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

Wild, Martin; Folini, Doris; Hakuba, Maria Z.; Schär, Christoph; Seneviratne, Sonia I.; Kato, Seiji; Rutan, David; Ammann, Christof; Wood, Eric F.; König-Langlo, Gert

doi:10.1007/s00382-014-2430-z

Open Access
Published: 11 December 2014

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

Martin Wild¹,
Doris Folini¹,
Maria Z. Hakuba¹,
Christoph Schär¹,
Sonia I. Seneviratne¹,
Seiji Kato²,
David Rutan²,
Christof Ammann³,
Eric F. Wood⁴ &
…
Gert König-Langlo⁵

Climate Dynamics volume 44, pages 3393–3429 (2015)Cite this article

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Abstract

The energy budgets over land and oceans are still afflicted with considerable uncertainties, despite their key importance for terrestrial and maritime climates. We evaluate these budgets as represented in 43 CMIP5 climate models with direct observations from both surface and space and identify substantial biases, particularly in the surface fluxes of downward solar and thermal radiation. These flux biases in the various models are then linearly related to their respective land and ocean means to infer best estimates for present day downward solar and thermal radiation over land and oceans. Over land, where most direct observations are available to constrain the surface fluxes, we obtain 184 and 306 Wm⁻² for solar and thermal downward radiation, respectively. Over oceans, with weaker observational constraints, corresponding estimates are around 185 and 356 Wm⁻². Considering additionally surface albedo and emissivity, we infer a surface absorbed solar and net thermal radiation of 136 and −66 Wm⁻² over land, and 170 and −53 Wm⁻² over oceans, respectively. The surface net radiation is thus estimated at 70 Wm⁻² over land and 117 Wm⁻² over oceans, which may impose additional constraints on the poorly known sensible/latent heat flux magnitudes, estimated here near 32/38 Wm⁻² over land, and 16/100 Wm⁻² over oceans. Estimated uncertainties are on the order of 10 and 5 Wm⁻² for most surface and TOA fluxes, respectively. By combining these surface budgets with satellite-determined TOA budgets we quantify the atmospheric energy budgets as residuals (including ocean to land transports), and revisit the global mean energy balance.

Introduction

The energy balance of the Earth is a fundamental determinant of the climatic conditions on our planet. Thanks to impressive progress in space-based observation systems in the past decade, we now know the exchanges of radiative energy flows between our planet and surrounding space with unprecedented accuracy. This has enabled detailed assessments of the radiation budgets at the top of atmosphere (TOA) in climate models (e.g., Potter and Cess 2004; Trenberth and Fasullo 2010; Wang and Su 2013; Dolinar et al. 2014). However, the distribution of the radiative energy within the climate system has not been established with the same accuracy, since it cannot be directly measured from satellites. Accordingly, estimates on the magnitude of the energy balance components at the surface and within the atmosphere as presented in the literature largely vary even on a global annual mean basis (e.g., Budyko 1956; Hartmann et al. 1986; Ramanathan 1987; Ohmura and Gilgen 1993; Kiehl and Trenberth 1997; Wild et al. 1998; Hatzianastassiou et al. 2005; Trenberth et al. 2009; Stephens et al. 2012; Stevens and Schwartz 2012; Wild et al. 2013a; Trenberth and Fasullo 2012). Also the surface radiation budgets as represented in climate models thus traditionally largely differ (e.g., Wild et al. 1995b, 2013a; Wild 2008; Stephens et al. 2012; Li et al. 2013).

