On the Relationship Between Gravity Waves and Tropopause Height and Temperature Over the Globe Revealed by COSMIC Radio Occultation Measurements

atmosphere

Article On the Relationship between Gravity Waves and Tropopause Height and Temperature over the Globe Revealed by COSMIC Radio Occultation Measurements

Daocheng Yu 1, Xiaohua Xu 1,2,*, Jia Luo 1,3,* and Juan Li 1 1 School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China; [email protected] (D.Y.); [email protected] (J.L.) 2 Collaborative Innovation Center for Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China 3 Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, 129 Luoyu Road, Wuhan 430079, China * Correspondence: [email protected] (X.X.); [email protected] (J.L.); Tel.: +86-27-68758520 (X.X.); +86-27-68778531 (J.L.) Received: 4 January 2019; Accepted: 6 February 2019; Published: 12 February 2019

Abstract: In this study, the relationship between gravity wave (GW) potential energy (Ep) and the tropopause height and temperature over the globe was investigated using COSMIC radio occultation (RO) dry temperature profiles during September 2006 to May 2013. The monthly means of GW Ep with a vertical resolution of 1 km and tropopause parameters were calculated for each 5◦ × 5◦ longitude-latitude grid. The correlation coefficients between Ep values at different altitudes and the tropopause height and temperature were calculated accordingly in each grid. It was found that at middle and high latitudes, GW Ep over the altitude range from lapse rate tropopause (LRT) to several km above had a significantly positive/negative correlation with LRT height (LRT-H)/ LRT temperature (LRT-T) and the peak correlation coefficients were determined over the altitudes of 10–14 km with distinct zonal distribution characteristics. While in the tropics, the distributions of the statistically significant correlation coefficients between GW Ep and LRT/cold point tropopause (CPT) parameters were dispersive and the peak correlation were are calculated over the altitudes of 14–38 km. At middle and high latitudes, the temporal variations of the monthly means and the monthly anomalies of the LRT parameters and GW Ep over the altitude of 13 km showed that LRT-H/LRT-T increases/decreases with the increase of Ep, which indicates that LRT was lifted and became cooler when GWs propagated from the troposphere to the stratosphere. In the tropical regions, statistically significant positive/negative correlations exist between GW Ep over the altitude of 17–19 km and LRT-H/LRT-T where deep convections occur and on the other hand, strong correlations exist between convections and the tropopause parameters in most seasons, which indicates that low and cold tropopause appears in deep convection regions. Thus, in the tropics, both deep convections and GWs excited accordingly have impacts on the tropopause structure.

Keywords: gravity waves; potential energy; tropopause; COSMIC

1. Introduction The tropopause is the transition layer between the upper troposphere and the lower stratosphere, which are distinct from one another in vertical mixing timescales, static stabilities, trace constituents, and thermal balance [1]. The variations of the tropopause, which are the responses to any changes in the physical, chemical, and thermal characteristics of the two regions, are linked closely to the stratosphere-troposphere exchange as well as climate variability and change [2–4].

Atmosphere 2019, 10, 75; doi:10.3390/atmos10020075 www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, 75 2 of 15

Different definitions and concepts exist for the determination of the tropopause [5]. The thermal tropopause, which is also called the lapse rate tropopause (LRT), was defined by the World Meteorological Organization (WMO) as the lowest level at which the lapse rate decreases to 2 K·km−1 or less, provided that the average lapse rate between this level and all higher levels within 2 km does not exceed 2 K·km−1. LRT can be obtained from vertical profiles of atmospheric temperature and are applied globally, both in the tropics and in the extra-tropics [6]. The cold point tropopause (CPT), which is usually applied in the tropics, is the level of the temperature minimum as the temperature decreases with height from the surface up to certain altitude and then increases at higher altitudes in the stratosphere [7]. The CPT is an import indicator of stratosphere-troposphere coupling and exchange [2]. The variations of the tropopause height and temperature show sub-seasonal, seasonal and inter-annual variabilities [8–12] and are closely related to atmospheric waves [8,10,13–16], among which the effects of Gravity waves (GWs) [10,17,18] are significant. Gravity waves (GWs) are usually excited in the troposphere and propagate upward, transferring energy, momentum, and water vapor and depositing vertical mixing of heat [19], which affects tropopause temperature directly or indirectly [18]. GW activities play important roles in the global circulation and the temperature and constituent structures, such as water vapor, ozone concentrations, and other chemical constituents [20,21]. Although there are a number of works on the variations of the structure of tropopause [22–25] and GW activities [21,26,27], studies on the relationship between GWs and the tropopause are meager. Reference [10] investigated the structure and variability of temperature in the tropical upper troposphere and lower stratosphere (UTLS) using the Global Positioning System Meteorology (GPS/MET) data during April 1995 to February 1997. They found that much of the sub-seasonal variability in CPT temperature and height appeared to be related to GWs or Kelvin waves. Using ~114 h mesosphere-stratosphere-troposphere (MST) radar data at Gadanki, references [17,28] studied the wind disturbances, tropopause height, and inertial gravity wave (IGW) associated with a tropical depression passage, and they found that the tropopause height and IGW had similar periodograms, which clearly showed that the tropopause height was modulated by inertial GW. Reference [18] investigated the relationship between GWs and the temperature and height of CPT and water vapor over Tibet using the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) Radio Occultation (RO) temperature data during June 2006 to February 2014. Their results showed that GW potential energy (Ep), CPT temperature, and water vapor had good correlation with each other and that GWs affected the CPT temperature and water vapor concentration in the stratosphere. These works about the relationship between GWs and tropopause were mainly focused on certain geographic regions. The effects of GW activity on the tropopause structure over the globe needs further investigation. The COSMIC RO temperature profiles with high vertical resolution, high accuracy, long-term stability, and global coverage are ideal data sources to study the tropopause structures [4,25,29] and are applicable to analyze the global characteristics of GW activity [21,30,31]. In this study, we used COSMIC level 2 dry temperature (atmPrf) profiles during September 2006 to May 2013 to investigate the relationship between GWs and the tropopause height and temperature over the globe. Data and methods are introduced in Section2. The results and analyses are presented in Section3. Section4 discusses the possible underlying mechanism. Finally, conclusions are given in Section5.

2. Experiments

2.1. COSMIC RO Data The COSMIC dry temperature profile is from near the ground up to 60 km with a good vertical resolution (~1 km); however, due to the a priori information used in the inversion process and the residual ionospheric effects, it typically exhibits increased noise at upper levels [27,32]. Although COSMIC RO dry temperature data is used to analyze GW activity up to 50 km, it is indicated that Atmosphere 2019, 10, 75 3 of 15 the upper height level of the COSMIC temperature profiles most appropriate for GW study is below 40 km [27]. The vertical wavelengths of GW derived from COSMIC temperature are equal or greater than 2 km [32]. This work uses COSMIC post-processed level 2 dry temperature profiles (atmPrf files) of the version 2010.2640 from September 2006 to May 2013 produced by the COSMIC Data Analysis and Archive Center (CDAAC) of the University Corporation for Atmospheric Research (UCAR) to analyze the relationship between GWs and the tropopause.

