Editorial Type:
Article
Article Type:
Research Article

Impacts of Ice Clouds on GPS Radio Occultation Measurements

X. Zou Department of Earth, Ocean and Atmospheric Sciences, The Florida State University, Tallahassee, Florida, and Center of Data Assimilation for Research and Application, Nanjing University of Information Science and Technology, Nanjing, China

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S. Yang Center of Data Assimilation for Research and Application, Nanjing University of Information Science and Technology, Nanjing, China

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P. S. Ray Department of Earth, Ocean and Atmospheric Sciences, The Florida State University, Tallahassee, Florida

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Print Publication:
01 Dec 2012
DOI:
https://doi.org/10.1175/JAS-D-11-0199.1
Page(s):
3670–3682
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Abstract

Mathematical solutions accounting for the effects of liquid and ice clouds on the propagation of the GPS radio signals are first derived. The percentage contribution of ice water content (IWC) to the total refractivity increases linearly with the amount of IWC at a rate of 0.6 (g m−3)−1. Measurements of coincident profiles of IWC from CloudSat in deep convection during 2007–10 are then used for estimating the ice-scattering effects on GPS radio occultation (RO) measurements from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC). The percentage contribution of IWC to the total refractivity from CloudSat measurements is consistent with the theoretical model, reaching about 0.6% at 1 g m−3 IWC.

The GPS RO refractivity observations in deep convective clouds are found to be systematically greater than the refractivity calculated from the ECMWF analysis. The fractional N bias (GPS minus ECMWF) can be as high as 1.8% within deep convective clouds. Compared with ECMWF analysis, the GPS RO retrievals have a negative temperature bias and a positive water vapor bias, which is consistent with a positive bias in refractivity. The relative humidity calculated from GPS retrievals is usually as high as 80%–90% right above the 0°C temperature level in deep convection and is about 15%–30% higher than the ECMWF analysis. The majority of the data points in deep convection are located on the negative side of temperature differences and the positive side of relative humidity differences between GPS RO retrievals and ECMWF analysis.

Corresponding author address: Dr. X. Zou, Department of Earth, Ocean and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4520. E-mail: xzou@fsu.edu

Abstract

Mathematical solutions accounting for the effects of liquid and ice clouds on the propagation of the GPS radio signals are first derived. The percentage contribution of ice water content (IWC) to the total refractivity increases linearly with the amount of IWC at a rate of 0.6 (g m−3)−1. Measurements of coincident profiles of IWC from CloudSat in deep convection during 2007–10 are then used for estimating the ice-scattering effects on GPS radio occultation (RO) measurements from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC). The percentage contribution of IWC to the total refractivity from CloudSat measurements is consistent with the theoretical model, reaching about 0.6% at 1 g m−3 IWC.

The GPS RO refractivity observations in deep convective clouds are found to be systematically greater than the refractivity calculated from the ECMWF analysis. The fractional N bias (GPS minus ECMWF) can be as high as 1.8% within deep convective clouds. Compared with ECMWF analysis, the GPS RO retrievals have a negative temperature bias and a positive water vapor bias, which is consistent with a positive bias in refractivity. The relative humidity calculated from GPS retrievals is usually as high as 80%–90% right above the 0°C temperature level in deep convection and is about 15%–30% higher than the ECMWF analysis. The majority of the data points in deep convection are located on the negative side of temperature differences and the positive side of relative humidity differences between GPS RO retrievals and ECMWF analysis.

Corresponding author address: Dr. X. Zou, Department of Earth, Ocean and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4520. E-mail: xzou@fsu.edu
Keywords: Clouds; Cloud water/phase; Clouds

1. Introduction

The Global Positioning System (GPS) radio occultation (RO) technique provides measurements determined by the vertical gradient of atmospheric refractivity. GPS RO measurements are of high accuracy, high precision, and high vertical resolution. They meet the stringent climate monitoring requirements of 0.5-K accuracy and better than 0.10 K decade−1 stability (Ohring et al. 2005; Luntama et al. 2008). Therefore, RO observations are well suited for establishing a stable, long-term record required for climate monitoring (Steiner et al. 2009; Foelsche et al. 2009, 2011; Wickert et al. 2009). The precision of temperature profiles derived from Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC)/Formosa Satellite Mission 3 (FORMOSAT3, hereafter referred to as COSMIC for brevity) were estimated to be about 0.05°C in the upper troposphere and lower stratosphere (Anthes et al. 2008).

It is generally recognized that GPS RO measurements are primarily affected by dry-air atmospheric constituents and water vapor and are insensitive to clouds and precipitation. The terms associated with cloud effects in atmospheric refractivity are two orders of magnitude smaller than the terms of dry air and water vapor. Thus, impacts of clouds and precipitation on GPS RO measurements are often neglected in most applications. However, for deep convective clouds where the cloud ice water content is high, the impact of ice clouds on the refractivity exists but it is not well studied and documented. This study extends part of the work by Lin et al. (2010) to a 4-yr period (2007–10) and evaluates large-scale analysis biases within deep convective clouds. More importantly, contributions from cloud ice water content (IWC) to refractivity are estimated using IWC observations from CloudSat. A similar study investigating contributions of cloud liquid water content (LWC) to GPS refractivity can be found in Yang and Zou (2012).

