Investigating Tropical Cyclone Warm Core and Boundary Layer Structures with Constellation Observing System for Meteorology, Ionosphere, and Climate 2 Radio Occultation Data

Abstract

The Constellation Observing System for Meteorology, Ionosphere, and Climate 2 (COSMIC-2) collects data covering latitudes primarily between 40 degrees north and south, providing abundant data for tropical cyclone (TC) research. The radio occultation data provide valuable information on the boundary layer. However, quality control of the data within the boundary layer remains a challenging issue. The aim of this study is to obtain a more accurate COSMIC-2 radio occultation (RO) dataset through quality control (QC) and use this dataset to validate warm core structures and explore the planetary boundary layer (PBL) structures of TCs. In this study, COSMIC-2 data are used to analyze the distribution of the relative local spectral width (LSW) and the confidence parameter characterizing the random error of the bending angle. An LSW less than 20% is set as a data QC threshold, and the warm core and PBL composite structures of TCs at three intensities in the Northwest Pacific Ocean are investigated. We reproduce the warm core intensity and warm core height characteristics of TCs. In the radial direction of the typhoon eyewall, the impact height of the PBL increases from 3.45 km to 4 km, with the tropopause ranging from 160 hPa to 100 hPa. At the bottom of the troposphere, the variations in the positive and negative bias between the RO-detected and background field bending angles correspond well to the PBL heights, and the variations in the positive bias between the RO-detected and background field refractivity reach 14%. This research provides an effective QC method and reveals that the bending angle is sensitive to the PBL height.

1. Introduction

Tropical cyclones (TCs) are cyclonic low-pressure systems with warm core structures that are often accompanied by extreme weather, such as strong winds and heavy rainfall. In the horizontal direction, TCs are divided into three regions from the center outward: the eye, eyewall, and outer gale regions. The eye region is dominated by subsiding airflow with almost no clouds or rain, the eyewall region is characterized by intense convective activity, and the outer gale region contains convective structures such as convective cloud masses and spiral rainbands. In the vertical direction, the strength and height of the warm core are important descriptive features in TC systems. The warm core strength refers to the maximum positive temperature anomaly, and the warm core height refers to the height at which this positive temperature anomaly is located. These two physical quantities reflect changes in TC intensity [1,2]. The tangential wind generally decreases with height in TC circulation. To maintain the thermal wind balance, and there is a negative radial temperature gradient; thus, the temperature increases inward and forms the warm core structure of the TC. The change in TC surface pressure is closely related to the change in the warm core structure based on the hydrostatic balance [3]. The ability to establish an upper-tropospheric warm core is vital for TC formation and intensification [4]. Numerous studies have shown that the development and strengthening of the warm core is a necessary condition for TC intensification [5,6,7]. In addition to the warm core strength, TC intensity is also very sensitive to the warm core height [4]. Both observational [8] and theoretical studies [9,10] have illustrated that a high-level warm core has an important effect on the strengthening of a TC. The radio occultation (RO) technique is an active proximity observation technique via satellite remote sensing that has high vertical resolution, long-term stability, all-weather applicability, rare influences of clouds and rain, unbiased data, and low instrument cost. Since the first launch of a global navigation satellite system (GNSS) RO project in 1995, RO technology has become an important tool for improving the accuracy of numerical weather prediction (NWP).

As the latest generation of GNSS RO observation programs, the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC)-2, was launched in 2019. Using GPS receivers mounted on low-Earth-orbit (LEO) satellites, two long-wave signals ($f_{L1}$ = 1575.42 MHz and $f_{L2}$ = 1227.60 MHz) emitted by GPS satellites and passing through the atmosphere can be detected. As the refractivity of the atmosphere changes in the vertical direction, the signals are refracted. Therefore, the phase change of the two signals at different frequencies can be measured to characterize information such as bending angles and impact parameters. This constellation consists of six LEO satellites with orbital inclinations of 24 degrees, which cover the region within 40 degrees north–south latitude and are concentrated in the tropics. COSMIC-2 employs more powerful satellite antennas and a higher sampling frequency, where 4000 to 5000 atmospheric profiles can be acquired per day [11]. Additionally, with its advanced open-loop tracking technique, approximately 85% of COSMIC-2 RO profiles can be detected at heights less than 1 km, even close to the ocean surface [12]. These observational capabilities yield valuable data for studying the internal and boundary layer structures of TCs.

