The reply to this question is definitely affirmative and is based on observations. As noted by Ångström (1915), a pioneer of the measurement and modelling of radiation, the first observations relating to the problem of Earth’s (LW) radiation to space were made between the years 1780 and 1850. Ångström (1915, p. 16) cites some sporadic measurements by several researchers for the period 1887-1912. From these measurements and from experiments in the 19th century, it was understood that the major constituents of the atmosphere, i.e., nitrogen (N₂) and oxygen (O₂), are transparent to LW radiation. In contrast, some minor constituents, particularly WV, carbon dioxide (CO₂) and ozone (O₃), absorb and reemit LW radiation, thus being RAG. Tyndall (1865) pioneered our understanding of the dominance of WV in this process, of the importance of its presence for climate and life, and of the minor contribution of CO₂ in the ARE.

Ångström (1915, p. 16) provided his own systematic measurements, as well as a rough quantification of ARE in the following way:

Since the introduction of Penman’s (1948) celebrated equation for natural evaporation from an open water surface, the quantification of the ARE has become part of the routine hydrological calculations for real-world problems, such as those of the hydrological balance (of which evaporation represents a substantial component) and the irrigation needs in agricultural applications. Penman’s (1948) equation is based on the presence of WV in the atmosphere and disregards that of NC-RAGs such as CO₂. Notably, while the role of CO₂ in photosynthesis is important in biochemical terms, it becomes negligible in terms of its contribution to the surface energy balance. A recent study by Koutsoyiannis and Vournas (2024) analyzed a large set of LW radiation measurements distributed in time across a century, in which CO₂ has escalated from 300 to about 420 ppm. They concluded that the observed increase of the atmospheric CO₂ concentration has not altered the ARE in any discernible way. Thus, the ARE continues to be dominated by the quantity of WV in the atmosphere and CO₂ remains insignificant in the ARE.

Since the 1960s, detailed spectroscopic studies of RAGs were conducted, initially developed for military purposes and subsequently expanded to cover broader scientific use, evolving into an essential tool for atmospheric and astrophysical research. The results of these studies were compiled into HITRAN (High-Resolution Transmission), a molecular spectroscopic database designed to support the study of electromagnetic transmission and emission in gaseous media (McClatchey et al., 1973; Rothman et al., 1987; Goldman et al., 1988; Gordon et al., 2022). The database includes detailed line-by-line spectroscopic parameters for various molecular species.

Experimental verification of the theory at laboratory has been provided by Harde and Schnell (2022) and Schnell and Harde (2023) (see Supplementary Appendix SA). Empirical atmospheric data for testing the applicability of the theory had been provided early by Hanel and Conrath (1970) based on a Michaelson interferometer in a satellite. Recently, van Wijngaarden and Happer (2023) and van Wijngaarden and Happer (2025) using these data showed that theory is impressively consistent with the observations, as shown in Figure 1, reproduced from the latter publications.

Some discrepancy appears in the Antarctica case, as the observed radiation is higher than that emitted by the Earth’s surface. The explanation given by van Wijngaarden and Happer (2023) and van Wijngaarden and Happer (2025) is this:

We note though that the T = 190 K, as well as the entire atmospheric profile, are estimated, rather than observed. Hanel and Conrath (1970) mention that

Further examination of systematic ground temperature observations in the area shows that the assumed value of T = 190 K is unlikely. Specifically in the South Pole (station Amundsen-Scot; coordinates: 90°S, 0°E, prob: 2,770 m), the lowest daily temperature in April 1970 (the month of the experiment) did not fall below 204K. The Vostok station (coordinates: 78.45°S, 106.87°E, 3,420.0 m or prob: 3,468 m) is the location with the lowest temperatures among 41 GHCN-D stations in Antarctica, and its temperatures in April are, on average, 7 K lower than in Amundsen-Scot. Furthermore, the reconstructed vertical temperature profile given by Hanel and Conrath (1970) does not seem plausible as it has an abrupt increase of >30 K at the level of 700 hPa.

