Vertical Atmospheric Structures Associated with Positive Biases in COSMIC-2 Refractivity Retrievals

Paweł Hordyniec aSatellite Positioning for Atmosphere, Climate and Environment Research Centre, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia

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Robert Norman bSERC Limited, Weston Creek, Australian Capital Territory, Australia

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John Le Marshall cBureau of Meteorology, Melbourne, Victoria, Australia

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Abstract

Representation of complex vertical structures observed in the troposphere can vary depending on data sources. The radio occultation (RO) technique offers great advantages for sensing the atmosphere down to its lowermost layers using high-resolution measurements collected by satellites on low-Earth orbit (LEO). The structures are generally smoother in vertical when reproduced from atmospheric models. We evaluate the quality of troposphere retrievals from the COSMIC-2 mission and demonstrate that systematic effects in fractional refractivity deviations with respect to European Centre for Medium-Range Weather Forecasts (ECMWF) background fields are spatially correlated with positive refractivity gradients characterized as subrefraction. The magnitude of refractivity biases observed mostly over the equatorial regions can exceed 1% within altitudes of 3–5 km. Respective zonal means reveal seasonal trends linked with the distribution of atmospheric inversion layers and signal-to-noise ratio values in RO data. The positive biases are vertically collocated with significant refractivity gradients in COSMIC-2 retrievals that are not reflected in the corresponding ECMWF profiles. The analysis of gradients based on COSMIC-2 data, further supported by radiosonde observations, suggests that most of subrefractions is identified in the middle troposphere at around 4 km. While the altitudes of maximum refractivity gradients from COSMIC-2 and ECMWF data are in fairly good agreement, the magnitude of ECMWF gradients is significantly smaller and rarely exceeds positive values.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Hordyniec’s current affiliation: Institute of Geodesy and Geoinformatics, Wrocław University of Environmental and Life Sciences, Wrocław, Poland.

Corresponding author: Paweł Hordyniec, pawel.hordyniec@upwr.edu.pl

Abstract

Representation of complex vertical structures observed in the troposphere can vary depending on data sources. The radio occultation (RO) technique offers great advantages for sensing the atmosphere down to its lowermost layers using high-resolution measurements collected by satellites on low-Earth orbit (LEO). The structures are generally smoother in vertical when reproduced from atmospheric models. We evaluate the quality of troposphere retrievals from the COSMIC-2 mission and demonstrate that systematic effects in fractional refractivity deviations with respect to European Centre for Medium-Range Weather Forecasts (ECMWF) background fields are spatially correlated with positive refractivity gradients characterized as subrefraction. The magnitude of refractivity biases observed mostly over the equatorial regions can exceed 1% within altitudes of 3–5 km. Respective zonal means reveal seasonal trends linked with the distribution of atmospheric inversion layers and signal-to-noise ratio values in RO data. The positive biases are vertically collocated with significant refractivity gradients in COSMIC-2 retrievals that are not reflected in the corresponding ECMWF profiles. The analysis of gradients based on COSMIC-2 data, further supported by radiosonde observations, suggests that most of subrefractions is identified in the middle troposphere at around 4 km. While the altitudes of maximum refractivity gradients from COSMIC-2 and ECMWF data are in fairly good agreement, the magnitude of ECMWF gradients is significantly smaller and rarely exceeds positive values.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Hordyniec’s current affiliation: Institute of Geodesy and Geoinformatics, Wrocław University of Environmental and Life Sciences, Wrocław, Poland.

Corresponding author: Paweł Hordyniec, pawel.hordyniec@upwr.edu.pl

1. Introduction

Atmospheric soundings derived from the Global Navigation Satellite System (GNSS) radio occultation (RO) technique demonstrated their capability to serve as benchmark observations for climate studies (Cucurull et al. 2014; Steiner et al. 2013). On the other hand, the negatively biased refractivity observations in the lower troposphere is a well-known property of RO retrievals collected in anomalous atmospheric conditions characterized as ducting or superrefraction (Beyerle et al. 2006; Sokolovskiy 2003). Depending on the application, the bias can be either corrected (Wang et al. 2017) or the lowermost section of RO profile is discarded from the analysis (Dee 2005; Chen et al. 2011; Steiner et al. 2020a; Vergados et al. 2021). Complex atmospheric structures associated with refractivity irregularities causing random or systematic errors can also be observed in the bending angle domain (Liu et al. 2018), as well as in the temperature in the upper troposphere and lower stratosphere (UTLS) region (Zeng et al. 2019). While some of the aforementioned approaches utilize filtering methods to improve agreement between RO and numerical weather prediction (NWP) datasets for climatological applications, the inherent high vertical resolution of the RO technique is beneficial for the detection of inversion layers, such as the tropopause (Schmidt et al. 2006; Rieckh et al. 2014; Scherllin-Pirscher et al. 2017) or planetary boundary layer (PBL) (Xie et al. 2012; Ao et al. 2012). Unlike the lowermost troposphere retrievals, where the RO refractivity is typically underestimated (Schreiner et al. 2020), the UTLS is a core region of the technique with nearly unbiased observations (Scherllin-Pirscher et al. 2011).

