The energy balance over land and oceans: an assessment based on direct observations and CMIP5 climate models

3.1.1 Solar radiation

The global distributions of the solar radiation budgets at the TOA, within the atmosphere and at the surface as simulated by the 43 CMIP5 models over the years 2000–2004 in the historical “all forcings” experiment (Sect. 2) are presented in Fig. 4. Displayed are multimodel annual mean climatologies (left column) as well as the local spreads between the individual model climatologies in terms of their absolute and relative standard deviations (center and right column). The solar radiation budgets averaged over global land surfaces as determined by the individual models are presented in Fig. 5. The statistics of the model-calculated land mean budgets in Fig. 5 are summarized in Table 2 in terms of their multimodel-mean, range of values covered by the 43 models, and the standard deviation of these values. It is evident that the models vary substantially in their absorbed solar radiation over land in the total (surface + atmosphere) system, as well as within the atmosphere and at the surface, covering a range of more than 20 and 30 Wm⁻² for the land mean total (solar net TOA) and surface absorption, respectively (Table 2). Considering the lower absolute amount of atmospheric and surface absorption compared to total (TOA) absorption, this suggests that the relative (percentage) differences between the model estimates increases from the TOA to the surface, i.e. the land mean model estimates vary for the TOA absorption in a range of 10 % of their absolute amounts, and for the surface absorption in a range of 23 % of their absolute amounts. This is largely a consequence of the model tuning towards the available observational constraints for the TOA budgets from satellites, while the surface budgets are not directly measurable from space and thus are usually not considered in the tuning process. Models are typically tuned within their cloud schemes to match their simulated TOA fluxes with reference values on a global mean basis as can be obtained with highest accuracy from the CERES EBAF satellite dataset (Sect. 2). From this dataset we determined a mean total absorption of solar radiation in the climate system above land surfaces (Solar net TOA land) of 213.3 Wm⁻² (Table 3) (average over the period 2001–2005, c.f. Sect. 2). This is within 2 Wm⁻² of the CMIP5 multimodel land mean of 211.4 Wm⁻² (Table 2). Thus, although the individual CMIP5 models deviate in their solar TOA budgets averaged over land by up to 14 Wm⁻² from the CERES reference value of 213 Wm⁻² (Fig. 5) with a corresponding standard deviation of 6.1 Wm⁻², the multi-model mean bias is, at 1.9 Wm⁻², not substantial (Tables 2, 3). On more regional scales, discrepancies between the different models increase, as shown in Fig. 4b, c and also noted by Trenberth and Fasullo (2010) using the models from the preceding Coupled Model Intercomparison Project Phase 3 (CMIP3).

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Table 2

Simulated energy balance components averaged over land, oceans and the entire globe from 43 CMIP5/IPCC AR5 models at the TOA, atmosphere, and surface

Component	Land			Oceans			Globe
	Mean	Range	SD	Mean	Range	SD	Mean	Range	SD
TOA
Solar down	324.8	7.1	1.6	348.4	4.4	1.1	341.3	3.4	0.8
Solar up	−113.4	19.4	5.7	−97.6	14.6	4.0	−102.0	12.6	3.1
Solar net	211.4	21.5	6.1	250.8	16.2	4.1	239.2	11.2	3.0
Thermal up	−231.2	13.4	3.6	−240.9	11.7	3.0	−238.0	11.7	2.9
Atmosphere
Solar net	70.3	16.8	4.0	76.5	9.0	2.5	74.7	9.9	2.8
Thermal net	−162.6	29.0	5.0	−186.9	22.3	3.8	−179.8	22.5	3.8
Surface
Solar down	191.9	41.3	9.7	188.3	19.6	5.4	189.1	18.6	4.8
Solar up	−50.8	20.9	4.4	−14.0	9.8	2.1	−24.7	10.5	2.2
Solar net	141.1	32.5	7.5	174.3	20.8	5.0	164.5	17.2	4.2
Thermal down	301.8	33.3	7.2	355.6	20.7	4.2	340.1	18.5	4.4
Thermal up	−370.3	21.0	4.4	−409.6	16.8	3.2	−398.4	11.8	2.6
Thermal net	−68.6	26.2	6.0	−54.0	13.5	3.1	−58.3	15.7	3.3
Net radiation	72.5	28.7	5.4	120.3	18.6	4.6	106.2	17.2	3.9
Latent heat	−40.4	14.4	3.8	−104.8	19.7	5.1	−85.8	13.9	3.9
Sensible heat	−31.3	26.8	5.1	−13.6	14.8	2.3	−18.9	13.1	2.6

Averages are taken over the period 2000–2004 from the historical (“all forcing”) simulations. The statistics include multimodel mean, range of model values and standard deviation (SD) of the components. Negative values indicate energy loss. Units Wm⁻²

Table 3

Estimates for land, ocean, and global mean energy balance components in the present and other recent studies

Component	This study			Trenberth et al. (2009)			ERA-Interim			CERES EBAF
	Landa	Oceana	Globea,b	Land	Ocean	Globe	Land	Ocean	Globe	Land	Ocean	Globe
TOA
Solar down	324.7	346.6	340.4	330.2	345.4	341.3	329.2	350.2	344.2	324.7	346.6	340.4
Solar up	−111.4	−94.9	−99.7	−113.4	−97.8	−101.9	−110.6	−95.5	−99.9	−111.4	−94.9	−99.7
Solar net	213.3	251.7	240.7	216.8	247.7	239.4	218.6	254.7	244.3	213.3	251.7	240.7
Thermal up	−232.4	−242.9	−239.8	−232.4	−240.8	−238.5	−238.5	−248.2	−239.0	−232.4	−242.9	−239.8
Atmosphere
Solar net	77.3	81.7	80.7	78.0	78.2	78.2	78.9	80.5	80.0	74.2	79.6	78.1
Thermal net	−166.4	−189.9	−183.8	−152.8	−183.4	−175.5	−171.8	−195.8	−182.5	−169.5	−193.6	−186.3
Surface
Solar down	184	185	184.7	184.7	184.4	184.3	187.2	188.4	188.1	186.5	186.6	186.7
Solar up	−48	−15	−24.6	−39.6	−16.6	−23.1	−47.5	−14.2	−23.8	−47.5	−14.5	−24.1
Solar net	136	170	160.1	145.1	167.8	161.2	139.7	174.2	164.3	139.1	172.1	162.6
Thermal down	306	356	341.5	303.6	343.3	333	303.9	356.2	341.2	311.5	359.0	345.3
Thermal up	−372	−409	−398.2	−383.2	−400.7	−396	−370.6	−408.6	−397.7	−374.4	−408.3	−398.8
Thermal net	−66	−53	−56.7	−79.6	−57.4	−63	−66.7	−52.4	−56.5	−62.9	−49.3	−53.5
Net radiation	70	117	103.3	65.5	110.4	98.2	73	121.8	107.8	76.2	122.8	109.1
Latent heat	−38	−100	−82.0	−38.5	−97.1	−80.0	−44.3	−99.3	−83.5
Sensible heat	−32	−16	−20.7	−27	−12	−17	−28.2	−13.1	−17.4