On the other hand, the ERA5 Reanalysis data suggest that there is a permanent state of temperature inversion (increasing temperature with increased altitude) between the atmospheric levels of 700 and 600 hPa (Figure 2), albeit not that big. This explains the discrepancy seen in Figure 1. The presence of the temperature inversion over the Antarctic Plateau has been studied by Sejas et al. (2018), who found that, along with the scarcity of free tropospheric water vapor, it causes a negative greenhouse effect. In addition, Lindzen (2012) stated that in the case of temperature inversion, RAGs actually cool, rather than warm, the atmosphere. (See additional explanation in Section 3.4 below.).

In their recent work, van Wijngaarden and Happer (2023) stated: “In the absence of greenhouse gases, the isothermal atmosphere will not change with time, since there is no thermal gradient to drive heat flow”. They also asserted that “without greenhouse gases, a thermally isolated adiabatic atmosphere would slowly evolve to an isothermal atmosphere because of conductive heat flow from the warmer lower atmosphere to the colder upper atmosphere”. Here we examine these statements with a slightly different formulation as seen in the question in the heading of this subsection.

It is well known that a gas in equilibrium tends to become isothermal, but here we examine the question also including gravity in the analysis. In fact, this problem is very old and is known as the Loschmidt paradox after Loschmidt (1876) who asserted that gravity could counteract the temperature uniformity implied by the second law as the kinetic energy of the molecules of a gas should be lower at higher elevation in compensation for the higher potential energy. The paradox puzzled many for years, yet both James Clerk Maxwell and Ludwig Boltzmann reacted negatively, supporting the isothermal hypothesis, as detailed in a recent analysis by Darrigol (2021).

Nonetheless, we deemed it useful to perform our own investigation in reply to this question independently of past arguments and using two methods. First, we maximize the entropy of a single molecule which is in motion in a vertical column under gravity. The single-molecule method has been successfully used before to derive the Clausius-Clapeyron equation (Koutsoyiannis, 2014). The development and application of the method to a spherical monoatomic and to a diatomic molecule are presented in Supplementary Appendices SB, SC, respectively. In brief, the thermal (internal) energy per molecule turns out to be the same for all altitudes, equal to ε θ = β ε / β + 2 , where β is the number of degrees of freedom of a molecule and ε is its total energy. This results in 3 ε / 5 for monoatomic molecules and 5 ε / 7 for diatomic molecules. The remaining energy ε g = 2 ε / β + 2 is the average dynamic energy due to gravity. The temperature is also constant, independent of the altitude, equal to T = 2 ε θ β k = 2 ε β + 2 k (1) where k is the Boltzmann constant. In other words, entropy maximization results in an isothermal atmosphere.

The same result emerges when we approach the problem with our second method, without invoking the principle of maximum entropy—by instead simulating the motion of molecules, modeled as perfectly elastic hard spheres, using only Newton’s laws. Once again, the temperature is found to remain constant with altitude, as shown in Figure 3 and discussed in detail in Supplementary Appendix SD. In other words, none of the approaches predicts a decrease in temperature with altitude, which is the observed behavior as will be explained in Section 3.3.

It is common knowledge that Earth’s atmosphere is not isothermal. The temperature decreases with altitude in the troposphere, then it remains constant in the lowest layer of the stratosphere and continues to change at even higher altitudes. The typical atmospheric temperature profile is represented by the standard atmosphere adopted by the International Civil Aviation Organization (ICAO, 1993). According to the U.S. Standard Atmosphere (1976), the standard atmosphere is “A hypothetical vertical distribution of atmospheric temperature, pressure and density which, by international agreement, is roughly representative of year-round, midlatitude conditions.” It is based on large inventories of observational data and is widely used for meteorological and engineering applications. The vertical profile of temperature vs. altitude and atmospheric pressure is shown in Figure 4, with the temperature being 15°C or 288.15 K at the surface, linearly decreasing in the troposphere with the (minus) gradient Γ ≔ − d T / d z being 6.5 K/km up to the altitude of 11 km, and taking a constant value of 216.65 K above this up to 20 km.

