GNSS-RO Deep Refraction Signals from Moist Marine Atmospheric Boundary Layer (MABL)

Abstract

The marine atmospheric boundary layer (MABL) has a profound impact on sensible heat and moisture exchanges between the surface and the free troposphere. The goal of this study is to develop an alternative technique for retrieving MABL-specific humidity (q) using GNSS-RO data in deep-refracted signals. The GNSS-RO signal amplitude (i.e., signal-to-noise ratio or SNR) at the deep straight-line height (H_SL) was been found to be strongly impacted by water vapor within the MABL. This study presents a statistical analysis to empirically relate the normalized SNR (S_RO) at deep H_SL to the MABL q at 950 hPa (~400 m). When compared to the ERA5 reanalysis data, a good linear q–S_RO relationship is found with the deep H_SL S_RO data, but careful treatments of receiver noise, SNR normalization, and receiver orbital altitude are required. We attribute the good q–S_RO correlation to the strong refraction from a uniform, horizontally stratiform and dynamically quiet MABL water vapor layer. Ducting and diffraction/interference by this layer help to enhance the S_RO amplitude at deep H_SL. Potential MABL water vapor retrieval can be further developed to take advantage of a higher number of S_RO measurements in the MABL compared to the Level-2 products. A better sampled diurnal variation of the MABL q is demonstrated with the S_RO data over the Southeast Pacific (SEP) and the Northeast Pacific (NEP) regions, which appear to be consistent with the low cloud amount variations reported in previous studies.

1. Introduction

The atmospheric boundary layer (ABL), an interface between the free troposphere and the surface, plays a key role in regulating exchanges of sensible heat and moisture fluxes through turbulent processes, as well as in the transport of aerosols, pollutants, and greenhouse gases [1]. In the case of marine ABL (MABL), cloud formation and atmosphere–ocean interactions are determined by key variables such as ABL height (ABLH) and water vapor mixing ratio (q) abundance. Because of large ABL variability and complex processes in this shallow layer, lack of all-sky q and ABLH measurements on a global basis means poor constraints on model parameterization schemes and hinders the understanding and representing of these processes in global climate models (GCMs) [2,3,4]. As a result, large uncertainties remain in current GCMs and their low-cloud feedback processes [5].

It has been a great challenge to remotely sense MABL q from space, not only because MABL is a shallow layer but also because clouds often prevent sensors from penetrating into this layer. While the total column of water vapor (CWV) can be measured well with satellite microwave (MW) [6] and shortwave-IR (SWIR) [7] sensors, the q observations within the MABL are still limited. Millan et al. [8] attempted to use the differencing between MW-CWV and SWIR-CWV above cloud to infer MABL q, but the technique requires accurate knowledge of MABL cloud top and temperatures. Thus, the inferred MABL q with this differential technique is prone to SWIR-CWV errors above clouds.

Global Navigation Satellite System Radio Occultation (GNSS-RO) has emerged as a promising new technique to remotely sense MABL on a global all-weather basis. Because GNSS-RO can penetrate clouds from a rapidly growing number of SmallSat/CubeSat constellations, the technique has the advantage of providing the needed global spatiotemporal sampling to better characterize the MABL q and its variability. The GNSS-RO technique offers a good (~200 m) vertical resolution and sensitivity to the ABL top associated with a sharp vertical gradient in moisture/temperature profiles, which produce a measurable signal in the bending angle (a) or refractivity (N) profile. The gradient method for the a or N profile has been successfully applied to GNSS-RO data to measure ABLH [9,10,11,12].

However, MABL q measurements are still lacking, because only a small fraction of the a or N profiles in GNSS-RO operational Level-2 products can reach below ABLH to provide the MABL q measurement. Approximately 50% of the RO profiles from COSMIC-1 (Constellation Observing System for Meteorology, Ionosphere, and Climate-1) can reach to 1 km above the surface in the tropics, and less than 10% down to 0.5 km. It requires a good signal-to-noise ratio (SNR) from GNSS-RO to produce the useful excess phase measurements, of which the latter is essential to retrieve the a or N profile. Because the lower tropospheric RO SNR decreases with height due to atmospheric defocusing effects, the number of useful excess phase measurements for the a or N retrievals drops substantially as the signal becomes noisy. As a result, most of the GNSS-RO water vapor measurements and intercomparison studies have been limited to the regions above the ABL at pressures <900 hPa or over landmasses where radiosonde observations are available from the routine operation [13,14,15]. In addition, the RO N retrieval from the Abel inversion is known to have a low bias in the lower troposphere, which leads to a dry bias in the derived MABL q [16,17]. It remains as an active research topic to understand its root cause and develop correction methods. Because of these limitations, the GNSS-RO a or N data in the lower troposphere (<8 km) have not been used in most of the global forecast and data reanalysis systems [18].

