The Relationship between Stratospheric Gravity Wave Potential Energy and Tropospheric Parameters over South America  inferred from COSMIC-2 and METOP Radio Occultation Measurements

doi:10.21203/rs.3.rs-2326789/v1

Using COSMIC-2 and METOP radio occultation measurements during the years 2020 and 2021, the study presents the first direct and independent relationship between the potential energy (E_p) in the stratosphere, precipitable water vapour (PWV), tropopause heights, and cold-point heights over South America. The South American continent comprises the tropical region, the Andes Mountain range, and the mid-latitude climates. The seasonal mean of the potential energy (E_p), the PWV, and the tropopause parameters height (TPH and CPH) were obtained to investigate the relationship between the SGW E_p and the tropospheric parameters (PWV, TPH, and CPH). Around the Andes Mountains to the east, there is significantly less water vapour (PWV < 10 mm) and relatively high gravity wave E_p (E_p > 8 kJ kg^− 1). A good correlation of variability was found between the PWV and the lower stratospheric gravity wave (SGW) E_p in summer over the tropical region (± 20^◦). Our result affirmed the possibility that convective activity was a major driver of the tropical gravity waves over South America. In the subtropical (30^◦-40^◦) region, especially in the winter, the tropospheric parameters make little or no contribution to gravity wave activity in the region. The tropopause and the cold-point temperature showed an anti-correlation (r > − 0.6) with SGW over the South American tropics. The SGW activities in the tropical region showed an impact on the structure of the tropopause parameters, which could be a result of the convective activity in this region.

Atmospheric gravity waves are critical for large-scale atmospheric circulation, thermal structure, component distributions, and transport of chemical constituents to various altitudes, and atmospheric variability from the troposphere to the thermosphere (Son et al. 2011). The atmospheric gravity waves assist in the transportation of atmospheric elements such as water vapor and affect the thermal structure of the tropopause (Xian and Fu 2015; Yu et al. 2019). Due to their critical role in climate dynamics, the upper troposphere and lower stratosphere (UTLS) have recently attracted more interest. The tropopause is the layer that separates the upper troposphere and the lower stratosphere in terms of vertical mixing durations, trace components, and thermal balance (Son et al. 2011). The gravity waves (GWs)propagate upwards and their amplitudes increases exponentially due to the exponential decrease in the atmospheric density. GWs break or dissipate in the upper altitudes due to instability or critical level filtering (Fritts and Alexander 2003).

The tropopause’s fluctuations, which are caused by changes in the physical, chemical, and thermal features of the troposphere and the stratosphere, are intimately connected to stratosphere-troposphere interchange, as well as climatic variability and change (Schmidt et al. 2008b,a). The tropopause has several definitions and theories (Schmidt et al. 2006). The World Meteorological Organization (WMO) defined the thermal tropopause, also known as the tropopause, as the lowest level at which the lapse rate drops to 2K km^− 1 or less, provided that the average lapse rate between this level and all higher levels within 2km does not exceed 2K km^− 1 (Fueglistaler et al. 2009). The tropopause is derived from vertical profiles of atmospheric temperature and is used internationally, in both the tropics and extra-tropics (Liu et al. 2014). The cold-point tropopause height is the height at which the minimum temperature occurs when one ascends from the surface to a specific altitude and then rises as one ascends farther into the stratosphere (Randel and Jensen 2013). The cold-point tropopause is a critical parameter for determining stratosphere-troposphere interaction and exchange (Yu et al. 2019). Tropopause parameters height and temperature fluctuations show seasonal and inter-annual variability (Zhou and Holton 2002; Randel et al. 2003; Seidel and Randel 2006) and are closely linked to atmospheric waves (Satheesan and Murthy 2005; Jain et al. 2006), particularly the effects of gravity waves (Das et al. 2010; Khan and Jin 2016).

The relationship between the tropospheric parameters and the stratospheric gravity wave (SGW) potential energy (E_p) has become an important subject since the launch of the Radio Occultation (RO) satellites, especially the Constellation Observing System for Meteorology, Ionosphere, and Climate (COS- MIC) satellites. The GW E_p is an important parameter to measure the GW impacts in the atmosphere due to it dependency on only atmospheric temperature profile for the derivation of GWs in the atmosphere (Cai et al. 2017; Baumgarten et al. 2018; Yang et al. 2021; Strelnikova et al. 2021; Gisinger et al. 2022). South America continent comprises different sources of gravity waves and the peculiar characteristics of these sources with their link with the SGWs have received lesser attention. Even though, several research on the changes in tropopause structure (Seidel et al. 2001; Schmidt et al. 2004) and mostly on the global SGW activity (Wang and Alexander 2010; Hierro et al. 2012), there are few studies on the interaction between SGWs and the tropospheric parameters mainly focusing on the regional sections like the South American sector. For example, Khan and Jin (2016) studied the connection between SGWs and the temperature and height of cold-point tropopause and water vapour over Tibet from June 2006 to February 2014 using the first set of COSMIC RO satellites’ temperature data. Their findings indicated a strong association between SGW E_p, cold-point tropopause temperature, and water vapour, and that SGWs affected the cold-point tropopause temperature and water vapour concentration in the stratosphere. These studies on the connection between SGWs and tropopause were mostly regional in scope.

