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Marine Boundary Layer Heights in the Tropical and Subtropical Oceans Derived from COSMIC-2 Radio Occultation Data


doi: 10.1007/s00376-022-2052-z

  • Using the global navigation satellite system (GNSS) and radio occultation (RO) refractivity data from the Constellation Observing System for Meteorology Ionosphere and Climate-2 (COSMIC-2) mission from January 2020 to December 2021, the spatial and temporal variability of Marine Boundary Layer Heights (MBLHs) over the tropical and subtropical oceans are investigated. The MBLH detection method is based on the wavelet covariance transform (WCT) algorithm, while the distinctness (DT) parameter, which reflects the significance of the maximum WCT function values, is introduced. For the refractivity profiles with indistinct maximum WCT function values, the available surrounding RO-derived MBLHs are used as auxiliary information, which helps to improve the objectiveness of the inversion process. The RO-derived MBLHs are validated with the MBLHs derived from the collocated high-vertical-resolution radiosonde observations, and the seasonal distributions of the RO-derived MBLHs are presented. Further comparisons of the magnitudes and the distributions of the RO-derived MBLHs with those derived from two model datasets, the European Centre for Medium-Range Weather Forecasts (ECMWF) analyses and the National Centers for Environmental Prediction (NCEP) Aviation (AVN) 12-hour forecast data, reveal that although high correlations exist between the RO-derived and the model-derived MBLHs, the model-derived ones are generally lower than the RO-derived ones in most parts of the tropics and sub-tropic ocean areas during different seasons, which should be partially attributed to the limited vertical resolutions of the model datasets. The correlation analyses between the MBLHs and near-surface wind speeds demonstrate that over the Pacific Ocean, near-surface wind speed is an important factor that influences the variations of the MBLHs.
    摘要: 大气边界层是对流层底部对天气气候、空气质量有显著影响的大气区域。本文采用2020年至2021年的COSMIC-2掩星折射指数资料系统地研究了中低纬海洋边界层高度的时空分布特征。边界层高度的提取基于小波协方差变换(WCT)算法,并针对算法中存在的多极值问题提出了新的约束参数。同时对于受次极值影响的廓线通过引入时空相邻的边界层高度信息来改进WCT算法的反演性能。验证分析表明掩星反演的边界层高度与探空结果具有较好的一致性。进一步的比较分析表明掩星反演的边界层高度在四个季节均高于ECMWF和NCEP的结果,产生差异的原因可能与模式数据有限的垂直分辨率有关。在热带太平洋地区边界层高度变化与近海面风速呈正相关,表明风速是影响边界层发展演变的重要气象因子。
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  • Figure 1.  (a) Latitude-longitude distribution of the number of COSMIC-2 refractivity profiles over the marine areas between 40°S to 40°N binned within a grid of 2.5° × 2.5° for the period 1 January 2020 to 31 December 2021, and (b) the distribution (blue bars) and the cumulative distribution (red line) of the penetration depths of these profiles. The pink cross symbols in (a) represent the positions of the four radiosonde stations, which provide data for the comparison with RO-derived MBLHs in section 3.1.

    Figure 2.  Two examples of COSMIC-2 refractivity profiles with different DT values, as well as the collocated sounding profiles. The time and locations of the two RO events are (a) 2 December 2020, 12.59°S, 96.89°E and (b) 28 December 2021, 18.58°N, 157.63°W. In each subfigure, the two thin solid lines represent the RO refractivity profile (in green) and the collocated sounding refractivity profile (in orange). The bold solid lines represent the Wf profiles corresponding to the RO (in green) and the sounding (orange) refractivity profiles (labeled at the top of the subfigure). The green dotted line and the green dashed line represent the heights of $ {Z}_{{W}_{f}^{{\rm{max}}}} $ and $ {Z}_{{W}_{f}^{{\rm{submax}}}} $, respectively, and the orange dotted line represents the sounding-derived MBLH. The blue dashed line in subfigure (b) represents the height of $ {Z}_{{\rm{inp}}} $.

    Figure 3.  Flow chart for MBLH detection algorithm.

    Figure 4.  The MBLH retrieval success rate and the proportions of COSMIC-2 refractivity profiles which are rejected due to the 0.5 km penetration constraint or the DT parameter constraint at different latitude bands between 40°S and 40°N.

    Figure 5.  The latitude-longitude distributions of (a) the DT values calculated from the COSMIC-2 RO refractivity data and (b) the 500 hPa vertical velocity derived from the ERA5 dataset on a 0.25° × 0.25° grid.

    Figure 6.  MBLHs derived from collocated pairs of COSMIC-2 RO and radiosonde observations. The black line represents the least-squares regression line.

    Figure 7.  Seasonal MBLH climatology at the latitudes of 40°S to 40°N derived from COSMIC-2 refractivity data from 2020 to 2021. The dotted blue line at the left (a, c) or right (b, d) side of each panel denotes the latitudinal variation of MBLH on a 4° grid. The seasons are defined as follows: March–April–May (MAM), June–July–August (JJA), September–October–November (SON), and December–January–February (DJF).

    Figure 8.  (a–d) The scatterplots for the values of MBLH_C2 and MBLH_ECM during different seasons. In each subfigure, the red line and the parameter R denote the least-squares regression line and the corresponding correlation coefficient, respectively, which is statistically significant (p<0.05). SD and RMS (units: km) denote the standard deviation and root mean square of all ΔMBLHC–E values. (e–h) The distribution of the values of ΔMBLHC–E during different seasons; the blue bars at the left (e, g) or right (f, h) side of each panel show the corresponding values of ΔMBLHC–E in 4°- latitudinal bins. (i–k) The seasonal variations of ΔMBLHC–E for three different ocean areas, the box-and-whisker plots display the 5th, 25th, 50th, 75th, and 95th percentiles of ΔMBLHC–E, with their means, and SDs marked by red circles and red crosses, respectively.

    Figure 9.  Similar to Fig. 8 but for the comparison of the values of MBLH_C2 and MBLH_AVN.

    Figure 10.  Monthly variation of the MBLHs derived from the three different data sources in the region of the (a) TNP (Tropical Northwestern Pacific: 10°–20°N, 130°–170°E) and (b) TSP (Tropical Southwestern Pacific: 10°–20°S, 160°E–160°W).