Motivated by the need for more accurate MABL q observations, the goal of this study is to develop an alternative technique for MABL q using the GNSS-RO measurements from deep-refracted signals. Here we focus on the relationship between the MABL q abundance and the SNR at straight-line heights (H_SL) below −80 km where the RO receiver is far into the occulted situation. We found that the SNR from deep H_SL is correlated strongly with the MABL q abundance at 950 hPa (or 400 m) above the sea level (Z_s). To better understand the causes and limitations of deep H_SL SNR signals, we investigated the signals from different H_SL levels as well as the potential applications of these deep H_SL SNRs in MABL q data assimilation.

2. Method and Data Analysis

Systematic studies of GNSS-RO SNR from deep H_SL are enabled by the now-widely used open-loop (OL) operation since successful experiments on planetary [19] and terrestrial atmospheres [20]. The OL operation allows the RO signal to be tracked continuously at deep H_SL even where SNR becomes noisy or experiences a temporary loss. Unlike a closed-loop (CL) operation, in which a phase-locked loop (PLL) circuit is used to track the signal frequency based on previous measurements, in an OL operation, the receiver relies on a modeled reference signal frequency from orbit dynamics, receiver clock drift, and estimated atmospheric bending effects to track the anticipated RO signal regardless of SNR fluctuations. The CL operation works well in cases where SNR is strong, but a long period of low SNRs would prevent the PLL from updating the reference signal and result in a loss of tracking the GNSS signal. The introduction of the OL operation is meant to reduce the number of loss-of-tracking incidences so as to improve the sampling at low H_SL. In most current GNSS-RO operations, the transition from CL and OL occurs approximately at H_SL = −20 km, and the hybrid CL-to-OL operation is implemented for both rising and setting RO soundings.

2.1. GNSS-RO Bending in a Moist Atmosphere

Although both RO SNR and phase measurements contain information about MABL properties, the SNR-based techniques are least explored in GNSS-RO research. Because GNSS-RO SNR is a radiometric signal, a proper calibration scheme, in either the absolute or relative sense, must be established before RO radiometry can be applied for physical variable retrievals. It remains as an active research area to fully understand how a thin atmospheric layer refracts the transmitted radio signal down to these deep H_SL in the RO sounding. In a research monograph, Melbourne [21] provided a comprehensive review on spaceborne GNNS-RO fundamentals, system error sources, and diffraction effects associated with the RO signal. Like Fresnel diffraction from an obstacle’s edge, the Earth’s limb and a sharp MABL can produce a diffractive effect on the RO signal. This diffractive effect can extend the signal below the sharp edge of the obstacle but with a limited depth. It requires both refractive and diffractive processes in the radio wave propagation to produce the RO signal at deep H_SL. In a simulation study using the multiple phase screen (MPS) model [21], sensitivity analysis confirmed that the diffraction and refraction from a thin moist layer can strongly impact characteristics of RO signals at deep H_SL, as predicted from the analytical solution [21]. Sokolovskiy et al. [22] also showed that the deep H_SL signal depends not only on the vertical gradient of MABL but also on the horizontal extend of the stratiform layer.

The GNSS-RO phase-based technique, which is employed in the operational Level-2 data processing, determines the atmospheric refractivity profile from bending-induced excess phase measurements. The excess phase is the difference between straight-line distance and bended/delayed wave propagation length. The refractivity N of radio wave propagation can be modulated by atmospheric pressure (P), temperature (T), moisture pressure (P_w), and ionospheric electron density (n_e), as in Equation (1)

$$N=\left(n-1\right)\times {10}^6=76.6\frac{P}{T}+3.73\times {10}^5\frac{P_w}{T^2}-4.03\times {10}^7\frac{n_e}{f^2}$$

(1)

where n is the atmospheric/ionospheric refractive index, P and P_w are in hPa, T is in K, n_e is in m⁻³, and f is the RO frequency in Hz. Water vapor-specific humidity q is related to P and P_w in $q\approx 0.622·P_w/\left(P-0.378·P_w\right)$. As shown in Figure 1, the vertical gradient of the atmospheric N profile plays a critical role in the bending effect on the GNSS-RO signals. Any sharp N gradient can induce strong scintillation, ducting, and diffraction effects, causing a temporary loss of RO signals. As summarized below, these effects are common in the GNSS-RO observations in the lower atmosphere:

