We present detailed line-by-line radiation transfer calculations, which were performed under different atmospheric conditions for the most important greenhouse gases water vapor, carbon dioxide, methane, and ozone. Particularly cloud effects, surface temperature variations, and humidity changes as well as molecular lineshape effects are investigated to examine their specific influence on some basic climatologic parameters like the radiative forcing, the long wave absorptivity, and back-radiation as a function of an increasing CO2 concentration in the atmosphere. These calculations are used to assess the CO2 global warming by means of an advanced two-layer climate model and to disclose some larger discrepancies in calculating the climate sensitivity. Including solar and cloud effects as well as all relevant feedback processes our simulations give an equilibrium climate sensitivity of
The Fifth Assessment Report (AR5) [
Although in all these fields of climate sciences great progress has been achieved over the last decades and our knowledge about the Earth-atmosphere system (EASy) could significantly be improved, explanations of the observed global warming over the last century in particular the anthropogenic contributions to this warming are still quite contradictorily discussed.
All the more it is surprising that many of the consulted analyses and also the AR5 itself do not better and clearly distinguish between an anthropogenic emission of CO2 and a naturally generated part, where the latter even contributes more than 95% to the overall emission, and its generation rate and the respective absorption rate sensitively respond on global temperature variations; that the IPCC claims it would be extremely likely that more than half of the observed increase in global average surface temperature from 1951 to 2010 was caused by the anthropogenic increase in greenhouse gas concentrations and other anthropogenic forcings, while contributions from natural forcing and an internal variability both would only likely be in the range of −0.1°C to 0.1°C; that the meanwhile well known delayed response of CO2 and methane (CH4) to sea and air temperature changes (see, e.g., Petit et al. [ that quite uncertain data about cloud feedbacks and studies of the radiative forcing (RF) of greenhouse (GH) gases are referred, which are mostly valid for clear sky conditions, while the introduction of clouds is usually omitted (AR5-WG1- Chap.8.3.1); that the IPCC denies any noticeable solar influence on the actual climate, although strong evidence of an increasing solar activity over the last century exists (see, e.g., Hoyt & Schatten [ that obviously important effects like convection and evaporation feedback, which can contribute to significant negative feedback (Harde-2014 [
Nevertheless, despite these deficits and simplifications the mean equilibrium climate sensitivity is specified with high confidence, and the GH gases are even assigned with very high confidence (95%) to be responsible for the actual climate changes.
Here we will focus on the assessment of one of the most important quantities in climate sciences and its validation, the ECS, which has to be scrutinized in more detail. Due to its far reaching consequences for future climate predictions it is particularly important to understand and to discover the large discrepancies between different accounting methods applied for this quantity. Also the weighting of some quite different and even counteracting processes which control our climate, but which are not always well understood, has carefully to be investigated with its implications on the climate sensitivity. A quite critical report of actually published ECS values and accounting methods expanded in AR5 has been published by Lewis and Crok [
In this contribution we will also retrace the main steps of the IPCC’s preferred accounting system and compare this with our own advanced two-layer climate model (2LCM), which is especially appropriate to calculate the influence of increasing CO2 concentrations on global warming as well as the impact of solar variations on the climate (Harde-2014 [
The objective of our studies is not to present a new only “true ECS” but to identify some of the different assumptions and approximations with their far reaching consequences in climate politics. It is without any doubt that the ECS is the most important measure for the CO2 influence on our climate, but it is also clear that this quantity does not distinguish between anthropogenic and natural CO2 emissions. Therefore, as long as any natural variations in the CO2 concentrations are not accurately known, the ECS cannot be used as a reliable indicator only for an anthropogenic global warming. All this in mind the reader may have his own reservations about the published data for this measure and its significance for a man-made climate change.
For the assessment of the ECS the IPCC favors the concept of radiative forcing (RF), which is supposed to be appropriate to describe the transition of the surface-troposphere system from one equilibrium state to another in response to an externally imposed perturbation. Therefore, in Section
Section
In particular, these studies show that the observed cloud changes within the ISCCP cannot exclusively be explained by pure thermally induced cloud cover changes but obviously are additionally controlled by a further cloud forcing mechanism. Since there exists strong evidence that the solar activity also has a powerful influence on the cloud cover, it is reasonable to postulate such a solar induced cloud feedback (see, e.g., Svensmark [
Our simulations predict a solar contribution of about 60% and a CO2 induced contribution of 40% to global warming over the last century with an equilibrium climate sensitivity of 0.7°C, which is almost a factor of five smaller than published in AR5.
The concept of RF is well established in climate sciences and used to assess the global warming as a result of an external perturbation of EASy (AR5-WG1-Chap.8). This perturbation can result from solar anomalies, from increased GH gas concentrations or volcanic activities. In all cases a direct proportionality of the Earth’s temperature increase Δ
Eq. (
In this context it should be noticed that alternative definitions of RF have been developed, each with its own advantages and limitations (see AR5-WG1-Chap.8). Here we only consider the instantaneous RF, which refers to an instantaneous change in the net (down minus up) radiative flux (sw plus lw) due to an imposed change. This forcing is usually defined in terms of flux changes at the top of the atmosphere (TOA) or at the tropopause.
In this contribution, particularly the influence of CO2 on global warming is of interest. Therefore, in the next subsection we present some actual radiation transfer (RT) calculations, from which the instantaneous RF due to increasing CO2 in the atmosphere and also some related quantities, which are of relevance for our two-layer climate model, can be derived. Since for these model calculations it is not sufficient only to consider the net radiative fluxes at the tropopause, neglecting the downwelling absorption changes in the troposphere and the upwelling absorption changes over the stratosphere, we apply the RT concept from the surface to TOA and vice versa. The sw absorption changes over the full atmosphere and this as a function of the CO2 concentration can be captured from our previous investigations (Harde-2014 [
As already outlined, an important reference for the influence of CO2 is the temperature increase at doubled CO2 concentration under steady state conditions, which is known as the equilibrium climate sensitivity ECS or
So, due to (
Expressing the downwelling atmospheric intensity
Then, with (
Since it is obvious that the cloud cover has a strong influence on the up- and downwelling fluxes in the atmosphere and also on the strength of the GH effect, we have performed line-by-line radiation transfer (LBL-RT) calculations under different cloudiness conditions, ground temperatures, and humidity to evaluate the influence of CO2 on global warming. We also briefly investigate the influence of lineshape effects on RT calculations and their consequences for the ECS.