Recently, progress has been made to better constrain these budgets not only at the TOA, but also at the surface, taking into account latest modeling efforts and surface observations on the one hand (Wild et al. 2013a) as well as improved satellite retrievals from both passive and active sensors on the other hand (Kato et al. 2013). Here we expand the study of Wild et al. (2013a) to further decompose the global mean energy balance estimates as shown in Fig. 1 into their land and ocean domains. This is illustrated in a schematic form in Fig. 2, which summarizes some of the findings of this study. Knowledge of the energy balance over oceans is critical, for example, for the coupling of 3 dimensional dynamical models of the ocean and the atmosphere, and the related exchange of energy and water at the ocean–atmosphere interface. Accurate knowledge of the surface energy fluxes at the atmosphere/ocean interface is also critical for the determination of the ocean heat budget and transports of heat in the ocean (Trenberth and Caron 2001; Trenberth and Fasullo 2008). The energy balance over land is of eminent importance for the representation of land surface processes in Earth system models and the determination of climate and ecology of the immediate human environments (e.g., Seneviratne et al. 2010). The considerable uncertainties and lack of agreed-upon reference values particularly of the surface flux components of the land and ocean energy balances have traditionally hampered the coupling of land surface and ocean models to the atmospheric component. In the present study we try to use the information contained in direct observations to pose additional constraints on these budgets over land and oceans.

As in Wild et al. (2013a), the approach taken here relies on a combination of direct observations and modeling results performed within the Coupled Model Intercomparison Project Phase 5 (CMIP5) for the latest 5th IPCC assessment report (IPCC-AR5). This goes along with a validation of the land and ocean energy budgets of the comprehensive set of climate models that is now available in the CMIP5 archive. Compared to Wild et al. (2013a) more than twice the number of climate models were available in the CMIP5 archive for the present study.

Emphasis in the present study is placed on the land surface energy balance, which is best constrained by direct surface observations, since the vast majority of direct flux measurements are taken over land surfaces. In addition and for completeness, an attempt is made to derive estimates for the energy balance components averaged over oceans, which are consistent with the land mean energy balance derived here and the global mean energy balance derived in Wild et al. (2013a), as well as with the limited information from direct observations taken in maritime environments. We further discuss our estimates in light of other recent land and ocean-separated estimates relying on independent approaches based on reanalyses and satellite products, to assess the consistency and robustness of these recent independent estimates. Finally, we recompose the global mean energy balance by combining the land and ocean mean energy balances derived here, to check its consistency with our previously published global estimates (Wild et al. 2013a, b).

Section 2 describes the observational data and climate models used in this study. Section 3 discusses the energy balance over land as simulated in the CMIP5 models, and infers best estimates for its components. Section 4 focuses on the energy balance over oceans. Section 5 reassembles the global mean energy balance from the land and ocean mean energy balances. Section 6 summarizes the main findings of this study.

Observational data and models

As in Wild et al. (2013a), the observational reference values for the radiative fluxes at the TOA are taken from the spaceborne Clouds and the Earth’s Radiant Energy System (CERES, Wielicki et al. 1996), but now separated into fluxes over land and oceans. CERES measures filtered radiances in the solar (between 0.3 and 5 μm), total (0.3 and 200 μm), and window (8 and 12 μm) regions on board of the NASA satellites Terra and Aqua, with thermal radiances determined as differences between total and solar channel radiances. The uncertainty in the solar reflected TOA fluxes from CERES due to uncertainty in absolute calibration is ~2 % (2 − σ), or equivalently 2 Wm⁻². The uncertainty of the outgoing thermal flux at the TOA as measured by CERES due to calibration is ~3.7 W m⁻² (2 − σ) (Loeb et al. 2009). In the CERES energy balanced and filled (EBAF) dataset, solar and thermal TOA fluxes are adjusted within their range of uncertainty to be consistent with independent estimates of the global heating rate based upon in situ ocean observations, and are made available on a 1° grid (Loeb et al. 2009). We calculated global land and ocean averages of the TOA radiative flux components from CERES EBAF for the periods 2001–2005 and 2001–2010, based on version EBAF 2.7 (Loeb et al. 2012), using a 10′ land-sea mask provided by CERES. We include in the global land budget Greenland and Antarctica as well as the ice shelves, whereas sea ice and inland seas are considered in the ocean budgets. This applies for all variables and results discussed in this study.