• Normal bending: As radio waves pass through the atmosphere, their paths are bended by the atmospheric refractivity N profile with a vertical gradient. This vertical N gradient acts as an optical prism to refract and diverge the RO beam, causing a weaker power per receiving area compared to the free-space case. This is known as the defocusing effect [17]. Thus, the RO signal amplitude, or SNR in voltage (V/V), decreases gradually at lower H_SL due to the defocusing effect. In the presence of a sharp N vertical gradient, such as the ABL top, a threshold may be used to detect ABLH [9,23].
• Grazing reflection: Unlike GNSS-R, which acquires GNSS signals at a larger reflection angle, grazing reflection takes place at a bending angle similar to the RO sounding. The reflected signal at a grazing angle does not necessarily reverse polarization, which allows the direct and reflected signals to interfere with each other at the RO receiver. Thus, grazing reflection is a multi-path problem in GNSS-RO observations. The interference generates coherent or semi-coherent signals that manifest themselves in a radiohologram of the RO sounding. The reflective surface can be either a smooth ground surface or an elevated atmospheric layer (e.g., water vapor layer). Both RO grazing reflection and GNSS-R signals can be used to detect smooth, flat surfaces [24,25].
• Super-refraction (SR) effect: This occurs where atmospheric bending exceeds the Earth’s curvature (dN/dz < −157 N-unit/km). In such cases, the RO path is bended down more than the Earth’s curvature such that the signal is unable to reach the RO receiver [26]. However, the SR condition is sensitive to the angle of incidence with respect to the refractive surface in such an impact. As the GNSS-RO sounding progresses, especially during the open-loop operation, the incident angle would vary with H_SL and allow the RO signal to re-emerge from a temporary loss. The re-appearing signals are still partially affected by the SR interface and can cause a systematic negative bias in the N retrieval (i.e., negative N-bias) [17].
• Ducting effect: The RO propagation can be trapped in a thin atmospheric layer or between the surface and a reflective atmospheric layer (e.g., ABL top). Under a proper refraction–reflection condition, the layer can act as a duct to channel the RO propagation to reach a farther distance. Sokolovskiy et al. [22] studied the RO ducting effect with numerical model simulations and found that the length of ducting could play a key role in the deep H_SL RO signals. The longer the duct length, the deeper the RO signal can reach. The simulations also showed that ducting can induce a temporary loss of RO signals or a U-shape in the SNR profile due to multi-path interference. The U-shape essentially bifurcates the RO signal, as illustrated by two blue lines Figure 1, and induces a minimal SNR before the signal re-emerges at a lower H_SL.
• Diffraction effect: Like the light passing through a sharp edge object, the RO signal also experiences diffraction effects as it passes through a sharp layer such as ABL. The diffraction fringes are present in the RO signal amplitudes at deep H_SL, as simulated from a sharp ABL [17,18,19,20,21,27]. Consequently, modeling with wave optics must be employed to comprehend the SNR signals in these situations. The RO diffraction effect is more pronounced in the object without an atmosphere, such as the lunar occultation [28], but it is often overwhelmed by the other aforementioned effects when an atmosphere is present.

In reality, complex atmospheric moisture layers can produce a mixed effect in the RO sounding from all the above. It is often difficult to distinguish one from the other in an observed RO profile. As a result, sophisticated tools such as radiohologram and canonical transform are employed to diagnose the GNSS-RO measurements and improve the RO retrievals. Radio holography is useful to identify coherent oscillations within an RO sounding, such as the reflection-induced interference features. The canonical transform method allows a reconstruction of multi-path propagation from the full-spectrum inversion that makes use of both the RO phase and amplitude profiles. Nevertheless, a number of these tools involve tedious, time-consuming calculations and are impractical as an operational algorithm for processing a large-volume of data.

2.2. GNSS-RO Radiometry

In this study we analyzed multi-years of the Level-1B GNSS-RO data (e.g., atmPhs and conPhs) published at CDAAC (COSMIC Data Analysis and Archive Center) and focused on the signal amplitude (i.e., SNR) at H_SL < −80 km. Instead of using the standard Level-2 products derived from the excess phase (f_ex), we sought an alternative approach for the MABL q that could overcome the sampling and bias problems associated with the f_ex measurement. One of the advantages of using the SNR measurement is its availability in every RO sounding at very low H_SL, as long as MABL q can produce a detectable signal from refraction. In the cases where the SNR is weak and the f_ex measurements are too noisy to produce the useful bending angle retrieval, the SNR data are still available and can be used to infer the MABL q. Thus, this study was motivated to establish a robust relationship between deep H_SL SNR and MABL q so that a retrieval algorithm could be developed.

To properly analyze the deep H_SL RO signal amplitude for radiometry, we first normalized the L1 (f = 1.57542 GHz) SNR profile by its value in the free atmosphere (SNR₀) to account for large profile-to-profile SNR variations in RO observations (Appendix A). The self-sufficient normalization divides each SNR profile by its SNR0 derived from H_SL = 40–60 km, where the atmospheric bending is negligible. This normalization provides a relative radiometric calibration with respect to its power in the free atmosphere. Because the RO SNR can vary with the transmitter power and receiver antenna pattern (Appendix A), the normalized SNR profile greatly reduces these effects, so that it can be used to infer atmospheric properties. In addition to SNR₀ variations, the RO SNR measurement noise ($\sigma$) has a secondary effect on radiometry and must be taken into account in the normalization. As an RO receiver-dependent variable, it is subtracted from the SNR profile based on the RO receiver–transmitter pair (Table A1 in Appendix A). The receiver noise effect becomes noticeable in analyzing the weak signal at deep H_SL. The final normalized SNR (S_RO) is given by,

$$S_{RO}=\left(SNR-\sigma \right)/\left(SN{R}_0-\sigma \right)$$

(2)

The SNR noise ($\sigma$) is determined individually for each group of GNSS-RO measurements from very deep H_SL. More detailed discussions can be found in Appendix A, and the measurement noise from various GNSS-RO pairs are listed in Table A1.