Clearly, the standard atmosphere is far from isothermal. Here we extensively use the standard atmosphere as satisfactorily representing reality, even though newer data and research (Wiencke, 2021) support slightly lower values of Γ, particularly at high latitudes. This will be verified below (Section 3.7). It is interesting to note that the average temperature in the standard atmosphere, calculated (by numerical integration) from the coordinates of Figure 4, is T ¯ = ∫ 0 ∞ T z ρ z d z ∫ 0 ∞ ρ z d z = 250   K   = − 23   ° C (2) where, by the ideal gas law, the air density ρ is proportional to p / T , with p denoting air pressure.

Figure 5 shows that temperature gradients appear in other planets and satellites in our solar system, and even in extrasolar planets (for additional rocky exoplanets see also Malik et al., 2019). In other words, isothermal atmospheres never seem to actually exist in planets.

Another important case, additional to the isothermal, is the isentropic atmosphere, where the per-molecule entropy is constant, independent of altitude. Following van Wijngaarden and Happer (2023) here we use the adjectives adiabatic and isentropic interchangeably, even though under some conditions, adiabatic processes can differ from isentropic processes. It is well known that in the absence of water vapor (dry conditions) the atmosphere has a constant temperature gradient equal to Γ d = g c p d = 9.8   K / km (3) where g = 9.81 m/s is the gravity acceleration (typical value for the troposphere) and c p d = 1004 J kg^–1 K⁻¹ is the specific heat capacity of the dry air for constant pressure. This is depicted in Figure 6 for the troposphere and lower stratosphere.

Another limiting case is the moist (pseudo-)isotropic profile, also shown in Figure 6. To calculate it we have used the following equation (Beers, 1945, p. 359; Koutsoyiannis, 2000) which gives a satisfactory approximation for both the isentropic change of saturated air (in which the liquid water remains in the space considered) and saturated pseudo-adiabatic change (in which the liquid water precipitates immediately): c p d ⁡ ln ⁡ T − R d ⁡ ln p − e T + λ   r T T = const (4)

In this, R d = 287 J kg^–1 K⁻¹ is the gas constant of dry air, λ = 3.139 × 10 6 − 2336 T / K J kg^–1 is the latent heat of vaporization, and e T and r T are the saturation water vapor pressure and mixing ratio, respectively, for temperature T. By taking derivatives in Equation 4, setting e T = r T = 0 , and performing algebraic manipulations we readily find as a special case Equation 3 for dry conditions.

The saturation water vapor pressure e T is given by the Clausius-Clapeyron equation, as reformulated for water vapor by Koutsoyiannis (2012): e T = e 0 ⁡ exp 24.921 1 − T 0 T   T 0 T 5.06 ,   T 0 = 273.16   K , e 0 = 6.11657  hPa (5) with T ₀ and e ₀ representing the coordinates of the triple point of water. The mixing ratio is r T = ε   e T p − e T (6) where ε = 0.622 is the ratio of molar masses of water vapor and dry air.

It is seen in Figure 6 that the moist adiabatic atmosphere does not have a constant temperature gradient. Rather the gradient is low (4.9 K/km) at the surface and becomes equal to the dry adiabatic rate (9.8 K/km) at high altitudes. This is a consequence of the fact that at low temperatures the saturation vapor pressure is close to zero and, as already explained, Equation 4 switches to Equation 3. The standard atmosphere has a profile close, but not identical, to that of the moist adiabatic one. Its slope is constant (6.5 K/km) for the entire troposphere. The differences become large at high altitudes near the tropopause and above.