A consideration of clouds and precipitation effects in the refractivity forward operators and its adjoint operator can benefit significantly to GPS RO remote sensing of cloud parameters and numerical weather prediction (NWP) data assimilation in cloud and precipitation environment. Because GPS RO operates at low frequencies through a limb-sounding technique, atmospheric states in clouds can be profiled at a very high vertical resolution. This capability will complement passive visible, infrared, and microwave techniques that provide the vertically integrated cloud ice water path but with better horizontal resolution (King et al. 2003, 2004; Platnick et al. 2001; Weng and Grody 2000). In visible and infrared wavelengths, satellite observations can be used to estimate cloud ice water path associated with optically thin clouds such as cirrus. For passive microwave sensors at frequencies higher than 85 GHz, cloud ice water path and particle mean size can be estimated simultaneously (Weng and Grody 2000; Zhao and Weng 2002; Bennartz and Petty 2001; Bennartz and Bauer 2003). Here, a theoretical derivation for the LWC/IWC terms accounting for the absorption and scattering effects from water droplets and ice particles on atmospheric refractivity is first provided. Numerical results assessing the role of ice scattering and its impact on GPS retrievals are presented.

The paper is arranged as follows. Section 2 provides a brief description of COSMIC ROs and CloudSat observations. A theoretical derivation for the LWC/IWC terms accounting for the effects of cloud water droplets and ice particles on atmospheric refractivity is provided in section 3. Numerical results on assessing the role of ice scattering and its impact on GPS retrievals are discussed in section 4. Summary and conclusions are found in section 5.

2. Data description

The COSMIC satellite system consists of a constellation of six low-earth-orbit (LEO) microsatellites and was launched on 15 April 2006 into a circular, 72° inclination orbit at 512-km altitude (Anthes et al. 2008). The first COSMIC GPS RO global datasets of atmospheric parameters (e.g., refractivity, pressure, temperature, etc.) were provided on 21 April 2006. The daily occultation count was about 2500 soundings. The vertical resolution ranges from better than 100 m in the lower troposphere to approximately 0.5 km in the stratosphere. Each GPS RO measurement quantifies an integrated refraction effect of the atmosphere along a ray path over a few hundred kilometers of space, with the largest effect centered at the perigee point (Kursinski et al. 1996). The RO data used in this study are obtained from the University Corporation for Atmospheric Research (UCAR) COSMIC Data Analysis and Archival Center (CDAAC; Kuo et al. 2004). Vertical profiles of temperature, water vapor, and pressure have also been made available, which were derived using a one-dimensional variational data assimilation (1DVAR) wet retrieval algorithm1 (http://cosmic-io.cosmic.ucar.edu/cdaac/doc/documents/1dvar.pdf). The European Centre for Medium-Range Forecasts (ECMWF) analyses were used as the first guess field.

In this study, the GPS RO profiles within deep convective ice clouds identified by CloudSat during 2007–10 are selected, where collocation is defined by a time difference of no more than 1 h and a spatial separation of less than 60 km. The RO soundings within ice clouds were selected based on CloudSat data. CloudSat was launched into a 705-km near-circular sun-synchronous polar orbit on 28 April 2006. It orbits earth approximately once every 1.5 h, finishing the so-called one observation granule. The primary observing instrument on CloudSat is a 94-GHz, nadir-pointing cloud-profiling radar (CPR), which measures the returned power backscattered by clouds. The along-track temporal sample interval equals 0.16 s, resulting in more than 30 000 vertical profiles of radar reflectivity. The CPR does not scan, resulting in a rather narrow track. The along-track spatial resolution is about 1.1 km, with an effective field of view (FOV) of approximately 1.4 km × 2.5 km. Besides reflectivity, LWC, IWC, cloud layers (with a maximum of five layers), cloud type, as well as the altitudes of cloud tops and cloud bases are also provided by CloudSat (Stephens et al. 2002).

3. Atmospheric refractivity formula including cloud parameters

The atmospheric refractivity N is a function of the pressure P, temperature T, water vapor pressure Pw, and LWC W through the following relationship (Kursinski 1997):
e1
where P is in hectopascals, T is in kelvins, Pw is in hectopascals, Wwater is liquid water content in grams per cubic meters, and Wice is the ice water content in grams per cubic meters. The first term on the right-hand side of (1) is referred to as the “dry” term Ndry, the second one is the “wet” term Nvapor, the third one is the liquid water term NLWC, and the fourth term is the ice term NIWC. To understand how clouds physically affect refractivity, the third and fourth terms in (1) are derived in the following.
Clouds containing liquid and ice can affect the propagation of the GPS RO signals through their scattering and absorption. Since the GPS wavelengths are operated at approximately 20 cm (e.g., 1.5-GHz frequency), water droplets and ice particles are much smaller than the GPS RO wavelength. In general, the Mie theory (Mie 1908) (assuming spherical particles) can be used to derive the scattering and absorption coefficients. For cloud particles having a size parameter () much less than one, where the r is the particle radius and λ is the GPS wavelength, the scattering and absorption coefficients can be expressed in Rayleigh approximation. Also, the cloud absorption dominates the attenuation of the GPS RO wave propagation. In this case, the cloud absorption coefficient is (Bohren and Huffman 1983):
e2
where m is the complex index of refraction and Im is the imaginary part. The refractive indices for water and ice at 1.5 GHz or 20-cm wavelength are (Ray 1972)
e3a
e3b
respectively. The corresponding GPS RO phase shift is (Bohren and Huffman 1983)
e4
where Re is the real part.
Following Gresh (1990), the change of electric field resulting from a thick model of a group of scattering particles is
e5
where Ei is the incident electrical field,
e6
is the total attenuation of the hydrometeors in the slab of thickness , and is the particle density distribution function. As pointed out by Atlas (1964), cloud and ice concentrations decrease exponentially with size and thus the distribution of number concentration becomes narrow and can be considered to be monodisperse. With the monodisperse assumption, τ equals the cross-sectional area of the droplets times the number of drops per unit pathlength times the pathlength times the absorption coefficient, as indicated by the second equation in (7). Similarly, under the same assumption, the total cross-sectional area times the phase change per event is
e7
A collection of particles behaves as a homogeneous slab if
e8
where and are the refractive indices for scatters and air, respectively. Equating the real and imaginary parts of the above equation gives
e9
The refractivity due to scattering is defined as . Therefore, (9) can be written as
e10
Substituting (7) for and (4) for P into (10) one obtains
e11
The LWC and IWC is the total mass of water and ice per unit volume, respectively, that is, , and . The refractivity for liquid water and ice can thus be written as
e12a
e12b
Based on (3) the real part of the term in the parenthesis in (12) is 0.966 for water and 0.423 for ice. For water at 0°C with the density ρw = 1 g cm−3, the refractivity due to scattering by water droplets is approximately equal to
e13
This is the same result as reported by Solheim et al. (1999) and others. For ice at 0°C with the density ρi = 0.92 g cm−3, the refractivity due to scattering by ice particles is approximately equal to
e14
Densities for ice range from about 0.5 g cm−3 in some graupel to near 0.92 g cm−3 for frozen water or most crystals. The relationship (12) is valid for all densities of ice as long as the particles are in the Rayleigh region and W is expressed in grams of liquid water per cubic meters. The difference between these and previously published results stem from our use of less approximate values for the physical properties of liquid water and ice. The difference between (14) and the fourth term in previously published results (1) stems from the use of more accurate values for the density of pure ice.