In the middle troposphere, the positive refractivity biases can be occasionally identified in the seasonal means, particularly in the equatorial region (Xie et al. 2006; Ao et al. 2003). Analysis of Challenging Minisatellite Payload (CHAMP) refractivity retrievals revealed positive biases exceeding 1% over Amazon and Indonesian regions (Beyerle et al. 2006); however, their origin has not been studied nor fully explained. Sokolovskiy (2004) demonstrated a possible propagation mechanism that can affect the structure of observed radio signals and result in overestimated refractivity values in the presence of positive refractivity gradients associated with subrefractive conditions. While subrefractions are generally regarded as the least frequently observed refractive conditions (Tang et al. 2012), the presence of both strong temperature and dewpoint inversions favors their development (Babin 1995), resulting in poor performance of radar and microwave communications. The potential contribution of subrefractive effects to the overall error budget of RO neutral atmosphere retrievals should be of concern for global climate monitoring that requires consistent long-term data records (Steiner et al. 2020b). The systematic errors in refractivity statistics can be partially explained by forward modeling approaches that neglect cloud contributions (Yang and Zou 2017; Hordyniec 2018), hence RO signals that accumulate total atmospheric contributions result in larger refractivity values than corresponding background observations. On the other hand, the biases of RO inversions depend on the methodologies adopted in the retrieval chain (Sokolovskiy et al. 2010), with the effect of noise and decreasing signal-to-noise ratio (SNR) values in the troposphere contributing to the overall uncertainty (Sokolovskiy et al. 2019). The most recent COSMIC-2 mission is peculiar with regard to the signal strength since the measurements are characterized by the highest SNR values among all RO missions allowing deeper penetration of the troposphere (Chen et al. 2021). However, the preliminary analysis (Schreiner et al. 2020; Ho et al. 2020) suggests that COSMIC-2 refractivity can be still affected by positive biases between altitudes of 2–6 km.

In the following study, the quality estimates for the refractivity retrievals from the COSMIC-2 mission are presented and discussed. The statistical assessment of COSMIC-2 neutral atmosphere profiles is performed using background meteorological data from ERA5 fields produced by European Centre for Medium-Range Weather Forecasts (ECMWF). The patterns in monthly mean fields of fractional refractivity deviations are analyzed considering distribution of PBL heights that reveal similar seasonal characteristics. The analysis of SNR values estimated for the tropospheric section of RO retrievals closely resembles the distribution of refractivity biases. We particularly focus on positive refractivity deviations that are found to be spatially coherent with low SNRs and vertically collocated with strong positive gradients, characterized as subrefractions. The spatial distribution of subrefractions in the equatorial COSMIC-2 observations is compared with corresponding refractivity structures in ERA5 background data and echPrf product, further supported with radiosonde observations.

2. Observational datasets

a. COSMIC-2 occultation data

The occultation data delivered as a part of FORMOSAT‐7/COSMIC‐2 neutral atmospheric provisional release 1 are primarily studied in terms of quality of refractivity retrievals. Given the low inclination orbits of six low-Earth-orbiting satellites of COSMIC-2 constellation and cancellation of the second phase with another six polar-orbiting satellites, the RO observations are collected within ±45° latitudes, resulting in the occultation counts on the order of 5000 profiles a day (Schreiner et al. 2020). The variables of interests are provided in the level-2 atmPrf product. The generic quality control (QC) check is performed on refractivity data prior to the analysis. Profiles are required to penetrate the atmosphere down to at least 1-km altitude. The altitude grids need to form monotonic series and refractivity values are allowed to vary from 0 to 500 N-units. The vertical grid of COSMIC-2 refractivity is provided with ∼20-m spacing and the uppermost level of profiles reaches 60-km altitude. To identify subrefractions manifested by positive gradients in the refractivity, we focus on the tropospheric section of COSMIC-2 profiles up to the altitude of 10 km. The inversion from bending angle profile to refractivity through the RO processing chain can utilize radio-holographic filtering methods in the impact parameter domain (Gorbunov et al. 2006), or alternatively in the time domain (Hocke et al. 1999), for the noise reduction due to multipath propagation. Depending on the filtering window of the running spectra, which acts as a smoothing window, the large variations in the bending angle are removed consequently yielding reduced uncertainties and smaller values of retrieved refractivities (Sokolovskiy et al. 2010). Therefore, no further smoothing or filtering is applied to provided COSMIC-2 refractivity values in order to capture very thin subrefraction layers and to fully benefit from the capability of RO measurements to provide detailed information on the vertical structure of the atmosphere. Seasonal variations in COSMIC-2 data are presented in monthly mean fields constructed from regular equal-angle bins of 5° × 5° resolution weighting the individual observations by the cosine of the latitude to compensate for the meridian convergence toward higher latitudes.

b. ECMWF background fields

Background meteorological data from ECMWF are used for the statistical assessment of refractivity differences and their seasonal variations. Moisture profiles from high-resolution ECMWF gridded fields collocated with occultations are provided by COSMIC Data Analysis and Archive Center (CDAAC) in level-2 echPrf product. These profiles are operationally used for comparison purposes and quality monitoring of RO products from CDAAC retrieval system. In the near-real-time COSMIC-2 provisional dataset the moisture profiles are sourced from forecast fields (instead of analysis) that are interpolated to time of occultation using the nearest preceding and following model file. The forecasts are provided in 3-hourly temporal resolution and can vary in terms of initialization of model runs (0000, 1200 UTC) and forecast lead times. The initial assessment presented in Fig. 1 suggests that the impact of forecast lead time on the refractivity deviations in the middle troposphere is statistically insignificant as only marginal negative biases can be identified. The increase in uncertainties is mostly observed in the random properties of the error.

Fig. 1.
Fig. 1.