It is useful to compare these profiles with observational data. To this aim, we enroll in the ERA5 reanalysis over the period 1940 – 2024 and find the global average temperature over this period at the available pressure levels, as well as the global average geopotential heights for these pressure levels. The results, areally averaged over the torrid and the north frigid zones, are shown in Figure 7. To adapt the standard profile to the conditions of Figure 7 we take the following steps: (a) we replace the standard ground temperature of 288.15 K with the average temperature of the zone at 1,000 hPa, (b) we apply the standard gradient Γ = 6.5 K/km up to the altitude where the temperature takes the standard stratospheric value of 216.65 K, and (c) we keep a constant value of 216.65 K above this altitude up to 20 km.

We observe that in the tropics the actual average temperature profile is located between those of the moist adiabatic and the standard atmosphere, but above 12.5 km it is closer to the former than the latter. However, in the polar area, observations are totally irrelevant to the moist adiabatic profile. Notice that the moist adiabatic conditions would suggest greater gradients in colder conditions (right panel) than in hotter (left panel) because of the Clausius-Clapeyron equation which results in lower WV quantities for lower temperatures (compare the gradients at the surface level, 4.0 and 7.7 K/km in the two panels). The reality is the exact opposite as seen in Figure 7 (see also Figures 12, 13 below). This means that the moist adiabatic process, despite often being invoked in the literature to explain atmospheric conditions, is not sufficient a tool to describe and explain what happens in reality. All these support the conclusion that the standard atmosphere, despite its empirical basis and its low explanatory power, is more representative for the entire range of conditions on Earth, while the moist adiabatic profile is representative only for the tropics. The dry adiabatic profile is always very different from average conditions. For this reason, the analyses that follow are based on the standard atmosphere.

To address the question in the heading, we apply the established greenhouse theory, without considering doubts that have been cast on the validity of the theory or alternative hypotheses (e.g., Nikolov and Zeller, 2017; Miskolczi, 2023). Rather, we enroll the RRTM software, which calculates at each atmospheric level z the SW and LW radiation going up and down, namely, the four quantities R S W up , R S W down , R L W up , R L W down . The algebraic sum of the four quantities for z equal to the ground level is the net radiation balance at the surface, which is used in evaporation calculations. While, due to its “rapid” characteristic this software is not the most accurate, we deem it satisfactory for the exploratory character of this research. Taking the differences at two adjacent levels z 1 , z 2 we calculate the quantities Δ R S W up , Δ R S W down , Δ R L W up , Δ R L W down , the total radiative energy imbalance Δ R tot , and finally the radiative energy imbalance slope, REIS, based on the following equations. Δ R tot ≔ Δ R S W up + Δ R S W down + Δ R L W up + Δ R L W down , REIS ≔ Δ R tot Δ z (7)

By convention, R quantities directed up are taken as positive and those directed down as negative. If REIS turns out to be positive at a certain layer, between the levels z 1 , z 2 , this means that the layer receives energy of another type, such as sensible or latent thermal energy. This should be equal to REIS, so that the total energy balance be reinstated.

Figure 8 depicts examples of these quantities between the elevations z = 0 and z = 426 m (the fourth altitude given as output by RRTM) and for conditions specified in the figure caption, which include both RAGs and clouds. Two cases are examined, an isothermal atmosphere (Γ = 0) and the standard atmosphere (Γ = 6.5 K/km). In the former case, REIS is almost zero, which means that no forcing appears to drive the atmospheric state away of the equilibrium. Therefore, the atmosphere would remain at the equilibrium (isothermal) state, despite the presence of RAGs and clouds.

In contrast, for the standard atmosphere gradient a positive REIS appears, which means that the total energy balance needs to be reinstated by other energy forms. These forms are indeed present and are the sensible heat due to warm air parcels moving from the Earth’s surface up, and the latent heat due to evaporation, again moving from the surface up.

A more complete picture is provided in Figure 9, where REIS is calculated and plotted for the entire range of altitudes modeled by RRTM, for four different cases of ARE (RAG with clouds, RAG without clouds, no NC-RAG with clouds, no NC-RAG without clouds) and for two cases of temperature gradient, Γ = 6.5 K/km (standard atmosphere; upper row of panels) and Γ = 0 (isothermal atmosphere, lower row of panels). What was discussed with respect to Figure 8 is confirmed in Figure 9 for all cases examined and for all altitudes in the troposphere. The isothermal case yields almost zero REIS in the entire troposphere (z < 11 km) in all cases, which means that the presence of RAGs, whether NC or WV, is not enough for the observed gradient to emerge, nor for the ARE to appear.

