The near-real-time high spatial resolution of atmospheric water vapor distribution is vital in numerical weather prediction. GPS tomography technique has been proved effectively for three-dimensional water vapor reconstruction. In this study, the tomography processing is optimized in a few aspects by the aid of radiosonde and COSMIC historical data. Firstly, regional tropospheric zenith hydrostatic delay (ZHD) models are improved and thus the zenith wet delay (ZWD) can be obtained at a higher accuracy. Secondly, the regional conversion factor of converting the ZWD to the precipitable water vapor (PWV) is refined. Next, we develop a new method for dividing the tomography grid with an uneven voxel height and a varied water vapor layer top. Finally, we propose a Gaussian exponential vertical interpolation method which can better reflect the vertical variation characteristic of water vapor. GPS datasets collected in Hong Kong in February 2014 are employed to evaluate the optimized tomographic method by contrast with the conventional method. The radiosonde-derived and COSMIC-derived water vapor densities are utilized as references to evaluate the tomographic results. Using radiosonde products as references, the test results obtained from our optimized method indicate that the water vapor density accuracy is improved by 15 and 12 % compared to those derived from the conventional method below the height of 3.75 km and above the height of 3.75 km, respectively. Using the COSMIC products as references, the results indicate that the water vapor density accuracy is improved by 15 and 19 % below 3.75 km and above 3.75 km, respectively.

The temporal and spatial variation of water vapor is quite important in numerical weather forecasting especially for several hours of small-scale disastrous-weather monitoring and forecasting (Hamill and Church, 2000; Hart and Forbes, 1999; Posada et al., 2012). Accurate and reliable weather forecasting requires high-accuracy water vapor distribution information in both horizontal and vertical directions. Traditionally, the radiosonde sounding, microwave radiometer, meteorological satellite and laser radar technology are employed to obtain water vapor vertical distribution (Brettle and Galvin, 2003). These observation means have some drawbacks such as low temporal or spatial resolutions, high cost and weather dependence. In recent years, GPS tomography technique has been demonstrated as an effective means to acquire the three-dimensional (3-D) distribution of water vapor and can compensate for these disadvantages (Troller et al., 2006; Bender and Raabe, 2007; Bender et al., 2011; Champollion et al., 2009; Lutz et al., 2010; Perler et al., 2011; Rohm, 2013; Jiang et al., 2014; Benevides et al., 2016).

In the GPS tomography technology, the input observations are the slant water vapor (SWV). To obtain the SWV, the zenith troposphere delay (ZTD) is firstly determined using GPS double-difference methods. The ZTD is composed of two parts, namely zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) (Davis et al., 1985). The ZHD can be obtained by empirical models and then the ZWD is obtained by removing the ZHD from the ZTD. Afterwards, the ZWD can be projected to the slant wet delay (SWD) along the line of sight using a Niell mapping function (Niell, 1996). Eventually, the SWD is converted to the SWV with a humidity transforming factor. In order to reconstruct the 3-D distribution of the water vapor, the tomography area is discretized into voxels in both horizontal and vertical directions. Then, the SWV can be expressed by an integral of the water vapor density along the ray path from the receiver to the top boundary of the grid (Flores et al., 2000; Troller et al., 2006; Bender and Raabe, 2007; Bender et al., 2011; Perler et al., 2011).

In the tomography processing, the wet tropospheric delay, humidity transforming factor, grid division and tomography model are four crucial aspects affecting the tomography results. To obtain the ZWD, the ZHD is essential to remove from the ZTD. The ZHD is usually computed using the classical models such as Saastamoinen model, Hopfield model and Black model (Saastamoinen, 1972; Hopfield, 1971; Black, 1978). However, the classical models are inaccurate because they require measurements of pressure with a precision of 0.1 hPa, which can be obtained from local meteorological stations coupled to GPS stations (Tregoning and Herring, 2006). However, these measurements are usually obtained from climatological models such as ERA (Each Re-Analysis)-Interim and NCEP (National Center for Environmental Prediction) with lower precision. As a result, the accuracy of estimated ZWD will be degraded.

