Comparing Different Tropopause Estimates From High‐Resolution Ozonesondes

Since the tropopause was first identified, the quality and resolution of weather balloons has dramatically improved. NOAA Earth System Research Laboratories (ESRL) have provided high resolution and very high quality ozonesondes from eight locations: Fiji; American Samoa; Greenland; Antarctica; and several locations in USA (Hawai'i, Colorado, California and Alabama). These locations collectively cover polar regions, mid‐latitudes and tropics. Using this publicly archived data set, we studied the variability of the tropopause for all eight locations for one complete year (2016). Along with the standard estimates of the tropopause provided by NOAA ESRL, we developed four alternative tropopause definitions each based on changes in one of the following: (a) molar density; (b) temperature lapse rates; (c) water vapor content; (d) ozone content. These old and new tropopause definitions appear to hold over all eight locations—for all seasons and from the tropics to the poles. The cohesiveness between all five of these independent tropopause definitions is remarkable, although the NOAA ESRL estimates sometimes identify higher tropopause onsets than the other estimates. Therefore, each tropopause definition could potentially be used as proxies for other tropopause definitions. However, it also confirms that the troposphere/tropopause transition is a multi‐faceted physical and chemical phenomenon associated with more than just temperature changes. Finally, these high‐resolution results suggest that the original term “tropopause” might be a misnomer since they suggest increases in temperature lapse rate variability, rather than the “pausing” implied by lower resolution data or by lapse rates that are averaged over large distances.


Introduction
In the early 20th century, with advancements in weather balloon technology that provided measurements from higher altitudes than before, it was discovered that above heights of roughly 10-15 km, the temperature lapse rate changes in ways that were completely unexpected at the time (Hoinka, 1997).The temperature lapse rate is the change in temperature with increasing altitude.For the lower atmosphere ("troposphere"), the temperature lapse rate is mostly negative.That is, temperatures decrease with height-except within so-called "temperature inversion layers."However, at higher altitudes, temperatures remain relatively constant ("pause") with altitude.This region was given the name "tropopause."At even higher heights, temperatures start to increase with height, in a region now known as the "stratosphere." In 1957, the World Meteorological Organization (WMO) tried to standardize the definition of the "tropopause." The WMO chose the following definition: "the lowest level at which the lapse rate decreases to 2°C/km or less, provided also the average lapse rate between this level and all higher levels within 2 km does not exceed 2°C/km" (WMO, 1957).Nowadays, this definition is often called the "lapse-rate tropopause" (L.L. Pan et al., 2014;Ravindrababu et al., 2014;Reichler et al., 2003;Seidel et al., 2001).Since 1957, various other definitions have been proposed for the tropopause.
One approach is to use model-based reanalysis data sets to define the "dynamical" tropopause using potential vorticity calculations (Holton et al., 1995;Hoskins et al., 1985;Reed, 1955).A limitation of these definitions is that they cannot be calculated from an individual weather balloon.Another way of defining the tropopause and the transition between the troposphere below and the stratosphere above is in terms of the "static stability" (or "Brunt-Väisälä frequency") of the air-a metric calculated from the theoretical "potential temperature," θ, that the air should reach if brought adiabatically down to the surface (T.Birner, 2006;Thomas Birner et al., 2002; L. L. Pan et al., 2014;Sunilkumar et al., 2017).
In the tropics, a common definition for the tropopause is the "cold-point tropopause."This is the height where the temperature lapse rate changes from negative to positive (Highwood & Hoskins, 1998;Kim & Son, 2012; L. L. Pan et al., 2014Pan et al., , 2018;;Mehta et al., 2008;Ravindrababu et al., 2014;Seidel et al., 2001;Zhou et al., 2001).However, in the tropics, the thermally-based tropopause definitions tend to yield a very narrow "tropopause region" whether using the single-point "cold-point tropopause" definition or the more general lapse-rate tropopause.This is because in tropical regions, the air tends to cool down with altitude to an absolute minimum ("coldpoint") and then begins warming with altitude without the "pausing" in lapse rate observed for higher latitudes (Seidel et al., 2001).That is, in terms of thermal definitions, the tropical atmosphere appears to switch from the troposphere to the stratosphere without "pausing" at a tropopause.
That said, when the tropics are studied in terms of the other tropopause definitions, it appears that there are indeed definite transitions in behavior between the tropical troposphere and the tropical stratosphere that take place over several kilometers in altitude (Fueglistaler et al., 2009;L. L. Pan et al., 2014;Mehta et al., 2008;Sunilkumar et al., 2017;Tegtmeier et al., 2020;Vömel et al., 2002).Hence, it has become common to refer to the vertical region above and below the tropopause in the tropics as the "tropical tropopause layer" or "tropical transition layer" (TTL in both cases) (Fueglistaler et al., 2009;L. L. Pan et al., 2014L. L. Pan et al., , 2018;;Sunilkumar et al., 2017;Tegtmeier et al., 2020).
It is worth noting that the WMO tropopause definition based on lapse-rates often yields multiple secondary "tropopauses" for the same atmospheric profile.The primary tropopause is defined as "the lowest level" for which the lapse rate conditions are met.However, this approach also can yield secondary or even tertiary tropopauses at higher levels (WMO, 1957).In this study, we will focus on the primary tropopauses.
Depending on the research goals of a particular study, each definition of "the tropopause" has its own advantages and disadvantages.For instance, the cold-point tropopause does not have the potential ambiguity of the WMO definition's multiple tropopauses.However, it is largely confined to tropical regions (Highwood & Hoskins, 1998;Kim & Son, 2012; L. L. Pan et al., 2014Pan et al., , 2018;;Mehta et al., 2008;Ravindrababu et al., 2014;Seidel et al., 2001;Zhou et al., 2001).Meanwhile, the various chemical tropopause definitions require measurements of the relevant trace gases, whereas the temperature-based definitions only require temperature and altitude/pressure measurements.And, as mentioned above, the potential vorticity-based definitions cannot be determined solely from an individual radiosonde.
From one perspective, the fact that "the tropopause" now has so many different "definitions" might initially lead one to wonder how much physical relevance the concept has any more for understanding the physical and chemical behavior of the atmosphere.However, the corollary of this fact is that we now realize that many different physical and chemical properties are associated with the transition between the troposphere and the stratosphere.Also, most of these largely-independent definitions identify the "tropopause" pressure/altitude at fairly similar locations to each other (Bethan et al., 1996;T. Birner, 2006;Fueglistaler et al., 2009;Gettelman et al., 2011Gettelman et al., , 2011;;Hoor et al., 2002;Kim & Son, 2012;Mehta et al., 2008;L. L. Pan et al., 2004L. L. Pan et al., , 2014L. L. Pan et al., , 2018;;Ravindrababu et al., 2014;Reichler et al., 2003;Schäfler et al., 2021;Seidel et al., 2001;Sunilkumar et al., 2017;Tegtmeier et al., 2020;Vömel et al., 2002).
Moreover, as our observational technology and techniques have improved over the decades, researchers have been able to study the tropopause with a much wider variety of (often ingenious) methods than the original early weather balloon observations that noted a (then unexpected) change in the temperature lapse rate with altitude (Hoinka, 1997).These new techniques include: aircraft sampling of the air (Hoor et al., 2002); aircraft lidar observations (Schäfler et al., 2021); ground-based mesosphere-stratosphere-troposphere (MST) radar measurements (Mehta et al., 2008;Ravindrababu et al., 2014); satellite-based radio occultation (RO) calculations (Kim & Son, 2012;Rieckh et al., 2014;Sunilkumar et al., 2017); as well as the use of semi-empirical reanalysis models that interpolate various different weather observations using a weather forecasting or climate model (Reichler et al., 2003;Tegtmeier et al., 2020).These different techniques consistently confirm and often provide new insights into the tropopause phenomenon.Therefore, while our definition of this phenomenon that we call "the tropopause" has become increasingly multifaceted over the years, this multi-faceted nature of the phenomenon also points to both (a) its crucial importance for understanding the physics and chemistry of the atmosphere and (b) the importance of considering "the tropopause" in terms of many different physical and chemical changes associated with the transitions between the troposphere and stratosphere.Hence, in this study, we investigate the tropopause using multiple different metrics all derived from different measurements recorded by the same ozonesondes.
Above, we noted that there are now many more experimental techniques for studying the tropopause than the use of weather balloons (Kim & Son, 2012;Mehta et al., 2008;Ravindrababu et al., 2014;Reichler et al., 2003;Rieckh et al., 2014;Sunilkumar et al., 2017;Tegtmeier et al., 2020).However, the quality, resolution, reliability and range of measurements that can be provided by weather balloons has also dramatically improved since the early-to-mid-20th century observations that led to that 1957 WMO lapse-rate tropopause definition (Durre et al., 2006(Durre et al., , 2018)).As well as the standard weather balloons that are currently launched twice daily from hundreds of weather stations around the world (Durre et al., 2006(Durre et al., , 2018)), several research groups also have been semiregularly launching ozonesondes for several decades now (Sterling et al., 2018;Tarasick et al., 2021;Thompson et al., 2017;Witte et al., 2017).Typically, an ozonesonde involves attaching an electrochemical concentration cell (ECC) for measuring ozone concentrations to a weather balloon in addition to the standard radiosonde circuit used by typical weather balloons for measuring temperature, pressure, wind velocity and humidity.
NOAA Earth System Research Laboratories (ESRL) is one of the main groups conducting a widespread ozonesonde program and they provide access to their data through their public archive at https://gml.noaa.gov/ozwv/ozsondes/index.html(Last accessed on 1 February 2024).They launch ozonesondes roughly once per week at eight locations across the world, covering the tropics, mid-latitudes and polar regions collectively (Sterling et al., 2018).This is a continuation of a decades-long observation program that began at two sites (Boulder, Colorado and South Pole, Antarctica) in 1967.
These modern 21st century balloon sondes provide a much higher resolution and quality than those of the earliest weather balloon observations.As summarized by Sterling et al. (2018), during the analog era , NOAA used VIZ radiosondes that only provided measurements approximately one minute (∼300 m) apart.In 1991, NOAA switched to using Vaisala RS-80 radiosondes that had a higher resolution of ∼7 s, and in 1998, this was improved to ∼1 s (with an average of ∼7 m between measurements).Then, in 2009, NOAA switched to using iMet radiosondes (manufactured by International Met Systems) that also include a GPS receiver (Sterling et al., 2018).Technical specifications on the current iMet-4 radiosondes can be downloaded from https://www.intermetsystems.com/wp-content/uploads/2022/01/202084-12_iMet-4_Technical_Data_Sheet.pdf(accessed on 5 April 2023).
As well as having a much higher resolution than the earliest ozonesondes, the latest instrumentation also seems to be able to measure the water content throughout much of the balloon flight.Up until the late 1990s, the instrumentation would often only provide water content measurements for the first 5-10 km of the atmosphere, that is, the lower-to-mid-troposphere.There have also been several significant technological improvements in the quality and reliability of the ozone measurements over the years (Stauffer et al., 2020(Stauffer et al., , 2022;;Sterling et al., 2018).
For all these reasons, this publicly archived, high quality data set is very useful for analyzing the troposphere/ stratosphere transitions in terms of ozone content, water content and the various other measurements recorded by standard radiosondes.This was not possible for the earliest studies of the tropopause due to the lower resolution at the time.Therefore, we compare and contrast five different approaches to determining the tropopause using this high resolution data set.
Each of the five definitions is applied to different sets of measurements that were simultaneously recorded by different recording devices attached to the exact same balloons.Hence, all five definitions of "the tropopause" will be applied to the exact same atmospheric profile that was sampled by each balloon sounding.This allows us to simultaneously compare and contrast different facets of the multi-faceted phenomenon that is collectively called "the tropopause." We note that the analysis in this paper could also be extended to consider ozonesondes from other ozonesonde networks that have also switched to using similarly high-resolution instrumentation over the years (Stauffer et al., 2020(Stauffer et al., , 2022;;Tarasick et al., 2021;Thompson et al., 2017;Witte et al., 2017), such as the Southern Hemisphere ADditional OZonesondes (SHADOZ) network (Thompson et al., 2017;Witte et al., 2017) (four of the NOAA ESRL stations are also part of the SHADOZ network).However, since the NOAA ESRL network already spans a fairly large geographical region from the poles to the tropics, in this study, we have confined our analysis to this particular data set.
We have already presented some of the preliminary findings from our analysis in a conference proceedings paper - Dingley et al. (2022).That initial presentation described the original processing of the ozonesonde data and initial calculations.Here, we provide and discuss the final results of our analysis.We also provide a more detailed discussion of our calculations and methodology than was possible in the shorter proceedings paper.

