assumed to be a perfect blackbody in the longwave, which then absorbs all incident longwave radiation. In reality the Earth’s surface is globally indeed fairly close to a blackbody in the longwave, yet not perfectly, allowing for a few percent of the downward longwave fluxes to be reflected at the surface. However, since the all-sky and clear-sky downward longwave fluxes overall differ globally by only about 28 Wm⁻² (Table 2 and following Section below), the difference in the surface reflected longwave flux under clear- and all-sky conditions is less than 1 Wm⁻². This slight difference is thus neglected in Figs. 1 and 14, which display identical surface upward longwave fluxes under clear-sky and all-sky conditions. With a surface upward and downward clear-sky longwave radiation of 398 and 314 Wm⁻², this results in a best estimate for the surface net longwave clear-sky radiation of − 84 Wm⁻². This allows then also the estimation of the atmospheric clear-sky longwave net radiation (longwave atmospheric clear-sky divergence) at − 183 Wm⁻², calculated as a residual between the clear-sky outgoing and surface net longwave radiation of − 267 and − 84 Wm⁻², respectively. The corresponding value for the atmospheric clear-sky longwave net radiation as derived in CERES-EBAF according to Kato et al. (2013) amounts to − 182 Wm⁻². Thus, as with the shortwave clear-sky atmospheric absorption, also our estimates for its longwave counterpart closely agree with the corresponding independent CERES-EBAF estimates.

The clear-sky radiation balance derived in the previous section can then be used as a reference state to isolate and quantify the overall radiative effects of clouds, through a comparison with the corresponding all-sky radiation balance. Figure 14 contrasts the two radiation budgets, including clouds (left, as estimated in Wild et al. 2015) and excluding clouds (right, as estimated in the present study). This not only allows the estimation of the overall effects of clouds on the global mean radiation budget at the TOA, but also within the atmosphere and at the Earth’ surface, as given in Fig. 15.

Open image in new window

The TOA shortwave absorption under all-sky and clear-sky conditions as determined from CERES-EBAF (Loeb et al. 2018), at 287 and 240 Wm⁻², respectively, differs by 47 Wm⁻². This suggests that the overall effect of clouds is to reduce the absorption of shortwave radiation in the climate system by − 47 Wm⁻² (TOA shortwave cloud radiative effect). Since the cloud radiative effect is defined as the difference between the all-sky and clear-sky fluxes, and since this indicates a cooling of the climate system, this value obtains a negative sign (Table 2; Fig. 15). Accordingly, the longwave cloud radiative effect at the TOA, as the difference between the outgoing longwave radiation under all-sky and clear-sky conditions determined from CERES-EBAF Edition 4.0, becomes positive at 28 Wm⁻², since this states an energy gain for the climate system (Table 2; Fig. 15). The net (shortwave and longwave combined) cloud radiative effect at the TOA then results in an overall energy loss of − 19 Wm⁻² (Table 2; Fig. 15).

In addition to these widely published TOA cloud radiative effects, our study further allows the estimation of the global mean shortwave, longwave and net cloud radiative effects within the atmosphere and at the surface in a similar way, based on the respective all-sky and clear-sky estimates given in Fig. 14. At the surface the shading effects of clouds are estimated to reduce the downward shortwave radiation globally from 247 to 185 Wm⁻², thus by − 62 Wm⁻². In terms of absorbed (net) shortwave radiation at the Earth surface, the reduction by clouds amounts to − 54 Wm⁻² globally (from 214 to 160 Wm⁻²), which corresponds to the net surface shortwave cloud radiative effect (Table 2; Fig. 15). On the other hand, clouds are estimated to enhance the global mean surface downward longwave radiation by 28 Wm⁻², from 314 to 342 Wm⁻² (Table 2; Fig. 15). The same amount applies also to the net surface longwave cloud radiative effect (i.e. the cloud effect on the net longwave balance at the surface), since the all-sky and clear-sky upward longwave radiation is nearly identical within this framework (see discussion above). The surface net cloud radiative effect, defined as the sum of the surface net shortwave and longwave cloud effects, thus amounts then to − 26 Wm⁻² globally (Table 2).

In the atmosphere, the presence of clouds is estimated to enhance the shortwave absorption by 7 Wm⁻² from 73 Wm⁻² (Fig. 14 right), to 80 Wm⁻² (Fig. 14 left). This is slightly higher than corresponding estimates obtained from most climate models and the CERES EBAF datasets, at 5 Wm⁻² between 60°N and 60°S (Hakuba et al. 2016), and 4.1 Wm⁻² globally (Kato et al. 2018).

Since the cloud radiative effect on the longwave budget of the atmosphere is virtually zero (as a residual of surface and TOA longwave cloud radiative effects of 28 Wm⁻² each), the atmospheric net cloud radiative effect also remains at 7 Wm⁻² (Table 2; Fig. 15).