Monthly data for January 2020 showing (top) refractivity deviations with respect to the forecast lead time and (bottom) histogram with number of data pairs.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

To produce monthly mean fields of refractivity deviations, the fractional differences between COSMIC-2 and ECMWF forecast data are first computed in the vertical using 100-m spacing. The deviations are then gridded to regular latitude–longitude monthly grid of 5° resolution. In addition, ECMWF ERA5 fields of monthly data describing distribution of inversion layers in the lowermost troposphere, such as PBL height and duct base height, are studied to demonstrate potential seasonal relationship with computed refractivity statistics.

c. NOAA/ESRL radiosonde

The mandatory and significant levels of traditional meteorological variables measured during the ascend flight of balloon-borne sondes are used to reconstruct refractivity profiles and support the existence of subrefractions. Two soundings per day routinely collected at 0000 and 1200 UTC are extracted from the radiosonde data archive of National Oceanic and Atmospheric Administration (NOAA)/Earth System Research Laboratory (ESRL).

Typically, a single radiosonde profile comprises of 150 levels with the average vertical resolution of 200 m and the uppermost altitude of ∼30 km. To compute refractivity values, the dewpoint depression Td is first converted to water vapor partial pressure using the formula
Pυ=6.11×107.5 Td/(273.3+Td).
The refractivity (N) is then computed from a functional relation of air pressure (P), water vapor pressure (Pυ), and temperature (T) following Smith and Weintraub (1953):
N=77.6PT+3.73×105PυT2.

The humidity sensor typically contributes with the largest error to the overall quality of radiosonde refractivity values. Moreover, the variability of humidity-related measurements often results in significant horizontal spikes that can lead to exaggerated vertical refractivity gradients. To minimize humidity-induced variations, the QC is applied to relative humidity values and profiles with variations in vertical exceeding 50% are marked as “bad” and removed from the analysis. For more smooth vertical structures in QC-approved profiles, the running mean filter is applied to observed radiosonde refractivity data limiting the vertical resolution to 150 m. Such preprocessed refractivity profiles are then upsampled to high-resolution vertical grid with cubic splines in the troposphere (up to 10 km). The methodology is adopted to ensure optimal magnitudes of observed vertical gradients of refractivity so that the induced systematic effects in RO retrievals can be more robustly attributed to the existence of subrefractions.

3. Characteristics of refractivity gradients

The refractivity parameter combines contributions of pressure, temperature, and water vapor partial pressure to provide a physical property of a medium allowing to explain interactions with radio waves. The atmospheric dynamics is dominated by variations in its vertical structure (and to a lesser extent in the horizontal). Certain criteria related to vertical distribution of the refractivity, once met, can eventually lead to anomalous propagation of signals. The significance of atmospheric conditions can be expressed by the magnitude of the vertical refractivity gradient (dN/dz). The generic classification for the purpose of this study is summarized in Table 1. For the subrefraction, the condition dN/dz > 0 is satisfied once the refractivity increases with height, which causes the radio waves to propagate upward off Earth’s surface. The threshold −157 km−1 that allows distinguishing between standard refraction and ducting (superrefraction) involves the relationship of Earth’s radius re = 6371 km. As long as dN/dr = −106/re the propagation trajectory is normal to Earth and would refract downward in the presence of standard refraction with a curvature less than that of Earth’s. The ducting occurs when the curvature is exceeded typically leading to negative refractivity biases in RO retrievals (Sokolovskiy 2003; Ao 2007; Beyerle et al. 2006).

Table 1

Classification of refractive conditions based on vertical gradients.

Table 1

Phantom refractivity profile describing standard refraction can be computed from analytical relationship which reads as follows:
NA(h)=N0×exp(hH0) ,
using surface refractivity N0 = 400, scale height H0 = 8 km, and altitude grid h. The exponential form of the phantom refractivity profile NA in Eq. (3) can be modified to represent ducting conditions according to Sokolovskiy (2001):
NM(h)=NA(h)[10.05(2π)atan(hhDw)] ,
where hD is the altitude of disturbance and factor w corresponds to its width. Figure 2 shows modified refractivity profile NM characterized by hD = 6 km and w = 50 m, which results in negative refractivity gradient on the order of −200 km−1. By changing the sign of the amplitude in the disturbing component of Eq. (4) we can form analogical expression to represent the subrefraction by modified profile NM:
NM(h)=NA(h)[1+0.05(2π)atan(hhDw)] ,
further following parameterization based on individual factors (hD, w) as for the case of ducting, which yields the vertical structure with a positive gradient showed in Fig. 2.
Fig. 2.
Fig. 2.

(a) Analytical refractivity profiles and (b) their vertical gradients for different conditions: standard refraction (black dotted line), ducting (blue solid line), and subrefraction (red solid line). The profiles of (c) bending angle vs impact height were retrieved by Abel transforming respective refractivity profiles, whereas wave optics simulations were used to compute (d) the amplitude of the signal with respect to HSL.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Figure 2 shows simulation results for various refractive conditions to illustrate different propagation mechanisms induced by strong refractivity gradients at 3-km altitude. The refractivity values in the profile characterized as subrefraction are larger above the inversion layer than those of standard refraction or ducting. The inversion layers are reflected by different bending angle spikes that coincide vertically at around 5-km impact height. However, simulation of the amplitude suggests that subrefractions might require more shallow penetration depth (relative to ducting) to capture associated variations. The independent variable for the amplitude is represented by height of straight line (HSL) connecting a pair of GNSS and LEO occulting satellites. The amplitude fluctuations associated with subrefraction are concentrated around −60 to −40 km, whereas significant variations induced by the ducting layer are observed at much lower HSL below −80 km. At this height the amplitude for standard and subrefractive condition reaches a noise level and no longer exhibit fluctuations.