The last observation may sound counterintuitive to many who regard the presence of RAGs as a sufficient reason for the temperature gradient. However, our finding is consistent with experimental evidence reported by Harde and Schnell (2022), who stated:

It further agrees with the following two statements by Lindzen (2012) and Lindzen (2018), respectively):

On the other hand, with the standard atmosphere gradient (Γ = 6.5 K/km) there is a positive REIS in the entire troposphere, which leaves room for sensible and latent heat to act, reinstating the total energy balance and stabilizing the temperature gradient.

Given the analysis of the previous subsection, it becomes clear that it is not the ARE that creates and maintains the temperature gradient. Rather the mechanisms responsible for the temperature gradient are:

• the warming of the soil and liquid water by the sunshine during the day and their cooling during the night;

These are not static forcings, but processes, i.e., perpetual changes in the climatic system. The processes occur on different time scales, some of which are too small to drive the atmosphere to the equilibrium (isothermal) state. It is noted that the processes occur at a macroscopic level, with the motion of masses of air, typically referred to as parcels. And as noted by van Wijngaarden and Happer (2023), because of the very small thermal conductivity of air, it takes a very long time for appreciable heat to flow into or out of a parcel of reasonable size.

The driving mechanisms of these processes are the following:

1. Clouds form and disappear, strongly affecting the SW and LW radiation processes.

A rough quantification of changes produced by these mechanisms is shown in Table 2, where it is seen that some of them are of the order of 100%, reaching the absolute maximum of 200% on a daily scale. This quantification is just indicative and is unable to quantitatively predict the observed temperature profiles as seen in Figure 7. It is also unable to produce the standard temperature gradient of 6.5 K/km, which here we regard as an empirical model with satisfactory accuracy in representing the average conditions over the entire globe. It incorporates all mechanisms discussed here, but it can hardly be inferred from them by deduction. Sometimes the literature connects it to the moist adiabatic profile but the data above (particularly the right panel in Figure 7) do not support this idea.

The information provided in the different panels of Figure 9 includes the surface temperature at each of the cases examined (A1-A4, B1-B4). A summary of the results is given in Figure 10, along with some additional hypothetical cases. The first imaginary-world case is a planet shaped as a disk perpendicular to the Sun’s rays, without an atmosphere and receiving the average radiative energy that the Earth does. In this case, the so-called effective temperature is easy to calculate from the Stefan-Boltzmann law, i.e., T 0 = I 4   1 − α ε σ 1 4 (8) where I = 1360 W/m² is the solar irradiance with I/4 = 340 W/m² representing the average solar energy received by (the spherical) Earth’s surface, while σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ is the Stefan–Boltzmann constant, ε is the emissivity of the radiating body and α is its albedo. Taking ε = 1 and using the Earth’s current albedo α = 0.3 , so that I / 4 1 − α = 238 W/m², the result is T 0 = 254.5 K.

About the same (T = 252 K) would be the temperature in the imaginary-world case where there is an atmosphere but no ARE (no RAG and no clouds; second bar in Figure 10) or even with NC-RAGs, but without WV and clouds and without a temperature gradient. If the gradient of 6.5 K/km is present (third bar in Figure 10) the temperature increases to 262 K. Therefore, the effect of the NC-RAGs is zero for an isothermal atmosphere and 10 K for an atmosphere with temperature gradient of 6.5 K/km. By no means is it close to about 30 K as typically implied in the literature.

In general, in an isothermal atmosphere, the effect of RAGs, including NC-RAGs, WV and clouds, is practically zero, as shown by the continuous (blue) line in Figure 10, which fluctuates only slightly, from 249 to 256 K. In contrast, if there is a gradient of 6.5 K/km, the temperature increases up to ∼288 K in the realistic case A1, in which the atmosphere contains all RAGs and clouds.