Although studies have been conducted to analyze the internal structure of TCs via numerical model simulations [13,14], relatively few direct observations exist. Bi and Zou [15] revealed the structures of typhoon Muifa in brightness temperature observations at microwave humidity sounder-2 from Fengyun-3E. They found a significant symmetric component in the eyewall and inner core and deep convective systems of Muifa. Conventional remote sensing tools such as microwave temperature sounders and atmospheric infrared sounders have provided direct observational data on TCs, including changes in the size and intensity and warm core structures of TCs, but they still have the shortcomings of insufficient vertical resolution and strong attenuation of the detection signal by clouds and rain [1,16,17,18]. These shortcomings limit our understanding of the internal structure and evolution of TCs. Few studies have investigated the structure of TCs via COSMIC-2. Anthes et al. [19] compared deviations between COSMIC-2 and other reanalysis data in a hurricane and reported that COSMIC-2 had smaller deviations, but they did not explore the internal structure of TCs. In general, the value of COSMIC-2 RO information has not been well exploited, especially when it is applied to TCs.

Traditionally, the boundary layer height is determined mainly by the maximum potential temperature gradient; however, for RO data, the refractivity contains both temperature and humidity information, so a method based on the refractivity gradient can be used to determine the boundary layer height more accurately [20]. The local gradient method proposed by Wang et al. [21], in which the spherically symmetric refractivity is subtracted from the traditional refractivity gradient, highlights the local variability in the atmosphere and improves the accuracy of boundary layer height determination. Garnés-Morales [22] determined the atmospheric boundary layer height from COSMIC-2 refractivity data. We hope that COSMIC-2 data can be used to facilitate discoveries from different perspectives.

This paper focuses on proposing an effective quality control scheme to reduce the random error of COSMIC-2 RO data. We can improve the quality of GPS RO data and reveal TC structures. Our research provides a quality control method with a physical principle and improves the range of applications of COSMIC-2 RO. We observe the warm core structure of TCs by GPS RO. Moreover, we explore the structure from the perspective of the bending angle and deviation in the refractivity in the TC boundary layer. We find that the bending angle is sensitive to the boundary layer height, which provides a new method for determining the boundary layer height. However, this method is unable to be used for determination via refractivity.

This paper is arranged as follows: Section 2 describes the COSMIC-2 RO and TC data used in this study and provides a quality control scheme to reduce the random error of the bending angle. Section 3 presents an analysis of the statistical characteristics of the warm core structure at different TC intensities and an analysis of the boundary layer structure in terms of the bending angle and refractivity deviation relative to the background field. Discussions and conclusions are provided in Section 4. Detailed flowchart (Figure 1) is as follows.

2. Data and Methods

2.1. Description of RO Data

The GNSS RO profiles used for this study are obtained from the COSMIC-2 satellites, which are provided by the COSMIC Data Analysis and Archival Center (CDAAC) [23], from October 2019 to December 2022. In this study, we use secondary products of COSMIC-2, including atmospheric profiles (atmPrfs), one-dimensional variational (1D-Var) wet retrieval profiles (wetPf2s), and model profiles provided by the European Center for Medium-Range Weather Forecasts (ECMWF) (echPrfs). The atmPrf product provides impact parameters, bending angles, altitudes, refractivity, and spatial field information such as atmospheric pressure and temperature without vapor. The wetPf2 product includes information on the pressure, temperature, and specific humidity in the actual atmospheric state (considering water vapor). The echPrf product provides information on the temperature, pressure, and water vapor pressure of the numerical model data at the location of the RO event.

2.2. Description of the Best Track Data

In this study, we use the Western Pacific Typhoon Best Track dataset from 2019 to 2022 for typhoon monitoring. This dataset is provided by the National Oceanic and Atmospheric Administration (NOAA) and archived in the International Best Track Archive for Climate Stewardship (IBTrACS). The dataset includes information on the latitude, longitude, maximum wind speed, minimum pressure, and intensity level of the TCs at each observation point, as well as additional information on other parameters, such as the radius of the maximum wind speed and the environmental field pressure. The temporal resolution is 3 h. The agency classifies TCs into three categories on the basis of the 1 min mean wind speed, namely, tropical depression (TD, <34 kts), tropical storm (TS, 34–64 kts), and typhoon (TY, >64 kts), where TYs are divided into five classes on the basis of their intensity (from Cat 1 to Cat 5). This dataset provides the best track information for all oceans and is important for analyzing TCs.