Further analysis is needed on the impact of stratospheric gravity wave activity on the tropopause structure around the globe. Yu et al. (2019) also studied the connection between SGW E_p and tropopause height and temperature around the globe using COSMIC-1 dry temperature profiles from September 2006 to May 2013. They discovered correlation factors between E_p values at various altitudes, and the tropopause height and temperature were estimated correspondingly in each grid. Yu et al. (2019) also found that SGW E_p had a significant positive correlation with lapse-rate tropopause (LRT) height (LRT-H) and a significantly negative correlation with LRT temperature (LRT-T) in the stratosphere with distinct zonal distribution characteristics at middle and high latitudes. While in the tropics, the distributions of the statistically significant correlation coefficients between SGW E_p and tropopause parameters were dispersive, and the peak correlation was computed across altitudes of 14–38 km.

The second set of COSMIC satellites (COSMIC-2) recently launched provided much more numbers ofoccultations than COSMIC-1, at ± 40^◦ which provides the opportunity to do a more quantitative and regional study of gravity waves in the stratosphere. The objective of this study is to establish the relationship between the SGWs and the tropospheric parameters, namely, the precipitable water vapour (PWV), the tropopause height (TPH), cold-point height (CPH).

Observation data

The COSMIC-2 GNSS RO observation produce about 4000 to 5000 RO events per day with high accuracy and precision. RO can obtain more data than the other satellite missions launched previously. On average, COSMIC-2 produces about 15 000 to 17 000 occultations per month over South America obtained from the CDAAC web site (http://cdaac-www.cosmic.ucar.edu/cdaac), providing many chances to study the atmospheric variations on this continent. COSMIC-2 produces different types of products, which include the dry atmospheric temperature profile (atmPrf). The wet atmospheric temperature profile (wetPrf) is negligibly different from the dry atmospheric temperature profile, the ionospheric profiles (ionPrf) e.t.c.

The “atmPrf” is an atmospheric profile without moisture information at level-2 of the COSMIC-2 data processed operationally in near-real-time (nrt). A single atmPrf file contains full resolution profiles of physical parameters such as dry pressure, dry temperature, refractivity, bending angle, impact parameters, tropopause parameters (TPH and CPH), geometric height above mean sea level. One of the leading products in the “atmPrf” is the raw temperature obtained from the COSMIC-2 mission. The COSMIC-2 level 2 “atmPrf” profiles provide dry temperature from the surface to about 60 km, with a vertical resolution of about 1 km in the stratosphere. We noted that COSMIC-1 had a limitation to a relative temperature profile above 45 km due to the symmetric spherical assumption modeling. These errors have been significantly improved in the COSMIC-2 satellites raising the occultation height up to 60 km, but the limitations are still large above 55 km. Therefore, in this study, upper limit of 50 km in the stratosphere is used. Figure 1 shows the coverage of temperature profile points available for E_p calculations from COSMIC-2 over South America. Each of the panels shows the example of occultation points for one day (02/Apr/2020), a month (April), a season (summer), and the whole year 2020. These points were used to obtain the E_p.

The Gravity Wave Potential Energy

The atmospheric temperature profile (T) from the COSMIC-2 is a function of height (h) which consist of the background temperature profile T (z) and the fluctuating component T ^′(z). The E_p has been used as a proxy to studying the gravity wave activities as presented by Tsuda et al. (2000) is given by:

$${E}_{p}={\left(\frac{g}{N}\right)}^{2}{\left(\frac{\overline{{T}^{{\prime }}}}{\overline{T}}\right)}^{2}$$

1

where g is the acceleration due to gravity, N is the Brunt-Vaisala frequency, and $\stackrel{-}{T}$, and ${T}^{{\prime }}$ is our background temperature and the temperature fluctuations caused by gravity wave activities, respectively. The E_p calculation is based on the accurate extraction of T ^′, which is given by:

$${ T}^{{\prime }}=T-\overline{T}$$

2

and the $N$ is given as follows:

$${N}^{2}=\frac{g}{\overline{T}}\left[\frac{\partial \overline{T}}{\partial h}+\frac{g}{{C}_{p}}\right]$$

3

Where ${C}_{p }$is the specific heat capacity of air at constant pressure and h is the altitude.

The temperature profile obtained from the COSMIC Data Analysis and Archive Center (CDAAC) is referred to in this paper as the raw temperature profile measured by the COSMIC-2 satellite in the Earth’s atmosphere. The gravity wave E_p is calculated using Eq. (1). The E_p depend only on the raw temperature profile, which can be separated into the background temperature (T), and the temperature fluctuation (T ^′). In calculating E_p, the T ^′ is the main issue that requires careful attention. There are different methods of deriving T ^′. For example, Hei et al. (2008) used a selected cell size of 20^◦× 10^◦ of longitude and latitude. They obtained all the available COSMIC-2 data in an individual cell in one month. The mean temperature profiles obtained in each cell are low-pass filtered by using a 4 km vertical running mean to get the T, and later applied the Fast Fourier Transformation (FFT) between 12–33 km of altitude to extract T ^′ with a vertical wavelength shorter than 7 km. De la Torre et al. (2006) used the band-passed filtering method between 4 − 10 km cutoffs. Also, Baumgaertner and McDonald (2007) used a high-pass filter with a Hamming window using a cutoff wavelength of 10 km.

However, the above methods have limitations. They do not remove the influences from the other waves in the atmosphere that are not gravity waves. Scherllin-Pirscher et al. (2021) stated that the band-pass filtering is a poor method for separating gravity wave components. Filtering short vertical wavelength fluctuations includes only the gravity waves within the filter band and eliminates the rest of the gravity waves. Short vertical wavelength features include some global-scale waves.

