Global trends in atmospheric layer thickness since 1940 and relationships with tropical and extratropical climate forcing

Global warming necessitates continual insights into changing atmospheric temperatures to enhance climate change monitoring and prediction. The thickness of an atmospheric layer serves as an effective proxy for the average temperature of that layer, playing a pivotal role in weather forecasting, understanding atmospheric dynamics, and detecting shifts in extreme weather conditions. This study investigates the global trends in thickness of the layer between 1000 hPa and 500 hPa, from 1940 to the present and evaluates the impact of tropical and extra-tropical climate modes on these trends. Our findings reveal a consistent, statistically significant positive trend in atmospheric layer thickness. However, the magnitude of this trend varies both regionally and seasonally. The most substantial absolute changes are observed in the high latitudes during their respective winter seasons; however, when considering global changes relative to each location’s unique historical variability, the most pronounced increase occurs in the tropics, specifically over central Africa, with a standard deviation increase of up to 0.03 σ yr−1. Based on the relative changes, the thickness over the Southern Hemisphere’s high-latitude landmasses is increasing at a faster pace during its winter compared to the Northern Hemisphere during its winter. Furthermore, our analysis of the impact of dominant tropical and extra-tropical climate modes revealed a strong correlation (R ∼ 0.9) between sea surface temperature changes in the Pacific warm pool region and the global average thickness. This relationship accounts for about 76% to 78% variance of the inter-annual variability in thickness. Consequently, we identify the increase in sea surface temperature in the Indo-Pacific warm pool as a significant controller of the rate and magnitude of atmospheric layer thickness changes globally. This underscores the crucial role of oceanic-atmospheric interactions in driving global climate variations and extremes.


Introduction
The thickness of an atmospheric layer represents the vertical distance between two pressure levels, and is mostly a function of how warm or cold a layer of the atmosphere is, though it is also impacted by the varying moisture content of that layer.Therefore, atmospheric layer thickness provides key insights into temperature variations, moisture distribution, and indirectly, into circulation patterns in the atmosphere [1].It is a crucial parameter in the study of global climate dynamics [2] as well as climate forecasts such as rain/snow predictions [1].As the Earth's climate continues to undergo rapid changes, improving the predictability of atmospheric layer thickness as well as understanding its spatial and temporal trends becomes essential for anticipating future impacts on global climate and society at large.
Variations in atmospheric layer thickness are linked to an interplay of several factors that can influence temperature and moisture, such as atmospheric circulation, radiative processes, topography, land use changes, and anthropogenic climate change [3,4].Large-scale climate phenomena such as the El Niño-Southern Oscillation (ENSO), and the annular modes might also impact the atmospheric layer thickness by influencing global temperatures and moisture circulation [5].During El Niño events, anomalously warm sea surface temperatures (SST) lead to increased convection and rising air in the eastern tropical Pacific [6,7].This warming process causes the troposphere to expand vertically, thus increasing atmospheric layer thickness.
In terms of atmospheric circulation, layer thickness can be a good indicator of warm and cold air advection and the positioning of surface fronts.The thickness layer is more variable seasonally in the northern hemisphere (NH) than in the southern hemisphere (SH), due to the relative differences in the spatial distribution of landmasses in each hemisphere (figure S1).The spatiotemporal variability of the atmospheric thickness layer necessitates a detailed analysis that advances the understanding of the variability and long-term changes of the atmospheric layer height as well as the factors modulating the changes.
Since atmospheric layer thickness is directly related to the temperature and the moisture content of the atmosphere [1], shifts in thickness would signal corresponding shifts in regional temperature and precipitation patterns.Such changes would likely be concurrent with changes to the frequency and intensity of extreme weather events, in turn affecting vital aspects of human societies, such as water resources, agriculture, and infrastructure.Given the potential link between changes in atmospheric layer thickness and impacts on underlying natural systems and human societies, it is prudent to examine global thickness trends and underlying physical mechanisms, which are lacking in the existing literature.
This study aims to address this knowledge gap by analyzing the global trends in atmospheric layer thickness since 1940 across different seasons.We also examine the role of large-scale modes of climate variability in the tropics and high latitudes in modulating the spatio-temporal variability of thickness through time.By advancing our knowledge of atmospheric layer thickness trends, variability, and their drivers, this study will contribute to the broader understanding of global climate change.This information can be instrumental in informing climate adaptation strategies, risk management practices, and policy development to mitigate the effects of a changing climate on human populations and ecosystems.