The land and ocean mean TOA reference fluxes determined this way for the period 2001–2005 are found to be within a few tenths of a W/m⁻² as compared to the same quantities averaged over the period 2000–2010, the entire period now available from CERES EBAF (c.f. also Trenberth et al. 2014). Thus the exact length of the CERES EBAF record is not very critical for the present purpose of determining climatological land and ocean mean budgets. In sensitivity tests with different available land sea masks, we noted that differences up to 1 Wm⁻² in the land and ocean averaged TOA insolation can emerge depending on whether floating ice shelve areas (predominantly in Antarctica) are considered as land or ocean. We define them here as land areas. Differences in the definition of fractional land/sea boxes along coastlines were found to cause differences of no more than a few tenth of a W/m⁻² at the maximum in the land and ocean mean TOA insolation, whereas adding or dismissing interior lakes in the land-sea mask has a negligible impact on this quantity.

Observational constraints for surface fluxes primarily stem from two databases for worldwide measurements of radiative fluxes at the Earth surface, the global energy balance archive (GEBA, Gilgen et al. 1998; Ohmura et al. 1989) and the database of the Baseline Surface Radiation Network (BSRN, Ohmura et al. 1998; König-Langlo et al. 2013). GEBA, maintained at ETH Zurich, is a database for the worldwide measured energy fluxes at the Earth’s surface and currently contains 2500 stations with 450‘000 monthly mean values of various surface energy balance components. By far the most widely measured quantity is the solar radiation incident at the Earth’s surface, with many of the records extending back to the 1950s, 1960s or 1970s. This quantity is also known as global radiation, and is referred to here as downward solar radiation. Gilgen et al. (1998) estimated the relative random error (root mean square error/mean) of the downward solar radiation values at 5 % for the monthly means and 2 % for yearly means.

BSRN became operational in the early 1990s and provides radiation measurements with the highest available accuracy and high temporal resolution of 1 min at a limited number of sites in various climate zones. To date 54 anchor sites exposed to different climate regimes report their data to the BSRN Archive at the Alfred Wegener Institute (AWI) (http://www.bsrn.awi.de/). The accuracy of the BSRN solar and thermal radiation measurements used in this study is discussed in detail in Wild et al. (2013a).

At oceans surfaces, downward solar and thermal radiation is increasingly recorded from measurements on buoys with sensors that compose the Improved Meteorological (IMET) system (Colbo and Weller 2009). The quality of these unmanned sites is, however, not at the level of the BSRN measurements. Records are typically still fairly short, covering a few years only. For downward solar radiation, 48 buoys provide data that enable the determination of at least one monthly mean for each month of the year, thus allowing for the calculation of annual means from complete annual cycles and excluding the risk of spurious biases due to incomplete seasonal cycles. Out of these 48 buoys, 17 buoys stem from the Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) (Bourles et al. 2008), 18 buoys from the Tropical Atmosphere Ocean/Triangle Trans-Ocean Buoy Network (TAO/TRITON) in the Tropical Pacific (McPhaden et al. 1998), 10 buoys from the Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction (RAMA) in the Indian Ocean (McPhaden et al. 2009), and three buoys from the Woods Hole Oceanographic Institution, located in the Northwest Tropical Atlantic (15°N, 51°W), East Tropical Pacific (20°S, 85°W, off northern Chile) and north of Hawaii, respectively (Colbo and Weller 2009). We further excluded 5 buoys from the PIRATA network, whose measurements were shown to be biased low due to the contamination of the domes of the radiometers with dust (Foltz et al. 2013), leaving a total of 43 buoy sites for the analysis of solar radiation. From the 53 buoys measuring the downward thermal radiation at the above networks, only 17 buoys fulfill the criterion of providing a complete annual cycle. These stem from PIRATA (2 buoys), RAMA (2 buoys), TAO/TRITON (9 buoys), and Woods Hole (3 buoys). The uncertainty of these buoy measurements is estimated at 5–6 Wm⁻² for annual mean downward solar and 4 Wm⁻² for annual mean thermal radiation (Colbo and Weller 2009).