The humidity conversion factor is dependent on the atmospheric weighted mean temperature (Mateus et al., 2014), which can usually be estimated utilizing the surface temperature measurements. In the actual calculation of the SWV, the humidity conversion factor is usually determined using empirical models or even simply regarded as a constant (Shi and Gao, 2009; Bosy et al., 2012; Shangguan et al., 2013; Adavi and Mashhadi-Hossainali, 2014; Chen and Liu, 2014). However, the conversion factor is varied in different areas and seasons (Jiang et al., 2014).

In the tomography model, the grid is usually divided in an even vertical height with a constant top height of 10 km and the water vapor density is considered to be same inside each voxel (Flores et al., 2000; Hirahara, 2000; Troller et al., 2006; Nilsson and Gradinarsky, 2006; Bastin et al., 2007). However, such a grid model does not take into account the significant difference of actual water vapor distribution inside or outside each voxel for the vertical direction.

In this study, an optimized method for near real-time GPS 3-D troposphere tomography is developed using the external radiosonde and COSMIC historical data. Specifically, radiosonde and COSMIC products are utilized to improve the estimation accuracy of tropospheric ZHD as well as humidity conversion factor. Furthermore, the water vapor layer top (WVLT) and the dense layer of vapor top (DLVT) are dynamically determined for the purpose of grid division with an uneven voxel height and an unfixed grid top. In addition, a Gaussian exponential interpolation method is proposed to consider the water vapor variations within each vertical voxel. The ground-based GPS observation data from the Hong Kong SatRef network in February 2014 are used to verify the feasibility and superiority of the optimized tomography method.

The rest of the paper is organized as follows. Section 2 presents the improved methods in the aspects of ZHD estimation, humidity conversion factor, grid division and interpolation function. Section 3 analyzes the result improvement with the proposed tomography methods. Section 4 presents the validation of the tomographic results. The conclusions are included in Sect. 5.

The traditional troposphere tomography model based on discrete voxels was
first proposed by Flores et al. (2000). It can be described by the formula
below:

ZWD is obtained using GPS double-difference method and then is projected to
the SWD through the Niell mapping function (Niell, 1996). Further, the SWD
can be transformed to the SWV using a conversion factor

Due to the nearly cone geometry of the GPS observations, the GPS signals
cannot pass through all voxels (Bender and Raabe, 2007; Benevides et al.,
2016). As a result, the tomographic system cannot be inverted due to too
many zeros in the design matrix. Therefore, proper constraints have to be
imposed to solve this issue. In horizontal direction, the Gaussian weighted
method (Song, 2004) can be used for horizontal constraint. Given that the
vertical water vapor is usually decreased with the increase of the height,
the Gaussian exponential model is used to model the vertical distribution as

The a priori water vapor information is necessary to be used as the initial
values of tomography solutions. In order to obtain more accurate a priori
information of water vapor density, it will be helpful to improve the
accuracy of atmospheric elements by assimilating surface meteorological
observations into tomographic system (Perler et al., 2011; Jiang et al.,
2014). Since the synoptic observation products contain the pressure,
temperature and relative humidity of the station, we interpolate the
temperature and relative humidity into all of the grids. In the beginning,
we interpolate horizontal relative humidity using Gaussian weighted constraint
method and vertical relative humidity using Eq. (

As mentioned in Sect. 1, the ZHD is required in order to achieve the ZWD
which is associated with the tomography input observations of SWV. The
computation of ZHD is usually made using empirical models with input of
atmospheric pressure and temperature. However, the empirical models are not
accurate enough in some areas where there exists significant height
difference (Liu et al., 2000). In these cases, the radiosonde and radio
occultation data products can be utilized to compensate the shortcomings of
the empirical models. Equation (

The humidity conversion factor

The parameter conversion factor

In general, the lower limit and upper limit of the tomography grid is the height from the ground to tropopause. But in fact the water vapor is mainly concentrated at a height significantly lower than the tropopause. If the tropopause is chosen as the grid top, the solutions of the tomography inversion are possibly negative as the water vapor is very sparse near the height of the tropopause (Flores et al., 2000). In this study, we define a varied water vapor layer top (WVLT) as the upper limit of the tomography grid based on the precipitable water vapor (PWV) variations acquired from the radiosonde and COSMIC data. Thus, the height of the grid top is decreased, conversely increasing the effective number of the satellite rays. In the tomography, only the rays that penetrate into the grid from the top boundary are used for the tomography processing.

