Abstract

The fluctuation of radio occultation (RO) signals in the presence of refractivity irregularities in the moist lower troposphere results in uncertainties of retrieved bending angle and refractivity profiles. In this study the local spectral width (LSW) of RO signals, transformed to impact parameter representation, is used for the characterization of the uncertainty (random error) of retrieved bending angle and refractivity profiles. A large LSW has some correlation with the large mean difference (bias) of retrieved refractivity and bending angle from radiosondes and European Centre for Medium-Range Weather Forecasts analyses based on data from 2008 to 2014. An LSW-based quality control (QC) procedure is developed to eliminate low-quality (large random errors and biases) profiles from data assimilation. The LSW-based QC procedure is tested and evaluated in the assimilation of Constellation Observing System for Meteorology, Ionosphere and Climate RO data using the NCAR Data Assimilation Research Testbed and the Weather Research and Forecasting Model. Preliminary results, based on a 2-week data assimilation cycle, show that the LSW-based QC procedure improves water vapor analyses in the moist lower troposphere.

1. Introduction

Atmospheric remote sensing using signals from the global positioning system (GPS) has become an important global observing technique for improving operational numerical weather prediction (NWP) skill (Anthes 2011 With a receiver on board a low-Earth-orbiting satellite, changes in the phase and amplitude of GPS radio waves traversing the atmosphere on limb paths can be measured (Ware et al. 1996; Kursinski et al. 1997). This measurement technique, known as GPS radio occultation (RO), provides vertical profiles of bending angle and refractivity that can be retrieved from the phase and amplitude measurements of the radio waves propagating through the atmosphere.

Since the launch of the first GPS RO mission, GPS/Meteorology (MET), in April 1995, several other GPS missions have been launched. Of special interest is the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) RO mission, which was launched in 2006. RO bending angle and refractivity data have been widely used by operational NWP centers and the NWP research community. RO data assimilation has long been demonstrated to contribute significantly to the improved accuracy of the atmospheric state above the moist lower troposphere (Zou et al. 2000, 2004; Liu et al. 2001; Healy and Thépaut 2006; Healy 2008; Poli et al. 2010; Rennie 2010; Cucurull and Derber 2008; Cucurull 2010; Huang et al. 2016) as well as to the improved prediction of the tracks and intensities of tropical cyclones (Kuo et al. 2008; Liu et al. 2012; Chen et al. 2015).

In the tropical lower troposphere, refractivity profiles retrieved from RO raw observations may have biases as a result of superrefraction (Sokolovskiy 2003; Ao et al. 2003; Ao 2007; Xie et al. 2010). A low signal-to-noise ratio, insufficient tracking depth, and nonspherically symmetric fluctuations of refractivity in the moist lower troposphere may also introduce biases in RO bending angle and refractivity profiles (Sokolovskiy et al. 2010; Gorbunov et al. 2015). The effect of inversion errors related to nonspherically symmetric and systematic (nonrandom) variations in atmospheric refractivity could be reduced by using nonlocal operators to model RO observables (e.g., Zou et al. 1999; Liu and Zou 2003; Poli and Joiner 2004; Syndergaard et al. 2005; Sokolovskiy et al. 2005a,b). RO signal tracking (in closed-loop mode) may also result in biases (Beyerle et al. 2006), but this does not apply to the COSMIC RO data used in this study, which are tracked in open-loop mode.

Currently available operational and research data assimilation systems assume that observations have no biases. Any substantial biases in observations can lead to the suboptimal assimilation of observations into NWP models. Therefore, observations with substantial biases should be either discarded or corrected prior to assimilation (Dee 2005). In the tropical lower troposphere, a very tight check for departures of RO observations from the NWP model forecast is usually done so that RO data with large biases are discarded (e.g., Cucurull and Derber 2008; Chen et al. 2011; Huang et al. 2016). The effectiveness of such an approach depends not only on the data quality but also on the accuracy of NWP model forecasts. Good-quality RO data may be discarded by this approach when the model forecast has substantial errors and biases.

To reduce the negative effect of the departure check procedure, a quality control (QC) procedure to eliminate problematic data that uses RO signals only and that does not depend on the accuracy of model forecasts is needed. In this study the local spectral width (LSW) of COSMIC RO signals (transformed to impact parameter representation) is used to estimate the physical uncertainty of any individual RO bending angle and refractivity profile associated with significant random fluctuations of atmospheric refractivity in the tropical lower troposphere. Also, based on COSMIC RO data, it is shown that large LSWs may be associated with the large biases of COSMIC RO bending angle and refractivity data. An LSW-dependent QC procedure is developed to eliminate those RO data with large LSW values. Then, this new QC procedure is incorporated into RO data assimilation over a tropical region to examine its usefulness and effectiveness by comparing the analysis with that obtained with the model forecast–based tight departure check procedure.

This paper is organized as follows: A derivation of the LSW of RO signals is presented in section 2. The statistical relationship between LSW and differences in bending angle and refractivity retrieved from COSMIC RO signals and either radiosonde observations or European Centre for Medium-Range Weather Forecasts (ECMWF) analyses is examined in section 3. An LSW-based QC procedure is introduced and its impact on the assimilation of COSMIC RO refractivity observations is examined using the Weather Research and Forecasting (WRF) modeling system in section 4. A summary and conclusions are provided in section 5.

2. LSW as a measure of the RO bending angle uncertainty in the tropical lower troposphere

Vertical gradients of refractivity can be quite large in the tropical lower troposphere, resulting in the multipath propagation of RO signals from a transmitter to a receiver. In the lower troposphere, RO bending angles are commonly calculated using wave optics (WO) methods that transform complex RO signals (phase and amplitude) from time to an impact parameter representation (Gorbunov 2002; Jensen et al. 2003, 2004; Gorbunov and Lauritsen 2004). If the atmosphere is spherically symmetric, there is only one ray associated with a given impact parameter. The WO transform effectively disentangles multiple rays that can be viewed as sorting rays according to their impact parameters.

In the case of multipath propagation in the spherically symmetric atmosphere, the spectrum of RO signals in the time representation can be complicated and broad. However, the spectrum of the WO-transformed signal is quasi monochromatic, and its local frequency for a given impact parameter determines the bending angle. In this case the local spectrum of the WO-transformed signal is very narrow under low-noise conditions, and the uncertainty in bending angle is low.