2.2. GW Ep The potential energy (Ep) can well represent the feature of GW and is given by:

1 g 2 T0 2 Ep = (1) 2 N T

g ∂T g N2 = + (2) T ∂z cP where g is the gravitational acceleration, N is the Brunt-Väisälä frequency, cp is the isobaric heating capacity, z is the height, and T, and T0 is the background temperature and the temperature perturbations caused by GWs, respectively. It is important to separate T and T0 from the raw COSMIC 0 temperature (T). The accurate Ep is based on the extraction of T , which is given by:

T0 = T − T (3)

We extracted Ep values from COSMIC RO temperature profiles following closely the method used by references [21,32]. At first, the daily COSMIC temperature profiles between 8 km and 38 km are gridded to 10◦ × 15◦ latitude and longitude resolution with a vertical resolution of 0.2 km, based on which the mean temperature of each grid is calculated for each height level. Then, the S-transform was used for each latitude and altitude, obtaining the zonal wave number 0–6 which represents the background temperature for zonal mean temperature. The S-transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum [33]. In the next step, this background temperature was interpolated back to the positions of raw COSMIC RO profiles and subtracted from T using Equation (3) to get the temperature perturbations T0. Finally, GW Ep was calculated by Equations (1) and (2). To further analyze the relationship between GW Ep and tropopause parameters, daily Ep values were binned and averaged in 5◦ × 5◦ longitude–latitude grid cells with a vertical resolution of 1 km. Following the above procedure, reference [34] presented an example of calculating the temperature perturbation profile and the Ep profile corresponding to a COSMIC RO dry temperature profile. The temperature perturbation profile in Figure1b of [ 34] presented a wavelike structure around 0 K, which is consistent with reference [21]. References [34,35] further investigated the seasonal and interannual variations of the global stratospheric GW activities.

2.3. LRT and CPT Temperature and Height COSMIC RO atmPrf products provided by CDAAC include the tropopause parameters, such as the temperature and height of LRT and CPT. Reference [36] reported that the LRT temperature and height from COSMIC RO provided by CDAAC are consistent with those derived from the high-resolution Modern-Era Retrospective Analysis for Research Application (MERRA). In this work, the LRT and CPT temperature and height, which were obtained directly from the atmPrf ﬁles, were binned into 5◦ × 5◦ longitude-latitude grids. The time-latitude plots of the monthly means of LRT height (LRT-H), LRT temperature (LRT-T), CPT height (CPT-H), and CPT temperature (CPT-T) during September 2006 to May 2013 are shown in Figure1. Because the CPT parameters are Atmosphere 2019, 10, 75 4 of 15

Atmosphere 2019, 10, x FOR PEER REVIEW 4 of 15 most applicable in the tropics [37], the variations of CPT-H and CPT-T are only shown for the latitude parameters are most applicable in the tropics [37], the variations of CPT-H and CPT-T are only region of 30◦ S–30◦ N. shown for the latitude region of 30° S–30° N.

Figure 1. Time-latitudeTime-latitude plots of monthly means means of of (a) (a) lapse lapse rate rate tropopause tropopause height height (LRT-H), (LRT-H), (b) (b) lapse lapse raterate tropopausetropopause temperaturetemperature (LRT-T),(LRT-T), ((c)c) cold point tropopause tropopause height height (CPT-H), (CPT-H), and and (d) (d )cold cold point point tropopause temperature (CPT-T).tropopause temperature (CPT-T). It can be seen from Figure1a that the LRT-H is around 16 km in the tropics, while it decreases to It can be seen from Figure 1a that the LRT-H is around 16 km in the tropics, while it decreases to 9 km in the polar regions, which is consistent with reference [23]. In the tropics, the LRT-H presents 9 km in the polar regions, which is consistent with reference [23]. In the tropics, the LRT-H presents signiﬁcant seasonal variations with higher LRT in boreal winter and lower one in boreal summer. significant seasonal variations with higher LRT in boreal winter and lower one in boreal summer. While in middle and high latitudes, the seasonal variation of LRT-H is opposite. Figure1b shows that While in middle and high latitudes, the seasonal variation of LRT-H is opposite. Figure 1b shows the LRT-T increases from the tropics to the poles. In the tropics and in the middle and high latitudes that the LRT-T increases from the tropics to the poles. In the tropics and in the middle and high of the Northern Hemisphere (NH), the LRT-T is higher in boreal summer and lower in boreal winter; latitudes of the Northern Hemisphere (NH), the LRT-T is higher in boreal summer and lower in while in the middle and high latitudes of the Southern Hemisphere (SH), it presents the opposite boreal winter; while in the middle and high latitudes of the Southern Hemisphere (SH), it presents seasonal variation. The comparison between Figure1a,b shows that LRT is higher and colder in the the opposite seasonal variation. The comparison between Figure 1a,b shows that LRT is higher and tropics and lower and warmer at middle and high latitudes. colder in the tropics and lower and warmer at middle and high latitudes. From Figure1c, it can be seen that the CPT-H in the low latitudes is between 16–18 km and From Figure 1c, it can be seen that the CPT-H in the low latitudes is between 16-18 km and presents the seasonal variation with higher and lower values in boreal winter and summer, respectively. presents the seasonal variation with higher and lower values in boreal winter and summer, From Figure1d, it is evident that the CPT-T is higher in boreal summer and lower in winter, which is respectively. From Figure 1d, it is evident that the CPT-T is higher in boreal summer and lower in opposite to the seasonal variation of the CPT-H. So the CPT is higher and colder in boreal winter and winter, which is opposite to the seasonal variation of the CPT-H. So the CPT is higher and colder in lower and warmer in summer, which is consistent with reference [38]. In the tropics, the parameters of boreal winter and lower and warmer in summer, which is consistent with reference [38]. In the the LRT and CPT are close to each other and present similar seasonal variation patterns. tropics, the parameters of the LRT and CPT are close to each other and present similar seasonal The characteristics of the temporal and spatial variability of the LRT and CPT heights and variation patterns. temperatures shown in Figure1 are generally consistent with those of the available literatures. Thus, The characteristics of the temporal and spatial variability of the LRT and CPT heights and the tropopause parameters provided by CDAAC is reliable and can be applied to this study. temperatures shown in Figure 1 are generally consistent with those of the available literatures. Thus, the2.4. tropopause Statistical Method parameters provided by CDAAC is reliable and can be applied to this study.