4. Positive biases in COSMIC-2 refractivity

The fractional refractivity deviations are computed based on COSMIC-2 observations and ECMWF background fields according to the following relationship (NONB)/NB. The geographical distribution of monthly mean O minus B statistics is illustrated in Fig. 3 as a belt encircling Earth between 45° latitudes for two representative periods: October and January. The fractional differences are presented for altitudes between 3 and 5 km where significant refractivity gradients, such as for ducting, contributing to negative biases should not be present (von Engeln et al. 2003). Most of negative refractivity differences is on the order of −0.5% with exceptions of over −1.5% biases observed over western Australia and northern tip of South America. The latter is surrounded by positive biases on the order of 1% in monthly means for October 2019, which decrease in January 2020 covering regions located southward—mostly the Amazon and a tongue over the Central Atlantic. The most significant positive biases are found over the Indian and western Pacific Oceans both reaching the magnitude of 1.5%. The trend remains in January 2020 with however reduced coverage to narrower equatorial belt. There are no visible differences when GPS-only or GLONASS-only retrievals are considered as they result in a comparable quality (not shown). The error characteristics are partially driven by intertropical convergence zone (ITCZ) associated with the trade winds and the so-called near-equatorial trough (Byrne et al. 2018). Since ITCZ appears as a band of clouds bringing intensified precipitation rates over tropical regions, the neglected contributions to refractivity due to its nongaseous components can amplify the magnitude of biases (Zou et al. 2012; Yang and Zou 2017). Simulation experiments of cloud contributions suggest that refractivity differences on the order of 0.5% are statistically probable (Hordyniec 2018). As clouds and water vapor are spatially heterogeneous factors of atmospheric radiative transfer (Clark et al. 2018), the column integrated water vapor (IWV) in Fig. 4 is used to illustrate the distribution of associated ITCZ based on ERA5 monthly mean fields. The southward shift of 40 kg m−2 contour line in January relative to October agrees with distribution of fractional refractivity differences presented in Fig. 3 supporting their seasonality.

Fig. 3.
Fig. 3.

Monthly mean refractivity deviations between COSMIC-2 and ECMWF at altitudes 3–5 km for (top) October 2019 and (bottom) January 2020. The statistics are based on a 5° × 5° latitude–longitude grid.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Fig. 4.
Fig. 4.

ERA5 monthly mean fields of column integrated water vapor (IWV) associated with ITCZ. Contour lines represent the value of 40 kg m−2 for October 2019 (red) and January 2020 (blue).

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Vertical distribution of refractivity differences presented in Fig. 5 results in fairly unbiased characteristics within altitudes 3–10 km in the globally averaged data. Seasonal effects mostly contribute to the magnitude of biases at 3-km altitude or lower. However, as opposed to global means, pronounced positive biases develop above the boundary layer in the regionally averaged refractivity differences computed from the Indonesian subset. Similar error characteristics were reported by Ao et al. (2003) and Beyerle et al. (2006) based on the analysis of CHAMP RO data. Depending on the season, the positive biases in COSMIC-2 can vary in the vertical extent and magnitude. As illustrated for October, the refractivity differences become positive as low as 1 km with the maximum of around 2% at 3-km altitude. In January, the differences are negative within the first 2.5 km from the surface with the largest positive bias developing at 3.5 km. We study the error characteristics relative to two main potential drivers that are discussed in the following sections.

Fig. 5.
Fig. 5.

Mean biases (thick lines) and standard deviations (thin lines) of refractivity between COSMIC-2 and ECMWF: global statistics (gray) and Indonesian subset (black) for October 2019 (dashed lines) and January 2020 (solid lines).

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

a. Dependence on PBL height

The distribution of PBL heights often manifested by sharp inversion layers is a main driving factor of near-surface negative biases shown in Fig. 5. Significantly underestimated refractivity retrievals observed in the lowermost troposphere have been analyzed extensively by GNSS RO community (Beyerle et al. 2006; Ao 2007; Xie et al. 2010; Schreiner et al. 2020) and therefore fall outside of the scope of presented study. However, feedback mechanism between PBL and positive N biases can also be demonstrated from the analysis of respective seasonal means. Though number of RO-based definitions for the PBL exist (Xie et al. 2012; Ao et al. 2012), the ECMWF-based heights are used to provide the most probable estimate of their geographical distributions since the O minus B statistics of refractivity are based on ECMWF fields. Figure 6 shows zonal monthly means of PBL height that varies with respect to the equator and becomes the lowest during equinoxes and the highest during solstices. The seasonality of PBL is reflected in the distribution of positive N biases shown in Fig. 7. The zonal averages computed from refractivity differences between altitudes 3–5 km illustrate seasonal asymmetry of the biases about the equator that coincides well with narrow equatorial band of monthly minima in the PBL. Both the positive biases and shallow PBL exhibit seasonal march from the Northern Hemisphere low latitudes in October 2019 to the Southern Hemisphere low latitudes in February 2020 with the largest positive biases oscillating from 0.7% at latitude of 10°N down to 0.4% at 5°S, respectively.

Fig. 6.
Fig. 6.

Zonal monthly means of PBL height derived from ERA5 fields.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Fig. 7.
Fig. 7.