The band-pass method eliminates gravity waves with longer vertical wavelengths. The vertical wave- lengths of gravity waves change with height if wind shear is present in the atmosphere. If the intrinsic phase speed (vertical wavelength is proportional to intrinsic phase speed) increases due to changes in the background wind, the band-pass filter naturally removes those gravity waves vertical wavelength in wind shear. Since winds vary seasonally, the vertical wavelengths will also vary at different seasons. This means that the band-pass filter will automatically filter out the gravity waves with shorter or longer vertical wavelengths depending on seasonal wind changes, and not necessarily make any real changes in the E_p of the gravity waves (Scherllin-Pirscher et al. 2021).

Wang and Alexander (2009, 2010) used the daily COSMIC-1 temperature profiles are divided into cell sizes of 20^◦ × 10^◦ of longitude and latitude, between 20 and 50 km of altitude, using a vertical resolution of 0.1 km. The mean temperature profile of each grid is calculated. The Stockwell transform was used to obtain the mean background temperature at each latitude and altitude along the longitude. Also, the zonal wavenumbers between 0–6 are obtained using the wavelet transform method to estimate the background temperature (T). The T is interpolated back to the positions of raw COSMIC-1 profiles and subtracted from the raw temperature profile using Eq. (2) to obtain T ^′. The analysis can resolve gravity waves with a vertical wavelength greater than ∼2 km, which is twice the vertical resolution of the COSMIC-1 temperature profile data (Wang and Alexander 2009).

In the present study, following the example of Wang and Alexander (2009, 2010), the raw temperature profile obtained from COSMIC-2 is first interpolated to 100 m intervals along the altitudes. Each temperature profile is divided into cell size of 20^◦ × 10^◦ of longitude and latitude between 10 and 50 km of altitude and the mean temperature of each grid is calculated. The mean temperature profile is decomposed using a Continuous Wavelet Transform (CWT) to obtain the background temperature (T). The T is interpolated back to the positions of temperature profiles and subtracted from the raw temperature profile using Eq. (2) to obtain T ^′.

Precipitable Water Vapour Content

The COSMIC-2 “wetPrf” provides multiple levels of precipitable water pressure data. The specific humidity is easily calculated by water vapour pressure, and air pressure, using Eq. (4) (Wang and Zhang 2008). The average specific humidity is calculated by taking the bottom layer specific humidity and top layer specific humidity given in Eq. (5).

$$q=\frac{\epsilon e}{p-(1-\epsilon )e}$$

4

The mean specific humidity is given as:

$$\stackrel{-}{q}=\frac{{q}_{h,i-1}+{q}_{h,i}}{2}$$

5

where $\epsilon$ is the constant of the ratio of the molecular weight of precipitable water to dry air, which equals 0.622, $e$ is the precipitable water pressure, $p$ is the total atmospheric pressure, and $q$ is the specific humidity.

To calculate the PWV value from a single wet profile, the specific humidity of each height is integrated from the surface to the retrieved maximum height, using the Eq. (6).

$$PWV=-\frac{1}{g}\sum _{{P}_{s}}^{0}\text{‍}q{\Delta }p$$

6

In Eq. (6), PWV value in mm, Ps is the surface air pressure, g is the value of acceleration due to gravity, q is the specific humidity, and the ∆P is change in pressure. The PWV is calculated to compare with the gravity wave E_p in the stratosphere to study the connection between the gravity wave activities and the deep convection.

Statistical Method

In order to see a clear relationship and correlations between the E_p and the tropospheric parameters, the two parameters are normalized with the same scale using the mean normalization formula according to Abraham et al. (2018, p. 400) given in Eq. (7). The mean normalization method returns the values between − 1 and 1, enabling the comparison and correlation of the gravity wave E_p and the tropospheric parameters.

$${x}^{{\prime }}=\frac{x-\mu }{\text{m}\text{a}\text{x}\left(x\right)-\text{m}\text{i}\text{n}\left(x\right)}$$

7

where ${x}^{{\prime }}$ is the normalized value of $x$, the $\mu$ is the mean value of $x$, and $x$ is the original value of ${\text{E}}_{\text{p}}$ and the tropospheric parameters. Also, the correlation coefficients between the SGW ${\text{E}}_{\text{p}}$ and the tropospheric parameters in the tropical, subtropical, and extratropical regions were calculated. The correlation measures the strength of the relationship between variables and is the scaled measure of their covariance. The relationship between the two concepts can be expressed using the following Equation ?:

$$r(X,Y)=\frac{Cov(X,Y)}{{\sigma }_{X}{\sigma }_{Y}}$$

8

Where $r(X,Y)$ is the correlation between the variables $X$ and $Y$, $Cov(X,Y)$ is the

Temperature profiles obtained from COSMIC-2 measurements over South America (30^◦W − 85^◦W and 20^◦N − 60^◦S) were used to study the SGW activity in 2020. The goal of this research is to demonstrate how SGWs influence tropopause height, as well as to investigate the effect of precipitable water vapour on SGWs. SGWs have an important role in controlling stratospheric water vapour by producing mean updraft or fluctuating tropopause parametric structures. The results will be presented in the altitude range from 20 to 50 km for COSMIC-2 profiles to minimize the errors. The COSMIC-2 satellites measure up to the altitude of 60 km, but as stated by Schreiner et al. (2020) errors due to the symmetric spherical assumption modeling has been significantly improved in the new COSMIC-2 satellites. However, the errors are still large above the altitude of 55 km. Subsequently in this section, the latitudes will be divided into the following ranges: 1) 20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S, and 20^◦S − 30^◦S are the tropical regions; 2) 30^◦S − 40^◦S is the subtropical region. In order to quantify the troposphere influence on the SGWs, the tropospheric parameters are taken from the upper troposphere to get the tropopause parameters.