The purpose of GPS tomography is to reconstruct the vertical distribution of water vapor density. The vertical grid division is vital to affect the tomography solutions. Traditionally, there are two ways to divide the grid. One is uniform division (Flores et al., 2000; Xia et al., 2013) and the other is non-uniform division (Perler et al., 2011; Rohm, 2012, 2013; Chen and Liu, 2014, and Jiang et al., 2014). Considering the actual distribution characteristics of water vapor density that is sparse in high layers and dense in low layers, we use non-uniform division in this study.

Perler et al. (2011) proposed a numerical integration model parameterization (NIMP) tomography method. The basic idea is that the water vapor within each voxel is considered to be unevenly distributed and can be calculated by the horizontal and vertical interpolation methods.

In this study, the difference of water vapor density within each voxel is
also taken into account. The horizontal and vertical interpolations are made
to obtain the water vapor density values of interior voxels. In the
horizontal direction, the Barnes interpolation algorithm (Jiang et al.,
2014) is normally used. In the vertical direction, there are many
interpolation methods such as linear interpolation and cubic spline
interpolation (Perler et al., 2011). The linear interpolation algorithm is
simple but its accuracy is relatively poor. The cubic spline interpolation
is complex in implementation. Besides, these traditional interpolation means
belong to pure mathematics methods, without taking into account the inherent
characteristics of the water vapor density variations in the vertical
direction. In this study, a Gaussian exponential-based interpolation algorithm
derived from Eq. (

The COSMIC (Constellation Observation System for Meteorology Ionosphere and Climate) occultation is a joint Taiwan–US science mission for weather, climate, space weather and geodetic research (Schreiner et al, 2007; Anthes et al., 2008). The radiosonde sounding technique is an important means for meteorology study from the ground to the lower stratosphere. Both COSMIC and radiosonde observations have been the important data source for weather research and climate analysis (Kuo et al., 2005; Kishore et al., 2011).

The COSMIC Data Analysis and Archive Center (CDAAC) provides both the
real-time and post-processed data products (

Radiosonde data was collected at the 45004th radiosonde station equipped with
a Vaisala RS92 sensor, which offers the world's highest level of performance
in measuring the meteorological parameters, including pressure, temperature
and humidity. The atmospheric pressure and temperature measured by the sensor
have accuracies of better than 1 hPa and 0.5

The ground-based GPS observation data are collected from the Hong Kong SatRef
network, which consists of a total number of 12 continuous operational
stations with inter-station distance of 10–15 km, as seen in Fig. 1. LEICA
GRX1200

The GPS station distribution and horizontal grid division in Hong Kong.

In order to simulate a near-real-time GPS tomographic experiment, it is good to use a sliding time window strategy (Foster et al., 2005). We use a 6 h interval time window and step forward 1 h at a time (Benevides et al., 2015). The ZTD estimates are obtained using GAMIT software in this study (Herring et al., 2010; Benevides et al., 2015).

The historical radiosonde data collected at the “45004th” radiosonde
station in February from 2007 to 2013 are used to calibrate the ZHD model.
The radiosonde product only provides the atmosphere element below the height
of 30 km. Therefore, we use the ERA-Interim product
(

In order to assess the feasibility of Eq. (

Correlation coefficients between the ZHD offset and temperature and pressure.

As seen in Table 1, the

ZHD offsets before and after calibrations with respect to radiosonde-derived ZHD using datasets in Hong Kong in February 2014.

Figure 2 shows the ZHD offsets before and after calibrations with respect to radiosonde-derived ZHD. The largest ZHD offsets using the calibrated model are only 5.2 mm, and the rms of the ZHD offsets is 3.2 mm, which is significantly smaller than the ones before calibration at 14.1 mm. From the statistical results, it is concluded that the established ZHD calibration model by using the radiosonde historical data improves the ZHD accuracy.

Derived humidity conversion factor for consecutive 7 days using improved method. Date format is YYYY/MM/DD.

According to Eqs. (

As an example, Table 2 displays the derived humidity conversion factors from 1 to 7 February 2014 using our improved method. The humidity conversion factors vary around 0.161, which is different from the constant value of 0.1538.

PWV comparison in Hong Kong in February 2014 using traditional and improved conversion factors (mm).

