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

<a href="/goto?url=http://www.mdpi.com/journal/atmosphere" target="_blank">atmosphere </a>Article On the Relationship between Gravity Waves and Tropopause Height and Temperature over the Globe Revealed by COSMIC Radio Occultation Measurements <ul style="display: flex;"><li style="flex:1">Daocheng Yu 1, Xiaohua Xu 1,2,*, Jia Luo 1,3, </li><li style="flex:1">*</li><li style="flex:1">and Juan Li 1 </li></ul>1School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China; [email protected] (D.Y.); [email protected] (J.L.) 23Collaborative Innovation Center for Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China 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.) <a href="/goto?url=http://www.mdpi.com/2073-4433/10/2/75?type=check_update&version=1" target="_blank">ꢀꢁꢂꢀꢃꢄꢅꢆꢇ </a><a href="/goto?url=http://www.mdpi.com/2073-4433/10/2/75?type=check_update&version=1" target="_blank">ꢀꢁꢂꢃꢄꢅꢆ </a>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]. <ul style="display: flex;"><li style="flex:1">Atmosphere 2019, 10, 75; doi:<a href="/goto?url=http://dx.doi.org/10.3390/atmos10020075" target="_blank">10.3390/atmos10020075 </a></li><li style="flex:1"><a href="/goto?url=http://www.mdpi.com/journal/atmosphere" target="_blank">ww</a><a href="/goto?url=http://www.mdpi.com/journal/atmosphere" target="_blank">w</a><a href="/goto?url=http://www.mdpi.com/journal/atmosphere" target="_blank">.</a><a href="/goto?url=http://www.mdpi.com/journal/atmosphere" target="_blank">mdpi.com/journal/atmosphere </a></li></ul>Atmosphere 2019, 10, 75 2 of 15 <ul style="display: flex;"><li style="flex:1">Different definitions and concepts exist for the determination of the tropopause [ </li><li style="flex:1">5]. The thermal </li></ul>tropopause, which is also called the lapse rate tropopause (LRT), was defined by the Wor−ld1 Meteorological Organization (WMO) as the lowest level at which the lapse rate decreases to 2 K·km 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 [ exchange [2]. 7]. The CPT is an import indicator of stratosphere-troposphere coupling and The variations of the tropopause height and temperature show sub-seasonal, seasonal and inter-annual variabilities [ 12] and are closely related to atmospheric waves [ 10 13 16], among which the effects of Gravity waves (GWs) [10 17 18] are significant. Gravity waves (GWs) are usually excited <ul style="display: flex;"><li style="flex:1">8– </li><li style="flex:1">8, </li><li style="flex:1">,</li><li style="flex:1">–</li></ul><ul style="display: flex;"><li style="flex:1">,</li><li style="flex:1">,</li></ul>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]. <ul style="display: flex;"><li style="flex:1">Although there are a number of works on the variations of the structure of tropopause [22 </li><li style="flex:1">–25] </li></ul><ul style="display: flex;"><li style="flex:1">and GW activities [21 26 27], studies on the relationship between GWs and the tropopause are </li><li style="flex:1">,</li><li style="flex:1">,</li></ul>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 <ul style="display: flex;"><li style="flex:1">stability, and global coverage are ideal data sources to study the tropopause structures [ </li><li style="flex:1">4,25,29] and </li></ul><ul style="display: flex;"><li style="flex:1">are applicable to analyze the global characteristics of GW activity [21 30 31]. In this study, we used </li><li style="flex:1">,</li><li style="flex:1">,</li></ul>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 Section 2. The results and analyses are presented in Section 3. Section 4 discusses the possible underlying mechanism. Finally, conclusions are given in Section 5. 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 <ul style="display: flex;"><li style="flex:1">residual ionospheric effects, it typically exhibits increased noise at upper levels [27 </li><li style="flex:1">,32]. Although </li></ul>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: <ul style="display: flex;"><li style="flex:1">ꢂ</li><li style="flex:1">ꢃ</li></ul>2<ul style="display: flex;"><li style="flex:1">ꢀ</li><li style="flex:1">ꢁ</li></ul>212gNT0 TEp = (1) (2) <ul style="display: flex;"><li style="flex:1">ꢂ</li><li style="flex:1">ꢃ</li></ul>gT∂T ∂z gN2 = +cP where capacity, gis the gravitational acceleration, N is the Brunt-Väisälä frequency, cp is the isobaric heating zis the height, and T, and T0 is the background temperature and the temperature perturbations caused by GWs, respectively. It is important to separate temperature (T). The accurate Ep is based on the extraction of T0, which is given by: Tand T0 from the raw COSMIC 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◦ grid cells with a vertical resolution of 1 km. ×5◦ longitude–latitude 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 Figure 1b 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 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 Figure 1. Because the CPT parameters are ×5 longitude-latitude grids. The time-latitude plots of the monthly Atmosphere 2019, 10, 75 4 of 15 most applicable in the tropics [37], the variations of CPT-H and CPT-T are only shown for the latitude region of 30◦ S–30◦ N. <ul style="display: flex;"><li style="flex:1">Figure 1. Time-latitude plots of monthly means of ( </li><li style="flex:1">a) lapse rate tropopause height (LRT-H), ( </li></ul>b) lapse rate tropopause temperature (LRT-T), ( c) cold point tropopause height (CPT-H), and ( ) cold point dtropopause temperature (CPT-T). 