ERA-Interim output is available from 1979 to the present on an approximately 80 km horizontal grid and with 750–1250 m vertical resolution in the UTLS , where the UTLS is defined here as the 8–18 km altitude layer. JRA-55 is available from 1958 to the present on a ∼60 km horizontal grid . Similar to ERA-Interim, JRA-55 has 750–1250 m vertical grid spacing in the UTLS. MERRA-2 is available from 1979 to the present on a 0.5∘×0.625∘ longitude–latitude grid and at ∼1100 m vertical resolution throughout the UTLS . CFSR is available from 1979 to 2010 on a 0.5∘×0.5∘ longitude–latitude grid and at 700–900 m vertical resolution in the UTLS. CFSR output is extended to the year 2015 in this study using analyses from the Climate Forecast System version 2 (CFSv2) model. For a more detailed discussion of these reanalyses and their differences (including profiles of vertical resolution), see . All tropopause analyses are performed using daily 00:00 UTC fields from each reanalysis (though not shown, analyses using alternative synoptic times for shorter time periods are consistent). Geopotential height was computed for each reanalysis model-level output using the moisture-included hypsometric equation. Meteorological parameters are interpolated linearly to a regular 1∘×1∘ longitude–latitude grid in the horizontal for analysis to enable 1-to-1 comparison (this choice has a negligible impact on the reported results). Temperature profiles are linearly interpolated to a regular 200 m vertical resolution prior to tropopause identification.

Radiosonde data used in this study were obtained from the Integrated Global Radiosonde Archive (IGRA) Version 2 . The IGRA database provides historical radiosondes from locations around the world that have been comprehensively quality controlled and corrected for gross errors. These data are the best long-term historical record available for studies of the vertical structure of the UTLS (global satellite-based observations, such as radio occultation, are available for only the last ∼18 years). IGRA radiosonde observations are mainly available twice daily at 00:00 and 12:00 UTC. Given that a small number of stations launch radiosondes at nonstandard times, we included launches that occurred between 21:00 and 03:00 UTC in the 00:00 UTC analysis and those between 09:00 and 15:00 UTC in the 12:00 UTC analysis. The IGRA radiosondes are provided at mandatory (conventional pressure levels) and significant levels, which preserves any substantial lapse-rate changes in the original data (observations are typically taken at 6 s intervals, resulting in ≤50 m vertical resolution), but can result in coarse vertical resolution in the UTLS (>1 km). Such coarse resolution of the profile can prevent successful application of the lapse-rate tropopause by limiting the number of observations used to satisfy the second criterion of the WMO definition and the criterion for identifying multiple tropopauses (see Sect.  below), as is true for the reanalysis output. Thus, in order to enable thorough evaluation of the WMO criteria and reliable tropopause identification, radiosonde data are also linearly interpolated to a 200 m regular vertical grid prior to tropopause identification. Only soundings that have valid observations between 5 and 22 km in altitude are used to identify the tropopause. The original high-vertical-resolution (∼5 m) profiles from select National Weather Service sites in the United States were also retrieved for illustration purposes only (see Fig. ).

As outlined in the Introduction, we employ the WMO lapse-rate tropopause definition for analysis in this study. The WMO definition defines the first tropopause in a profile as “the lowest level at which the lapse rate falls to 2 ∘C km-1 or less, provided the average lapse rate between this level and all higher levels within 2 km also does not exceed 2 ∘C km-1” . The WMO definition allows for a secondary tropopause “if above the first tropopause the average lapse rate between any level and all higher levels within 1 km exceeds 3 ∘C km-1, then a second tropopause is defined by the same criterion.” To avoid boundary layer inversions and false tropopause identification, as well as secondary tropopauses above the altitude of that typically observed for the primary tropopause in the tropics, the algorithm is applied only to altitudes ranging from 5 to 22 km. Lapse rates are calculated for each profile using a forward (upward) difference scheme in the form Γ(zi)=-∂T/∂z≈-(Ti+1-Ti)/(zi+1-zi), where Γ is the lapse rate in degrees Celsius per kilometer, T is temperature in degrees Celsius, and z is altitude in kilometers. Tropopause altitudes from reanalysis are geopotential altitudes.