Data Used
We downloaded the ozonesonde data for this analysis from NOAA ESRL's ozonesondes website at https://gml.noaa.gov/ozwv/ozsondes/index.html (Last accessed on 1 February 2024).This publicly archived data set provides data for 8 main weather stations that are globally distributed (mostly sited in USA or its territories).As can be seen from Figure 1 and Table 1, these stations include locations in the tropics, mid-latitudes and polar regions (Sterling et al., 2018).
As we described in Dingley et al. (2022), "Some of these stations have longer records than others-in particular, both the Colorado and Antarctica archives include some low-resolution sondes as early as 1967.However, some of the stations are relatively recent and several appear to have been discontinued in recent years.Additionally, the reliability, quality and resolution of the ozonesonde instruments has substantially improved in recent years (Sterling et al., 2018).Therefore, we have confined our analysis in this study to the year 2016, since all eight stations were active for this year and the data is of a very high quality."See Figure 2 for a summary of the improvements in resolution and station density over the decades.For more details, Sterling et al. (2018) provide a graphical breakdown of the available data up to 2017 along with the documented historical instrumentation changes for each station in their Figure 1.
Table 1 shows that, for 2016, most of the stations launched ozonesondes roughly once per week, except for Fiji and American Samoa that launched once every few weeks.Three hundred sixty-one sondes were collectively launched in 2016 for these eight stations.However, as we already noted in Dingley et al. (2022), "in a few cases (5 out of 361, 1.4%), the sondes did not have sufficient data for analysis.Therefore, our analysis was based on 356 of the 361 sondes." As described in Dingley et al. (2022), "The exact format of the data in the archive varies somewhat between stations and over time."However, in general, NOAA ESRL provide two main versions of the data: Earth and Space Science 10.1029/2024EA003584 1.The raw native resolution files that, for the 2016 sondes, are reported roughly every second.2. Interpolated "100 m average" versions that have been interpolated by NOAA ESRL from the raw data into smoother but lower resolution sondes." For our analysis we use the raw data files.However, to reduce noise, we typically use a 31-point centered running average for our plots and discussion.
While the data is reported roughly every second, we should caution that the instrumental response time for several of the measurements we use is slower.For our analysis, we collectively use the following measurements: pressure; temperature; altitude; relative humidity and ozone concentration.The first four are recorded by the iMet4 instrument attached to the weather balloon and the ozone concentrations are measured using an electrochemical concentration cell (ECC) also attached to the same balloon.According to the technical datasheet for the iMet4 instrument (https://www.intermetsystems.com/wp-content/uploads/2022/01/202084-12_iMet-4_Tech-nical_Data_Sheet.pdf,accessed on 5 April 2023), the response times and resolutions for each of these measurements are as follows: • Pressure = 0.5 ms; 1 Pa • Temperature = less than 1 s in moving air at 5 m s 1 (100,000 Pa); 0.01 K  • Relative humidity = 0.6 s at ∼300 K to 61 s at ∼230 K; 0.1% RH • Altitude (i.e., pressure-derived geopotential height) = resolution of 0.1 m Meanwhile, the response time for the ozone measurements is typically 20-30 s (Stauffer et al., 2020;Tarasick et al., 2021;Witte et al., 2017).

