In this study, we focused on the retrieval of atmospheric water vapor density
by optimizing the tomography technique. First, we established a new
atmospheric weighted average temperature model that considers the effects of
temperature and height, assisted by Constellation Observing System for
Meteorology, Ionosphere and Climate (COSMIC) products. Next, we proposed a
new method to determine the scale height of water vapor, which will improve
the quality of vertical constraints. Finally, we determined the smoothing
factor in the horizontal constraint based on Interim European Centre for
Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) products. To
evaluate the advantages of the optimized technique over the traditional
method, we used GPS datasets collected in Hong Kong in August 2016 to
estimate the vertical distribution of water vapor density using both methods.
We further validated the tomography results from the optimized technique
using radiosonde products. The results show that the water vapor density
quality obtained by the optimized technique is 13.8 % better below 3.8
GPS technology has recently started being used to detect the Earth's atmosphere. Many studies have been carried out to retrieve the two-dimensional (2-D) or three-dimensional (3-D) distribution of atmospheric water vapor (Flores et al., 2000; Champollion et al., 2005; Nilsson and Gradinarsky, 2006; Jin and Luo, 2009; Esteban et al., 2013; Jiang et al., 2014; Chen and Liu, 2014). The obtained atmospheric water vapor product can be assimilated into a numerical weather prediction (NWP) model. By applying the NWP model to weather forecasting, we have discovered the usefulness of GPS tomography to estimate water vapor distribution (Jin et al., 2011; Esteban et al., 2013). Combined with the space-based GNSS (Global Navigation Satellite System) occultation technique, it can provide neutral-atmosphere products with high precision, high vertical resolution and low-cost near-real-time all-weather global coverage. In addition, it can contribute to scientific research on the ionosphere (Kursinski et al., 1997; Rocken et al., 1997; Hajj et al., 2002; Kuo et al., 2007).
In ground-based GPS meteorology, GPS signal propagation through the
atmosphere is slowed, thus causing path delay on the GPS measurements, which
is termed tropospheric delay (Kouba and Héroux, 2001). Zenith total
delay (ZTD) is one of the most important error sources in GNSS navigation
and positioning; however, it is a very reliable information source in GNSS
meteorology (Jacob et al., 2007; Jin et al., 2007, 2009; Falconer
et al., 2009). ZTD consists of two parts: zenith wet delay (ZWD) and zenith
hydrostatic delay (ZHD) (Davis et al., 1985). Usually, ZHD can be calculated
with high accuracy from empirical models, and ZWD can then be easily derived
from ZTD based on the formula ZWD
ZHD is usually estimated in GNSS meteorological research using the
Saastamoinen model (Flores et al., 2000; Troller et al., 2006; Champollion
et al., 2009; Perler et al., 2011; Jiang et al., 2014). The atmospheric
weighted mean temperature
In space-based GNSS meteorology, GNSS radio occultation (RO) is regarded as
a valuable data source for atmospheric change studies (Rocken et al., 1997;
Kursinski et al., 1997; Hajj et al., 2002; Beyerle et al., 2005). The
Constellation Observing System for Meteorology, Ionosphere and Climate
(COSMIC) is housed within the University Corporation for Atmospheric Research
(UCAR). The mission of the COSMIC RO is to develop the weather, climate,
space weather and geodetic research (Liou et al., 2007). The University
Corporation for Atmospheric Research COSMIC Data Analysis and Archive Center
(UCAR/CDAAC) supplies two different types of products from the COSMIC
mission: real-time data and postprocessed data products. Of these
postprocessed products, wet atmospheric profiles (wetPrfs) offer water
vapor pressure, temperature, etc. Shi and Gao (2009) compared the bias of PWV
between wetPrf-derived and precise point positioning (PPP)-derived data and
suggested that they have comparable accuracy levels. Kishore et al. (2011)
discussed the difference in specific humidity between wetPrfs and radiosonde
data. They concluded that both sources have good correlation
(
To improve the accuracy of water vapor derived using the GNSS technique, we
optimized several key techniques for GNSS tomography. First, we precisely
derived the
The rest of this paper is organized as follows. Section 2 introduces the principles of GNSS tomography and the optimized technique for establishing the atmospheric weighted average temperature model and deriving the scale height of water vapor. Section 3 describes the data processing. Section 4 presents the validation of the optimized method, and the quality control process for the tomography results. The discussions and conclusions are given in Sect. 5.