    Figure 11.  Monthly cycle of the MBLH_C2 values versus near-surface wind speed at 950 hPa over the two regions of the (a) TNP and (b) TSP.

    Figure 12.  Longitudinal variations of the MBLH_C2 values versus the near-surface wind speeds at 950 hPa in different latitude bands over the Pacific Ocean.

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Manuscript received: 26 February 2022
Manuscript revised: 26 September 2022
Manuscript accepted: 19 October 2022
通讯作者: 陈斌, bchen63@163.com
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Marine Boundary Layer Heights in the Tropical and Subtropical Oceans Derived from COSMIC-2 Radio Occultation Data

    Corresponding author: Xiaohua XU, xhxu@sgg.whu.edu.cn
  • 1. School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
  • 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

Abstract: Using the global navigation satellite system (GNSS) and radio occultation (RO) refractivity data from the Constellation Observing System for Meteorology Ionosphere and Climate-2 (COSMIC-2) mission from January 2020 to December 2021, the spatial and temporal variability of Marine Boundary Layer Heights (MBLHs) over the tropical and subtropical oceans are investigated. The MBLH detection method is based on the wavelet covariance transform (WCT) algorithm, while the distinctness (DT) parameter, which reflects the significance of the maximum WCT function values, is introduced. For the refractivity profiles with indistinct maximum WCT function values, the available surrounding RO-derived MBLHs are used as auxiliary information, which helps to improve the objectiveness of the inversion process. The RO-derived MBLHs are validated with the MBLHs derived from the collocated high-vertical-resolution radiosonde observations, and the seasonal distributions of the RO-derived MBLHs are presented. Further comparisons of the magnitudes and the distributions of the RO-derived MBLHs with those derived from two model datasets, the European Centre for Medium-Range Weather Forecasts (ECMWF) analyses and the National Centers for Environmental Prediction (NCEP) Aviation (AVN) 12-hour forecast data, reveal that although high correlations exist between the RO-derived and the model-derived MBLHs, the model-derived ones are generally lower than the RO-derived ones in most parts of the tropics and sub-tropic ocean areas during different seasons, which should be partially attributed to the limited vertical resolutions of the model datasets. The correlation analyses between the MBLHs and near-surface wind speeds demonstrate that over the Pacific Ocean, near-surface wind speed is an important factor that influences the variations of the MBLHs.

摘要: 大气边界层是对流层底部对天气气候、空气质量有显著影响的大气区域。本文采用2020年至2021年的COSMIC-2掩星折射指数资料系统地研究了中低纬海洋边界层高度的时空分布特征。边界层高度的提取基于小波协方差变换(WCT)算法,并针对算法中存在的多极值问题提出了新的约束参数。同时对于受次极值影响的廓线通过引入时空相邻的边界层高度信息来改进WCT算法的反演性能。验证分析表明掩星反演的边界层高度与探空结果具有较好的一致性。进一步的比较分析表明掩星反演的边界层高度在四个季节均高于ECMWF和NCEP的结果,产生差异的原因可能与模式数据有限的垂直分辨率有关。在热带太平洋地区边界层高度变化与近海面风速呈正相关,表明风速是影响边界层发展演变的重要气象因子。

    • The planetary boundary layer (PBL) in the lower troposphere is the transition between the earth’s surface and the free atmosphere (Stull, 1988; Garratt, 1992). In oceanic areas, marine boundary layer (MBL) processes affect the vertical transportation of heat and moisture, thereby playing an important role in atmosphere–ocean coupled modeling (Zeng et al., 2004). Moreover, the structure of the MBL, which is closely connected with cloud type and cloud fraction (Betts and Boers, 1990; Albrecht et al., 1995; Serpetzoglou et al., 2008), further impacts the global radiation budget, weather, and climate. The height of the MBL top (MBLH) is a key parameter characterizing the marine boundary layer in global climate models (Norris, 1998; Basha et al., 2019). However, the climatology of MBLH is generally not available over much of the oceanic areas due to the scarcity of situ observations.

      Satellite remote sensing technologies, such as the Global Navigation Satellite System (GNSS) radio occultation (RO), the Atmospheric Infrared Sounder (AIRS), the Moderate Resolution Imaging Spectroradiometer (MODIS), the CloudSat spaceborne cloud radar, and the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP), provide promising opportunities for obtaining MBLHs. For example, Wood and Bretherton (2004) presented the MBLH of the tropical and subtropical eastern Pacific by using satellite observations from both the MODIS and the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). Luo et al. (2016) analyzed the spatial and seasonal variations of the MBL structure in the eastern Pacific Ocean based on the observations of the A-train satellites, including AIRS, CloudSat, and CALIOP. However, the coarse vertical resolution of MODIS and AIRS data presents a challenge for detecting the MBLH precisely, and the limited temporal and spatial coverages of CALIOP restrict its applications in MBLH studies (Wu et al., 2008).

      As a limb-viewing measurement, GNSS RO technology has unique advantages, including high vertical resolution, excellent spatial coverage, and signal propagation which is not affected by clouds and precipitation (Wickert et al., 2001; Anthes et al., 2008; Xu et al., 2009), and the value of GNSS RO data for detecting the MBLH has been confirmed by many previous studies. Guo et al. (2011) derived the spatial and temporal variations of the MBLHs over the oceanic areas between 60°S to 60°N by using the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) RO data and the RO-derived MBLHs were validated with those derived from the radiosonde data with high vertical resolution. Using the COSMIC RO data, Ao et al. (2012) analyzed the latitudinal variability of the MBLHs over the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) Pacific Cross-Section Intercomparison (GPCI) transect and found that the RO-derived MBLH variation pattern is consistent with that derived from the European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis Interim (ERA-Int) data. Ho et al. (2015) analyzed the longitudinal, diurnal, and inter-seasonal variabilities of the MBLHs over the southeastern Pacific by using the COSMIC RO data and found that the MBLHs determined by RO are in good agreement with those from CALIOP and radiosonde data.