2.3. Collocation Criteria

Owing to the small amount of COSMIC-2 RO data from a single TC at a given moment, we adopt a method of synthetic analysis to obtain the composite structural characteristics of TCs. In this study, we combine COSMIC-2 RO profiles near multiple TCs at various times, consolidating data around the same TC center to increase the data volume and enrich the meteorological information available for TC research. Based on the classification criteria from the IBTrACS, we categorize TC intensity into three levels: TDs, TSs, and TYs. We collocate COSMIC-2 RO profiles with TCs in a spatiotemporal framework, creating composite structures for each intensity category: TD composite structure, TS composite structure, and TY composite structure. The concrete collocation criteria between the RO profiles and TC cases are set to a temporal difference of less than one hour and a radial distance of less than 1000 km from the TC centers. The radial distances from the TC center are averaged every 50 km. From these datasets, the eligible RO profile TC datasets are filtered to obtain synthetic field information.

2.4. Method of Quality Control

Yang et al. [24] used RO data to study the structure of the temperature and water vapor fields of TCs. In that study, the results before and after quality control were compared, which revealed that the structural features of TCs would have been greatly distorted if outliers had not been excluded. Therefore, quality control is necessary before the COSMIC-2 RO data can be assimilated.

The temperature and water vapor fields of TCs retrieved from the 1D-Var method is based on the refractivity retrieval, which is in turn obtained through the Abel transform under the assumption of local spherical symmetry. Therefore, when RO rays pass through TCs, if the atmospheric state exhibits a strong horizontal gradient, it will affect the accuracy of the retrieved observations. The wave optics (WO) method in the lower troposphere is usually used to calculate the RO bending angle. When the atmosphere is in a state of nonspherical symmetry, multiple rays have the same impact parameter, so the spectrum of the RO signal calculated via the WO method contains multiple wave components, thereby increasing the overall width of the spectrum [25,26]. For this reason, Gorbunov et al. [27] introduced a method for estimating errors based on the local spectral width (LSW). The LSW is a physical quantity that characterizes the random error of the bending angle in RO detection [28].

Another physical quantity that is closely related to the quality of the bending angle data is the confidence parameter, which is given by the following equation.

$$CP=1-{\displaystyle \frac{P_2}{P_1}}$$

(1)

where $P_1$ and $P_2$ denote the intensities of the largest and second largest peaks in the local wave spectrum of the bending angle, respectively. The clearer the maximum spectral component is, the larger the confidence parameter [29]. The characteristics of the spatial distribution of the LSW and the confidence parameters (Figure 2) include all the collocated data. The horizontal coordinate is the radial distance from the center of the TC, and the vertical coordinate is the impact height. The LSW broadens with decreasing impact height, up to ${10}^{-2}$ rad. The confidence parameter is greater than 95% above 8 km and decreases with decreasing impact height below 8 km, with a value of 27% at the bottom of the troposphere. This finding indicates that the confidence is low in the lower TC troposphere, with large uncertainties in the bending angle. In addition, the lowest detectable impact height of the COSMIC-2 RO profile can reach 2.4 km, which translates to an altitude of approximately 0.6 km. This lowest penetration height is lower than the boundary layer height of the TC; thus, the boundary layer information of the TC can be obtained directly from the RO observations.

Since the bending angle varies exponentially with height, it is tens of times greater in the lower troposphere layer than in the upper troposphere layer, so the characteristics of the random error distribution cannot be elucidated by the LSW alone. In this work, the LSW is expressed as a percentage, where the distribution of the random error of the bending angle is explored from the perspective of the change in the LSW relative to the bending angle, as shown in the following formula, which is subsequently referred to as simply the LSW.

$$\mathrm{L}\mathrm{S}\mathrm{W}={\displaystyle \frac{\mathrm{L}\mathrm{S}\mathrm{W}}{\mathrm{B}\mathrm{A}}}\times 100\mathrm{\%}$$

(2)