Here we only present global RT calculation with averaged values for the temperature, water vapor concentration, and an average lapse rate, since separate computations for the tropics mid- and high-latitudes with individual profiles and averaging over the climate zones with an area weighting factor gave almost the same results (see also Harde [
Table
RT-calculations for different CO2 concentrations at clear sky (
CO2 |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
0 | 290.72 | 201.03 | 283.40 | 484.43 | 303.09 | 77.06 | 58.50 |
35 | 272.70 | 194.92 | 295.40 | 490.32 | 315.00 | 80.08 | 60.25 |
70 | 269.62 | 193.96 | 297.54 | 491.50 | 317.13 | 80.62 | 60.54 |
140 | 266.26 | 193.22 | 300.08 | 493.30 | 319.75 | 81.29 | 60.83 |
210 | 264.08 | 192.86 | 301.08 | 493.94 | 321.57 | 81.75 | 60.95 |
280 | 262.40 | 192.64 | 303.16 | 495.80 | 323.02 | 82.12 | 61.15 |
350 | 261.01 | 192.50 | 304.31 | 496.81 | 324.27 | 82.44 | 61.25 |
380 | 260.48 | 192.45 | 304.75 | 497.20 | 324.76 | 82.57 | 61.29 |
420 | 259.81 | 192.41 | 305.32 | 497.73 | 325.38 | 82.72 | 61.34 |
490 | 258.75 | 192.36 | 306.23 | 498.59 | 326.40 | 82.98 | 61.42 |
560 | 257.78 | 192.34 | 307.08 | 499.42 | 327.34 | 83.22 | 61.49 |
630 | 256.90 | 192.35 | 307.86 | 500.21 | 328.23 | 83.45 | 61.55 |
700 | 256.08 | 192.37 | 308.60 | 500.97 | 329.07 | 83.66 | 61.60 |
760 | 255.42 | 192.40 | 309.21 | 501.61 | 329.76 | 83.84 | 61.64 |
|
|||||||
380–760 | 5.06 | 0.05 |
|
|
|
|
|
|
5.05 |
As an average over the three climate zones the water vapor concentration at ground was assumed to be 14,615.3 ppm and decreasing with altitude due to the Clausius-Clapeyron equation (for details see Harde-2014 [
Our calculations cover a spectral interval from 10 to 2500 cm−1, corresponding to 99.86% of a Planck radiator at
Comparison of the two last values in column 2 of Table
Since in this case the first two terms in (
In general, however, it should be clear that the surface temperature also depends on the emission characteristic of the atmosphere, which changes with the GH gas concentration as well as with the cloud cover and is determined by the first two terms in (
In a more advanced model, as this will be discussed later with a radiation and energy balance at TOA and at the surface, including heat fluxes of sensible and latent heat or from neighbouring climate zones, as well as sw and lw absorption losses, even at clear sky conditions the atmospheric emission characteristic is of relevance, which can well be represented by the fraction
The relative absorption of terrestrial radiation by the GH gases and its variation with increasing CO2 concentration are listed in column 7. It is normalized to the incident terrestrial flux and in this way represents the lw absorptivity
Lw absorptivity
Whereas the above calculations reflect a somewhat artificial situation, assuming clear sky and a global mean temperature of 16°C, we know that with declining cloud cover the average surface temperature is significantly climbing up. So, from observations within the International Satellite Cloud Climatology Project (ISCCP) [
Therefore, to get a better understanding of how such higher temperature modifies the respective fluxes in the atmosphere and especially this affects the CO2 radiative forcing, we have performed additional calculations for a surface temperature of 20.3°C. At this temperature and a surface emissivity of 100% the terrestrial radiation climbs up to 420 W/m2. But with the higher temperature also the humidity increases and therefore affects the absorptivity of the GH gases. From the measured water vapor concentrations as well as the temperatures at mid-latitudes and the tropics we deduce at the higher temperature a growth of the vapor concentration of 3,738 ppm with a new total mean concentration near the surface of 18,353 ppm.
Calculations for this higher ground temperature and water vapor concentration are shown in Table
RT-calculations for CO2 concentrations of 380 and 760 ppm at a surface temperature of 20.3°C (293.45 K) and clear sky (
CO2 ppm |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
380 | 270.22 | 203.99 | 334.02 | 538.01 | 353.52 | 84.08 | 62.08 |
760 | 264.76 | 203.31 | 338.34 | 541.65 | 358.30 | 85.22 | 62.46 |
|
|||||||
|
5.46 | 0.68 |
|
|
|
|
|
Since for an evaluation of CO2 with its influence on the radiation budget it is sufficient to concentrate on the fluxes at single and doubled CO2 concentration, here we only present this reduced data set. Compared to the lower temperature calculations the radiative forcing increases by 0.4 W/m2, which is mainly due to changes in the upward atmospheric emission with
The absorptivity as calculated under these modified conditions is shown in Figure
Lw absorptivity
Under regular cloud cover significant changes from clear sky conditions have to be expected for the up- and downwelling fluxes due to the strong shielding effect of clouds not only for sw but also for lw radiation. In our radiation transfer calculations the clouds are considered as a single thinner layer, which absorbs the incident lw radiation from up or down direction with a cloud absorptivity
The Global Energy and Water Cycle Experiment (GEWEX) Radiation Panel, which compares the available global long-term cloud data products with the ISCCP and consists of 12 satellite measurement teams, specifies the global total cloud amount between 56% and 74% (Stubenrauch et al. [
Our RT calculations under otherwise identical conditions as described in Section
RT-calculations for different CO2 concentrations at mean cloud cover of 66%, a cloud altitude of 5.1 km, and cloud emissivity of 63% (
CO2 |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
0 | 262.82 | 210.01 | 308.62 | 518.63 | 342.97 | 79.34 | 59.51 |
35 | 248.31 | 202.49 | 317.89 | 520.38 | 349.96 | 81.09 | 61.09 |
70 | 245.88 | 201.31 | 319.57 | 520.88 | 351.21 | 81.40 | 61.35 |
140 | 243.24 | 200.22 | 321.55 | 521.77 | 352.76 | 81.78 | 61.63 |
210 | 241.49 | 199.49 | 322.83 | 522.32 | 353.78 | 82.05 | 61.81 |
280 | 240.21 | 199.08 | 323.89 | 522.97 | 354.64 | 82.29 | 61.93 |
350 | 239.62 | 199.26 | 326.14 | 525.40 | 355.41 | 82.49 | 62.07 |
380 | 239.22 | 199.22 | 326.49 | 525.71 | 355.77 | 82.57 | 62.10 |
420 | 238.72 | 199.01 | 326.93 | 525.94 | 356.06 | 82.67 | 62.16 |
490 | 237.92 | 198.80 | 327.64 | 526.44 | 356.66 | 82.83 | 62.24 |
560 | 237.20 | 198.64 | 328.29 | 526.93 | 357.21 | 82.97 | 62.30 |
630 | 236.54 | 198.50 | 328.90 | 527.40 | 357.74 | 83.10 | 62.36 |
700 | 235.93 | 198.38 | 329.47 | 527.85 | 358.23 | 83.21 | 62.42 |
760 | 235.45 | 198.38 | 329.94 | 528.32 | 358.70 | 83.31 | 62.45 |
|
|||||||
|
3.77 | 0.84 |
|
|
|
|
|
|
3.77 |
But respective differences between single and doubled CO2 concentrations, which are here of main interest, in general are getting smaller. So, the radiative forcing reduces to
Because of this smaller alteration in the atmospheric emission the 1st term in (
To deduce the lw absorptivity at cloudiness from the radiation transfer calculations, the absorbed intensity listed in column 6 of Table
Figure
Lw absorptivity
Simulations at higher cloud altitudes under otherwise same constrains give a reduced upwelling flux
While the preceding calculations are based on the standard molecular collision theory, considering collisional broadening of spectral transitions, which are characterized by a Lorentzian lineshape or at higher altitudes also by a Voigt profile, we have also performed extensive calculations using a more sophisticated lineshape as given by the molecular response theory (MRT) (Harde et al. [
This continuum water vapor background together with the far wing contributions of the other molecules significantly modifies the absolute up- and downwelling fluxes. Therefore, to further satisfy the radiation and energy balance of the TFK-scheme, in the radiation transfer calculations the cloud altitude has to be increased to 6 km and the cloud absorptivity = emissivity reduced to 47.8%.