The geographical distribution of the radiation sites used in this study is shown in Fig. 3. The distribution of sites is widespread and covers all major climate regimes, but gaps remain particularly in remote land areas and over the extratropical oceans.

We use data from 43 global climate models (GCMs) from the CMIP5 archive as frozen for the IPCC AR5 in June 2013 in our analysis. This includes all models available in the frozen CMIP5 database, except for the four models CanCM4, EC Earth, FIOESM and GFDL-CM2p1, which did not include the complete set of energy balance components. Thus, we are able to include more than twice the number of models compared to our previous study (Wild et al. 2013a) that was based on 21 CMIP5 models as available in June 2012. The 43 models used in this study are listed in Table 1, together with their host institutions, and their abbreviations as used in this manuscript. The model flux fields analyzed in this study are taken from the “historical” experiments that attempt to reproduce the climate variations of the twentieth century as accurately as possible, and include all major natural and anthropogenic forcings, such as changes in atmospheric greenhouse gases, solar output, aerosol loadings (tropospheric and volcanic) and land use. The “historical” experiments start around 1860 and are carried out up to at least to 2005. After 2000, CMIP5 models tend to slightly underestimate the stratospheric aerosol optical depth compared to satellite observations (Neely et al. 2013; Santer et al. 2014). A number of institutions provide several realizations of this experiment with differing initial conditions (ensemble simulations). However, we found that the choice of the ensemble member does not critically affect our results, since the relevant differences amongst the ensemble members are typically an order of magnitude smaller than the detected biases against observations in the specific analyses carried out in this study. Therefore, and also to avoid an overrating of a specific model, we include only one ensemble member from those models with several ensemble realizations.

Table 1 Brief listing of the 43 models used in this study, together with their abbreviations, host institutions and horizontal resolution

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The GCM radiation budgets representing the conditions at the beginning of the twenty-first century are determined as averages over the five-year period 2000–2004, which state the final five complete years of the historical experiments available from all investigated models. The slight shift in period by 1 year compared to the CERES radiation budgets (2001–2005, see above) is irrelevant for the comparisons since the GCMs are not deterministic by nature, and both ocean and land mean budgets are insensitive to the exact choice of the period as outlined above. Specifically, a shift in the CMIP5 radiation budget climatologies by 1 year typically introduces differences in the tenth of a Wm⁻² range only, thus negligible for the accuracy level considered in this study. Similar to the CERES EBAF land and ocean mean budgets, the CMIP5 budgets are calculated using the land-sea masks of the individual GCMs and the Climate Data Operators (CDO) software package (https://code.zmaw.de/projects/cdo).

Energy balance over land

Assessment of land radiation budgets in CMIP5 models

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).

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

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Table 3 Estimates for land, ocean, and global mean energy balance components in the present and other recent studies

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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).

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).

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

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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).

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).

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).

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).

Best estimates for the downward solar and thermal radiation at land surfaces

To obtain best estimates of land mean surface downward solar and thermal radiation we use the approach introduced in Wild et al. (2013a). In this approach we related the biases in downward solar and thermal radiation of 21 CMIP5 models at the surface sites to their respective global mean values. Here we adjust this approach, as we compare the model biases of 43 CMIP5 model no longer against their global means, but rather their land means. This is done in Figs. 12 and 13 for the land mean downward solar radiation. Thus, in Fig. 12, each cross signifies a CMIP5 model, with its mean bias in downward solar radiation compared to the 760 surface sites from GEBA (as given in Fig. 7) on the horizontal axis, and its respective land mean value (given in Fig. 6, upper panel) on the vertical axis. Generally, the higher the land mean value of a model, the stronger is also its overestimation relative to the observations from the GEBA sites. The correlation coefficient is almost 0.9. This is somewhat larger than the correlation coefficient of 0.8 derived in Wild et al. (2013a) where the global mean values rather than the land mean values were correlated with the model biases. The higher correlation with the land mean values is not unexpected as the density of the reference stations is highest over land. We apply a linear regression between the model biases and their respective land means shown in Fig. 12 (significant at the 95 % level). We use the orthogonal regression method that minimizes the distances orthogonal to the regression line, in contrast to the standard least y-squares regression that only minimizes the distances along the vertical axes. In this way the uncertainties in both x and y directions are accounted for. A best estimate for the land mean downward solar radiation is then deduced from the linear regression at the intersection where the bias with respect to the surface observations becomes zero, as indicated by the dotted lines in Fig. 12. This results in a best estimate for the land mean downward solar radiation at Earth’s surface of 183.7 (±1.8) Wm⁻² The value in brackets gives the 2σ confidence interval for the line intercept resulting from the regression analysis.