Example WMO lapse-rate tropopause altitudes calculated for two randomly selected radiosonde profiles launched at the Corpus Christi, Texas, National Weather Service office (97.5∘ W longitude, 27.78∘ N latitude) in the United States are shown in Fig. . Both of these profiles have two WMO tropopauses. Here, we show both the full-resolution temperature profile obtained by each radiosonde and the reduced-resolution profile from the IGRA archive to demonstrate common differences in the level of detail between native data and those reported at mandatory and significant levels. As demonstrated in both profiles, the IGRA data preserve all significant lapse-rate transitions and result in nearly equivalent tropopause altitude definitions to those computed using the full-resolution profile (differences are ≤100 m). Consistent results are found when selecting profiles randomly from other stations and time periods (not shown). Thus, we are confident that mandatory and significant levels included in the IGRA data are suitable for tropopause analyses following the methods employed here. Coincident temperature profiles and tropopause altitudes from each reanalysis model are superimposed in Fig.  and show much less detail than the higher-resolution observations and a general inability to capture multiple tropopause altitudes. These example profiles have shallow inversion layers above the primary lapse-rate tropopause altitude, which are often not well captured in the coarse-resolution reanalysis model profiles. As a result, the secondary tropopause is often erroneously classified as the primary tropopause altitude in model output e.g., see also Figs.  4 and 6 and discussion from. Extensive comparisons of tropopause altitudes and multiple tropopause frequencies between the radiosondes and reanalyses are provided in Sect. .

Trends over the 35-year analysis period (1981–2015) of this study are calculated using monthly mean primary tropopause altitudes and the monthly fraction of profiles with double tropopauses. For radiosondes, we require a station to have at least 20 days of suitable profiles (all from either 00:00 or 12:00 UTC and including mandatory and significant levels up to an altitude of 22 km or higher) to compute a monthly mean tropopause altitude or double tropopause fraction. Trends are only calculated for radiosonde stations that have sufficient observations for at least half of the total number of months in the 35-year period and a roughly even distribution of data points throughout the period (data gaps <5 years and no missing data near the beginning and end of the time series) for adequate trend analysis. Monthly tropopause time series from both radiosondes and reanalyses are then deseasonalized using a high-pass filter that removes variability at timescales less than or equal to 1 year. Linear regression is used on the filtered time series to measure trends over the 35-year period. Trends are deemed significant if they exceed the 3σ uncertainty of the measured slope, which is analogous to statistical significance at the 99 % confidence level for a Gaussian distribution.

For reanalyses, trends are also calculated in an alternative coordinate system. A sharp discontinuity in the primary lapse-rate tropopause altitude is found near the subtropical jet and known as the “tropopause break” e.g.,. Tropopause altitudes are uniformly high (≥15 km) in the tropics and uniformly low (mostly 8–12 km altitude) in the extratropics. In fact, as shown by , , and others, global and hemispheric frequency distributions of tropopause altitude are bimodal. As a result, the tropopause break is easily defined in model output as globe circling contours of a threshold tropopause altitude or pressure coinciding with the frequency minimum between the tropical and extratropical modes typically ∼14 km or ∼150 hPa; e.g., see. Because the location (latitude) of the subtropical jets and tropopause breaks varies considerably in space and time, trend analyses in the vicinity of the tropopause breaks can be adversely impacted by their variability and potential long-term changes in latitude. Thus, to remove this variability and evaluate trends within the tropical and extratropical reservoirs separately, we also analyze trends in the reanalyses using a latitude coordinate relative to the tropopause break. Tropopause break latitudes are identified at each 00:00 UTC analysis using contours of the tropopause altitude that coincides with the frequency minimum between tropical and extratropical modes in each hemisphere. Monthly means are then calculated by averaging the instantaneous tropopause fields on the relative latitude grid in each hemisphere. For plotting, analyses relative to the tropopause break are mapped using the long-term mean break latitudes and any data extending beyond the Equator and pole are trimmed from each hemisphere.

Note that time series used for trend analysis were not adjusted for potential discontinuities and/or biases owing to changes in instrumentation or other factors e.g., see. Thus, some elements of the trend analyses (especially for the radiosonde observations) may be impacted by these artifacts. However, a substantial number of time series with large, significant trends (see Sect. ) were manually evaluated and no discontinuities were found (not shown). Thus, we expect such factors to have a minimal impact on the results outlined below.