The results of such a calculation at a mean cloud cover of 66% and at otherwise same conditions as described in Section
RT-calculations with MRT lineshape for CO2 concentrations of 380 and 760 ppm at mean cloud cover of 66%, a cloud altitude of 6.0 km, and cloud emissivity of 47.8% (
CO2 |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
380 | 239.47 | 199.48 | 329.41 | 528.89 | 355.78 | 89.77 | 62.28 |
760 | 235.68 | 198.50 | 332.59 | 531.09 | 358.60 | 90.48 | 62.62 |
|
|||||||
|
3.79 | 0.98 |
|
|
|
|
|
For this insensitivity to a different collision and lineshape theory we see three main reasons: first, because of the larger absolute flux variations, caused by the different wing absorption and WV continuum, the outgoing fluxes were recalibrated to the TFK-scheme via cloud altitude and absorptivity to ensure comparable absolute fluxes in agreement with the observations. Second, we only consider flux differences at single and doubled CO2 concentration for the same shape, so that discrepancies to another shape are not directly observed and smaller absolute variations with the CO2 concentration are to some extent cancel out. Third, the interference of the CO2 spectrum with strong water vapor lines and the underlying WV continuum further attenuates any CO2 lineshape effects.
So, calculations based on the classical collision theory obviously reproduce quite reliable data of any radiation changes in the atmosphere. Since the far wings of the CO2 lines are found to decay more rapidly than a Lorentzian and thus should contribute less to the total absorption (see, e.g., Edwards and Strow [
With a further increasing cloud cover and thus a stronger shielding of the sw radiation also the surface temperature further drops, and owing to the ISCCP observations at 100% cloudiness then a reduced temperature of approximately 2.2°C compared to mean cloudiness is expected.
Respective radiation transfer calculations at 100% cloud cover, a surface temperature of 13.8°C with a terrestrial intensity of 384 W/m2, and a further reduced water vapor concentration at ground of 12,703 ppm, otherwise using the same conditions as in Section
RT-calculations for different CO2 concentrations at 100% cloudiness, a cloud altitude of 5.1 km, and cloud emissivity of 63% (
CO2 |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
380 | 223.80 | 197.75 | 321.34 | 519.09 | 357.86 | 81.55 | 61.90 |
760 | 220.84 | 196.72 | 324.27 | 520.99 | 359.79 | 82.05 | 62.24 |
|
|||||||
|
2.96 | 1.03 |
|
|
|
|
|
The absorptivity
Lw absorptivity
The changes in absorptivity from single to doubled CO2 with
So, from these calculations it is clear that the up- and downwelling fluxes and also the absorption in the atmosphere are significantly varying with the cloud clover and, therefore, they will also significantly influence the global mean surface temperature. But it can also well be recognized, that changes with the CO2 concentration by trend get smaller with increasing cloudiness.
Different to general circulation models, which try to predict local climate variations over some time period and, therefore, have to solve complex coupled nonlinear differential equations with a large number of parameters, making these calculations extremely time consuming and even unstable, for computing the equilibrium climate sensitivity
But independent of the model’s complexity, almost all known models are based on the simple relation given by (
Thus, the simplest way to assess that the Planck sensitivity that it is difficult to distinguish between different forcings with different feedbacks; that this method only considers a radiation balance at the tropopause or TOA, but not an additional radiation and energy balance at the surface; that it does not consider the feedback of the atmosphere to the surface and vice versa, caused by radiation changes as well as changes of sensible and latent heat; that some feedback processes and their evaluation are not really retraceable from other sources; and that for simplicity reasons often sw feedback effects are completely neglected.
Therefore, here we use our own advanced two-layer climate model, which is free from these deficits and which then can be compared with the IPCC accounting scheme or other methods. In addition, we investigate the effect and the size of the slightly changing reradiation of the atmosphere with increasing CO2 concentration as represented by the back-radiated fraction
Our two-layer climate model is especially appropriate to calculate the influence of the increasing CO2 concentrations on global warming as well as the impact of solar variations on the climate. The model describes the atmosphere and the ground as two layers acting simultaneously as absorbers and Planck radiators. It includes additional heat transfer between these layers due to convection and evaporation, and it considers cloud effects for the sw and lw radiation as well as all relevant feedback effects like water vapor, lapse rate, albedo, cloud cover, convection, and evaporation. At equilibrium both the atmosphere and the ground release as much power as they absorb from the Sun and the neighbouring layer. An external perturbation, caused by variations of the solar activity or the GH gases, then forces the system to come to a new equilibrium with new temperature distributions of EASy. Figure
Two-layer climate model for the Earth-atmosphere system with the main parameters.
Different to other schemes, in our model the key parameters are not the radiative forcing, but the sw and lw absorptivities
Parameter set at mean global cloud cover and mean temperature to reproduce the TFK data.
Parameter | Symbol | Unit | Value |
---|---|---|---|
averaged solar flux |
|
W/m2 | 341.3 |
cloud cover |
|
% | 66.0 |
sw molec. scattering coef. |
|
% | 13.2 |
sw cloud scattering coef. |
|
% | 18.14 |
sw Earth reflectivity |
|
% | 17.0 |
sw ozone absorptivity |
|
% | 8.0 |
sw cloud absorptivity |
|
% | 12.15 |
sw H2O-CO2-CH4 absorptivity |
|
% | 14.51 |
lw Earth's reflectivity |
|
% | 0.0 |
lw cloud scattering coef. |
|
% | 20.9 |
lw cloud absorptivity |
|
% | 54.1 |
lw H2O-CO2-CH4-O3 absorptivity |
|
% | 82.58 |
Earth’s emissivity |
|
% | 100.0 |
atmospheric emissivity |
|
% | 87.5 |
back-radiated fraction |
|
% | 61.8 |
sensible heat flux |
|
W/m2 | 17.0 |
latent heat flux |
|
W/m2 | 80.0 |
Compared to our previous simulations (Harde-2014 [
For the temperature response of EASy and, thus, the calibration of the model we relate to the temperature anomaly data of the Hadley Centre and Climate Research Unit (HadCRUT3) as a function of the monthly global cloud cover data of the ISCCP (scatter diagram of O. Humlum,
Our climate model also contains a parameter for the lw scattering at clouds (
The up- and downward fluxes as calculated by the two-layer climate model are compiled in Table
Comparison of calculated fluxes under regular atmospheric conditions with the TFK data.
