Over the past 30 years, observations of radiative fluxes associated with Earth’s atmosphere from satellite and Earth-based platforms have improved our understanding of the Earth energy budget, as described by Rossow and Zhang (1995) [1
], Kiehl and Trenberth (1997) [2
], Wild et al. (2013) [3
], Wild et al. (2015) [4
] and Wild et al. (2017) [5
]. These researchers have developed increasingly accurate empirical energy budgets based on direct observations and modeling results performed within global climate models. The results of Wild et al. (2015) represent the more recent results of Earth energy balance studies, in which direct observations from both surface and space, in combination with 43 Coupled Model Intercomparison Project Phase 5 (CMIP5) models are used to determine the energy balance over land and oceans. Improvements in space-based observation systems enabled more accurate assessments of the top of atmosphere (TOA) radiation budgets, notably using the Clouds and Earth’s Radiant Energy System (CERES). Wild et al. [3
] used surface radiation observations from the global energy balance archive (GEBA), the Baseline Surface Radiation Network (BSRN), and ocean buoys to constrain surface fluxes, which cannot be directly measured from satellites. These authors recognize that the energy distribution within the climate system and at the Earth surface is less well-defined, with flux uncertainties that are larger than TOA fluxes. The global climate models that are used in determining and validating the surface fluxes consider all of the major natural and anthropogenic forcings, including change in atmospheric greenhouse gases, aerosol loadings, solar output, and land use.
Recent developments in the field of energy budget models include the sub-division of the energy budget into land and ocean components, which is the main subject of Wild et al. (2015) [4
], building on their previous all-globe model in Wild et al. (2013) [3
]. Future refinements and developments in the field will include large-scale surface albedo estimates and the representation of surface skin temperatures derived from upward surface flux. The better estimation of non-radiative flux components is also an area for further development. Another development is the further regionalization of energy budgets at a finer scale than global, land, and ocean means, which is currently underway in Europe.
This study aims to provide a new derivation of atmospheric radiative fluxes at the planetary scale, by determining the controls on average surface temperature as functions of incoming solar insolation, planetary bond albedo, and bulk atmospheric emissivity, which are applicable to Earth and other rocky planets in the solar system. I investigate the agreement between this model and the global energy budget of Wild et al. (2015) [4
] and the output of global climate models. A further aim of this study is to calculate the time-series behavior of Earth’s radiative fluxes, absorbed solar insolation, and emissivity to identify possible causes of the increased surface flux over the period 1979–2015. The derivation of the more uncertain surface fluxes [3
] is of particular interest to this study.
Importantly, the model derived in this study is impartial, in the sense that no restrictions are placed ab initio on the behavior of the independent variables of solar insolation, albedo, and bulk atmospheric emissivity, which together determine the upward surface flux and top of atmosphere fluxes in the equilibrium model. The behavior of these variables is determined from the time-series datasets of incoming solar insolation, planetary bond albedo, and bulk atmospheric emissivity. The non-equilibrium model is thus capable of identifying, and in fact does identify, a decrease in the bulk atmospheric emissivity over the period 1979–2015. This is possible because changes in atmospheric water vapor, as well as the increase in atmospheric non-condensing greenhouse gases, contribute to the bulk emissivity. Decreasing atmospheric water vapor may offset the effect of increases in the other greenhouse gas species, and reduce atmospheric bulk emissivity. Atmospheric models that assume that increasing non-condensing greenhouse gas abundance must result in an increased bulk emissivity cannot identify a scenario of decreasing bulk atmospheric emissivity by definition.
lists the datasets used in the validation of the adiabatic radiative model. Section 3
summarizes the model, then derives the equilibrium and non-equilibrium radiative models for an idealized planetary atmosphere. The radiative model uses the properties of a one-dimensional quasi-adiabatic atmosphere, in which the atmosphere acts as a non-symmetric emitter of absorbed radiation. The model is then validated by comparison with the land plus sea model of Wild et al. (2015) [4
] in Section 3.3
, and is shown to be in agreement.
The equilibrium model is applied to other planetary bodies in the solar system in Section 3.4
, and their greenhouse factors are discussed. The application of the non-equilibrium model to Earth over the period 1979–2015 is discussed in Section 3.5
. Outcomes of the model that at first glance appear counterintuitive—in particular a decrease in the strength of the greenhouse factor over the period—are explained with reference to the definition of the atmospheric bulk emissivity.