In addition to the mean S_RO value, S_RO scintillations in each profile contain valuable information on layered structures in the atmosphere. As discussed above, a sharp vertical gradient in N can induce a strong response in refraction/defocusing/interference effects associated with large scintillations near the height where the gradient occurs. To characterize the scintillation intensity, we computed a profile of the 1 s S_RO variance from the difference between S_RO and its 1 s running mean ($\overline{S_{RO}}$), as defined below,

$${\sigma }_S^2=var\left(S_{RO}-\overline{S_{RO}}\right)$$

(3)

Like S_RO, ${\sigma }_S^2$ is a function of H_SL, but the vertical resolution of the 1 s average may differ from occultation to occultation, depending on relative motions between GNSS and LEO satellites. Typically, it varies between 1 and 2 km. Thus, as the RO passes through horizontally stratified atmospheric layers, strong scintillations may occur to enhance ${\sigma }_S^2$.

The zonal mean climatology of S_RO and ${\sigma }_S^2$ from January 2008 reveals several interesting features induced by atmospheric layered structures (Figure 2) The lower atmospheric q (primarily from the ABL) is responsible for the enhanced S_RO and ${\sigma }_S^2$ seen at H_SL < −80 km. The RO signals extended below H_SL = −100 km, mostly from the moist tropical atmosphere, are far below the cutoff height in the Level-2 bending angle retrievals. The gradual decreasing S_RO with H_SL is a manifestation of the defocusing effect from the atmosphere. The bulk of the S_RO enhancement is biased slightly towards the summer hemisphere where there is more solar isolation and water vapor abundance in the subtropics. A similar S_RO enhancement is evident at H_SL = −10 km for mid-to-low latitudes, with a sharp transition at ~55° S and ~45° N. This height (H_SL = −10 km) is above the CL-to-OP transition, which typically occurs at H_SL = −20 km. Near the tropopause, the S_RO exhibits a low value, likely due to the defocus effect caused by the sharp vertical temperature gradient.

The GNSS-RO vertical resolution, defined by the first-Fresnel-zone dimension, varies from ~1.5 km in the stratosphere to 0.1–0.5 km in the lower troposphere [29,30]. Such a high-resolution sounding makes the technique very sensitive to atmospheric thin layers with a sharp vertical refractivity gradient. The regions with a sharp vertical gradient can be readily seen in Figure 2b from the variance ${\sigma }_S^2$. The most prominent regions with thin layers include the tropopause, upper-tropospheric water vapor, and sporadic-E (E_s) in the ionosphere.

2.3. Geometric and Wave Optics

To fully understand the deep H_SL GNSS-RO signals from MABL, one must adopt the wave optics theory for the sounding. In the cases where the vertical dimension of atmospheric structures is comparable to the first Fresnel zone of the RO path, wave optics or the hybrid wave-ray methodology must be invoked in analyzing the radio wave propagation process. In a comprehensive monograph, Melbourne [21] described in detail how multi-path propagation and atmosphere-induced spectral broadening can lead to ambiguity in geometric–optic solutions to the GNSS-RO sounding. Figure 3 provides a schematic view of the multi-path problem in the GNSS-RO sounding, where the radio wave propagates through a thin atmospheric layer and is split to waves propagating in the different directions. In essence, this RO split can be seen as an analogy to the single-slit light experiment. As a result, modulated SNR is expected due to self-interference at the RO receiver end, a U-shape feature in the SNR profile. Using a thin-screen model, Melbourne [21] obtained an analytical simulation of the SNR response from a 0.5 km atmospheric layer with a sharp negative N gradient (dN/dz < 0) at the top and positive gradient (dN/dz > 0) at the bottom. The U-shape response in the SNR profile is a result of the Fresnel response and the so-called “throw-back” rays from layer diffraction. According to the model simulation, the U-shape gap is related to the layer thickness and can be extracted from the GNSS-RO observation. A similar technique was applied for ionospheric E_s layers to infer the E_s thickness [31].

The RO multi-path propagation through a thin atmospheric layer can induce constructive interference, causing re-emerged signals at deep bending angles or H_SL < −130 km, as seen in Figure 3. A model simulation study showed that the ducting layer with a finite horizontal extension can effectively generate these short-burst deep H_SL SNRs [22]. Such ducting layers, either elevated or near the surface, are able to channel the radio propagation through a longer distance and be refracted far into the occulted condition. These simulations showed that the deep H_SL S_RO is proportional to the horizontal length and vertical gradient of refractivity from the ducting layer.