To evaluate the fidelity of tropopause altitudes in the reanalyses, we first compare tropopause altitudes from the gridded reanalysis output with the radiosonde data at 00:00 UTC only. Instantaneous tropopause altitudes computed on the 1∘×1∘ longitude–latitude grids are interpolated linearly in space to the locations of the radiosondes for comparison. Results of these comparisons are shown for individual months during each season: January, April, July, and October between 1981 and 2015. In total, 317 radiosonde stations and approximately 9.9×104 profiles are used for this validation, with their geographic locations shown as circles and squares in Fig. . Biases and errors (rms differences) in primary reanalysis tropopause altitudes from this comparison are listed in Table . More than half of the primary tropopause altitudes in MERRA-2 are found to have a positive bias, whereas the majority of biases in the remaining reanalyses (ERA-Interim, JRA-55, and CFSR) are negative. Errors in the tropopause altitudes range from 950 to 1200 m, which is comparable to the vertical grid spacing of the reanalyses.

All reanalyses produce too few double tropopauses compared to the radiosonde observations. Double tropopause frequency in the reanalyses is significantly underestimated, with 67 %–85 % of the sample having a negative bias. Biases are largest in JRA-55, with over 22 percentage points fewer double tropopauses than observed, and biases are smallest in CFSR, which has 13 percentage points fewer double tropopauses than observed. Errors in double tropopause frequency show similar differences among the reanalyses. The lower double tropopause frequency in reanalyses is likely due to the coarse vertical resolution of the models. As outlined in Sect.  and illustrated in Fig. , accurate tropopause identification requires vertical resolution of ≤1 km to detect shallow low- and high-stability layers that are often responsible for the occurrence of multiple tropopauses. CFSR, which has the lowest bias and error, also has the finest vertical grid resolution in the UTLS, while MERRA-2 typically has finer resolution than ERA-Interim and JRA-55 at the altitude of the secondary tropopause. The differences in bias and rms error between models with approximately equivalent vertical grids, such as ERA-Interim and JRA-55, suggest that the representation of atmospheric processes and/or the data assimilation system used could also be responsible for some of the underrepresentation of double tropopause events.

To better evaluate the role of model vertical resolution as a source for the observed tropopause differences, we repeated the validation with degraded radiosonde observations. In particular, each IGRA radiosonde profile was linearly interpolated to the fixed model-level grid of each reanalysis in order to limit the detail of the observed temperature profile to that available from each model. These degraded radiosonde profiles were then used to calculate unique observation-based tropopause altitudes to compare with each reanalysis and determine the resulting bias and error, which is expected to be reduced (especially for double tropopauses). Table  shows these evaluations using the degraded radiosonde profiles and confirms that the biases and errors in both primary tropopause altitude and double tropopause frequency largely decrease. However, some bias and error remain (and for MERRA-2 tropopause altitudes, increases), which suggests that alternative sources of error (e.g., data assimilation, model physics and dynamics) are significant.

In addition to overall performance of the reanalyses, there are seasonal and regional variations in the tropopause biases and errors. In order to better understand the source of these variations, we group the comparisons by latitude to reduce potential sources of uncertainty from the nonuniform global distribution of the radiosonde locations. Figures  and  show the bias and rms error for primary tropopause altitudes and double tropopause frequency, respectively, within five latitude bands: two in the extratropics of each hemisphere (45–90∘ N and 45–90∘ S), two in the subtropics of each hemisphere (20–45∘ N and 20–45∘ S), and one in the deep tropics (20∘ S–20∘ N). The Southern Hemisphere subtropics and extratropics tend to have larger errors than their counterparts in the Northern Hemisphere, likely due to (in part) fewer data sources for assimilation and fewer profiles used for analysis. Regionally, the largest primary tropopause errors are found within the subtropics of each hemisphere – commonly associated with the location of the subtropical jet and tropopause break. The complicated stability structure within the subtropics is known to lead to large errors in tropopause altitudes within models and is primarily the result of inadequate representation of multiple tropopauses and the precise location of the tropopause break . The largest differences within the subtropics occur during the winter season of each hemisphere, which is consistent with the time period during which the subtropical jet reaches its maximum intensity and double tropopauses are more frequent e.g.,. The tropopause break is also sharpest in the vicinity of the subtropical jets at this time due to thermal wind balance (i.e., the latitudinal temperature gradients in the vicinity of the jet are largest). Biases and errors in double tropopause frequency are largest in the subtropics and extratropics of each hemisphere and small within the tropics, where multiple tropopauses are generally infrequent. Biases and errors are also largest in the winter of each hemisphere and smallest during the summer.