Flux (W/m2) | This model | TFK data |
---|---|---|
sw: incoming solar radiation | 341.3 | 341.3 |
|
||
backscattered from molecules | 14.1 | |
backscattered from clouds | 65.0 | |
together backscattered | 79.0 | 79 |
reflected at Earth’s surface | 22.9 | 23 |
total reflected solar radiation | 101.9 | 101.9 |
|
||
absorbed by O3, | 27.3 | |
clouds, | 19.1 | |
water vapor, CO2, CH4 | 31.6 | |
total absorption of atmosphere | 78.0 | 78.0 |
|
||
absorption in surface | 161.3 | 161 |
|
||
lw: surface radiation | 396.3 | 396 |
|
||
absorbed by GH-gases | 327.3 | |
absorbed by clouds | 19.5 | |
backscattered by clouds | 9.5 | |
absorb. & scat. surface radiation | 356.3 | 356 |
|
||
sensible heat | 17.0 | 17 |
latent heat | 80.0 | 80 |
|
||
total absorption in atmosph. | 521.8 | |
|
||
outgoing radiation fr. atmosph. | 199.3 | 199 |
outgoing directly from surface | 40.0 | 40 |
total outgoing radiation | 239.4 | 238.5 |
|
||
back-radiation | 331.9 | 333 |
net emission of surface | 64.4 | |
|
||
total outgoing radiation at TOA | 341.3 | 340.4 |
It should also be noticed that the direct flux from the surface to TOA with 40 W/m2 can only be realized with a relatively high lw cloud scattering and medium cloud absorption. These parameters mainly determine the reference temperature
Since the objective of our investigations here is to evaluate the influence of CO2 on global warming, the parameters in Table
First we consider the simplest case, neglecting any feedback processes and looking only to the direct influence of CO2 on global warming. With the sw and lw absorptivities as well as the back-radiated fraction integrated in the climate model, the Earth’s surface temperature and the lower tropospheric temperature are simulated as a function of the CO2 concentration. For details, how these temperatures are calculated by the 2LCM and how they are defined, see Harde-2014 [
For the case of clear sky (
Calculated Earth temperature
The reason for this discrepancy is twofold. So, the new RT calculations (see Section
A higher cloudiness not only reduces the average surface temperature but also diminishes the climate sensitivity. This can be seen from Figures
The green graphs in Figure
For the special case
Compilation of some figures at clear sky, global mean cloud cover, and total cloudiness.
Quantity/parameter | Symbol | Unit | Value | ||
---|---|---|---|---|---|
cloud cover |
|
% | 0 | 66 | 100 |
surface temperature |
|
°C | 20.3 | 16.0 | 13.8 |
climate sensitivity |
|
°C | 1.79 | 1.09 | 0.89 |
CO2 radiative forcing |
|
W/m2 | 5.46 | 3.77 | 2.96 |
Planck sensit. this model |
|
W−1 m2 |
0.33 | 0.29 | 0.30 |
Planck feedb. this model |
|
W/m2/°C | −3.05 | −3.47 | −3.31 |
Planck feedback, AR5 |
|
W/m2/°C | −3.20 |
In this context it should be emphasized that the climate sensitivities from our model were derived with the sw absorptivity changes included, while
While the declining temperatures are a direct consequence of the dominating shielding effect for solar radiation, the smaller sensitivities are the result of the increasing influence of the lw cloud absorption and backscattering, by which the importance of the GH-gases is more and more repelled.
We also see that in comparison to the surface the lower atmosphere is responding less sensitively to the CO2 changes. This may be explained due to the changing radiation and energy balance between the surface and atmosphere with an increasing up- and downward emission of the atmosphere. But the difference between the two curves is more and more reducing at higher cloudiness.
Many climate models agree within acceptable limits in their prediction for the CO2 climate sensitivity, as long as feedback effects are excluded. But big discrepancies can be observed, when different feedback processes and also climate drivers are included. One reason may be the complexity of these effects, from which their interrelated actions and their mutual interference are not really known. Another reason can also be a wrong or undifferentiated assignment of the feedbacks to a specific climate driver, or the simple neglect of an effect.
In this subsection we first consider the influence and size of the well known feedback processes caused by water vapor, the lapse rate, or albedo. Further we investigate the additional effects of convection, evaporation, and cloud cover feedback, which in this form are not discussed and the first ones are even not mentioned in AR5.
Water vapor (WV) is by far the largest contributor to the natural GH effect and, therefore, plays an essential role in Earth’s climate (AR5-WG1-Chap.8.1). Since its amount in the atmosphere is only controlled by the air temperature, rather than by emissions, scientists consider it as a feedback agent, rather than a forcing to climate change.
In AR5 we read as follows: “the contribution of water vapor to the natural greenhouse effect relative to that of CO2 depends on the accounting method, but can be considered to be approximately two to three times greater.” With respect to their relative concentrations in the atmosphere this proportion appears very small, as an amplifier for the basic climate sensitivity; however, it is quite significant and has to be investigated in more detail.
Indeed, different methods can be applied to estimate this ratio, and their results deviate significantly, depending on what is made responsible for the GH effect and its definition. So, similar to the procedure used to determine the RF at doubled CO2, one way is first to calculate the total upwelling intensity without WV,
Therefore, another way of accounting is to consider the differences of the downwelling intensities, which at cloudiness result in
With respect to feedback processes these numbers look quite dramatic. But the contribution of a gas or vapor to the GH effect does not automatically determine its influence as a feedback agent. Therefore, this has to be considered more extensively.
Due to the Clausius-Clapeyron equation the WV content is rapidly increasing with rising temperatures. So, from GPS-measurements (Vey [
Our own investigations, however, show a less dramatic influence of water vapor. One aspect is that, similar to CO2, also the water lines are already strongly saturating over wider spectral regions. Therefore, with increasing vapor concentration only the far wings of these lines and weak absorption bands can further contribute to an additional absorption, which roughly logarithmically increases with the vapor concentration.
Another aspect is that always both sw and lw absorption have to be considered. Whereas the lw outgoing radiation is more efficiently blocked and thus contributes to a positive feedback, the sw radiation is also more strongly absorbed in the atmosphere, and less of it reaches the surface, which supplies a negative feedback contribution.
Table
sw absorptivity
Climate |
|
|
|
|
|
---|---|---|---|---|---|
High-lat. |
|
2,359 | 12.5 | 81.5 | 59.2 |
Mid-lat. | 8 | 7,253 | 13.4 | 85.5 | 61.0 |
Tropics | 26 | 22,900 | 15.2 | 90.8 | 62.9 |
Figure
sw absorptivity (blue squares and fit), total lw absorptivity (red triangles and fit) and back-radiated fraction (green circles and fit) for high-latitudes, mid-latitudes, and the tropics. Additionally shown is the predicted back-radiated fraction due to CMIP5 as magenta line.