Zonal monthly means of refractivity differences between COSMIC-2 and ECMWF within altitudes 3–5 km.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

b. Dependence on SNR

Sokolovskiy et al. (2010) emphasizes that lower troposphere biases may substantially depend on the processing scenarios in the GNSS RO retrieval chain. Higher SNR values are expected to reduce the magnitude of positive N biases (Sokolovskiy et al. 2019). Consequently, observations affected by low SNR might be susceptible to inversion errors. The SNR computed at 80 km is used to estimate the noise of occultations whereas SNR values calculated in the lower troposphere can also serve as a measure of atmospheric activity. Figure 8 shows that the minimum SNR values at 80 km are generally observed over high latitudes outside of subtropics and at the equator that is also affected by the largest SNR spread varying from 500 to 2500 V V−1. Figure 9 presents geographical distribution of mean SNR computed in the lower troposphere between −40- and −20-km HSL (approximately 5-km altitude). The SNR experiences similar behavior to estimates at 80 km, with generally lower values down to 100 V V−1 found near the equator and higher latitudes. The pattern of SNR resembles corresponding fractional refractivity differences showing equatorial positive N bias (and to a lesser extent in the higher latitudes). The majority of positive biases is observed in occultations having voltage SNR of around 300 V V−1 or lower. In the selected occultations, significant positive gradients in the vertical structure of retrieved refractivity are identified between altitudes 3–5 km either as a consequence of low SNR or complex vertical structures associated with subrefractions developing in the atmosphere.

Fig. 8.
Fig. 8.

Daily distribution of L1 SNR at 80-km HSL with respect to latitude of occultation point for 23 Jan 2020.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Fig. 9.
Fig. 9.

Daily distribution of COSMIC-2 profiles observed on 4 Oct 2019 with subrefractions identified between altitudes 3–5 km: (top) mean SNR computed between −40- and −20-km HSL and (bottom) corresponding mean fractional refractivity differences with respect to ECMWF.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

5. Distribution of subrefractions

Occurrences of subrefractive conditions are assessed based on collocations of COSMIC-2 retrievals with ECMWF and radiosonde refractivity profiles. The sensitive regions near the equator have been particularly analyzed in terms of positive refractivity gradients to explain the associated N biases. The observation domain for the analysis of radiosonde data is restricted to the Indonesian region as depicted in Fig. 10. The island stations marked with WMO identifiers and provided in Table 2 are located in the area of persistent positive biases in the COSMIC-2 refractivity and will be investigated in detail.

Fig. 10.
Fig. 10.

Distribution of radiosonde stations over Indonesian region.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Table 2

Locations of selected radiosonde stations in the Indonesian region.

Table 2

a. Assessment based on ECMWF

Figure 11 presents vertical structures of refractivity gradients based on selected occultations observed in October 2019 in the Indonesian region. The considered profiles are provided in Table 3. COSMIC-2 retrievals collocated with ECMWF profiles show distinctive characteristics that could be partially attributed to their different vertical resolutions. The smooth ECMWF profiles fail to reproduce rapid changes in the vertical occurring in COSMIC-2 data mostly at middle altitudes in the troposphere. The sharp gradients usually tend to positive values creating subrefractive conditions. When contrasted with corresponding refractivity statistics, the magnitude of N biases increases with the magnitude of gradients. Profile A1 in Fig. 11 with subrefractions around altitudes of 3 and 4 km results in positive biases on the order of 5%. Similar characteristics can be identified in profile B1. Number of thin layers with positive refractivity gradients develops within altitude 4–6 km in profile C1. Therefore, the N bias in profile C2 appears relatively high in the troposphere. Profile D1 with rather insignificant positive gradients is biased by up to 3% with fairly well captured subrefraction at 3 km in the ECMWF profile. However, the retrievals below 1 km in occultations D, E, and F are substantially different as large negative gradients in ECMWF are reflected by positive gradients in COSMIC-2. Moreover, anomalously large subrefractions can be identified in the lowermost troposphere, especially in occultations in October, possibly due to surface fluxes or erroneous retrievals due to low SNR and strong multipath.

Fig. 11.
Fig. 11.

(top) Vertical gradients of refractivity from COSMIC-2 (black solid line) and ECMWF (green dotted line). (bottom) Corresponding fractional refractivity differences. The profiles E and F show anomalously large subrefractions near the surface.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Table 3

Details of selected occultation in Fig. 11 collected over the Indonesian region.

Table 3

Figure 12 shows a scatterplot with altitudes indicating the maximum dN/dz found in COSMIC-2 and respective ECMWF refractivity profiles. While most of data pairs suggests good linear relationship, the noisiness reduces the correlation from strong to moderate. While the altitudes correspond to maximum refractivity gradients, their magnitudes in ECMWF-based profiles rarely meet or exceed the positive value. Figure 13 displays fraction of profiles for which the condition of subrefraction is identified in the troposphere section below 10-km altitude. The monthly statistics for October are gridded to 5° bins and show substantially different distributions with very high data counts in COSMIC-2. The global median for subrefractions is on the order of 80%, whereas corresponding ECMWF subrefractions results in mere 13%. The equatorial region over the western Pacific and northern Indian Ocean, where most of positive refractivity biases occur (Fig. 3), has particularly low subrefraction occurrences in ECMWF dataset. This is not the case for COSMIC-2 as nearly 90% of profiles result in positive refractivity gradients leading to larger refractivity values as demonstrated in Fig. 11.

Fig. 12.
Fig. 12.

Scatterplot of COSMIC-2 vs ECMWF altitudes of maximum dN/dz.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

b. Assessment based on radiosondes

Figure 14 shows seasonal differences in the vertical distribution of gradients based on radiosonde refractivity profiles from Yap Island (WMO 91413) which is representative for the region of positive N biases. The gradients observed in October are relatively small and more homogeneous in the vertical. The atmosphere dynamics in January is reflected by significant negative gradients exceeding −200 km−1 that develop at 2-km altitude accompanied by strong positive gradients from low to middle troposphere (2–5 km). The inversion layers manifested by negative gradients are supported in higher PBL tops in zonal mean fields from ERA5 (Fig. 6), as opposed to subrefraction layers developing above that are not reflected in background fields over Indonesian region, as shown in Fig. 13.