CERES EBAF determined from dataset version 2.7 described in Loeb et al. (2012) and Kato et al. (2013), ERA-Interim values published in Berrisford et al. (2011). Values cover the period 2000–2005, except for ERA-Interim (1989–2008). Negative values indicate energy loss. Units Wm⁻²

^aTOA fluxes as in CERES EBAF

^bDetermined as area-weighed average of the land and ocean estimates (land area 29.2 %, ocean area 70.8 %)

Unlike for the TOA mean radiation budgets, so far there have been no corresponding generally accepted observational references for the surface mean radiation budgets, which could serve as model tuning targets. Accordingly the surface budgets vary greatly between the various CMIP5 models. Discrepancies over land become even larger when the downward rather than the absorbed solar radiation is considered (Fig. 6, upper panel). Downward solar radiation incident on land surfaces varies in a range of more than 40 Wm⁻² amongst the CMIP5 models, from 169 to 210 Wm⁻², with a standard deviation of almost 10 Wm⁻². This is the component with the largest spread within the CMIP5 models amongst all land and ocean mean energy balance components (c.f. Table 2). The spread in terms of standard deviations further increases when proceeding to more local (gridpoint) levels (Fig. 4k, l).

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This unsatisfactorily large spread causes considerable discrepancies in various aspects of the model-simulated land surface climates, as the downward solar radiation constitutes a key energy input for a variety of land surfaces processes. Since this component is directly measured by the land-based radiation networks, we make use of the information contained in these records to better constrain this spread. For this purpose, we extract datasets from both GEBA and BSRN. From GEBA we use 760 observation sites with multiyear records of downward solar radiation, that allow the formation of site-representative climatologies. We previously used this station-based dataset in analyses of earlier model generations, namely the models used in the Atmospheric Model Intercomparison Project (AMIP, Wild 2005), the CMIP3 models (Wild 2008) and a subset of the models of CMIP5 used here (Wild et al. 2013a). As in our previous studies, for comparison of the gridded flux fields with point observations, the 4 surrounding grid points weighted by their inverse spherical distance were taken into account (Wild et al. 1995b). Hakuba et al. (2013) estimated the random error caused by the comparison of the simulated solar flux of a typical 1° GCM grid box with a point observation to be on the order of 3 Wm⁻² on a climatological timescale, which is attributed to the subgrid-scale variability not resolved by the GCM grid. The average bias for each model at the 760 sites is shown in Fig. 7 and in Table 4. Further documented in Table 4 are Root Mean Square (RMS) differences for the individual models (corresponding for each model to the combined effect of its average climatological mean bias and the standard deviation of its climatological mean biases at the individual sites). Most models show a RMS in the range of 20–30 Wm⁻², with a multimodel mean and median RMS near 22 Wm⁻². The vast majority of the GCMs (38 out of the 43 models) overestimate the downward solar radiation when averaged over the 760 sites. The multimodel mean overestimation amounts to 7.4 Wm⁻² and the median overestimation is 6.5 Wm⁻² (Table 4). If we further group the GEBA sites into 5° latitude bands and apply a latitudinal area weighting of the zonally-averaged biases (Wild 2008), the overall biases of the individual models are mostly similar, and multimodel mean and median biases amount to 8.1 and 7.2 Wm⁻², respectively, thus within 1 Wm⁻² of the simple unweighted average over the 760 sites given above at 7.4 Wm⁻² (mean) and 6.5 Wm⁻² (median).

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Table 4

Root mean square (RMS) and average differences between climatological annual mean downward solar and thermal surface fluxes as calculated in the various CMIP5 models and as observed at GEBA/BSRN sites. Units Wm⁻²

Model	Downward solar 760 GEBA sites		Downward solar 38 BSRN sites		Downward thermal 41 BSRN sites
	RMS	Mean bias	RMS	Mean bias	RMS	Mean bias
ACCESS1-0	23.7	15.7	17.8	14.2	8.9	−2.0
ACCESS1-3	23.5	13.4	16.5	12.1	12.1	−0.9
bcc-csm1-1	20.5	−4.1	11.9	−3.2	7.8	−2.5
bcc-csm1-1-m	19.0	2.1	11.9	−0.2	8.9	0.0
BNU-ESM	18.3	1.8	11.6	2.6	8.8	−0.5
CanESM2	22.2	11.2	18.5	13.4	10.2	−4.9
CCSM4	22.1	11.2	15.4	9.1	9.7	−3.9
CESM1-BGC	22.2	11.5	16.0	10.0	9.8	−4.2
CESM1-CAM5	19.9	0.3	12.3	2.8	7.9	−0.6
CESM1-CAM5-1-FV2	22.0	−5.4	14.7	−2.1	9.8	2.9
CESM1-FASTCHEM	22.9	12.4	17.0	10.8	9.0	−3.3
CESM1-WACCM	21.1	3.9	13.5	3.6	10.3	4.0
CMCC-CESM	29.8	−15.3	29.9	−18.1	10.3	3.6
CMCC-CM	20.5	−6.5	15.4	−1.5	10.4	−7.6
CMCC-CMS	25.2	−11.8	19.5	−6.1	6.4	−0.9
CNRM-CM5	20.2	8.8	14.1	7.2	10.3	−8.4
CSIRO-Mk3-6-0	23.2	12.4	19.0	14.1	9.5	−3.6
FGOALS-g2	18.6	2.3	26.3	4.7	15.5	−12.6
GFDL-CM3	20.3	6.5	11.9	3.7	8.6	−1.3
GFDL-ESM2G	20.1	4.1	14.0	2.0	6.7	−2.2
GFDL-ESM2 M	20.4	4.0	13.0	1.8	7.0	−0.4
GISS-E2-H	22.0	5.4	19.7	−3.5	15.4	7.8
GISS-E2-H-CC	22.0	5.6	19.1	−2.4	15.4	7.2
GISS-E2-R	21.9	6.5	18.8	−0.4	13.2	4.7
GISS-E2-R-CC	22.0	6.7	18.8	−0.7	14.3	3.9
HadCM3	19.5	2.2	20.5	2.0	10.1	−6.2
HadGEM2-CC	23.3	15.9	17.2	13.8	11.3	−7.7
HadGEM2-ES	23.4	15.9	19.4	16.0	9.8	−5.1
inmcm4	27.1	19.0	17.9	13.0	13.8	−0.1
IPSL-CM5A-MR	35.2	23.8	24.9	17.4	17.0	−13.9
IPSL-CM5A-LR	35.0	22.8	24.0	14.5	19.9	−16.7
IPSL-CM5B-LR	30.2	18.4	21.4	10.6	20.1	−14.7
MIROC4 h	24.0	14.4	21.8	17.3	8.4	−5.6
MIROC5	19.9	10.1	17.9	9.2	6.9	2.6
MIROC-ESM	21.6	8.5	20.7	11.5	10.3	−1.9
MIROC-ESM-CHEM	21.5	8.4	21.2	10.6	10.7	−3.1
MPI-ESM-LR	20.4	2.3	17.6	6.1	6.8	0.2
MPI-ESM-MR	21.1	3.0	16.9	6.0	6.1	1.8
MPI-ESM-P	20.9	2.2	18.9	8.1	7.3	−0.1
MRI-CGCM3	27.1	20.4	18.9	14.1	14.8	−12.6
MRI-ESM1	26.8	19.9	18.0	12.5	13.4	−10.6
NorESM1-M	18.4	3.4	13.2	1.7	10.0	−5.1
NorESM1-ME	18.4	3.6	13.0	0.9	10.4	−5.3
Mean of all models	22.7	7.4	17.7	6.0	10.8	−3.0
Median of all models	22.0	6.5	17.9	6.1	10.1	−2.2