      The COSMIC-2, the follow-up mission of FORMOSAT-3/ COSMIC, is composed of six low earth orbit (LEO) satellites launched into circular, 24° inclination orbits on 25 June 2019. Each LEO satellite of COSMIC-2 is equipped with an advanced Tri-GNSS radio occultation system instrument (TGRS), observing both the signal of the Global Positioning System (GPS) and the Russian Global Navigation Satellite System (GLONASS) satellites (Schreiner et al., 2020), which greatly increases the number of RO events over middle and low latitude regions. Moreover, the RO profiles of COSMIC-2 have deeper penetrations down into the lower troposphere compared with previous RO missions, with about 50% reaching within 0.2 km above the surface (Schreiner et al., 2020). These distinctive characteristics make COSMIC-2 more powerful for detecting the MBLHs over the tropical and subtropical oceans than other RO missions. Despite being operational for more than two years, studies about MBLHs based on COSMIC-2 RO data are few thus far.

      Among GNSS RO products, bending angle and refractivity are the two basic derived variables, while temperature and water vapor need more theoretical assumptions (Kursinski et al., 2000; Yan et al., 2019). Although the bending angle profile is less biased in principle and is of higher vertical resolution, it is not straightforward to compare this type of observation to other measurements or atmospheric model output (Ao et al., 2012), and the definition for MBLH based on the bending angle profile is difficult to interpret (Basha and Ratnam, 2009). Therefore, we prefer to use the refractivity data to obtain MBLHs in the present study. Different methods were applied for inverting the MBLHs from RO refractivity data, including the minimum gradient method (Ao et al., 2012), the breakpoint method (Guo et al., 2011), and the wavelet covariance transform (WCT) method (Ratnam and Basha, 2010). When applying the minimum gradient method to derive the MBLHs from RO refractivity profiles, Chan and Wood (2013) found that the local minimum values in the vertical refractivity gradients will impact the accuracy of the derived MBLHs; they solve this problem by setting constraints on the local minimum values. Compared with the other two methods, the WCT method has better anti-noise ability and is more robust in the presence of weak inversions (Baars et al., 2008; Ratnam and Basha, 2010). However, local extreme values will also affect the accuracy of the MBLHs derived by the WCT method. In the present study, we applied a modified WCT method on the COSMIC-2 RO refractivity profiles for deriving the MBLHs, with a modification that aimed to improve the objectivity of the inverted MBLH when ambiguities existed in the maximum and the sub-maximum of the WCT function values of the refractivity profile.

      As for the mechanisms behind the variations of the PBL structures, abundant research efforts have attempted to reveal the influence of wind speeds on the variation of PBL heights (Guo et al., 2016; Zhang and Li, 2019; Li et al., 2021). Since radiosonde data was generally used in these studies, PBL heights over the land areas were their greatest concern. Using COSMIC RO data, Ho et al. (2015) and Winning et al. (2017) investigated the variabilities of the MBLHs over the Southeastern Pacific Ocean and the central North Pacific Ocean, respectively, while related activity over the western Pacific Ocean was not addressed by either study. In Basha et al. (2019), the global climatology of PBL top was derived using multi-satellite GPS RO observations from 2006 to 2015, while the association of the variation of the PBLHs to that of the meteorological parameters was not addressed. In the present study, we use the COSMIC-2 RO data over two years, from January 2020 to December 2021, to study the variability of the MBLHs over the ocean areas between the latitudes of 40°S to 40°N. On this basis, the relationships between the variations of MBLHs and wind speeds (including the temporal variations of the MBLHs over two typical regions of the western Pacific Ocean and wind speeds, as well as the spatial variations of the MBLHs over the Pacific Ocean and wind speeds) are further analyzed.

      The remainder of this paper is structured as follows. Section 2 introduces the data used and describes the MBLH detection algorithm. In section 3, after evaluating the MBLH values derived from the COSMIC-2 RO data with those derived from the collocated radiosonde observations with high vertical resolution, we present the seasonal MBLH climatology estimated using the COSMIC-2 RO data, and compare it with those from the ECMWF analyses and the NCEP AVN 12-hour forecast data comprehensively. The correlations between the variations of MBLHs and near-surface wind speeds and other potential factors which might have impacts on the variation of the MBLHs are discussed in section 4. Finally, we summarize the main conclusions in section 5.

    2.   Data and methods
    • The COSMIC-2 RO dataset, provided by the University Corporation for Atmospheric Research (UCAR) COSMIC Data Analysis and Archive Center (CDAAC) via the website www.cosmic.ucar.edu, consists of more than 4000 atmospheric parameter profiles per day. The present work uses refractivity profiles with vertical resolutions of 50 m, which are stored in the “wetPf2” files. The spatial distribution of the number of COSMIC-2 refractivity profiles over marine areas between 40°S to 40°N from January 2020 to December 2021 and the statistics about the penetration depth of these profiles are shown in Fig. 1. From Fig. 1a, it can be seen that the refractivity profiles are not evenly distributed. Most of them are located within the latitude zone of 30°S–30°N, and in the tropical latitudes of 15°S–15°N, the number of profiles is significantly larger than that in the subtropical areas, which is due to the low inclination of the LEO satellites. It can be seen from Fig. 1b that the frequency decreases with an increased penetration depth of the COSMIC-2 refractivity profiles. To ensure that the MBLHs occurring near the surface can be detected, we only use those profiles with penetration depths lower than 0.5 km (Basha and Ratnam, 2009), which account for about 60% of all the profiles. It should be noted that despite the constraints on the penetration depths of the RO profiles, shallow MBLHs may still be undersampled in our statistics (Basha et al., 2019).

      Figure 1.  (a) Latitude-longitude distribution of the number of COSMIC-2 refractivity profiles over the marine areas between 40°S to 40°N binned within a grid of 2.5° × 2.5° for the period 1 January 2020 to 31 December 2021, and (b) the distribution (blue bars) and the cumulative distribution (red line) of the penetration depths of these profiles. The pink cross symbols in (a) represent the positions of the four radiosonde stations, which provide data for the comparison with RO-derived MBLHs in section 3.1.