The deep H_SL S_RO (below the U-shape) and grazing reflection features (above the U-shape) appear to be related to each other in moist MABL situations, according to these earlier studies [21,22]. The U-shape S_RO profile is indicative of the bifurcation generated by a thin ABL layer where the ducting may occur. As expected from a thin-layer model (Appendix B), the grazing reflection can come from the surface as well as an elevated atmospheric layer. While the reflection features contain coherent oscillations in the S_RO profile, the deep H_SL signals below the U-shape exhibit little coherence in general. Since ABL thickness is mostly < 2 km, any interference features would be packed as low-frequency power in the S_RO power spectrum as suggested by the thin-film model. The deep H_SL S_RO power spectrum shows mostly red noise with weak and coherent amplitudes. Hence, in this study we simply calculate an average power of the deep H_SL S_RO and develop an empirical relationship of S_RO to MABL q.

2.4. S_RO on H_SL Coordinate

One of the disadvantages of working with the GNSS-RO Level-1B data is the lack of information on bending angle and tangent height (h_t) that are derived from Level-2 processing. These high-level physical quantities or products require an inversion from the f_ex measurements. In the case of low S_RO at deep H_SL, this inversion is impractical because the f_ex measurements are too noisy. Thus, the purely geometric variable H_SL becomes a legitimate coordinate to register the S_RO profile.

As shown in Figure 4, H_SL can be different for the RO profile coming from the same bending angle if the LEO satellite altitudes are different. This difference must be taken into account when comparing the S_RO measurements from different LEOs. For the satellite altitude variations over a small range, an H_SL correction can be made approximately using a scaling factor as below,

$${\widehat{H}}_{SL}=H_{SL}·\left[1+0.0006·\left(812-H_{SAT}\right)\right] \mathrm{for} H_{SL}<0 \mathrm{km},$$

(4)

to shift H_SL to a new coordinate ${\widehat{H}}_{SL}$, where $H_{SAT}$ is the LEO satellite altitude with reference at 812 km. Figure 5 shows significant differences between SRO profiles as a function of H_SL and ${\widehat{H}}_{SL}$. By applying Equation (4) to four satellites orbiting at different altitudes, Figure 6 shows that the derived monthly climatologies for August are in general agreement with each other after registering S_RO on ${\widehat{H}}_{SL}$.

2.5. S_RO on ${\varphi }_{\mathrm{exL}1}$ Coordinate

An alternative method to register the S_RO profile without relying on Level-2 products is to use the L1 excess phase profile (${\varphi }_{\mathrm{exL}1}$). ${\varphi }_{\mathrm{exL}1}\left(h_t\right)$ is proportional to the atmospheric refractivity $N\left(h_t\right)$ at tangent height $h_t$, which is proven to be a good first-order approximation (Appendix C). Since the refractivity is proportional to atmospheric density, this approximation suggests that we may interpret the S_RO–${\varphi }_{\mathrm{exL}1}$ relation roughly as an S_RO–pressure relation.

Figure 7 shows the same August S_RO climatologies from the four satellites but on the Log10(${\varphi }_{\mathrm{exL}1}$) coordinate. Unlike in Figure 6, no empirical scaling is applied to the ${\varphi }_{\mathrm{exL}1}$-based vertical coordinate. All S_RO and ${\varphi }_{\mathrm{exL}1}$ profiles come directly from the Level-1B data. As seen from Figure 7, the S_RO on the Log10(${\varphi }_{\mathrm{exL}1}$) coordinate shows a consistent climatology among four RO sensors, despite their different satellite orbital altitudes. Hence, the Log10(${\varphi }_{\mathrm{exL}1}$) method is considered as a preferred approach when comparing multiple satellite S_RO observations.

2.6. Data Quality Control

The S_RO data need to be screened for short profiles, failed OL tracking, and very low SNR to ensure data quality for ABL studies. An RO profile is excluded if it produces no data at H_SL = 50 km or below −20 km. The operation CL-to-OL transition often occurs at H_SL = −20 km, but it can fail in some cases, producing no signal below −20 km. These failed profiles create essentially the measurement noise at deep H_SL and must be excluded for the data analysis. A threshold method based on S_RO mean and standard deviation is developed to identify and exclude the profile with a failed CL-to-OL transition. Finally, the RO profiles with a very poor signal (SNR < 200) are excluded in this study, since the measurement noise would become too important in these cases.

The deep H_SL S_RO measurements are sensitive to the jamming of GNSS signals, and these artifacts were not removed in this study. As shown in Appendix D, the jamming of GPS signals has increased substantially in recent years, particularly in the conflict zones, showing large spatial and temporal variations. Although the jamming occurred mostly over land, it produced a significant S_RO amplitude in the Mediterranean Sea and some coastal regions.