In Section 4
, further features of the model are discussed, and comparisons are made with the means of CMIP5 models. A more detailed description of how the model quantifies the components of downwelling longwave radiation (DWLR) is given, and shows how increased absorbed solar radiation profoundly affects DWLR.
2. Materials and Methods
The adiabatic radiative model is derived from application of the Stefan-Boltzmann law to an atmosphere that is modeled with a non-emitting top surface, as described in Section 3.1
and Section 3.2
. Analysis of the model uses satellite-based measurements of outgoing longwave radiation and incident total solar insolation, the surface temperature record, and the ocean heat content record. The outgoing longwave radiation dataset is the High-resolution Infrared Radiation Sounder (HIRS) v.2.2. OLR provided by the National Center for Environmental Information [6
], with monthly values averaged over the globe. The solar insolation dataset is from the Physikalisch-Meteorologisches Observatorium Davos and World Radiation Centre (PMOD/WRC) [7
]. For surface temperatures, absolute values are required for the direct calculation of a proxy for surface radiative flux. Global averaged monthly values of NOAA Extended Reconstructed Sea Surface Temperature (ERSST) v5 [8
] over oceans and Global Historical Climatology Network and Climate Anomaly Monitoring System (GHCN CAMS) [9
] over land were weighted 70.8% and 29.2%, respectively, to derive average surface temperatures. These datasets are obtained via the Koninklijk Nederlands Meteorlogisch Instituut (KNMI) Climate Explorer website [10
]. Other evidence for the implications of the adiabatic model includes the atmospheric Total Water Vapor measurements from the D2 dataset provided by the International Satellite Cloud Climatology Project (ISCCP) [11
], using mean monthly values averaged over the globe, and average annual Total Precipitable Water from the NASA Water Vapor Project (NVAP-M) dataset [12
] provided by Vonder Haar et al. (2012) [13
]. Ocean heat content data for use in the non-equilibrium radiative model was obtained from Cheng et al. (2017) [14
]. Planetary parameters for solar insolation and surface temperature are taken from the NASA planetary data sheets. Titan data was taken from Yelle et al. (1997) [15
]. CERES [16
] top of atmosphere shortwave flux—all sky data and incoming solar flux data—were used to validate albedo derived from the radiative model over the period 2000–2015.
The adiabatic radiative model, which was derived from a consideration of a theoretical non-radiating top of atmosphere, approximates average planetary surface flux as a function of absorbed solar radiation and a scaling factor, the greenhouse factor, which quantifies the greenhouse effect of an atmosphere on the surface temperature. The model is applicable to all of the rocky planets in the solar system. By allowing for the small non-equilibrium conditions on Earth quantified by changes in ocean heat content, the model was compared directly with the empirical, observation-based energy budget derived by Wild et al. (2015) [4
], and was found to be in close agreement. One strength of the model is that it provides a framework for analyzing changes in radiative fluxes for any given set of surface temperature, ocean heat content, OLR, and TOA incoming solar data sets, and identifies which variables are contributing to each flux change. The weakness of such an impartial model as this is that it offers no root-cause explanation or mechanisms for changes in the determining variables S
, or a
. These must be determined independently. Thus, for Earth, the model identifies a weakening of the greenhouse effect, and a decreasing planetary albedo, without giving a cause. Decreasing atmospheric water vapor was tentatively identified as a possible cause, but supporting evidence must be sought elsewhere, as it is not available in the model. Another limitation is that the adiabatic model provides no insight into the internal structure and dynamics of the atmosphere: however, the boundary fluxes at the base and top of atmospheres are firmly defined.
The results of the application of the adiabatic model do not negate that the increase in non-condensing atmospheric greenhouse gases in Earth’s atmosphere drives an increase in the surface temperature. It is quite clear that increasing ε will drive an increase in the surface flux; however, the influence of atmospheric water vapor variability appears to be a determining factor in the behavior of bulk atmospheric emissivity.