Table 3 shows the PWV comparison based on datasets in entire February 2014
in Hong Kong using different conversion factors. From the comparison
results, it is found that PWV rms is significantly smaller using the
improved

It is well known that WVLT varies with regions and seasons. Since the radiosonde product and COSMIC occultation product provide the vertical distribution of PWV, we use radiosonde product and COSMIC product to estimate the changes of the PWV for determining the WVLT. Specific steps are as follows: (1) use the CPT (cold point tropopause) method to determine tropopause; (2) estimate the PWV at different heights; (3) calculate the proportion of PWV at different height over the sum at all heights; and (4) take the height as WVLT if the proportion is less than or equal to 0.001. Figure 3 shows the obtained WVLT using radiosonde and COSMIC products, respectively.

The top of the water vapor layer and the top of the water vapor dense layer obtained by radiosonde and COSMIC products.

From the blue curves in Fig. 3, it can be seen that the PWV approaches 0 from the height of WVLT to tropopause. The estimated PWV using radiosonde product and COSMIC product exhibits an exponential distribution as seen in the blue curve. We define DLVT (dense layers of vapor top) as the corresponding height of the blue points whose distance is the nearest from the coordinate origin, as seen in Fig. 3. From the ground to the DLVT, the decreasing rate of the PWV becomes faster with the increase in height, whereas the decreasing rate of the PWV is slower from the DLVT to WVLT.

3-D tomographic water vapor distribution in Hong Kong on 19 February 2014.

Since the GPS network in Hong Kong area is dense, we divide grids into
10 km

The same datasets as described in Sect. 3.1 are used for the result
validations. The radiosonde balloon is carried aloft once every 12 h at the
45004th station, and the configured sensors on the radiosonde measure
profiles of temperature, pressure, relative humidity and so on. In addition,
the “wetPrf” profiles provide the water vapor pressure, temperature,
pressure and so on. Thus, the “wetPrf” profiles collocated in Hong Kong
and the 45004th radiosonde products in February 2014 are used to
evaluate the accuracy of the tomography results. We utilize GAMIT software
to obtain the ZTD based on GPS data from the Hong Kong SatRef network with
IGS (International GNSS Service) ultra-rapid product orbit file. The
Saastamoinen model is calibrated using observations from the
“45004th”
radiosonde station and the humidity conversion factor is determined using
the COSMIC products and radiosonde products in Hong Kong. Then, the ZHD is
obtained using Eq. (

Figure 4 describes the water vapor density changes at different heights. It shows that the water vapor density significantly changes below 3.75 km and decreases in the latest few hours. In order to evaluate our optimized method, the tomography results are compared with those derived from the traditional tomography method in which exponential model is used as the vertical constraint and cubic spline is used for vertical interpolation. In addition, the ZHD and the humidity conversion factor before optimization are used in the traditional method. Tomography solutions are compared with external results derived from the radiosonde and COSMIC products. As the water vapor density remains stable above DLVT (3.75 km), whereas it changes significantly below DLVT (3.75 km), the statistics of tomography-derived water vapor density are made above 3.75 km and below 3.75 km.

For the sake of convenient comparison, the tomography results in
grams per cubic meter are transformed into the PWV in millimeters using Eq. (14)
(Esteban et al., 2013):

Comparisons of PWV obtained from tomography and radiosonde product in February 2014. “RadP-ImpP” represents the difference of radiosonde-derived and optimized tomography-derived PWV. “RadP-TradP” represents the difference of radiosonde-derived and traditional tomography-derived PWV.

As can be seen from Fig. 5, the tomography solutions have a good agreement with radiosonde results. Using our optimized methods, the rms of the difference between tomography-derived and radiosonde-derived PWV is 1.8 mm, whereas it is 2.3 mm for the traditional method.

Radiosonde products provide 3-D distribution of atmospheric elements, such as temperature, pressure, dew point, mixing ratio and relative humidity. We can obtain the “wet” pressure according to the pressure and mixing ratio and further use the “wet” pressure to compute water vapor density (Song, 2004). Figure 6 shows the comparisons of water vapor densities obtained from tomography and radiosonde products on 16–17 February 2014.

Comparisons of water vapor densities (WVDs) obtained from tomography and radiosonde on 16–17 February 2014. “Rad” represents the radiosonde-derived water vapor density. “Impr” represents the tomography-derived water vapor density using our optimized method, and “Trad” represents the tomography-derived water vapor density using the traditional method.