The LSW broadens with decreasing impact height before quality control is applied, where significant broadening is concentrated in the lower troposphere, from 12% to 28% within 1 km range (Figure 3). The LSW broadens with increasing distance from the center of the TCs below 4 km, from 12% to 15% at 300 km and from 15% to 18% at 550 km from the center. Moreover, the vertical gradient of refractivity suddenly increases at 500 km away from the TC center [30]. Therefore, the large refractivity gradient associated with the large water vapor gradient in the tropics is one reason why the random error in the bending angle becomes larger. The LSW is close to 30%, and the confidence parameter is less than 30% in the lower troposphere, which decreases the reliability of the results of RO inversion. Therefore, strict quality control of the RO data is necessary.

The deviation between the bending angle observations and the background field represents the systematic bias of the bending angle. We find that the deviation in bending angle observations from the background field can be effectively reduced by screening the LSWs within a specific range. Thus, we divide the LSW into three intervals—LSWs less than 20%, an LSW in the interval of 20–35%, and LSWs greater than 35%—to explore its systematic bias (Figure 4).

In the lower troposphere, the deviation in bending angle observations from the background field is mainly negative. Below 3.7 km, the deviation decreases to a minimum value and then increases. The deviation remains fluctuating slightly above 3.7 km. As the LSW decreases, the deviation between the bending angle observations and the background field decreases notably. When the LSW is less than 20%, the negative deviation is less than −12%, which is lower than the observation error in the bending angle calculated via the three-cornered hat method [31]. Therefore, in this study, an LSW of less than 20% is used as the threshold for determining the quality of RO data to ensure the reliability and accuracy of the data.

The quality control implemented in this study is divided into two main steps to ensure the reliability of the data. The first step is a range check, which eliminates data with negative refractivity and removes records with temperatures lower than −150 °C and higher than 80 °C. This step also removes RO profiles that do not penetrate to a sufficiently low level, as defined by the threshold value of 850 hPa. The second step is to exclude RO data with an LSW greater than 20%.

The comparison reveals that quality control removes the region in which the LSW broadens markedly in the lower troposphere (Figure 5). Although the LSW still increases with decreasing impact height after quality control, its maximum width is limited to 16%. More than 60% of the data are reserved above the impact height of 2.8 km. Although quality control removes a large amount of data, more than 20% of the data are retained below 2.8 km. In addition, the number of RO profiles that correspond with quality control criteria increases with increasing distance from the centers of TCs. More than 100 profiles in the range greater than 100 km and above 3.2 km are retained. The number of RO profiles can reach tens of profiles in the range of 0 to 100 km from the centers of TCs.

The mean deviation in the bending angle is reduced by 60% via quality control below 4 km (Figure 6a), indicating that the mean deviation in the bending angle is notably reduced to 1% at the bottom of the troposphere. Above 6.4 km, the mean deviation in the bending angle remains almost stable. The standard deviation of the bending angle decreases by nearly 60% when quality control is applied at the bottom of the troposphere (Figure 6b), indicating that quality control significantly improves the consistency of the data. In contrast, the standard deviation decreases by 2% in the impact height range of 2.8–7 km, whereas the standard deviation of the bending angle remains constant above 7 km. These results show that the adopted quality control scheme is particularly effective for the bottom of the troposphere, notably reducing the random errors of the bending angle in the lower atmosphere.

3. Results

To assess whether COSMIC-2 has enough data to be used in weather systems independently, we choose the TC structure as an example for analysis. We separate all the collocated data into three fields, namely, TDs, TSs, and TYs, via composite analyses. The number of collocated profiles exceeds 10,000, and the number of collocated TCs reaches 93, of which 200–300 profiles can be collocated throughout the whole life cycle of a single typhoon on average. The amount of data eligible for matching increases with distance from the center of the TCs (Figure 7). More than 400 TS profiles located 900–1000 km from the center of the TCs are collocated. The number of RO profiles in the eyewall and eye regions is relatively small, but it is still possible to attain dozens of profiles. Among the intensities, TSs have the largest sample size, TDs have the second-largest sample size, and TYs have the smallest sample size. These findings indicate that the profiles are sufficient for observing the structural characteristics of TCs from the eye region to the spiral rainband and the outer gale region.

