Effects of Liquid Clouds on GPS Radio Occultation Profiles in Superrefractions

Abstract

Inversion of radio occultation (RO) measurements to atmospheric parameters in the neutral atmosphere utilizes the assumption of spherical symmetry by implementation of the Abel transform. The main contribution to the retrieved refractional angle and other geophysical parameters comes from gaseous properties of the atmosphere. The atmospheric refraction is expressed by a function of air pressure, air temperature, and water vapor pressure. Such commonly adopted methodology results in highly comparable RO retrievals with background models. However, in the lowermost troposphere referred to as planetary boundary layer, inversion in spherically symmetric atmosphere is an ill‐conditioned problem. The presence of superrefractions introduces negative errors in the RO‐retrieved refractivity (N‐bias). We show that significant refractivity gradients are frequently collocated with clouds over oceans in tropical and subtropical regions. Based on gridded monthly means we show that superrefractions usually occur at altitudes up to 2 km and the largest cloud fractions tend to suspend at underlying layers. The magnitude of clouds expressed in terms of refractivity units can exceed 1.5, which corresponds to 0.5% in terms of fractional differences. We use both geometrical optics and wave optics techniques to illustrate propagation mechanisms in RO retrievals. Simulation experiments suggest that RO inversions in cloudy planetary boundary layer lead to larger negative N‐biases. Low‐level clouds retrieved from numerical weather prediction model could therefore be used as an indicator of erroneous RO observations. A better agreement with RO refractivity could be achieved by incorporating cloud variables into background fields especially over the Pacific and Atlantic Oceans.

1

Introduction

Tropospheric limb soundings in Global Positioning System (GPS) radio occultation (RO) technique utilize a link between a pair of satellites while they both set or rise behind Earth's horizon during an occultation event (Kursinski et al., ). The signal transmitted by a navigational satellite traverses the atmosphere and experiences a refraction before reaching a low‐Earth orbiter (LEO). The geophysical parameters can be derived from the received phase and amplitude of the signal by solving the inverse problem in spherically symmetric atmosphere (Kuo et al., ). By means of wave optical methods (Gorbunov, ; Jensen et al., , ), which commonly rely on Fourier integral operators, signals composed of more than one tone can be disentangled in multipath regions. Currently, both L1 and L2 GPS signals can be tracked in the open loop mode (Ao et al., ) providing continuous cancelation of ionospheric refraction in occultation profiles deep down in the troposphere (Sokolovskiy et al., ). RO observations in the neutral atmosphere have been proven a reliable climate benchmark record (Davis & Birner, ; Schmidt et al., ; Scherllin‐Pirscher et al., ; Steiner et al., ) and a powerful data source for assimilation systems in numerical weather prediction (NWP; Cucurull et al., ; Healy et al., ; Healy & Thépaut, ).

An ill‐conditioned problem is introduced to RO data inversions due to missing direct rays at LEO orbit, absorbed by the Earth's surface. The presence of significant refractivity gradients associated with the superrefraction causes propagating rays to bend downward and collide with the Earth. The generalization to the Abel integral (Fjeldbo et al., ) leads to negatively biased refractivity retrievals below altitudes of superrefraction layers also called ducting altitudes (Ao et al., ; Beyerle et al., ; Sokolovskiy, ). Moreover, signatures of reflected signal components are expected to be visible in radioholograms (Benzon & Høeg, ) and their contributions should be removed to improve troposphere retrievals (Beyerle & Hocke, ; Beyerle et al., ). The ill‐posed problem of RO inversions is usually considered in terms of analytical solutions to the standard Abel retrieval in order to properly reconstruct profiles under superrefractions (Ao, ; Xie et al., ). The lowermost layer of the troposphere, namely, the planetary boundary layer (PBL), manifests itself with pronounced top heights due to strong temperature inversions and sharp moisture gradients (Garratt, ) that leave an effect on troposphere profiling with RO technique (Basha & Ratnam, ; Ho et al., ). The PBL height can be detected from occultation profiles using a sharpness parameter (Guo et al., ; Sokolovskiy et al., ) or the minimum refractivity gradient (Ao et al., ; Xie et al., ). Low‐level clouds are often found trapped below the PBL inversion. The phenomenon is utilized in the remote sensing from nadir‐viewing platforms to provide an estimate of PBL altitude based on cloud top height measurements (Garay et al., ; Jordan et al., ; Zhao et al., ). It is recognized that extinction caused by suspended liquid and solid water introduce microwave propagation delays (Solheim et al., ). The refractivity retrieved from RO cloudy profiles can be positively biased (Yang & Zou, , ; Zou et al., ). The positive N‐bias with respect to underestimated background fields results from simplifications in the refractivity modeling. Hordyniec () shows that cloud contributions can be propagated to RO observables. However, negative N‐biases in RO refractivity due to superrefractions and their dependency on cloudy PBL have not been investigated.

