By Andy May

It all began eight years ago when I read and reviewed Ronan and Michael Connolly’s first three papers on their ideas about the “molar density intersection” which is located just below the tropopause. I was quite fond of Michael Connolly, who sadly and suddenly passed away in August 2025, we all miss him.

As I explain in my paper (May, 2025), the molar density atmospheric profile forms two intersecting least squares best fit lines when plotted versus air pressure as illustrated in figure 1. The Connolly’s intersection is identified with the horizontal dashed line.

The data used to make figure 1 is from 1,136 weather stations, each with multiple weather balloon radiosonde ascents per day from 1990 to 2025. This is a subset of the full 2,921 weather station IGRA2 radiosonde database. The radiosonde data used is comprised of ascents that had at least 90 pressure levels, so they define the troposphere well. This subset was reduced to bin averages vertically in 10 hPa (hectopascals are 100 Pascals, or one millibar) bins. Thus, figure 1 is the overall global average molar density intersection plot and it still shows a distinct kink and intersection at 204 hPa (~11.8 km). This change in slope is unexpected, the formula for molar density is:

In the equation “D” is the molar density in mol/m³, “P” is the pressure in Pascals, “R” is the gas constant (= 8.3145), and “T” is the temperature in Kelvin. As the equation makes clear, the slope of the molar density versus pressure plot should be a line of constant slope, if the atmospheric composition and state do not change. But as figure 1 shows a distinct change does take place, on average, at about 11.8 km. At that altitude the average molar density is 11.9 mol/m³, the average temperature is -53.8°C, and the relative humidity is 21 %. The intersection is just below the classic WMO tropopause everywhere on Earth, except at the very cold South Pole, where neither the classic WMO lapse-rate tropopause nor the intersection techniques work very well (WMO & Ashford, 1957) and (Xian & Homeyer, 2019).

The classic lapse-rate WMO tropopause doesn’t work very well in the higher latitudes in general. It frequently defines multiple tropopauses, probably because atmospheric Rossby waves cause mixing of tropospheric and stratospheric air (Xian & Homeyer, 2019). As a result of the confusion, many replacement definitions have been proposed (Connolly et al., 2024), (Reichler et al., 2003), and (Reutter & Spichtinger, 2025). These are based on relative humidity changes, ozone concentration changes, and other changes that take place in that region of the atmosphere. However, the most globally consistent measure is the molar density intersection. The only problem is we don’t really know why it occurs or why it is so consistent. But regardless of the cause, it is a good marker, and its detection can be automated. The R code to detect it is available in the supplementary materials to my paper, as well as in the paper’s Appendix (May, 2025).

Michael and Ronan did not map their weather balloon results; they always looked at the results through atmospheric profiles and never in 3D. When Michael Connolly gave a talk in Tuscon, Arizona (Connolly M. , 2025) he received an interesting question from John Clauser (Connolly M. , 2025) (see here, about 38 minutes in) about ocean gyres and the Hadley circulation. In short Dr. Clauser thinks the gyres are evidence of the Hadley circulation (Hadley, 1735) and Dr. Michael Connolly thought they are not (Connolly et al., 2021).

That conversation lit a fire under me, and I wrote some R programs to map and profile wind speed and direction. It turns out that the Hadley circulation is real and it does relate to the ocean gyres. Figure 2 diagrams the circulation.

Figure 2 (as well as figures 3, 4, and 5) show speed-weighted vector-averaged “wind arrows” where the x axis is wind speed, the y axis is air pressure, and the arrows point in the direction the wind is blowing (opposite the meteorological convention). The details of how the wind direction is computed, and the R code can be seen in the supplementary materials and in Appendix A of the paper. Figure 2 is only for the month of January and for weather stations between 10°S and the equator (slice “-10”, slices are named for their southern boundary). The wind direction changes when the wind speed slows between about 450 to 500 hPa. Above the slow down, the winds are blowing away from the equator and the Intertropical Convergence Zone (ITCZ, about 5°S in January on average) and the speed of the wind increases with altitude. Below the slow down the winds reverse and blow equatorward (northwest in this case) and speed slightly increases toward the surface.