Fig. 13.
Fig. 13.

Fraction of refractivity profiles containing positive vertical gradients below 10-km altitude observed in October 2019: (top) COSMIC-2 and (bottom) ECMWF background.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

Fig. 14.
Fig. 14.

Magnitude of vertical refractivity gradients based on monthly observations at radiosonde station WMO 91413 for (left) October 2019 and (right) January 2020.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

The statistical assessment of subrefractions based on radiosonde and COSMIC-2 refractivity is demonstrated on monthly data in Fig. 15. The refractivity structures modeled from radiosoundings launched from island stations marked in Fig. 10 and provided in Table 2 are compared with neighboring COSMIC-2 retrievals collected within a 300-km mismatch distance and a ±1-h time difference. The data counts describe number of profile points with positive refractivity gradients identified within specified altitude ranges. The statistics for COSMIC-2 are calculated from 1655 profiles in October 2019 and 1865 profiles in January 2020. Due to much lower temporal resolution of radiosondes, the datasets consist of 339 profiles in October 2019 and 335 profiles in January 2020. Two representative months are considered to illustrate different seasonal features. Profile sections below 1 km are excluded due to often found unrealistic variations of refractivity in COSMIC-2 retrievals. Generally, occurrence of subrefractions can be modeled fairly well by normal distribution. Most of positive refractivity gradients is found in the middle troposphere with fairly well agreement between COSMIC-2 and radiosonde datasets. While slightly asymmetric toward lower altitudes (left skewed), the subrefractions in radiosonde data are mostly centered at 5-km altitude in October and 3 km in January. The monthly data counts for COSMIC-2 are more consistent as most of subrefractions can be found around 4-km altitude for both October and January.

Fig. 15.
Fig. 15.

Frequency distribution of subrefractions identified in COSMIC-2 refractivity profiles (thick lines) and radiosonde observations (thin lines) over Indonesian region. The monthly statistics for two representative periods correspond to data counts in 1-km altitude ranges.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0026.1

6. Conclusions

The quality assessment of COSMIC-2 retrievals from provisional dataset covering a period from October 2019 to February 2020 reveals positive biases in monthly mean fields of refractivity deviations with respect to ECMWF background data. The biases are restricted to altitudes within 3–5 km and tend to develop over equatorial regions between 10°N and 10°S. The magnitude of positive N biases is generally smaller than negative biases that are typically induced by sharp inversion layers associated with the PBL. However, understanding of potential error sources is important for climate applications. Although the positive N biases are observed above PBL tops, potential feedback mechanism can be demonstrated based on geographically coherent distributions. The zonal averages of refractivity differences vary from 0.7% in October to 0.4% in February and exhibit similar seasonal march around the equator to the shallow PBL. The seasonality is reflected in the variability of ITCZ that can affect the error characteristics due to associated moisture, rainfall, and clouds contributions.

Pronounced positive N biases exceeding 1% are observed over Indonesian and Amazon regions, which agree in the distribution and magnitude with previous studies on RO refractivity estimates. The analysis of COSMIC-2 voltage SNR suggests that the quality of refractivity retrievals might depend on the signal’s strength due to spatially correlated N biases. The noisiness of occultations estimated as SNR in the free atmosphere (at 80-km altitude) shows that low latitude regions are characterized by the largest SNR spread varying from 500 to 2500 V V−1. When estimated in the lower troposphere, the SNR occasionally drops down to 100 V V−1 and the retrieved refractivity is found to be positively biased. The reason for this might be twofold. First, given the early stage of COSMIC-2 data release, neutral atmosphere retrievals might be more susceptible to inversion biases due to not-yet-optimized processing methodologies. In the light of continuous developments (Sokolovskiy et al. 2019; Schreiner et al. 2019) and changes in the receiver firmware (Hordyniec et al. 2021), the detailed analysis of retrieval errors is difficult and falls out of the scope of the study. However, the relationship between SNR drops and N biases suggests that the magnitude of errors can be influenced by the low signal’s voltage. Second, the positive N biases can be attributed to mismodeling of refractivity fields that are reproduced differently in COSMIC-2 and corresponding ECMWF background meteorology. The positive N biases are often found to be vertically aligned with significant spikes in the vertical structure of COSMIC-2 refractivity. The spikes are manifested by strong positive gradients, which are indicative of subrefractive conditions. However, such structures are not reflected in ECMWF refractivity profiles. As a consequence, the COSMIC-2 refractivity at and above a subrefraction layer is larger than for standard refractive conditions in ECMWF background profiles with smooth vertical distribution, thus resulting in a positive N bias. The existence of subrefractions is supported based on radiosonde refractivity observations. The majority of positive gradients in both COSMIC-2 and radiosonde data is found in the middle troposphere at around 4 km, where the largest positive N biases are also observed. The spatially scarce subrefractions identified in monthly ECMWF fields emphasize distinctive characteristics of background and COSMIC-2 refractivity data, especially over regions affected by significant positive biases, such as Indonesia and Amazon.

Acknowledgments.

This work has been supported by the Australian Antarctic Program—Grant 4469. We thank UCAR and NSPO for providing access to FORMOSAT-7/COSMIC-2 neutral atmosphere provisional data release 1. This study was carried out within the Memorandum of Understanding between Wroclaw University of Environmental and Life Sciences and National Space Organization, National Applied Research Laboratories on Cooperative Research on GNSS Science and Application. The constructive and detailed comments on this manuscript by two anonymous reviewers are greatly acknowledged.

Data availability statement.

