By Andy May
The moist‑adiabatic theory (Durran & Klemp, 1982) is one of the central organizing ideas in atmospheric thermodynamics, and it is used—both explicitly and implicitly—throughout modern climate models, especially in the tropics where it works best. It stems from thermodynamics and says that a rising parcel of humid air cools more slowly than a dry parcel because cooling causes condensation of water vapor which releases latent heat that warms the parcel. Adiabatic simply means that the strict theory requires, unrealistically, that no heat enters or leaves the air parcel being modeled from the environment around it, that is, the air surrounding the parcel.
Climate models use this concept, along with an estimate of the amount of “outside” air that mixes with the modeled air parcel over time to construct a vertical atmospheric temperature gradient. The theory is used mostly to evaluate and quantify greenhouse gas feedbacks (Feldl et al., 2026) in the lower latitudes. Inevitably, this modeling procedure has flaws, especially in the very active troposphere. The most obvious flaw is the tropical mid-troposphere model “hot spot” made famous by John Christy and Ross McKitrick as I have previously discussed here. You can see the climate model “hot spot,” in a tropospheric cross section of the Canadian Climate Model output in figure 3 here. Most models have a tropical hot spot, yet the spot does not show up in weather balloon or satellite observations, as conclusively shown by McKitrick and Christy (McKitrick & Christy, 2020 & 2018). This climate model flaw is serious and freely admitted in BAMS State of the Climate (Blunden & Arndt, 2020, p. S109), IPCC AR5 (IPCC, 2013, p. 892), and AR6 reports (IPCC, 2021, p. 444).
Christy pointed out this model flaw when he reviewed early drafts of the IPCC AR5 report in 2012 (pers. communication) and the IPCC published a figure, with little comment, illustrating the problem in Chapter 10 of the AR5 report on page 892. The AR5 illustration (shown on the right in figure 1) suggests that if the CO2 effects are not included in climate model runs the erroneous tropical “hot spot” is reduced or eliminated.
The problem has not gone away, and seems to have gotten worse with time, as shown in the AR6 graph to the left in figure 1 (note the x axis scale change between AR5 and AR6). Christy first reported the climate model problem in the tropical troposphere more than thirteen years ago and yet it has not been fixed in two IPCC iterations. This raises the question, “Why?”
Usually, any model can be fixed to eliminate such an obvious problem given enough time and effort. So why does the problem still exist? Is it due to some fundamental problem in the climate model structure? I think so. In my opinion, it seems that the root cause is the reliance of models on the moist adiabatic theory. I don’t think this theory can be used to recreate the critical tropospheric tropical lapse rate.
The Moist Adiabat and RAE
As explained by Timothy Cronin and Malte Jansen (Cronin & Jansen, 2016), the lapse rate in higher latitudes increases dramatically with surface temperature, relative to both the mid-latitudes and the tropics. This is illustrated in figure 2. This plays a role in polar amplification of warming. However, Cronin & Jansen show that, regardless of the pattern in figure 2, the lapse rate in the higher latitudes is more stable in the sense it is less sensitive to surface temperature vertically than in the tropics. The middle latitudes lie between these extremes.
The climate processes in the higher latitudes are fundamentally different than in the tropics. While the moist-adiabatic theory can get in the ballpark of the deep tropical lapse rate as shown later in this post, the higher latitudes are clearly in a different domain. Cronin and Jansen call this the radiative-advective equilibrium or RAE. The high latitudes are very sensitive to season and climate processes are not a function of surface temperature, but of a variety of forcings including changes in clouds, water vapor, surface albedo, and the variable transport of thermal energy and water vapor from the lower latitudes (see the Winter Gatekeeper Hypothesis).
In its simplest form, Cronin and Jansen state that RAE is a high latitude tug of war between two strong forces, radiative cooling to space and horizontal heat transport from the lower latitudes. Equilibrium is only achieved when these two forces balance. Thus, surface temperature plays a much smaller role in driving climate changes in the high latitudes. This post doesn’t address RAE, here we will discuss the limitations in the moist adiabatic theory in its wheelhouse, the deep tropics, where seasonal effects are minimal.
The tropospheric lapse rate
In the deep tropics (0-20°N/S) vertical convection is vigorous, and the environmental or actual lapse rate (Γ_env) is expected to relax toward Γₘ (the moist adiabatic lapse rate) because convection mixes the troposphere and should drive the lapse rate toward a moist adiabatic temperature profile. The middle latitudes have more dry air and Γenv < Γₘ. As discussed above, there is very little deep convection in the high latitudes and Γenv << Γₘ. The tropical lapse rate is closer to the moist adiabatic lapse rate, and the high latitude lapse rate is much farther from it. This is generally what is observed, as shown in figure 3.
In figure 3 the moist adiabatic lapse rate is computed using IGRA2 weather balloon and radiosonde data using the standard equation (Durran & Klemp, 1982). The actual lapse rate is computed directly from the IGRA2 temperature and height data. In this plot, as in the others in post, the IGRA data are run through a QC function that eliminates anomalous data. The function checks for reverse trends in the data and other anomalies.