The SGW E_p in Figs. 2 and 3 are divided into three segments: 1) the lower stratosphere (20–30 km); 2) middle stratosphere (30–40 km); 3) the upper stratosphere (40–50 km). These segments have their peculiar characteristics according to the mixing of air in these regions (Salby 1996). Also, the seasons are categorized as summer (December–January–February), autumn (March–April–May), winter (June–July–August), and spring (September–October–November). Tables 1 and 2 present the Pearson correlation coefficients of SGW with the PWV and the tropopause parameters in the tropics and over the Andes Mountain, respectively in 2020 and 2021.

Potential Energy Climatology

The potential energy (E_p) is an efficient parameter to study the gravity wave activities in the atmosphere (e.g ., (Tsuda et al. 2000; Schmidt et al. 2004, 2008a)). Figures 2 and 3 show the climatology of the SGW E_p over South America for the years 2020 and 2021. It is observed that the SGW E_p for the years 2020 and 2021 showed similar pattern. The SGW E_p over South America in summer of 2021 showed higher values than 2020 at around ± 10^◦. At the lower stratosphere (Figs. 2 and 3, 20–30 km), it can be seen that the gravity wave E_p values range from 6 to 10 J kg^− 1 in the equatorial region (± 30^◦) for all the seasons. In this region, it is observed that the E_p is higher in autumn ± 10^◦ latitude around the equator. Generally, the gravity wave E_p had a higher value in the equatorial region in all the seasons than in other regions. In the middle stratosphere, it is observed that the E_p have higher values (Figs. 2 and 3) in autumn around the equatorial region.

The convective activities are more intense in the equatorial region, which could be responsible for the increase of the gravity wave E_p values, rising to more SGW activity. There is also evidence of the effect of the wind in the tropical region, called the Northeast and Southeast trade winds, as the gravity waves appear to be more prevalent at higher latitudes. This result agrees with what was reported by Tsuda et al. (2000). Xu et al. (2017) found that the distributions of gravity wave E_p over 20–30 km exhibited similar seasonal and spatial variations compared to our result. In the tropics, the gravity wave E_p is symmetric to the equator in autumn and spring. The distribution of gravity wave E_p around tropical latitudes corresponds to deep convection which is the principal cause of gravity wave across tropical latitudes (Ratnam et al. 2004).

In the middle stratosphere, Figs. 2 and 3 (30–40 km), There is less or no SGW activity during winter in the tropical region in the middle stratosphere (30–40 km). There is higher gravity wave activity near the equator in autumn in the middle stratosphere than in other seasons. The gravity wave activity is low (maximum 5 J kg^− 1) compared to the lower stratosphere (maximum 10 J kg^− 1). It is also observed that the gravity wave E_p in winter increases from the lower to the upper stratosphere (20–50 km) over Andes and the Patagonian mountains. This can be attributed to the increase in zonal wind speed, aiding the increase of the SGWs activity (Alexander et al. 2009).

The gravity wave activity disappears from the lower to the upper stratosphere in the tropical region. In autumn, high gravity wave E_p values (∼7 J kg^− 1) were observed over Southern Argentina (Patagonia). In spring, the E_p in the tropics declined with height to ∼50% across the altitude ranges (∼ 3.5 J kg^− 1 in the middle stratosphere, and ∼1.5 J kg^− 1 in the upper stratosphere (40–50 km)). It is also noted that the gravity wave E_p values remain unchanged from the middle to the upper stratosphere in the summer. This consistency in the gravity wave E_p values at the middle to the upper stratosphere shows that the gravity waves are not likely subjected to wave dissipation. The high gravity wave activity decreases at the upper stratosphere showing the gravity wave activity descending toward the south. Gravity wave activities can also be seen around the equator in the summer, spring, and winter below 40^◦S.

Seasonal Variation Of Sgw Potential Energy

To further describe the seasonal variability of SGWs E_p is presented in Fig. 4, at each latitudinal distribution (20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S, 20^◦S − 30^◦S, and 30^◦S − 40^◦S), in the stratosphere for the year 2020 and 2021. The SGWs E_p latitudinal distribution for both years is very similar in both tropical and subtropical regions. Our result showed that ± 20^◦ in the tropical region accounts for most of the SGW activities (∼15–25%, ± 10^◦ account for 20–25% of the total mean SGW E_p) in the lower stratosphere (Fig. 4 left panel), which seemed to be clear evidence of convective activities in the tropical region. The increase in the total mean SGW E_p decreased to ∼15–20% in the upper stratosphere. We suggest this could be a result of the gravity wave filtering.

At 20^◦S − 30^◦S account for ∼10–13% of the total mean SGW E_p with the highest percentage in the winter (13%) in the lower stratosphere. The SGW activity increases in the middle stratosphere (∼12–15%), in the upper stratosphere (∼15–20%), and also increases in the middle and upper stratosphere (Fig. 4). This could be the contribution of the mountain waves generated by the extension of the Andes Mountain range (in the winter) combined with the convective activities in the amazon rain forest region (in the summer and spring). A consistent increase in the SGW activities is seen in the total mean SGW E_p percentage at 30^◦S − 40^◦S across 2020 from the lower to upper stratosphere, which is more conspicuous in the winter and spring (Fig. 4).

Precipitable Water Vapour Content

The PWV over South America for 2020 and 2021 are shown in Fig. 5. The PWV pattern over South America in both years is seen to be very similar. The PWV is concentrated in the tropical region and mostly at ± 10^◦ in all the seasons. The PWV in the summer and autumn are higher in the tropics. It is observed that the PWV is higher in the summer and lower in the winter. Most of the PWV is over the land, especially over the Amazon rain forest. The western Andes showed no PWV due to the air movement over the Andes Mountains.