In this section, we first introduce the GPS tomography model. We then illustrate the optimized techniques for the ZHD model and the humidity conversion coefficient determination. Finally, we present the constraint model.
To reconstruct 3-D images of water vapor density distributions, the SWV along
ray paths traversing the imaged region should first be obtained from
dual-frequency GNSS data. This is defined by the line integral of water
vapor density along the ray path from satellite to receiver (Flores et al.,
2000), as follows:
Equation (1) reveals that the accuracy of water vapor density mainly depends on
the quality of the SWV. Generally, ZTD can be precisely estimated using the
double-difference or PPP method. ZWD can be obtained by removing ZHD from
ZTD. After the humidity conversion coefficient is determined, the SWV will
be computed, providing the SWD is known (MacMillan, 1995), as follows:
The humidity conversion coefficient
Usually, the observation equation of the tomographic approach is rank deficient because the GPS signal cannot pass through all of the grids. Horizontal constraints, vertical constraints, priori information value constraints and boundary constraints must be added to avoid this deficiency. With these constraints, we can use an iterative reconstruction algorithm, or a noniterative reconstruction algorithm to resolve the tomography equation.
The horizontal constraint is the Gauss distance weighting function (Song,
2004), as follows:
The vertical distribution of water vapor does not follow the ideal-gas law,
particularly in the lower levels. Currently, there is no accurate model
function to fit the spatial distribution of water vapor. The vertical
constraint of atmospheric tomography can be obtained using an exponential
model (Jiang et al., 2014; Ye et al., 2016), as follows:
Based on Eq. (2) and the Niell mapping function (Niell, 1996), ZWD can be
estimated in real-time. PWV can then be obtained according to Eq. (4). The
relationship between PWV and
The a priori humidity information can be used for the background field of troposphere tomography and will enhance the computing speed and tomography accuracy. The synoptic observation data include the atmospheric pressure, atmospheric temperature and relative humidity observed in the station, and the atmospheric temperature and relative humidity can be interpolated into all of the voxels using Eqs. (10) and (14). Thus, the water vapor density of every voxel can be calculated (Jiang et al., 2014).
Data used to remotely sense atmospheric water vapor contain ground-based GNSS
observations and meteorological data, as well as space-based COSMIC wet profiles.
UCAR/CDAAC supplies two different types of products: real-time profiles and
postprocessed profiles. The former can be available within a few hours and
the latter can be available with a 6-week latency (
We used ground-based GNSS observations and meteorological products from the
Hong Kong SatRef network (
Distribution of the Hong Kong SatRef sites (blue triangles) inside
the tomography horizontal grid (black dotted lines) and the King's Park radiosonde station (red star). The region was discretized into an
The reconstruction region covered an area ranging from latitude 22.22 to
22.52
Bevis et al. (1994) first put forward the global
The weighted average temperature
Considering height and surface temperature to establish the
As shown in Fig. 2, the new model's
New
The statistical results comparing the model-derived and COSMIC-derived
Summary of the
Summary of the
As shown in Tables 1 and 2, the new
The smoothing factor
Smoothing factor derived by ERA-Interim products at different heights.
In each level, the humidity information of one grid point equals the
weighted average of its neighbors (Rius et al., 1997), as follows:
Table 3 shows that the smoothing factors present a nonlinear change for
increasing heights below 6
The purpose of GNSS tomography technique is to derive the 3-D distribution
of water vapor. Thus, the accuracy of the vertical constraint will directly
affect the quality of the tomography results. Because water vapor randomly
varies in time and space, it is difficult to precisely probe the spatial
distribution of water vapor. Traditionally, Eq. (14) was used as a vertical
constraint and the parameter
Statistical results from Eq. (11)-derived and radiosonde-derived
PWV (
As shown in Table 4, the water vapor density derived from the
To evaluate our optimized method, we obtained ZTDs from the Hong Kong SatRef
network in August 2016, based on Bernese 5.2 (nondifference) software. The
ZHDs were estimated using the Saastamoinen mode. The SWV was then obtained
using the Niell mapping function (Niell, 1996) and the calibrated humidity
conversion coefficient. The WVLT was determined as 9.5
3-D tomographic water vapor distribution in Hong Kong on 1 and 2 August 2016.