3.1. Warm Core Structure of Tropical Cyclones

To validate the RO data, we choose warm cores as a concrete feature because they are among the most distinctive features of TCs. Through strict quality control, we successfully invert the temperature anomalies of TCs at different intensities and calculate the tropopause height on the basis of the rate of temperature decrease. The COSMIC-2 data clearly depict the warm core structures of TCs and the cold temperature anomalies above the tropopause. From the TDs (Figure 8a) to the TSs (Figure 8b) and then to the TYs (Figure 8c), the range of warm temperature anomalies increases from 400 hPa to 150 hPa; the structure of the warm core gradually becomes clear, and the structure of the double warm core appears in the TSs, with the maximum temperature anomaly reaching 5 °C; the warm core height increases from 450 hPa to 280 hPa; and there are corresponding cold temperature anomalies in the stratosphere above the region of the warm core. The two sets of temperature maxima at 50–100 km and 150–200 km from the center of the TYs may be related to the release of latent heat from many particles in the eyewall region or spiral rainband of the TYs, respectively. Notably, the warm temperature anomaly in the eyewall region of the TYs is accompanied by a lift in the tropopause of approximately 50 hPa, resulting from intense convective activity in the eyewall region. In general, the upper-middle troposphere of TYs has the strongest warming anomaly, the largest vertical range of warming, and the highest warm core height, followed by those of TSs, and the TDs have the weakest warming anomaly, the smallest vertical range of warming, and the lowest warm core height.

The above results indicate that the warm core strength and warm core height increase as TCs strengthen, and the tropopause height increases markedly in the TY eyewall region. This finding means that the warm core strength and warm core height are closely related and that the results reflect the activity of the internal thermal mechanism of TCs.

3.2. Boundary Layer Structure of Tropical Cyclones

Since COSMIC-2 data can be used to detect boundary layer information, we explore the boundary layer structure of TCs through RO data. In this study, we characterize the boundary layer height in terms of the gradient extremes of the bending angle profile and analyze the boundary layer structure of TCs from the perspectives of the bending angle and refractivity. The formulas for the deviation of the bending angle and the atmospheric refractivity are given first as follows:

$$a_{anomaly}={\displaystyle \frac{\alpha -{\alpha }_b}{\alpha }}\times 100\mathrm{\%}$$

(3)

$$N_{anomaly}={\displaystyle \frac{N-N_b}{N}}\times 100\mathrm{\%}$$

(4)

where $\alpha$ and $N$ represent the observed values of the bending angle and refractivity, respectively, and where ${\alpha }_b$ and $N_b$ represent the background fields of the bending angle and refractivity, respectively.

In the TC boundary layer, the deviation in the bending angle shows dramatic numerical changes (Figure 9). The deviation in the bending angle with respect to the background field changes from negative (~−50%) to positive (~40%) from the bottom up in the lower troposphere. Quality control results in an overall increase in the boundary layer height and eliminates anomalously large values in the eyewall region. After quality control, the boundary layer heights of TCs uplift among the radial direction, which is consistent with the result of airborne observations [30]. The boundary layer heights of TCs generally manifest an upward-arching feature while different intensities change to different degrees. In the eye region, boundary layer height increases from 3.3 km (TSs) to 3.45 km (TYs). At distances of 500 km and farther than the center of the TSs and TYs, boundary layer height locates just between the positive and negative deviations in the bending angle. But boundary layer height of TDs does not have such obvious features, because TDs do not have a mature structure. Therefore, the positive and negative variations in the bending angle relative to the background field can be used to determine the boundary layer height, and the bending angle can capture the detailed information in the boundary layer, representing a potential new metric for determining the TY boundary layer height.

The variation in the atmospheric refractivity in the boundary layer becomes less pronounced as the bending angle changes (Figure 10). Overall, the refractivity is dominated by positive deviations below 5 km. From 2.3 km to 3.5 km, the refractivity has positive deviations of more than 10%, and they can reach a maximum of 14%. The positive deviation of the refractivity focuses mainly on 2–4 km in the vertical direction and within 350 km in the radial direction. Before and after quality control, the deviation in the refractivity remains relatively constant, as does the boundary layer height. Notably, the positive refractivity deviations are concentrated above the boundary layer height, especially 300 km from the center of the TCs, which reflects the strong convective activity of the TC eyewalls or spiral rainbands that produce rain from clouds. Previous research has shown that in deep convective clouds, the contributions of liquid and ice water are neglected in the observational operators of GPS RO, which is the main reason for the positive bias within clouds [32,33,34]. This positive bias increases further in the TC boundary layer structure, indicating that the liquid and ice water terms cannot be neglected in the inversion process. In summary, the bending angle can capture the detailed information in the boundary layer and indicate the boundary layer height, whereas the refractivity is not sensitive to the boundary layer.