There is a less amount of PWV (25–50 mm) in the southward subtropics (20^◦ − 40^◦S) with PWV lowest in the winter. The extratropical region showed little or no PWV, particularly in the winter. These observations are in good agreement with the results of Hierro et al. (2012); Teng et al. (2013); Zhang et al. (2018). The average PWV reaches a maximum value of 70 mm or more in tropical areas and then decreases to nearly 0 mm in the 40^◦S − 60^◦S region (mainly in winter). The regional and seasonal variability of PWV is strongly linked to the sources of water vapour and as a direct heat of surface temperature (Zhang et al. 2018). The detailed analyses of the relationship of PWV with the SGW E_p are discussed in the sections below.

Tropopause Parameters

The tropopause and the cold-point height are given in the “global attributes” of the “netcdf” files of the COSMIC-2 and METOP RO data. In this study, we focus only on the tropopause and cold-point tropopause heights. Subsequently, the tropopause height is designated as TPH, respectively, while the cold-point height is designated as CPH. The tropopause height (TPH) is the height at which the temperatures variation is not more than 2K within 2km between the troposphere and the stratosphere. The cold point tropopause is the coldest region that demarcates the thermal boundary between the troposphere and stratosphere. The cold point’s thermal properties have been studied in-depth due to their importance in the troposphere-stratosphere coupling and exchange (Randel et al. 2003). Figures 6 and 7 show that the TPH and the CPH in 2020 and 2021 have a similar trend and an average height of ∼17 km at ± 30^◦. The CPH showed more variability trend and ∼5 km difference from the TPH at 30^◦S -60^◦S. This suggests that the WMO’s definition of the tropopause is more valid at the equatorial regions. The tropopause and the cold-point height variability at the equatorial region (± 30^◦) appeared to be more consistent than the higher latitudes. It is also observed that at higher latitudes (40^◦S -60^◦S), the CPH is about 5–10 km higher than TPH in all the seasons. The height of the tropopause is about 5 km higher in the tropical areas to middle latitudes in both summer and winter (Seidel and Randel 2006; Schmidt et al. 2008b). A dramatic change in the height (Figs. 6 and 7) is noticed to be ∼30^◦S with ∼5 km, and in altitude to be ∼5 km at the same latitude. The change in temperature and height can be explained by the boundary between the Hadley cell and the Ferrel cell in the atmospheric air circulation, which varies monthly and seasonally. The air parcels blow warm air towards the equator in the Hadley cell. Hence, the tropopause and cold point heights are achieved at lower temperatures at high altitudes (Reid and Gage 1981).

In autumn and winter in 2020, the cold point altitudes are higher, closer to the lower end of the Ferrel cell. In spring, the cold point altitudes are higher, closer to

the lower end of the Hadley cell (Randel et al. 2000). The CPH in the Hadley cell followed the same trend as the TPH in the Hadley and Ferrel cells. The tropopause and cold point heights (Figs. 6 and 7) exhibit the same characteristics in summer and spring and the opposite in autumn and winter. The tropopause heights are much higher in the Hadley cell (∼25 km) and lower in the Ferrel cell (∼13–14 km). It is observed that the tropopause altitudes are higher in the summer and lowest in the winter in the Hadley cell. There are no apparent changes to the tropopause in the Ferrel cell. This result agrees with the findings of Schmidt et al. (2004); Kishore et al. (2006). The CPH characteristics have been classified as intraseasonal variabilities correlated with tropical convective activity (Zhou and Holton 2002; Randel et al. 2003; Randel and Wu 2005). The detailed analyses on the relationship of the tropopause parameters with the SGW E_p in the tropics and over the Andes region are discussed below.

Potential Energy Vs Tropospheric Parameters In The Tropics

In this section, we analyzed the latitudinal variation of SGW E_p and the tropospheric parameters (PWV, TPH, and CPH) and their respective correlation coefficient in the tropics during the years 2020 and 2021. The latitudinal ranges are divided into four, namely: 20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S. Figure 8 shows the relationship between the normalized SGW E_p and PWV at the four different latitudinal regions (20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S). Figure 9 also shows the relationship between the normalized SGW E_p, TPH, and the CPH at the same four different latitudinal regions. Positive correlations were found mostly in the summer and spring with a negative correlation in the winter across all the latitudinal ranges. Figure 8 shows that the SGW E_p and PWV have a similar trend along the seasons in the latitudinal range of 20^◦N − 20^◦S. The relationship between convection and the thermal structure of the upper troposphere is linked with warm anomalies in the upper troposphere and cold anomalies at the tropopause (Kim and Son 2012; Xian and Fu 2015; Yu et al. 2019). We found a significant negative correlation in the winter (JJA) between SGW E_p and PWV (refer to Table 1 for details) in the tropics.

and the water vapour (PWV) (red line) for 20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S at 2020 and 2021. Each panel shows the mean E_p distribution and the PWV at 20–30 km altitude. Figures 8 and 9 showed similarities in the trend between the SGW E_p and PWV. Although, this similarity in the tropics and the non-similarities in the subtropics does not necessarily mean correlation and anti- correlation because our focus was not to investigate the relationships between the tropopause parameters. From Fig. 8, the SGW and the tropopause parameters (TPH and CPH) showed interchanging trends in the summer, autumn, and spring. The statistical relationship showed a negative correlation at 20^◦N − 20^◦S with r > − 0.6 on average. In the tropical winter, the SGW showed that there is no relationship with the tropopause parameter temperature at 20^◦N − 10^◦N, 10^◦S − 20^◦S, and over the Andes at 20^◦S − 30^◦S. These results are consistent with the findings of

(Randel et al. 2000; Santer et al. 2003; Schmidt et al. 2008a).