The long-term trend in the tropopause altitude is considered to be an indicator of climate change. Here, we evaluate trends in Eulerian monthly mean primary tropopause altitudes using both radiosondes and reanalyses (Fig. ). Statistically significant trends in tropopause altitude are found in the radiosonde observations for many locations across the globe. Most trends point to an increase in tropopause altitude over time, with the largest increases (100–200 m per decade) found over western China, the contiguous United States, eastern Europe, and Indonesia. A small region of significant decreasing primary tropopause altitudes is found over Siberia and the subtropical Pacific.

Significant tropopause altitude trends in the reanalyses are in broad agreement with those identified from the radiosonde observations. In particular, regions with dense radiosonde coverage and large, positive trends are well represented in each reanalysis. The small, negative trend identified over Siberia is also reproduced in each reanalysis and agrees with previous studies , but this behavior may be an artifact of changes in instrumentation and quality control of the radiosonde data over time . Trends in the reanalyses are generally larger and more variable outside of the regions with dense radiosonde coverage. Some notable features are the upward/downward tropopause altitude trend dipoles found over the eastern subtropical Pacific in ERA-Interim, JRA-55, and MERRA-2. This dipole is not found in CFSR and the magnitudes of the trends and spatial extent of the dipole vary considerably in the remaining reanalyses. Moreover, the dipole is consistent with significant narrowing of the tropics over the eastern Pacific that has been identified in the reanalyses via subtropical jet and tropopause break analysis .

Another notable difference among the reanalyses is the depiction of tropopause trends across the tropics, where MERRA-2 and CFSR show considerably larger upward trends than ERA-Interim and JRA-55. ERA-Interim also depicts a downward trend over the central Pacific, which is not observed in the remaining reanalyses. Trends in JRA-55 and MERRA-2 appear to be more consistent with the limited number of radiosondes available in the tropics, especially over Indonesia, the central Pacific, and northern Australia. Finally, the tropopause altitude trends over Antarctica are found to be inconsistent among the reanalyses. Namely, a rising trend is found over Antarctica in ERA-Interim and MERRA-2, while a less extensive decreasing trend is found in JRA-55 and CFSR.

As discussed briefly in the previous section, recent studies have identified significant regional changes in the width of the tropics that introduce some uncertainty to the precise nature of tropopause changes when diagnosing trends in an Eulerian framework. Therefore, in order to mitigate the effects of a meandering tropopause break and focus on tropopause changes in the tropical and extratropical reservoirs alone, we employ a coordinate relative to the tropopause break here. Figure  shows the geographic distribution of primary tropopause altitude trends in a latitude coordinate relative to the tropopause break for each reanalysis from 1981 to 2015. Considerable differences are found in the diagnosed trends here compared to those using the Eulerian monthly mean fields. In particular, significant trends are larger in magnitude in the coordinate relative to the tropopause break and are more consistent amongst the reanalyses, especially over the eastern subtropical Pacific. ERA-Interim, JRA-55, and MERRA-2 are broadly consistent with one another, with large upward trends in tropopause altitude in the extratropics over the Pacific and similar patterns and signs of significant trends elsewhere.

MERRA-2 shows substantially different trends throughout the tropics relative to ERA-Interim and JRA-55, with both larger upward magnitudes and unique patterns over the western Pacific and Indian oceans. CFSR shows some consistency with MERRA-2 in the tropics in terms of the trend magnitude, but is inconsistent in pattern (especially over the Americas). In ERA-Interim, JRA-55, and MERRA-2, trends in the tropics are largest immediately equatorward of the tropopause break latitude in each hemisphere, while CFSR shows the greatest trends in the deep tropics. However, the Eulerian mean trends in Fig.  show more consistent behavior amongst the reanalyses in the depiction of these poleward maxima in altitude trends within the tropics, which is in agreement with previous analyses e.g.,. Outside of the tropics, CFSR is in broad disagreement with the remaining reanalyses and suggests largely decreasing trends in tropopause altitude.