The sw and lw absorptivity changes can well be represented by straight lines with the slopes
The back-radiated fraction
Now, taking advantage of (
The result of such a calculation with WV feedback is illustrated in Figure
Calculated Earth temperature
Compared to AR5-WG1-Tab.9.5, where the WV feedback is specified as a model mean of
The reasons for this discrepancy are manifold. So, as already mentioned, our calculations also consider the sw absorptivity, which causes a negative feedback, while this is not clear for the feedbacks specified in AR5. The main differences, however, go back to the procedures applied to determine the changes of
Quite generally we can distinguish two effects and write
The partial derivative
Lw water vapor absorptivity
In this context it has to be mentioned that the absorptivities, reflecting integrals of the absorption coefficients and, thus, integrals of the cross-sections over the altitude and over the spectral distribution (see Harde-2014 [
In AR5-WG1-Chap.8.3.1 we can read that most intercomparison studies of the RF of GH gases are for clear sky and aerosol-free conditions, while the introduction of clouds would greatly complicate the targets of research and are usually omitted in the intercomparison exercises of GCM radiation codes and LBL codes. Therefore, obviously also for an assessment of the WV feedback cloud effects were neglected. In addition, most of the GCMs emanate from a mean WV concentration of 7,750 ppm, in agreement with the US Standard Atmosphere 1976, representing mid-latitude but not global mean conditions. The slope to the clear sky WV absorptivity at 7,750 ppm then gives
So, under these assumptions the IPCC data can well be reproduced. But as outlined above, this approach omits clouds, emanates from a lower WV concentration, and neglects any surface temperature dependence of the absorption cross-section of the GH gases.
Our own considerations include a spectral overlap and interference of WV with other GH gases as well as with clouds, and we assume a global mean WV concentration (at standard conditions) of 14,615 ppm. Both aspects contribute to a larger total absorptivity
The temperature variation of
The direct comparison of the different approaches clearly shows the different assumptions and their influence on the WV feedback. Whereas our result only contributes to an increase of the direct CO2 influence (basic climate sensitivity) of 14%, the IPCC follows from a gain of 100%, which is more than 7 times larger than our result.
The average temperature decrease with altitude over the troposphere is specified as 6.5°C/km and assumed to be constant up to the tropopause at about 11 km altitude [
It is well known that the tropopause height is significantly varying with the climate zone (also over the seasons) and in so far directly related to the local ground temperature. A detailed description of the tropopause altitude and its variation with latitude has been given by Hoinka [
On the other side in AR5 we can read “
So, global circulation models predict an enhanced warming in the upper troposphere of tropical regions, particularly in response to an increasing water vapor concentration, which should result in a negative feedback. On the other hand, at mid- to high-latitudes, a larger low level warming is expected as response to the positive radiative warming, thus, providing a positive feedback, as this is expected from the previous considerations. Since the influence of the tropics is assumed to dominate, in AR4 a resulting negative feedback of −0.85 W/m2/°C was predicted [
Since the water vapor has a more or less stronger influence on the lapse rate, both effects are often considered together. For the combined feedback we then find
It is well known that changes to the physical properties of the land surface and sea ice will perturb the climate, both by exerting an RF and by modifying other processes such as the fluxes of latent and sensible heat or the transfer of momentum from the atmosphere. Also the other way round is climate influencing the surface properties, which again act back on the climate. So, an increasing ground temperature reduces the Earth’s reflectivity via melting ice shields in the polar regions and it changes the vegetation. With varying reflectivity particularly the sw radiation balance will be modified in such a manner that with reducing sw reflectivity
This surface albedo influence is estimated as a positive feedback of
Sensible heat represents the energy transfer through thermal conduction and convection from the warmer surface to the colder atmosphere. At the reference CO2 concentration of 380 ppm and temperature
Since in first approximation
Due to the second term in this equation any changes in the surface and atmospheric temperature, which may be induced by CO2, initiate a feedback on EASy. We call this convection feedback.
From Figure
This feedback gets maximum, when the first term on the right side of (
From Figures
With
Latent heat describes the energy transfer resulting from phase transitions of evaporating water or sublimating ice at the surface and their subsequent release of the vaporization energy in the atmosphere, when the water vapor condenses and falls back as precipitation. Similar to sensible heat but even more pronounced this contributes to cooling of the surface. Since an increasing Earth temperature further forces these processes, they also result in a negative feedback, which we call evaporation feedback. Although in more general terms this is also one part of convection, we further distinguish convection and evaporation feedbacks to assign them to sensible and latent heat contributions.
Generally, according to Kirchhoff’s equation (see, e.g., Salby [
At clear sky and maximum
Similar results for the convection and evaporation feedback were derived by Andrews et al. [
Clouds respond to climate forcing mechanisms in multiple ways, and differences in cloud feedbacks constitute by far the primary source of spread of both equilibrium and transient climate responses simulated by climate models (Dufresne & Bony [
Indeed quite contradictory observations of could effects can be found in the literature, where on the one side regional meteorological conditions over the Pacific are reported, providing modelling evidence for a positive low level cloud feedback in this region on decadal time scales (Clement et al. [
Different to any detailed investigations, which are focusing on individual contributions of low- or high-level clouds to a feedback, here we concentrate on a more general description, how such a feedback can be derived and quantified from global cloud observations and how it can be incorporated into a climate model. Cloud feedbacks can have different origin and importance, depending on the individual forcings, which are responsible for a rebound on the climate via clouds. In this subsection we look closer to CO2 as the responsible climate driver, which initiates a temperature increase and might induce a temperature induced cloud feedback (TICF). In Section
Our preceding simulations, which were performed for clear sky and at cloudiness, already demonstrate the dominant influence of the clouds as part of the total atmospheric convection on the global temperature and the self-adjusting fluxes between the surface, the atmosphere, and space. So, the climate sensitivity drops to about 60% of its value it had at clear sky conditions, and the ground temperature approximately changes from 20 to 16°C, when the cloud cover increases from 0 to 66%. This temperature response was adopted from the ISCCP observations of the global warming and mean cloud cover variations over the period 1983–2010 [
It is obvious that the observed temperature changes will not exclusively result from cloud variations or vice versa but will also be affected by variations of the solar radiation, the humidity, or internal oscillations. Therefore, the worst case will be to attribute any response of the cloud cover
To reproduce the cloud variations in agreement with the ISCCP observations, a cloud cover parameter of
In this context it is important to note that a larger assumed temperature response of the model to cloud changes, as this follows from an inverse scatter plot based on the BEST temperatures, has no influence on the feedback parameters and the climate sensitivities, since due to the reciprocity a larger temperature response of the model is compensated by a smaller cloud cover parameter
In any case, this distinctly lower feedback therefore indicates that obviously the observed cloud changes cannot exclusively be traced back to global warming by CO2, but additional overlaying temperature variations or counteracting processes are present and/or the cloud changes are additionally or alone controlled by a further climate forcing mechanism.
We will come back to these aspects in Section
The main results of our simulations for the individual and collective feedbacks with their effect on the climate sensitivity are listed in Table
Calculated equilibrium climate sensitivities under different feedback conditions.