When the atmosphere has nonspherically symmetric irregularities—for example, strong moist convection in the tropical lower troposphere—multiple rays may have the same impact height. The corresponding spectrum of WO-transformed RO signals will contain multiple spectral components, leading to an increase in the overall width of the spectrum (Gorbunov et al. 2006; Sokolovskiy et al. 2010). Figure 1 shows a two-dimensional sliding spectrogram of the RO signal transformed to an impact height representation for a COSMIC occultation that occurred in the tropics at (4.8°N, 60.7°W). Because the bending angle is proportional to the derivative of the phase and thus to the local frequency of the WO-transformed signal (Jensen et al. 2004), the spectrogram in Fig. 1 is plotted using the coordinates’ impact height and bending angle instead of frequency. Above the impact height of ~9 km, the local spectrum is very narrow, and the bending angle can be determined with little uncertainty. The spectrum starts to become broader below the impact height of ~8 km and becomes the broadest below ~4 km. Figure 2 shows the local power spectrum at the impact height of 3.75 km. The main frequency component is not pronounced because the local power spectrum is very broad. Accurately determining the bending angle is difficult in this case. The LSW provides a measure of the uncertainty of the RO bending angle (and thus the refractivity) in the presence of nonspherically symmetric refractivity irregularities, which are most pronounced and result in the largest RO inversion errors in the moist (tropical) lower troposphere.

Fig. 1.

Sliding spectrogram of the RO signal transformed to an impact parameter representation for the COSMIC RO that occurred at 0344 UTC 1 Apr 2012 at a location in the tropics (4.8°N, 60.7°W). The retrieved bending angle profile is shown in red.

Fig. 1.

Sliding spectrogram of the RO signal transformed to an impact parameter representation for the COSMIC RO that occurred at 0344 UTC 1 Apr 2012 at a location in the tropics (4.8°N, 60.7°W). The retrieved bending angle profile is shown in red.

Fig. 2.

Local power spectrum corresponding to the spectrogram in Fig. 1 at the impact height of 3.75 km (black curve), the integral of the spectrum (red curve), and the piecewise linear least squares fit of the integral of the spectrum (blue line). See text for a detailed explanation of the fitting function. The units and scales for the spectrum and the integral are not defined, because they do not affect the LSW.

Fig. 2.

Local power spectrum corresponding to the spectrogram in Fig. 1 at the impact height of 3.75 km (black curve), the integral of the spectrum (red curve), and the piecewise linear least squares fit of the integral of the spectrum (blue line). See text for a detailed explanation of the fitting function. The units and scales for the spectrum and the integral are not defined, because they do not affect the LSW.

Gorbunov et al. (2006) introduced an error estimation based on LSW, aimed at accounting for signal-tracking errors as part of the measurement errors for German Challenging Minisatellite Payload (CHAMP) RO data. For RO instruments without tracking errors, analyses of the spectrograms show that in most cases, an increase in LSW in the lower troposphere, and especially in the tropics, is related to random refractivity irregularities causing fluctuations of the bending angle. The resulting error is deemed a measurement error, since these fluctuations cannot be modeled deterministically. Note that the LSW may also increase for other reasons. For example, in the presence of strong inversion layers, the LSW increases as a result of the significant change in the bending angle within the window used for the spectral analysis. In the presence of horizontally inhomogeneous refractivity structures that are not random, the LSW may increase if the bending angle becomes a multivalued function of the impact parameter in a deterministic sense. In those cases the LSW could be considered as a proxy for not only measurement errors but also representativeness and modeling (inversion) errors. A classification of various types of observation errors can be found online (https://www.ecmwf.int/sites/default/files/ObsErrors_2015_v2.pdf).

This study focuses on a tropical region with strong moist convection. The LSW is used to account for the errors introduced by random refractivity irregularities in the lower troposphere and is thus treated as a proxy for the measurement error. We follow Gorbunov et al. (2006) but use a different definition of the LSW. A raw bending angle is derived from the RO signal transformed to the impact height representation by phase matching (Jensen et al. 2004) using 1-m impact height steps. The raw bending angle profile is smoothed by low-pass filtering with a window of 0.1 km. The smoothed bending angle profile is used as a model to shift the mean frequency of the transformed RO signal to near zero. The transformed frequency-downshifted RO signal is subject to spectral analysis in a sliding window of 0.5 km. An example of the local power spectrum is shown in Fig. 2. For each interval centered at a given impact height, we calculate the integral of the spectrum and apply a piecewise linear least squares fit. The fitting function consists of two constant pieces corresponding to the values of the integral at the left and right sides of the spectrum that are connected by the linear function. We determine two bending angles, called BA1 and BA2, as the break points of the fitting function by minimizing the root-mean-square (RMS) deviation of the whole function from the integral in the whole spectral interval. The LSW is defined as the difference between BA2 and BA1, that is, LSW = BA2 − BA1. Hereafter, we also express LSW as a fraction of the retrieved bending angle, that is, in percent. The LSW defined in this way is a function of the impact height at the center of the sliding window. The magnitude of the LSW at a given impact height reflects the amount of uncertainty in the RO-retrieved bending angle resulting from nonspherically symmetric irregularities of the atmospheric refractivity. Sirmans and Bumgarner (1975) demonstrated that for a Gaussian spectrum, the standard deviation of the frequency is approximately proportional to the spectral width (we note that the bending angle is determined by the local frequency of the WO-transformed RO signal). The quantity LSW/2 can thus be considered as a proxy for the RMS of the random error of the bending angle. The LSW can also be considered as a proxy for the refractivity RMS error because refractivity is retrieved from the bending angle. However, it is an indirect proxy because the Abel inversion is a nonlocal transform.

As demonstrated by Gorbunov et al. (2015), nonspherically symmetric refractivity irregularities in the lower troposphere cause not only random errors but also systematic errors (i.e., biases) of the bending angle. Establishing a useful relation between the characteristics of the fluctuation and the bias of the bending angle is difficult. In this study we attempt to empirically use the LSW as the proxy for not only random bending angle and refractivity errors but also as the proxy for the biases.