Figure 4 presents the 3-D tomographic water vapor distribution in Hong Kong
for heights lower than 9.5
Radiosonde products contain 3-D distribution of meteorological elements such
as atmospheric temperature, atmospheric pressure, mixing ratio and relative
humidity. The “wet” pressure can be obtained based on the pressure and
mixing ratio and can be utilized to compute the water vapor density (Song,
2004). To verify the advantage of the optimized GPS tomography method, using
radiosonde products as references, the tomography results were compared with
those derived from the traditional tomography technique using the
Saastamoinen dry model, a traditional humidity conversion coefficient
(0.1538), a smoothing factor (Eq. 10), and
Water vapor densities obtained from tomography-derived and radiosonde-derived data. Rad is the water vapor density derived using radiosonde products, Trad is the water vapor density derived using the traditional tomography method, and Opti is the water vapor density derived using the optimized method.
It can be observed in Fig. 5 that the changing trends of water vapor with
height across the tomography-obtained and radiosonde-obtained data have a good
agreement. However, when the “inversion layer” occurs, GPS tomography
cannot accurately reflect this situation. In Table 5, we present the
deviation statistics for GNSS tomography-obtained and radiosonde-obtained
water vapor density at heights above and below 3.8
Statistics for tomography-derived and radiosonde-derived water
vapor density above and below 3.8
Table 5 provides the statistics values of the differences between GNSS
tomography-obtained and radiosonde-obtained results. As seen from the
statistical results, the root mean square (RMS) and mean values of troposphere tomography using
the optimized technique is less than that based on the traditional
method for altitudes below 3.8
We also studied the differences in the entire humidity profile between the
tomography-derived and radiosonde-derived results. We used the RMS and Pearson product-moment correlation coefficient (PCC) as the
evaluation index correlated between the two profiles. PCC is a commonly used
measure of the degree of correlation of two sequences of parameters, and the
mathematical model is as follows (Lee and Nicewander, 1988):
Time series of PCC and RMS for August 2016. Opti is the optimized tomography-derived water vapor density, and Trad is the traditional tomography-derived water vapor density.
Statistical results of PCC and RMS for August 2016 (%).
As shown in Table 6, the success rate of the optimized technique is nearly 10 % higher than that of the traditional technique, and the degree of improvement is evident. In fact, the principles of radiosonde and GPS tomography techniques are different. Radiosonde products reflect the state of the atmosphere at a certain time at the instrument's location, but GPS tomography techniques mirror the average water vapor state. Thus, it is difficult to determine an absolute standard to evaluate the success of GPS tomography results.
In this study, several key techniques in the GNSS tomography method were optimized to improve the accuracy of water vapor density. First, we re-established an atmospheric weighted average temperature model using COSMIC wetPrfs. According to the spatial distributions of water vapor provided by COSMIC products, we used the exponential model to fit the vertical variation of water vapor. The exponential function is usually utilized as the vertical constraint, and we proposed a new method to compute the scale height of water vapor. We determined the smoothing factor of the Gauss distance weighting function using ERA-Interim products. Finally, we used GPS datasets from Hong Kong in August 2016 to compute the PWV and the vertical distribution of water vapor density.
To evaluate the quality of the optimized technique, we compared the
optimized and traditional technique results with radiosonde-obtained water
vapor. The statistical results show that the water vapor density quality
obtained by the optimized technique is 13.8 % better below 3.8
The Survey and Mapping Office of the Lands Department
(2017), Hong Kong Special Administrative Region, provides GPS data and
meteorological data. These datasets are from the Hong Kong Satellite
Positioning Reference Station (SatRef) and can be made freely available for
public access (
PX conceived and designed the work that led to the submission; SY acquired data and played an important role in interpreting the results. PJ and LP drafted and revised the manuscript, and MG approved the final version.
The authors declare that they have no conflict of interest.
The financial support from the National 973 Program of China (no. 2012CB957701), National Natural Science Foundation of China (no. 41074008), Key Laboratory of Geospace Environment and Geodesy, Ministry of Education (no. 16-02-09), and Henan Province 2018 Science and Technology Research Project (Science and Technology/Industry) (no. 182102210315) are greatly appreciated. The topical editor, Vassiliki Kotroni, thanks two anonymous referees for help in evaluating this paper.