Similar to the global mean estimates in Wild et al. (2013a), we also tested the robustness of this land mean estimate, by repeating the analyses using the 38 worldwide distributed BSRN sites instead of the 760 GEBA sites as observational references (Fig. 13). The correlation between the model biases, now determined at the 38 BSRN sites (as given in Fig. 8), and their respective land mean values of downward solar radiation (as given in Fig. 6, upper panel) is again high, at 0.9. The slope of the corresponding linear regression in Fig. 13 deviates slightly more from one than the respective slope when using the 760 GEBA sites, indicative of the lower spatial sampling with the BSRN sites. Still, the best estimate deduced from the linear regression in Fig. 13 using the 38 BSRN sites as reference is very similar to the one obtained with the GEBA sites as references in Fig. 12. With the BSRN sites as reference, the best estimate for the land mean downward solar radiation amounts to 184.0 (±1.6) Wm⁻² (2σ uncertainty given in the parentheses), closely matching the 183.7 (±1.8) Wm⁻² inferred above based on the GEBA sites. The close agreement, despite entirely different and independent surface reference networks, suggests that the best estimate inferred in this way is fairly robust.

As a conservative uncertainty range for this estimate, we expand the 2σ regression uncertainty range to cover all land mean values calculated by those GCMs which show only marginal biases compared to the surface stations, in line with the conceptual approach applied here that infers land mean estimates from GCMs which show no biases. Land mean estimates from models with no obvious biases against the surface sites strictly cannot be disqualified as being biased in this approach. Thus, in Figs. 12 and 13 we note also land mean downward solar radiation values of 182 and 187 Wm⁻² (rounded) which stem from GCMs with marginal biases (defined here as smaller than 1 Wm⁻²) and thus should be included in the uncertainty range. With this definition, the uncertainty range for the land mean downward solar radiation, encompassing all GCM land mean values as defined above, extends from 182 to 187 Wm⁻².

Interestingly, the above estimate for the land mean downward solar radiation around 184 Wm⁻² is also nearly identical to the land mean estimate given in Trenberth et al. (2009) of 184.7 Wm⁻² derived independently using the International Satellite Cloud Climatology Project (ISCCP FD) surface flux dataset with an adjustment for underestimated water vapor absorption (Kim and Ramanathan 2008), thereby not taking into account in any way the surface observations (Table 3). From the satellite-based surface flux dataset “Surface EBAF Ed2.7” (Kato et al. 2013) we calculated a slightly higher land mean surface downward solar radiation of 186.5 Wm⁻² (Table 3), which is within the uncertainty range derived above. This product determines surface irradiances using observational constraints given by the TOA irradiances from CERES, and again, is independently derived from the approach taken here. Compared to Kato et al. (2011), a better treatment of the diurnal cycle in adjusting surface shortwave irradiance significantly reduced the downward solar radiation in this product (Kato et al. 2013; Rutan et al. 2014), which improves the agreement with the present study and Trenberth et al. (2009). ERA-Interim, yet another independent approach based on reanalysis, determines a slightly higher land mean downward solar radiation, at 187.2 Wm⁻² (Table 3; Berrisford et al. 2011). The similar estimates obtained by these independent approaches, covering a range of only 3 Wm⁻², gives additional confidence that we have now a better handle on the magnitude of the land mean downward solar radiation.