Figure 3 shows the vertical distributions of the monthly mean LSW divided by the corresponding RO bending angle for COSMIC ROs during the time period 1–30 April 2012 within the global tropics (30°S–30°N), midlatitudes (30°–60°S and 30°–60°N), and high latitudes (60°–90°S and 60°–90°N). Reprocessed COSMIC RO data (2013 version) are used. The height used in Fig. 3 is related to the impact height (used in the definition of the LSW) through the Abel transform and represents the tangent point height for the bending angle or the height for refractivity. The mean LSW in the tropics is substantially larger than in the middle and high latitudes and increases monotonically downward at all latitudes.

Fig. 3.

Vertical variations in the LSW divided by the corresponding bending angle (%) averaged over all COSMIC ROs that occurred in April 2012 within the global tropics (red curve; 30°S–30°N), midlatitudes (green curve; 30°–60°S and 30°–60°N), and high latitudes (black curve; 60°–90°S and 60°–90°N).

Fig. 3.

Vertical variations in the LSW divided by the corresponding bending angle (%) averaged over all COSMIC ROs that occurred in April 2012 within the global tropics (red curve; 30°S–30°N), midlatitudes (green curve; 30°–60°S and 30°–60°N), and high latitudes (black curve; 60°–90°S and 60°–90°N).

The geographic distribution of COSMIC RO bending angle profiles in the 30°S–30°N latitudinal band for LSW values greater than 35%, between 20% and 35%, and less than 20% at an altitude of 1.5 km from 21 to 25 April 2012 are provided in Fig. 4. Most of the high LSWs occurred over the tropical oceans, indicating that COSMIC RO data in those regions had high uncertainties. On the other hand, a majority of the low LSWs occurred over the subtropics, including continents where moisture was relatively low, suggesting that COSMIC data in those regions had low uncertainties. Many of the ROs with small LSWs occurred over tropical oceans, which supports the use of measurement-based QC. In the next section, we will focus on an investigation of RO data with high LSWs over the tropical oceans.

Fig. 4.

Spatial distribution of COSMIC ROs that penetrated down to 1.5 km from 21 to 25 Apr 2012 with LSW values > 35% (red circles), between 20% and 35% (blue circles), and <20% (green circles). Also shown are the locations of the radiosonde profiles used for the comparison between COSMIC RO and radiosonde refractivity (black dots). The radiosonde observations in the black outlined region are used in the WRF Model water vapor analysis shown in Fig. 11.

Fig. 4.

Spatial distribution of COSMIC ROs that penetrated down to 1.5 km from 21 to 25 Apr 2012 with LSW values > 35% (red circles), between 20% and 35% (blue circles), and <20% (green circles). Also shown are the locations of the radiosonde profiles used for the comparison between COSMIC RO and radiosonde refractivity (black dots). The radiosonde observations in the black outlined region are used in the WRF Model water vapor analysis shown in Fig. 11.

3. Bias estimate of COSMIC refractivity and bending angle observations with high LSWs

In this section possible biases of COSMIC RO refractivity and bending angle observations are investigated by examining the mean differences in refractivity between COSMIC and radiosonde observations as well as mean differences in refractivity and bending angle between COSMIC observations and ECMWF global analyses. Of particular interest are those cases with high LSWs in the tropical lower troposphere.

a. Data and methodology

COSMIC refractivity and bending angle observations from 2008 to 2014, which were processed with the 2013 version of the COSMIC Data Analysis and Archive Center (CDAAC) inversion software, are used. The LSW is a new parameter added to the CDAAC Level 1b data product. COSMIC refractivity, bending angle, and LSW profiles are sampled at a geometric height above mean sea level with a vertical resolution of ~200 m. We first compare COSMIC refractivity profiles with those derived from radiosonde observations that are routinely used by the National Centers for Environmental Prediction for operational analysis. We use only those radiosondes that are located within a spatial distance of 300 km and have a time difference of less than 2 h from COSMIC RO profiles. Refractivity profiles calculated from the radiosonde observations and ECMWF analyses are interpolated to the vertical levels of the collocated COSMIC profiles for comparison purposes. COSMIC RO data collocated with ECMWF analyses data having a vertical gradient of refractivity exceeding −157 N-unit km−1 are discarded. Only a couple of such RO profiles per day were discarded.

Figure 4 also shows the spatial distribution of available radiosonde observations. These observations were mainly distributed over the continents and the western Pacific Ocean. There were also some radiosonde observations over the eastern Pacific Ocean and a few over the Indian and Atlantic Oceans.

We also compare COSMIC refractivity and bending angle observations with global ECMWF analyses, which are a useful reference for estimating RO observation biases, especially over tropical oceans. The refractivity and bending angle profiles computed from the 6-hourly ECMWF analysis are interpolated to the spatial locations and times of the COSMIC refractivity profiles.

b. Systematic differences in RO refractivity with respect to radiosonde

Figure 5 shows mean differences in refractivity as a function of LSW in the tropical troposphere within 1.5–3 km (Fig. 5a) and 0–1.5 km (Fig. 5c). Mean differences in refractivity are calculated within each consecutive 2% LSW bin for all COSMIC–radiosonde collocated data within the specified altitude ranges. The data counts involved in the calculations for the mean refractivity profiles are also shown. Refractivity differences are negative for all ranges of LSW and their magnitudes increase rapidly with increasing LSW in both vertical layers. Specifically, when LSW is less than 20%, the differences are relatively small (from about −0.2% to −0.9% in the 0–1.5-km layer and from about −0.2% to −0.5% in the 1.5–3-km layer). RO data with small LSWs (<20%) account for about 55% and 67% of all RO data in the 0–1.5- and 1.5–3-km layers, respectively. When LSW is greater than 20%, the differences increase quickly. When LSW is equal to 60%, the differences are quite large, approximately −6% in the 0–1.5-km layer and −3% in the 1.5–3-km layer. The number of observations decreases rapidly when LSW is greater than 20%. About 16% of the RO data have an LSW greater than or equal to 35% below 3 km. These results are qualitatively consistent with those obtained by Gorbunov et al. (2015) from theoretical simulations.

Fig. 5.

(a),(c) Mean differences (black curves) and standard deviations (red curves) of refractivity between collocated RO and radiosonde observations (collocation criteria: maximum 300-km spatial and 2-h temporal separations) in the 1.5–3- and 0–1.5-km layers, respectively. (b),(d) Number of observations in each LSW bin (bin size = 2%) for the 1.5–3- and 0–1.5-km layers, respectively. The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Fig. 5.