FORMOSAT-7/COSMIC-2 neutral atmosphere provisional data release 1 can be downloaded from https://data.cosmic.ucar.edu/gnss-ro/cosmic2/provisional. ECMWF background fields were downloaded from Copernicus Climate Change Service Climate Data Store (CDS) available under https://cds.climate.copernicus.eu (last access: 2020-04-14). NOAA/ESRL Radiosonde Database is available for download from https://ruc.noaa.gov/raobs/.

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Save
  • Ao, C. O., 2007: Effect of ducting on radio occultation measurements: An assessment based on high-resolution radiosonde soundings. Radio Sci., 42, RS2008, https://doi.org/10.1029/2006RS003485.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ao, C. O., T. Meehan, G. Hajj, A. Mannucci, and G. Beyerle, 2003: Lower troposphere refractivity bias in GPS occultation retrievals. J. Geophys. Res., 108, 4577, https://doi.org/10.1029/2002JD003216.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ao, C. O., D. E. Waliser, S. K. Chan, J.-L. Li, B. Tian, F. Xie, and A. J. Mannucci, 2012: Planetary boundary layer heights from GPS radio occultation refractivity and humidity profiles. J. Geophys. Res., 117, D16117, https://doi.org/10.1029/2012JD017598.

    • Search Google Scholar
    • Export Citation
  • Babin, S. M., 1995: A case study of subrefractive conditions at Wallops Island, Virginia. J. Appl. Meteor., 34, 10281038, https://doi.org/10.1175/1520-0450(1995)034<1028:ACSOSC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beyerle, G., T. Schmidt, J. Wickert, S. Heise, M. Rothacher, G. König-Langlo, and K. Lauritsen, 2006: Observations and simulations of receiver-induced refractivity biases in GPS radio occultation. J. Geophys. Res., 111, D12101, https://doi.org/10.1029/2005JD006673.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Byrne, M. P., A. G. Pendergrass, A. D. Rapp, and K. R. Wodzicki, 2018: Response of the intertropical convergence zone to climate change: Location, width, and strength. Curr. Climate Change Rep., 4, 355370, https://doi.org/10.1007/s40641-018-0110-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S.-Y., C.-Y. Huang, Y.-H. Kuo, and S. Sokolovskiy, 2011: Observational error estimation of FORMOSAT-3/COSMIC GPS radio occultation data. Mon. Wea. Rev., 139, 853865, https://doi.org/10.1175/2010MWR3260.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S.-Y., C.-Y. Liu, C.-Y. Huang, S.-C. Hsu, H.-W. Li, P.-H. Lin, J.-P. Cheng, and C.-Y. Huang, 2021: An analysis study of FORMOSAT-7/COSMIC-2 radio occultation data in the troposphere. Remote Sens., 13, 717, https://doi.org/10.3390/rs13040717.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clark, S. K., Y. Ming, I. M. Held, and P. J. Phillipps, 2018: The role of the water vapor feedback in the ITCZ response to hemispherically asymmetric forcings. J. Climate, 31, 36593678, https://doi.org/10.1175/JCLI-D-17-0723.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cucurull, L., R. Anthes, and L.-L. Tsao, 2014: Radio occultation observations as anchor observations in numerical weather prediction models and associated reduction of bias corrections in microwave and infrared satellite observations. J. Atmos. Oceanic Technol., 31, 2032, https://doi.org/10.1175/JTECH-D-13-00059.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., 2005: Bias and data assimilation. Quart. J. Roy. Meteor. Soc., 131, 33233343, https://doi.org/10.1256/qj.05.137.

  • Gorbunov, M., K. Lauritsen, A. Rhodin, M. Tomassini, and L. Kornblueh, 2006: Radio holographic filtering, error estimation, and quality control of radio occultation data. J. Geophys. Res., 111, D10105, https://doi.org/10.1029/2005JD006427.

    • Search Google Scholar
    • Export Citation
  • Ho, S.-P., and Coauthors, 2020: Initial assessment of the COSMIC-2/FORMOSAT-7 neutral atmosphere data quality in NESDIS/STAR using in situ and satellite data. Remote Sens., 12, 4099, https://doi.org/10.3390/rs12244099.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hocke, K., A. Pavelyev, O. Yakovlev, L. Barthes, and N. Jakowski, 1999: Radio occultation data analysis by the radioholographic method. J. Atmos. Sol.-Terr. Phys., 61, 11691177, https://doi.org/10.1016/S1364-6826(99)00080-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hordyniec, P., 2018: Simulation of liquid water and ice contributions to bending angle profiles in the radio occultation technique. Adv. Space Res., 62, 10751089, https://doi.org/10.1016/j.asr.2018.06.026.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hordyniec, P., Y. Kuleshov, S. Choy, and R. Norman, 2021: Observation of deep occultation signals in tropical cyclones with COSMIC-2 measurements. IEEE Geosci. Remote Sens. Lett., 19, 1002905, https://doi.org/10.1109/LGRS.2021.3092511.