2.4. StatisticalThe monthly Method means of GW Ep with a vertical resolution of 1 km and tropopause parameters were calculated for each 5◦ × 5◦ longitude-latitude grid. The annual cycle of Ep at each height layer The monthly means of GW Ep with a vertical resolution of 1 km and tropopause parameters and the tropopause heights and temperatures were subtracted from the monthly means to get the were calculated for each 5° × 5° longitude-latitude grid. The annual cycle of Ep at each height layer corresponding monthly anomalies, as shown by equation (4): and the tropopause heights and temperatures were subtracted from the monthly means to get the corresponding monthly anomalies, as shown by equation1 n (4): ∆Fi,j = Fi,j − ∑ Fi,j (4) n1i=n1 Δ=F FF − ij,, ij ij , (4) n = where n is the number of years. i = 1, 2, ...... n is the ithi 1 year and j = 1, 2, ...... 12 is the jth month = =…… Wherein one year.n is theFi ,numberj and ∆F ofi,j years.represents in1,2,...... the monthly is the meani th year and and the monthlyj 1, 2, anomaly 12 is the of j Epth atmonth certain in Δ one year. Fij, and Fij, represents the monthly mean and the monthly anomaly of Ep at certain height layer or of tropopause parameters for the j th month in the i th year, respectively. In each

Atmosphere 2019, 10, x FOR PEER REVIEW 5 of 15 grid, the correlation coefficient between GW Ep for certain height interval and the tropopause parameters was calculated accordingly.

3. Results

3.1. Calculation Example GW Ep and the LRT-H at a certain grid (50° N, 25° W) is taken as an example in this section. The time series of the monthly means and the monthly anomalies of GW Ep at the altitude of 13 km and Atmosphere 2019, 10, 75 5 of 15 the LRT-H over this grid are shown in Figure 2. The monthly anomalies were calculated by the statistical method presented in Section 2.4. heightFrom layer Figure or of tropopause2a, it can be parameters seen that the for Ep the monthlyjth month means in the (blueith year, solid respectively. line) at 13 km In eachover grid,this thegrid correlation fluctuated coefﬁcientmainly between between 2.5 GWJ·kg− Ep1 and for 10 certain J·kg−1, height while intervalLRT-H monthly and the tropopausemeans (red dotted parameters line) wasoscillated calculated mainly accordingly. between 10 km and 12 km. The temporal variation pattern of Ep was similar to that of LRT-H, which means that high values of Ep correspond to high values of LRT-H and vice versa. 3.The Results Pearson correlation coefficient between the two lines shown in Figure 2a is 0.62, which passes through the significance test of the confidence level of 99%. Figure 2b shows that Ep monthly 3.1. Calculation Example anomalies fluctuate between −2 J·kg−1 and 4 J·kg−1, while LRT-H monthly anomalies fluctuated betweenGW − Ep0.5 and km theand LRT-H 0.5 km. at The a certain Pearson grid correlation (50◦ N, 25 coefficient◦ W) is taken between as an examplethe two lines in this shown section. in TheFigure time 2b series was 0.39, of the which monthly also means passes and through the monthly the significance anomalies test of of GW the Ep confidence at the altitude level of of 13 99%. km andThe thecorrelation LRT-H over coefficient this grid between are shown the in monthly Figure2 .anomalies The monthly was anomalies smaller than were calculatedthat between by thethe statisticalmonthly means. method presented in Section 2.4.

Figure 2. (a) The monthly means and (b) the monthly anomalies time series of gravity wave potential energyFigure 2. (GW (a) Ep)The atmonthly 13 km andmeans the and LRT-H (b) the over monthly the grid anomalies (50◦ N, 25 time◦ W). series of gravity wave potential energy (GW Ep) at 13 km and the LRT-H over the grid (50° N, 25° W). From Figure2a, it can be seen that the Ep monthly means (blue solid line) at 13 km over this grid3.2. The fluctuated Vertical Structure mainly between of the Correlation 2.5 J·kg− Between1 and 10 Ep J·kg and−1 Tropopause, while LRT-H Parameters monthly means (red dotted line) oscillated mainly between 10 km and 12 km. The temporal variation pattern of Ep was similar To investigate the vertical structure of the correlation between Ep and LRT and CPT parameters, to that of LRT-H, which means that high values of Ep correspond to high values of LRT-H and vice we gave the longitude-altitude cross sections of Pearson correlation coefficients between the time versa. The Pearson correlation coefficient between the two lines shown in Figure2a is 0.62, which series of Ep and those of LRT-H (LRT-T) and CPT-H (CPT-T) over different latitudes in Figure 3 and passes through the significance test of the confidence level of 99%. Figure2b shows that Ep monthly Figure 4, respectively. anomalies fluctuate between −2 J·kg−1 and 4 J·kg−1, while LRT-H monthly anomalies fluctuated Figure 3 shows the longitude-altitude cross sections of the Pearson correlation coefficients between −0.5 km and 0.5 km. The Pearson correlation coefficient between the two lines shown between Ep and LRT-H and between Ep and LRT-T at 70° N, 0°, and 50° S, which can represent high, in Figure2b was 0.39, which also passes through the significance test of the confidence level of low, and middle latitude, respectively. The comparisons between the subfigures in Figure 3 show 99%. The correlation coefficient between the monthly anomalies was smaller than that between the that the vertical distributions of the correlation coefficients between GW Ep and LRT-H vary greatly monthly means. at different latitudes. It is shown in Figure 3a that, at 70° N, the statistically significant Pearson 3.2.correlation The Vertical coefficients Structure between of the Correlation Ep values Between and EpLRT-H and Tropopauseare mostly Parameters positive and are large at the altitudes between the height of LRT and 14 km, while the correlation coefficients of Ep values and LRT-HTo were investigate small and the verticalnot statistically structure significant of the correlation below the between LRT-H Ep or andabove LRT 14 and km. CPT parameters, we gave the longitude-altitude cross sections of Pearson correlation coefficients between the time series of Ep and those of LRT-H (LRT-T) and CPT-H (CPT-T) over different latitudes in Figures3 and4, respectively. Figure3 shows the longitude-altitude cross sections of the Pearson correlation coefficients between Ep and LRT-H and between Ep and LRT-T at 70◦ N, 0◦, and 50◦ S, which can represent high, low, and middle latitude, respectively. The comparisons between the subfigures in Figure3 show that the vertical distributions of the correlation coefficients between GW Ep and LRT-H vary greatly at different latitudes. It is shown in Figure3a that, at 70 ◦ N, the statistically significant Pearson correlation coefficients between Ep values and LRT-H are mostly positive and are large at the altitudes between Atmosphere 2019, 10, 75 6 of 15 the height of LRT and 14 km, while the correlation coefficients of Ep values and LRT-H were small and notAtmosphere statistically 2019, 10, significant x FOR PEER belowREVIEW the LRT-H or above 14 km. 6 of 15 At the equator, the distributions of the correlation coefficients that are statistically significant are dispersed,At the as equator, shown inthe Figure distributions3b. At 50 ◦ofS, the Ep correlation mostly has acoefficients significant that positive are correlationstatistically with significant LRT-H betweenare dispersed, the height as shown of LRT in andFigure 14 km,3b. At as shown50° S, Ep in Figuremostly3 c.has a significant positive correlation with LRT-H between the height of LRT and 14 km, as shown in Figure 3c.