(a),(c) Mean differences (black curves) and standard deviations (red curves) of refractivity between collocated RO and radiosonde observations (collocation criteria: maximum 300-km spatial and 2-h temporal separations) in the 1.5–3- and 0–1.5-km layers, respectively. (b),(d) Number of observations in each LSW bin (bin size = 2%) for the 1.5–3- and 0–1.5-km layers, respectively. The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Figure 6 shows the vertical distributions of the mean fractional refractivity differences between COSMIC RO and radiosonde data when LSW is less than 20%, between 20% and 35%, and greater than 35% below 5 km in the tropics (30°S–30°N). Mean differences are the largest below 2 km and decrease with altitude. Mean fractional refractivity differences are relatively large (about −3% at 1.5 km) when LSW is greater than 35%. Above 3 km mean fractional refractivity differences reduce to less than −1.5%. Refractivity data with intermediate LSWs have smaller differences (about −1.5% at 1.5 km). Refractivity data with small LSWs (<20%) have small mean fractional differences (about −0.65% around 1.5 km and −0.25% at 2 km), suggesting that COSMIC RO data with LSWs less than 20% are of good quality. In conclusion, COSMIC refractivity observations with large LSWs (e.g., >35%) have large negative systematic differences below 3 km compared with collocated radiosonde observations. Note that mean differences above 3 km for the 20%–35% LSW range increase slightly above 3 km. This may be partly due to the limited number of RO observations that were collocated with radiosonde observations.

Fig. 6.

Vertical distributions of the (a) means (solid curves) and standard deviations (dashed curves) of the differences in refractivity between collocated RO and radiosonde observations, and (b) data counts when LSW is >35% (red curves), between 20% and 35% (black curves), and <20% (green curves). The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Fig. 6.

Vertical distributions of the (a) means (solid curves) and standard deviations (dashed curves) of the differences in refractivity between collocated RO and radiosonde observations, and (b) data counts when LSW is >35% (red curves), between 20% and 35% (black curves), and <20% (green curves). The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

c. Systematic differences in RO refractivity with respect to the ECMWF analysis

The global ECMWF analysis used in this study has a horizontal resolution of ~25 km with 92 vertical levels and a model top at ~0.01 hPa. Figure 7 shows the variations in refractivity and bending angle differences averaged in consecutive 2% LSW bins as a function of LSW for data over the global tropical troposphere within the 1.5–3- and 0–1.5-km layers. The data counts, which are also shown in the figure, are larger by approximately an order of magnitude than those ROs collocated with radiosonde observations (see Fig. 5). The variation in systematic fractional refractivity differences between COSMIC refractivity observations and the ECMWF analysis with respect to LSW (Fig. 7) shows a trend similar to that of the mean fractional refractivity differences between COSMIC observations and radiosonde observations (see Fig. 5). The fractional refractivity differences in both comparisons are negative and increase substantially in magnitude with respect to the LSW within both 0–1.5- and 1.5–3-km vertical layers. When LSW is less than 20%, the mean differences are about −1% in the 0–1.5-km layer and −0.5% in the 1.5–3-km layer. When LSW increases to 60%, the mean fractional refractivity differences reach −3.1% in the 0–1.5-km layer and −1.7% in the 1.5–3-km layer. These maximum negative biases (Fig. 7) are about half of those obtained from RO–radiosonde comparisons (Fig. 5). Possible reasons for the smaller biases include the different spatial coverages of the radiosonde and the ECMWF analysis and possible biases in the ECMWF analysis, especially over the interior of the oceans. In fact, RO biases are expected to be the largest over the interior of tropical oceans, where the LSW is the largest compared to over land (Fig. 4).

Fig. 7.

Mean differences (black curves) and standard deviations (red curves) of (a),(d) refractivity and (b),(e) bending angle between RO observations and the ECMWF analysis. (c),(f) Number of RO observations in each LSW bin (bin size = 2%). The results for the (top) 1.5–3- and (bottom) 0–1.5-km layers. The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Fig. 7.

Mean differences (black curves) and standard deviations (red curves) of (a),(d) refractivity and (b),(e) bending angle between RO observations and the ECMWF analysis. (c),(f) Number of RO observations in each LSW bin (bin size = 2%). The results for the (top) 1.5–3- and (bottom) 0–1.5-km layers. The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Mean bending angle differences (Figs. 7b,d) show similar biases with respect to the ECMWF analysis; that is, negative biases increase substantially in magnitude with respect to LSW. For example, when LSW increases to 35% and 60%, biases reach up to −10% and −20%, respectively, in the 0–1.5-km layer.

Figure 8 shows vertical distributions of fractional refractivity and bending angle differences averaged over all COSMIC RO observations with LSW less than 20%, between 20% and 35%, and greater than 35% with respect to the ECMWF analysis below 5 km. Refractivity differences are the largest at the lowest altitudes and decrease rapidly with increasing altitude. For ROs with large LSWs (>35%), mean fractional refractivity differences are about −2.0% and −4.5% at 1.2 and 0.5 km, respectively. Mean refractivity differences for intermediate and small LSWs are about −1.2% and −1.0% around 1.2 km. Differences above 3 km are less than −1% in all cases.

Fig. 8.

Vertical distributions of the means (solid curves) and standard deviations (dashed curves) of the differences in (a) refractivity and (b) bending angle between ROs and the ECMWF analysis. (c) Data counts when the LSW is >35% (red curves), between 20% and 35% (black curves), and <20% (green curves). The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Fig. 8.

Vertical distributions of the means (solid curves) and standard deviations (dashed curves) of the differences in (a) refractivity and (b) bending angle between ROs and the ECMWF analysis. (c) Data counts when the LSW is >35% (red curves), between 20% and 35% (black curves), and <20% (green curves). The domain is the global tropics (30°S–30°N), and the time period covered is January 2008–April 2014.

Mean bending angle differences show similar vertical distributions (Fig. 8) to mean refractivity differences (Fig. 6). For ROs with the largest LSWs (>35%), differences reach up to −15% at 1 km.