Hence, it is the temperature gradient that makes the surface-level temperature increase from about 252 K (which is close to the average T ¯ = 250 K of Equation 2) to about 288 K (i.e., by 36 K). This increase is usually attributed to the “greenhouse effect”, but it is mainly the result of the temperature gradient, whose origin is not the ARE but the processes described in section 3.5. This is another reason why it is necessary to stop using the term “greenhouse effect” when talking about the climatic system.

We stress that, among the various cases shown in Figure 10, only cases A1 and A2 are realistic, while all the others are hypothetical. A final hypothetical case shown at the rightmost end of the figure is where the NC-RAGs are doubled. This results in a temperature increase of zero in comparison to case B1 or 1.5 K in comparison to case A1.

While the temperature gradient is the determinant factor that maintains the Earth’s temperature much higher than the effective temperature of 254.5 K, with the mechanisms causing this gradient being also causes of maintaining warm conditions, the RAGs also play a significant role as can be inferred from Figure 10. An atmosphere free of RAGs (both WV and NC) and clouds would keep the temperature close to the average, i.e. 252 K (second bar in Figure 10). However, this case is equally imaginary as that of no atmosphere (first bar in Figure 10) and does not represent planet Earth. For Earth is massively (71%) covered by water, which evaporates, thus giving rise to WV and clouds in the atmosphere. Even without NC-RAGs but with WV and clouds, the surface temperature would be 277 K (case A3)—a substantial increase with respect to the effective temperature.

While Figure 10 provides information on the importance of different agents of Earth’s warming, it should be stressed that the figure compares the realistic cases (A1, A2) with several imaginary-world cases (all others). Hence, it cannot be a basis for understanding the importance of each factor in real-world conditions. The scientific approach for the latter task is to determine the partial derivatives of a suitable multivariate function representing the ARE, such as the downwelling or outgoing LW radiation, at the point of the current conditions and compare them. Such an analysis has been done in Koutsoyiannis (2024b) with the following resulting percent contributions: (a) for downwelling LW radiation, WV and clouds 95%, CO₂ 4%, all other 1%; (b) for outgoing LW radiation, WV and clouds 87%, CO₂ 5%, all other 8% (primarily due to the influence of the stratospheric ozone).

Water vapor, besides being the determinant RAG and the cause of clouds, also has overwhelmingly more impact than CO₂ because its quantity in the atmosphere varies substantially over time and space. This makes WV an agent of perpetual change on all time scales. Relevant changes, mostly on hourly to annual time scales, have already been described in Section 3.5. However, changes also occur at decadal, centennial scales and beyond. These long-term changes are inherent in all geophysical processes, including hydroclimatic ones, and are described in stochastic terms by the so-called Hurst-Kolmogorov dynamics (Koutsoyiannis, 2013; Koutsoyiannis, 2021; Koutsoyiannis, 2024a; O’Connell et al., 2016; Dimitriadis et al., 2021).

As far as long-term changes are concerned, the CERES satellite data show a decline in the albedo of about 0.004 for the entire observation period (post 2000), which translates to 1.4 W/m² (higher than the average imbalance of 0.4 W/m² shown in case 7 of Table 2). This is consistent with an observed decline in cloud area fraction (Koutsoyiannis et al., 2023; Appendix A.2, Koutsoyiannis and Vournas, 2024; Appendix B; see also Goode et al., 2021; Nikolov and Zeller, 2024). Interestingly, a recent study by Goessling et al. (2025) identifies a record-low planetary albedo in 2023, apparently caused largely by a reduced low-cloud cover in the northern mid-latitudes and tropics, in continuation of a multi-annual trend, all of which contributing to the recent global temperature surge.