We utilize cloud products modeled from global NWP fields to study marine PBL. We propagate cloud liquid water contents to refractivity fields to assess the altitude distribution for the most significant fractions. We show that low‐level cloud tops are spatially collocated with minimum refractivity gradients exceeding the critical condition. The analysis in terms of monthly means is supported by statistical assessment of refractivity errors in RO observations. Cloud contributions to refractivity are generally neglected in background fields, and hence, the model can be affected by positive N‐biases with respect to RO data. Based on simulation methods using geometrical optics and wave optics, we illustrate the problem of superrefractions in RO retrievals. We demonstrate that cloudy PBL can introduce larger negative biases to RO refractivity due to the ill‐conditioned inversion in the spherically symmetrical atmosphere.

2

RO Observations

RO profiles from FORMOSAT‐3/COSMIC mission are utilized for level 2 atmPrf product provided by COSMIC Data Analysis and Archive Center. Refractivity retrievals determined at mean sea level altitudes are used in the study. The geolocation of profiles follows from latitude and longitude of perigee point at occultation point. Since the tropical troposphere is a particularly active region, the observation domain is restricted to the equatorial belt within latitudes ±35°. Observations are screened in a quality control procedure to remove unrealistic quantities from analysis. Profiles are ensured to be monotonic series of altitudes. The refractivity must be within the range of 0 to 500 ppm. The fractional difference within the upper troposphere and lower stratosphere region (5–35 km) cannot exceed 10% with respect to NWP model. Retrievals with the lowermost altitude of perigee point larger than 2 km are discarded to fully capture PBL properties of tropical and subtropical troposphere.

3

Background Model

Background meteorological variables are derived from National Centers for Environmental Prediction Global Forecast System (GFS) model on 0.5° × 0.5° horizontal grid. Forecasts fields are analyzed for the period of one year in 2016. Due to the model cycle (00, 06, 12, and 18 UTC) and output time step (+03), eight background fields in 3‐hourly basis were considered daily. Geopotential surfaces on 26 layers were used to create vertical profiles extending up to approximately 30 km. In the following study, the vertical representation of profiles at geometric altitudes requires conversion of background geopotential heights. We follow methodology provided by Somigliana (). The deviation between the reference ellipsoid and the geoid is calculated from EGM96 model (Lemoine et al., ).

The GFS model primarily serves as a source of cloud properties in the lowermost troposphere. A study of Yoo and Li () provides useful quality estimates of GFS cloud vertical structures based on multiple satellite observations. Meteorological variables of the GFS model are mapped to the refractivity to be consistent with RO observations. Background profiles containing contributions from the cloud water content are extracted from forecast fields. Together with cloud structures, the vertical gradient of refractivity is computed. Profile‐specific characteristics therefore consist of parameters describing the minimum refractivity gradient and the maximum cloud water refractivity together with their respective altitudes. The variables are analyzed seasonally in terms of monthly mean climatologies. Gridded data are generated from daily GFS profiles downsampled from 0.5° × 0.5° model resolution to a coarser 2.5° × resolution. The coverage of the GFS background model is limited to ±35° latitudinal band.