It is further interesting to note that the estimate for land mean downward solar radiation derived here matches its global mean estimate of 184.6 Wm⁻² derived in Wild et al. (2013a) to within 1 Wm⁻². The close agreement between global and land mean downward solar radiation does not only emerge from the present analysis, but we note this concurrence also in other estimates of the global and land mean energy balance. From Trenberth et al. (2009) we take that their estimates for the global and land mean downward solar radiation, at 184.3 and 184.7 Wm⁻², respectively, differ by only 0.4 Wm⁻². From the same study we take that also the ISCCP-FD satellite derived land mean surface downward solar radiation differs only by 0.6 Wm⁻² from its global mean value. Further, the above-mentioned land mean estimate of 186.5 Wm⁻², which we determined from the Surface EBAF Ed2.7 (Kato et al. 2013) differs by only 0.1 Wm⁻² from the respective global mean estimate. In terms of reanalyses, we find in Berrisford et al. (2011) that also the ERA-Interim and the ERA-40 show differences of only 0.9 and 1.1 Wm⁻² between their global and land mean estimates, respectively. The close similarity between the global and land mean estimates across various independent observation-based estimates gives some trust in the robustness of this finding. It also has implications for the ocean budget discussed in Sect. 4, as the above notion implies a close agreement between land and ocean mean surface downward solar radiation. In the CMIP5 climate models, global and land mean downward solar radiation differ in the multimodel mean by 2.8 Wm⁻² (Table 2).

As above for the solar radiation, we further determine a best estimate for the land mean downward thermal radiation. Thus, in Fig. 14, land mean values of downward thermal radiation as calculated in 43 CMIP5 models are displayed as function of their biases averaged over 41 BSRN sites. A significant linear regression appears again between the model biases and their land mean values, with a high correlation of nearly 0.9, similar to the solar radiation above. There is an obvious tendency that the more a model underestimates the downward thermal radiation at the BSRN sites, the lower is also its land mean value. The zero model bias corresponds to a best estimate for a land mean downward thermal radiation of 305.7 (±1.2) Wm⁻² (2σ uncertainty). Also this land mean estimate is robust with respect to a differing surface-based reference dataset of downward thermal radiation, consisting of 26 sites from GEBA and 19 sites from BSRN, which has also been used to test the robustness of the respective global mean estimate in Wild et al. (2013a).

We enlarge also the 2σ regression uncertainty range for this land mean downward thermal radiation estimate, to accept all land mean values from GCMs with marginal (<1 Wm⁻²) biases. In Fig. 14 land mean values ranging from 302 to 309 Wm⁻² fulfill this criterion and form a conservative uncertainty range for this estimate.

The estimate of ERA-Interim is, at 304 Wm⁻² (Table 3), very close to the estimate derived here. ERA-Interim includes the Rapid Radiation Transfer Model (RRTM, Mlawer et al. 1997), which was shown to substantially improve the downward thermal fluxes at the surface when included in a climate model (Wild and Roeckner 2006). In addition, reanalyses take into account the possibly best available estimates of atmospheric temperature and humidity profiles at high temporal frequency in their radiative transfer calculations, which further contributes to an accurate determination of the downward thermal radiation. It is interesting to note that also the estimate of Trenberth et al. (2009) (303.6 Wm⁻², Table 3), who did not directly determine the magnitude of the downward thermal radiation, but inferred it as a residual of the other surface energy balance components, is close to our best estimate derived here.

Discussion of the energy balance over land

Figure 2 (upper panel) depicts a schematic representation of the land mean energy balance, which includes the estimates of land-mean downward solar and thermal radiation derived above along with best estimates for the other land energy balance components as discussed in the following.

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 ⁴_skin , 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).

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.

Energy balance over oceans