2.7. MABL Sampling

The number of Level-1B S_RO measurements after quality screening is still significantly higher than the number of Level-2 products (e.g., temperature, specific humidity) in the MABL. For example, because the number of COSMIC-1 Level-2 products in the MABL is so low, it is impossible to generate a monthly map, let alone to study the diurnal variation of MABL q. In addition, for those Level-2 retrievals that reach the MABL, there is likely a bias to the situations where the MABL tops were not too sharp to induce the super-refraction condition.

Figure 8 compares the tropical sampling statistics between Level-2 (COSMIC-1 version 2013.3520 and COSMIC-2 version 0001.0001) and Level-1B (COSMIC-1 atmPhs version 2013.3520 and COSMIC-2 conPhs version 0001.0001) products from the COSMIC Data Analysis and Archive Center (CDAAC) in terms of percentage over the total number of S_RO profiles in the tropical (30° S–30° N) MABL. The number of Level-2 atmPrf profiles drops sharply with height from the mid-troposphere to MABL. At 400 m, the number of Level-2 retrievals from January and July 2008 are, respectively, 6.2% and 7.3% of the number of Level-1B S_RO profiles that reaches H_SL = −100 km. The percentages for the global (not shown) are similar to the tropical statistics. The lower number of Level-2 retrievals (i.e., refractivity, water vapor, and pressure) at MABL is largely because it requires ${\varphi }_{\mathrm{exL}1}$ measurements at deep H_SL, which are unavailable where S_RO is too noisy or SNR is too low. In the case where there exists a strong vertical N gradient at the top of MABL, the Level-2 algorithm is often unable to carry out the refractivity inversion to the heights below the MABL top.

The statistics of COSMIC-2 retrievals, however, improved significantly, as expected, from the more capable TGRS (TriG GNSS Receiver System) [32,33]. The tropical MABL penetration percentage increased to 71% and 73% in COSMIC-2 atmPrf for January and July 2020, respectively, and to 56% and 59% in COSMIC-2 wetPf2, with respect to the Level-1B sampling at 400 m. The TGRS employs a 6-element antenna array technology for beamsteering and beamforming to improve the gain and SNR of received RO signals, which results in better penetration to the MABL than COSMIC-1 receivers. Together with the matured OL operation, the fast TGRS onboard real-time positioning determination and scheduling also produce more RO profiles per receivers than COSMIC-1. Nevertheless, COSMIC-2 lacks coverage of high latitudes, and therefore in this study we still use the COSMIC-1 data in the following analysis.

In addition to the sampling differences between the Level-2 and Level-1B data, the Level-2 q is known to have a dry bias due to the so-called negative N bias from the Abel inversion. It is found that the N bias cases are often associated with the Abel inversion of the profiles impacted by ducting layers or strong vertical N gradients at the ABL top [16,34]. These biased situations are often found over stratus-topped MABL where the super-refraction and ducting often occur. As indicated in Equation (1), retrieving q or P_w from N requires knowledge about the T profile in the MABL. This auxiliary information usually comes from an atmospheric model or assimilated data. A 1% error in T would lead to a 2% error in the N-to-q conversion.

Hence, the S_RO-based technique offers a promising approach for the MABL q retrieval without requiring a priori information about the atmosphere. The deep H_SL S_RO profiles do not cut off because of a sharp ABL top, which can produce an unbiased sampling of stratus-topped clear-sky or cloudy-sky conditions in the MABL. A single-level S_RO technique from deep H_SL S_RO, as shown in the next section, has a limited sensitivity range for the MABL q. However, this limitation can be largely mitigated by using the S_RO data from multiple H_SL levels. Adequate characterization of the MABL q variability requires a full diurnal coverage without sampling bias for both clear and cloudy skies, and the S_RO-based technique has great potential for achieving this goal. Finally, the unbiased sampling is also important for model-observation comparisons and evaluation. As shown in the next section, the MABL q observations over broken clouds and sea ice pose a great challenge for both numerical models, data assimilation, and remote sensing from space.

3. Results

3.1. S_RO Sensitivity to MABL H₂O

To evaluate the S_RO sensitivity to MABL q, we compared the monthly mean S_RO at a deep H_SL from COSMIC-1 with the monthly mean-specific humidity (q) at 950 hPa or ~400 m altitude from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5). We selected the S_RO data from the single level at H_SL = −100 km or Log₁₀(f_exL1) = 3.25 but excluded those from high elevation and rough landmasses in comparison with ERA5 q. Figure 9 and Figure 10 show the mean S_RO maps from January and July 2008 at H_SL = −100 km and Log₁₀(f_exL1) = 3.25 and their comparisons with the ERA5 q. There existed a good correlation between the deep H_SL S_RO amplitudes and the ERA5 q at 950 hPa or 400 m, especially at mid-latitudes where q varied between 3 and 13 g/kg. The correlations of the 950 hPa q with the S_RO were similar for both H_SL = −100 km and Log₁₀(f_exL1) = 3.25 levels, but perhaps with slightly tighter scatters with the S_RO data from Log₁₀(f_exL1) = 3.25. We evaluated the correlation between the 400 m q and other S_RO levels; the Log₁₀(f_exL1) = 3.25 level exhibited the highest coefficient.