The changing trends of water vapor density (WVD) between tomography-derived and radiosonde-derived results have a very good agreement. Despite a significant difference between tomography and radiosonde WVD in the lower height, the result from our optimized method is better than the results from the traditional method since the blue curve is closer to the green curve. In addition, we also provide the statistical results between tomography-derived and radiosonde-derived water vapor densities above 3.75 km and below 3.75 km, respectively, using 28-day datasets in February 2014 in Hong Kong (Table 4).

The statistical results between tomography-derived and
radiosonde-derived water vapor density above 3.75 km and below 3.75 km,
respectively (g m

Table 4 provides both the mean and the rms of the differences between tomography-derived and radiosonde-derived water vapor density. In terms of the statistical results, the accuracy of tomography based on our optimized method is significantly better than the traditional method at heights above 3.75 km as well as below 3.75 km. Compared with radiosonde products, the rms statistical results indicate that the water vapor density accuracy from our optimized method is improved by 15 and 12 % compared to traditional method below 3.75 km and above 3.75 km, respectively.

COSMIC “wetPrf” profile provides “wet” pressure, temperature and pressure. Water vapor density (WVD) can be estimated using “wet” pressure (Song, 2004). We selected the COSMIC radio occultation events which occurred near or inside Hong Kong. Figure 7 depicts the comparisons of water vapor densities obtained from tomography and COSMIC products on 5 and 13 February 2014.

Comparisons of water vapor densities obtained from tomography and COSMIC products on 5 and 13 February 2014. “COSMIC” represents the water vapor density derived from wetPrf product. “Impr” represents the tomography-derived water vapor density using our optimized method, and “Trad” represents the tomography-derived water vapor density using the traditional method.

It can be seen that the changing trends of water vapor density have a good consistency between tomography-derived and COSMIC-derived results in Fig. 7. The WVD derived from our optimized method is better than the WVD from the traditional method since the pink curve is closer to the grey curve. Total eight COSMIC occultation events occurred near or inside Hong Kong in February 2014. These results are used to compare with the results of tomography-derived water vapor above and below the height of 3.75 km, respectively, as seen in Table 5.

The rms and mean of differences between tomography-derived and
COSMIC-derived water vapor density above 3.75 km and blow 3.75 km,
respectively (g m

Table 5 provides both the mean and the rms of the differences between tomography-derived and COSMIC-derived water vapor density. In terms of the statistical results, the accuracy of tomography based on our optimized method is significantly better than the traditional method. Compared with COSMIC products, the rms statistical results confirm that the water vapor density accuracy from our optimized method is improved by 15 and 19 % compared to the traditional method below 3.75 km and above 3.75 km, respectively.

The tomography technique is optimized in a few aspects under the help of radiosonde and COSMIC historical data. Firstly, in order to improve the zenith wet delay (ZWD) accuracy, the regional zenith hydrostatic delay (ZHD) models are optimized by compensating the estimates from the Saastamoinen model. Secondly, the regional conversion factor of converting the ZWD to the perceptible water vapor (PWV) is refined by improving the quality of the tropospheric weighted mean temperature. Next, we develop a method for dividing the tomography grid with an uneven voxel height and a varied water vapor layer top. Finally, we propose a Gaussian exponential vertical interpolation method which can better reflect the vertical variation characteristic of water vapor.

GPS datasets collected in Hong Kong in February 2014 are used to assess the
optimized tomographic method with a comparison to the conventional method.
The radiosonde-derived and COSMIC-derived water vapor density values are
used as references to analyze the tomographic results. Using radiosonde
products as references, the test results obtained from our optimized method
indicate that the water vapor density rms is 2.52 and 0.86 g m

The Survey and Mapping Office of the Lands Department (2016), 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
(

The financial support from National 973 Program of China (no. 2012CB957701), National Key Research and Development Plan (no. 2016YFB0501803), and National Natural Science Foundation of China (nos. 41074008 and 41674039) is greatly appreciated. We thank Zhizhao Liu at The Hong Kong Polytechnic University for providing radiosonde data. The topical editor, M. Salzmann, thanks two anonymous referees for help in evaluating this paper.