Coming back to the results shown in Figure 10, a relevant issue to stress is that the analysis made is unidimensional. Is that representative for the average condition of Earth, which is spherical? A negative reply has been suggested by Nikolov and Zeller (2017), who showed that the mean physical temperature of a spherical body is always lower than its effective radiating temperature computed from the globally integrated absorbed solar flux. This happens because of Hölder’s inequality between integrals and the fact that Stefan-Boltzmann law is a power law with an exponent 4.

This suggestion indeed makes sense for the condition of a planet without an atmosphere (first bar in Figure 10), where an integration over the Earth’s sphere would result in a lower value than shown in the figure. However, if we consider the realistic conditions of Earth, in particular cases A1 and A2 of Figure 10, rather than the imaginary-world conditions, the cautionary note by Nikolov and Zeller does not apply. For the relationship between outgoing radiation and temperature is no longer a power law but a virtually linear relationship, as shown in Figure 11, constructed from CERES radiation data and ERA5 Reanalysis near-surface temperature data. Additional information on this linear relationship is provided by Koll and Cronin (2018), Figure 1 and Koutsoyiannis (2024b), Figure 6, which in essence confirm early observations and analyses by Budyko (1969). Hence, the quantities depicted in Figure 10 are representative of average conditions for the (spherical) Earth, at least for the realistic cases A1 and A2, albeit not for the imaginary case of an atmosphere-free Earth.

Once we have recognized that the temperature gradient is a result of macroscopic changes on Earth (Section 3.5) and that it is a critical factor determining the climate (Section 3.6), it is useful to monitor and analyze its changes, which are certainly much more influential than the famed changes in CO₂ concentration. To this end, Figure 12 (upper) shows the variation of the atmospheric temperature averaged over the five geographical zones at two pressure levels, 1,000 and 200 hPa, as given by the ERA5 reanalysis.

By using the geopotential height at these pressure levels, also available in the ERA5 dataset, we determined and plotted in Figure 12 (lower) the evolution of the vertical temperature gradient per geographical zone, calculated as the (minus) ratio of differences of temperature and geopotential heights between these two levels.

It is clear from Figure 12 that, as we move from the equator to the poles and the surface temperatures decrease, so do the temperature gradients. This is fully compatible with the analyses of Sections 3.4– 3.6, according to which higher gradients lead to higher surface temperatures (see also Figure 13, left).

Surface temperatures present increasing trends over time in all zones. In contrast, the temperatures at the level of 200 hPa do not show geographical or temporal changes. It is interesting to examine the temporal trends of temperature gradients, visualized in Figure 12 (lower) and summarized in Figure 13 (right). At the torrid zone we observe a falling trend, which can be viewed as negative feedback to the increasing surface temperatures. In contrast, at the frigid zones the trends are increasing, and hence we would expect greater warming. In the temperate zones no notable trends appear.

Indeed, the zonal distribution of the climatic surface temperature differences between the latest and oldest 30-year periods (for which ERA5 Reanalysis data are available in the CLIMEXP platform), seen in Figure 14, confirm these observations. The figure plots show that for the greatest part of Earth, between latitudes 50°S and 50°N there has been a warming trend of about 1.4 K/century, slightly increasing as we move north, as the percentage of land increases. Between 50°N and the Arctic Circle there is a further warming trend, while between 50°S and the Antarctic Circle the trend becomes cooling. The greatest increases of surface temperature are observed in the frigid zones, where we have increasing temperature gradient trends.

All the above observations are consistent with the evidence from paleoclimatic studies, which suggests that the surface equator-to-pole temperature gradients were weaker during warm periods, while tropical temperatures changed very little (Budyko, 1977, p. 17; Huber et al., 2000, p. 289; Huber, 2008; Lee, 2014; Lindzen, 2020). They are also consistent with the recent study by Ma et al. (2025), which identified wind stilling (compatible with the decrease in the surface equator-to-pole temperature gradient), resulting in weaker evaporation in two-thirds of the ocean and a slight decreasing trend in global-averaged ocean evaporation during 2008–2017. In addition, as already mentioned, the falling multiyear trend in the planetary albedo, largely caused by a reduced low-cloud cover, has been a main driver of the recent global temperature.