Data and methods
Geopotential data at the 500 hPa and 1000 hPa atmospheric pressure levels were obtained from the ERA5 reanalysis dataset [8], spanning from 1940 to 2022 at a monthly temporal resolution.The ERA5 dataset provides global coverage at a high spatial resolution of 0.25 • in both longitude and latitude.In order to prevent the disproportionate representation of higher latitudes in our analysis, particularly when calculating global spatial averages, we resampled the ERA5 grid to conform to the equal area scalable Earth grid, where the distance between consecutive grid points is 25 km along both the x-axis (longitude) and y-axis (latitude).This grid system is a global projection that preserves surface area, ensuring that each cell on the grid represents an equivalent surface area.By transitioning to the equal area scalable Earth grid, before spatial averaging, we ensure a consistent spatial resolution that avoids oversampling at higher latitudes.The atmospheric layer thickness between the 500 hPa and 1000 hPa pressure levels was calculated as the difference in geopotential at these levels, normalized by the acceleration due to gravity (9.81 m s −2 ).We specifically chose the 500 and 1000 hPa pressure levels to represent the thickness of a large portion of the lower and middle troposphere.This range is often used in atmospheric studies because it covers the altitude range where most weather phenomena occur and where the bulk of the atmospheric mass is found.Moreover, the 500 hPa-1000 hPa thickness is a commonly-used proxy for the temperature and moisture content of the lower atmosphere (and impacting the surface) at synoptic and larger scales.
We investigate climate modes of variability that have a hemispherical/global scale impact on the temporal changes in the global thickness.For that, we examined the impact of the annular modes which are hemispherical modes (especially for the high latitudes); for the tropical modes, we examine ENSO's role, as well as the warmest ocean region in the world-the Indo-Pacific warm pool (figure S2).The high temperatures of the Indo-Pacific warm pool have important implications for the global climate, as this region is a significant source of heat and moisture to the atmosphere, driving a large portion of global atmospheric circulation and influencing weather patterns far beyond the region itself [9][10][11].We have characterized the SST in the Indo-Pacific warm pool with the Pacific warm pool index (PWPR), defined as area-averaged SST over 60 • E-170 • E, 15 • S-15 • N. Classical or 'canonical' El Niño events, characterized by significant warming anomalies in the eastern equatorial Pacific Ocean, are typically measured using the Niño 3 index, which averages SST anomalies within the geographic boundaries of 150 • -90 • W and 5 • S-5 • N, and the Niño 3.4 index, which does the same for the region within 170 • -120 • W and 5 • S-5 • N.Here we use Niño 3.4 index to characterize the classical ENSO mode.The Arctic oscillation (AO) and the Southern annular mode (SAM) were used to characterize the NH and SH modes, respectively.The Niño 3.4, AO, SAM, and PWPR indices were obtained from https://psl.noaa.gov/data/climateindices/list/.
Prior to calculating the seasonal trends during January to March (JFM) and June to August (JJA), we first calculated the JFM and JJA mean thickness for each year, respectively.Our selection of JFM rather than the conventional DJF allows for more consistent annual trend analysis.This is because using JFM places the focus on the changes occurring at the beginning of each calendar year, thereby ensuring a smoother continuity and consistency in our annual trend analysis.We calculated trends for two sets of seasonal data.First is the JFM and JJA mean thickness for each year from 1940 to 2022, and second is the seasonal z-score standardized thickness for the same analysis period.For the latter, at each grid box, we calculated the z-score by subtracting the mean of all these averages from each individual seasonal average value and dividing by the standard deviation of all the seasonal averages.This results in a seasonal z-score for each season, providing a standardized measure of how each seasonal average thickness value deviates from the long-term average of that season.
To ensure the consistency of the trends, we calculated them at each grid box using both linear regression and the moving average method.However, since the results with each method were fairly similar (suggesting the trends were mostly linear), for brevity and clarity, we limit our discussion below to the linear regression results.We tested the trends for statistical significance at a 95% confidence level using the modified Mann-Kendall test [12].Since we are examining trends across different geographic locations with different climate conditions, standardizing the (seasonal) mean atmospheric layer thickness is crucial.This is because the absolute changes in atmospheric thickness may not be as large in some regions, but the changes are substantial when compared to the normal range of variability for the regions.This could potentially make these areas more susceptible to extreme weather events, as these changes represent a departure from the conditions to which local ecosystems and human communities are adapted.
Regression and (partial) correlation analysis were used to examine the association between the climate modes of variability and the thickness layer.The correlation coefficient was tested for statistical significance at a 95% confidence level using a t-test, while the regression coefficients were tested using the Student's t-test.We conducted partial correlations to control for the influences of individual climate modes when assessing their relationships with the long-term thickness trends.To achieve this, we first computed the residuals from the regression of time in a specific climate mode, and the residuals from the regression of thickness in the same climate mode.Subsequently, we calculated the correlation between these two sets of residuals.This provides us with a correlation between thickness and time that has been adjusted to remove the linear effects of a given climate mode, such as ENSO.Owing to the multiple tests conducted in our study, these p-values were further adjusted using the false discovery rate approach [13], to effectively control the occurrence of false positives.