      High-vertical-resolution observations from four radiosonde stations, which are located on the islands of Hilo (19.72°N, 155.05°W), St. Helena (15.93°S, 5.66°W), the Cocos (12.18°S, 96.83°E), and Lord Howe (31.53°S, 159.06°E), are used in the present work for the validation of RO-retrieved MBLHs, and the positions of these stations are marked with cross symbols in Fig. 1a. A total number of 3323 sounding profiles which are with an average vertical resolution of about 10 m were obtained from the four stations between 2020 to 2021. These observations are carried out during different seasons and under different meteorological conditions. Profiles of different atmospheric variables measured by radiosondes, including temperature, virtual potential temperature, mixing ratio, et al., can all be used for deriving MBLHs, while the MBLHs obtained from different atmospheric variables tend to reveal different aspects of the MBLH characteristics and have inevitable differences (Seidel et al., 2010; Guo et al., 2016). To reduce the uncertainty raised by different methods, we applied the same refractivity-based definition of MBLH for the radiosonde measurements. The radiosonde-measured refractivity data are calculated from the direct observations of pressure, temperature, and humidity, the details of which can be found in (Ho et al., 2015).

      The European Centre for Medium-Range Weather Forecasts (ECMWF) analyses data and the National Centers for Environmental Prediction (NCEP) Aviation (AVN) 12-hour forecast data, which are interpolated to the time and locations of the COSMIC-2 RO observations by the CDAAC as the “echPrf ” and the “avnPrf” files, respectively, are also used in the present work. Over the tropical and subtropical ocean areas, the magnitudes and the distribution patterns of the MBLHs derived from the two model datasets are compared with those derived from the COSMIC-2 RO data. It is worth noting that only the ECMWF profiles with no less than 30 vertical levels in the height range of 0 to 5 km and NCEP profiles with no less than 18 vertical levels in that height range are used. In addition, the 500 hPa vertical velocity and the 950 hPa wind speed from the fifth generation ECMWF atmospheric reanalysis of the global climate (ERA5) dataset, which has a horizontal resolution of 0.25° × 0.25°, are utilized for potential mechanism interpretations in sections 2.2 and 4, respectively.

    • The MBLH detection algorithm applied here is modified from the WCT method. The WCT method introduced by Gamage and Hagelberg (1993) has been frequently used for estimating the MBLH. The principle of WCT method is given as follows.

      For a specific refractivity profile, f(z), the Haar function $h\left[{(z-b)}/{a}\right]$ is defined as (Brooks, 2003):

      where z is the observation height, and a and b are the dilation and the center of the Haar function, respectively. For certain values of a and b, the corresponding WCT function of the refractivity profile is further defined as:

      where $ {Z}_{a} $ and $ {Z}_{b} $ are the upper and lower limits of the height of the refractivity profiles, respectively. The refractivity profiles are interpolated to 10 m vertical height grids, and $ {Z}_{a} $ is set to 5 km, considering that the MBL top is located in the lower troposphere (Stull, 1988). It can be seen that for a specific refractivity profile, the value of the corresponding WCT function is determined by the values of a and b. The unknown dilation parameter, a, essentially equivalent to the depth of the transition zone (Brooks, 2003), is set as 0.2 km in the present work following Ratnam and Basha (2010). For a specific refractivity profile, the value of the corresponding WCT function, Wf, will vary along with the variation of the center of the Haar function, i.e., the parameter b, and the specific value of b, which corresponds to the maximum value of Wf as identified as the MBLH.

      The WCT method performs better than the direct gradient method when the MBL-induced inversion in the refractivity profile is weak (Ratnam and Basha, 2010). While ambiguities still exist when the computed maximum value and sub-maximum value of Wf are very close or during multiple inversions. In Ratnam and Basha (2010), the height of the lowest inversion is considered as the MBL top when multiple inversions are detected, which might be subjective in some cases. In the present study, we define the distinctness (DT) parameter to depict the significance of the maximum value of Wf :

      where ${W}_{f}^{{\rm{max}}}$ and ${W}_{f}^{{\rm{submax}}}$ are the maximum and the sub-maximum values of Wf, respectively. It can be seen that a large DT value means that the difference between the maximum and the sub-maximum values of Wf is distinct. Figures 2a and b show two examples of RO refractivity profiles that correspond to different levels of the distinctness of ${W}_{f}^{{\rm{max}}}$, and for each example, the collocated sounding profile with a spatial distance of less than 300 km and a temporal difference of less than 2.5 h is also presented. The DT value of the RO refractivity profile shown in Fig. 2a is 0.17. For this RO refractivity profile, ${W}_{f}^{{\rm{max}}}$ is distinctly larger than ${W}_{f}^{{\rm{submax}}}$, thus the MBLH can be determined unambiguously as the height corresponding to ${W}_{f}^{{\rm{max}}}$ ($\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r},{Z}_{{W}_{f}^{{\rm{max}}}}$), which is marked by the green dotted line, in this case equal to 2.16 km. Also, $ {Z}_{{W}_{f}^{{\rm{max}}}} $ is in good agreement with the MBLH estimated from the collocated sounding profile, which is marked by the orange dotted line and is equal to 2.06 km. While for the RO refractivity profile shown in Fig. 2b, the corresponding DT value is only 0.07, indicating that the value of $ {W}_{f}^{{\rm{max}}} $ is approximately equal to ${W}_{f}^{{\rm{submax}}}.$ Due to the fact that the difference between the maximum and the sub-maximum values of Wf is not sufficiently distinct, to directly define the MBLH as $ {Z}_{{W}_{f}^{{\rm{max}}}} $ might introduce errors in the MBLH estimation. In this case, the heights that correspond to $ {W}_{f}^{{\rm{max}}} $ and $ {W}_{f}^{{\rm{submax}}} $ (i.e., $ {Z}_{{W}_{f}^{{\rm{max}}}} $ and $ {Z}_{{W}_{f}^{{\rm{submax}}}} $) are 2.45 km and 0.9 km, respectively, and the difference between the two heights is 1.55 km, which should not be ignored in the MBLH detection.

      Figure 2.  Two examples of COSMIC-2 refractivity profiles with different DT values, as well as the collocated sounding profiles. The time and locations of the two RO events are (a) 2 December 2020, 12.59°S, 96.89°E and (b) 28 December 2021, 18.58°N, 157.63°W. In each subfigure, the two thin solid lines represent the RO refractivity profile (in green) and the collocated sounding refractivity profile (in orange). The bold solid lines represent the Wf profiles corresponding to the RO (in green) and the sounding (orange) refractivity profiles (labeled at the top of the subfigure). The green dotted line and the green dashed line represent the heights of $ {Z}_{{W}_{f}^{{\rm{max}}}} $ and $ {Z}_{{W}_{f}^{{\rm{submax}}}} $, respectively, and the orange dotted line represents the sounding-derived MBLH. The blue dashed line in subfigure (b) represents the height of $ {Z}_{{\rm{inp}}} $.