Figure 3. Longitude-altitude cross sections of Pearson correlation coefficients coefficients between Ep and LRT-H ◦ ◦ ◦ (left column), and and between between Ep Ep and and LRT-T LRT-T (right (right column) column) at at(a,d (a), d70°) 70 N, (N,b,e ()b 0°,e) and 0 and(c,f) (50°c,f) S. 50 TheS. Theregions regions where where the correlation the correlation coefficients coefficients pass pass throug throughh the thesignificance significance test test of the of the confidence confidence level level of of95% 95% are are marked marked with with crosses. crosses. The The LRT LRT height height is represented is represented by by black black dotted dotted lines. lines (a (–af–)f ).

Figure3 3d–fd–f showshow thatthat thethe signsign ofof thethe correlationcorrelation coefficientscoefficients betweenbetween EpEp andand LRT-TLRT-T isis generallygenerally opposite toto that that between between Ep andEp and LRT-H. LRT-H. Negative Negative correlation correlation coefficients coefficients that are statisticallythat are statistically significant ◦ existsignificant near andexist above near theand LRT above at 70the N,LRT as at shown 70° N, in as Figure shown3d, in and Figure in the 3d, height and in range the betweenheight range the ◦ LRTbetween and 14the km LRT at and 50 S,14 as km shown at 50° in S, Figure as shown3f. Figure in Figure3e shows 3f. Figure that at 3e the shows equator, that the at distributionsthe equator, the of thedistributions correlation of coefficients the correlation that coefficients are statistically that significantare statistically are dispersed. significant are dispersed. From the above analyses, it can be seen thatthat atat middlemiddle andand highhigh latitudes,latitudes, concentratedconcentrated distributions ofof statisticallystatistically significant significant positive positive (negative) (negative) correlation correlation coefficients coefficients between between GW GW Ep and Ep LRT-Hand LRT-H (LRT-T) (LRT-T) are generally are generally calculated calculated in the height in the range height between range thebetween LRT and the severalLRT and kilometers several above.kilometers While above. in the While tropics, in the the tropics, distributions the distri ofbutions the correlation of the correlation coefficients coefficients between Epbetween and LRT Ep parametersand LRT parameters that are statistically that are statistically significant significant are dispersed. are dispersed. Figure 4 shows the longitude-altitude cross sections of the Pearson correlation coefficients between Ep and CPT-H and between Ep and CPT-T over the latitudes of 30° N, 0° and 30° S. It can be seen from Figure 4 that at all the three latitudes, the sign of the correlation coefficients between Ep and CPT-H was generally opposite to that between Ep and CPT-T, and the distributions of the correlation coefficients that are statistically significant were not concentrated. Both Figure 3 and

Atmosphere 2019, 10, 75 7 of 15

Figure4 shows the longitude-altitude cross sections of the Pearson correlation coefficients between Ep and CPT-H and between Ep and CPT-T over the latitudes of 30◦ N, 0◦ and 30◦ S. It can be seen from Figure4 that at all the three latitudes, the sign of the correlation coefficients between Ep and CPT-H was generally opposite to that between Ep and CPT-T, and the distributions of the correlation coefficientsAtmosphere 2019 that, 10, x are FOR statistically PEER REVIEW significant were not concentrated. Both Figures3 and4 show7 that of 15 in the tropics, the distributions of the statistically significant correlation coefficients between Ep and tropopauseFigure 4 show parameters that in are the dispersed. tropics, the distributions of the statistically significant correlation coefficients between Ep and tropopause parameters are dispersed.

Figure 4. Longitude-altitude cross sections of Pearson correlation coefficientscoefficients between Ep and CPT-H ◦ ◦ ◦ (left(left column), and and between between Ep Ep and and CPT-T CPT-T (right (right column) column) at at(a,d (a), d30°) 30 N, N,(b,e ()b 0°,,e) and 0 , and(c,f) (30°c,f) S. 30 TheS. Theregions regions where where the correlation the correlation coefficients coefficients pass pass throug throughh the thesignificance significance test test of the of the confidence confidence level level of of95% 95% are are marked marked with with crosses. crosses. The The CPT CPT height height is represented is represented by by black black dotted dotted lines. lines (a (–af–)f ). 3.3. The Horizontal Structures of the Correlations Between Ep and Tropopause Parameters 3.3. The Horizontal Structures of the Correlations Between Ep and Tropopause Parameters The horizontal structures of the correlations between GW Ep values and the tropopause The horizontal structures of the correlations between GW Ep values and the tropopause parameters are investigated in this section. Figure3 reveals that over different latitudes, the correlation parameters are investigated in this section. Figure 3 reveals that over different latitudes, the coefficients between Ep values and LRT-H /LRT-T that are statistically significant are generally correlation coefficients between Ep values and LRT-H /LRT-T that are statistically significant are positive/negative. Figure5 further shows the distributions of the peak positive/negative correlation generally positive/negative. Figure 5 further shows the distributions of the peak positive/negative coefficients between Ep values and LRT-H /LRT-T and the corresponding heights where these peak correlation coefficients between Ep values and LRT-H /LRT-T and the corresponding heights where correlation coefficients were calculated based on the 5◦ × 5◦ longitude-latitude grids. these peak correlation coefficients were calculated based on the 5° × 5° longitude-latitude grids. From Figure 5a,b, it can be seen that in the tropics, the peak positive correlation coefficients between GW Ep values and LRT-H are generally smaller than 0.4, which are calculated at the heights between 14 km and 38 km. The distributions of both the peak correlation coefficients and the corresponding heights were dispersed. In the middle and high latitudes, the latitudinal distribution of the peak correlation coefficients between GW Ep values and LRT-H were distinct. Over the latitudes 45° N–75° N, most of the peak correlation coefficients between GW Ep values and LRT-H were between 0.5 and 0.8, and the corresponding heights were mainly located above the LRT at 11 km to 14 km. While over 45° S–75° S latitudes, most of the peak correlation coefficients were around 0.6, and the corresponding height were also mainly located above the LRT. Compared with the same

Atmosphere 2019, 10, x FOR PEER REVIEW 8 of 15 latitudes in the NH, the peak positive correlation coefficients between GW Ep values and LRT-H over the 45° S–75° S latitudes were smaller, and the latitude zone with distinct peak correlation coefficients had a poorer continuity and a narrower width. Figure 5a,b show that the distributions of the peak correlation coefficients between Ep and LRT-H in the NH and SH were not symmetrical, while the distributions of the corresponding heights were basically symmetrical. Figure 5c,d show the distributions of the peak negative correlation coefficients between Ep and LRT-T and the corresponding heights where these peak coefficients were calculated. The horizontal distributions of the peak negative correlation coefficients between Ep values and LRT-T were similar to those of the peak positive correlation coefficients between Ep values and LRT-H. In the tropics, the peak negative correlation coefficients between Ep values and LRT-T were between −0.2 and −0.4 with the corresponding heights mainly at 14 km to 38 km. Over the 45°–75° latitudes in the NH and

SH,Atmosphere zonal2019 regions, 10, 75 existed where the peak negative correlation coefficients were between −0.48 and of 15 −0.6 and the corresponding heights were over the LRT at 11 km to 14 km.