Line number | Clouds | Water |
Lapse rate |
Albedo |
Convection |
Evaporation |
Feedback |
| ||
---|---|---|---|---|---|---|---|---|---|---|
|
|
(°C) | Rel. | |||||||
1 | 0 | — | — | — | — | — | — |
|
1.79 | 1.00 |
2 | 0 | — | on | — | — | — | — |
|
2.81 | 1.57 |
3 | 0 | — | — |
|
— | — | — |
|
1.55 | 0.87 |
4 | 0 | — | — | — |
|
— | — |
|
2.01 | 1.12 |
5 | 0 | — | — | — | — | 13 | — |
|
1.68 | 0.94 |
6 | 0 | — | — | — | — | — | 5 |
|
1.06 | 0.59 |
7 | 0 | — | on |
|
|
2.25 | 1.26 | |||
8 | 0 | — | on |
|
|
— | — |
|
2.61 | 1.46 |
9 | 0 | — | on |
|
|
13 | — |
|
2.20 | 1.23 |
10 | 0 | — | on |
|
|
5 | 5 |
|
1.33 | 0.74 |
|
||||||||||
11 | 66 | 0 | — | — | — | — | — |
|
1.09 | 1.00 |
12 | 66 | 0 | on | — | — | — | — |
|
1.24 | 1.14 |
13 | 66 | 0 | — |
|
— | — | — |
|
0.93 | 0.85 |
14 | 66 | 0 | — | — |
|
— | — |
|
1.19 | 1.10 |
15 | 66 | 0 | — | — | — | 13 | — |
|
1.07 | 0.98 |
16 | 66 | 0 | — | — | — | — | 5 |
|
0.61 | 0.56 |
17 | 66 | 1.05 | — | — | — | — | — |
|
1.31 | 1.21 |
18 | 66 | 5.4 | — | — | — | — | — |
|
2.53 | 2.33 |
19 | 66 | 0 | on |
|
— | — | — |
|
1.04 | 0.95 |
20 | 66 | 0 | on |
|
|
— | — |
|
1.13 | 1.04 |
21 | 66 | 0 | on |
|
|
13 | — |
|
1.06 | 0.98 |
22 | 66 | 0 | on |
|
|
— | 5 |
|
0.62 | 0.57 |
23 | 66 | 1.05 | on |
|
|
5 | 5 |
|
0.74 | 0.68 |
24 | 66 | 5.4 | on |
|
|
5 | 5 |
|
1.22 | 1.12 |
|
||||||||||
AR5 | 66 | 1.05 |
|
|
— | — |
|
2.93 | 2.70 |
Additionally assuming CO2 induced cloud feedback with a cloud cover parameter
It is also worth noting that with an increasing negative evaporation feedback the convective part, which under mean cloudiness is already quite small (see line 15), is still further pressed down and under special conditions even can get slightly positive. In general, however, when a moderate heat convection coefficient is chosen to allow also advective heat transfer, a convective feedback can completely be neglected. From this behavior we also see that the total feedback is by far not only the sum of the individual contributions.
Due to the above assumptions that the observed cloud changes within the ISCCP program are only thermally induced and the respective temperature increase over this period is only caused by CO2 (maximum cloud feedback
With a cloud response of
As direct comparison to our calculations we have also listed a simulation assuming the feedbacks as used in AR5-WG1-Tab.9.5 with a WV plus lapse rate feedback of
Altogether, we see that the dominating positive feedbacks, originating from clouds and albedo, are partially compensated or in the case of a moderate cloud feedback are even overcompensated by negative WV lapse rate and evaporation feedback. Particularly clouds have two stronger opposing influences on the energy balance, which can neutralize each other or can even have an overall attenuating impact on the ECS, dependent on the mechanisms responsible for cloud changes.
So, up to now it is not clear if the ISCCP observations are really only a consequence of the increased temperature as assumed in Section
An important criterion for a serious validation, which mechanism really might control the cloud cover changes, we can derive from model simulations, which additionally include the solar anomaly over the last century and compare this directly with the observed global warming over this period. Similar investigations have been performed by Ziskin and Shaviv [
To verify the existence and size of such a solar effect in the total energy budget we have performed quite similar analyses, which also include solar variations and orientate at the observed warming over the last century, but which are based on our two-layer model, including all discussed feedback processes and especially reproducing the ISCCP observations of cloud cover changes. Of course, any conclusions deduced from such comparison sensitively depend on the reliability of the measured cloud cover, the solar activity, and temperature changes over this period.
In the same way as the GH gases have an influence on the radiation and energy budget of EASy, this is the case for a varying solar activity. Both are external perturbations, causing an imbalance, to which EASy has to respond with a new distribution for the respective temperatures at the surface and in the atmosphere.
Such response on a varying solar activity can easily be simulated with our two-layer climate model by changing the solar constant (total solar irradiance, TSI) or the average solar flux in our parameter list in Table
But for a serious assessment of the solar influence on global warming we further have to discuss two contributions, which can modify the basic solar sensitivity an amplification by a possible temperature induced cloud feedback, which works in the same way as discussed for the CO2 induced cloud feedback but now results from the solar heating, and a temperature independent mechanism, which acts back on the cloud formation when the solar activity is changing and in this way contributes to an amplification of
We first look to their individual contributions before we unify them in a common model which orientates at the global warming over the last century and allows an assessment of the influence of the two climate drivers, the CO2, and the Sun, on our climate.
When a thermally induced cloud feedback (TICF), as discussed in Section
With a thermal cloud response of
Both together give a warming over the last century of 0.83°C which is slightly more than the observed temperature boost over the last 120 years of 0.74°C (GISS [
Only with a reduced solar anomaly of Δ
On the other hand using a cloud feedback as assumed by the IPCC with
Since the amount of clouds varies over the solar cycle, there exists strong evidence that the solar activity variations also modulate the cloud cover. Actual publications of Svensmark [
Another proposed mechanism is hypersensitivity of the climate system to ultraviolet (UV) radiation, which typically varies 10x stronger over a solar cycle than the TSI (Haigh [
Obviously both these mechanisms play a role, depending on the climatic conditions and altitude (Voiculescu et al. [
A reduced cloud formation at an increased solar activity then reinforces the initial TSI induced temperature increase and can be included in the 2LCM as a feedback term similar to the thermally induced cloud changes, but now depending on changes of the solar constant, supposing that variations in
Assuming that the cloud cover variation over the period 1983–2000 of −4% is only determined by an observed increase of the TSI of
With this additional solar induced cloud feedback (SICF) the basic solar sensitivity of 0.09°C rises to
When SICF is the only responsible process controlling the cloud cover, also for the CO2 climate sensitivity TICF has to be cancelled and
With a solar anomaly of Δ
Similar to Shapiro et al. [
If the solar anomaly (related to the last century) should have been overestimated and would only be Δ
Here we do not discuss any additional influence of aerosols over this period, since any reliable figure of such effect is largely unknown and is not the subject of feedback processes. Implicitly aerosols are already enclosed in our model via atmospheric and cloud backscattering, so that any aerosol impact could easily be modelled by varying the sw backscattering parameters and if necessary also the cloud absorption.