4. Numerical results

Collocations between COSMIC GPS ROs and CloudSat IWC profiles were searched globally during the 4-yr period from 2007 through 2010. A total of 232 global COSMIC RO profiles are found with IWC measurements, which are all located in deep convection. Figure 1 illustrates the geographical distribution of GPS RO profiles collocated with deep convective ice clouds. The temporal separation of the observing time between COSMIC GPS RO and CloudSat data is less than 1 h. Further, the height of the middle of the convection, determined by CloudSat, is used to determine the location of the same height in the GPS RO. This distance must be within 60 km for the RO to be used. Figure 2 shows the vertical distributions of IWC within deep convective ice clouds collocated with COSMIC GPS ROs, with their observed latitudes indicated. It is seen that these deep convective clouds were usually initiated at about 1 km, with ice particles formed at about 3.5 km in low latitudes above the 0°C temperature altitude. The height of the top of the ice clouds can extend to as high as 15 km in the tropics, decreasing with increasing latitudes, and reaching about 6 km at about 60°–70°N. The IWC values observed by CloudSat are generally less than 1.2 g m−3.

Fig. 1.
Fig. 1.

Geographical distribution of COSMIC GPS ROs collocated with deep convective ice clouds.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

Fig. 2.
Fig. 2.

Vertical distribution of IWC (g m−3) within deep convective clouds collocated with COSMIC GPS ROs plotted at their observed latitudes. Each vertical bar is drawn from cloud base to cloud top. Areas without IWC data are indicated in black. Blue curve indicates the altitude where temperature is 0°C.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

To examine how well the GPS RO refractivity observations compare with ECMWF analysis within these ice clouds, the vertical profiles of fractional N biases, which is defined as the mean of , where is calculated by the first two terms in (1) and is the COSMIC data, of all COSMIC GPS ROs collocated with those CloudSat ice profiles shown in Fig. 2 are plotted in Fig. 3a. For each ice cloud profile, a vertical line is drawn from its cloud base to cloud top in Fig. 3a. Positive N biases are found within ice clouds, with the maximum value of about 1.8% being located at about 4 km.

Fig. 3.
Fig. 3.

(a) Mean fractional N difference (black solid) of all collocated COSMIC GPS ROs in deep convection between cloud top and cloud base. Vertical lines are drawn from cloud base to cloud top in deep convection (red). (b) Mean IWC (solid) and cloudy data points counted within 100-m interval (dotted). (c) Fractional N bias (solid) and standard deviation (vertical bars) in deep convective clouds for all data between cloud top and cloud base. (d) Variation of standard deviation of IWC for deep convection.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

The maximum mean value of CloudSat measured IWC is around 0.2 g m−3 for deep convective ice clouds (Fig. 3c). The IWC maxima are located at about 7.5 km (Fig. 3b). The LWC below the zero temperature altitude may have a more significant contribution than IWC. Such a contribution is difficult to estimate because no CloudSat measurements of LWC were available below the ice clouds as shown in Fig. 2. Variations of the mean and standard deviations of fractional N differences with IWC are shown in Fig. 3c. The fractional N bias is about 1% when IWC is less than 0.6 g m−3 and decreases to about 0.25% when IWC is greater than 0.6 g m−3 in deep convective ice clouds. The standard deviations of the fractional N differences are slightly larger than the biases. The standard deviations of IWC are rather small (Fig. 3d). The standard deviation at large IWC is less reliable owing to a much smaller sample size.

GPS RO bending angles were assimilated in ECMWF analyses with given error estimates of refractivity. There are also other measurements and model physics that determine the analysis increments. The altitude where the fractional N bias reaches the maximum (Fig. 3a) is significantly below the altitude of the maximum IWC (Fig. 3b). All these suggest that the neglect of IWC in the forward model for bending-angle assimilation played little role, if any, in causing the positive N bias within deep convection seen in Fig. 3a. It may suggest a need to develop a bias-correction algorithm for GPS RO data assimilation in cloudy conditions.