3.1

Background Refractivity Fields

The real and positive nondispersive part of the neutral atmospheric refraction consists of a dry term (N_d) and water vapor term (N_v) in a functional relation of air pressure (P), water vapor pressure (P_v), and temperature (T; Smith & Weintraub, ) [Image Omitted. See PDF] which with an addition of nongaseous part related to liquid water (N_w) can be expressed as N=N_d+N_v+N_w. The influence of suspended water droplets on radio waves is parameterized by means of their concentration M_w in mass content per unit of air volume (g/m³). The liquid water density is derived from the relation M_w=ρ_dQ_w using dry air density ρ_d=(P−P_w)/(R_dT) with gas constant for dry air R_d=287.058 in J/K/kg and cloud water mixing ratio Q_w (g/kg). Rayleigh approximation of Mie's scattering theory (van de Hulst, ) allows for computation of real part of refractivity for nonprecipitating clouds based on the complex term [Image Omitted. See PDF] with the density of the liquid water ρ_w≈1 g/cm³. The double‐Debye model for pure water expresses the complex permittivity ϵ_w using principal and secondary relaxation frequencies (Liebe et al., ). A permittivity model for ice reported by Hufford () can be omitted since temperatures below freezing were not observed in the tropical troposphere. The complex term N_w is generalized to the real part related to the scattering factor and associated with the respective phase delay. The impact on the amplitude attenuation due to the imaginary part is not analyzed since only RO phase measurements are inverted to profiles of the neutral atmosphere.

4

Monthly Mean Climatologies

A yearly analysis based on the GFS background allowed to isolate tropospheric conditions affected by critical refractions. Large vertical gradients in the refractivity are mostly driven by a high water vapor content commonly observed in the tropical and subtropical troposphere. Figure illustrates the impact of significant refractivity structure on RO raypaths. Substantial bending starts to occur in the lower troposphere together with increasing vertical gradient of refractivity. From the total number of 5,366,255 considered profiles, in over 10% of cases the refractivity gradient reached or exceeded the critical condition (dN/dz ≤ 157 ppm/km). The frequency distribution is presented in Figure a. The most typical refractivity gradients are introduced by challenging conditions (−100 > dN/dz ≥ −157 ppm/km), which occur in more than 50% profiles. On the other hand, superrefractions exceeding a gradient of −250 ppm/km are marginal and rarely found although Beyerle et al. () show the gradient can become as low as −600 ppm/km based on in situ data from radiosondes. von Engeln et al. () demonstrate that the vertical resolution of NWP models can contribute to smaller magnitude of tropospheric ducts. Constraints introduced in the numerical modeling to derive GFS meteorological variables could be another factor affecting frequency distribution.

Geometrical ray tracing in spherically symmetric atmosphere characterized by (a) vertical refractivity gradient exceeding the critical value dN/dz = −157 ppm/km (dashed line). (b) Simulated raypaths at different tangent points showing large variations at SR layer where they no longer follow a circular shape. (c) The corresponding profile of tangent point latitudes. Rays inside and below the SR layer are internally refracted and have no tangent points. External rays start to emerge from the multipath zone at 1.45 km. Note that there still might be some external rays within ray heights of 1.95–1.45 km not shown in (c) due to vertical sampling in the ray tracer.

Frequency distributions for (a) vertical refractivity gradients (dN/dz). Dashed line indicates threshold for the critical condition (dN/dz = −157 ppm/km). (b) Altitudes for minimum dN/dz (solid black) and maximum refractivity of the liquid water Nw (solid blue). (c) Distribution of Nw magnitude in profiles affected by superrefractions.

With a scope of critical refractions, refractivity profiles were analyzed in terms of altitudes where the minimum negative gradient is found. Figure b suggests that most of tropospheric ducts occur under 2 km. Over 70% of observations is within the altitude range between 1.25 and 1.75 km. An interesting dependency is found after considering liquid water contained in the superrefractions. The altitude distribution for maximum liquid water refractivity suggests the most frequent occurrence at the underlying model's layer between 0.9 and 1.25 km.

Figure c displays the distribution in the magnitude of the liquid water refractivity associated with superrefractions. The frequency distribution decreases together with increasing magnitude, which is expected. The lowermost limit (0.5 ≤ N_w<0.6 ppm) is represented by 40% cases since liquid water below 0.5 ppm is considered insignificant and filtered out from the analysis. In contrary, cloud fractions with refractivity above 1.5 ppm are highly unlikely to suspend in the lowest troposphere. Thus, it serves as the uppermost limit for the assessment of associated propagation effects due to scattering.