Results
Figure 1 shows the seasonal trend of annual mean z-score standardized global atmospheric thickness between 1000 hPa and 500 hPa, which represents global changes relative to each location's unique historical variability.The absolute changes in annual mean thickness are displayed in figure 2, which identifies the largest changes in the high latitudes.Figure 3 shows the time series of the globally (spatial)-averaged atmospheric thickness since 1940.Figures 2 and 3 show that atmospheric layer thickness has a positive trend that is statistically significant (α = 0.05) in large parts of the globe during JFM and JJA, implying that the height of the 500 hPa level is increasing with time.The average (absolute) change is approximately +0.26 m per year during both JFM and JJA (figures 2 and 3). Figure 1 also shows that the relative changes in the thickness exhibit seasonal and spatial variability.Generally, from figure 1, on the spatial scale, the positive trend magnitude is largest over the tropical land mass in Africa and the adjacent oceans, as well as over the Pacific warm pool region with a trend of up to +0.03σ per year.There are also a few regions where the trend is negative, such as the south of Greenland during JFM and some western parts of Asia during JJA.Further, during the NH winter (JFM), the positive trend is statistically significant over most of the regions in high latitudes of the NH as compared to the high latitudes of the SH (figures 1 and 2).In contrast, during the SH winter (JJA) the reverse can be seen as the positive trend is statistically significant over most of the regions in high latitudes of the SH as compared to the NH (figures 1 and 2).Specifically, while for both hemispheres, the increasing trend in atmospheric layer thickness over the high latitudes is higher during the respective winters, the spatial extent (globally) of increases appears greatest in JJA (figures 1 and 2).Change point detection tests, for the time series in figure 3 suggest that 1978 marks the change point for the increasing trend during both JFM and JJA.The seasonal and spatial variations in the trend become more obvious in figure 4. Examining seasonal trends over the land and ocean separately (i.e., based on the z-scores), figures 5(a) and S2, show that trends over the SH high-latitude land are also larger during the SH winter compared to the respective trend in NH high-latitude land during the NH winter.During the SH winter, on average the increase in thickness is equally higher in the land compared to the ocean (figure S2).Therefore, relative to a location's historical variability, the thickness over SH high latitude landmasses in SH winter is increasing at a faster rate compared to the thickness over NH landmasses     during their winter (figure 5(a)).Over the ocean, very similar patterns in figure 4 were reproduced (figure 5(b)).Though when considering the absolute changes, figure 4(b) suggests that the magnitude of the increasing thickness over the NH high latitudes is higher.
Next, we applied partial correlations (and partial regression) to examine if tropical modes-ENSO variations, characterized by the Niño 3.4 index, and the PWPR-as well high latitude modes-Antarctic oscillation, characterized by the SAM index, and the Artic oscillation, characterized by the AO index, impact changes of the global atmospheric layer thickness over time.The correlation maps are shown in figure 6 for JFM and JJA, respectively.We carried out the analysis by correlating atmospheric layer thickness with time ('Main' in figure 6) and subsequently controlling the influence of one of the tropical/high latitude modes of climate variability, respectively, using partial correlations.Hence the partial correlations aim at investigating how the hemispherical/tropical modes impact the temporal changes in the global thickness.Table 1 further quantifies how the temporal change in the thickness is impacted when either of the hemispherical/tropical modes is controlled.Table S1 shows the same result but uses regression for the seasonal z-score and seasonal absolute values.
It becomes obvious from tables 1 and S1, figures 6-7 that over vast regions PWPR (see figure S3 for the spatial extent of the PWPR) has a notable impact on the changes in atmospheric layer thickness over time both during JJA and JFM.The statistical significance of the changes over time, the direction, and the magnitude of the trends are influenced by PWPR such that the net increase in atmospheric layer thickness robustly disappears (for most regions) when the PWPR signal is controlled.Based on correlations between global thickness and the PWPR index, we found that the spatially averaged global atmospheric layer thickness is strongly associated with the PWPR index (Pearson correlation is ∼+0.88 during both JJA and JFM), which can be linked to the strong trend in PWPR (figure S4).SST changes in the PWPR explained 76% variance of the inter-annual variability of the global average thickness layer during JJA and 78% during JFM.
From figures 6 and 7 and table 1, in terms of the spatial extent, the impact of the AO, ENSO, and SAM on the seasonal trends are localized compared  ).During JJA, the impact of ENSO is less apparent.For the high latitudes, during JJA, the AO and the SAM also have some regionalized impact (figures 6(b) and 7(b)).Adjusting for the effective sample size reduces the magnitude of the t-statistics and increases the p-values, making them less significant.However, the strength and direction of the correlation remained the same.Thus, the relationships (in table 1) between thickness changes and the control variables (AO, Nino3.4,SAM, PWPR) remain statistically significant, indicating that these relationships are robust to the considerations of autocorrelation.Indeed, while ENSO, SAM, and AO are primarily known for their interannual variations, their impacts can be superimposed on longer-term regional temperature trends.For example, if there are more frequent or intense El Niño events over a particular period, this could introduce a warming bias in regions typically influenced by El Niño.Conversely, frequent La Niña events could introduce a cooling bias.Over time, these biases can lead to abrupt shifts in the climate system and can be superimposed on longer-term warming or cooling trends in specific regions.In the same paradigm, the trend towards more frequent positive SAM and AO phases can lead to consistent regional temperature anomalies.Over time, these patterns can similarly influence the longterm temperature trends observed in the areas that they tend to impact.In essence, these climate modes can modulate regional temperature trends by consistently influencing atmospheric circulation patterns over extended periods.If one of these modes exhibits a trend (e.g. the more frequent positive SAM and AO phases), the regions influenced by this mode might see temperature trends that differ from the global average or from what might be expected based solely on factors like greenhouse gas concentrations.