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 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. Figure 1b shows that the LRT-T increases from the tropics to the poles. In the tropics and in the middle and high latitudes of the Northern Hemisphere (NH), the LRT-T is higher in boreal summer and lower in boreal winter; while in the middle and high latitudes of the Southern Hemisphere (SH), it presents the opposite seasonal variation. The comparison between Figure 1a,b shows that LRT is higher and colder in the tropics and lower and warmer at middle and high latitudes. 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. From Figure 1d, it is evident that the CPT-T is higher in boreal summer and lower in winter, which is opposite to the seasonal variation of the CPT-H. So the CPT is higher and colder in boreal winter and lower and warmer in summer, which is consistent with reference [38]. In the tropics, the parameters of the LRT and CPT are close to each other and present similar seasonal variation patterns. The characteristics of the temporal and spatial variability of the LRT and CPT heights and temperatures shown in Figure 1 are generally consistent with those of the available literatures. Thus, the tropopause parameters provided by CDAAC is reliable and can be applied to this study. 2.4. Statistical Method The monthly means of GW Ep with a vertical resolution of 1 km and tropopause parameters were calculated for each 5◦ and the tropopause heights and temperatures were subtracted from the monthly means to get the corresponding monthly anomalies, as shown by equation (4): ×5◦ longitude-latitude grid. The annual cycle of Ep at each height layer n1<ul style="display: flex;"><li style="flex:1">∆F = F − </li><li style="flex:1">F</li></ul>i,j (4) <ul style="display: flex;"><li style="flex:1">i,j </li><li style="flex:1">i,j </li></ul>∑ni=1 where n is the number of years. i = 1, 2, . . . . . . n is the in one year. ith year and j = 1, 2, . . . . . . 12 is the jth month Fi,j and ∆F represents the monthly mean and the monthly anomaly of Ep at certain i,j Atmosphere 2019, 10, 75 5 of 15 height layer or of tropopause parameters for the jth month in the ith year, respectively. In each 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 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. Figure 2. (a) The monthly means and (b) the monthly anomalies time series of gravity wave potential <ul style="display: flex;"><li style="flex:1">◦</li><li style="flex:1">◦</li></ul>energy (GW Ep) at 13 km and the LRT-H over the grid (50 N, 25 W). From Figure 2a, it can be seen that the Ep monthly means (blue solid line) at 13 km over this grid fluctuated mainly between 2.5 J·kg−1 and 10 J·kg−1, while LRT-H monthly means (red dotted line) oscillated mainly 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. The 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 anomalies fluctuate between −2 J·kg−1 and 4 J·kg−1, while LRT-H monthly anomalies fluctuated between −0.5 km and 0.5 km. The Pearson correlation coefficient between the two lines shown in Figure 2b was 0.39, which also passes through the significance test of the confidence level of 99%. The correlation coefficient between the monthly anomalies was smaller than that between the monthly means. 3.2. The Vertical Structure of the Correlation Between Ep and Tropopause Parameters To investigate the vertical structure of the correlation between Ep and LRT and 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 Figures 3 and 4, respectively. Figure 3 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 Figure 3 show that the vertical distributions of the correlation coefficients between GW Ep and LRT-H vary greatly at ◦different latitudes. It is shown in Figure 3a 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 not statistically significant below the LRT-H or above 14 km. At the equator, the distributions of the correlation coefficients that are statistically significant are ◦dispersed, as shown in Figure 3b. At 50 S, Ep mostly 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 between Ep and LRT-H d) 70◦ N, (b e) 0◦ and (c f) 50◦ S. (left column), and between Ep and LRT-T (right column) at (a, , , The regions where the correlation coefficients pass through the significance test of the confidence level of 95% are marked with crosses. The LRT height is represented by black dotted lines (a–f).

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

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