The global mean value of IWC (see Fig. 3b) is rather small because of the fact that majority numbers of ice clouds have very small IWC values. Figure 4 presents the frequency distributions of the IWC measurements (Fig. 4a) and (Fig. 4b) within deep convective clouds. Ice clouds with smaller IWC values are more populated than those of large LWC values. It is also seen that the higher the altitude of an ice cloud is located, the smaller the IWC. The fractional N differences are definitely positively biased.

Fig. 4.
Fig. 4.

Frequency distributions of (a) IWC and (b) with measurements within different cloud layers (color, km).

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

The fractional contribution of IWC in individual clouds can be as large as 0.6%–0.7% (Fig. 5a), which is much larger than the mean value (black curve in Fig. 5a). Above 5 km within deep convective clouds, the IWC term (NIWC) can be a few times larger than the total differences of refractivity between GPS and ECMWF analysis (e.g., NGPS − NECMWF) as shown in Fig. 5b, where NGPS is the sum of dry and water vapor terms calculated using GPS wet retrievals. It is thus concluded that the neglect of IWC might introduce significant errors in individual profiles from GPS RO wet retrievals.

Fig. 5.
Fig. 5.

Scatterplots of (a) (%) and (b) . The black curve in (a) represents the averaged percentage contribution of IWC, that is, . The amount of IWC is indicated by colors (g m−3).

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

Figure 6 presents variations of the fractional contribution of IWC to GPS refractivity () with respect to IWC (Fig. 6a), as well as the variations of the differences between NGPS and Nobs with respect to IWC (Fig. 6b). It is seen in Fig. 6 that NGPS is quite close to Nobs in high altitudes but not in the low troposphere. The differences between NGPS and Nobs (Fig. 6b) are not correlated with NIWC (Fig. 6a). When IWC increases from 0 to 1 g m−3, the fractional IWC contribution increases to more than 0.5% depending on the altitudes. The higher the ice particles are located in deep convective clouds, the faster the fractional IWC contribution increases with IWC. The fact that NGPS is very close to Nobs because the forward model errors arising from neglecting the LWC and IWC terms are not accounted for in the retrieval of temperature and water vapor pressure profiles using the 1DVAR formulation. It is probably best to either include contributions to total refraction from ice particles in the GPS RO forward simulation or to add a bias correction in the 1DVAR retrieval.

Fig. 6.
Fig. 6.

Variations of (a) and (b) with respect to IWC within deep convection. The color convention indicating the altitudes of observations is as in Fig. 4.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

It is pointed out that refractivity from GPS RO represents a weighted average of the dry atmosphere, water vapor, cloud liquid water, and cloud ice within the GPS swath. The maximum weighting is located at the perigee point. Since CloudSat LWC or IWC measurement is a point measurement, the inconsistency of observation resolution between GPS RO and CloudSat will lead to certain uncertainty in estimating cloud liquid water or cloud ice contributions to the path refractivity using CloudSat data. On the other hand, although CloudSat has narrow swath and does not provide sufficient information of cloud environment within the GPS RO swath, it does provide cloud-type information. There are ample LWC measurements from CloudSat for six different cloud types by CloudSat. To minimize the impact of this uncertainty caused by inconsistent resolutions between GPS RO and CloudSat, an effort was made in Yang and Zou (2012) to evaluate separately the cloud liquid water impacts on refractivity within different cloud types. Consistent results for different cloud types were obtained, suggesting the adequacy of the approach of using CloudSat for investigating cloud ice contributions to GPS RO measurements. Because of relatively high IWC values are found mostly in deep convection and IWC contribution to refractivity is smaller than LWC [see Eq. (1)], cloud ice impacts on GPS RO refractivity is only assessed using GPS RO and CloudSat data within deep convection.

Differences between GPS RO retrievals obtained without considering IWC effects on GPS RO propagation and ECMWF analysis for temperature and water vapor pressure within deep convective clouds shown in Fig. 2 are shown in Fig. 7. The vertical structures of temperature and water vapor pressure within deep convective clouds are also provided in Fig. 7. The GPS RO–derived water vapor pressure is in general greater than the ECMWF analysis except near the cloud base. The differences of temperature between GPS RO and ECMWF have an opposite sign to those of water vapor pressures. Over cloud regions with water vapor pressure differences around 0.5 hPa, the temperature from GPS RO is a few degrees colder than the ECMWF analysis and vice versa.

Fig. 7.
Fig. 7.

Differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) for (a) temperature (K) and (b) water vapor pressure (hPa) within deep convective clouds shown in Fig. 1. (c) The ECMWF water vapor analysis (hPa).

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

Figure 8 presents the vertical distribution of relative humidity in deep convection from GPS RO retrievals and ECMWF analysis (Figs. 8a,b), as well as the differences between the two (Fig. 8c). The vertical pattern of relative humidity from GPS RO and ECMWF is rather different. The peak of relative humidity from RO is located around the middle of clouds and that from ECMWF near the cloud bases. The GPS RO relative humidity reaches 80%–90% above the 0° temperature altitude and is about 15%–30% higher than the ECMWF analysis. But the relative humidity reduces to as low as 40%–50% in the upper one-third of the clouds.

Fig. 8.
Fig. 8.