Discussion and conclusions
Several studies have investigated changes in low-level air temperatures [14][15][16].The poles, particularly the Arctic, have been warming at a rate approximately twice as fast as the global average [15].This rapid warming at the surface, coupled with our findings on the significant change in thickness values in the polar regions (>0.8 m per year, figure 2), indicates the pronounced vertical temperature changes occurring in polar regions.Similarly, using surface temperatures, [16] reported that the tropical regions display a significant warming trend.This warming, combined with our findings on the increase in relative thickness over the tropics (about 0.03σ per year, figure 1), suggests vertical temperature changes in the tropics.
Considering that prior studies primarily focused on changes near the Earth's surface, thereby providing a relatively narrow perspective; assessing the thickness changes between 1000 hPa and 500 hPa offers a broader viewpoint, capturing the bulk changes in temperature across a significant portion of the lower and middle troposphere.This metric provides insights into the vertical structure of the atmosphere, essential for understanding the overall atmospheric dynamics.Hence while prior studies have documented that global temperature is rising and there are a wide variety of associated indicators of this change, along with potential impacts [16][17][18][19], this study applied ERA5 reanalysis data to examine how global atmospheric layer thickness has changed since 1940.
We calculated trends for the raw seasonal average thickness between 500 hPa and 1000 hPa and for the standardized seasonal thickness data.This dual perspective-looking at both absolute changes and changes relative to historical variability-provides a more nuanced understanding of the spatial heterogeneity of climate change impacts.It underscores the fact that climate change does not affect all regions equally and that different regions may face different types of climate risks, relative to their normal range of climate variability.This, in turn, supports the need for tailored, region-specific strategies to mitigate and adapt to these risks [20].Our results show that during the analysis period, the global average atmospheric thickness exhibited a positive trend (figures 1-3), which is spatiotemporally heterogeneous.We observed that the most pronounced increases in the seasonal mean thickness occur in the high latitudes, particularly in the Arctic and Antarctic regions (figures 2 and 3(b)).This is likely related to polar amplification, a phenomenon where changes in climate are amplified at the poles [21,22].This polar amplification is typically linked to the retreat of sea ice, leading to a decrease in surface albedo and subsequent absorption of more solar radiation.This, in turn, warms the atmosphere above, contributing to an increase in the thickness of the atmospheric layer in these regions [23].Furthermore, the advection of heat from lower latitudes could also play a role in the increased atmospheric thickness in these polar regions [24].
Conversely, looking at changes relative to each location's own historical variability, we found that the largest changes are occurring in the tropics, indicating a trend that is greater relative to the usual variability in atmospheric thickness height in these regions (figures 1 and 3(a)).Such spatiotemporally-relative trends in tropical climates have also been noted elsewhere [25].Specifically, central Africa demonstrated notable fluctuations.As atmospheric layer thickness is directly related to temperature and atmospheric moisture content, these changes suggest that tropical regions are becoming increasingly susceptible to climate change and the associated impacts.Thus, while the greatest raw increases are in the polar regions when examining trends in z-scores, the tropical Atlantic, Africa, and Indonesia are hot spots for increased layer thickness.This result is consistent with results from prior research [25] that suggest that relative to the usual amount of variability each location on Earth experiences, the tropics are changing just as fast as the poles.