Methods
As described in Dingley et al. (2022), "each balloon provides in situ measurements approximately every second throughout their vertical ascent and descent in the troposphere, tropopause and stratosphere (typically up to at least ∼30-35 km altitude) with readings of: altitude (h); pressure (P); temperature (T); water vapor (H 2 O); ozone (O 3 ); horizontal wind speed and direction; and vertical ascent and descent velocity.For our analysis here, we will not be considering the horizontal wind measurements or vertical velocity measurements.However, we note that our preliminary analysis (not shown here) suggests that there might also be some systemic changes in these measurements associated with the troposphere/tropopause transition." Indeed, others have already noted that the troposphere/stratosphere transitions are associated with changes in wind velocities (T.Birner, 2006;Fueglistaler et al., 2009).The data from these ozonesondes would also be suitable for investigating the horizontal mass fluxes (Connolly et al., 2021).However, this more detailed analysis is beyond the scope of this study.
Figure 2 shows the data availability from this data set in terms of five metrics.We have plotted the data for all 10 stations on the same plots to provide an overall view of the changes in data over time.For interested readers, we also provide less cluttered versions of the plots in Supporting Information S1 where the data for each of the 10 stations is plotted in separate panels in Figures S1--S5 in Supporting Information S1.
At any rate, the data availability from this data set has considerably improved over the decades for multiple reasons.First, the station coverage has generally improved over time.Although two stations were already launching ozonesondes in 1967 (Antarctica and Colorado), the other stations only began launching ozonesondes in the 1980s (Hawai'i, American Samoa); late 1990s (Fiji, California, Galapagos and Alabama); early 2000s (Rhode Island, Greenland).Two of these stations were dropped from our analysis because they apparently stopped observations before our study period (Rhode Island in 2011; Galapagos in 2016).
Second, the resolution of the measurements has improved dramatically from the early ozonesondes that only recorded measurements every ∼60 s (with an average of ∼300 m between measurements) to current ozonesondes that take measurements roughly every ∼1 s (with an average of ∼7 m between measurements).Third, although there are still debates over the accuracy of some measurements (Stauffer et al., 2020(Stauffer et al., , 2022;;Tarasick et al., 2021), the quality of the instrumentation has continued to improve.For example, by comparing Figures 2d and 2e, it can be seen that until the 21st century, water content measurements often stopped in the lower atmosphere.
As representative examples, Figure 3 plots the key measurements used for our analysis from a typical ozonesonde launched from each of three sites: Summit Station, Greenland (12 March 2016); Huntsville, Alabama (1 October 2016) and Hilo, Hawai'i (28 September 2016).Dingley et al. ( 2022) also provides a similar analysis for an ozonesonde launched from the Boulder, Colorado site-13 October 2016.
For each ozonesonde, NOAA provide their calculated estimate of the tropopause height, that we convert into the corresponding atmospheric pressure because our analysis is predominantly based on pressures instead of heights, as will be discussed later.These tropopause estimates are indicated with horizontal dashed (gray) lines in each panel.These estimates appear to be based on the tropopause definition of WMO (1957) when applied to the temperature lapse rates derived from the interpolated data.
In addition to NOAA's estimates of the tropopauses that are provided by NOAA with the ozonesonde data, we have developed four additional approaches for estimating the tropopause based on the above data.Each of these estimates focuses on a different metric that substantially changes behavior between the troposphere and the tropopause/stratosphere regions: (a) molar densities; (b) temperatures; (c) water content; and (d) ozone content, as we will see.
In our various estimates, we primarily consider the changes in a given metric with pressure, but we also consider the rates of change of this metric with respect to height or pressure.See Figure S6 in Supporting Information S1 for a visualization of the rates of change of pressure and height per measurement or per time elapsed over the entire profiles of the three ozonesondes shown in Figure 3.
As mentioned before, we calculated the rates of change of all metrics using a 31-point centered box car average.That is each value is the mean over the ∼15 s before and after a given set of measurements.
In Sections 2.2.1-2.2.4,we will describe the procedure we applied for each of these four independent definitions of the tropopause.An example set of calculations for each definition will be provided in Figures 4-7 respectively when applied to the three ozonesondes plotted in Figure 3.For clarity, we have expanded the x-and y-axes for each panel to emphasize the changes in each metric close to the tropopause.However, for interested readers, we have also plotted the equivalent metrics over the entire ozonesondes in Figures S7-S10 in Supporting Information S1.
In our opinion, the changes in atmospheric behavior from the troposphere to the tropopause to the stratosphere are better understood in terms of atmospheric pressure profiles instead of altitudinal profiles.That is, with y-axes showing the atmospheric pressure-with the bottom value corresponding to the (largest) ground pressure and the top value corresponding to the smallest measured pressure, that is, the pressure at which the balloons burst.This is because the atmospheric pressure at a given altitude is a function of the mass and density of the air at that point (and above that point).We believe that this has considerable relevance for understanding the changes in atmospheric behavior associated with the transitions between the troposphere, tropopause and stratosphere.In contrast, the altitude merely represents the vertical distance above mean sea level.This is of course an important factor, but in our opinion, the atmospheric pressure has a bit more relevance for understanding the changes in atmospheric chemistry and physics.
It also makes sense from an experimental perspective given that aside from the lower resolution GPS altitudes provided with recent ozonesondes, most of the altitude "measurements" are derived metrics that are calculated from the pressure readings using the barometric formula (Lente & Ősz, 2020).However, we appreciate that, historically, researchers are often more used to studying balloons profiles in terms of altitudinal profiles.Therefore, we have included the equivalent plots in terms of altitudes in Figures S11-S14 in Supporting Information S1.
We also appreciate that, historically, researchers typically analyze weather balloon soundings using non-SI units and/or non-base SI units, for example, temperatures in degrees Celsius (°C) instead of Kelvin (K); atmospheric pressures in units of millibar (mb) or hectopascal (hPa) instead of Pascals (Pa); altitude in kilometers (km) instead of meters (m).For our analysis, we find the use of base SI units simplifies many of the calculations.Therefore, we have first transformed the reported ozonesonde measurements into base SI units where appropriate before our calculations.However, for the benefit of readers that are more accustomed to working in other units, for Figures 3-7 and Figures S7-S10 in Supporting Information S1, we have also included a secondary y-axis for the atmospheric pressure in units of hPa (where 1 hPa = 1 mb = 100 Pa) and for Figures S11-14 in Supporting Information S1 in units of km (1 km = 1,000 m).