Some notable differences were seen between the S_RO and ERA5 q maps in the subtropical MABL, such as the Southeast Pacific (SEP) and the Southwest Atlantic (SWA) in January 2008 (Figure 9) and the Northeast Pacific (NEP) and the Northeast Atlantic (NEA) in July 2008 (Figure 10). These are the MABL regions with frequent occurrence of broken clouds that can be affected by complex processes including surface latent heat flux, enhanced precipitation, downwelling longwave radiative flux, large scale divergence, and aerosol forcing [35]. A comparison of the ERA5 and COSMIC-1 Level-2 q suggested a likely dry bias in the ERA5 data at 3 km [36]. A dry bias of the reanalysis data was also found in the MABL when compared to ship-based radiosonde observations [37]. This bias was on the top of the COSMIC-1 dry bias due to the negative-N bias, as identified in the Abel retrieval method [16,17]. Nevertheless, this was a challenging measurement and required further validation from observations. The S_RO-based method revealed significant differences from the reanalysis data and COSMIC Level-2 products, which can serve as an independent source of global MABL q measurements for future validation.

In the regions where the MABL q > 13 g/kg, the correlation with S_RO at H_SL = −100 km and Log₁₀(f_exL1) = 3.25 degraded significantly, due to possible saturation by a large CWV in the troposphere. As seen in Figure 9 and Figure 10, these regions were generally associated with the Intertropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ). Although the correlation was poor for this single-level S_RO, the MABL q was found to correlate with the S_RO at other levels (not shown) in a non-linear way. Thus, a new study is ongoing to apply a machine learning and artificial intelligence (ML/AI) method to the MABL q retrieval by utilizing the S_RO measurements from all levels. The preliminary results suggest that the ML/AI algorithm is very promising and can retrieve the large q values over the deep convective regions as well as the MABL q at mid-to-high latitudes. The ML/AI MABL q retrievals will be validated against ship-based radiosonde observations from field campaigns.

In the high-latitude dry regions where q was below 3 g/kg, the S_RO values from H_SL = −100 km or Log₁₀(f_exL1) = 3.25 were too small to establish a meaningful correlation with the ERA5 q. However, a good correlation was identified by comparing the July ERA5 950 hPa q with the S_RO from Log₁₀(f_exL1) = 3.10 (approximately, H_SL = −80 km) for the polar region (Figure 11). As expected, the larger S_RO values at Log₁₀(f_exL1) = 3.10 helped to establish a good q–S_RO relationship at low MABL q values under the drier condition. Nevertheless, the positive q–S_RO correlation appeared to be only evident in the Arctic for q > 3.5 g/kg. Little correlation was found in the Antarctic, where a large part of the domain is covered by sea ice and the ERA5 MABL q was mostly less than 3 g/kg. There were also significant differences over the Arctic Ocean, where sea ice and open water are mixed during this time of the year. The ERA5 q appeared to have difficulty of reporting values below ~3.5 g/kg and lacked features over the Arctic Ocean. A cluster of the 950 hPa q values was assigned arbitrarily to a fixed value (3.5 g/kg) in ERA5 as a minimum in the Arctic. It is worth noting that the ERA5 q could go below 3.5 g/kg at the midlatitudes outside the polar region where there is no sea ice. These low q values at midlatitudes were positively correlated with the S_RO from Log₁₀(f_exL1) = 3.10, suggesting that the 3.5 g/kg problem could be related to the Arctic surface conditions. In the Antarctic, ERA5 did not produce the enhanced features as seen by S_RO over the Weddell Sea and the Ross Sea, which is likely due to the similar challenge over sea ice in the Arctic.

In summary, we found that the deep H_SL S_RO is useful to infer the MABL q, after the GNSS-RO SNR signal is properly normalized. The S_RO-based method could offer an alternative for global MABL q observations, especially over the challenging domains with broken clouds and sea ice. The S_RO measurements showed good correlation with the MABL q at 950 hPa (~400 m), particularly for the subtropical and mid-latitude q with the S_RO at H_SL = −100 km and the high-latitude q with the S_RO at H_SL = −80 km. The deep H_SL S_RO results support the refractive interference theory for radio wave propagation through a thin moist MABL, which would allow the RO signal to reach the deep H_SL from a ducting layer. The S_RO-based MABL q retrieval has ~1500% (40%) more measurements than the COSMIC-1 (COSMIC-2) Level-2 products. The MABL q inferred from the stratus-topped subtropics does not seem to have the low bias as seen in the standard Level-2 q products. Improved sampling from the S_RO-based method is critically needed for studying the MABL q and its large spatiotemporal variability.