Figure 5. The peak positive/negative correlati correlationon coefficients coefﬁcients between between Ep Ep and and (a) (a )LRT-H, LRT-H, (c) (c )LRT-T. LRT-T. The height height at at which which these these peak peak corre correlationlation coefficients coefﬁcients between between Ep Epand and (b) (LRT-H,b) LRT-H, (d) LRT-T (d) LRT-T are calculated.are calculated.

ItFrom can Figurebe seen5a,b, from it canFigure be seen5 that that at inmiddle the tropics, and high the peaklatitudes, positive the correlationpeak positive/negative coefficients correlationbetween GW coefficients Ep values between and LRT-H GW Ep are and generally LRT-H/LRT-T smaller were than 0.4,calculated which above are calculated the LRT at the altitudeheights betweenrange of 14 11 km km and to 38 14 km. km, The while distributions in the tropics, of both the peakpeak correlationcorrelation coefficients coefficients and were the distributedcorresponding dispersively heights were at the dispersed. altitude In range the middle between and 14 high km latitudes, and 38 km, the latitudinalwhich is also distribution shown in of Figurethe peak 3 and correlation Figure 4. coefficients between GW Ep values and LRT-H were distinct. Over the latitudes 45◦ N–75In the◦ N, following most of thepart peak of this correlation study, we coefficients will focus between on the GWcorrelations Ep values between and LRT-H GW wereEp at between certain altitude0.5 and 0.8,ranges and near the correspondingand above the heights tropopause were mainlyand the located tropopause above parameters the LRT at 11over km the to 14globe. km. ConsideringWhile over 45 that◦ S–75 the◦ heightS latitudes, of LRT most decreases of the peakgradua correlationlly from the coefficients equator to were the aroundpoles, this 0.6, altitude and the rangecorresponding was chosen height as 13 were km at also middle mainly and located high latitudes above the and LRT. 17 km–19 Compared km in with the tropics. the same Figure latitudes 6a,b showsin the NH,the global the peak distributions positive correlation of the correlation coefficients coefficients between between GW Ep valuesEp values and and LRT-H LRT-H, over and the those45◦ S–75 between◦ S latitudes Ep and were LRT-T, smaller, respectively. and the latitudeThe contour zone plots with distinctof the means peak correlationof outgoing coefficients longwave radiationhad a poorer (OLR) continuity during andSeptember a narrower 2006-May width. Figure2013 are5a,b also show shown that the in distributionsthe tropics ofin thethe peaktwo subfigures.correlation coefficientsOLR data betweenis downloaded Ep and LRT-H from in the the NHClimate and SHDiagnostics were not symmetrical,Center Website while the(at http://www.cdc.noaa.gov).distributions of the corresponding The regions heights where were basicallyOLR < symmetrical.240 W/m2 are where deep convections occurred.Figure 5c,d show the distributions of the peak negative correlation coefficients between Ep and LRT-T and the corresponding heights where these peak coefficients were calculated. The horizontal distributions of the peak negative correlation coefficients between Ep values and LRT-T were similar to those of the peak positive correlation coefficients between Ep values and LRT-H. In the tropics, the peak negative correlation coefficients between Ep values and LRT-T were between −0.2 and −0.4 with the corresponding heights mainly at 14 km to 38 km. Over the 45◦–75◦ latitudes in the NH and SH, zonal regions existed where the peak negative correlation coefficients were between −0.4 and −0.6 and the corresponding heights were over the LRT at 11 km to 14 km. It can be seen from Figure5 that at middle and high latitudes, the peak positive/negative correlation coefficients between GW Ep and LRT-H/LRT-T were calculated above the LRT at the altitude range of 11 km to 14 km, while in the tropics, the peak correlation coefficients were distributed dispersively at the altitude range between 14 km and 38 km, which is also shown in Figures3 and4. In the following part of this study, we will focus on the correlations between GW Ep at certain altitude ranges near and above the tropopause and the tropopause parameters over the globe. Considering that the height of LRT decreases gradually from the equator to the poles, this altitude range Atmosphere 2019, 10, 75 9 of 15 was chosen as 13 km at middle and high latitudes and 17 km–19 km in the tropics. Figure6a,b shows the global distributions of the correlation coefficients between Ep values and LRT-H, and those between Ep and LRT-T, respectively. The contour plots of the means of outgoing longwave radiation (OLR) during September 2006–May 2013 are also shown in the tropics in the two subfigures. OLR data is downloaded from the Climate Diagnostics Center Website (at http://www.cdc.noaa.gov). The regions Atmosphere 2019, 10, x FOR PEER REVIEW 9 of 15 where OLR < 240 W/m2 are where deep convections occurred.