The key problem with the molar density discussion in Connolly and Connolly (2014 and 2014a) was they did not map their results. Thus, they could not see evidence of the Hadley circulation (Hadley, 1735) and speculated that it might not exist (Connolly et al., 2021). In May 2025, I argue that it does exist, but it is a complex 3D circulation and not a simple 2D north-south circulation as it is often portrayed in the literature (Dima & Wallace, 2003) and (Cook & Webster, 2004). A similar view of a more complex 3D Hadley circulation is presented in (Karnauskas & Ummenhofer, 2014), where they also explain some of the processes involved.

High in the troposphere, the rising air in the ITCZ is diverted horizontally when it hits the highly stratified stratosphere and progresses poleward in both hemispheres. The force of the rising air in the ITCZ also pushes the tropical stratosphere higher than 14 km. It then begins a long path down to the surface as water vapor freezes out of it, which increases the air density (water vapor has a molecular weight of 14 versus 29 for dry air). When the dehydrated air reaches the surface, it warms and creates a high-pressure arid region.

The Hadley circulation is hard to detect because the area of rising humid tropical air, the center of the ITCZ, is constantly moving north and south with the sun as the seasons change. You must check the air flow at the right spot and at the right time. Fortunately, the ITCZ in January is roughly at 5°S (May, 2025) on average and in the Northern Hemisphere winter the Hadley circulation is slightly stronger than in other months (Nguyen, et al., 2013).

The other evidence for the existence of the Hadley circulation are the subtropical deserts, like the Sahara, the Australian Outback, and the Atacama Deserts, these desert regions are circled in figure 3.

The upper tropospheric wind in the desert regions is blowing in the opposite direction from the tropical winds and often with a slightly poleward vector. These deserts occur where the upper troposphere winds reverse direction and have the slowest horizontal wind speed, thus they are over high-pressure regions where the wind is falling, taking dehumidified air with them. The ocean gyres that also result from this circulation are visible in the upper troposphere, but not as clearly as they are in the lower troposphere as shown in figure 4.

Figure 4 shows how the location of the continents, combined with the lower troposphere wind direction reversal at low wind speed between 20° and 30° north/south help form the gyres. The propagation of the low wind speed wind direction reversal is illustrated in figure 5.

As figure 5 shows, the wind direction reversal starts at about 300 hPa (~9 km) at the equator in April and disappears at the surface in the 30°N to 40°N latitude slice. The surface wind direction (again a speed-weighted vector-average) is slightly poleward in the 10°N to 20°N slice but turns equatorward in the 20°N to 30°N slice. A similar pattern is also seen in the Southern Hemisphere.

Discussion

When studying a 3D problem, it is best to study it with 3D tools. Simple 2D graphs will not do the job. When the radiosonde data is mapped and profiled using speed-weighted vector-average wind arrows the Hadley circulation shows up. It isn’t seen in 2D plots of wind direction because the general wind direction in the critical latitudes is either east-west (tropics) or west-east (mid-latitudes), the critical low-speed wind direction shift is not normally seen. The low-speed wind speed change in direction in the sub-tropics is narrow and constantly moving with the seasons. This pattern can be seen in the maps in the supplementary materials where the monthly movements of the ITCZ are noted.

The entire Hadley circulation can only rarely be seen in one profile, as it is in figure 2, because it is a complex 3D wind pattern that changes continuously with time. We could call it a complex 4D wind pattern. Figure 2 is ideally located such that the ITCZ is always located in that latitude slice in that month, and it is near the equator where the rising humid air has pushed the molar density intersection very high. The ITCZ is relatively narrow, particularly the rising air column portion of it, so it is hard to locate. The region, in both hemispheres, where the cool dehydrated air falls is very large, but the meridional wind component is small.

The easiest, and most consistent, way to see the Hadley circulation is to profile the falling low-speed wind direction reversal shown in figure 5. This low-speed region reaches the surface at about 30°N/S, the latitudes of the large ocean gyres. This is also the latitude of the subtropical deserts seen in figure 3. It is the movement of the low-speed wind direction shift that best and most clearly characterizes the Hadley circulation.

This is all discussed in much more detail in my new paper, which can be downloaded here. It is in opposition to what Michael has written and believed, but I’m very sad that he passed away before I finished this work. Knowing him, he would not be upset, he would enjoy seeing the data presented this way and excited to debate the ideas with me. He was always a very data-driven guy.