Table 1.: The correlation coefficient between E_p and the tropopause parameters in the tropical regions.

	TROPICS
	20 − 10				10 − 0				0–10				10 20
	DJF	MAM	JJA	SON	DJF	MAM	JJA	SON	DJF	MAM	JJA	SON	DJF	MAM	JJA	SON
VP 2020	0.38	0.47	-0.05	0.63	0.20	0.56	-0.39	0.38	0.77	-0.18	-0.61	0.41	0.46	-0.41	0.16	0.48
VP 2021	0.38	-0.03	-0.26	0.07	-0.13	-0.26	-0.33	-0.18	0.17	-0.20	-0.22	0.87	0.33	-0.04	-0.04	0.53
TPH 2020	0.55	0.44	-0.1	0.65	0.44	-0.06	0.47	0.63	0.36	0.19	0.44	0.02	0.66	-0.04	0.23	0.46
TPH 2021	0.61	0.39	-0.31	-0.08	0.75	-0.03	0.11	0.52	0.45	0.09	0.30	0.58	0.13	0.41	0.31	0.61
CPH 2020	-0.07	0.27	-0.41	0.26	-0.06	-0.25	0.24	-0.24	-0.36	0.19	0.44	0.02	-0.77	-0.51	0.03	-0.42
CPH 2021	0.32	-0.08	-0.14	0.09	-0.46	-0.34	0.09	-0.36	-0.45	0.09	0.30	0.58	-0.79	-0.37	0.71	0.18

There are inconsistent variations of TPH and CPH, resulting in different correlation coefficient results between SGW, TPH, and CPH (Fig. 9). In the tropics, SGW and the TPHs in 2020 and 2021 are positively correlated in the summer, while CPH is negatively correlated (Table 1). Our result showed that the lower the CPH, the higher the SGW or vice versa. At 20^◦S − 30^◦S, the TPH and CPH exhibit a strong relationship with a positive correlation in the summer, autumn, and spring, while there is no correlation in the winter. This appears to be the extension of the deep convective systems over the Amazon region. In winter, TPH and CPH have negatively correlated SGW E_p at 20^◦N-10^◦N and positively correlated at 10^◦N − 20^◦S (Table 1).

Potential Energy Vs Tropospheric Parameters Over The Andes

In this section, we analyzed the latitudinal variation of SGW E_p and the tropospheric parameters (PWV, TPH, and CPH) and their respective correlation coefficient over the Andes during the years 2020 and 2021. The latitudinal ranges are divided into four, namely: 20^◦N − 10^◦N, 10^◦N − 0^◦, 0^◦ − 10^◦S, 10^◦S − 20^◦S. The area of interest is marked with the black dotted rectangular box in Figs. 10 and 11. At 20^◦S − 30^◦S over the Andes Mountain (70^◦W − 80^◦W), the SGWs and the PWV relationship showed an opposite trend, which does not necessarily signify an anti-correlation. Over the Andes mountains at 20^◦S − 30^◦S showed that there is a positive correlation in the summer, autumn, and winter (Table 2), a negative/positive correlation in 2020/2021 (r = − 0.12, − 0.15 in 2020, and r = 0.34, 0.24 in 2021) in the spring, respectively. At 30^◦S − 40^◦S over the Andes Mountain region, there is also a positive correlation in summer and spring in 2020 and 2021. In winter, our result showed a negative correlation (r = − 0.58 and r = − 0.69, respectively) in 2020 and 2021. This result showed that the lesser the water vapour content over the Andes the more the gravity wave activities in the stratosphere. In the Andes Mountains region, the water vapour significantly drops, the E_p rises considerably, and the PWV starts to increase from 70^◦W eastward across the seasons. Also, at 20^◦S − 30^◦S (Fig. 4), the PWV increases with a significant decrease in the gravity wave E_p at 70^◦W − 30^◦W. In contrast, the PWV and the gravity wave E_p showed a similar trend at 30^◦S − 40^◦S of 70^◦W − 80^◦W in all the seasons.

In these regions, a descending trend is observed from West to East in both E_p and PWV. This could be due to the northern and southern trade winds blowing westward. Zhang et al. (2018) observed that the changes in PWV suggest atmospheric water vapour is strongly tied to the supply of water vapour (oceans and seas) and heat (surface temperature). The PWV variations are complex because it is unclear how these two factors interact to produce water vapour in the high atmosphere. In the latitudinal range of 20^◦S − 30^◦S and 30^◦S − 40^◦S showed an anti-correlation between the E_p and PWV over the Andes mountains and after the Andes mountains towards the East in the winter. Also, Zhang et al. (2018) observed a much smaller PWV in the midlatitude, with higher values in summer than in other seasons.

At 30^◦S − 40^◦S, our result showed that the SGW E_p is negatively correlated with CPT in the summer, autumn, and spring (r = 0.53 and r = 0.83, respectively) and a positive correlation in winter. Meanwhile, the TPH showed a positive correlation (Table 2) with the SGW E_p in the summer and winter (r = 0.53 and r = 0.83, respectively) and a negative correlation in the autumn and spring (r = − 0.59). Our findings are consistent with those of Alexander et al. (2008), who determined that the mean E_p surpasses 2.4 J kg^− 1 in the Himalayas and Eastern China during the winter.