In summary, compared with collocated radiosonde observations and the ECMWF analysis, COSMIC refractivity observations with large LSWs possess substantial systematic fractional negative biases in the lower troposphere over the tropics. COSMIC bending angle observations with large LSWs possess similar substantial negative biases, compared to the ECMWF analysis.

4. An LSW-dependent QC and its impacts on RO data assimilation

a. An LSW-dependent QC procedure for RO data assimilation

Here, we propose a QC procedure to discard those COSMIC RO observations with large LSWs so that the associated large negative RO biases in the tropical lower troposphere can be reduced. One way to determine whether the negative biases of RO data are too large to assimilate is to compare these biases to the observational error specified in the assimilation system. If the bias is much smaller than the observational error, then the impact of the bias on the analysis would be small. If the bias is close to or larger than the specified observational error, then the impact of the bias on the analysis will be substantial, and the assimilation of RO data becomes suboptimal (Dee 2005).

Theoretical, empirical, and statistical estimates of RO refractivity observational errors are used in current operational and research assimilation systems. The errors vary from 1% to 2% in the tropical lower troposphere (e.g., Kuo et al. 2004; Cucurull 2010; Chen et al. 2011; Wee and Kuo 2016). Statistically determined RO refractivity observational errors are ~2% below 1.5 km and 1.8% between 1.5 and 3 km (Kuo et al. 2004; Chen et al. 2011; Wee and Kuo 2016). Based on these results and the estimated relationship between the LSWs and the COSMIC refractivity observation biases shown above, we choose a tentative LSW threshold of 35% for discarding COSMIC RO observations; that is, RO profiles are truncated below the height where the LSW first becomes larger than the threshold (descending in height). This threshold may be further fine-tuned through assimilation experiments. Unlike the standard forecast-based outlier QC, this approach allows for the use of all RO data with low LSWs in RO data assimilation.

b. Setup of RO refractivity assimilation

COSMIC refractivity data assimilation numerical experiments are carried out using the Data Assimilation Research Testbed of the National Center for Atmospheric Research (Anderson et al. 2009) and the WRF Model. The WRF Model is widely used for tropical forecasts and in particular tropical cyclone forecasts. RO data assimilation experiments are performed over the equatorial western Pacific Ocean (18°S–28°N, 90E°–180°), which is outlined in black in Fig. 4, during the 2-week period of 16–30 April 2012. Besides COSMIC ROs, other observations assimilated are conventional observations, such as radiosonde wind and temperature, cloud-track wind, aircraft-measured temperature and wind, and land- and ship-based surface pressure. Those RO refractivity observations collocated with the ECMWF analysis that have large vertical gradients in refractivity (i.e., <−157 N-unit km−1) are not used to avoid potential contamination by superrefraction. RO refractivity observations with a vertical resolution of 200 m are assimilated using a local refractivity operator. The statistical observational errors estimated by Kuo et al. (2004) are used for the RO observations. All observations are assimilated in a 6-h window centered on 0000, 0600, 1200, and 1800 coordinated universal time (UTC). To see more clearly how the modified RO QC affects RO data assimilation, satellite radiance data are withheld in the assimilation experiments. Radiosonde observations of water vapor, which are not used in the assimilation, serve as independent verification data.

Two data assimilation experiments are performed. The only difference between the two is the RO QC scheme. In the first data assimilation experiment, a standard QC procedure (STQC) is applied to RO data. RO refractivity observations are discarded if their departures from WRF 6-h forecasts are larger than one or three times the RO observational errors below or above 4 km, respectively. This STQC is similar to those used in research and operational assimilation systems (e.g., Chen et al. 2011; Huang et al. 2016; Cucurull and Derber 2008). The second data assimilation experiment (LSWQC) is the same as the STQC experiment except for replacing the standard QC procedure with the LSW-dependent QC below 4 km.

The assimilation experiments employ an ensemble assimilation technique (Anderson et al. 2009; Liu et al. 2012) with 64 ensemble members. The WRF Model configuration has a horizontal resolution of 16 km and 45 levels from the surface to ~30 hPa. The physical schemes include the Noah land surface model, the Goddard microphysics scheme, the Kain–Fritsch cumulus scheme with a new shallow convection parameterization, the Yonsei University boundary layer scheme, the Rapid Radiative Transfer Model longwave radiation scheme, and the Goddard shortwave radiation scheme (Skamarock et al. 2008). The initial and boundary conditions are from ECMWF global analyses.

c. Numerical results

Differences between the two different QC strategies are illustrated in Fig. 9, which shows the spatial locations of COSMIC ROs during 16–30 April 2012 at 3 km for ROs that passed STQC and LSWQC, STQC only, and LSWQC only. There are ROs that would have been eliminated by the LSWQC procedure but are retained by the STQC procedure (red circles in Fig. 9). There are also many ROs with low LSWs that would pass the LSWQC procedure but not the STQC procedure (green circles in Fig. 9). The different COSMIC ROs assimilated in the two data assimilation experiments will cause differences in the analyses.

Fig. 9.

Locations of the COSMIC RO refractivity observations at 3 km that are assimilated in the STQC experiment only (red circles), in the LSWQC experiment only (green circles), and in both STQC and LSWQC experiments (black circles). The time period covered is 16–30 Apr 2012.

Fig. 9.

Locations of the COSMIC RO refractivity observations at 3 km that are assimilated in the STQC experiment only (red circles), in the LSWQC experiment only (green circles), and in both STQC and LSWQC experiments (black circles). The time period covered is 16–30 Apr 2012.

Figure 10a shows the temporal distribution of the number of COSMIC RO refractivity data points at 3 km used in the two experiments for the 2-week assimilation period. About 40% more RO data points pass the LSWQC procedure and are assimilated into the LSWQC experiment.

Fig. 10.

The temporal evolution of (a) the number of RO refractivity data assimilated in the two experiments, and mean differences (biases) between COSMIC RO refractivity data O and the WRF 6-h forecast (background B), i.e., OB, and between O and the analysis, i.e., OA, for the (b) STQC and (c) LSWQC assimilations. (d) Analysis increments in the two assimilation experiments. The time period covered is 16–30 Apr 2012.

Fig. 10.

The temporal evolution of (a) the number of RO refractivity data assimilated in the two experiments, and mean differences (biases) between COSMIC RO refractivity data O and the WRF 6-h forecast (background B), i.e., OB, and between O and the analysis, i.e., OA, for the (b) STQC and (c) LSWQC assimilations. (d) Analysis increments in the two assimilation experiments. The time period covered is 16–30 Apr 2012.