      For cases similar to the example shown in Fig. 2b, we introduce an auxiliary strategy that helps to make the MBLH inversion process more objective. First, a threshold is set for the DT parameter to distinguish those profiles greatly affected by the sub-maximum value of Wf. For a specific refractivity profile, if the corresponding DT value is larger than the threshold, then $ {Z}_{{W}_{f}^{{\rm{max}}}} $ is defined as the MBLH. Otherwise, it is considered that the difference between $ {W}_{f}^{{\rm{max}}} $ and $ {W}_{f}^{{\rm{submax}}} $ is not significant, and to derive the MBLH as $ {Z}_{{W}_{f}^{{\rm{max}}}} $ would not be objective enough. In this situation, the available surrounding MBLH values, which are derived from the refractivity profiles located within certain space and time windows that have DT values larger than the threshold, will be used as auxiliary information which helps to determine whether $ {Z}_{{W}_{f}^{{\rm{max}}}} $ or $ {Z}_{{W}_{f}^{{\rm{submax}}}} $ should be chosen as the MBLH. The two values, $ {Z}_{{W}_{f}^{{\rm{max}}}} $ and $ {Z}_{{W}_{f}^{{\rm{submax}}}} $, were compared with the interpolated height value using the surrounding MBLH values, $ {Z}_{{\rm{inp}}} $. The value closer to $ {Z}_{{\rm{inp}}} $ was defined as the final MBLH. In the present study, the space and time windows allotted for searching for the surrounding refractivity profiles were set to ±2.5° and ±1.5 h, respectively.

      The threshold of the DT parameter determines how large the difference between $ {W}_{f}^{{\rm{max}}} $ and $ {W}_{f}^{{\rm{submax}}} $ can be considered distinct enough so that an MBLH derived independently using the WCT algorithm can be regarded as objective. If the threshold value is too small, the effect of the modified strategy on the improvement of the objectiveness of the results will be very limited. If the threshold value is too large, auxiliary information will be needed even when the WCT algorithm can perform well independently, which reduces the efficiency of the inversion process and the retrieval success ratio. In our experiment, we compared different threshold values between 0.05 and 0.1 and determined that a threshold value set to 0.1 should provide a good balance between the efficiency and the objectiveness of the inversion process. With this threshold, if the DT value of the profile was equal to or smaller than 0.1, then the two values, $ {Z}_{{W}_{f}^{{\rm{max}}}} $ and ${Z}_{{W}_{f}^{{\rm{submax}}}}$, were compared with $ {Z}_{{\rm{inp}}} $, and the one that was closer to $ {Z}_{{\rm{inp}}} $ was chosen as the final MBLH. For the case shown in Fig. 2b, the interpolated $ {Z}_{{\rm{inp}}} $ that corresponds to the RO refractivity profile was derived using the above strategy and marked by the blue dashed line in the subfigure. It can be seen that the derived $ {Z}_{inp} $, equal to 0.74 km, is closer to $ {Z}_{{W}_{f}^{{\rm{submax}}}} $ compared with $ {Z}_{{W}_{f}^{{\rm{max}}}} $. Therefore, the final RO-inverted MBLH is consistent with $ {Z}_{{W}_{f}^{{\rm{submax}}}} $, which is equal to 0.9 km. Figure 2b also shows that for this case, compared with $ {Z}_{{W}_{f}^{{\rm{max}}}} $, $ {Z}_{{W}_{f}^{{\rm{submax}}}} $ agrees better with the MBLH estimated from the collocated sounding profile, which is marked by the orange dotted line and equal to 0.88 km.

      Figure 3 presents the flow chart for the final MBLH inversion process. A refractivity profile will only be used for MBLH detection only if its penetration height is lower than 0.5 km. To derive the MBLH from a refractivity profile, the corresponding Wf profile is obtained first, then the values of ${W}_f{^{\rm{max}}}$ and $ {W}_{f}^{{\rm{submax}}} $ are calculated before the DT parameter is derived. For refractivity profiles with DT values larger than the threshold of 0.1, the derived $ {Z}_{{W}_{f}^{{\rm{max}}}} $ will serve as the final MBLH. While for each refractivity profile having a DT value less than or equal to 0.1, if $ {Z}_{{\rm{inp}}} $ can be obtained, the interpolated $ {Z}_{{\rm{inp}}} $ will be used to aid in the decision as to whether $ {Z}_{{W}_{f}^{{\rm{max}}}} $ or $ {Z}_{{W}_{f}^{{\rm{submax}}}} $ should be chosen as the final MBLH. Otherwise, the inversion process for this refractivity profile will be marked as failed. Notably, the upper limit of the practical MBLH is set as 3.5 km (Guo et al., 2016). So if the inverted MBLH is higher than this value, the inversion process will also be marked as failed.

      Figure 3.  Flow chart for MBLH detection algorithm.

      Each COSMIC-2 RO refractivity profile located within the marine areas between 40°S and 40°N is processed following the above procedure. As shown in Fig. 3, a profile is marked as failed due to one of the three reasons: 1) the penetration depth was higher than 0.5 km, 2) the DT parameter did not exceed the threshold value, and at the same time, the surrounding MBLHs were unavailable, or 3) the retrieved MBLH was higher than 3.5 km. The final success rate for MBLH inversion is calculated as the ratio of the total number of output MBLH values to the number of the original refractivity profiles processed. Figure 4 displays the percentages of the COSMIC-2 RO refractivity profiles rejected due to the penetration depth constraint or the DT parameter threshold constraint and the final retrieval success rates in different latitude bands of the tropics and sub-tropic ocean areas. The percentage of profiles rejected due to the constraint on the highest possible MBLH is less than 0.5% in total, which is not shown here. It can be seen that the highest retrieval success rates were in the ocean area bounded by 30°–40°S, and the lowest rates were found in the ocean area of 10°S–20°S. In general, the retrieval success rate is affected to a greater extent by the penetration depth constraint compared to the DT threshold constraint. For the ocean areas between 40°S and 40°N, as a whole, around 40% of the RO refractivity profiles were rejected due to the penetration depth constraint, and 20% of the profiles were rejected due to the DT threshold constraint, thereby yielding an overall final retrieval success rate of 40%.