These estimates for the surface, atmospheric and TOA global mean shortwave, longwave and net cloud radiative effects inferred here and illustrated in Fig. 15 can then be compared to the respective values determined in the various CMIP5 models (multi-model means in Table 2, individual models in Figs. 16, 17, 18). In the multi-model global mean, both shortwave and longwave cloud radiative effects agree within a few Wm⁻² with the reference estimates derived here (Table 2). Global mean cloud radiative effects of individual models, however, vary substantially, with largest spreads and standard deviations occurring in the simulated surface estimates (Table 2; Figs. 16, 17, 18). This leads in some of the models to substantial deviations compared to the reference values developed here, in some cases exceeding 10 Wm⁻² on a global mean basis (Figs. 16, 17, 18). The deviations of the model-calculated surface cloud radiative effects from the reference values, together with the biases in their associated clear-sky fluxes, may give an indication for each individual model to what extent its cloud-free atmosphere or its clouds contribute to the overall biases noted in the simulated (all-sky) surface fluxes in previous studies.

Open image in new window

Open image in new window

Open image in new window

The global energy balance quantifies the distribution of radiative energy in the climate system. In previous studies we derived estimates for the magnitudes of the components of the “all-sky” global mean energy balance, taking into account the information provided by direct observations from surface and space as well as climate model estimates (Wild et al. 2013, 2015). In the present study we made an attempt to derive complementary estimates for the global mean energy fluxes under cloud-free (“clear-sky”) conditions. While reference values for the energy fluxes in and out of the climate system under cloud-free conditions at the TOA are now available with high accuracy from satellite-based measurements (CERES EBAF), corresponding estimates for the atmospheric and surface clear-sky budgets are less straightforward to obtain. Yet such reference values are needed, since climate models still show considerable spreads in their simulated clear-sky budgets, particularly at the Earth surface. As outlined in this study, these model spreads amount already in the global mean to as much as 16 and 24 Wm⁻² for the clear-sky surface downward shortwave and longwave radiation, respectively, which may further amplify on regional, seasonal and diurnal scales. We thus made an attempt to better constrain these fluxes using newly-derived clear-sky reference climatologies obtained at more than 50 worldwide distributed anchor sites from BSRN. The assessment has been slightly complicated by the fact that the monthly shortwave clear-sky BSRN reference climatologies are derived from measurements under truly cloud-free conditions, whereas the GCMs clear-sky fluxes are calculated continuously at every time-step solely by removing the clouds, yet otherwise retaining the prevailing atmospheric composition associated with the cloudy conditions. The quantitative effects of these different clear-sky definitions were estimated by comparing in multi-century GCM control simulations the clear-sky irradiances in months with lowest cloud amounts to their corresponding climatological mean clear-sky irradiances. The effects of the different clear-sky definitions between models and observations, estimated at 2 Wm⁻² on average, were individually determined for each model and month and adjusted accordingly for a proper comparison with the reference climatologies.

The subsequent assessment of the CMIP5 clear-sky surface flux climatologies at the BSRN sites identified a number of models with overall biases of no more than 1–2 Wm⁻² in their shortwave and/or longwave downward flux climatologies. However there remain also a number of models with substantially larger overall flux biases, indicative of strong overestimations of the downward shortwave fluxes, as well as both overestimations and underestimations of the downward longwave fluxes, with systematic biases up to more than 10 Wm⁻² when averaged over all BSRN sites.

To derive best estimates for the global mean clear-sky radiative fluxes at the Earth’s surface we then applied the approach presented in Wild et al. (2013, 2015) taking into account the bias structure of the 38 CMIP5 models with respect to the BSRN sites. The clear-sky radiative flux biases in the various models have thereby been linearly related to their respective global means. From the linear regression we inferred a best estimate (with zero bias against the surface observations) of 247 Wm⁻² for the global mean downward shortwave radiation at the surface under cloud-free conditions, and a corresponding surface absorption of 214 Wm⁻², assuming a global mean surface albedo of 13.5%. Combined with a best estimate for the global net influx of shortwave radiation at the TOA under cloud-free skies from CERES-EBAF of 287 Wm⁻², this leaves 73 Wm⁻² of shortwave radiation absorbed globally in the cloud-free atmosphere. This estimate nearly matches the completely independent estimates obtained from the state of the art satellite-retrieved dataset CERES-EBAF (Kato et al. 2013), as well as from a Monte Carlo Aerosol-Cloud-Radiation (MACR) model assimilated with satellite-derived input (Kim and Ramanathan 2008).

For the global mean downward longwave clear-sky radiation, a best estimate of 314 Wm⁻² was obtained, based on a regression between the GCM flux biases in downward longwave clear-sky radiation with respect to the BSRN references and their corresponding global means. Also this value matches the corresponding one from the independent CERES-EBAF satellite-retrieved dataset (Kato et al. 2013).

The close coincidence in the global magnitudes of key quantities describing the energy flows within the cloud-free climate system obtained in multiple independent approaches (based on surface observations and climate models as presented here on the one hand, and on state of the art satellite-derived products on the other hand) increases confidence in the robustness of the derived magnitudes of these global numbers.

Accurate knowledge of the global radiation budget of the cloud-free atmosphere is a prerequisite to quantify the global cloud radiative effects, through a comparison with consistently derived “all-sky” global radiation budget estimates. Quantitative estimates of the global cloud radiative effects at the TOA, within the atmosphere and at the surface have thus been derived in the present study, which may also be of use in climate model assessments and tuning.

While the focus in the present study was on a first-order quantification of the overall (global long-term mean) clear-sky budgets and cloud radiative effects, future studies should expand to assess these quantities in detail in their spatial as well as temporal variations.