Alternatively, we can compare the surface downward solar radiation of the 43 models against 38 sites from the BSRN network as used in Wild et al. (2013a). These sites can provide climatologies of surface downward solar radiation determined as the sum of the direct and diffuse radiation, measured with a pyrheliometer and a shaded pyranometer, respectively. This is considered a more accurate measurement method for surface downward solar radiation than the more simple total flux measurement with a pyranometer as typically used at the GEBA sites (Ohmura et al. 1998). Climatological RMS differences at the BSRN sites for the individual models are also given in Table 4 and range from 12 to 30 Wm⁻². They are typically smaller than at the GEBA sites (on average by 5 Wm⁻²), indicative of higher quality data and more representative locations. However, the mean biases averaged over the 38 sites are for most models very similar to their biases against the 760 GEBA sites (Fig. 8; Table 4). Surface downward solar radiation is overestimated at the BSRN sites in the multi-model mean by 6.0 Wm⁻² (median 6.1 Wm⁻²), which is close to the aforementioned bias at the GEBA sites (7.4 Wm⁻² mean, 6.5 Wm⁻² median). Thus, the overall biases appear robust with respect to the choice of the observational references, confirming findings based on fewer climate models in Wild et al. (2013a).

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The overestimation of solar radiation incident at the Earth’s surface is a long-standing issue in climate modeling, and is still present in many of the CMIP5 models (see e.g. Wild 2008 for a review and discussion of possible causes).

3.1.2 Thermal radiation

Figure 9 shows the global distributions of the outgoing thermal radiation at the TOA, net thermal radiation in the atmosphere, and net and downward thermal radiation at the surface as simulated by the 43 CMIP5 models over the years 2000–2004 in the historical “all forcings” experiment (c.f., Sect. 2). Displayed are again multimodel annual mean climatologies (left column) as well as the local spreads between the individual model climatologies in terms of their absolute and relative standard deviations (center and right column). Figure 6 (lower panel) and Fig. 10 show the corresponding thermal radiation budgets averaged over global land surfaces as calculated by the individual models, and the statistical summary is given in Table 2. Similar to the solar budgets, the thermal land mean budgets vary considerably amongst the models. Model estimates for the land mean outgoing thermal radiation at the TOA vary in a range of 13 Wm⁻². This roughly doubles when the net thermal radiation at the surface (26 Wm⁻²) and in the atmosphere (29 Wm⁻²) are considered (Table 2). The higher consistency at the TOA compared to the surface is again largely a consequence of the tuning of the models, which aims to match the simulated TOA outgoing thermal radiation with the one observed from satellites. From the CERES EBAF satellite dataset (Sect. 2) we determined a reference outgoing thermal radiation at the TOA over land of 232.4 Wm⁻² for the period 2001–2005 (232.2 Wm⁻² for the period 2001– 2010, with a standard deviation of 0.47 Wm⁻² in the annual values) (Table 3). This observed value differs from the CMIP5 multimodel mean of 231.2 Wm⁻² (Table 2) by no more than about 1 Wm⁻². Thus, as with the land mean solar radiation at the TOA, its thermal counterpart shows overall no systematic bias in the CMIP5 multimodel mean when compared to the best available observational estimates. The spread amongst the models on more regional scales is, however, evident, particularly in low latitude areas, where the standard deviations between the outgoing thermal radiation climatologies exceed 10 Wm⁻² (Fig. 9b).

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As noted above, the discrepancy between the model-calculated land mean thermal fluxes becomes larger at the surface. This is particularly evident in the land mean downward thermal radiation shown in Fig. 6 (lower panel) that varies in a range of as much as 33 Wm⁻², from 281 to 314 Wm⁻², with a standard deviation of 7.2 Wm⁻². From all land and ocean averaged thermal components as given in Table 2, this is thus the flux component with the largest spread among the climate models. This spread in downward thermal radiation also further enlarges on more regional scales (Fig. 9k). At the same time the downward thermal radiation is also the quantity that we can directly compare with surface observations. Here we use 41 sites from BSRN that have extended records of downward thermal radiation. As in previous studies we accounted for possible differences in the altitudes of the observation sites and the collocated model topography, using a height correction of 2.8 Wm⁻²/100 m (Wild et al. 1995a). The RMS of the various models with respect to the 41 sites varies between 6 and 20 Wm⁻² (Table 4), and is generally smaller than the corresponding RMS in the downward solar fluxes. Mean model biases of the various models at the 41 sites are illustrated in Fig. 11. Out of the 43 models, the majority of the GCMs, namely 33 models (77 %), show a negative bias, while 10 models (23 %) show positive biases. Interestingly, 8 models display a mean bias at the 41 observation sites of less than 1 Wm⁻². The multimodel mean bias of the 43 models is negative with an underestimation of −3.0 Wm⁻² (c.f. Table 4). The underestimation of the downward thermal radiation in climate models has also been a long-standing issue in GCM surface radiation budgets and partly induced by uncertainties in the formulation of the water vapor continuum (Iacono et al. 2000; Wild et al. 2001). However, considerable progress in reducing these biases over time is evident, with some of the models now showing negligible overall biases as noted above and pointed out in Ma et al. (2014).