Relative humidity from (a) GPS RO retrievals and (b) ECMWF analysis within deep convective clouds shown in Fig. 1. (c) Differences of relative humidity between GPS RO retrievals and ECMWF analysis.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

The fact that GPS RO retrievals are wetter and colder than the ECMWF analysis could be associated with the neglect of the IWC contribution in the retrieval. To estimate the uncertainty of temperature and relative humidity that could be introduced by an uncertainty in refractivity, we calculate the fractional increments of refractivity introduced by perturbations in temperature ΔT and relativity humidity (ΔRH), where
e15
The vertical profiles of temperature and relative humidity derived from a COSMIC GPS RO sounding that occurred at 2010 UTC 9 June 2007 and was located at (1.7°S, 86.9°E) is selected for calculating values defined by (15) (Fig. 9). Results calculated using this reference profile for in (14) are shown in Fig. 10. The fractional N differences are more sensitive to relative humidity than to temperature perturbations. A fractional N difference at 2-, 6-, and 9-km altitudes could be caused by a relative humidity perturbation of , , and , respectively. In other words, small errors introduced by neglecting IWC for GPS RO retrieval in ice clouds could introduce significant errors in GPS RO water vapor retrievals. The higher the altitude of ice particles, the larger the effects of IWC on relative humidity retrievals.
Fig. 9.
Fig. 9.

Vertical profiles of (a) temperature and (b) relative humidity derived from a COSMIC GPS RO sounding located at 1.7°S, 86.9°E that occurred at 2010 UTC 9 Jun 2007. (c) Refractivity calculated from temperature and relative humidity in (a),(b).

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

Fig. 10.
Fig. 10.

Fractional N differences introduced by perturbations in temperature (K) and relativity humidity (%) at 2, 6, and 9 km.

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

Figure 11 provides the frequency distributions of temperature and relative humidity differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) in deep convective clouds and clear-sky conditions. The same collocation criteria between GPS RO and CloudSat used for identifying cloudy GPS RO profiles are used for identifying clear-sky GPS ROs. It is seen that majority of the cloudy data points are located at the negative side of the temperature differences (Figs. 11a,c) and the positive side of the specific humidity differences (Figs. 11b,d) between GPS RO and ECMWF analysis. In other words, temperatures from GPS RO retrievals within ice clouds are in general colder than ECMWF analysis, and specific humidity from GPS RO retrievals within ice clouds are in general higher than ECMWF analysis. These are consistent with the theoretical results in Fig. 10. In contrast, the frequency distributions of temperature and relative humidity differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) in clear-sky conditions (Figs. 11e,f) are rather symmetric, showing no biases in both variables. In conclusion, there is a bias between GPS and ECMWF in deep convective clouds but none in clear-sky conditions.

Fig. 11.
Fig. 11.

Frequency distributions of (a),(c) temperature and (b),(d) relative humidity differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) in (a),(b) deep convection and (c),(d) clear-sky conditions. The altitudes of observations are indicated in color (km).

Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-11-0199.1

5. Summary and conclusions

The wavelength of GPS RO signals is approximately 20 cm or a frequency of 1.5 GHz. The influence of scattering from liquid cloud, rainwater, and ice is generally two orders of magnitude less significant than other atmospheric variables. For this reason, GPS RO measurements are often said to be insensitive to cloud. This study shows that scattering from ice clouds could affect the propagation of the signal to a significant level as the IWC increases, exceeding the measurement uncertainty. The reasons behind that is that even though the IWC is two orders of magnitude smaller than the dry air and water vapor terms in the refractivity expression, the uncertainty of refractivity is two orders of magnitude less than the refractivity itself.

The ice particle radius is much less than the GPS wavelength and its scattering and absorption can be treated as small spherical particles and derived using Rayleigh’s approximation. Assuming the absorption dominates extinction, the LWC and IWC contributions to atmospheric refractivity, Wwater and Wice, are derived, respectively.

Measurements of IWC from CloudSat in deep convection are used for estimating the potential ice-scattering effects on GPS RO measurements from COSMIC. More than 232 global COSMIC RO profiles with collocated IWC measurements within deep convective clouds are found in 4 yr of data from 2007 through 2010. The GPS RO refractivity observations in deep convective clouds are found to be systematically greater than the refractivity calculated from ECMWF analyses. Within deep convective clouds, the fractional N bias between GPS RO observations and ECMWF refractivity simulations can be as high as 1.8%, which exceeds the measurement uncertainty. The percentage contribution of IWC to the total refractivity increases linearly with the amount of IWC, reaching about 0.6% at 1 g m−3, which is close to the highest IWC value measured by CloudSat. It is thus suggested that IWC term be included in GPS RO retrieval and data assimilation, especially when the IWC exceeds 1 g m−3.

A sensitivity test shows that a 1% uncertainty in refractivity could introduce significant errors in derived water vapor profiles. In the upper half of the tropical convective clouds at about 9 km, relative humidity uncertainty can be as large as 20% if IWC exceeds 1%. Comparisons between GPS RO moisture retrievals and ECMWF analysis reveal an uncertainty of relative humidity of similar magnitude.

Assimilation of GPS RO–observed refractivity using a local scheme [see Eq. (1)] works better in weak-horizontal-gradient conditions. The two nonlocal observation operators, which were described by Sokolovskiy et al. (2005), could be used for GPS RO refractivity assimilation in strong gradient conditions. The horizontal gradient of refractivity is usually large within and around deep cumulus clouds, a nonlocal refractivity observation operator with a cloud ice term included shall be required to allow cloud ice effects contained in GPS RO data to make some expected contributions to model local ice water variable and others. It is anticipated that inclusion of a cloud ice term in GPS RO assimilation will benefit the cloudy radiance assimilation from Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS) onboard National Oceanic and Atmospheric Administration (NOAA) satellites (e.g., from NOAA-15 to NOAA-19) and European Organization for the Exploitation of Meteorological Satellites’ (EUMETSAT) satellites (e.g., from MetOp-A to future MetOp-B and -C) as well as the Advanced Technology Microwave Sounder (ATMS) onboard Suomi National Polar-Orbiting Partnership (NPP) satellite, which was recently launched in the United States. A combination of GPS RO data with passive microwave satellite radiances will greatly improve assimilation of massively available, largely unused, cloud-affected microwave radiances in active weather systems. When that time comes, scattering effects of water droplets and ice particles within clouds on GPS RO, which can be easily done, are best to be included in the GPS RO observation operator and will complement cloudy radiance assimilation.