The spatial distribution of cloudy conditions collocated with superrefractions was analyzed in terms of seasonal means and representative months are presented in Figure . The water bodies and coastal regions are particularly covered with data samples. In January grid boxes are mostly sampled with up to 500 profile points. In the Northern Pacific the average cloud refractivity (N_w) exceeds the value of 1 ppm. The data samples significantly increase in July over the East Pacific and the East Atlantic to over 2,000 observations. The mean cloud refractivity is generally up to 0.8 ppm. The magnitudes of N_w are proportional to data frequency distribution. The Southern Atlantic in October displays very high data counts reaching up to 5,000 samples per bin, which corresponds to visibly larger magnitudes of cloud refractivity relative to the surrounding region.

Gridded 2.5° × 2.5° monthly means for tropical and subtropical regions: (left column) data samples for superrefractions found within each bin and (right column) maximum Nw in profiles affected by ducting expressed in units of refractivity.

Figure shows altitudes for maximum profile‐specific refractivities due to cloud water contrasted with altitudes of minimum vertical refractivity gradients. Refractivity gradients are ensured to exceed the critical condition. The relationship of altitudes frequently follows a convention that maximum cloud refractivity suspends below superrefractions, thus being associated with PBL clouds. A very pronounced feature is observed over the North Pacific in January. Superrefractions develop at relatively high altitudes up to 2 km in the West Pacific and up to 1.8 km in the East Pacific in terms of monthly averages. The respective mean altitudes of maximum cloud refractivity do not exceed 1.6 km. The pattern in altitudes is maintained in analyzed months although superrefractions are generally found lower in the troposphere at around 1 km. Larger mean altitudes tend to occur over central oceanic regions than at their boundaries. Some distinct characteristics can be also indicated for individual bins, where the altitude of max N_w is larger than altitude of min dN/dz. Such examples are mostly localized around altitude of 2 km at coastal areas.

Gridded 2.5° × 2.5° monthly means for tropical and subtropical regions: (left column) altitude of minimum refractivity gradient and (right column) altitude of maximum Nw.

5

RO Inversions With Cloud Contributions

The end‐to‐end simulation chain in Figure allows to propagate refractivity fields to RO variables in a nonspherically symmetric atmosphere. The bending angle is computed from raw complex signal modeled with multiple phase screen method (Beyerle et al., ; Gorbunov & Gurvich, ; Knepp, ). We use high‐resolution grid described by 20,001 screens separated by vacuum in horizontal distance Δx=100 m to capture horizontal variability of refractivity field along a propagation plane. Each screen is composed of M=524,288 (2¹⁹) grid points with the vertical resolution Δz=1 m. The complex field at each screen is windowed by Gaussian function to exclude reflected signals and artificial diffraction effects (Sokolovskiy, ). The orbits of occulting satellites are taken to be circular and coplanar. The LEO satellite is moving in setting order, and the transmitter is stationary. The effect of ionosphere is excluded, and there is no tracking method implemented for the LEO satellite; hence, simulated phase and amplitude are unaffected by the receiver software (Ao et al., ; Beyerle et al., ; Sokolovskiy, ). Retrievals in the moist lower troposphere consist of several rays received at same arrival times, which are disentangled with Full Spectrum Inversion (FSI) method (Jensen et al., ) to yield the bending angle with respect to the impact parameter as a single‐valued function. Impact parameters reduced by Earth's radius r_e=6,378 km give impact heights. The end‐to‐end chain is closed by Abel transforming (Fjeldbo et al., ) the simulated bending angle profile α(p) to the refractive index profile n(r) [Image Omitted. See PDF] where n=1+N×10⁻⁶, a product χ=rn(r) is a refractional radius, and r−r_e yields corresponding geometric height z. The numerical integration is evaluated in the impact parameter space with the upper bound at 120 km. The differences in refractivity profiles between gaseous input N and simulated output N_S are calculated as [Image Omitted. See PDF] whereas fractional contributions of liquid water to cloud‐free refractivity are expressed in terms of N_w/N.

Simulation methodology for assessment of cloud impact on radio occultation inversions.