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3.3.1 Radiative components

The most accurate information currently available on the radiative energy exchanges at the TOA over land is compiled in the CERES EBAF Ed2.7 dataset. From this dataset we estimate the TOA land mean downward, upward and net solar radiation at 324.7, −111.4 and 213.3 Wm⁻², respectively, and the thermal outgoing radiation at −232.4 Wm⁻² (Table 3). All these estimates are averages over the period 2001–2005, with no significant change when averaged over the entire available period 2001–2010. They are displayed in Fig. 2 (upper panel), rounded to integers. Uncertainty ranges for land mean TOA fluxes correspond to those discussed in Wild et al. (2013a) for the global mean fluxes. Note that, in contrast to the global energy balance under equilibrium conditions, in the land energy balance the outgoing thermal radiation is not required to match the absorbed solar radiation at the TOA. Radiative imbalances can be induced by advective exchanges of latent and sensible energy in the atmosphere between the land and ocean domains. According to Table 3 and Fig. 2 (upper panel), the outgoing thermal radiation at the TOA over land is 19 Wm⁻² larger than the absorbed solar radiation. This imbalance implies a corresponding net atmospheric energy transport of sensible and latent heat from the ocean to the land surfaces which compensates the net radiative energy loss through the TOA over land surfaces. Comprehensive analyses of the energy transport from ocean to land have been performed by Fasullo and Trenberth (2008a, b) and Trenberth and Fasullo (2013), who identified a strong annual cycle in this quantity, with large energy transport in the northern winter onto land, and small net transport from land to ocean in northern summer. Trenberth and Fasullo (2013) further estimated that latent energy is the dominant component of the annual mean energy transport from ocean to land, i.e. the moisture convergence over land. The required transport of 19 Wm⁻² to compensate for the excess thermal emission compared to solar absorption over land according to CERES EBAF is illustrated in Fig. 2 (upper panel), and corresponds, when multiplied with the total land surface area of 149 × 10¹² m⁻², to a total annual energy transport of 2.8 × 10¹⁵ W  (2.8 PW), as also determined by Trenberth and Fasullo (2013). This is somewhat higher than the corresponding transport in the ERA Interim reanalysis of 2.5 PW established by Trenberth and Fasullo (2013). Trenberth and Fasullo (2013) inferred the ocean to land energy transport also from a number of other reanalyses and show that they differ in a range close to 1 PW. We use this range to infer a corresponding uncertainty range of 7 Wm⁻² for the transport in Fig. 2 (upper panel). The convergence of latent energy over land corresponds to the latent heat release of the excess precipitation formation compared to evaporation over land, which is transported in form of runoff back to the oceans (Trenberth and Fasullo 2013 and references therein). Thus, a net atmospheric transport of energy from oceans to land can be expected from hydrological considerations. The TOA land mean imbalance in the CMIP5 multimodel mean (19.8 Wm⁻²) differs by less than 1 W from CERES EBAF (Table 2), suggesting that the models overall adequately reproduce the net energy transport from oceans to land on an annual mean basis.

For the solar radiation incident at the land surface in Fig. 2 (upper panel), we take the best estimate of 184 Wm⁻² with uncertainty range as defined and derived in Sect. 3.2. As pointed out in Sect. 3.2 the close agreement of recent estimates based on entirely independent approaches enhances our confidence in this estimate. The magnitude of the downward solar radiation traditionally has been a major source of uncertainty, and still shows the largest discrepancies of all energy balance components in the latest (CMIP5) climate model generation (Table 2; Fig. 6, upper panel, Sect. 3.1).

To obtain an estimate for the land mean absorbed solar radiation at the surface, we need in addition information on the (radiation weighted) land surface albedo. The satellite-derived radiation weighted land mean albedo taken from MODIS (Moderate-resolution Imaging Spectroradiometer) amounts to 0.24 (Zhang et al. 2010). The various validation exercises of this albedo product in the literature indicate that the MODIS albedo might be overall slightly too low on the order of 0.02 (see Discussion in Hakuba et al. (2014) and references therein). From the surface solar upward and downward fluxes in Table 2 we infer that the CMIP5 models calculate a multimodel mean radiation weighted land albedo of 0.264. Similarly, from the surface CERES EBAF Ed2.7 product we obtain a land mean albedo estimate of 0.255 (Table 3). From Berrisford et al. (2011) we deduce an albedo of 0.253 and 0.246 for the ERA-Interim and ERA-40 reanalyses, respectively. For the determination of the surface reflected and absorbed solar radiation in Fig. 2 (upper panel), we use a radiation weighted land mean albedo of 0.26 close to the surface CERES EBAF Ed2.7 product, which is near to the median of the different estimates, and currently considered best suited for large scale surface albedo estimates (Crystal Schaaf, personal communication 2014). This gives a (rounded) land mean surface reflected and absorbed solar radiation of 48 and 136 Wm⁻², respectively (Fig. 2 upper panel). Uncertainties introduced by the surface albedo estimates, however, remain. Deducing a range of potentially realistic radiation weighted land mean albedo values between 0.24 and 0.27 from the above discussion results in an uncertainty range of 44–50 Wm⁻² for the surface reflected solar radiation, and enlarges the uncertainty range of the absorbed compared to the downward surface solar radiation accordingly (Fig. 2, upper panel).

With an absorbed land-mean solar radiation of 136 Wm⁻² at the surface and 213 Wm⁻² in the total system (TOA solar net), this leaves 77 Wm⁻² of solar radiation absorbed within the atmosphere over land surfaces (Table 3; Fig. 2, upper panel). The CMIP5 multi-model mean is, at 70.3 Wm⁻², more than 6 Wm⁻² lower than the best estimate inferred here. This suggests that in the majority of the models, the atmosphere over land surfaces is not absorptive enough for solar radiation, a feature common to several generations of GCMs.

For the land mean downward thermal radiation in Fig. 2 (upper panel), we use the value of 306 Wm⁻² and the uncertainty range as discussed in Sect. 3.2. The predominant part of the downward thermal radiation is absorbed at the surface. However, since the Earth surface is not a perfect blackbody, with a surface absorptivity/emissivity ε somewhat lower than 1, a small part of the downward thermal radiation is reflected upward, namely (1 − ε) times the downward thermal flux. The Earth surface emits radiation according to the Stefan–Boltzman law at εσT _skin ⁴ , with T_skin representing the surface skin temperature, and σ the Stefan–Boltzman constant (5.67 × 10⁻⁸ Wm⁻²K⁻⁴). The total upward thermal flux as shown in Figs. 1 and 2 consists thus of the above-mentioned surface emission plus a small contribution from the reflected part of the downward thermal flux. The upward thermal flux is not overly sensitive to the exact specification of the surface emissivity ε, since compensational changes between reflected downward and surface emitted radiation apply in the upward thermal flux when ε is changed, leading to an only small sensitivity of 0.5 Wm⁻² per percent emissivity change (e.g., Kato et al. 2013). Kato et al. (2013) estimated the uncertainty in land surface ε at 3 % based on different datasets, introducing thus an uncertainty of 1.5 Wm⁻² in the upward thermal radiation due to the specification of ε alone. For the determination of the land mean surface upward thermal radiation, we consider reanalyses as a useful source. Reanalyses assimilate the observed state of the atmosphere several times per day and determine the fluxes with high temporal frequency to capture also the full diurnal cycle (atmospheric time step of 30 min in the case of ERA-Interim). The assimilation of screen-level temperature observations in the reanalyses further helps to reduce long-term biases in their simulated surface skin temperatures used in the determination of the surface upward thermal radiation (Simmons et al. 2004), although screen and skin temperatures can greatly differ during the course of a day (e.g., Jin and Dickinson 2010). In Berrisford et al. (2011) we note that four different reanalysis products vary in a range of no more than 3 Wm⁻² with respect to the land mean surface upward thermal radiation. Specifically, Berrisford et al. (2011) give land mean values for ERA-Interim of 370.6 Wm⁻² covering the period 1989–2008, and 371.0 Wm⁻² for ERA-40 over the period 1989–2001. Considering an increase of 0.17 Wm⁻²/year in the land mean surface upward thermal radiation due to global warming (Wild et al. 2008), we apply an upward correction of 1 Wm⁻² for the slight shift in the period means between the published ERA values and the early 2000s considered here as reference period. This results in a best estimate of 372 Wm⁻² for the land mean surface upward thermal radiation. This value is in between the estimates of 374.4 Wm⁻² determined from the surface EBAF Ed2.7 product (Table 3) and the CMIP5 multimodel mean estimate of 370.3 Wm⁻² (Table 2), which also define the uncertainty range we attach to this flux in Fig. 2 (upper panel). The land surface temperatures simulated by the CMIP5 models show overall a slight cold bias in the annual mean (Mueller and Seneviratne 2014) which fits to the somewhat lower surface upward thermal radiation in the CMIP5 multimodel mean compared to the above estimates.