Acknowledgments

This research was jointly supported by Chinese Ministry of Science and Technology under 973 Project 2010CB951600 and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.

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  • Foelsche, U., B. Scherllin-Pirscher, F. Ladstädter, A. K. Steiner, and G. Kirchengast, 2011: Refractivity and temperature climate records from multiple radio occultation satellites consistent within 0.05%. Atmos. Meas. Tech. Discuss., 4, 1593–1615, doi:10.5194/amtd-4-1593-2011.

    • Search Google Scholar
    • Export Citation

  • Gresh, D. L., 1990: Voyager radio occultation by the Uranian rings: Structure, dynamics, and particle sizes. Ph.D. dissertation, Stanford University, 202 pp.

  • King, M. D., and Coauthors, 2003: Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS. IEEE Trans. Geosci. Remote Sens., 41, 442–458.

    • Search Google Scholar
    • Export Citation

  • King, M. D., S. Platnick, P. Yang, G. T. Arnold, M. A. Gray, J. C. Riedi, S. A. Ackerman, and K. N. Liou, 2004: Remote sensing of liquid water and ice cloud optical thickness and effective radius in the arctic: Application of airborne multispectral MAS data. J. Atmos. Oceanic Technol., 21, 857–875.

    • Search Google Scholar
    • Export Citation

  • Kuo, C., and Coauthors, 2004: High-resolution observations of the cosmic microwave background power spectrum with ACBAR. Astrophys. J., 600, 32–51.

    • Search Google Scholar
    • Export Citation

  • Kursinski, E. R., 1997: The GPS radio occultation concept: Theoretical performance and initial results. Ph.D. dissertation, California Institute of Technology, 289 pp.

  • Kursinski, E. R., and Coauthors, 1996: Initial results of radio occultation observations of Earth’s atmosphere using the Global Positioning System. Science, 271, 1107–1100.

    • Search Google Scholar
    • Export Citation

  • Lin, L., X. Zou, R. Anthes, and Y.-H. Kuo, 2010: COSMIC GPS cloudy profiles. Mon. Wea. Rev., 138, 1104–1118.

  • Luntama, J.-P., and Coauthors, 2008: Prospects of the EPS GRAS mission for operational atmospheric applications. Bull. Amer. Meteor. Soc., 89, 1863–1875.

    • Search Google Scholar
    • Export Citation

  • Mie, G., 1908: Considerations on the optics of turbid media, especially colloidal metal sols. Ann. Phys., 25, 377–442.

  • Ohring, G., B. Wielicki, R. Spencer, B. Emery, and R. Atlas, 2005: Satellite instrument calibration for measuring global climate change – Report of a workshop. Bull. Amer. Meteor. Soc., 86, 1303–1313.

    • Search Google Scholar
    • Export Citation

  • Platnick, S., J. Y. Li, M. D. King, H. Gerber, and P. V. Hobbs, 2001: A solar reflectance method for retrieving the optical thickness and droplet size of liquid water clouds over snow and ice surfaces. J. Geophys. Res., 106 (D14), 15 185–15 199.

    • Search Google Scholar
    • Export Citation

  • Ray, P. S., 1972: Broadband complex refractive indices of ice and water. Appl. Opt., 11, 1836–1844.

  • Solheim, F. S., J. Vivkanandan, R. H. Ware, and C. Rocken, 1999: Propagation delays induced in GPS signals by dry air, water vapor, hydrometeors, and other particulates. J. Geophys. Res., 104, 9663–9670.

    • Search Google Scholar
    • Export Citation

  • Sokolovskiy, S., Y.-H. Kuo, and W. Wang, 2005: Assessing the accuracy of a linearized observation operator for assimilation of radio occulation data: Case simulations with a high-resolution weather model. Mon. Wea. Rev., 133, 2200–2212.

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    • Export Citation

  • Steiner, A. K., G. Kirchengast, B. C. Lackner, B. Pirscher, M. Borsche, and U. Foelsche, 2009: Atmospheric temperature change detection with GPS radio occultation 1995 to 2008. Geophys. Res. Lett., 36, L18702, doi:10.1029/2009GL039777.

    • Search Google Scholar
    • Export Citation

  • Stephens, G. L., and Coauthors, 2002: The CloudSat mission and the A train. Bull. Amer. Meteor. Soc., 83, 1771–1790.

  • Weng, F., and N. C. Grody, 2000: Retrieval of ice cloud parameters using a microwave imaging radiometer. J. Atmos. Sci., 57, 1069–1081.

    • Search Google Scholar
    • Export Citation

  • Wickert, J., and Coauthors, 2009: GPS radio occultation: Results from CHAMP, GRACE and FORMOSAT-3/COSMIC. Terr. Atmos. Ocean. Sci., 20, 35–50, doi:10.3319/TAO.2007.12.26.01(F3C).

    • Search Google Scholar
    • Export Citation

  • Yang, S., and X. Zou, 2012: Assessments of cloud liquid water contributions to GPS RO refractivity using measurements from COSMIC and CloudSat. J. Geophys. Res., 117, D06219, doi:10.1029/2011JD016452.