Tropopause Estimates Based on Changes in Molar Density
The molar density, D, at each point is calculated from the corresponding pressure and temperature measurements, following the approach described by Connolly et al. (2021).That is, D = P/RT, where R = 8.314 J K 1 mol 1 is the ideal gas constant, P is the atmospheric pressure (in Pa units) and T is the temperature (in K units).The instrumental response times for molar density for the ozonesonde profiles is determined by the instrumental response times for both pressure and temperature measurements.However, since the response time for the pressure measurements (0.5 ms) is much faster, it is effectively determined by the thermometer response time.Nonetheless, apparently this is <1 s in moving air at 100,000 Pa.So, this should be rapid enough for our analysis based on 31-point moving averages.
Two of us (MC and RC) have described in detail the surprising utility of molar density calculations for analyzing weather balloon sondes in a series of working papers in 2014 (Connolly & Connolly, 2014a, 2014b, 2014c).More recently, Connolly et al. (2021) have shown that molar densities can also be converted into atmospheric mass fluxes when combined with the accompanying horizontal wind measurements.However, until now, the relevance of these relatively simple molar density calculations for studying the atmosphere appears to have been overlooked by the atmospheric science community.Therefore, a brief digression to consider this particular metric might be helpful.The molar density (in units of mol m 3 ) describes the average density of moles of gas (n, in units of mol) per unit volume (V, in units of m 3 ) of air.A mole is a standard scientific unit commonly used in chemistry for describing the number of molecules (or atoms) of a substance.One mole of molecules corresponds to ∼6.022 × 10 23 molecules.The fact that this property can be determined from just a weather balloon's pressure and temperature measurements might initially seem surprising, but it is a straightforward corollary if we explicitly assume the atmosphere follows the ideal gas law, PV = nRT, since D = n ÷ V = P ÷ (RT).Note that if the molar density is multiplied by the average molecular weight of air, this yields the mass density as considered by Lente and Ősz (2020).
It is well-known that the atmospheric pressure decreases with altitude as we move from ground toward space (Lente & Ősz, 2020).In general, we would expect the molar density of the atmosphere to decrease linearly with decreasing atmospheric pressure and to approach near zero in the vacuum of space.Broadly, this is what is observed in the regions covered by weather balloons (0-∼30-35 km).However, surprisingly, the slope of this linear decrease changes quite abruptly at the transition from the troposphere to the tropopause/stratosphere as described in detail for North America by Connolly and Connolly (2014a) and globally by Connolly and Connolly (2014b).Less abrupt deviations from linearity are also frequently observed in the lower troposphere in regions with high absolute humidity (typically corresponding to the "boundary layer") or polar winter conditions where a "temperature inversion" is observed (Connolly & Connolly, 2014a).
We recognize that many readers might initially be skeptical that this change in slope of molar density versus pressure between the troposphere and tropopause is as striking, systemic, and rapid, as described by those working papers (Connolly & Connolly, 2014a, 2014b, 2014c).Therefore, we have included, as Supporting Information S1, a 1-min video presenting on the left-hand side the temperature versus pressure profiles and on the right-hand side the D versus pressure plots for every radiosonde launched twice-daily in one year (2018) from one station (Tucson, AZ, USA).[This particular station was chosen because MC and RC were initially presenting it at a 2019 conference in Tucson].In the panels on the right-hand side of this video, the green dashed-lines correspond to the D versus pressure slope in the troposphere, while the yellow dashed-lines correspond to the slope in the tropopause/stratosphere.The horizontal black dashed-lines indicate the point of intersection of the two lines.This approximates the molar density-based tropopause definition we will discuss below.The yellow and green dashed curves on the left-hand side panels correspond to the equivalent temperature versus pressure profiles.We encourage interested readers to view this short video a few times and/or to carry out their own D versus pressure plotting for several weather balloon sondes from their chosen data set.
At any rate, returning to the present analysis, these abrupt changes in slope can be seen from Figures 4a, 4d, and 4g, where D is plotted against pressure in black for each of the three ozonesondes described in Figure 3 and for comparison a linear fit over the upper troposphere is shown by a yellow straight line.Extended versions of the graphs in Figure 4 that cover the entire ozonesonde are provided in Figure S1 in Supporting Information S1.For most of the troposphere, the yellow line is covered by the black line with some deviations apparent in Figure S1 in Supporting Information S1 in the boundary layer for the Alabama and Hawai'i ozonesondes.As we will see later, these deviations are associated with relatively high water contents.However, above the tropopause the slope of the line changes much more dramatically.
For our molar density-based estimates of the tropopause, we study these deviations of the observed D values from a linear fit (yellow straight line) in the upper troposphere region.As explained in Dingley et al. (2022), "This region is defined as 35,000-50,000 Pa for Greenland and Antarctica; 30,000-50,000 Pa for Colorado [and] Alabama; 25,000-45,000 Pa for California; 15,000-35,000 Pa for Hawai'i; 15,000-40,000 Pa for American Samoa and Fiji."We also use two related metrics: the rate of change of D with altitude, dD/dh; the rate of change of D with pressure, dD/dP.
We define the molar density-based tropopause as the pressure above the boundary layer at which: Molar density does not appear to have been used for estimating the tropopause until now, other than in the working papers mentioned above (Connolly & Connolly, 2014a, 2014b, 2014c).Therefore, let us now consider alternative definitions that use measurements that have already been used by others, that is, temperatures (L.L. Pan et al., 2018;WMO, 1957;Zhou et al., 2001), water concentrations (L.L. Pan et al., 2014;Teitelbaum et al., 2000;Vömel et al., 2002) or ozone content (Bethan et al., 1996;L. L. Pan et al., 2014).

Tropopause Estimates Based on Changes in Temperatures
Figures 5a, 5d, and 5g plot the changes in temperature with pressure for each of the three ozonesondes.We also plot the corresponding changes in the rate of change of temperature with altitude ("temperature lapse rate," dT/dh) in Figures 5b, 5e, 5h, and those with respect to pressure (dT/dP) in Figures 5c, 5f, 5i.Readers will probably note that, above the tropopause, the temperature lapse rate begins to oscillate quite wildly.This is somewhat ironic given that the original definition of the tropopause implied temperatures "paused" with altitude.
Indeed, the standard WMO definition of the tropopause (which NOAA's estimates appear to be based on) are strictly defined in terms of well-defined changes in average temperature lapse rates (WMO, 1957).However, we wish to highlight that the WMO definition from 1957 was developed based on much lower resolution weather balloon data than the modern instrumentation we are considering here.
Therefore, to calculate the tropopause from the temperature data, we take a different approach to the WMO definition.Instead of only focusing on the average temperature lapse rates, we define the temperature-based tropopause as the pressure above the boundary layer at which: 1. dT/dh crosses from being negative to being positive.This effectively corresponds to the so-called "cold-point tropopause" which is often used instead of the WMO definition for tropical regions (Highwood & Hoskins, 1998;Kim & Son, 2012;Laura L. Pan et al., 2018;Mehta et al., 2008;Zhou et al., 2001), but can also be used for extratropical regions (König et al., 2019).2. dT/dh and dT/dP begin to oscillate wildly.