The temporal evolution of the biases between RO refractivity (denoted as O in the figure) and the WRF 6-h forecast or background (denoted as B in the figure)—that is, OB—and between O and the analysis (denoted as A in the figure)—that is, OA—for the STQC and LSWQC experiments are also shown in Fig. 10. In the STQC experiment, the OB bias is small due to a tight OB outlier check. As a result, the OA bias from the STQC experiment changes little. In the LSWQC experiment, the OB and OA differences have mostly positive biases. The biases are substantially lower for OA. The refractivity analysis increment is mostly positive and has a large magnitude (up to 2%) in the LSWQC experiment (Fig. 10d). The analysis increment in the STQC experiment is substantially smaller (<0.5%). This suggests that refractivity of the RO data used in the LSWQC experiment are much higher than those in the STQC experiment.

Figure 11 shows the biases and RMS errors of the water vapor analysis based on radiosonde observations made over the 2-week assimilation period of the STQC and LSWQC experiments and within the assimilation region (the area outlined in black in Fig. 4). As mentioned before, these radiosonde water vapor observations were not assimilated in the STQC and LSWQC experiments. The water vapor analysis of the STQC experiment is consistently drier than that of the LSWQC experiment throughout the entire troposphere with a maximum of about −0.72 g kg−1 at 800 hPa. The LSWQC reduces the dry bias by ~10%. The LSWQC also slightly reduces the RMS errors of the water vapor analysis in the lower troposphere. These results confirm that the larger refractivity analysis increment associated with RO data in the LSWQC experiment, as shown in Fig. 10, is reasonable. The negative water vapor biases in the STQC and LSWQC analyses are likely due to deficiencies in the WRF Model physics.

Fig. 11.

Vertical distributions (g kg−1) of the (left) biases and (right) RMS errors of the (top) specific humidity Q analysis and (bottom) 6-h forecast from the RO data assimilation experiments using STQC (red curves) and LSWQC (black curves) compared with radiosonde observations. The domain is the region outlined in black in Fig. 4. The time period covered is 16–30 Apr 2012.

Fig. 11.

Vertical distributions (g kg−1) of the (left) biases and (right) RMS errors of the (top) specific humidity Q analysis and (bottom) 6-h forecast from the RO data assimilation experiments using STQC (red curves) and LSWQC (black curves) compared with radiosonde observations. The domain is the region outlined in black in Fig. 4. The time period covered is 16–30 Apr 2012.

We further examine the impact of the LSWQC on the analysis and forecast by verifying them against the ECMWF analysis. Figure 12 shows the geographic distributions of the mean differences (biases) between the total column precipitable water analysis and the ECMWF analysis averaged over the 2-week period. The STQC analysis shows an extensive negative bias over the interior of the domain. The bias between the LSWQC and ECMWF analyses is smaller over much of the assimilation domain, particularly the eastern part. There are also some areas where the LSWQC results in degradation. The impact of the LSWQC becomes smaller on the 6-h forecast (Fig. 13).

Fig. 12.

Spatial distributions of the mean differences in total column precipitable water (PW; mm) between the analyses from (a) the STQC experiment and the ECMWF analysis, and (b) the LSWQC experiment and the ECMWF analysis. (c) Differences between the two analyses (LSWQC − STQC). The time period covered is 16–30 Apr 2012.

Fig. 12.

Spatial distributions of the mean differences in total column precipitable water (PW; mm) between the analyses from (a) the STQC experiment and the ECMWF analysis, and (b) the LSWQC experiment and the ECMWF analysis. (c) Differences between the two analyses (LSWQC − STQC). The time period covered is 16–30 Apr 2012.

Fig. 13.

As in Fig. 12, but for the mean differences between the WRF 6-h forecast and the ECMWF analysis.

Fig. 13.

As in Fig. 12, but for the mean differences between the WRF 6-h forecast and the ECMWF analysis.

All of these results show that the LSWQC improves the analysis and forecast of water vapor in the lower troposphere. The impact of the LSW-based QC on the temperature analysis is negligible (figures omitted) because the water vapor distribution determines the variation in atmospheric refractivity in the tropical lower troposphere.

5. Summary and conclusions

In this study we first described the LSW of COSMIC RO bending angles that are retrieved with wave optics. We then examined statistical relationships of LSWs to differences in refractivity between COSMIC observations and either radiosonde observations or ECMWF analyses over the 7-yr period of 2008–14. COSMIC refractivity observations have systematic negative biases with magnitudes that increase substantially as LSW increases. For example, in the lowest 1.5 km of the tropical troposphere, the negative bias increased from less than −0.5% when LSW was 2% to between −1% and −2% when LSW was equal to 35% and to between −3% and −6% when LSW reached 60%. This suggests that COSMIC RO refractivity observations with large LSWs may be associated with a possible large negative bias in the tropical lower troposphere.

Based on the abovementioned findings, we proposed an RO QC procedure to discard COSMIC refractivity data when LSW exceeds 35% for RO data assimilation. The RO data assimilation experiments using a regional WRF Model over a 2-week period demonstrated that the LSW-based QC improved the quality of the water vapor analysis and the 6-h forecast of the WRF Model in the tropical lower troposphere over the analysis obtained using the standard forecast-based departure check. Assimilation of better-quality RO data that were discarded by the standard check had a positive impact.

The abovementioned results suggest that the LSW-based QC might be a worthy alternative to the standard departure check in assimilation, especially if models have significant biases.

COSMIC RO refractivity data accounted for only ~8% of the total number of all other observation types assimilated in this study. Many of the RO data did not penetrate deep into the tropical lower troposphere. More improvement from LSWQC on assimilation is expected once COSMIC-2 RO data are assimilated. In addition, the fixed boundary of the regional WRF weather model can limit the impact of the LSWQC on assimilation and the analysis within the assimilation domain. The impact of the LSWQC on assimilation is expected to be greater when a global model is used.

Results from this study have some other limitations. For example, the assimilation experiments were done only for a 2-week period and without the use of radiance data. Also, the STQC experiment did not implement all possible quality controls of RO data.