Code availability

A zip file that contains the R code, additional plots mentioned in the text of the paper, along with some test data can be downloaded from (https://andymaypetrophysicist.com/wp-content/uploads/2025/11/supplementary_materials_May_2025.zip) or (May, 2025b). The zip file also contains some code documentation and the plots used to choose the ITCZ latitudes for each month.

Data availability

The data used can be downloaded from (ftp.ncei.noaa.gov/pub/data/igra) or (https://www.ncei.noaa.gov/products/weather-balloon/integrated-global-radiosonde-archive). The ftp site is far more convenient, but it requires an ftp app, like filezilla.

This paper is also available on Researchgate here.

Afterword

Some will ask why I published this paper via OSF and outside the normal peer-reviewed journal route. It is simple, I’m retired and unless I have a specific invitation for a paper, like with our AJES article, or get a publication fee waiver, it is too expensive and not worth the money. I suppose if I were younger and needed to purchase the prestige of a peer-reviewed journal, it might be worth it, but the fees are several thousand dollars and I’m not interested. The true value is in the study I did and how I wrote it up, what journal it is in is just vanity. People will read it and comment regardless of where it is published.

Works Cited

Connolly, M. (2025). 20 Million weather balloons: How this data shows that all the climate models are based on wrong assumptions. Retrieved from https://www.youtube.com/watch?v=48Hp9CqSlMQ&t=1026s

Connolly, M., Connolly, R., Soon, W., Velasco Herrera, V., Cionco, R., & Quaranta, N. (2021). Analyzing Atmospheric Circulation Patterns Using Mass Fluxes Calculated from Weather Balloon Measurements: North Atlantic Region as a Case Study. Atmosphere, 12. https://doi.org/10.3390/atmos12111439

Connolly, M., Dingley, O., Connolly, R., & Soon, W. (2024). Comparing Different Tropopause Estimates From High-Resolution Ozonesondes. Earth and Space Science, 11(5). https://doi.org/10.1029/2024EA003584

Cook, K., & Webster, P. (2004). The Elementary Hadley Circulation. In H. F. Diaz, & R. S. Bradley, The Hadley Circulation: Present, Past and Future. https://doi.org/10.1007/978-1-4020-2944-8_2

Dima, I. M., & Wallace, J. M. (2003). On the Seasonality of the Hadley Cell. Journal of the Atmospheric Sciences, 60(12), 1522 – 1527. https://doi.org/10.1175/1520-0469(2003)060<1522:OTSOTH>2.0.CO;2

Hadley, G. (1735). Concerning the cause of the general trade-winds. Phil. Trans., 29, 58-62.

Karnauskas, K., & Ummenhofer, C. (2014). On the dynamics of the Hadley circulation and subtropical drying. Climate Dynamics, 42, 2259-2269. https://doi.org/10.1007/s00382-014-2129-1

May, A. (2025). The Molar Density Tropopause Proxy and its relation to the ITCZ and Hadley Circulation. OSF. https://doi.org/10.17605/OSF.IO/KBP9S, URL: https://osf.io/eq75t

May, A. (2025b, November 28). Supplementary Materials: The Molar Density Tropopause Proxy and Its Relation to the ITCZ and Hadley Circulation. https://doi.org/10.5281/zenodo.17752293

Nguyen, H., Evans, A., Lucas, C., Smith, I., & Timbal, B. (2013). The Hadley Circulation in Reanalyses: Climatology, Variability, and Change. Journal of Climate, 26(10), 3357 – 3376. https://doi.org/10.1175/JCLI-D-12-00224.1

Reichler, T., Dameris, M., & Sausen, R. (2003). Determining the tropopause height from gridded data. Geophysical Research Letters, 30(20). https://doi.org/10.1029/2003GL018240

Reutter, P., & Spichtinger, P. (2025). The frosty frontier: redefining the mid-latitude tropopause using the relative humidity over ice. Atmos. Chem. Phys., 25, 16303–16314. https://doi.org/10.5194/acp-25-16303-2025, 2025

WMO, & Ashford, O. M. (1957, October). Meteorology – A three-dimensional science, second session of the commission for aerology. WMO Bulletin, 6(4), 134-138.

Xian, T., & Homeyer, C. R. (2019). Global tropopause altitudes in radiosondes and reanalyses. Atmospheric Chemistry and Physics, 19(8), 5661–5678. https://doi.org/10.3390/atmos12111439