To further illustrate the utility of the adiabatic model, Table 3
below compares the output of the adiabatic model with the mean of the 22 CMIP5 / IPCC AR5 models used by Wild et al. (2013) [3
] (p. 3114). The values differ slightly from the Wild et al. (2015) energy budget of Figure 5
. First, the adiabatic model determines the variables S
, ε, and a
directly from the mean of the CMIP5 models, and then applies these variables to the “Value” column of Table 1
, which are derived from the radiative model of Figure 4
. Values for L
are also taken directly from the CMIP5 models. Surface components are well matched by the adiabatic model, and are well within the error margins, with differences less than 0.5 W/m2
One feature of the equilibrium model is the independence of the outgoing longwave radiation and the bulk atmospheric emissivity. In Equation (4), ε and
are not independent variables; the outgoing longwave radiation in the equilibrium model shown in Figure 3
depends only on the independent variables solar insolation S
and bond albedo a
. If I treat solar insolation S
as a constant, which is a reasonable approximation, then there are only two ways to significantly change average planetary surface temperature: by changes in P
through change in albedo, and by changes in the bulk atmospheric emissivity through altering greenhouse gas abundances. Consider an increase in bulk atmospheric emissivity at a constant value for P
. The model predicts that during the resulting non-equilibrium state, OLR will initially decrease due to B
. From an energy perspective, this is because the upward surface flux is the only available energy source for increasing the surface temperature, which is rerouted to the surface as part of the increased downwelling component
of longwave radiation in Figure 4
, and the energy must be deducted from the OLR. When B
= 0 and equilibrium is regained, the OLR returns to its initial value. Surface flux will increase during the non-equilibrium stage. Conversely, a reduction of ε with constant P
will result in a transient increase in OLR to
during the non-equilibrium state, and OLR will return to its initial value when B
= 0 and equilibrium is regained; meanwhile, surface flux will decrease during the non-equilibrium stage. Neither of these situations describes the evolution of the Earth’s radiative fluxes over the period from 1979–2015, which shows increasing OLR in excess of B
and increasing surface flux in a non-equilibrium state.
at constant ε will drive increases in both surface flux and OLR during the non-equilibrium state, and the energy source is additional solar insolation entering the system due to a reduction in albedo. Increasing P
will also drive an increase in downwelling longwave radiation, because the components
, as shown in Figure 4
, will also increase. This situation better describes the behavior of the Earth’s radiative fluxes over the period from 1979–2015. Changes in downwelling longwave radiation cannot be attributed solely to an increase in
without reference to changes in components P
Further clarification of downwelling longwave radiation is required. Some authors (e.g., Trenberth et al. 2009 [23
]) refer to this quantity as back radiation. Recall from Figure 4
that downwelling longwave radiation comprises
. For the purposes of this study, back radiation strictly refers to surface-emitted longwave radiation, which is absorbed by the atmosphere and re-emitted to the surface, and is the quantity
. It is the only component of the downwelling longwave radiation with partial dependence on
shows the 1979–2015 time-series behavior of the components of downwelling longwave radiation generated by the model. Here, neither P
are constant. The component
, our back radiation, in Figure 10
has seen a downward trend over the period, which is driven by a decreasing greenhouse factor. The component
, which is atmosphere-absorbed incoming solar re-radiated as longwave toward the surface, has increased due to increased P
, assuming constant atmospheric short wave emissivity
. The rate of non-radiative surface-to-atmosphere heat transfer L + Q
is assumed to be a constant value of 103 W/m2
over the same period. The sum of these components, as shown in the top curve in Figure 10
, shows an increase in total downwelling longwave radiation over the period, which is driven by
. Therefore, it is quite possible for total downwelling longwave radiation to increase, even when the greenhouse effect expressed through back radiation decreases. The graph demonstrates the principle, although the uncertainties associated with OLR used in the derivation of atmospheric absorbed solar and back radiation are significant.
Therefore, change in the time-series magnitude of total downwelling longwave radiation by itself is not diagnostic of any particular change in the greenhouse effect. The greenhouse factor,, which is independent of P, B, L, and Q, and is a function only of the bulk atmospheric emissivity with respect to surface emission, provides a more direct and unambiguous measure of the strength of the greenhouse effect.
Another feature of the model is that outgoing radiation is sourced entirely from the surface emission; the only route for absorbed solar energy to leave the system is by re-emission from the surface. This is a direct consequence of the non-radiating top of atmosphere, which prevents the atmosphere from radiating directly to space.