The trends we observed in the thickness of the atmospheric layer suggest increasing stability in the troposphere.However, the traditional concept of atmospheric stability is challenged by the work of [26].Lovejoy et al used high-resolution dropsonde data to show that these seemingly stable layers of the atmosphere can be further dissected into a complex hierarchy of smaller-scale unstable and stable sublayers, introducing a fractal-like structure.While this provides a profound insight into the intricacies of small-scale (microscale and mesoscale) atmospheric dynamics, it is important to note that these findings pertain primarily to these smaller scales.At the larger scale at which our study operates, the concept of atmospheric stability remains a useful and relevant framework for analysis, especially since the 500 hPa to 1000 hPa thickness is a commonly-used proxy for the temperature and moisture content of the lower atmosphere (and impacting the surface) at synoptic and larger scales.Thus, while the perspective of Lovejoy et al enriches and complements our understanding of atmospheric stability, it does not negate our approach, which considers stability at a larger scale.
It has been reported that the Indo-Pacific warm pool significantly influences global climate dynamics by emitting considerable quantities of water vapor and latent heat into the atmosphere [27,28].The Indo-Pacific warm pool is crucial in regulating upper ocean heat content, a factor that has been increasingly linked to contemporary climate change phenomena [29].Specifically, the Indo-Pacific warm pool region plays a significant role in the dynamics of Pacific SST modes such as ENSO events, the Inter-decadal Pacific Oscillation, and the Pacific Decadal Oscillation [30][31][32], which are known to have a profound influence on regional climates around the globe.Our results showed that when the SST signal over the PWPR is controlled, the magnitude of the temporal increase in atmospheric thickness weakened globally (figure 6, tables 1 and S1), suggesting that due to its large trends (figure S4), the PWPR might be an important regulator of global-scale trends in atmospheric layer thickness that are consequent with anthropogenic climate change.This is consistent with studies on the impact of tropical Pacific variability on the global climate system [32,33].Studies have documented that the warming trend in the PWPR over the past few decades aligns with changes in SST as predicted by global warming scenarios [9][10][11].Thus, the influence of PWPR on global atmospheric thickness can be interpreted as a reflection of the larger impacts of global warming.
ENSO, AO, and SAM, which are dominated by interannual time scales had little effect on the long-term trend of global thickness, nonetheless, they contribute to the inter-annual variability and regional long-term trend of thickness, over specific regions.During JFM El Niño was found to contribute to the increase in thickness across the tropical Pacific (figures 6 and 7).During El Niño events, the SST in the central and eastern tropical Pacific are warmer than average.This increased warming leads to more atmospheric heating, which in turn results in enhanced upward motion and expanded thickness in the troposphere due to the warmer air [7,34].Moreover, ENSO can lead to alterations in atmospheric circulation patterns, potentially affecting the redistribution of heat and influencing thickness trends [7].On the other hand, during JFM, SAM's and AO`s influence on the thickness trends in the middle and high latitudes might be related to their ability to modulate the strength and position of the mid-latitude westerly wind belt [35].Notably, there have been observed trends toward the positive phase of these high-latitude modes, which could play a role in regional long-term thickness trends in parts of the globe [36].
Therefore, global increases in the trend of atmospheric layer thickness can be attributed to a myriad of interconnected factors.Moreover, the atmospheric capacity for water vapor escalates with warming, leading to a moister and thus, a thicker atmosphere [37].Additionally, changes in cloud cover and albedo can indirectly impact atmospheric thickness by influencing the amount of solar radiation that is absorbed, in addition to their impact on outgoing longwave radiation [38].
In conclusion, our analysis underscores the spatial heterogeneity of climate change impacts.It highlights the need for region-specific mitigation and adaptation strategies, tailored to the unique climate challenges faced by different geographical areas.