10.1029/2024EA003584
The instrumental response times for the temperature measurements are apparently <1 s in moving air at 100,000 Pa.Therefore, this should be rapid enough for our analysis based on 31-point moving averages.
We stress that our temperature-based tropopause definition here is not identical to either the WMO definition or the "cold-point tropopause" definition, but it is related to both.Our definition avoids the ambiguity of the WMO definition that often yields secondary or even tertiary tropopauses.Meanwhile, unlike the cold-point tropopause definition which is largely confined to the tropics, it is applicable globally.

Tropopause Estimates Based on Changes in Water Content
Although much of the early research into the troposphere/tropopause transitions focused on temperature lapse rates, it has been well-established over the subsequent decades that there are also significant changes in the relative concentrations of various trace gases associated with these transitions -sometimes called "tracer gases."These include ozone (O 3 ), water vapor (H 2 O), methane (CH 4 ) and carbon monoxide (CO) (Bethan et al., 1996;Fischer et al., 2000;Folkins et al., 1999;Gettelman et al., 2011;Hoor et al., 2002;L. L. Pan et al., 2004L. L. Pan et al., , 2007L. L. Pan et al., , 2014L. L. Pan et al., , 2018;;Schäfler et al., 2021;Vömel et al., 2002).Hence, some groups have proposed using these changes to define a "chemical tropopause" (Bethan et al., 1996;Fischer et al., 2000;Folkins et al., 1999;L. L. Pan et al., 2004L. L. Pan et al., , 2018)).The ozonesonde data we consider here provides details on two of these trace gases-water vapor and ozone.Therefore, we define an additional two estimates of the tropopause based on each of these metrics.
For our water vapor content-based tropopause estimates, we calculate the rate of change with altitude, d(H 2 O)/dh and with pressure, d(H 2 O)/dP.Examples of these profiles are shown in Figure 6.We define the water-based tropopause as the pressure above the boundary layer at which: The instrumental response times for the relative humidity measurements are relatively slow-and they slow down with reduced temperatures.While the response time is less than 1 s at ∼300 K, it is apparently 61 s at ∼230 K. Therefore, at the low temperatures associated with the tropopause (∼190-230 K), there might potentially be problems in precisely identifying the exact location of the tropopause using absolute values of water concentration only, if there are rapid changes in relative humidity.That said, the third part of our definition specifically uses the ending of the rapid oscillation of water content with increasing height/decreasing pressure.So, collectively the three aspects of our water-based tropopause definition appear to be able to identify the onset of the tropopause with reasonable consistency, precision and accuracy.
We should briefly comment on the relationship between this water content-based definition of the tropopause and a similar phenomenon sometimes discussed in the literature known as the "hygropause" (MacKenzie et al., 2006;Teitelbaum et al., 2000).The hygropause refers to the region near the tropopause where water content reaches its stratospheric minimum.Our water-based tropopause definitions consider a less restrictive threshold, that is, they can occur in the region where the water content drops below 50 ppmv.This can potentially occur earlier in the sonde than the hygropause since the water content can drop lower than 50 ppmv for the stratospheric minimum.As for the relative humidity measurements, the instrumental response times for the ozone measurements are relatively slow, that is, ∼20-30 s (Stauffer et al., 2020;Tarasick et al., 2021;Witte et al., 2017).Therefore, this response time could potentially introduce problems in precisely identifying the exact location of the tropopause only using specific thresholds for ozone concentration, if there are rapid changes in ozone concentration in the Earth and Space Science 10.1029/2024EA003584 region.However, analogously to our water-based tropopause definition, the third part of our definition specifically uses the onset of the rapid oscillation of ozone concentration with increasing height/decreasing pressure.Therefore, by incorporating multiple metrics, our ozone-based definition seems to be able to identify the onset of the tropopause with reasonable consistency, precision and accuracy.

Tropopause Estimates Based on Changes in Ozone Content
Our ozone-based tropopause definition is similar to, but different from, that originally defined by Bethan et al. (1996).They defined their ozone tropopause as the lowest altitude where (a) d(O 3 )/dh > 60 ppmv km 1 ; (b) [O 3 ] > 80 ppbv (i.e., 0.08 ppmv); (c) and [O 3 ] > 110 ppbv (i.e., 0.11 ppmv) for the layers immediately above.While our definition uses a similar initial minimum threshold of [O 3 ] > 100 ppbv (i.e., 0.1 ppmv) and also requires ozone concentrations to continue to increase above our tropopause, we also use the onset of the rapid oscillations of ozone concentrations with increasing height/decreasing pressure as an additional metric.As mentioned above, this is important because the instrumental response time for ozone measurements is relatively slow, that is, ∼20-30 s (Stauffer et al., 2020;Tarasick et al., 2021;Witte et al., 2017).