    • Search Google Scholar
    • Export Citation

  • Zhao, L., and F. Weng, 2002: Retrieval of ice cloud parameters using the advanced microwave sounding unit (AMSU). J. Appl. Meteor., 41, 384–395.

    • Search Google Scholar
    • Export Citation
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Journal of the Atmospheric Sciences

  • Anthes, R., and Coauthors, 2008: The COSMIC/Formosat-3 mission. Bull. Amer. Meteor. Soc., 89, 313–333.

  • Atlas, D., 1964: Advances in radar meteorology. Advances in Geophysics, Vol. 10, Academic Press, 317–478.

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  • Bennartz, R., and P. Bauer, 2003: Sensitivity of microwave radiances at 85-183 GHz to precipitating ice particles. Radio Sci., 38, 8075, doi:10.1029/2002RS002626.

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  • Bohren, C. F., and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. Wiley-Interscience, 544 pp.

  • Foelsche, U., B. Pirscher, M. Borsche, G. Kirchengast, and J. Wickert, 2009: Assessing the climate monitoring utility of radio occultation data: From CHAMP to FORMOSAT-3/COSMIC. Terr. Atmos. Ocean. Sci., 20, 155–170, doi:10.3319/TAO.2008.01.14.01(F3C).

    • Search Google Scholar
    • Export Citation

  • Foelsche, U., B. Scherllin-Pirscher, F. Ladstädter, A. K. Steiner, and G. Kirchengast, 2011: Refractivity and temperature climate records from multiple radio occultation satellites consistent within 0.05%. Atmos. Meas. Tech. Discuss., 4, 1593–1615, doi:10.5194/amtd-4-1593-2011.

    • Search Google Scholar
    • Export Citation

  • Gresh, D. L., 1990: Voyager radio occultation by the Uranian rings: Structure, dynamics, and particle sizes. Ph.D. dissertation, Stanford University, 202 pp.

  • King, M. D., and Coauthors, 2003: Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS. IEEE Trans. Geosci. Remote Sens., 41, 442–458.

    • Search Google Scholar
    • Export Citation

  • King, M. D., S. Platnick, P. Yang, G. T. Arnold, M. A. Gray, J. C. Riedi, S. A. Ackerman, and K. N. Liou, 2004: Remote sensing of liquid water and ice cloud optical thickness and effective radius in the arctic: Application of airborne multispectral MAS data. J. Atmos. Oceanic Technol., 21, 857–875.

    • Search Google Scholar
    • Export Citation

  • Kuo, C., and Coauthors, 2004: High-resolution observations of the cosmic microwave background power spectrum with ACBAR. Astrophys. J., 600, 32–51.

    • Search Google Scholar
    • Export Citation

  • Kursinski, E. R., 1997: The GPS radio occultation concept: Theoretical performance and initial results. Ph.D. dissertation, California Institute of Technology, 289 pp.

  • Kursinski, E. R., and Coauthors, 1996: Initial results of radio occultation observations of Earth’s atmosphere using the Global Positioning System. Science, 271, 1107–1100.

    • Search Google Scholar
    • Export Citation

  • Lin, L., X. Zou, R. Anthes, and Y.-H. Kuo, 2010: COSMIC GPS cloudy profiles. Mon. Wea. Rev., 138, 1104–1118.

  • Luntama, J.-P., and Coauthors, 2008: Prospects of the EPS GRAS mission for operational atmospheric applications. Bull. Amer. Meteor. Soc., 89, 1863–1875.

    • Search Google Scholar
    • Export Citation

  • Mie, G., 1908: Considerations on the optics of turbid media, especially colloidal metal sols. Ann. Phys., 25, 377–442.

  • Ohring, G., B. Wielicki, R. Spencer, B. Emery, and R. Atlas, 2005: Satellite instrument calibration for measuring global climate change – Report of a workshop. Bull. Amer. Meteor. Soc., 86, 1303–1313.

    • Search Google Scholar
    • Export Citation

  • Platnick, S., J. Y. Li, M. D. King, H. Gerber, and P. V. Hobbs, 2001: A solar reflectance method for retrieving the optical thickness and droplet size of liquid water clouds over snow and ice surfaces. J. Geophys. Res., 106 (D14), 15 185–15 199.

    • Search Google Scholar
    • Export Citation

  • Ray, P. S., 1972: Broadband complex refractive indices of ice and water. Appl. Opt., 11, 1836–1844.

  • Solheim, F. S., J. Vivkanandan, R. H. Ware, and C. Rocken, 1999: Propagation delays induced in GPS signals by dry air, water vapor, hydrometeors, and other particulates. J. Geophys. Res., 104, 9663–9670.

    • Search Google Scholar
    • Export Citation

  • Sokolovskiy, S., Y.-H. Kuo, and W. Wang, 2005: Assessing the accuracy of a linearized observation operator for assimilation of radio occulation data: Case simulations with a high-resolution weather model. Mon. Wea. Rev., 133, 2200–2212.

    • Search Google Scholar
    • Export Citation

  • Steiner, A. K., G. Kirchengast, B. C. Lackner, B. Pirscher, M. Borsche, and U. Foelsche, 2009: Atmospheric temperature change detection with GPS radio occultation 1995 to 2008. Geophys. Res. Lett., 36, L18702, doi:10.1029/2009GL039777.

    • Search Google Scholar
    • Export Citation

  • Stephens, G. L., and Coauthors, 2002: The CloudSat mission and the A train. Bull. Amer. Meteor. Soc., 83, 1771–1790.