5.1

Results for Simulation Experiments

The impact of liquid water term is quantified in simulated profiles by means of refractivity fractional errors through inversion scheme depicted in Figure . Profiles extracted from GFS refractivity fields composed of nondispersive gaseous terms serve as the reference for comparisons with simulated profiles with included cloud water term. Figure shows the GFS refractivity field of liquid water along the occultation plane. The cloud is located within ±150 km with respect to the central screen just under the altitude of superrefraction (≈2 km). The fractional contribution of liquid water at the central screen to the cloud‐free refractivity reaches 0.2%. Cloud fractions introducing 1 and 1.5 ppm refractivities arise from a multiplication of the background cloud refractivity of 0.5 ppm so that the distribution in Figure c is satisfied. The fractional differences yield 0.4% and 0.6%, respectively.

(a) Profiles of liquid water refractivity at the central screen (x = 0 km) and their fractional contributions with respect to a cloud‐free refractivity profile. (b) Refractivity field of the liquid water along occultation plane corresponding to the profile with Nw = 0.5 ppm.

A consistent truncation of RO signals is relevant for the inversion to profiles of refractive index (Sokolovskiy, ). The liquid water will make the incoming rays at same LEO positions to accumulate slightly different refractivity contributions. Thus, the FSI inversion of received signals will yield small inconsistencies in retrieved impact heights relative to a cloud‐free environment, although applying cutoff at same altitude. Part of the effect is also due to the diffraction‐limited resolution in 200 Hz simulated occultation signals that result in ≈1 m sampling for the vertical resolution. The fractional differences in terms of refractivity are computed after introducing simulated profiles to consistent vertical grid with an input refractivity, which is achieved by linear interpolation.

Based on the representative cloud fractions (Figure ), the assumption of spherical symmetry was applied for the simulation of induced systematic effects in the presence of a tropospheric duct. Figure a illustrates inversion errors in retrieved refractivity profile, which is underestimated with respect to the true background due to the superrefraction effect. The negative bias in the retrieved refractivity composed of gaseous parts systematically increases up to a magnitude of around −4% at ∼1.5  km. Figure b shows that the inclusion of additional refractivity terms associated with liquid water in the inversion contributes to magnified negative bias. Thus, the background refractivity originally affected by a positive N‐bias due to neglected liquid water (Figure ) translates into a negative bias below SR layer as a result of ill‐conditioned inversion. Individual cloud contributions to the negative bias are separated in Figure c. The largest fractional difference N_w/N is about 1 order of magnitude smaller than the N‐bias induced by the inversion error (0.4% vs. 4%). The input profile of cloud refractivity is characterized by a single‐spike structure. The output from the simulation has an additional minor spike below altitude of 1 km, which in mainly because of vertical gradient of gaseous refractivity resulting from computed fractional differences. The PBL top manifested by the artifact in refractivity differences at around 2 km of altitude, where a positive bias occurs, originates from a number of factors. Refractivity profiles are inverted from bending angles, which result in infinitely extensive spikes at impact height corresponding to altitude of SR layer. Due to cloud water contributions, the spikes are misaligned with respect to gaseous retrieval. Moreover, Abel‐retrieved refractivity profiles end higher than the true background profile (Sokolovskiy, ). Application of 1 m integration in the Abel transform to refractivity minimizes the effect of numerical errors. Since the positive bias at PBL top cannot be identified in fractional differences between true and retrieved gaseous refractivities, the effect is driven by vertical gradients in cloud refractivity profiles. The propagation mechanism has been already observed by Hordyniec () and might be overcome by analytical corrections within altitudes of positive differences. The positive biases in Figure c are proportional to the magnitudes of respective cloud contributions. In order to satisfy the individual contributions to the background refractivity, as showed in Figure , the positive differences in inverted profiles could be attributed to negative biases under the SR layer.

Simulation results for superrefraction effects in spherical symmetry. (a) Inverted refractivity profile (solid black) and Global Forecast System‐derived “true” profile (dashed gray). (b) Negative N‐bias induced by superrefraction (solid black) with additional cloud contributions. (c) Individual contributions to the N‐bias due to clouds in the inverted profiles.