Results and Discussion
In Figures 3-7, we have plotted, as examples, the five estimates of the tropopause for three specific ozonesondes, that is, the three sondes plotted in Figure 3. See the horizontal lines in each panel of Figure S6 in Supporting Information S1 for an additional visual comparison of the different estimates for these three sondes.However, we have repeated the procedures described above for all of the NOAA ESRL ozonesondes launched in 2016.
Figure 8 shows all five estimates of the tropopause for all 356 ozonesondes-sorted by day of year (in 2016) and station.Note that, for convenience, we have replotted these Figure 8 results from our preliminary analysis in Dingley et al. (2022) since they offer a useful overview of the week-to-week variability for each station.We encourage further research into considering longer time periods, but we caution that a long-term analysis that combines the modern data with earlier data should consider the historical changes in instrumentation for each of the stations (Sterling et al., 2018).
All five estimates match very well.This can be statistically seen from Table 2 where the correlations between the tropopause estimates for each metric are compared to the others.That said, we note that NOAA's estimates often seem to deviate from the other estimates-typically implying a higher tropopause altitude than the other estimates.Examples of this deviation can be seen by comparing NOAA's estimates for the Alabama and Hawai'i ozonesondes in Figure 3 to the equivalent estimates in Figures 4-7.
The fact that the four new tropopause estimates match so well might initially seem surprising given that the instrument response times for each of the measurements involved is different-as discussed in Sections 2.1 and 2.2.That is, while the instrument response times for the temperature and molar density measurements are ∼1 s, that is, the approximate time between consecutive readings, the instrument response times for the water content (i.e., relative humidity) and ozone measurements are slower.For ozone measurements, the instrumental response time is typically 20-30 s (Stauffer et al., 2020;Tarasick et al., 2021;Witte et al., 2017).For relative humidity, the response time is less than 1 s at ∼300 K, but it is apparently 61 s at ∼230 K.This slower response time is particularly relevant given the low temperatures associated with the tropopause (∼190-230 K).
Hence, it might seem surprising that all four independent definitions give such similar estimates of the tropopause.However, as discussed in Sections 2.2.3 and 2.2.4,our water content and ozone content-based definitions are not solely reliant on the absolute concentrations.They also consider the rapidity of the changes in concentrations.This additional component to our definitions seems to allow us to identify the onset of the tropopause with a similar precision and accuracy as to the definitions based on measurements with a faster instrumental response time, that is, the temperature and molar density-based definitions.
In terms of the standard tropopause estimates provided with each ozonesonde, it is important to recall that the WMO (1957) tropopause definition was designed for use with much lower resolution weather balloon sondessee Figure 2. Therefore, while NOAA's estimates remain very useful for comparison with other data sets, we propose that the four new approaches to estimating the tropopause that we developed for use with this higher resolution data set could potentially provide new insights into the troposphere/stratosphere transitions that might not have been so obvious from the early weather balloon data.
As we described in Dingley et al. (2022), a perhaps surprising finding is that "the original concept of the tropopause was a region where the temperatures remained fairly constant ("paused").Yet, we note from the very high temporal resolution of this data set compared with the earlier weather balloons that if anything, the temperature lapse rate becomes much more chaotic and variable in the tropopause and stratosphere regions.Whereas the average temperature lapse rate is fairly constant in these regions, the short-term oscillations are surprisingly large."Dingley et al. (2022) illustrated this phenomenon for one station (Colorado), but it occurred for all of the ozonesondes we analyzed, as illustrated in Figures 5b, 5e, and 5h.
In recent years, several groups have begun emphasizing the use of changes in trace gas concentrations to identify the tropopause (Bethan et al., 1996;Fischer et al., 2000;Folkins et al., 1999;Gettelman et al., 2011;L. L. Pan et al., 2004L. L. Pan et al., , 2007L. L. Pan et al., , 2018) ) rather than focusing only on the temperature changes.Our analysis here confirms that the tropopause is indeed characterized by striking changes in the relative concentrations of trace gases (Bethan et al., 1996;Fischer et al., 2000;Folkins et al., 1999;Gettelman et al., 2011;L. L. Pan et al., 2004L. L. Pan et al., , 2007L. L. Pan et al., , 2018)).This can be seen visually by the example profiles for water content (Figure 6, Figures S9 and S13 in Supporting Information S1) and ozone content (Figure 7, Figures S10 and S14 in Supporting Information S1).
Specifically, we confirm that the water content of the atmosphere can be quite high (often several % by volume) in the lower troposphere, but steadily decreases in concentration up to the tropopause and above the tropopause it remains very "dry" in terms of water less than 50 ppmv (<0.005%) for most of the tropopause/stratosphere (e.g., see Figure 6, Figures S3 and S7 in Supporting Information S1).Meanwhile, ozone content shows almost the exact opposite pattern, that is, very low concentrations of less than 1 ppmv (<0.0001%) for most of the troposphere, but above the tropopause increasing by roughly one order of magnitude to having concentrations of ∼5-10 ppmv in the peak "ozone layer" in the stratosphere (e.g., see Figure 7, Figures S10 and S14 in Supporting Information S1).
These dramatic changes in water and ozone content associated with the troposphere to stratosphere transitions have already been well-documented by others, for example, (Bethan et al., 1996;Fueglistaler et al., 2009;L. L. Pan et al., 2004L. L. Pan et al., , 2014;;Schäfler et al., 2021;Vömel et al., 2002).However, the high-resolution data of these modern ozonesondes allows us to observe these chemical transitions in quite fine detail.
The most recent instrumentation for measuring water content also seems to be providing consistent measurements at much higher altitudes than was available even in the early 21st century.That is, until recently, the balloon-based water measurements for tropopause studies typically reached a maximum altitude of ∼25-27 km even if the balloons burst several kilometers higher, for example, (L.L. Pan et al., 2014;Vömel et al., 2002).However, nominally at least, the current ozonesondes typically provide water content measurements for the entire ozonesonde flight, for example, see Figures S9 and S13 in Supporting Information S1.
From these higher altitude water content measurements, we were somewhat surprised to note that many of the ozonesondes that reached 30-35 km in altitude suggested an apparent increase in water content beginning toward the end of the balloon flight.In many cases the apparent increase was very modest, but in some cases it involved increases of several hundred ppmv before the balloon burst.In Figures S9 and S13 in Supporting Information S1, this apparent increase is most pronounced for the Greenland ozonesonde, but readers might note that the other two ozonesondes also show slight upticks toward the end of the balloon flights.
We are not yet convinced that these apparent increases in water content are genuine since we find them hard to explain in terms of the current paradigms for explaining the "drying" of the tropopause that assume that the very limited amounts of water present in the tropopause/stratosphere have their origin in vertical transport from the troposphere (Fueglistaler et al., 2009;L. L. Pan et al., 2004L. L. Pan et al., , 2014;;Schäfler et al., 2021;Vömel et al., 2002).Therefore, it is plausible that they may be an artifact of some as of yet unidentified, but apparently systemic, instrumental error.Indeed, the identification of potential instrumental errors with radiosonde and ozonesonde measurements is an ongoing field of research (Stauffer et al., 2020(Stauffer et al., , 2022;;Tarasick et al., 2021;Vömel et al., 2002).
On the other hand, from preliminary exploration of this phenomenon, we are finding that this apparent increase in water content also appears to be frequently associated with an apparent additional change in the slope of molar density versus atmospheric pressure above the mid-stratosphere.At the time of writing, we still have not investigated this apparent correlation in sufficient detail to draw definitive conclusions.This is partially because the apparent phenomena start in the region where the balloons typically begin to burst, and therefore the available data is more limited.However, we encourage further research into this.In the meantime, we mention our preliminary observations because, if correct, this might suggest that the apparent increases in water content are genuine-since the molar density calculations are completely independent of the water content measurements.
Speaking of the molar density calculations, we emphasize the use of molar density as an especially insightful metric.It reveals a remarkable change in the slope of molar density versus pressure at the tropopause that we suggest indicates a major change in atmospheric behavior-see Figures 4a, 4d, and 4g.This change in slope also corresponds to the other changes in atmospheric behavior described by the other tropopause definitions.In other words, all of these very different metrics are describing different aspects of the same phenomenon that is called the troposphere/tropopause transition.
For this reason, we speculate that more research into why this change in the slope of molar density versus pressure occurs could lead to deeper insights into the troposphere/tropopause transitions.Two of us have offered some speculative explanations for this molar density behavior in a series of working papers in 2014 (Connolly & Connolly, 2014a, 2014b, 2014c).
As we mentioned earlier, as well as the dramatic change in slope observed at the tropopause, the calculations often reveal a more subtle deviation from linearity in the lower troposphere.This can be seen from a close inspection of the lower troposphere region of the Alabama and Hawai'i plots in Figure S7 in Supporting Information S1.Although it is less pronounced than the change in slope at the tropopause, it is possible to see from Figure S7d in Supporting Information S1 that up to about 80,000 Pa (800 hPa), the observed molar density (black line) for the Alabama sonde is slightly less than the linear extrapolation (yellow line).For the Hawai'i sonde, this deviation continues up to about 60,000 Pa (600 hPa)-see Figure S7g in Supporting Information S1.When we look at the equivalent plots for water content in Figure S9 in Supporting Information S1, we can see that these deviations from linearity correspond to relatively high water concentrations.That is, the water concentration only falls below ∼8,000 ppmv (∼0.8%) for the Alabama sonde at about 80,000 Pa and 60,000 Pa for the Hawai'i sonde.
At any rate, given the striking cohesiveness of all four of our new tropopause definitions, let us now approximate them as synonymous and consider the variability of the tropopause for each station over the year in terms of the average (mean) of all four estimates (excluding NOAA's estimates) in Figure 9.For each station, we have plotted these averages relative to the annual average for 2016.We note that all stations show some variability from weekto-week above and below the annual average throughout the year.However, we also note that there are sometimes periods where the tropopause remains relatively low or high for several weeks to months.Some of this could be associated with relatively long-lasting prevailing weather systems, but others could be related to seasonality.Further research that considers multi-year patterns could better clarify this.
For this study year, most of the stations show fairly similar trends to each other.However, some stations show unique features that are not apparent at any of the other seven stations, for example, the abrupt drop in the tropopause for Hawai'i after around Day 100 or the spike for Antarctica around Day 258.A detailed investigation into the causes for these localized changes in the location of the tropopause observed at these stations in 2016 is beyond the scope of this study.But we encourage more research into investigating these phenomena and other such events in other years.
In the meantime, some groups of the stations show much closer trends to each other than to the other stations.This is even more apparent from Figure 10, where we have grouped the eight stations into three groups: (a) the tropical stations of American Samoa, Fiji and Hawai'i; (b) the Northern Hemisphere mid-latitude stations of Alabama, Colorado and California; (c) the polar stations of Greenland and Antarctica.
Visually, we have emphasized the similarity of these clusters using "sun" and "ice" icons.We have emphasized the tropical nature of Figure 10a by the three "sun" icons for the entire year; and similarly the polar nature of Figure 10c by the three "ice" icons for the entire year.Meanwhile for the three mid-latitude Northern Hemisphere stations, in Figure 10b, we emphasize the strong seasonality for these locations via the "winter cold" icon at the start and end of the calendar year and the "summer warmth" in the middle of the calendar year.
We find it interesting that the average tropopause location for these stations appears to be closer to that of the polar average (horizontal blue dashed line) in the winter and closer to that of the tropical average (horizontal orange dashed line) during the summer.This suggests that much of the tropopause variability for the mid-latitude stations could be seasonal in nature.The seasonality of tropopause conditions has of course been well-documented by others, for example (T.Birner, 2006;Hoor et al., 2002;Kim & Son, 2012;Seidel et al., 2001) On the other hand, we find the fact that the changes in the tropopause location for both Greenland and Antarctica rise and fall over the year roughly in tandem to be intriguing given that the two stations are in opposite hemispheres.This hemispheric agreement at the poles suggests the possibility that, if there is a seasonality in the tropopause conditions for the polar stations, it might relate to the annually-repeating changes in the Earth-Sun distance due to the Earth's elliptical orbit of the Sun (with a minimum distance in January and a maximum distance in July), rather than summer/winter seasonality.
For these reasons, we suggest that future research should consider the trends over multiple years.However, already this preliminary analysis of one complete year (2016) provides considerable insights into the variability of the tropopause over the course of a year and from the tropics to the poles.