Together with the downward thermal radiation of 306 Wm⁻² this leaves a best estimate for the land mean net surface thermal radiation (downward minus upward) of −66 Wm⁻² (Table 3). Combining this estimate further with the above estimate for the land surface solar absorption of 136 Wm⁻² results in a best estimate for the land surface net radiation (also known as land surface radiation balance) of 70 Wm⁻². Thus, according to Fig. 2 (upper panel), about 70 Wm⁻² of radiative energy is available for the nonradiative components of the terrestrial surface energy balance. The land surface net radiation as calculated in the 43 CMIP5 models is shown in Fig. 15 (upper panel). In their multimodel mean, the CMIP5 models calculate a somewhat higher land surface net radiation of 72.5 Wm⁻² (Table 2; Fig. 15, upper panel) than estimated here. This may be due to the overestimated surface solar absorption over land and a slight underestimation of the upward thermal radiation in these models, which is only partly compensated by a slight overall underestimation of their downward thermal radiation (cf. Sect. 3.1). Quantitatively, according to Sect. 3.1, the overestimation in surface solar absorption over land in the multimodel mean amounts to 4–6 Wm⁻² (based on the above determined overestimation in the downward solar radiation of 6–8 Wm⁻² and a land albedo of 25 %), which is not fully compensated by the underestimation in downward thermal radiation on the order of 3 Wm⁻². The excessive downward solar and lack of downward thermal radiation is a long-known phenomenon in the surface energy balance of climate models (e.g., Wild et al. 1995b).

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3.3.2 Nonradiative components

Most of the radiative energy available at the land surface (70 Wm⁻² as estimated above) is used for the terrestrial fluxes of sensible and latent heat. Compared to these fluxes, the additional non-radiative energy balance components, namely ground heat flux and melt, are small (below 1 %) over land on a multiyear average basis (Ohmura 2004). They can be neglected here. The partitioning of the surface net radiation into sensible and latent heat flux over land, largely controlled by the availability of soil water and vegetation characteristics, is afflicted with considerable uncertainties, since very limited reliable observational constraints from surface or spaceborne measurements are available for these fluxes. Accordingly, also the CMIP5 models vary greatly in their calculation of the land mean latent and sensible heat fluxes (Fig. 15, middle and lower panel; Table 2).

Jimenez et al. (2011) estimated the land mean latent heat flux at 45 Wm⁻², based on an all-product land mean average of 12 latent heat flux products, including satellite‐based products and estimates from offline land surface models in addition to reanalyses. The spread amongst these estimates amounts to 20 Wm⁻². However, their analysis covered only 70 % of the land surfaces, neglecting particularly areas over Greenland and Northern Africa with low latent heat fluxes. Similarly, Mueller et al. (2011) noted in their investigation of a variety of observation-based evaporation datasets as well as climate models from the former CMIP3 model intercomparison project that the land mean latent heat fluxes are scattered around 46 Wm⁻² in the various products with a standard deviation of ±5 Wm⁻², excluding also Greenland and the Sahara, where latent heat fluxes are generally low. More recently, Mueller et al. (2013) merged 40 datasets of estimated land surface evapotranspiration into different categories (diagnostic datasets, land surface models and reanalyses) and found the merged land mean estimates to vary between 423 mm/year (merged land surface model datasets, corresponding to a latent heat flux of 34 Wm⁻²) and 563 mm/year (merged reanalysis datasets, corresponding to a latent heat flux of 45 Wm⁻²). The merging of all available datasets into the LandFlux-EVAL synthesis product gave a land mean evapotranspiration of 493 mm/year, corresponding to a latent heat flux of 40 Wm⁻² (Mueller et al. 2013), with a standard deviation of 12 Wm⁻². This synthesis product does not include Antarctica. A best estimate of the land mean latent heat flux as defined in the present study (including Antarctica) based on the synthesis product should be therefore slightly below 40 Wm⁻². A recent unpublished space-based estimate from the GEWEX LandFlux project uses four different retrieval algorithms for the period 1984–2006 and provides a multimodel mean and standard deviation estimate of 488.4 ± 38.3 mm/year (38.0 ± 3 Wm⁻²). We adopt this value of 38.0 Wm⁻² in Fig. 2 (upper panel), also in line with the LandFlux-EVAL synthesis product estimate as discussed above. This is also close to the land mean latent heat flux estimate given by Trenberth et al. (2009) of 38.5 Wm⁻² and near the 40 Wm⁻² inferred from the water budget estimates in Trenberth et al. (2007, 2011). The ERA-Interim land mean latent heat flux is somewhat higher, at 44 Wm⁻² (Table 3). Berrisford et al. (2011) note, however, that the latent heat flux in ERA-Interim may be overestimated by 9 %, which also favors a land mean latent heat flux in the vicinity of 40 Wm⁻². Other reanalyses vary in a range from 38 up to 54 Wm⁻² as can be deduced from the water budget analyses of Trenberth et al. (2011). Similarly to ERA-Interim, some of the CMIP5 models tend to overestimate the latent heat fluxes over terrestrial surfaces in the annual mean as evidenced by Mueller and Seneviratne (2014), related to excessive precipitation in these models. The uncertainty range given in Fig. 2 (upper panel) acknowledges the spread between the merged land surface model estimates (low end) and the merged reanalysis datasets (high end) given in Mueller et al. (2013). This range encompasses also most estimates of the CMIP5 models in Fig. 15 (middle panel).