  • Weng, F., and N. C. Grody, 2000: Retrieval of ice cloud parameters using a microwave imaging radiometer. J. Atmos. Sci., 57, 1069–1081.

    • Search Google Scholar
    • Export Citation

  • Wickert, J., and Coauthors, 2009: GPS radio occultation: Results from CHAMP, GRACE and FORMOSAT-3/COSMIC. Terr. Atmos. Ocean. Sci., 20, 35–50, doi:10.3319/TAO.2007.12.26.01(F3C).

    • Search Google Scholar
    • Export Citation

  • Yang, S., and X. Zou, 2012: Assessments of cloud liquid water contributions to GPS RO refractivity using measurements from COSMIC and CloudSat. J. Geophys. Res., 117, D06219, doi:10.1029/2011JD016452.

    • Search Google Scholar
    • Export Citation

  • Zhao, L., and F. Weng, 2002: Retrieval of ice cloud parameters using the advanced microwave sounding unit (AMSU). J. Appl. Meteor., 41, 384–395.

    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Geographical distribution of COSMIC GPS ROs collocated with deep convective ice clouds.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Vertical distribution of IWC (g m−3) within deep convective clouds collocated with COSMIC GPS ROs plotted at their observed latitudes. Each vertical bar is drawn from cloud base to cloud top. Areas without IWC data are indicated in black. Blue curve indicates the altitude where temperature is 0°C.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    (a) Mean fractional N difference (black solid) of all collocated COSMIC GPS ROs in deep convection between cloud top and cloud base. Vertical lines are drawn from cloud base to cloud top in deep convection (red). (b) Mean IWC (solid) and cloudy data points counted within 100-m interval (dotted). (c) Fractional N bias (solid) and standard deviation (vertical bars) in deep convective clouds for all data between cloud top and cloud base. (d) Variation of standard deviation of IWC for deep convection.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Frequency distributions of (a) IWC and (b) with measurements within different cloud layers (color, km).

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Scatterplots of (a) (%) and (b) . The black curve in (a) represents the averaged percentage contribution of IWC, that is, . The amount of IWC is indicated by colors (g m−3).

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Variations of (a) and (b) with respect to IWC within deep convection. The color convention indicating the altitudes of observations is as in Fig. 4.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) for (a) temperature (K) and (b) water vapor pressure (hPa) within deep convective clouds shown in Fig. 1. (c) The ECMWF water vapor analysis (hPa).

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Relative humidity from (a) GPS RO retrievals and (b) ECMWF analysis within deep convective clouds shown in Fig. 1. (c) Differences of relative humidity between GPS RO retrievals and ECMWF analysis.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Vertical profiles of (a) temperature and (b) relative humidity derived from a COSMIC GPS RO sounding located at 1.7°S, 86.9°E that occurred at 2010 UTC 9 Jun 2007. (c) Refractivity calculated from temperature and relative humidity in (a),(b).

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Fractional N differences introduced by perturbations in temperature (K) and relativity humidity (%) at 2, 6, and 9 km.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Frequency distributions of (a),(c) temperature and (b),(d) relative humidity differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) in (a),(b) deep convection and (c),(d) clear-sky conditions. The altitudes of observations are indicated in color (km).

Fig. 1.

Geographical distribution of COSMIC GPS ROs collocated with deep convective ice clouds.
Fig. 2.

Vertical distribution of IWC (g m−3) within deep convective clouds collocated with COSMIC GPS ROs plotted at their observed latitudes. Each vertical bar is drawn from cloud base to cloud top. Areas without IWC data are indicated in black. Blue curve indicates the altitude where temperature is 0°C.
Fig. 3.

(a) Mean fractional N difference (black solid) of all collocated COSMIC GPS ROs in deep convection between cloud top and cloud base. Vertical lines are drawn from cloud base to cloud top in deep convection (red). (b) Mean IWC (solid) and cloudy data points counted within 100-m interval (dotted). (c) Fractional N bias (solid) and standard deviation (vertical bars) in deep convective clouds for all data between cloud top and cloud base. (d) Variation of standard deviation of IWC for deep convection.
Fig. 4.

Frequency distributions of (a) IWC and (b) with measurements within different cloud layers (color, km).
Fig. 5.

Scatterplots of (a) (%) and (b) . The black curve in (a) represents the averaged percentage contribution of IWC, that is, . The amount of IWC is indicated by colors (g m−3).
Fig. 6.

Variations of (a) and (b) with respect to IWC within deep convection. The color convention indicating the altitudes of observations is as in Fig. 4.
Fig. 7.

Differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) for (a) temperature (K) and (b) water vapor pressure (hPa) within deep convective clouds shown in Fig. 1. (c) The ECMWF water vapor analysis (hPa).
Fig. 8.

Relative humidity from (a) GPS RO retrievals and (b) ECMWF analysis within deep convective clouds shown in Fig. 1. (c) Differences of relative humidity between GPS RO retrievals and ECMWF analysis.
Fig. 9.

Vertical profiles of (a) temperature and (b) relative humidity derived from a COSMIC GPS RO sounding located at 1.7°S, 86.9°E that occurred at 2010 UTC 9 Jun 2007. (c) Refractivity calculated from temperature and relative humidity in (a),(b).
Fig. 10.

Fractional N differences introduced by perturbations in temperature (K) and relativity humidity (%) at 2, 6, and 9 km.
Fig. 11.

Frequency distributions of (a),(c) temperature and (b),(d) relative humidity differences between GPS RO retrievals and ECMWF analysis (GPS minus ECMWF) in (a),(b) deep convection and (c),(d) clear-sky conditions. The altitudes of observations are indicated in color (km).
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