The points in the graph are IGRA2 weather balloon stations and the computed global means of 10° latitude bins. The values are the computed moist adiabatic lapse rate subtracted from the actual. Generally, the value is negative, meaning that the moist adiabatic lapse rate (Gamma_m or Γₘ) is larger than the actual lapse rate (Γenv), the exception is the lower troposphere from about 25°S to 10°N, where the mean actual lapse rate is higher than the moist adiabatic lapse rate suggesting vertical instability.
In the tropics, deep convection tends toward the moist adiabat (Cronin & Jansen, 2016), relative to the middle latitudes, it even exceeds it in the deep tropics as shown in figure 3. If the actual lapse rate is higher than the fully saturated moist adiabatic lapse rate, then air parcels cannot cool themselves naturally and accelerated vertical convection will occur, it initiates spontaneously. This is one way cloud towers form in the tropics and during thunderstorms.
It is easier to see what is happening if we compare the moist adiabatic lapse rate to actual, as shown in figure 4.
As illustrated in Figure 4, Γₘ is the cooling rate of a normally rising saturated air parcel, expressed in °C/km. The dry adiabatic lapse rate is about 9.8 °C/km, while the moist adiabatic lapse rate typically ranges from 3 to 7 °C/km, depending strongly on temperature and humidity. The actual lapse rate is strongly dependent upon latitude and varies from near zero in the polar regions to over six °C/km in the tropics. As noted above, when Γ_env is less than or equal to Γₘ, the atmosphere is stable or neutral: a rising saturated parcel cools as fast or faster than its surroundings and therefore does not accelerate upward. But when Γ_env exceeds Γₘ, a saturated parcel cools more slowly than the environment, becomes warmer and lighter than the surrounding air, and accelerates spontaneously. This conditionally unstable state triggers vertical overturning and deep convection.
AR6 tells us that:
“In the tropics, the vertical temperature profile is mainly driven by moist convection and is close to a moist adiabat.” (IPCC, 2021, p. 969).
The IGRA data reveal that while this statement is true, the story is more complex. AR6 relies on the relationship between the moist-adiabatic lapse rate and the actual lapse rate to evaluate feedbacks quantitatively, this includes water vapor feedback and aerosol feedback. While warming attributed to greenhouse gases alone is about one degree per doubling, the effect of feedbacks is estimated (by the IPCC) to exceed two degrees, so the evaluation of feedbacks is important, especially when combined with radiative-advective equilibrium or RAE (Feldl et al., 2026).
Deep convection in the lower troposphere intensifies rapidly once sea surface temperatures (SSTs) approach 30 °C, as shown in Figure 5. This is a natural thermostat or an atmospheric air conditioner that prevents surface temperatures from exceeding 30°C for any length of time over the oceans (Sud et al., 1999) & (Newell & Dopplick, 1979). For those interested, the first mention of the 30 °C limit is probably (Riehl & Malkus, 1958). Over land and close to shore there is no real limit.
The rapid acceleration of rising warm air when Γ_env > Γₘ causes many weather features like tropical thunderstorms and the ITCZ. The ITCZ is the most visible evidence of the effect and generally it lies between 10°N and 10°S, it is comprised of deep convective cloud towers.
The moist adiabatic theory and reality.
Figure 6 shows the observed tropospheric temperature between 10°N and 10°S in black and the moist adiabatic temperature in blue. The red line removes the “adiabatic” restriction on heat flow and allows some heat transfer between the “environment” and each air parcel, thus it lies between measured air temperature and the moist adiabatic temperature, I call it “T_entrain.”
Discussion
After making the model to entrain some of the surrounding environmental air into the moist adiabatic parcels (red line), I noticed that the shape of the moist adiabatic profile (blue) and the entrained profile were substantially different than the shape of the actual temperature curve. The relationship reminded me of the shape of the measured data, shown in black in figure 1, as compared to the AR5 and AR6 models shown in color. I do not think it is possible to adjust the simple air mixing parameter so that the entrained curve will match reality. In my opinion, this means we are missing something important. The moist adiabatic theory, alone, is not enough, even in the tropics.
Besides entrainment of surrounding air into a moist adiabatic air parcel, the environmental lapse rate is also affected by detrainment or the loss of humidity and heat to the environment. It is also affected by lateral winds bringing in dry air, cloud formation and destruction, possible air subsidence, cloud-radiative interactions, vertical wind shear, and inversions due to cloud formation. There are probably other factors as well that I can’t think of right now.
This is only considering the tropics; the higher latitudes are in a different world with regard to climate change. Nicole Feldl and Timothy Merlis (Feldl & Merlis, 2023) have proposed a composite model that blends the moist adiabatic theory in the tropics and the radiative-advective equilibrium theory for the higher latitudes. It supposedly allows climate changes to be a better function of only surface temperature. The IGRA2 data, as studied here, suggests that this sort of model will be an improvement to existing models, but will still be flawed, both in the tropics and in the higher latitudes. The bottom line is that climate change is not solely a function of surface temperature, there are other factors that play significant roles.
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