With a land mean surface net radiation of 70 Wm⁻² and latent heat flux slightly below 40 Wm⁻², this leaves slightly more than 30 Wm⁻² for the land mean sensible heat flux as a residual of the land surface energy balance. The estimated residual of 32 Wm⁻² for the land mean sensible heat flux in Fig. 2 (upper panel) is close to the multimodel mean CMIP5 estimate of 31.3 Wm⁻² (Table 2) which may be slightly biased low doe to excessive precipitation as pointed out above. The land mean sensible heat flux of 32 Wm⁻² is higher than the ERA-Interim value of 28.2 Wm⁻² (Table 3), but soil moisture is overestimated in ERA-Interim, particularly for dry land, as pointed out in Trenberth and Fasullo (2013) and Albergel et al. (2012), which may cause a low bias in the reanalysis sensible heat flux. The uncertainty in this component is, however, still particularly large, and the CMIP5 model estimates for the land mean sensible heat fluxes show larger ranges and standard deviations than for the corresponding latent heat fluxes, despite their lower absolute magnitudes (Table 2; Fig. 15). This justifies the above determination of the sensible heat flux as a residual in the surface energy balance. Excluding outliers outside two standard deviations, most land mean sensible heat fluxes simulated by the CMIP5 models lie between 25 and 36 Wm⁻², which constitutes the uncertainty range attached to the land mean sensible heat flux in Fig. 2 (upper panel). This range encompasses also the various reanalysis estimates, which show a tendency to cluster towards the lower end of the range (Trenberth et al. 2009; Berrisford et al. 2011).

The reduction in the uncertainties related to the partitioning of the surface net radiation into sensible and latent heat over land surfaces remains a major challenge in global energy balance studies.

4.1.1 Solar radiation

Ocean mean solar radiation budgets are displayed in Fig. 16 in terms of total (TOA), atmospheric and surface absorption. Their regional distributions can be inferred from Fig. 4. All model-calculated ocean budgets discussed in the following are again determined as averages over the years 2000–2004 in the historic “all forcings” experiments. Similar to the land mean budgets shown in Fig. 5, the models display a considerable spread in their solar budgets over ocean areas. From Table 2 we infer that the ranges and standard deviations of the model estimates are generally somewhat smaller than for the land budgets. This may partly be related to the more homogeneous surface boundary conditions as well as the larger averaging areas over ocean surfaces (covering 71 % of total area of the globe) than over the more heterogeneous land surfaces (covering 29 % of the globe), which tends to smooth out bias structures in the models more effectively over oceans than over land.

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At the TOA, the net solar flux averaged over oceans in the CMIP5 multimodel mean (250.8 Wm⁻²) is again close to the CERES EBAF TOA reference which we determined at 251.7 Wm⁻². As over land, no obvious bias in the simulated net solar flux at the TOA can be noted overall over oceans.

Again as over land, the differences between the solar budgets over oceans of the various CMIP5 models are larger at the surface (around 20 Wm⁻²) than at the TOA (around 16 Wm⁻²), despite the larger fluxes at the TOA (Figs. 16, 17; Table 2). Direct observations at the ocean surface to constrain the model-calculated surface downward solar fluxes are scarce. From BSRN, only 6 sites may be considered as representing to some extent maritime conditions, which at the same time provide records that are long enough to build representative climatologies. These are from West to East: Chesapeake Lighthouse, North Atlantic Ocean (36.9°N, 75.7°W); Bermuda Island, North Atlantic Ocean (32.3°N, 64.7°W); Cocos Island, Indian Ocean (12.1°S, 96.8°E); Manus Island, Central Pacific Ocean (2.0°S, 147.4°E); Nauru Island, Central Pacific Ocean (0.5°S, 166.9°E); Kwajalein, North Pacific Ocean (8.7°N, 167.7°E). Biases of the CMIP5 multimodel mean at these BSRN sites are shown in Fig. 18a. Although the biases vary largely, there is a general tendency for an overestimation of the downward surface solar radiation at these sites, as seen also over land surfaces. At individual stations, multimodel mean biases vary from strongly positive to close to zero. Specifically, biases are −0.4 Wm⁻² (Chesapeake Lighthouse), 4.8 Wm⁻² (Bermuda), 8.4 Wm⁻² (Cocos Island), 17.9 Wm⁻² (Manus), 14.6 Wm⁻² (Nauru), −1.6 Wm⁻² (Kwajalein). Averaged over all sites, 34 out of the 43 CMIP5 models (79 %) show an overestimation, while only 9 models (21 %) show an underestimation. Note that the Manus site has recently been shown to provide a representative set of measurements for the larger Tropical Western Pacific region (Riihimaki and Long 2014). This site is located very close to the coast, in a flat, near-sea level area of the island and is hardly affected by the local island meteorology, in contrast to a site more interior in the island.

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From GEBA, we used 20 sites with extended records in maritime environments. These sites include locations on various islands as shown in Fig. 3. Compared to these sites, the multimodel mean is higher by 4.2 Wm⁻² on average.

In addition, buoy data are available in the tropical Atlantic, Pacific and Indian Ocean, albeit at the expense of a substantially lower quality at these unmanned sites (see Sect. 2). We used data from 43 buoys as described in Sect. 2. Multimodel mean biases with respect to the different buoy networks are given in Fig. 19a. Models tend to calculate higher fluxes than measured on average at the PIRATA buoys in the Eastern tropical Atlantic by 1.5 Wm⁻², at the RAMA buoys in the Indian Ocean by 3.8 Wm⁻², and at the 3 Woodshole buoys by 11.0 Wm⁻², whereas the overall model bias is almost zero (−0.7 Wm⁻²) at the TAO/TRITON buoys in the Tropical Pacific (Fig. 19a). Thus, overall, radiation measurements representing maritime conditions still point towards an overestimation of the model calculated fluxes, as over land. Averaged over all 69 maritime GEBA, BSRN and buoy sites considered here, the CMIP5 multimodel mean overestimate amounts to 3.0 Wm⁻². Due to the small number of sites with high quality measurements, and the arguable quality of the buoy data, the model overestimation over oceans is, however, quantitatively on a less solid basis than over land.

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4.1.2 Thermal radiation

Thermal radiation budgets averaged over global oceans as calculated by the 43 CMIP5 models are depicted in Fig. 20, with the outgoing thermal radiation at the TOA (upper panel), the net thermal radiation within the atmosphere (middle panel) and at the surface (lower panel). Their regional distributions are displayed in Fig. 9. As for the solar budgets, the spread amongst the thermal budgets of the CMIP5 models averaged over oceans is substantial, but smaller than the corresponding budgets over land.