The previous investigations have made clear that the measured cloud cover changes by the ISCCP cannot satisfactorily be explained by a pure thermal mechanism. Either this gives too high global warming over the last century, or with the IPCC’s favored cloud feedback it results in a too small cloud cover variation over the eighties and nineties. Also a pure solar induced nonthermal cloud feedback with a solar anomaly of Δ
On the basis of our investigations reasons for a still stronger negative feedback are not so much expected, although we always assumed a more conservative assessment, for example, excluding an internal variability with its influence on the global temperature and cloud effects. This would even further increase the discrepancy to the IPCC’s assessment of the ECS. However, larger uncertainties exist for the solar anomaly over the last century and its influence on cloud cover changes. Since the size of this anomaly has far reaching consequences on both cloud changing mechanisms, it is necessary to consider this influence in more detail, and as long as it is not clear which of these mechanisms is the dominating feedback process it is even reasonable to discuss a combination of these effects.
One way to handle the simultaneous presence of TICF and SICF is to modify the thermal and the solar induced cloud cover parameters
Designation of the temperatures required for calculating global warming due to CO2 and solar variations by means of a mixed model considering thermal and solar cloud feedback.
First the weighting factor for the thermal to solar feedback has to be calculated, which specifies an additional admixture of the thermally induced cloud cover changes to the solar initiated changes, this with the objective to satisfy the warming balance over the last century. This weighting should not be mixed with the fraction of the CO2 initiated to the solar created warming, which can finally be derived as one important result of this calculation model. The weighting requires determining the temperature at 380 ppm CO2 with increased TSI (
The respective climate sensitivity is found from the maximum ECS (full TICF) times the thermal weighting, plus the minimum ECS (no TICF) times the solar weighting as follows:
Some typical results based on this combined accounting scheme are compiled in Table
Calculations for the climate and solar sensitivity with the extended accounting scheme (combined thermally and solar induced cloud feedback) for different solar anomalies
Line |
|
Weighting (%) |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|---|
Therm. | Solar | ||||||||
1 | 0.20 | 100 | 0 | 5.4 | 90 | 0.52 | 0.20 | 1.22 | 0.10 |
2 | 0.21 | 100 | 0 | 5.4 | 90 | 0.52 | 0.21 | 1.22 | 0.10 |
|
|||||||||
3 | 0.22 | 100 | 0 | 5.4 | 90 | 0.51 | 0.23 | 1.22 | 0.10 |
4 | 0.23 | 82.4 | 17.6 | 5.4 | 90 | 0.47 | 0.27 | 1.12 | 0.12 |
5 | 0.24 | 64.8 | 35.2 | 5.4 | 90 | 0.43 | 0.31 | 1.02 | 0.13 |
6 | 0.25 | 43.4 | 56.6 | 5.4 | 90 | 0.38 | 0.36 | 0.90 | 0.14 |
7 | 0.26 | 13.8 | 86.2 | 5.4 | 90 | 0.31 | 0.43 | 0.74 | 0.16 |
|
|
|
|
|
|
|
|
|
|
9 | 0.27 | 0 | 100 | 5.4 | 90 | 0.28 | 0.46 | 0.66 | 0.17 |
|
|||||||||
10 | 0.28 | 0 | 100 | 5.4 | 90 | 0.28 | 0.48 | 0.66 | 0.17 |
11 | 0.29 | 0 | 100 | 5.4 | 90 | 0.28 | 0.50 | 0.66 | 0.17 |
12 | 0.30 | 0 | 100 | 0 | 90 | 0.28 | 0.51 | 0.66 | 0.17 |
13 | 0.30 | 100 | 0 | 5.4 | 0 | 0.52 | 0.31 | 1.22 | 0.10 |
Whereas the last two rows in Table
With an anomaly of Δ
In this context it should be noticed that a larger assumed warming over the last century, for example, 0.85°C as considered by the IPCC, leaves the minimum or maximum possible ECS values unchanged; only the bounds for an appropriate solar anomaly satisfying the constraints are shifted to larger values.
The above calculations indicate (different to our previous studies, Harde-2014 [
A reasonable reference for thermally induced cloud changes, however, may be derived from AR5-WG1-Chap.7, where the cloud feedback is estimated as
From these studies we conclude that the measured temperature increase of 0.74°C over the time 1880–2000 and the observed cloud changes of −4% over the period 1983–2000 can best be explained by a cloud feedback mechanism, which is dominated by the solar influence, whereas thermally induced contributions only should have a minor influence.
While a cloud feedback, as estimated in AR5 together with the other feedbacks found in this paper, results in an ECS = 0.74°C, a solar anomaly of 0.27% or larger, as expected from Hoyt & Schatten [
A plot of the temperatures
Earth temperature
Our two-layer climate model together with the integrated radiation transfer calculations show good agreement with the AOGCMs so far, as the Planck sensitivity and the basic ECS only deviate by less than 10%, where these deviations can well be explained by the different concepts for calculating the key parameters (in our case the sw and lw absorptivities as well as the back-radiated fraction of the atmosphere, for the AOGCMs the CO2 radiative forcing) or by different radiation and energy budget schemes, to which the models are calibrated. Also a simulation with the same feedback parameters as compiled in AR5 reproduces the model mean ECS of the CMIP5 AOGCMs within these bounds (see AR5-WG1-Tab.9.5). So, despite very distinctive accounting schemes, this with respect to the concepts, and the expenditure, obviously our simulations give quite reliable results, at least as long as the GCMs can be assumed to be reliable references.
The big discrepancies, however, originate from the differently quantified WV feedback, and on the other side from the neglect of additional feedback processes, which are of fundamental importance for the stabilization of the climate system and which are obviously ignored or not explicitly discussed in AR5.
As outlined in Section We also consider sw WV absorptivity in the atmosphere, which reduces solar absorption at the ground and generates a negative feedback contribution, which cannot be identified in AR5. Our LBL-RT calculations for the lw WV absorptivity are valid for mean cloudiness, consider saturation and interference effects with other GH gases, and they use MRT lineshape profiles. We emanate from a WV concentration (based on satellite data), which is almost a factor of two larger than that applied in many other calculations. The higher concentration causes a stronger saturation of the WV absorptivity and thus results in a reduced sensitivity to temperature induced concentration changes. We additionally include a declining lw WV absorptivity at increasing atmospheric temperatures.