The LSW is a new variable available in the latest versions of the CDAAC Level 1b data product. It is named “Bend_ang_stdv” in the atmPrf files. Another possible application of the LSW is to use it to adjust RO observation errors in RO data assimilation. This approach is being investigated, and the results will be reported in a follow-on paper.

Acknowledgments

This research was jointly supported by National Science Foundation (NSF) Grant CAS AGS-1033112 and National Oceanic and Atmospheric Administration (NOAA) Grant NA14NES4320003. Drs. Tae-Kwon Wee and Shu-Peng Ho provided valuable comments on an earlier version of the manuscript.

REFERENCES

REFERENCES
Anderson
,
J. L.
,
T.
Hoar
,
K.
Raeder
,
H.
Liu
,
N.
Collins
,
R.
Torn
, and
A.
Avellano
,
2009
:
The Data Assimilation Research Testbed: A community data assimilation facility
.
Bull. Amer. Meteor. Soc.
,
90
,
1283
1296
, https://doi.org/10.1175/2009BAMS2618.1.
Anthes
,
R. A.
,
2011
:
Exploring Earth’s atmosphere with radio occultation: Contributions to weather, climate and space weather
.
Atmos. Meas. Tech.
,
4
,
1077
1103
, https://doi.org/10.5194/amt-4-1077-2011.
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.
Ao
,
C. O.
,
T. K.
Meehan
,
G. A.
Hajj
,
A. J.
Mannucci
, and
G.
Beyerle
,
2003
:
Lower troposphere refractivity bias in GPS occultation retrievals
.
J. Geophys. Res.
,
108
,
4577
, https://doi.org/10.1029/2002JD003216.
Beyerle
,
G.
,
T.
Schmidt
,
J.
Wickert
,
S.
Heise
,
M.
Rotacher
,
G.
Koenig-Langlo
, and
K. B.
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.
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
,
853
865
, https://doi.org/10.1175/2010MWR3260.1.
Chen
,
Y.-C.
,
M.-E.
Hsieh
,
L.-F.
Hsiao
,
Y.-H.
Kuo
,
M.-J.
Yang
,
C.-Y.
Huang
, and
C.-S.
Lee
,
2015
:
Systematic evaluation of the impacts of GPSRO data on the prediction of typhoons over the northwestern Pacific in 2008–2010
.
Atmos. Meas. Tech.
,
8
,
2531
2542
, https://doi.org/10.5194/amt-8-2531-2015.
Cucurull
,
L.
,
2010
:
Improvement in the use of an operational constellation of GPS radio occultation receivers in weather forecasting
.
Wea. Forecasting
,
25
,
749
767
, https://doi.org/10.1175/2009WAF2222302.1.
Cucurull
,
L.
, and
J. C.
Derber
,
2008
:
Operational implementation of COSMIC observations into the NCEP’s Global Data Assimilation System
.
Wea. Forecasting
,
23
,
702
711
, https://doi.org/10.1175/2008WAF2007070.1.
Dee
,
D. P.
,
2005
:
Bias and data assimilation
.
Quart. J. Roy. Meteor. Soc.
,
131
,
3323
3343
, https://doi.org/10.1256/qj.05.137.
Gorbunov
,
M. E.
,
2002
:
Canonical transform method for processing radio occultation data in the lower troposphere
.
Radio Sci.
,
37
,
1076
, https://doi.org/10.1029/2000RS002592.
Gorbunov
,
M. E.
, and
K. B.
Lauritsen
,
2004
:
Analysis of wave fields by Fourier integral operators and its application for radio occultations
.
Radio Sci.
,
39
,
RS4010
, https://doi.org/10.1029/2003RS002971.
Gorbunov
,
M. E.
,
K. B.
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.
Gorbunov
,
M. E.
,
V. V.
Vorob’ev
, and
K. B.
Lauritsen
,
2015
:
Fluctuations of refractivity as a systematic error source in radio occultations
.
Radio Sci.
,
50
,
656
669
, https://doi.org/10.1002/2014RS005639.
Healy
,
S. B.
,
2008
:
Forecast impact experiment with a constellation of GPS radio occultation receivers
.
Atmos. Sci. Lett.
,
9
,
111
118
, https://doi.org/10.1002/asl.169.
Healy
,
S. B.
, and
J.-N.
Thépaut
,
2006
:
Assimilation experiments with CHAMP GPS radio occultation measurements
.
Quart. J. Roy. Meteor. Soc.
,
132
,
605
623
, https://doi.org/10.1256/qj.04.182.
Huang
,
C.-Y.
,
S.-Y.
Chen
,
S. K. A. V. P. R.
Anisetty
,
S.-C.
Yang
, and
L.-F.
Hsiao
,
2016
:
An impact study of GPS radio occultation observations on frontal rainfall prediction with a local bending angle operator
.
Wea. Forecasting
,
31
,
129
150
, https://doi.org/10.1175/WAF-D-15-0085.1.
Jensen
,
A. S.
,
M. S.
Lohmann
,
H.
Benzon
, and
A. S.
Nielsen
,
2003
:
Full spectrum inversion of radio occultation signals
.
Radio Sci.
,
38
,
1040
, https://doi.org/10.1029/2002RS002763.
Jensen
,
A. S.
,
M. S.
Lohmann
,
A. S.
Nielsen
, and
H.
Benzon
,
2004
:
Geometric optics phase matching of radio occultation signals
.
Radio Sci.
,
39
,
RS3009
, https://doi.org/10.1029/2003RS002899.
Kuo
,
Y.-H.
,
T.-K.
Wee
,
S.
Sokolovskiy
,
C.
Rocken
,
W.
Schreiner
,
D.
Hunt
, and
R. A.
Anthes
,
2004
:
Inversion and error estimation of GPS radio occultation data
.
J. Meteor. Soc. Japan
,
82
,
507
531
, https://doi.org/10.2151/jmsj.2004.507.
Kuo
,
Y.-H.
,
H.
Liu
,
Y.-R.
Guo
,
C.-T.
Terng
, and
Y.-T.
Lin
,
2008