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From CERES EBAF, we determined an outgoing thermal radiation averaged over oceans at the TOA of 242.9 Wm⁻² for the usual period 2001–2005. The associated multimodel mean of the CMIP5 models is 240.9 Wm⁻² (Table 2), thus within 2 Wm⁻² of the CERES EBAF estimate. At the ocean surface, the flux that can be compared with direct observations is again the downward thermal radiation, shown for the CMIP5 models in Fig. 17 (lower panel). We compared also these fluxes with the 6 BSRN sites considered as representing maritime conditions (Fig. 18b). The overall multimodel mean bias averaged over the 6 sites is marginal, at −0.3 Wm⁻². The fluxes at 3 sites are underestimated by the multimodel mean (Bermuda −2.0 Wm⁻², Cocos Island −3.1 Wm⁻², Nauru −3.6 Wm⁻²), two sites show biases of less than 1 Wm⁻² (Kwajalein 0.5 Wm⁻², Manus 0.7 Wm⁻²), while one site (Chesapeake Lighthouse) shows an overestimation of 6.9 Wm⁻². The comparison with the 17 buoy sites with useful thermal measurements (Sect. 2) gave an overall 3.0 Wm⁻² lower value for the multimodel mean compared to observations. It has been argued that the lack of shading on the buoy measurements may cause an overestimation of the downward thermal measurements of a similar amount (Wang and Dickinson 2013 and references therein). This would reduce the overall bias similar to the one seen when compared to the BSRN sites. Thus, based on the limited observational evidence from BSRN and buoys, there seems no indication for a large bias of the model-calculated downward thermal fluxes over oceans, if anything, then a small underestimation. Regionally, the simulated multimodel mean fluxes show an almost zero bias at the TAO/TRITON buoys in the Tropical Pacific (Fig. 19b), as already noted with the simulated solar fluxes in this region (Fig. 19a). The simulated downward thermal fluxes overall are lower than the buoy observations in the Eastern Tropical Atlantic (PIRATA), at the RAMA buoys in the Indian Ocean, and at the 3 Woodshole buoys (Fig. 19b).

4.3.1 Radiative components

The best estimates for the TOA fluxes averaged over oceans inferred from CERES EBAF for the TOA solar incoming, reflected, and absorbed radiation amount to 346.6, −94.9 and 251.7 Wm⁻² respectively, and for the outgoing thermal radiation to −242.9 Wm⁻² (Table 3). They are displayed as rounded values in Fig. 2 (lower panel). Thus, 72.5 % of the corresponding TOA solar irradiance is absorbed in the ocean domain of the climate system, compared to a 65.7 % in the land domain (Fig. 2, upper panel), as might be expected from the higher surface albedo over land. Uncertainty ranges of these TOA fluxes are again as discussed in Wild et al. (2013a). The total solar absorption in the ocean domain is now larger than the thermal emission at the TOA, which compensates for the energy loss due to the net atmospheric energy transport away from the ocean domain onto land (c.f. Discussion in Sect. 3.3.1). Quantitatively, the excess absorption compared to thermal emission averaged over oceans amounts to 8.8 Wm⁻² (Table 2). Since close to 1 Wm⁻² is taken up by the oceans, 7.9 Wm⁻² remain to be exported from ocean to land, as indicated in Fig. 2 (lower panel). Note that the actual value associated with the arrow of the transport term from ocean to land (8 Wm⁻²) as well as its uncertainty range in the ocean energy balance diagram (Fig. 2, lower panel) are less than half of the corresponding value in the land energy balance diagram (Fig. 2 upper panel), due to the larger ocean domain. Multiplied by the global ocean area of 361 × 10¹² m⁻², this corresponds to the same 2.8 PW of ocean land transport as discussed in Sect. 3.3.1.

While the TOA fluxes are equally well known over both land and oceans from satellites, surface fluxes over oceans are less well constrained than over land, since direct observations at the ocean surface are much more scarce. For the downward ocean mean solar and thermal fluxes we use in Fig. 2 (lower panel) the estimates of 185 and 356 Wm⁻², derived together with their uncertainty ranges in Sect. 4.2. As outlined there, these estimates, inferred from GCMs and their biases with respect to direct observations, are remarkably close (within 4 Wm⁻²) to reanalysis (ERA-Interim) estimates and the CERES satellite derived products. This increases our confidence in the magnitude of the ocean mean surface downward solar and thermal fluxes, despite the limited availability of direct observations. As also noted above and evident from Fig. 2, the surface downward solar fluxes averaged over land and oceans are nearly identical, which seems a robust feature in various estimates (see Sect. 4.2). This is the case despite an insolation at the TOA which is higher by 22 Wm⁻² over ocean than over land, indicative of a stronger attenuation of the solar beam over oceans than over land, in line with higher water vapor content and cloudiness in the ocean domain, leading to stronger atmospheric reflection.

To determine the solar radiation absorbed by the oceans we need, in addition to the surface downward solar fluxes, also information on the albedo of the ocean surfaces. The surface CERES EBAF dataset incorporates a radiation weighted ocean mean albedo of 0.078, as can be deduced from Table 3. The albedo in this dataset is inferred from a coupled atmosphere/ocean radiative transfer model that has been extensively validated with BSRN data (Jin et al. 2002). From Berrisford et al. (2011) we deduce a radiation weighted ocean mean surface albedo used in ERA-Interim and ERA-40 of 0.075 and 0.077 respectively, while the average over the 43 CMIP5 models gives an ocean mean albedo of 0.074 (with a standard deviation of 0.01), as can be inferred from Table 2. From Trenberth et al. (2009) we take a value of 0.09 for their estimate of ocean mean albedo, as well as a value of 0.86 from the satellite derived ISCCP FD satellite-derived product. Assuming an ocean mean surface albedo of 0.08 (closely following the CERES EBAF value as over land) and our best estimate near 185 Wm⁻² for downward solar radiation, this implies a reflected solar radiation over oceans of around 15 Wm⁻², and an ocean mean absorbed surface solar radiation around 170 Wm⁻². As over land, an accurate determination of surface albedo remains a challenge and introduces additional uncertainties in the absorbed and reflected solar fluxes at ocean surfaces. The estimates of solar radiation reflected at ocean surfaces in the recent literature span a range from 13 to 18 Wm⁻² (Table 3; Berrisford et al. 2011; Trenberth et al. 2009) which confine the associated uncertainty range applied in Fig. 2 (lower panel).

The TOA and surface absorption of 252 and 170 Wm⁻² imply an average absorption of solar radiation in the atmosphere above oceans of 82 Wm⁻². This is 5 Wm⁻² more than in the CMIP5 multimodel mean. Thus we quantitatively find a similar underestimation of atmospheric absorption over land and oceans in the CMIP5 models (cf. Sect. 3.3.1). Percent wise, Fig. 2 (lower panel) and Table 3 suggest that 23.6 % of the incoming solar radiation at the TOA over oceans is absorbed within the atmosphere, while 49.0 % is absorbed at ocean surfaces. Over land 23.7 % of the TOA insolation is absorbed in the atmosphere, while 41.9 % is absorbed at land surfaces. Thus, the fraction of incoming solar radiation absorbed in the atmosphere is very similar over both land and oceans in Fig. 2. This is not in conflict with the abovementioned higher attenuation over oceans which is primarily caused by a higher atmospheric reflection from the increased cloudiness. On a more regional scale over Europe, Hakuba et al. (2014) estimated the atmospheric absorption at 23.1 % based on a dense network of surface observations collocated with CERES EBAF TOA fluxes, which is remarkably close to the large-scale estimates obtained here. They further noted the fraction of atmospheric absorption, near 23 %, to be a very robust estimate largely unaffected by variations in latitude and season.

