The Physics of the Tropospheric Lapse Rate Refutes the Radiative “Greenhouse Effect”

Introduction

There is a widespread belief in the climate science community, both among mainstream and sceptic researchers, that the lapse rate (i.e. the observed decrease of air temperature with altitude in the troposphere) is caused by either greenhouse gases or convective overturning. The lapse rate plays a key role in the radiative “greenhouse” theory of climate change, since it is used to calculate a putative warming effect of increased greenhouse-gas (GHG) concentrations on the surface. The theory claims that heightened GHG concentrations raise the effective radiating altitude of the planet, which results in surface warming due to applying of the lapse rate over a longer vertical distance. However, this purely “geometric” explanation of the GHG warming is at odds with standard thermodynamics, which postulates that a system’s heat content and temperature can only be altered by either diabatic (heat exchanging) or adiabatic (pressure modifying) processes. The geometry-based warming hypothesis could not have been maintained for decades, if climate researchers had a proper understanding of the true physical nature of the tropospheric lapse rate. This auricle aims to correct the current misunderstanding on this topic using textbook-level atmospheric physics.

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Definition of Dry Adiabatic Lapse Rate

The Dry Adiabatic Lapse Rate (DALR) in the troposphere () is the observed rate of decrease of air temperature with altitude under neutral-stability conditions, when the air is not saturated with moisture. DALR is the backbone of atmospheric lapse rates, since all other lapse rates can be derived from it by applying different correction factors. If the actual lapse rate (L) has an absolute value that is greater than DALR, then the atmosphere is considered unstable. If  , the atmosphere is viewed as more stable. Convective overturning is intensified with increasing atmospheric instability ( ) and suppressed with increasing atmospheric stability ().

The term adiabatic means “without heat exchange”, which implies that the internal energy of a gaseous system only changes in response to variations in the system’s internal pressure. Hence, an adiabatic lapse rate refers to a change of atmospheric temperature per unit altitude due to a decrease of pressure with height. In mathematical terms, DALR is defined as a product of two derivatives, i.e. the change of temperature (T) with pressure (P) and the change of pressure with altitude (z), i.e.:

We evaluate the component derivatives in Eq. (1) below.

What is an Adiabatic Process?

In thermodynamics, adiabatic process is formally defined as the one that fulfills the condition:

where P is gas pressure (Pa), V is gas volume (m³), γ is the adiabatic index given by the ratio of specific heat capacities of a gas at constant pressure () and constant volume (), respectively:

For the Earth’s atmosphere, .

Equation (2) can also be written in terms of pressure (P) and temperature (T) using the fact that gas volume is proportional to the ratio of pressure to temperature according to the Gas Law, i.e. .  This yields:

In the context of the atmosphere, Eq. (4) implies that, under neutral stability conditions and an unsaturated moisture regime, the product  remains constant with altitude. In other words,

where the subscripts o and z refer to the surface and an altitude z, respectively.

Equation (5) allows us to derive an expression for estimating the temperature at an altitude z as a function of the surface temperature and corresponding pressures at altitude z and the surface, i.e.

The power term on the right-hand side of Eq. (6) can be simplified by replacing  with  and employing Mayer’s relation connecting the specific heat capacities of a gas to the gas’s specific constant (), i.e. . This yields:

Equation (7) defines the relationship between temperature and pressure of dry air in the free troposphere under neutral-stability conditions. Note that, in order for the atmosphere to be vertically isothermal (i.e. ), Eq. (7) requires that , which is not physically possible for an air column in a gravitational field.

Derivation of the DALR Formula

Differentiating Eq. (7) with respect to  allows us to quantify  in Eq. (1), i.e.

Using the Ideal Gas Law one can substitute  on the right-hand side of Eq. (8a) with , where  is the density of air (kg m^-3). This simplifies Eq. (8a) to:

The derivative  in Eq. (1) is defined by the requirement for the atmosphere to be in a hydrostatic equilibrium. This means that, at any altitude, the outward-directed force of pressure (P) must be balanced by the inward-directed force of gravity (). This ensures stability of the atmospheric mass in time. The hydrostatic equilibrium is mathematically described as:

Combining Equations (8b) and (9) with Eq. (1) produces the final formula for DALR:

Equation (10) can be found in many standard references on atmospheric physics and thermodynamics. This definition of DALR is not just theoretical but practical as well, since Eq. (10) has been verified by NASA observations on all planets and moons with atmospheres. For the Earth’s atmosphere,  K/m (-9.8 K/km).

Adding a condensable gas such as water vapor to a tropospheric column reduces the lapse rate below  due to the release of latent heat by condensation at higher altitudes. For example, for the Earth’s troposphere, the moist unsaturated lapse rate () can be calculated using the approximation:

where  is the water-vapor mixing ratio (kg kg^-1) in the air.

Discussion

According to Eq. (10), the tropospheric DALR is proportional to the planet’s gravitational acceleration . This implies that gravity is directly responsible for the observed non-isothermal state of the troposphere. In other words, an atmospheric layer, which is primarily heated by energy fluxes from the surface such as the troposphere, cannot ever be vertically isothermal. What shifts an atmospheric layer toward an isothermal state is the presence of energy sources above the surface and throughout the atmospheric column. Examples of such energy sources include the condensation of water vapor at higher altitudes, which releases latent heat to the air, or the observed increased absorption of UV radiation by ozone molecules with altitude in the tropopause and the stratosphere. The release of latent heat by condensing water vapor reduces the average tropospheric lapse rate from the default dry diabatic value of -9.8 K/km to the environmental value of -6.5 K/km. The tropopause is isothermal, simply because the altitudinal gradient of UV radiation absorption by ozone completely offsets the pressure-dependent DALP.

Equation (10) also proves that DALR does not depend on convection (i.e. macroscopic atmospheric motion) or greenhouse-gas concentrations as believed by many researchers. Instead, the lapse rate controls the intensity of convection through its impact on atmospheric stability. In reality, gravity and the lapse rate together enable the convective overturning, which makes convection an effect rather than a cause of the lapse rate.

Finally, Equation (10) refutes the radiative “greenhouse effect” by showing that tropospheric temperatures increase from the tropopause toward the surface as a result of rising air pressure due to gravity and unrelated to radiative properties of the so-called “greenhouse gases”. The pressure-dependent lapse rate completely explains the measured tropospheric thermal effect on the surface, thus eliminating the need for any “greenhouse-gas radiative forcing”. The observed increase of the downwelling long-wave infrared flux with descending altitude is caused by rising air temperatures due to increasing total air pressure downward (i.e. by the lapse rate) and not by “heat-trapping” properties of certain trace gases as claimed by the greenhouse theory. The atmosphere being an open convective system cannot and does not trap heat, as this would violate the 2^nd Law of Thermodynamics! 

When discussing the lapse rate, it is important to distinguish between causative drivers and factors controlling its magnitude. This briefing paper addressed the root causes of the lapse rate, which include the thermodynamic dependence of temperature on pressure and the decrease of air pressure with altitude. The magnitude of the lapse rate at any given location and point in time is complex as it depends on the intensity of solar heating, windspeed, and the presence of energy sources throughout the atmospheric column.

Source: https://tallbloke.wordpress.com/2026/07/03/the-physics-of-the-tropospheric-lapse-rate-refutes-the-radiative-greenhouse-effect/