Figure 6. The global distribution of the correlation coefficients between Ep and (a) LRT-H, and (b) LRT-T. Figure 6. The global distribution of the correlation coefficients between Ep and (a) LRT-H, and (b) The height layer between 30◦ S–30◦ N is 17–19 km, and in middle and high latitudes is 13 km. The red LRT-T. The height layer between 30° S–30° N is 17–19 km, and in middle and high latitudes is 13 km. solid line and the red dashed line represents OLR = 240 W/m2 and OLR = 220 W/m2, respectively. The red solid line and the red dashed line represents OLR = 240 W/m2 and OLR = 220 W/m2, The regions where the correlation coefficients pass through the significance test of the confidence level respectively. The regions where the correlation coefficients pass through the significance test of the of 95% are marked with crosses. confidence level of 95% are marked with crosses. Figure6 shows that the statistically significant correlation coefficients between Ep and LRT Figure 6 shows that the statistically significant correlation coefficients between Ep and LRT parameters present distinct latitudinal distributions at middle and high latitudes, especially between parameters present distinct latitudinal distributions at middle and high latitudes, especially between 45◦ N–75◦ N and 45◦ S–75◦ S. From Figure6a, it is evident that GW Ep generally has a positive 45° N–75° N and 45° S–75° S. From Figure 6a, it is evident that GW Ep generally has a positive correlation with LRT-H over the globe. At the latitudes of 45◦ N–75◦ N and 45◦ S–75◦ S, the magnitudes correlation with LRT-H over the globe. At the latitudes of 45° N–75° N and 45° S–75° S, the of the correlation coefficients are between 0.3 to 0.6 over the zonal regions where the correlation magnitudes of the correlation coefficients are between 0.3 to 0.6 over the zonal regions where the coefficients are statistically significant. While in the tropics, the correlation coefficients between GW correlation coefficients are statistically significant. While in the tropics, the correlation coefficients Ep and LRT-H are smaller, which is 0.2–0.3, and the regions where the correlation coefficients pass between GW Ep and LRT-H are smaller, which is 0.2–0.3, and the regions where the correlation through the significance test of the confidence level of 95% are where deep convections occur. In the coefficients pass through the significance test of the confidence level of 95% are where deep tropics, convection is a main source of GW [26,34], and Ep has a significant correlation with LRT-H convections occur. In the tropics, convection is a main source of GW [26,34], and Ep has a significant over the regions where deep convections occur, which to some extent indicates that the tropopause correlation with LRT-H over the regions where deep convections occur, which to some extent structure is affected by the convections [39]. indicates that the tropopause structure is affected by the convections [39]. The signs of the correlation coefficients between Ep values and LRT-T shown in Figure6b were The signs of the correlation coefficients between Ep values and LRT-T shown in Figure 6b were opposite to those between Ep values and LRT-H, as shown in Figure6a. At middle and high latitudes, opposite to those between Ep values and LRT-H, as shown in Figure 6a. At middle and high the statistically significant negative correlation coefficients between Ep values and LRT-T showed latitudes, the statistically significant negative correlation coefficients between Ep values and LRT-T distinct latitudinal distributions, while in the tropics, the statistically significant negative correlation showed distinct latitudinal distributions, while in the tropics, the statistically significant negative coefficients between Ep values and LRT-T were mainly concentrated in the regions where deep correlation coefficients between Ep values and LRT-T were mainly concentrated in the regions convections occur. where deep convections occur. Figure7 shows the temporal variations of the monthly means and the monthly anomalies of GW Figure 7 shows the temporal variations of the monthly means and the monthly anomalies of Ep at 13 km and the LRT parameters at the latitudes of 50◦ N and 50◦ S. From Figure7a, it can be GW Ep at 13 km and the LRT parameters at the latitudes of 50° N and 50° S. From Figure 7a, it can be seen that at 50◦ N, the monthly means of both GW Ep and LRT-H show the same annual cycle with seen that at 50° N, the monthly means of both GW Ep and LRT-H show the same annual cycle with the maximum/minimum values calculated during boreal summer/winter. Although some studies the maximum/minimum values calculated during boreal summer/winter. Although some studies indicated that GW Ep usually became larger in boreal winter and smaller in boreal summer in lower indicated that GW Ep usually became larger in boreal winter and smaller in boreal summer in lower stratosphere at middle and high latitudes using RO data [26,35,40,41], the seasonal cycle of GW Ep stratosphere at middle and high latitudes using RO data [26,35,40,41], the seasonal cycle of GW Ep over 20 km were investigated in these studies. over 20 km were investigated in these studies. Figure 7a reveals that different from the seasonal variation characteristics of GW Ep over 20 km, the GW Ep near and over the tropopause was larger in boreal summer and smaller in boreal winter, which had a positive correlation with the seasonal variation of LRT-H with a statistically significant correlation coefficient of 0.9. Figure 7b shows that the variation pattern of the monthly anomalies of GW Ep at 13 km was similar to that of the LRT-H with a correlation coefficient of 0.61, which passed through the significance test of the confidence level of 99%. The temporal variations of the monthly means and the monthly anomalies of Ep and LRT-T at 13 km over the latitude 50° S are shown in Figure 7c,d. The seasonal cycle of GW activity was negatively correlated with that of LRT-T with a correlation coefficient of −0.84. The temporal variations of the monthly anomalies of Ep values were also negatively correlated with those of

Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 15

AtmosphereLRT-T with2019 ,a10 correlation, 75 coefficient of −0.37, which passed through the significance test of10 ofthe 15 confidence level of 99%.

Figure 7. (a) The monthly means and (b) the monthly anomalies time series of GW Ep at 13 km and Figure 7. (a) The monthly means and (b) the monthly anomalies time series of GW Ep at 13 km and the LRT-H at 50◦ N. (c) The monthly means and (d) the monthly anomalies time series of GW Ep at the LRT-H at 50° N. (c) The monthly means and (d) the monthly anomalies time series of GW Ep at 13 km and the LRT-T at 50◦ S. 13 km and the LRT-T at 50° S. Figure7a reveals that different from the seasonal variation characteristics of GW Ep over 20 km, 3.4.the GWThe Relationship Ep near and Between over the Convection tropopause and was Tropopause larger in in boreal the Tropics summer and smaller in boreal winter, whichIt hadhas abeen positive noticed correlation that the withtropical the seasonaltropopause variation is not only of LRT-H related with to aatmospheric statistically significantwaves but alsocorrelation related coefficient to deep convections of 0.9. Figure [10,42,43].7b shows thatFigure the 6 variation reveals patternthat in ofthe the tropics, monthly the anomalies statistically of significantGW Ep at 13correlation km was similar coefficients to that between of the LRT-H Ep and with LRT a correlationparameters coefficientwere mainly of 0.61,calculated which over passed in thethrough regions the where significance deep convection test of the confidenceoccurs. In this level se ofction, 99%. we will focus on the relationship between convectionThe temporal and LRT variations in the tropics. of the Figure monthly 8 shows means the and global the monthlydistribution anomalies of the averaged of Ep and seasonal LRT-T ◦ meansat 13 km of overLRT-H the latitudeand OLR 50 duringS are shown2006 to in 2013. Figure The7c,d. seasons The seasonal are categorized cycle of GW here activity as MAM was (March/April/May),negatively correlated withJJA that(June/July/August), of LRT-T with a correlation SON (September/October/November), coefficient of −0.84. The temporal variationsand DJF (December/January/February).of the monthly anomalies of Ep It valuescan be were seen alsothat negativelythe LRT-H correlated was higher with in DJF those and of LRT-Tlower in with JJA, a whichcorrelation is consistent coefficient with of − the0.37, seasonal which passedcycle shown through in the Figure significance 1a. In MAM test of and the confidenceSON, the deep level convectionsof 99%. were basically symmetric about the equator, and in these regions, the LRT-H was lower, especially in SON, such as the Indian Ocean and Central America. In JJA and DJF, convections are 3.4. The Relationship between Convection and Tropopause in the Tropics more active in the summer hemisphere than in the winter hemisphere [42]. Figure 8d shows that in DJF, Itdeep has convections been noticed are that accompanied the tropical by tropopause the lower isLRT, not such only as related in Southeast to atmospheric Asia, South waves Africa but andalso Central related South to deep America. convections In summary, [10,42,43 the]. FigureLRT-H6 was reveals lower that in deep in the convections tropics, the in statistically all the four seasons.significant correlation coefficients between Ep and LRT parameters were mainly calculated over in the regions where deep convection occurs. In this section, we will focus on the relationship between convection and LRT in the tropics. Figure8 shows the global distribution of the averaged seasonal means of LRT-H and OLR during 2006 to 2013. The seasons are categorized here as MAM (March/April/May), JJA (June/July/August), SON (September/October/November), and DJF (December/January/February). It can be seen that the LRT-H was higher in DJF and lower in JJA, which is consistent with the seasonal cycle shown in Figure1a. In MAM and SON, the deep convections were basically symmetric about the equator, and in these regions, the LRT-H was lower, especially in SON, such as the Indian Ocean and Central America. In JJA and DJF, convections are more active in the summer hemisphere than in the winter hemisphere [42]. Figure8d shows that in DJF, deep convections are accompanied by the lower LRT, such as in Southeast Asia, South Africa and Central South America. In summary, the LRT-H was lower in deep convections in all the four seasons.

Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 15

LRT-T with a correlation coefficient of −0.37, which passed through the significance test of the confidence level of 99%.

Figure 7. (a) The monthly means and (b) the monthly anomalies time series of GW Ep at 13 km and the LRT-H at 50° N. (c) The monthly means and (d) the monthly anomalies time series of GW Ep at 13 km and the LRT-T at 50° S.

3.4. The Relationship Between Convection and Tropopause in the Tropics It has been noticed that the tropical tropopause is not only related to atmospheric waves but also related to deep convections [10,42,43]. Figure 6 reveals that in the tropics, the statistically significant correlation coefficients between Ep and LRT parameters were mainly calculated over in the regions where deep convection occurs. In this section, we will focus on the relationship between convection and LRT in the tropics. Figure 8 shows the global distribution of the averaged seasonal means of LRT-H and OLR during 2006 to 2013. The seasons are categorized here as MAM (March/April/May), JJA (June/July/August), SON (September/October/November), and DJF (December/January/February). It can be seen that the LRT-H was higher in DJF and lower in JJA, which is consistent with the seasonal cycle shown in Figure 1a. In MAM and SON, the deep convections were basically symmetric about the equator, and in these regions, the LRT-H was lower, especially in SON, such as the Indian Ocean and Central America. In JJA and DJF, convections are more active in the summer hemisphere than in the winter hemisphere [42]. Figure 8d shows that in DJF, deep convections are accompanied by the lower LRT, such as in Southeast Asia, South Africa Atmosphere 2019, 10, 75 11 of 15 and Central South America. In summary, the LRT-H was lower in deep convections in all the four seasons.

Atmosphere 2019, 10, x FOR PEER REVIEW 11 of 15

Figure 8. Global distribution of 2006-2013 averaged seasonal means ((a) MAM, (b) JJA, (c) SON, and (d) DJF) of LRT-H and OLR. The red solid line and the red dashed line represents OLR = 240 W/m2 and OLR = 220 W/m2, respectively.

Figure 8.9Global shows distribution the global of 2006–2013distribution averaged of th seasonale averaged means seasonal ((a) MAM, means (b) JJA, of (c )LRT-T SON, and and (d )OLR duringDJF) 2006 of LRT-H to 2013. and From OLR. TheFigure red solid9b, it line is andeviden thet red that dashed in JJA, line lower represents LRT OLR temperature = 240 W/m is2 andbroadly foundOLR in the = 220 same W/m regions2, respectively. where deep convections occur, such as in India, Southeast Asia and the Western Pacific. Minima in LRT temperature appears over the Western Pacific and extends northwardFigure 9over shows the thesouth-Asia global distribution monsoon circulation of the averaged near the seasonal deep meansconvections. of LRT-T In Central and OLR America, during the2006 cold to 2013.LRT and From deep Figure convections9b, it is evident extend thatnorthwar in JJA,d to lower 25° N. LRT The temperature comparison is between broadly Figure found in8b andthe sameFigure regions 9b shows where that deep in JJA, convections the low and occur, cold suchLRT appears as in India, in Central Southeast America Asia and the Western Pacific,Pacific. Minimawhile the in high LRT temperatureand cold LRT appears appears over in the India. Western In the Pacific other and three extends seasons, northward as revealed over theby Figuresouth-Asia 9a,c,d, monsoon the coincidence circulation between near the low deep LRT-T convections. and deep In convections Central America, is even the more cold distinguished LRT and deep ◦ thanconvections that between extend LRT-H northward and deep to 25 convections.N. The comparison In summary, between the low Figures and cold8b and LRT9b appears shows thatin deep in JJA,convection the low regions. and cold LRT appears in Central America and the Western Pacific, while the high and coldThe LRT distribution appears in India.of OLR In and the otherCPT parameters three seasons, in th ase revealedtropics is bysimilar Figure to9 a,c,d,Figure the 8 and coincidence Figure 9 (Figureuresbetween low are LRT-T not and shown deep here), convections which is means even more thatdistinguished there is strong than correspondence that between LRT-H between and CPT-T/CPT-Hdeep convections. and Indeep summary, convections. the low and cold LRT appears in deep convection regions.

Figure 9. Global distributiondistribution ofof 2006–2013 2006-2013 averaged averaged seasonal seasonal means means (( a()(a) MAM, MAM, (b )(b) JJA, JJA, (c) (c) SON, SON, and and (d) 2 (d)DJF) DJF) of LRT-Tof LRT-T and and OLR. OLR. The The red red solid solid line line represents represents OLR OLR = 240= 240 W/ W/ m m2,, andand thethe redred dasheddashed line 2 represents OLR = 220 W/m 2. .

The distribution of OLR and CPT parameters in the tropics is similar to Figures8 and9 (Figureures Reference [42] analyzed the distribution and influence of convection in the tropical tropopause are not shown here), which means that there is strong correspondence between CPT-T/CPT-H and region using cold brightness temperatures from satellites and temperatures from contemporaneous deep convections. reanalysis. They found that there was a significant correspondence locally between the deepest Reference [42] analyzed the distribution and inﬂuence of convection in the tropical tropopause convection and coldest tropopause temperatures. Reference [10] investigated the structure and region using cold brightness temperatures from satellites and temperatures from contemporaneous variability of temperature in the tropical upper troposphere and lower stratosphere using GPS/MET reanalysis. They found that there was a signiﬁcant correspondence locally between the deepest RO data during April 1995 to February 1997. They found that low tropopause is associated with convection and coldest tropopause temperatures. Reference [10] investigated the structure and deep convections. Our results are consistent with both of these studies. The Pearson correlation coefficients between OLR and tropopause parameters over 5° S–5° N latitudes are shown in Table 1. It can be seen that the weakest correlation between OLR and LRT-H/CPT-H is calculated in MAM with a correlation coefficient of -0.12/0.11, which fails to pass the significance test of the confidence level of 95%. While during the same season, strong correlations exist between OLR and LRT-T/CPT-T, as revealed by the correlation coefficient of 0.63/0.64, which passes through the significance test of the confidence level of 99%. In the other three seasons, the correlation coefficients between OLR and tropopause height and temperature are all positive and pass through the significance test of the confidence level of 95%, indicating that a low and cold tropopause is generally associated with deep convections which is presented by low OLR.

Atmosphere 2019, 10, 75 12 of 15 variability of temperature in the tropical upper troposphere and lower stratosphere using GPS/MET RO data during April 1995 to February 1997. They found that low tropopause is associated with deep convections. Our results are consistent with both of these studies. The Pearson correlation coefficients between OLR and tropopause parameters over 5◦ S–5◦ N latitudes are shown in Table1. It can be seen that the weakest correlation between OLR and LRT-H/CPT-H is calculated in MAM with a correlation coefficient of −0.12/0.11, which fails to pass the significance test of the confidence level of 95%. While during the same season, strong correlations exist between OLR and LRT-T/CPT-T, as revealed by the correlation coefficient of 0.63/0.64, which passes through the significance test of the confidence level of 99%. In the other three seasons, the correlation coefficients between OLR and tropopause height and temperature are all positive and pass through the significance test of the confidence level of 95%, indicating that a low and cold tropopause is generally associated with deep convections which is presented by low OLR.