In case a two‐dimensional refractivity field is considered in the simulation, the impact of cloud in the inverted refractivity is expected to decrease with respect to the spherically layered atmosphere (Figure ). Figure shows corresponding errors in the bending angle and refractivity induced by the liquid water field with intensity of 0.5 ppm, as presented in Figure , and its multiplied fractions. Since the singularity in the bending angle profile induced by tropospheric ducts is no longer an issue in a horizontally inhomogeneous atmosphere, no significant residuals are observed at the top of PBL. For the cloud profile with N_w=1.5 ppm, the bending angle error is at the order of 2% and 0.2% in the retrieved refractivity. Hence, the contribution is three times smaller than indicated by the background cloud profile. Although a close inspection of bending angle errors at the very bottom of profiles shows a slight shift toward negative differences, no negatively biased sections are found in the refractivity errors. No simulation results are available below 1 km of altitude (3 km in terms of impact height) due to the noise in the FSI amplitude exceeding the threshold of 20%.

Effects of horizontal inhomogeneity (2‐D) in cloud refractivity fields propagated to (a) bending angle with respect to impact height and (b) refractivity in a function of altitude expressed in terms of fractional differences.

6

Systematic Effects in RO Observations

The gridded data set of seasonal means revealed two representative regions characterized by either (1) statistically significant samples of binned data and (2) particularly intensive contamination of the atmosphere with cloud water. The first case corresponds to the Atlantic region showed in Figure for October, which is preceded by a comparable data sample in September and followed in November. The second case refers to the Pacific region in January introducing mean cloud fractions N_w>1 ppm presented in Figure . In order to support the distribution and indicate particularly active regions in terms of cloud refractivity, individual profile‐specific contributions were also analyzed. Figure shows geolocations of profiles for which the N_w is greater or equal to 1 ppm. The highest fractions of liquid water are observed at Tropical Circles over the Pacific and Atlantic Oceans, up to 2 ppm. Generally, the larger the maximum cloud refractivity becomes, the magnitude of dN/dz tends to be less significant. The relationship supports the claim that superrefractions are mainly caused by vertical gradients of humidity (Garratt, ) in marine PBL, which is balanced by reduction in cloud content.

(a) Distribution of superrefractions with (b) cloud water contributions Nw ≥ 1 ppm under altitudes of minimum dN/dz. Altitude distributions for (c) minimum dN/dz and (d) maximum Nw.

In order to study the dependency of N‐bias in RO observations in cloudy PBL, we use collocated GFS profiles and corresponding FORMOSAT‐3/COSMIC refractivity profiles in 2.5° × 2.5° grid boxes. The fractional differences between RO observations and the GFS background model are computed as follows: [Image Omitted. See PDF] which averaged over data samples yield mean bias and standard deviation (one sigma). The background refractivity N_GFS is composed of the gaseous components only modeled with equation . The RO observations N_RO contain all contributions including other atmospheric particulates, such as cloud water, as well as the retrieval noise. The error characteristic for RO observations corresponds to the calculation scheme in equation  for RO simulations.

The Atlantic case for September, October, and November season is bounded by latitudes from 25°S equatorward and longitudes between 35°W and 20°E. Collected observations correspond to period within 245 and 335 day of year in 2016 and consist of 1,309 profiles. Figure shows computed differences of individual profiles together with their mean and standard deviation. When compared to the background model, the RO refractivity results in negative N‐bias up to 8% in terms of mean differences. The N‐bias affects retrievals up to the altitude of 1.5 km and becomes the most significant below the altitude of 1 km. This agrees with gridded data in Figure for statistically the largest sample in October, where the mean altitude of minimum dN/dz is under 1 km. The largest bias in the background data is expected at the altitudes within 0.5 to 1.2 km, where maximum N_w components were identified. The N‐bias is shown as positive since the background neglects the liquid water. The low‐level clouds can therefore be used to indicate negatively biased RO refractivity due to SR effects. On the other hand, the positive N‐bias could be mitigated by refining the refractivity formula in equation  with additional N_w term so that the background observation is more accurately represented. The individual profiles can be characterized by contributions up to the order of ∼0.5%. Averaging over the data sample leads to the mean N‐bias of 0.2%. Additional complexity to the N‐bias is introduced by propagation mechanism of RO inversions in cloudy PBL that can lead to more negatively biased retrievals below the SR layer, as demonstrated by numerical simulations.

Statistical analysis of refractivity profiles over the Atlantic region for September, October, and November season. (a) Fractional refractivity differences between GFS and radio occultation profiles. Red solid line represents mean bias and red dashed lines show one standard deviation. Gra area represents altitude range affected by clouds. Corresponding cloud water contributions derived from GFS in superrefractions are presented in terms of (b) fractional differences and (c) absolute values. GFS = Global Forecast System.