      Figure 4.  The MBLH retrieval success rate and the proportions of COSMIC-2 refractivity profiles which are rejected due to the 0.5 km penetration constraint or the DT parameter constraint at different latitude bands between 40°S and 40°N.

      Figure 5 shows the spatial distributions of the DT values and the vertical velocity at the 500-hPa pressure level (positive and negative vertical velocity represents sinking and rising air, respectively). It can be found that the DT values are generally positively correlated with the vertical velocity (i.e., large (small) DT values being obtained in the areas where there is strong sinking (rising) motion). The overall correlation coefficient between the DT values and the vertical velocity is 0.57, being statistically significant at the confidence level of 95%. Comparing Fig. 5a and Fig. 5b, it can be seen that in the Inter-Tropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ), convective motions make it difficult to determine the position of the MBL top. Consquently, the DT values in these regions are generally small. While along the west coasts of South/North America and Africa, and the southern regions of the Indian Ocean, where the respective atmospheres are dominated by large-scale subsidence, the transition between the boundary layer and the free atmosphere is stable, and the DT values in these ocean areas are generally large. Figure 5 indicates that the DT values in the ocean areas are, to a certain extent, related to the structural distinctness of the MBL top.

      Figure 5.  The latitude-longitude distributions of (a) the DT values calculated from the COSMIC-2 RO refractivity data and (b) the 500 hPa vertical velocity derived from the ERA5 dataset on a 0.25° × 0.25° grid.

    3.   Results and analyses
    • Using the algorithm presented in Fig. 3, we extract MBLHs from the refractivity profiles of COSMIC-2 RO and the other three data sources. In the following analyses, we use MBLH_C2, MBLH_RS, MBLH_ECM, and MBLH_AVN to represent the MBLHs derived using the RO data, the radiosonde observations, the ECMWF analyses data, and the NCEP AVN 12-hour forecast data, respectively.

    • The MBLHs derived from the COSMIC-2 RO data are first compared with those derived from collocated high-resolution radiosonde observations. Using the sounding data from the four radiosonde stations introduced in Section 2.1, 493 collocated RO and radiosonde observation pairs are selected within the temporal window of 2.5 h and spatial window of 300 km. It should be noted that in deriving the MBLHs from radiosonde data, the auxiliary surrounding MBLH information is unavailable. So we only used those radiosonde profiles with DT values larger than 0.1, which indicates that the radiosonde-derived MBLHs are obtained using the WCT algorithm independently. Figure 6 illustrates the comparison of the MBLHs derived from these collocated pairs of RO and radiosonde refractivity profiles. It can be seen that the values of MBLH_C2 and MBLH_RS are highly consistent, having a correlation coefficient reaching 0.96 and a mean difference of only 0.06 km. The standard deviation of MBLH_C2 compared with MBLH_RS is 0.2 km, likely due to the RO profiles not exactly lining up with the same points as the collocated radiosonde observations. Moreover, RO profiles represent horizontal averages, and this representative error introduces extra inconsistencies in the comparison (Guo et al., 2011).

      Figure 6.  MBLHs derived from collocated pairs of COSMIC-2 RO and radiosonde observations. The black line represents the least-squares regression line.

    • Figure 7 presents the latitude-longitude distributions and the overall latitudinal variations of the MBLHs at 40°S to 40°N in four different seasons, derived from the COSMIC-2 RO data. High-level MBLHs can be observed over the southeastern Pacific in all four seasons, likely associated with the cloud regimes in this region where widespread MBL clouds are always persistent (Ho et al., 2015). On the other hand, along the southwestern coast and the northwestern coast of the African continent, the western coast of the North American continent, and the ocean near Indonesia, much lower MBLHs with values less than 1.2 km exist, which are more distinct in JJA and SON compared with the other two seasons. In the northern hemisphere (NH), as stratocumulus clouds in the subtropical regions near the California coast gradually transition to cumulus in the tropical regions, MBLHs increase from relatively low values of around 1 km to higher values of around 2 km, which is evident during most seasons. These characteristics of MBLHs are consistent with previous studies (Ao et al., 2012; von Engeln and Teixeira, 2013; Basha et al., 2019). The comparison of the four subfigures of Fig. 7 demonstrates that the seasonal variation of the MBLHs is most significant over the Northwestern Pacific, where the MBLHs are highest in DJF and lowest in JJA, which is probably related to the wind field, noting that the sea surface wind speed in winter is greater there than in summer. Seasonal variations of MBLHs also exist in the southern Atlantic and the southern Indian Ocean. In these marine areas, the highest MBLHs are generally obtained in their local winter season (JJA), whereas in the equatorial eastern Indian Ocean, the seasonal variation of the MBLHs is relatively weak. Moreover, it is worth noting that the latitudinal distribution of MBLH also varies with seasons. In DJF and MAM, MBLHs peak at around 20°N and 20°S and fall to minimums near the equator. In JJA and SON, MBLHs reach the highest at around 20°S. Basha et al. (2019) concluded that the PBL heights peak at 30° latitudes of the two hemispheres on a global scale, which takes into consideration both the land and ocean areas.

      Figure 7.  Seasonal MBLH climatology at the latitudes of 40°S to 40°N derived from COSMIC-2 refractivity data from 2020 to 2021. The dotted blue line at the left (a, c) or right (b, d) side of each panel denotes the latitudinal variation of MBLH on a 4° grid. The seasons are defined as follows: March–April–May (MAM), June–July–August (JJA), September–October–November (SON), and December–January–February (DJF).