Table 2

The correlation coefficient between E_p and the tropopause parameters over the Andes region.
	OVER ANDES
	20–30				30–40
	DJF	MAM	JJA	SON	DJF	MAM	JJA	SON
VP 2020	0.64	-0.28	-0.94	0.05	0.03	-0.66	-0.58	0.22
VP 2021	0.21	0.23	-0.91	0.21	0.49	0.42	-0.69	0.48
TPH 2020	-0.66	0.85	0.64	0.04	-0.12	0.45	0.51	0.46
TPH 2021	0.08	0.21	0.49	0.52	-0.28	0.07	0.81	0.00
CPH 2020	-0.24	0.89	0.52	0.29	0.68	0.21	0.78	0.54
CPH 2021	-0.21	0.65	0.36	0.74	0.17	0.43	0.45	0.61

At 20^◦S − 30^◦S over the Andes (Table 2), the TPH and CPH are positively correlated in autumn, winter, and spring, and negatively correlated in the summer. In Fig. 11, there is a clear variation between TPH and CPH over the Andes Mountain at 30^◦S − 40^◦S. The correlation coefficient result from Table 2 showed that the CPH has a strong correlation in all the seasons with SGW E_p in 2020 and 2021 rather than TPH. The TPH showed a positive correlation with SGW E_p in autumn and spring while negatively correlated in the summer and winter.

The perturbations of atmospheric temperature caused by SGW activity as shown in Figs. 2 and 3. COSMIC RO temperature profiles are based on the estimation of temperature perturbations (T ^′) in order to calculate the SGW E_p. The illustration provided by Xu et al. (2017) shows that the COSMIC temperature profile varies in the tropopause and throughout the stratosphere. The GPS/MET temperature profiles show this variability as well (Randel et al. 2003; Tsuda et al. 2000). These temperature profile variations may be linked to SGWs, demonstrating that SGWs can influence tropopause temperatures. SGWs have been discovered to be critical in controlling the tropopause’s characteristics (Khan and Jin 2016). The tropopause characteristics are influenced by the breaking of SGWs in the stratosphere, which transports energy, momentum, chemical, and atmospheric elements (such as water vapour) across the tropopause to the surrounding environment (Yu et al. 2019). According to (Salby 1996; Khan and Jin 2016; Yu et al. 2019), the TPH and CPH exhibit unique properties in response to gravity wave transmission in the stratosphere.

Our results in Figs. 8 and 9 showed a positive correlation in the summer, autumn, and spring with a negative correlation in the winter between the tropospheric parameters and the SGW. This interesting result shows that the PWV may not be responsible for the excitation of SGWs in the winter due to a very low deep convection shifting towards the northern hemisphere in the winter (Yu et al. 2019). Yu et al. (2019) observed a correlation between convections and tropopause temperature and height, indicating that low and cold tropopause occur in deep convection areas (equator or tropics) and that both deep convections and gravity waves affect tropopause structure. The TPH and CPH variations may be linked to SGWs, indicating that gravity waves may impact tropopause temperature (Khan and Jin 2018). SGWs have been shown to be critical in controlling tropopause properties. Gravity waves breaking in the stratosphere transfer energy and atmospheric elements through the tropopause to the surrounds, modifying the tropopause parameters in the process (Wang 2003).

As previously shown, gravity waves move PWV and other atmospheric elements from the troposphere to the stratosphere (Wang 2003; Lane and Sharman 2006). The SGW activity is intensified over the Andes mountains during the winter season, reducing in PWV defusing into the stratosphere. When SGWs propagate and break, they not only transfer energy and momentum, but also vertical mixing of heat, directly or indirectly impacting the tropopause height. PWV and trace gases are defused into the stratosphere, increasing the concentration of PWV above the cold point height (Yu et al. 2019). As seen in Figs. 2 and 3, the spatial distributions of seasonal gravity wave E_p in the winter and summer are very similar to those seen in Faber et al. (2013) at June-July-August (JJA) and December- January-February (DJF). Higher gravity wave E_p values are seen in winter compared with the summer in extratropical areas (over the Andes and the Patagonian mountains) due to orographic and zonal wind effects. In the other global satellite, climatological studies of gravity waves such as AIRS, the same seasonal occurrence of gravity wave activities attributed to various sources have been linked to convection, orographic generation, wind shear, body forces, and frontal systems (Gong et al. 2012; Hoffmann et al. 2013). Figures 2 and 3 indicate that gravity wave E_p is higher in Southern Andes, as seen in previous studies in the winter (Yan et al. 2010; Faber et al. 2013).

In the tropics, there is a strong correlation between convections and tropopheric parameters, indicating that tropopause height appears in deep convection regions, as shown in Fig. 9 and Table 1. The results are consistent with the result of Gettelman et al. (2002); Randel and Jensen (2013). Although this correlation could be due to convective cooling of the tropopause or another factor, the former appears to be more likely. Figure 8, on the other hand, shows that in deep convection regions, the correlations between SGW E_p and PWV and temperature are significant, implying that tropopause parameter variability may be related to SGW activity. Randel and Jensen (2013) suggests that radiative forcing might be important for tropical tropopause which could be influenced by both deep convections and the SGWs generated by deep convection.