The statistical analysis of refractivity differences over the Pacific region corresponds to a domain in the Northern Hemisphere limited by latitudes from 25°N southward to the equator and longitudes from 135°E eastward to 135°W. One month of data in January consists of 818 RO profiles. Figure shows the negative N‐bias extending to the altitude of 2 km, which is by 0.5 km higher than over the Atlantic (Figure ). The largest bias occurs at 1 km and has a comparable order of magnitude as indicated for the Atlantic region, although being more vertically extensive over the Pacific. The cloud impact is however effective within heights of 1.3 to 1.7 km, which is higher than the altitude of the most negative mean N‐bias. The largest positive N‐bias in the GFS model is observed at ∼1.5 km. The cloud‐specific N_w/N in Figure are highly consistent with derived monthly means for January in Figure as well as individual profiles in Figure . The magnitude of the cloud impact in collocated profiles is at the order of 0.3% in terms of mean fractional differences.

As in Figure but for the Pacific region in January.

7

Conclusions

The ill‐conditioned inverse problem is a main challenge in troposphere profiling with RO technique. The turbulent PBL with sharp gradients at its top introduces superrefractions that lead to negatively biased RO refractivity below ducting layers. The effect arises from the presence of internal rays and missing tangent points in RO profiles. Cloud water, although commonly recognized to suspend at PBL top altitudes, is not considered in NWP models to better represent refractivity fields. Generally, the assumption of cloud‐free atmosphere results in the underestimated background since it introduces a positive N‐bias with respect to RO refractivity. However, such contributions can propagate to larger negative N‐biases below SR layers indicated by the altitude of minimum refractivity gradient.

The conducted analysis over tropical and subtropical regions proves a clear dependence of liquid water on ducting conditions based on predictions of the GFS model. Significant vertical gradients in refractivity are commonly followed by considerable cloud fractions in underlying atmospheric levels. Over 70% of superrefractions analyzed in 2016 were found at the mean altitude of 1.5 km, while nearly 80% of profiles had maximum cloud contributions at around 1 km. Cloud concentrations expressed in terms of liquid water refractivity can exceed a magnitude of 1.5 ppm which corresponds to 0.6% fractional differences. The monthly mean climatologies showed that superrefractions with cloud contributions are widely distributed over oceanic regions hence being associated with marine PBL. The phenomena is particularly frequent in the Pacific and Atlantic Oceans at the Tropical Circles both in the Northern and Southern Hemispheres.

Generally speaking, the scattering due to liquid water particulates contributes weakly to RO profiles of refractivity relative to the magnitude of N‐bias induced by superrefractions. Simulation experiments suggest that RO inversions with included liquid water term contribute to larger negative N‐bias below ducting layers in spherically symmetric atmosphere. The largest cloud impact is one order of magnitude smaller (−0.4%) than corresponding N‐bias in cloud‐free atmosphere (−4%). The systematic effect was supported by the statistical analysis of RO refractivity differences. RO observations compared to the background model showed the mean N‐bias of −8% in regions affected by superrefractions. The collocation of RO profiles with PBL clouds suggested the largest contributions within SR layers. The dependence of superrefractions on low‐level clouds under PBL can therefore serve as an additional indicator of negatively biased RO retrievals. Liquid water profiles from background models characterized by maximum point‐specific N_w and its altitude could be utilized as control parameters for quality checks.

Acknowledgments

This work has been supported by the National Science Centre, Poland Project 2015/19/N/ST10/02650 and the Australian Antarctic Program Grant 4469. We would like to thank UCAR and CDAAC for providing FORMOSAT‐3/COSMIC Data Products and NOAA/NCEP for GFS model. We acknowledge the Wroclaw Center of Networking and Supercomputing (www.wcss.wroc.pl): computational grant using Matlab Software License 101979. The observational data sets used in this study are publicly available: GPS RO data can be downloaded from UCAR/COSMIC website (https://cdaac-www.cosmic.ucar.edu/) and NCEP GFS forecast products can be retrieved from https://nomads.ncdc.noaa.gov/data/gfs4/ website. Simulation results are available from the corresponding author upon request.