    • Search Google Scholar
    • Export Citation
  • Liu, H., Y.-H. Kuo, S. Sokolovskiy, X. Zou, Z. Zeng, L.-F. Hsiao, and B. C. Ruston, 2018: A quality control procedure based on bending angle measurement uncertainty for radio occultation data assimilation in the tropical lower troposphere. J. Atmos. Oceanic Technol., 35, 21172131, https://doi.org/10.1175/JTECH-D-17-0224.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rieckh, T., B. Scherllin-Pirscher, F. Ladstädter, and U. Foelsche, 2014: Characteristics of tropopause parameters as observed with GPS radio occultation. Atmos. Meas. Tech., 7, 39473958, https://doi.org/10.5194/amt-7-3947-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scherllin-Pirscher, B., G. Kirchengast, A. Steiner, Y.-H. Kuo, and U. Foelsche, 2011: Quantifying uncertainty in climatological fields from GPS radio occultation: An empirical-analytical error model. Atmos. Meas. Tech., 4, 20192034, https://doi.org/10.5194/amt-4-2019-2011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scherllin-Pirscher, B., A. K. Steiner, G. Kirchengast, M. Schwärz, and S. S. Leroy, 2017: The power of vertical geolocation of atmospheric profiles from GNSS radio occultation. J. Geophys. Res. Atmos., 122, 15951616, https://doi.org/10.1002/2016JD025902.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schmidt, T., G. Beyerle, S. Heise, J. Wickert, and M. Rothacher, 2006: A climatology of multiple tropopauses derived from GPS radio occultations with CHAMP and SAC-C. Geophys. Res. Lett., 33, L04808, https://doi.org/10.1029/2005GL024600.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schreiner, W., and Coauthors, 2019: Performance assessment and requirement verification of COSMIC-2 neutral atmospheric radio occultation data. UCAR COSMIC Program Doc., 22 pp., https://www.romsaf.org/romsaf-irowg-2019/en/open/1570200603.b4c2a0b42191514125cfdaad83aac7be.pdf/Schreiner__UCAR-Schreiner-C2-CALVAL-09192019-final.pdf.

    • Search Google Scholar
    • Export Citation
  • Schreiner, W., and Coauthors, 2020: COSMIC-2 radio occultation constellation: First results. Geophys. Res. Lett., 47, e2019GL086841, https://doi.org/10.1029/2019GL086841.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, E. K., and S. Weintraub, 1953: The constants in the equation for atmospheric refractive index at radio frequencies. Proc. IRE, 41, 10351037, https://doi.org/10.1109/JRPROC.1953.274297.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sokolovskiy, S. V., 2001: Modeling and inverting radio occultation signals in the moist troposphere. Radio Sci., 36, 441458, https://doi.org/10.1029/1999RS002273.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sokolovskiy, S. V., 2003: Effect of superrefraction on inversions of radio occultation signals in the lower troposphere. Radio Sci., 38, 1058, https://doi.org/10.1029/2002RS002728.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sokolovskiy, S. V., 2004: Open loop tracking and inverting GPS radio occultation signals: Simulation study. Occultations for Probing Atmosphere and Climate, Springer, 3951, https://doi.org/10.1007/978-3-662-09041-1_4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sokolovskiy, S. V., C. Rocken, W. Schreiner, and D. Hunt, 2010: On the uncertainty of radio occultation inversions in the lower troposphere. J. Geophys. Res., 115, D22111, https://doi.org/10.1029/2010JD014058.

    • Crossref
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  • Fig. 1.

    Monthly data for January 2020 showing (top) refractivity deviations with respect to the forecast lead time and (bottom) histogram with number of data pairs.

  • Fig. 2.

    (a) Analytical refractivity profiles and (b) their vertical gradients for different conditions: standard refraction (black dotted line), ducting (blue solid line), and subrefraction (red solid line). The profiles of (c) bending angle vs impact height were retrieved by Abel transforming respective refractivity profiles, whereas wave optics simulations were used to compute (d) the amplitude of the signal with respect to HSL.

  • Fig. 3.

    Monthly mean refractivity deviations between COSMIC-2 and ECMWF at altitudes 3–5 km for (top) October 2019 and (bottom) January 2020. The statistics are based on a 5° × 5° latitude–longitude grid.

  • Fig. 4.

    ERA5 monthly mean fields of column integrated water vapor (IWV) associated with ITCZ. Contour lines represent the value of 40 kg m−2 for October 2019 (red) and January 2020 (blue).

  • Fig. 5.

    Mean biases (thick lines) and standard deviations (thin lines) of refractivity between COSMIC-2 and ECMWF: global statistics (gray) and Indonesian subset (black) for October 2019 (dashed lines) and January 2020 (solid lines).

  • Fig. 6.

    Zonal monthly means of PBL height derived from ERA5 fields.

  • Fig. 7.

    Zonal monthly means of refractivity differences between COSMIC-2 and ECMWF within altitudes 3–5 km.

  • Fig. 8.

    Daily distribution of L1 SNR at 80-km HSL with respect to latitude of occultation point for 23 Jan 2020.

  • Fig. 9.

    Daily distribution of COSMIC-2 profiles observed on 4 Oct 2019 with subrefractions identified between altitudes 3–5 km: (top) mean SNR computed between −40- and −20-km HSL and (bottom) corresponding mean fractional refractivity differences with respect to ECMWF.

  • Fig. 10.

    Distribution of radiosonde stations over Indonesian region.

  • Fig. 11.

    (top) Vertical gradients of refractivity from COSMIC-2 (black solid line) and ECMWF (green dotted line). (bottom) Corresponding fractional refractivity differences. The profiles E and F show anomalously large subrefractions near the surface.

  • Fig. 12.

    Scatterplot of COSMIC-2 vs ECMWF altitudes of maximum dN/dz.

  • Fig. 13.

    Fraction of refractivity profiles containing positive vertical gradients below 10-km altitude observed in October 2019: (top) COSMIC-2 and (bottom) ECMWF background.

  • Fig. 14.

    Magnitude of vertical refractivity gradients based on monthly observations at radiosonde station WMO 91413 for (left) October 2019 and (right) January 2020.

  • Fig. 15.

    Frequency distribution of subrefractions identified in COSMIC-2 refractivity profiles (thick lines) and radiosonde observations (thin lines) over Indonesian region. The monthly statistics for two representative periods correspond to data counts in 1-km altitude ranges.

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