: Impact of FORMOSAT-3/COSMIC data on typhoon and Mei-yu prediction. Recent Progress in Atmospheric Sciences: Applications to the Asia-Pacific Region, K. N. Liou and M. D. Chou, Eds., World Scientific, 458–483, https://doi.org/10.1142/9789812818911_0022.
Kursinski
,
E. R.
,
G. A.
Hajj
,
J. T.
Schofield
,
R. P.
Linfield
, and
K. R.
Hardy
,
1997
:
Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System
.
J. Geophys. Res.
,
102
,
23 429
23 465
, https://doi.org/10.1029/97JD01569.
Liu
,
H.
, and
X.
Zou
,
2003
:
Improvements to a GPS radio occultation ray-tracing model and their impacts on assimilation of bending angle
.
J. Geophys. Res.
,
108
,
4548
, https://doi.org/10.1029/2002JD003160.
Liu
,
H.
,
X.
Zou
,
H.
Shao
,
R.
Anthes
,
J.
Chang
,
J.
Tseng
, and
B.
Wang
,
2001
:
Impact of 837 GPS/MET bending angle profiles on assimilation and forecasts for the period June 20–30, 1995
.
J. Geophys. Res.
,
106
,
31 771
31 786
, https://doi.org/10.1029/2001JD000345.
Liu
,
H.
,
J. L.
Anderson
, and
Y.-H.
Kuo
,
2012
:
Improved analyses and forecasts of Hurricane Ernesto’s genesis using radio occultation data in an ensemble filter assimilation system
.
Mon. Wea. Rev.
,
140
,
151
166
, https://doi.org/10.1175/MWR-D-11-00024.1.
Poli
,
P.
, and
J.
Joiner
,
2004
:
Effects of horizontal gradients on GPS radio occultation observation operators. I: Ray tracing
.
Quart. J. Roy. Meteor. Soc.
,
130
,
2787
2805
, https://doi.org/10.1256/qj.03.228.
Poli
,
P.
,
S. B.
Healy
, and
D. P.
Dee
,
2010
:
Assimilation of global positioning system radio occultation data in the ECMWF ERA-Interim reanalysis
.
Quart. J. Roy. Meteor. Soc.
,
136
,
1972
1990
, https://doi.org/10.1002/qj.722.
Rennie
,
M. P.
,
2010
:
The impact of GPS radio occultation assimilation at the Met Office
.
Quart. J. Roy. Meteor. Soc.
,
136
,
116
131
, https://doi.org/10.1002/qj.521.
Sirmans
,
D.
, and
B.
Bumgarner
,
1975
:
Numerical comparison of five mean frequency estimators
.
J. Appl. Meteor. Climatol
,
14
,
991
1003
, https://doi.org/10.1175/1520-0450(1975)014<0991:NCOFMF>2.0.CO;2.
Skamarock
,
W.
, and Coauthors
,
2008
: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp, https://doi.org/10.5065/D68S4MVH.
Sokolovskiy
,
S.
,
2003
:
Effect of super-refraction on inversions of radio occultation signals in the lower troposphere
.
Radio Sci.
,
38
,
1058
, https://doi.org/10.1029/2002RS002728.
Sokolovskiy
,
S.
,
Y.-H.
Kuo
, and
W.
Wang
,
2005a
:
Assessing the accuracy of a linearized observation operator for assimilation of radio occultation data: Case simulations with a high-resolution weather model
.
Mon. Wea. Rev.
,
133
,
2200
2212
, https://doi.org/10.1175/MWR2948.1.
Sokolovskiy
,
S.
,
Y.-H.
Kuo
, and
W.
Wang
,
2005b
:
Evaluation of a linear phase observation operator with CHAMP radio occultation data and high-resolution regional analysis
.
Mon. Wea. Rev.
,
133
,
3053
3059
, https://doi.org/10.1175/MWR3006.1.
Sokolovskiy
,
S.
,
C.
Rocken
,
W. S.
Schreiner
, and
D. C.
Hunt
,
2010
:
On the uncertainty of radio occultation inversions in the lower troposphere
.
J. Geophys. Res.
,
115
,
D22111
, https://doi.org/10.1029/2010JD014058.
Syndergaard
,
S.
,
E.
Kursinski
,
B.
Herman
,
E.
Lane
, and
D.
Flittner
,
2005
:
A refractive index operator for assimilation of occultation data
.
Mon. Wea. Rev.
,
133
,
2650
2668
, https://doi.org/10.1175/MWR3001.1.
Ware
,
R.
, and Coauthors
,
1996
:
GPS sounding of the atmosphere from low Earth orbit: Preliminary results
.
Bull. Amer. Meteor. Soc.
,
77
,
19
40
, https://doi.org/10.1175/1520-0477(1996)077<0019:GSOTAF>2.0.CO;2.
Wee
,
T.-K.
, and
Y.-H.
Kuo
,
2016
: Characterization of various data uncertainties involved in comparing collocated soundings of radiosonde and GPS radio occultation. 2016 AGU Fall Meeting, San Francisco, CA, Amer. Geophys. Union, Abstract GC41A-1076.
Xie
,
F.
,
D. L.
Wu
,
C. O.
Ao
,
E. R.
Kursinski
,
A. J.
Mannucci
, and
S.
Syndergaard
,
2010
:
Super-refraction effects on GPS radio occultation refractivity in marine boundary layers
.
Geophys. Res. Lett.
,
37
,
L11805
, https://doi.org/10.1029/2010GL043299.
Zou
,
X.
, and Coauthors
,
1999
:
A ray-tracing operator and its adjoint for the use of GPS/MET refraction angle measurements
.
J. Geophys. Res.
,
104
,
22 301
22 318
, https://doi.org/10.1029/1999JD900450.
Zou
,
X.
,
B.
Wang
,
H.
Liu
,
R.
Anthes
,
T.
Matsumura
, and
Y.-J.
Zhu
,
2000
:
Use of GPS/MET refraction angles in 3D variational analysis
.
Quart. J. Roy. Meteor. Soc.
,
126
,
3013
3040
, https://doi.org/10.1002/qj.49712657003.
Zou
,
X.
,
H.
Liu
,
R. A.
Anthes
,
H.
Shao
,
J. C.
Chang
, and
Y.-J.
Zhu
,
2004
:
Impact of CHAMP radio occultation observation on global analyses and forecasts in the absence of AMSU radiance data
.
J. Meteor. Soc. Japan
,
82
,
533
549
, https://doi.org/10.2151/jmsj.2004.533.

Footnotes

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).