4. Discussion and Conclusions

In this study, we analyzed the distributions of the relative LSW and confidence parameters characterizing the random errors in the bending angle via COSMIC-2 RO data. We found that when the LSW is less than 20%, the deviation and standard deviation of the bending angle observation from the background field at the bottom of the troposphere are reduced by 60%, making the deviation in the bending angle smaller than the observation error. By setting an LSW of less than 20% as the quality control threshold, we explored the warm core characteristics and boundary layer structure of TCs with high-precision data from the COSMIC-2 RO observing system.

The relationships between the intensities of TCs and warm core characteristics were discussed first. We found that the temperature anomaly and height of the warm core increase significantly as TCs develop. During TDs, the temperature anomaly of the warm core is approximately 3 °C, whereas during TYs, this temperature anomaly can increase to 5 °C. Correspondingly, the height of the warm core increases from the lower-pressure layer (~450 hPa) to the higher-pressure layer (~280 hPa). These increases in temperature anomalies and warm core heights not only reveal the close connection between TC intensity and warm core properties but also reflect the activity of the internal thermal mechanism of TCs. This study verified that COSMIC-2 data can be used as independent observation data to detect the internal structure of TCs. As a result, COSMIC-2 can be assimilated into numerical model simulations.

We also discussed the characteristics of the boundary layer structure of TCs. The height of the boundary layer increases with increasing radial distance from the center of a concrete TC, especially in regions with strong convective activity (300 km radius). For TYs, for example, the impact height of the boundary layer increases from 3.45 km to 4 km from the center of TYs to a radial distance of 1000 km, and the tropopause height increases from 160 hPa to 100 hPa. In addition, the impact height of the boundary layer in the eye region increases from 3.3 to 3.45 km from TSs to TYs. The impact height is accompanied by a corresponding increase in the tropopause, which reflects the increase in energy transport and convective activity within the boundary layer.

Furthermore, we analyzed the relationship between the boundary layer structure and the thermodynamics of TCs. A close correlation exists between the deviation in the bending angle observations from the background field and the boundary layer height. At the bottom of the troposphere, the deviation in the bending angle is −50% at 3.7 km but increases to 40% at 4.2 km. This shows that the positive and negative changes in the deviation in the bending angle correspond well to the changes at the top of the boundary layer. The refractivity exhibits a significant positive deviation at the top of the boundary layer, reaching 14%. These findings reveal the dynamic and thermodynamic properties of the boundary layer of TCs and emphasize the importance of bending angle measurements in capturing the details of the boundary layer.

This study demonstrates the remarkable potential of RO data in providing a deep understanding of the internal structure of TCs. Although RO observation data in the eye region of TCs are still limited, which affects the detailed analysis of the structure of individual TYs, with the rapid development of commercial small-satellite technologies, such as the Tianmu and Yunyao RO projects in China and the Spire and GeoOptics RO projects in the United States, global atmospheric observations with higher quality will become available. These advances will greatly facilitate detailed analyses of the complex structural features of TCs, making it possible to analyze the integrated structure of individual TYs. As the data source only comes from COSMIC-2, we will consider incorporating comparisons between COSMIC-2 and other remote sensing sources into future in-depth research, including cross-validation with datasets to confirm the reliability of the COSMIC-2 observations.

In conclusion, applying LSW as a QC metric enhances the integrity of the retrievals by filtering out data impacted by strong horizontal gradients that could violate the local spherical symmetry assumption, particularly in complex TC environments. This approach aligns the theoretical framework with the observed data, minimizing inconsistencies introduced by atmospheric asymmetries. By using LSW to select data that is more likely to meet the spherical symmetry assumption, we strengthen the robustness and reliability of the retrievals, making them more suitable for subsequent applications.