Altogether this results in an amplification due to WV feedback of only 14%, whereas the IPCC assumes a gain of 100%, which is more than 7 times larger. The combined WV lapse rate feedback is even slightly negative with
While the spectral data of the HITRAN-database [
The same holds for the convection and evaporation feedback, which together produce significant negative feedback. So, it is without any doubt that, in an energy balance scheme including sensible and latent heat, these fluxes will directly be influenced by surface temperature variations. Respective changes then have to be integrated as feedback processes in an ECS calculation, and, slightly dependent on the assumed advective flux as well as the used radiation and energy budget scheme (see, e.g., Trenberth et al. [
Considerably larger uncertainties result from cloud feedbacks with different cloud mechanisms, which constitute by far the primary source of spread in the ECS calculations. When any solar anomaly is completely neglected, this in contradiction to several references (see, e.g., Hoyt & Schatten [
Assuming the IPCC’s most likely value for the cloud feedback with
Since from Hoyt & Schatten [
Due to the larger spreads in the solar anomaly and the cloud cover changes we find a maximum range for the ECS of 0.6°C to 1.2°C but with a most reasonable value of
The deviation to our previous publication (
Our calculations in principle confirm the investigations of Ziskin and Shaviv [
We assert that our result is also in good agreement with Lindzen and Choi [
Finally it should be emphasized that in their scenarios the IPCC emanates from the assumption that the actually observed CO2 increase is almost exclusively determined by the 4% of anthropogenic emissions, while the 96% of natural production over a year is considered to be absolutely independent of any solar or temperature variations, this in contradiction to paleoclimatic investigations (e.g., Petit et al. [
The equilibrium climate sensitivity ECS as the key parameter for an evaluation of the influence of CO2 on our climate is still one of the most controversially discussed quantities in climate sciences. Calculations of this measure diverge by more than a factor of 10 starting at about 0.4°C and ending at more than 8°C. Also the actual IPCC assessment report, which mainly refers to AOGCM calculations within the CMIP5 program, still specifies this quantity with a relatively wide range of 1.5°C to 4.5°C. Due to the far reaching consequences for future climate predictions it is extremely important to better understand and to discover some of the large discrepancies between different accounting methods applied for this measure. Therefore, in this contribution, we have tried to scrutinize some of these discrepancies by comparing the main steps of the IPCC’s preferred accounting system with our advanced two-layer climate model (2LCM), which is especially appropriate to calculate the influence of increasing CO2 concentrations on global warming as well as the impact of solar variations on the climate (Harde-2014 [
As an expansion of our previous investigations we present here detailed line-by-line radiation transfer calculations for the GH gases water vapor, carbon dioxide, methane, and ozone, this under clear sky, at regular cloudiness, at different ground temperatures and humidity, and for different lineshapes. From these calculations we derive the CO2 radiative forcing as the main parameter in most climate models, also in the IPCC accounting scheme, and additionally we get from these calculations the sw and lw absorptivities as well as the back-radiated fraction of the atmospheric emission, which are the key parameters in our model.
We find quite good agreement for the Planck sensitivity and the basic climate sensitivity, which match within 8% with the model mean of the AOGCMs; however big discrepancies show up for the ECS, when feedbacks are included. While the lapse rate and albedo influence are adopted from literature, the water vapor feedback is derived from the sw and lw absorptivity calculations performed for three climate zones with different surface temperatures and humidity. With a feedback of 0.43 W/m2/°C and an amplification at mean cloud cover of 1.14 these values are significantly smaller than compiled in AR5 with
Since our calculations show that with increasing CO2 concentration the air temperature is less rapidly increasing than the surface temperature, the sensible heat flux at the bound of both layers rises with the concentration. As a consequence more thermal energy is transferred from the surface to the atmosphere. Similarly, with increasing surface temperature also evaporation and precipitation are increasing with the ground temperature. Both these effects contribute to negative feedback and are additionally included in the simulations. While the respective contribution due to sensible heat rapidly declines with increasing cloudiness, the evaporation feedback absolutely dominates with
A special situation is found for the influence of clouds on the radiation and energy budget. Different to any detailed investigations, which are focusing on individual contributions of low- or high-level clouds to a feedback, here we concentrate on a more general description, how such feedback can be derived and quantified from global cloud observations and how it can be incorporated into a climate model. From these observations over a period of 27 years it is deduced that the global mean temperature is increasing with decreasing cloud cover (ISCCP [
A deliberate approach which mechanism really controls the cloud cover is derived from model simulations, which additionally include the solar effect and compare this with the measured temperature increase over the last century. These simulations, considering both effects, show that the observed global warming of 0.74°C (GISS [
Altogether, we see that the positive feedbacks, originating from clouds, water vapor, and albedo, are partially compensated or in the case of a moderate cloud feedback are even overcompensated by lapse rate and evaporation feedback. Particularly clouds have two stronger opposing effects on the energy balance, which can neutralize each other or can even have an overall attenuating impact on the ECS, dependent on the mechanisms responsible for cloud changes. From these studies we conclude that all constraints can best be explained by a cloud feedback mechanism, which is dominated by the solar influence, while thermally induced contributions only should have minor influence.
Our investigations further indicate that a CO2 climate sensitivity larger than 1°C seems quite improbable, whereas a value of 0.6–0.8°C, depending on the considered solar anomaly, fits well with all observations of a changing solar constant, the cloud cover, and global temperature. A climate sensitivity as specified in AR5 (1.5–4.5°C) would only be possible when any solar influence could completely be excluded and the negative feedbacks further be attenuated.
Maybe the most important message of this investigation is that on the basis of well retraceable physical interrelations there exist several stronger arguments for the inclusion of some effects, which obviously were not considered in the IPCC reports and which can significantly attenuate the influence of CO2 on global warming. The discrepancies primarily go back to an overall negative feedback we find in our calculation, and to the inclusion of solar effects.
two-layer climate model
anthropogenic global warming
long wave absorptivity (of CO2, WV, CH4, and O3)
short wave absorptivity (of CO2, WV, and CH4)
Fourth Assessment Report of the IPCC (2007)
Fifth Assessment Report of the IPCC (2013)
atmosphere-ocean general circulation model
Berkley Earth Surface Temperature
Coupled Model Intercomparison Project Phase 5
cloud cover
equilibrium climate sensitivity
water vapor concentration
temperature induced cloud cover parameter
solar anomaly over last century
solar anomaly over the eighties and nineties
Earth-atmosphere system
equilibrium climate sensitivity
downward directed fraction of atmospheric radiation
feedbacks: WV, lapse rate, surface albedo, convection, and evaporation
cloud feedbacks: thermally or solar induced
general circulation model
Global Energy and Water Cycle Experiment
greenhouse gases
Goddard Institute for Space Studies
global positioning satellite
Coupled Model Intercomparison Project Phase 5
Hadley Centre and Climate Research Unit
convection heat transfer coefficient
Intergovernmental Panel on Climate Change
International Satellite Cloud Climatology Project
Planck sensitivity, climate sensitivity parameter
latent heat transfer coefficient
long wave radiation
molecular response theory
solar induced cloud feedback
outgoing long wave radiation
Pacific Decadal Oscillations
parts per million by volume
radiative forcing
radiation transfer calculations
solar induced cloud cover parameter
solar induced cloud feedback
Southern Oscillation Index
solar sensitivity, temperature increase at 0.1% increase of TSI
short wave radiation
atmospheric temperature
Earth (surface) temperature
reference temperature (16°C)
energy and radiation budget scheme after Trenberth et al. [
top of the atmosphere
thermally induced cloud feedback
total solar irradiance
water vapor.
The author declares that he has no competing interests.
The author thanks D. Grischkowsky from Oklahoma State University and W. Happer from Princeton University for very helpful discussions on spectral lineshape effects, W. Soon from Harvard-Smithsonian Center for Astrophysics for his valuable advice on solar and temperature correlations, and M. Salby, formerly Macquarie University Sydney, for his many constructive suggestions when preparing the paper.