      Figures 8ad present scatterplots which show comparisons of the values of MBLH_C2 and MBLH_ECM at the latitudes of 40°S to 40°N during different seasons. Figures 8eh present the seasonal variation of the distributions of the values of ΔMBLHC–E, which is equivalent to MBLH_C2 minus MBLH_ECM. It can be seen that despite the correlation coefficients between MBLH_C2 and MBLH_ECM exceeding 0.8, as shown in Figs. 8ad, widespread positive values of ΔMBLHC–E can be found in all four seasons, and the magnitudes of the biases vary with locations and seasons, as shown in Figs. 8eh. Small biases of less than 0.2 km exist in the areas with large DT values, including the southeastern Pacific, the southern Atlantic, the southern Indian Ocean, and the region near the west coast of North America, mainly due to the large-scale subsidence that exists in these areas. Moderate to large biases of around 0.4 km to 0.8 km are observed in the tropical regions and the northern Atlantic Ocean. Although at the latitudes between 40°S to 40°N, negative values of ΔMBLHC–E can be found in some ocean areas, the percentage of these areas is very small, less than 5% in total. The statistics related to the latitudinal variations of the values of ΔMBLHC–E show that the mean values of ΔMBLHC–E in different 4°-latitude bins mainly vary between 0.1 km and 0.5 km, with generally higher values existing at latitudes between 20°S–20°N compared to subtropical latitudes, further noting that the latitudinal mean values of ΔMBLHC–E are generally smaller in SON than in the other three seasons. Figures 8ik further present the seasonal variations of the statistics for the values of ΔMBLHC–E in three different ocean areas, i.e., the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean. It can be seen that in each of the three ocean areas, the mean values of the ΔMBLHC–E are positive in all four seasons, and the smallest mean values are observed in SON.

      Figure 8.  (a–d) The scatterplots for the values of MBLH_C2 and MBLH_ECM during different seasons. In each subfigure, the red line and the parameter R denote the least-squares regression line and the corresponding correlation coefficient, respectively, which is statistically significant (p<0.05). SD and RMS (units: km) denote the standard deviation and root mean square of all ΔMBLHC–E values. (e–h) The distribution of the values of ΔMBLHC–E during different seasons; the blue bars at the left (e, g) or right (f, h) side of each panel show the corresponding values of ΔMBLHC–E in 4°- latitudinal bins. (i–k) The seasonal variations of ΔMBLHC–E for three different ocean areas, the box-and-whisker plots display the 5th, 25th, 50th, 75th, and 95th percentiles of ΔMBLHC–E, with their means, and SDs marked by red circles and red crosses, respectively.

      Similar to Fig. 8, Fig. 9 presents the comparisons between MBLH_C2 and MBLH_AVN at the latitudes of 40°S to 40°N in different seasons and in the subfigures of Figs. 9ek, ΔMBLHC–A denotes MBLH_C2 minus MBLH_AVN. Notably, positive values of ΔMBLHC–A also exist extensively in all four seasons.

      Figure 9.  Similar to Fig. 8 but for the comparison of the values of MBLH_C2 and MBLH_AVN.

      The overall means for ΔMBLHC–E and ΔMBLHC–A values are 0.25 km and 0.17 km, respectively. The underestimation of MBLHs by ECMWF model data compared to those obtained by RO data has been confirmed by many previous studies (Guo et al., 2011; Ao et al., 2012; Basha et al., 2019). Moreover, it is revealed that MBLHs estimated by NCEP-2 model data are underestimated over the Pacific Ocean compared to radiosonde measurements (Guo et al., 2021). It is worth highlighting that the MBLH differences derived from RO and model datasets are not specific to the WCT method. By using other MBLH detection methods, such as the minimum refractivity gradient method (Ao et al., 2012) and the breakpoint method (Guo et al., 2011), it was also found that the MBLHs derived from model datasets are underestimated compared with those derived from COSMIC RO data, which indicates that the discrepancy between the MBLHs derived from model data and those from RO should not be attributed to the detection method. The insufficient penetration depth of RO data might contribute partly to the inconsistency of the RO-derived and the model-derived MBLHs. As verified by Ao et al. (2012), this factor only accounts for a fraction of the differences in the MBLHs derived from COSMIC RO and model datasets. Considering that the penetration depths of the RO data from COSMIC-2 have distinctly improved compared with those from COSMIC (Schreiner et al., 2020), the impact of this factor should be even weaker. The limited vertical resolutions of model datasets should contribute to the model biases considering that the detection of the MBL top is sensitive to the vertical gradients in the profiles of atmospheric parameters. In addition, errors may also exist when model datasets are generated by assimilating different types of observations to reproduce basic meteorological parameters, which might also be a factor related to the differences between the RO data-derived and the model data-derived MBLHs (Basha et al., 2019).

    • Two tropical ocean regions, the TNP (Tropical Northwestern Pacific: 10°–20°N, 130°–170°E) and the TSP (Tropical Southwestern Pacific: 10°–20°S, 160°E–160°W), were selected to analyze the monthly variations of the MBLHs in the tropical Pacific, and the results are presented in Fig. 10. In these two regions, on average, MBLH_ECM and MBLH_AVN were 0.31 km and 0.20 km lower than MBLH_C2, respectively. While Fig. 10 demonstrates that all three groups of MBLH values, i.e., MBLH_C2, MBLH_ECM, and MBLH_AVN, showed the same monthly variation patterns. Specifically, in the region of TNP, MBLH_C2 fluctuated between 0.91 km (in September) and 1.87 km (in December) from 2020 to 2021, and the fluctuation height range during different months is 0.96 km. In the TSP region, MBLH_C2 varies between 1.08 km, which occurred in March, and 1.67 km, which occurred in August, and the fluctuation height range was only 0.59 km. Using the multi-satellite (COSMIC, GRACE, TERRA-X, and CNOFS) RO observations, Basha et al. (2019) found that the MBLH over the western north Pacific is generally high during local winter compared with other seasons. Our results demonstrate that the TNP and TSP regions both exhibit higher MBLHs in their local winter months.

      Figure 10.  Monthly variation of the MBLHs derived from the three different data sources in the region of the (a) TNP (Tropical Northwestern Pacific: 10°–20°N, 130°–170°E) and (b) TSP (Tropical Southwestern Pacific: 10°–20°S, 160°E–160°W).