Conclusions
Since the tropopause and stratosphere were first identified in the early 20 th century, the remarkable contrasts between the atmospheric behavior in the tropopause and stratosphere relative to that in the troposphere has been a source of fascination (Hoinka, 1997).More than a century later, the quality and resolution of the balloon data available to us has substantially improved.An example of this is the high quality ozonesonde archive of NOAA ESRL.Therefore, in this study we have used this very high resolution data set to investigate the tropopause.
As well as considering the standard estimates of the tropopause provided by NOAA ESRL with each ozonesonde, we also have developed four alternative tropopause definitions each based on changes in one of the following: (a) molar density; (b) temperature lapse rates; (c) water vapor content; (d) ozone content.We found a remarkable degree of agreement between all five of these independent tropopause definitions, although the NOAA ESRL estimates sometimes identified higher tropopause onsets than the other estimates.This confirms that the troposphere/tropopause transition is a physical and chemical phenomenon that is associated with more than just temperature changes.
Recognition of this relative cohesiveness between these different tropopause definitions offers the community two helpful aspects to consider when investigating the tropopause: 1. Researchers investigating the tropopause in terms of just one of the definitions (or alternative definitions) could probably use their results as a reasonable approximation of the tropopause in terms of the other definitions.This could be useful if the data sets being used only provide the data for one of the definitions.2. Meanwhile, researchers using data sets allowing multiple definitions can use the different estimates from each definition to investigate the interplay between the different physical and chemical aspects of the troposphere/ tropopause transitions.
We stress that three of our four alternative tropopause definitions have some similarity to existing tropopause definitions.However, all four of these definitions were developed specifically for this particular ozonesonde archive and therefore have some differences to similar-sounding tropopause definitions.The previous definitions might be more useful for other data sets but these new definitions have been optimized for this data set.The new temperature-based definition is not affected by the ambiguity of secondary "tropopauses" associated with the standard WMO definition.Moreover, unlike the cold-point tropopause definition that is largely confined to the tropics, it works for all seasons and all eight locations studied (from the poles to the tropics).
Existing water content-based and ozone concentration-based definitions are often hampered in their accuracy by the relatively slow instrumental response time for standard balloon instrumentation (20-30 s for ozone and >60 s at tropopause temperatures for water).However, the definitions used here have substantially reduced this problem by incorporating changes in the volatility of the respective trace gas concentrations as additional indicators of the troposphere/tropopause transition.
For the other new tropopause definition, we use a metric which does not appear to have been considered beforeother than in a series of working papers in 2014 by two of us (Connolly & Connolly, 2014a, 2014b, 2014c).That is, the use of molar density-a concept that should be relatively familiar to chemists, but does not appear to have received much attention in the analysis of weather balloons until now (Connolly et al., 2021).
Our analysis did not consider interannual trends, since our analysis was confined to just one year (2016).Further research could extend our analysis to consider longer trends from this high-resolution ozonesonde data set and/or those of comparable ozonesonde networks such as the Southern Hemisphere ADditional OZonesondes (SHADOZ) network (Thompson et al., 2017;Witte et al., 2017).However, we caution that assessments of longterm trends should consider the potential non-climatic biases introduced by the various changes in instrumentation over the years (Stauffer et al., 2020(Stauffer et al., , 2022;;Sterling et al., 2018;Tarasick et al., 2021;Thompson et al., 2017;Witte et al., 2017).
In the meantime, our analysis of the 2016 NOAA ESRL data already provides considerable insights into the variability of the tropopause that might not have been as obvious from lower resolution balloon data: 1.As we noted from a preliminary analysis of this data, "Contrary to the original concept of the tropopause being a region with very little temperature variability, the high temporal resolution of this data set reveals that this only applies to the averages over large distances.Over shorter distances/time intervals, the temperature lapse rate varies quite wildly in the tropopause/stratosphere-especially when compared to the troposphere" (Dingley et al., 2022).2. Two of the tropopause definitions that we considered are based on changes in the relative concentrations of trace gases, that is, water vapor and ozone.This supports the work of other groups that have been highlighting the striking changes in the concentrations of trace gases associated with the transition between the troposphere, tropopause and stratosphere (Bethan et al., 1996;Fischer et al., 2000;Folkins et al., 1999;Gettelman et al., 2011;L. L. Pan et al., 2004L. L. Pan et al., , 2007L. L. Pan et al., , 2018)).3. Another one of our definitions is based on molar density calculations.Molar density plots reveal a remarkable change in the slope of molar density versus pressure at the tropopause that we suggest indicates a major change in atmospheric behavior.This change in slope also corresponds to the other changes in atmospheric behavior described by the other tropopause definitions.Therefore, we suggest that further research into the reasons for this change in slope could provide a more fundamental understanding of the many physical and chemical phenomena associated with the troposphere/stratosphere transitions.Two of us (MC and RC) have already provided some speculative hypotheses on this (Connolly & Connolly, 2014a, 2014b, 2014c), and we continue research in to these hypotheses.But we also encourage the exploration of other potential explanations.
We are impressed by the cohesiveness of all four new independent definitions in identifying the onset of the tropopause for each ozonesonde.This reinforces the fact that for all regions studied (poles to tropics) and times of year, the transition from troposphere to tropopause is a multifaceted phenomenon.Again, it also suggests that each definition is also a reasonable proxy for the tropopauses identified by the other three.
That said, we recognize that these four new definitions are based on very high resolution ozonesondes and might not be as practical for analyzing lower resolution balloon sondes, which includes most of the older archived radiosonde data.With that in mind, it is encouraging that the original WMO (1957) tropopause definition based on temperature lapse rates yields similar estimates to the four new definitions, albeit sometimes it estimates the tropopause height higher than the other estimates.
Earth and Space Science 10.1029/2024EA003584

Figure 1 .
Figure 1.Map of the ozonesonde station locations.