3.2. Diurnal Variations of S_RO

One of the pronounced tropical and subtropical variabilities is the diurnal variation of MABL q. Assuming the MABL q is proportional to the deep H_SL S_RO, we compiled its seasonal statistics as a function of local time for two regions, namely, the Southeast Pacific (SEP) and the Northeast Pacific (NEP), which are defined as (105° W–75° W, 0° S–35° S) and (150° W–120° W, 0° N–35° N), respectively. Because the diurnal variation of MABL q can be a strong function of latitude and longitude, we averaged the S_RO data from all the longitudes in each region but kept the local time variation as a function of latitude.

The SEP diurnal variations exhibited very different characteristics from season to season (Figure 12). In June–August (JJA) and September–November (SON), the local time variation was generally larger at subtropical latitudes between 10° S and 25° S. The maximum S_RO occurred between noon and early afternoon, with the subtropics lagging slightly behind the tropics. The diurnal cycle was weaker in December–February (DJF) and March–May (MAM), mostly at latitudes between 20° S and 30° S. There was an indication of a semidiurnal variation near 5° S in MAM, which had the highest mean S_RO among all seasons. The S_RO diurnal variation, as expected for the MABL q, was consistent with those reported for cloud amount [38] and cloud liquid water path (LWP) [39] over the same region. A higher cloud amount and LWP were found at night compared to the afternoon. The higher LWP implies a lower MABL q, as seen in Figure 12, because a colder temperature freezes the MABL q into clouds at night. Modeling studies suggested that the cloud and q diurnal cycles in the SEP are mainly driven by the large-scale subsidence originating from the diurnal heating in northern Chile/southern Peru [40]. The observed seasonal variation of the S_RO diurnal amplitudes also agreed with the LWP data [39], showing a smaller amplitude in the winter than in the summer.

Compared to the SEP region, the S_RO diurnal variations in the NEP region were weaker in all seasons (Figure 13), which is consistent with the observed cloud amount variations [41]. The most significant local time variations were perhaps at latitudes between 20° N and 30° N in MAM and JJA, showing an S_RO maximum in the afternoon. The low cloud fraction over the NEP was generally lower compared to that in the SEP, which agreed with the higher S_RO values in the NEP over the SEP. Given the observed correlation between the S_RO amplitude and low cloud fraction variations, it warrants further investigation of this correlation in other regions and under different meteorological conditions.

4. Conclusions and Future Work

Processes within the MABL play an important role in global cloudiness and require a reliable observational constraint in order for better understanding of their climate sensitivity [42]. Although thermodynamic properties of atmospheric water vapor and temperature are generally available from satellite observations under the Program of Record (POR), lack of vertical resolution, diurnal sampling, and measurement accuracy has been the major obstacle to achieving complete characterization and understanding of the role of MABL in a changing climate.

In this study we presented a promising technique that makes use of the GNSS-RO signal amplitudes at deep H_SL to infer the MABL q at 950 hPa (~400 m). The single-level S_RO measurements from H_SL = −100 km show a good correlation with the MABL q, especially at the subtropical and midlatitudes, while the S_RO from H_SL = −80 km is useful for the polar region. The S_RO-based technique offers an alternative approach for the MABL q retrieval without requiring a priori information (e.g., temperature) about the atmosphere. It provides significantly more measurements than the operational Level-2 products, which are needed to cover the full diurnal cycle unbiasedly for clear and cloudy skies, as well as for sharp and smooth ABL tops.

Significant diurnal variations were observed in the deep H_SL S_RO amplitudes over the Southeast Pacific (SEP) and the Northeast Pacific (NEP) regions. Consistent with low cloud fraction and LWP observations, the GNSS-RO S_RO diurnal variations are anticorrelated with the low cloud amount, as expected if the deep H_SL S_RO amplitude is proportional to the MABL q. Given the good correlation between the S_RO amplitude and low cloud fraction variations in the SEP and NEP, further investigation of this relationship in other regions and under different meteorological conditions is warranted.

The inferred MABL q from S_RO also revealed significant differences to ERA5 over broken cloud and sea ice conditions. These regions are known to have challenges for numerical models, data assimilation, as well as for remote sensing from space, and they require further validation from other independent MABL q observations. The good q–S_RO correlation found in this study sheds light on developing a new S_RO-based MABL q retrieval, especially for these challenging conditions. A subsequent study will apply an ML/AI approach to the MABL q retrieval in which the S_RO data from multiple H_SL levels are used. It is anticipated that the ML/AI algorithm will be able to overcome the saturation limitation and non-linear dependence of the single-level q–S_RO relationships.