    4.   Discussion
    • Wind speed affects the horizontal transport of surface pollutants (Elminir, 2005) and contributes to the intensity of turbulence through mechanical effects (Banta and White, 2003). Due to the fact that turbulence is the basic motion of the MBL atmosphere, to investigate the potential physical mechanisms underlying the temporal and spatial variation patterns of the MBLHs, wind speed is an important factor that should be taken into consideration. Here, we compared the monthly variations of the MBLHs to those of the near-surface wind speeds over the two regions in the tropical Pacific Ocean (TNP and TSP). The results are presented in Fig. 11. It can be seen in Fig. 11a that the MBLH and the near-surface wind speed demonstrate similar monthly variation patterns in the TNP region, with higher and lower values appearing in the local winter and summer months, respectively. Figure 11b shows that in the TSP region, the agreement between the monthly variation pattern of near-surface wind speed and that of MBLH is even higher. The correlation coefficients between the monthly variation of MBLH and that of near-surface wind speed are higher than 0.8 (p<0.05) in both of the two regions, which indicates that wind speed should be the meteorological factor that is most closely related to the monthly evolution of MBLH across the tropical Pacific Ocean.

      Figure 11.  Monthly cycle of the MBLH_C2 values versus near-surface wind speed at 950 hPa over the two regions of the (a) TNP and (b) TSP.

      Besides the relationship between the monthly variation patterns of the MBLHs and wind speeds, we further explore the relationship between the spatial variation of MBLH and that of the near-surface wind speed over the Pacific Ocean. Figure 12 shows the longitudinal variations of MBLHs and near-surface wind speeds in five different tropical and subtropical latitudinal bands with a longitudinal width of 100°. It can be seen that in each of the five latitude bands, MBLH and near-surface wind speed exhibit significant positive correlations with correlation coefficients higher than 0.7 (p<0.05). In Guo et al. (2021), the positive correlation between PBL height and wind speed on a global scale was verified using radiosonde observations, while the radiosonde observations over marine areas are very sparse. Our results concerning the high correlation between MBLH and near-surface wind speed over the Pacific Ocean should complement previous work. The mechanism behind this correlation should be that when the near-surface wind speed increases, the horizontal transportation will be strengthened and the turbulence generated by the mechanical effects will be enhanced, which is known to support the development of the MBL, thus resulting in a higher MBL top, and vice versa.

      Figure 12.  Longitudinal variations of the MBLH_C2 values versus the near-surface wind speeds at 950 hPa in different latitude bands over the Pacific Ocean.

      Notably, over the tropical Pacific Ocean, aside from the wind speed, other factors should also be considered in the mechanism analysis of MBLHs. One factor is the near-surface air temperature, the thermal factor which drives the development of the MBL (Liu et al., 2013), indicative of the overall energy of the lower atmosphere (Guo et al., 2019). Considering that near-surface air temperatures differ only slightly over the tropical Pacific Ocean, our analyses (not presented here) investigating the relationship between the MBLH and the near-surface temperature show that no significant correlation exists between them, indicating that the thermal factor may not be an important driver that governs the variability of MBLH over the tropical Pacific Ocean. Another factor that needs to be considered is marine pollution, such as plastic pollution, which has increased greatly in recent years and has significantly affected the marine environment (Cole et al., 2011). As the MBL is the layer directly influenced by the sea surface, the possible effect of marine pollution on the variation of the MBLH requires special attention. How to address these multiple effects and the interaction among them is a complex topic that needs long-term investigation in the future.

    5.   Summary
    • The latest COSMIC-2 RO observations with high density and high vertical resolution provide a powerful database for detecting the MBLHs over the tropical and subtropical oceans and analyzing their spatial and temporal variation patterns. In the present work, we use COSMIC-2 RO refractivity data from January 2020 to December 2021 to study the characteristics of MBLH in the latitude regions between 40°S and 40°N. The MBLHs are essentially detected using the WCT algorithm. To improve the objectivity of the MBLH inversion process, a DT parameter is defined. For a profile with DT value less than the threshold value of 0.1, the computed maximum value and the sub-maximum value of Wf are very close. Rather than directly defining the MBLH as the height corresponding to the maximum value of Wf, we use the interpolated height based on the MBLHs retrieved from the surrounding refractivity profiles for the final determination of the MBLH value.

      Using the modified WCT algorithm, all the COSMIC-2 RO refractivity profiles located within the marine areas between 40°S and 40°N are processed, and the distributions of the retrieved MBLHs are analyzed. We find that a positive correlation exists between the DT parameter and the vertical velocity, i.e., DT parameters are generally large in areas with intense subsidence and small in areas with deep convection, which indicates that the DT parameter could be recognized as an indicator for the distinctness of the MBL top structure. The MBLH values derived from COSMIC-2 and those from collocated radiosonde observations demonstrate consistency. Compared with MBLH_C2, both MBLH_ECM and MBLH_AVN have negative biases in most parts of the tropical and sub-tropical ocean areas during all four seasons, which is consistent with previous studies and should be partly attributed to the limited vertical resolutions of the model datasets.

      We establish an MBLH climatology during different seasons over the middle- and low-latitude oceans where situ observations are insufficient. MBLHs exhibit obvious seasonal variations over the northwestern Pacific Ocean, the southern Atlantic Ocean, and the southern Indian Ocean, with peak values appearing during the local winter season. The monthly variation patterns of MBLHs over the TNP and the TSP regions show remarkable positive correlations with their near-surface wind speeds. Moreover, significant positive correlations also exist between the longitudinal variations of MBLHs and those of the near-surface wind speeds in different latitude bands of the Pacific Ocean. The present work represents a great potential contribution of COSMIC-2 RO data for studies concerning tropical and subtropical MBL structures. It can be expected that continued COSMIC-2 RO observations will prompt further insights into the temporal and spatial variations of MBLHs and help to facilitate a thorough understanding of the related background mechanisms.

      Acknowledgements. This work is supported by the National Natural Science Foundation of China (Grant Nos. 42174017, 42074027, 41774033, and 41774032). The authors would like to express their gratitude to the University Corporation for Atmospheric Research (UCAR) for providing the COSMIC-2 RO data. The European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) Aviation (AVN) 12-hour forecast data, interpolated to the time and locations of the COSMIC-2 RO observations, were also provided by the CDAAC. Radiosonde data were obtained from the University of Wyoming via the website http://weather.uwyo.edu/upperair/bufrraob.shtml.

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