Table 1. The Pearson correlation coefﬁcient (CC) and the corresponding conﬁdence level (CL) between OLR and the tropopause parameters over 5◦ S–5◦ N in each season during 2006–2013.

OLR and LRT-H OLR and LRT-T OLR and CPT-H OLR and CPT-T ?Season CC CL CC CL CC CL CC CL MAM −0.12 67.8% 0.63 99.9% 0.11 60.7% 0.64 99.9% JJA 0.62 99.9% 0.34 99.6% 0.57 99.9% 0.37 99.9% SON 0.40 99.9% 0.52 99.9% 0.46 99.9% 0.54 99.9% DJF 0.26 97.4% 0.54 99.9% 0.44 99.9% 0.56 99.9%

4. Discussion Section 2.1 pointed out that as GWs can cause the perturbations of temperature, the key to calculate the GW Ep by COSMIC RO temperature profiles is the estimation of temperature perturbations (T0). In the example presented by Figure1a of reference [ 34], it is shown that in the tropopause and throughout the stratosphere, there is a “wavy” variability in the COSMIC temperature profile (blue line), and it also appeared in GPS/MET temperature profiles [10,40,44] and radiosonde observations [29]. The “wavy” variability of temperature profile might be attributed to GWs [10,40,44], which indicates that GWs can influence the tropopause temperature. It has been revealed that GWs play a main role in regulating tropopause parameters [18]. The breaking of GWs in the stratosphere transports energy, momentum, chemical, and atmospheric constituents (i.e. water vapor) across the tropopause to the surroundings [45], which affected the tropopause parameters accordingly [18]. In middle and high latitudes, significant correlations between GW Ep and LRT height and temperature appears about several kilometers above the tropopause, as shown by Figure3, and GW Ep at 13 km has a positive correlation with LRT-H and a negative correlation with LRT-T, as shown by Figure6. The seasonal cycles of the monthly means and the monthly anomalies of GW Ep and LRT-H/LRT-T shown in Figure7 reveals that LRT-H/LRT-T increases/decreases with the increase of Ep values in middle and high latitudes. All these results indicate that close relations exist between GWs and LRT parameters in middle and high latitudes, which might be attributed to that LRT is lifted and becomes cooler when GWs propagate from the troposphere to stratosphere. It is interesting that our results are opposite to that of reference [18], who investigated the relationship between GWs at 17 km and the temperature and height of CPT in Tibet and concluded that the enhancements of GW Ep lead to the increase of CPT-T. The reasons might be attributed to that GW Ep at different height layers are concerned about by reference [18] and by this work. In the tropics, strong correlation exists between convections and tropopause parameters, which indicates that low and cold tropopause, appears in deep convection regions, as revealed by Figure8, Figure9 and Table1. The result is consistent with references [ 7,42]. Although this correlation might be a result of convective cooling of the tropopause, or a tropopause cooled by other means such as radiative cooling, the former factor appears more likely [42]. On the other hand, Figure6 Atmosphere 2019, 10, 75 13 of 15 shows that the correlations between GW Ep and tropopause height and temperature are significant in deep convection regions, which indicates that tropopause parameters variability might also have close relationship with GW activity. Reference [7] indicates that radiative forcing might be important for tropical tropopause on monthly time scales, while the majority of tropopause temperature and height variability appears to be related to wave-like variability. They also found that there were significant correlations between GPS/MET temperature and OLR in the tropics, which quantified the influence of deep convection on temperatures in the tropical tropopause region. In summary, the tropopause parameters in the tropics might be affected by both deep convections [7] and the GWs excited by deep convection.

5. Conclusions In this study, the relationship between gravity wave (GW) potential energy (Ep) and the tropopause height and temperature over the globe was investigated using COSMIC radio occultation (RO) dry temperature profiles during September 2006 to May 2013. The longitude-altitude cross sections of the Pearson correlation coefficients between Ep and LRT parameters over the globe and those between Ep and CPT parameters over the latitudes 30◦ S–30◦ N showed that at middle and high latitudes, concentrated distributions of statistically significant positive (negative) correlation coefficients between GW Ep and LRT-H (LRT-T) were generally calculated in the height range between the LRT and several kilometers above. In the tropics, the distributions of the correlation coefficients between GW Ep and LRT and CPT parameters that are statistically significant were dispersive. The global distributions of the peak positive/negative correlation coefficients between GW Ep and LRT-H/LRT-T and their corresponding altitudes showed that at middle and high latitudes, most of the peak positive/negative correlation coefficients between GW Ep and LRT-H/LRT-T were around 0.5~0.8/−0.4~−0.6, which were calculated over the altitudes of 10~14 km with distinct zonal distribution characteristics, while in the tropics, the peak correlation coefficients, which are only 0.2~0.4/−0.2~−0.4, were calculated dispersively over the altitudes of 14~38 km. At middle and high latitudes, the statistically significant positive/negative correlation coefficients between GW Ep over the altitude of 13 km and LRT-H/LRT-T present distinct zonal distribution features, while in the tropical regions, statistically significant positive/negative correlations existed between GW Ep over the altitude of 17~19 km and LRT-H/LRT-T where deep convections occur. At the latitudes 50◦ N and 50◦ S, the temporal variations of the monthly means and the monthly anomalies of the LRT parameters and GW Ep over the altitude of 13 km show that LRT-H/LRT-T increases/decreases with the increase of Ep, which might be attributed to that LRT is lifted and becomes cooler when GWs propagate from the troposphere to the stratosphere. The distribution of 2006–2013 averaged seasonal means of OLR and LRT parameters over the tropics and the correlation coefficients between OLR and LRT parameters over 5◦S–5◦N show that strong correlations between convections and the tropopause parameters exist in most seasons over the tropics, which indicates that low and cold tropopause appears in deep convection regions. It can be concluded that GW activities affects the variations of the tropopause parameters. At middle and high latitudes, the tropopause was lifted and becomes cooler when GWs propagate from the troposphere to stratosphere, while in the tropics, both deep convections and GWs excited accordingly had impacts on the tropopause structure.

Author Contributions: D.Y., X.X., and J.L. (Jia Luo) conceptualized the initial idea and experiment design; D.Y. analyzed the data; D.Y., X.X. and J.L. (Jia Luo) wrote the main manuscript text; J.L. (Jia Luo) and J.L. (Juan Li) contributed grammar correcting of the text. Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 41774033 and 41774032) and the National Basic Research Program of China (973 Program) (Grant No. 2013CB733302). Acknowledgments: The authors would like to thank UCAR for providing COSMIC RO data through CDAAC, and NOAA for providing OLR data through the Climate Diagnostics Center. Conﬂicts of Interest: The authors declare no conﬂict of interests. Atmosphere 2019, 10, 75 14 of 15

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