With respect to the thermal fluxes, for the upward thermal radiation at the ocean surfaces, estimates from reanalyses should be superior to those from the CMIP5 models, as they use prescribed observed sea surface temperatures as an approximation of skin temperature in their calculation of the surface emission rather than interactively calculated sea surface temperatures as in the CMIP5 models which can be biased. Note that also reanalyses consider a surface emissivity/absorptivity ε slightly lower than 1, thus the surface upward thermal radiation consists of the surface emission plus a small contribution of the upward reflected part of the downward thermal radiation, as outlined in Sect. 3.3.1. As also emphasized in that section, the sensitivity of the surface upward thermal radiation to uncertainties in ε is small, due to compensational effects between the surface emission and reflected part of the downward thermal radiation. In addition, the range of ε changes, which can be induced by temperature and windspeed changes, is well less than 1 % (Kato et al. 2013). Indeed reanalysis products are very consistent in their ocean mean upward thermal radiation, with values of 408.6 Wm⁻² over the period 1989–2008 (ERA-Interim), 408.5 Wm⁻² over the period 1989–2001 (ERA-40), 407.9 Wm⁻² over the period 1989–2008 (NRA2) and 409.6 Wm⁻² over the period 1989–2008 (JRA-25) (Berrisford et al. 2011). Since the center years of these periods are shifted back in time by some years compared to the period considered here (2000–2004), requiring a slight upward correction for the additional warming on the order of 0.5 Wm⁻², we take a best estimate towards the upper bound of these values (409 Wm⁻²) in Fig. 2 (lower panel). This value is also very close to the CMIP5 multimodel mean (409.6 Wm⁻², Table 2), even though the simulated sea surface temperatures in these fully coupled atmosphere–ocean models are not observationally constrained, in contrast to the aforementioned reanalyses. Also the estimate given by CERES EBAF (408.3 Wm⁻²) for the period 2000–2005 is very close to the above values. The uncertainty range, defined by the range of these estimates in absence of uncertainty information on the individual estimates, is accordingly also fairly narrow. Combining the 409 Wm⁻² upward thermal flux with the best estimate of 356 Wm⁻² for the downward thermal radiation (Sect. 4.2) leaves an amount of −53 Wm⁻² for the net thermal cooling (upward minus downward) at ocean surfaces. Together with an absorbed solar radiation at the ocean surface of 170 Wm⁻², this adds up to 117 Wm⁻² of radiative energy available for the non-radiative energy fluxes over oceans. This best estimate for the surface net radiation over oceans is 3 Wm⁻² lower than calculated by the CMIP5 multimodel mean (Table 2; Fig. 23). The higher surface net radiation in the CMIP5 multimodel mean is in line with the evidence for an overestimation of the downward solar radiation at ocean surfaces in the CMIP5 multimodel mean, which is not fully compensated by the small biases in the downward thermal radiation in these models (Sect. 4.1).

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4.3.2 Non-radiative components

As over land, there are very limited direct observational constraints for the sensible and latent heat fluxes over oceans. Accordingly, also the CMIP5 models show a substantial spread in their ocean mean surface sensible and latent heat fluxes (Fig. 23). However, in contrast to the land mean estimates in Sect. 3.3.2, the simulated ocean mean latent heat fluxes show now both larger ranges and standard deviations than the corresponding sensible heat fluxes, as can be expected from their larger absolute values. We therefore determine here the latent heat flux as a residual of the ocean surface energy balance.

The CMIP5 model-calculated ocean mean sensible heat flux values cover a range from 11 to 17 Wm⁻², when outliers exceeding 2 times the standard deviation are neglected (Fig. 23 lower panel). Reanalysis products give for the same quantity a very similar range of 11–16 Wm⁻² (Trenberth et al. 2009; Berrisford et al. 2011). However, Clayson et al. (2014) recently estimated a higher ocean sensible heat flux of 17.8 Wm⁻² over the 10 years period 1998–2007, based on the Seaflux dataset, which relies almost exclusively on satellite observations. This suggests that values towards the upper end of the model and reanalysis estimates may be more realistic than towards the lower end. Therefore we use a value of 16 Wm⁻², corresponding to the highest reanalysis estimate, for the ocean mean sensible heat flux in Fig. 2 (lower panel). At the same time we acknowledge the mostly lower reanalyses and CMIP5 values and the slightly higher Seaflux value by adjusting the associated uncertainty range in Fig. 2 (lower panel) so that it covers the different reanalysis estimates as well as the Seaflux estimate, in absence of more specific uncertainty information and direct observational constraints. We thereby also acknowledge that to date, the uncertainties in this flux component remain substantial, particularly in relative terms, with the different estimates covering a range of almost half the absolute flux magnitude.

With a surface net radiation of 117 Wm⁻² over oceans, a sensible heat flux near 16 Wm⁻², and a subsurface ocean heat flux of the order of 1 Wm⁻² due to the current imbalance of the climate system (e.g., Hansen et al. 2011), this leaves around 100 Wm⁻² as a residual for the latent heat flux over oceans. This value comes very close to the ERA-40 and ERA-Interim ocean mean latent heat flux values of 99.0 and 99.3 Wm⁻², respectively (Berrisford et al. 2011), and is also not too far from the estimate given in Trenberth et al. (2009) of 97.1 Wm⁻². The value adopted here is, however, substantially higher than the value of 90.3 Wm⁻² estimated in Seaflux (Clayson et al. 2014). The Seaflux value is the lowest recently published latent heat flux estimate over oceans and therefore also confines the uncertainty range at the low end in Fig. 2 (lower panel). Estimates of ocean mean latent heat fluxes from eight different reanalyses cover a wide range from 90 to 109 Wm⁻² as can be deduced from the water budget estimates given in Trenberth et al. (2011). Our best estimate for the ocean mean latent heat flux near 100 Wm⁻² is still considerably lower than the multimodel mean of the CMIP5 models of 104.8 Wm⁻² (Table 2; Fig. 23). The higher value of the CMIP5 multimodel mean is a consequence of a higher surface net radiation over oceans due to a higher (and likely overestimated) surface solar radiation (cf. Sect. 4.1.1), as well as a somewhat lower sensible heat flux than estimated here. Estimates of ocean mean latent heat flux exceeding the multimodel mean value are therefore considered unrealistic, as it would require either an unrealistically high surface net radiation, or an unrealistically low sensible heat flux. We therefore use the CMIP5 multimodel mean value of 105 Wm⁻² to confine the uncertainty range of the ocean mean latent heat flux at the upper end, in absence of other more stringent observational constraints.

In summary, the energy balance over oceans as schematically displayed in Fig. 2 (lower panel) is derived in a framework that is consistent with the land energy balance in Fig. 2 (upper panel), and does not violate the limited observational constraints. Uncertainties remain, as over land, particularly also in the partitioning of the available radiative energy at the ocean surface between the sensible and latent heat flux components.