Our results in Figs. 10 and 11 over the Andes Mountain range agreed with (Khan and Jin 2016) who revealed the SGWs influence on the water vapour concentration in the stratosphere. Water vapour, CPT, and gravity wave E_p have a strong relationship with each other above the cold points, and water vapour rises with rising gravity wave E_p. SGWs created by mountains have effect on the mesoscale circulations by carrying energy and momentum from the lower troposphere to the lower and higher stratosphere and balancing their momentum and energy (Fritts and Alexander 2003). Additionally, it was claimed that gravity waves are generated primarily by topography, frontal activity, wind shear, jet stream, convection, and cyclones. Mountain waves are quasi-stationary and propagate vertically upwards, which shows that the North-South alignment could be favorable to the propagation of the mountain waves (Alexander et al. 2010). A consistent increase in the SGW activities is seen in the total mean SGW E_p percentage in Fig. 4 could be attributed to aiding mean zonal wind blowing eastward (Alexander et al. 2008; Faber et al. 2013).

The study analyzes and investigates the relationship between the SGW activities using the dry temperature profile to obtain the SGW Ep and the tropospheric parameters: TPH, CPH, and PWV. We instigate the correlation coefficients of SGW E_p independently with the PWV, TPH, and CPH. The SGW E_p climatology showed little or no evidence of gravity wave activities in the summer at mid-latitudes. There is also evidence of the wind effect in the tropical region, called the Northeast and Southeast trade winds, as the gravity waves appear more conspicuous at higher altitudes. Our result showed little or no gravity wave activity during winter in the tropical region at 30–40 km, which is an evidence of wave filtering. The gravity wave E_p increases in winter along with altitude over the Andes Mountain, which can be attributed to the increase in wind intensity, aiding the increase of the gravity waves activity. We observed that the gravity wave activities experience a slight reduction in the gravity wave E_p values in winter at the upper stratosphere (40–50 km). However, the reduction in the gravity wave E_p appears not strong enough to dissipate the wave. Finally, it was found that the gravity wave in winter and spring showed a consistent increase from the lower to the upper stratosphere.

Our result found that PWV is concentrated in the tropical region and mainly in the equatorial region in all seasons. The PWV is higher in the summer and lower in the winter. Most of the PWV is over the land, especially the Amazon rain forest. The western Andes showed no PWV due to the air movement over the Andes Mountains. The average PWV reaches a maximum value of 70 mm or more in tropical areas and decreases to nearly 0 mm in the extratropical region (mainly in the winter). Over the Andes at 30^◦S − 40^◦S and 70^◦W − 80^◦W, the gravity wave E_p in the stratosphere and PWV have an anti-correlation in winter. Also, at 20^◦S − 30^◦S, the PWV increases with a significant decrease in the gravity wave E_p at 70^◦W − 80^◦W. In the tropics, TPH and CPH are positively correlated with SGW E_p in all the season. During the winter, SGW activity above the Andes mountains increases, which decreases PWV defusing into the stratosphere. The TPH showed a correlation with SGW E_p at 20^◦N − 10^◦N and 10^◦S − 20^◦S in summer and spring. CPH mostly depicted negative or no correlation in all the seasons. Over the Andes in the summer and winter, TPH/CPH showed a negative/positive correlation with SGW E_p. It may be established that SGW activities affect the tropopause parameters. The vertical mixing of heat that occurs during the propagation and breaking of SGWs has an impact on the tropopause height either directly or indirectly. It could be concluded that SGW activities have an impact on changes in tropopause properties. In the tropics, both deep convections and SGWs excited correspondingly had an impact on the tropopause structure, however at higher latitudes the tropopause height displayed more fluctuation when GWs propagate from the troposphere to stratosphere.

Availability of data and materials

The data used in this study is exclusively provided by CDAAC and they were obtained from http://cdaac-www.cosmic.ucar.edu/cdaac.

Competing interests

The authors declare that there is no competing interests or state.

Funding

The Brazilian Ministry of Science, Technology, and Innovations (MCTI) and the Brazilian Space Agency (AEB), grant number 20VB.0009 and the Conselho Nacional de Desenvolvimento Cientıfico e Tecnol´ogico (CNPQ) with the process number 141373/2019 − 9.

Authors’ contributions

For research articles with several authors, a short paragraph specifying their individual contributions must be provided. The following statements should be used “Conceptualization, Ayorinde, T. T., Wrasse, C. M., and Takahashi H.; methodology, Ayorinde, T. T.; software, Ayorinde, T. T.; validation, Wrasse, C. M., and Takahashi H.; formal analysis, Ayorinde, T. T.; investigation, Ayorinde, T. T.; resources, CDAAC; data curation, Ayorinde, T. T.; writing—original draft preparation, Ayorinde, T. T.; writing— review and editing, Wrasse, C. M., Takahashi H., Figueiredo, C. A. O. B.; visualization, Barros D., Lomotey, S. O., Essien P. and Anderson B. V.; supervision, Wrasse, C. M., and Takahashi H.; project administration, Ayorinde, T. T.; funding acquisition, Wrasse, C. M.

Acknowledgments

The authors acknowledged CDAAC for providing the data. We also acknowledge the financial support provided by the Brazilian Ministry of Science, Technology, and Innovations (MCTI) and the Brazilian Space Agency (AEB) and the Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPQ).

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TTAManucsriptAbstract2.jpg

The Relationship between Stratospheric Gravity Wave Potential Energy and Tropospheric Parameters over South America inferred from COSMIC-2 and METOP Radio Occultation Measurements

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Methodology

Observation data

The Gravity Wave Potential Energy

Precipitable Water Vapour Content

Statistical Method

Results

Potential Energy Climatology

Seasonal Variation Of Sgw Potential Energy

Precipitable Water Vapour Content

Tropopause Parameters

Potential Energy Vs Tropospheric Parameters In The Tropics

Potential Energy Vs Tropospheric Parameters Over The Andes

Discussion

Conclusion

Declarations

References

Supplementary Files

Status:

Journal Publication

Version 1