As outlined in Sect. , double tropopause frequencies often have large bias and error in the reanalyses, which is mainly attributed to their coarse vertical grid resolution. To better understand the nature of these errors, maps of annual-mean double tropopause frequency are presented for the radiosondes and reanalyses in Fig. . These maps are consistent with similar analyses of radiosondes, satellite observations, and reanalyses in prior studies e.g.,, and show that there are belts of high double tropopause frequency in the northern subtropics and midlatitudes of each hemisphere, largely near and poleward of the subtropical jets and tropopause breaks. The patterns and spatial extent of these belts are consistent between the radiosonde observations and reanalyses, but there are considerable differences in the frequency values. Radiosondes show that these high-frequency belts are characterized by values ≥40 %, while the reanalyses are at least 10 %–20 % lower. The magnitudes of the differences between the radiosonde and reanalysis frequencies within the high-frequency belts are consistent with those found in the overall bias and error evaluation (Fig. ). Outside of the high-frequency belts, there is a unique feature found within the tropics in CFSR. Namely, a narrow band of double tropopause frequency between 10 % and 30 % is seen along the Equator stretching from central Africa to eastern Indonesia. This feature does not exist in the remaining analyses and is poorly sampled by the radiosonde network. However, the small number of stations available in western Indonesia do show consistent double tropopause frequencies. These double tropopauses may be driven (in part) by shallow, lateral transport of extratropical lower stratospheric air into the tropical upper troposphere on the eastern edge of the Asian monsoon anticyclone e.g.,, but the lack of continuity of this feature between the midlatitude high-frequency belt and the enhanced frequency belt along the Equator suggests that the dynamics of the monsoon anticyclone may also be important to their formation.

Eulerian mean trend maps for double tropopause frequency during 1981–2015 are shown for the radiosondes and reanalyses in Fig. . Trends in the double tropopause frequency are found to be statistically significant at almost all of the radiosonde locations and show substantial increases in frequency (≥2 % per decade) nearly everywhere. The largest increasing trends (≥3 % per decade) for double tropopause frequency are found in the midlatitudes in each hemisphere and poleward of the high-frequency belts in the long-term climatology, with some small (mostly <1 % per decade) decreasing trends over Siberia, southern China, and the Caribbean (locations with climatologically low double tropopause frequency). The midlatitude increasing trends are comparable to those diagnosed in between 1970 and 2006 for the 30–60∘ N and 30–60∘ S latitude belts, which were 3.3 % and 6.6 % per decade, respectively. Taken together with the climatological double tropopause distribution, these trends imply that the area of frequent double tropopause environments is increasing in each hemisphere, mostly indicating a northward expansion of the high-frequency belts.

Areas of significant increasing trends in double tropopause frequency are largely consistent between the radiosondes and reanalyses, with CFSR being the only exception. In particular, ERA-Interim, JRA-55, and MERRA-2 all show large increases in double tropopause frequency along and mostly north of the tropopause break. CFSR shows mostly decreasing trends in double tropopause frequency across the globe and is broadly inconsistent with the radiosonde observations. Where areas of significant trends agree in pattern and sign between the reanalyses and radiosondes, the magnitudes are largely consistent near the tropopause break and inconsistent poleward of the break. ERA-Interim, JRA-55, and MERRA-2 do not reproduce the poleward extent of the significant increasing trends in observations well, especially over North America. A unique increasing trend is found along the Equator in MERRA-2, which is consistent with the location of the narrow band of moderate double tropopause frequency found in the CFSR climatology. While none of the remaining reanalyses show this feature, it is consistent with trends observed in the small number of radiosonde stations over western Indonesia and the western Pacific. Finally, the double tropopause frequency trends over Antarctica are decreasing in all reanalyses, but the area and magnitude of the trend vary considerably. The most consistent element of this feature is found over western Antarctica, but there are no radiosonde observations in this region to validate such a trend and the climatological frequencies in this region are small.

Maps of annual-mean double tropopause frequency and frequency trends in coordinates relative to the tropopause break from the reanalyses are shown in Figs.  and , respectively. In general, there is less variation in the patterns of both high-frequency double tropopause regions and increasing double tropopause frequency trends between the Eulerian and analyses relative to the tropopause break. Annual-mean frequencies are higher in coordinates relative to the tropopause break and maximize poleward of the mean tropopause break latitude throughout each hemisphere. Significant increasing double tropopause frequency trends are also found primarily poleward of the tropopause breaks in each hemisphere, but are otherwise mostly consistent with the Eulerian analysis. Two notable exceptions are the areas of significant increasing trends over the northern and southern east Pacific and east Atlantic in ERA-Interim, JRA-55, and MERRA-2, where the largest increasing trends were found to be mostly equatorward of the mean tropopause break latitude in the Eulerian analysis. In coordinates relative to the tropopause break, the areas of greatest increasing trends are generally centered on or poleward of the tropopause break in the Northern Hemisphere and poleward of the tropopause break in the Southern Hemisphere.