Figure 2 .
Figure 2. Data provided by NOAA ESRL's ozonesonde data set from 1967 to present.Two stations in the data set (Galapagos and Rhode Island) were dropped from our analysis since they did not have enough data for the study year (2016).(a) The number of measurements taken by each ozonesonde has steadily increased over the decades.This is because the average (b) time and (c) distance between measurements has decreased accordingly.The year in which the WMO defined the "tropopause," that is, 1957, is plotted for reference(WMO, 1957).Although (d) the maximum altitude reached by each ozonesonde has remained relatively high, (e) the maximum altitude at which water content (including humidity) measurements were recorded has become more consistently high.Less cluttered versions (separating the data for each of the 10 stations) of the above plots are provided in Figures S1-S5 in Supporting Information S1.

Figure 3 .
Figure 3.The key measurements versus atmospheric pressure for three representative ozonesondes-(a)-(e) launched from Summit Station, Greenland on 12 March 2016; (f)-(j) launched from Huntsville, Alabama, USA on 1 October 2016; (k)-(o) launched from Hilo, Hawai'i, USA on 28 September 2016.(a, f, and k) Time elapsed since the sonde was launched; (b, g, and l) altitude; (c, h, and m) temperature; (d, i, and n) water content; (e, j, and o) ozone content.NOAA's estimates of the tropopauses (as provided with each ozonesonde record) are denoted by horizontal dashed gray lines.The ground level is denoted by green boxes in each panel.

Figure 4 .
Figure 4. Metrics used for calculating the tropopause from molar densities for the same ozonesondes as Figure 3. (a)-(c) Summit Station, Greenland, 12 March 2016; (d)-(f) Huntsville, Alabama, USA, 1 October 2016; (g)-(i) Hilo, Hawai'i, USA, 28 September 2016.(a, d, and g) The observed molar densities are plotted in black along with a straight line slope in yellow that is fit over the relevant regions discussed in the text; (b, e, and h) molar density lapse rate in mol m 4 ;(c, f, and i) molar density lapse rates with respect to pressure in mol m 3 Pa 1 .All lapse rates are calculated using a 31-point centered box car average.The different tropopause estimates from each approach in Figures3-7are indicated on the corresponding panels by horizontal dashed lines with distinct colors matching those in Figure8.

Figure 5 .
Figure 5. Metrics used for calculating the tropopause from temperatures for the same ozonesondes as Figure 3. (a)-(c) Summit Station, Greenland, 12 March 2016; (d)-(f) Huntsville, Alabama, USA, 1 October 2016; (g)-(i) Hilo, Hawai'i, USA, 28 September 2016.(a, d, and g) Temperature; (b, e, and h) temperature lapse rates in K m 1 ; (c, f, and i) temperature lapse rates with respect to pressure in K Pa 1 .All lapse rates are calculated using a 31-point centered box car average.The different tropopause estimates from each approach in Figures 3-7 are indicated on the corresponding panels by horizontal dashed lines with distinct colors matching those in Figure 8.

Figure 6 .
Figure 6.Metrics used for calculating the tropopause from water content for the same ozonesondes as Figure 3. (a)-(c) Summit Station, Greenland, 12 March 2016; (d)-(f) Huntsville, Alabama, USA, 1 October 2016; (g)-(i) Hilo, Hawai'i, USA, 28 September 2016.(a, d, and g) Water content; (b, e, and h) water content lapse rates in ppmv m 1 ;(c, f, and i) water content lapse rates with respect to pressure in ppmv Pa 1 .Note that the x-axes are different for each station given that the average atmospheric water content is quite different for each station.All lapse rates are calculated using a 31-point centered box car average.The different tropopause estimates from each approach in Figures3-7are indicated on the corresponding panels by horizontal dashed lines with distinct colors matching those in Figure8.

Figure 7 .
Figure 7. Metrics used for calculating the tropopause from ozone content for the same ozonesondes as Figure 3. (a)-(c) Summit Station, Greenland, 12 March 2016; (d)-(f) Huntsville, Alabama, USA, 1 October 2016; (g)-(i) Hilo, Hawai'i, USA, 28 September 2016.(a, d, and g) Ozone content; (b, e, and h) ozone content lapse rates in ppmv m 1 ; (c, f, and i) ozone content lapse rates with respect to pressure in ppmv Pa 1 .All lapse rates are calculated using a 31-point centered box car average.The different tropopause estimates from each approach in Figures 3-7 are indicated on the corresponding panels by horizontal dashed lines with distinct colors matching those in Figure 8.

For
our ozone content-based tropopause estimates, we calculate the rate of change with altitude, d(O 3 )/dh and with pressure, d(O 3 )/dP.Examples of these profiles are shown in Figure 7.We define the ozone-based tropopause as the pressure above the boundary layer at which: 1.The ozone content, [O 3 ], is greater than 0.1 ppmv.2. d(O 3 )/dh increases substantially and d(O 3 )/dP decreases substantially.3. d(O 3 )/dh and d(O 3 )/dP both begin to oscillate-see Figure 4d for an example for d(O 3 )/dh.

Figure 8 .
Figure 8. Changes in the location of the tropopause for the eight stations for the entire year of 2016, as calculated using each of the metrics described in the text: (a) Greenland; (b) California, USA; (c) Colorado, USA; (d) Alabama, USA; (e) Hawai'i, USA; (f) American Samoa; (g) Fiji; (h) Antarctica.The colors used for each estimate are the same ones used for the equivalent horizontal lines in Figures 3-7.

Figure 9 .
Figure 9. Plots of the pressures of the average tropopause estimates (mean of the four estimates described in the manuscript, excluding NOAA's estimates) for each station in 2016, relative to their average value for the year, that is, the horizontal black line in each panel.Values above or below the average for the year are indicated with red or blue shading respectively.(a) Greenland; (b) California, USA; (c) Colorado, USA; (d) Alabama, USA; I) Hawai'i,USA; (f) American Samoa; (g) Fiji; (h) Antarctica.

Figure 10 .
Figure 10.Comparison of the tropopause changes over the year of 2016 for all eight stations sorted into: (a) the tropical stations; (b) the mid-latitude stations; (c) the polar stations.The average tropopause pressure for each subset is indicated by colored dashed horizontal lines.

Table 2 A
Table of the Correlation Coefficients (r, Where 0 = Uncorrelated; 1 = Exactly Correlated; and 1 = Exactly Anti-Correlated) Between the Tropopause Estimates From Each Approach and the Other Estimates Based on Over All of the Ozonesondes for Each Station for 2016 The last column of the table corresponds to the averages for all eight stations.These results were also presented by us in Dingley et al. (2022) but have been replicated here for convenience.
CONNOLLY ET AL.