Figure 1 .
Figure 1.Seasonal trend in annual mean z-score standardized atmospheric layer thickness between 500 hPa and 1000 hPa from 1940 to 2022 for boreal winter (top) and austral winter (bottom).Only grids with statistically significant values at a 95% confidence level are shaded.Units are the slope of the trend (σ yr −1 ).

Figure 2 .
Figure 2. Seasonal trend in annual mean atmospheric thickness between 500 hPa and 1000 hPa from 1940 to 2022.Only grids with statistically significant values at a 95% confidence level are shaded.

Figure 3 .
Figure 3.Time series of the seasonal average global thickness between 500 hPa and 1000 hPa from 1940 to 2022.Red line is the 10 year moving average and shading is 95% confidence interval.

Figure 4 .
Figure 4. Latitudinal profile of the trend (of z-scores; in figure 1) in the thickness between 500 hPa and 1000 hPa (1940-2022) (a), and trend of seasonal mean data in figure 2(b).Vertical axis (trend) units in (a) are σ yr −1 .

Figure 5 .
Figure 5. Latitudinal profile of the mean trend (of z-scores; in figure 2) in the thickness over the global landmass (a) and over the oceans (b) between 500 hPa and 1000 hPa (1940-2022).Vertical axis (trend) units are in σ yr −1 .

Figure 6 .
Figure 6.Partial correlation examining the impact of various high latitude and tropical climate signals on the changes in the thickness between 500 hPa and 1000 hPa over time during JFM (a) and during JJA (b).Only grids with statistically significant values at a 95% confidence level are shaded.

Figure 7 .
Figure 7.The normalized difference between the correlation map of 'Main' (i.e. the correlation between the seasonal mean thickness and time) and the maps with one of the climate modes controlled in figure 6 during JFM (a) and JJA (b).

Table 1 .
Average Pearson correlation between the global thickness layer (500 hPa and 1000 hPa) at the grid boxes and time (1961-2021), i.e. 'Main' in the table, and partial correlations, controlling the signal of the climate modes on temporal changes of the global thickness layer.Averages were computed as the mean correlation coefficient at all the grid boxes, under each set-up.