An optimal tropospheric tomography approach with the support … · 2020. 6. 19. · years. A ray-tracing water vapour model has been applied by Rohm and Bosy (2011) to estimate the

Ann. Geophys., 36, 1037–1046, 2018https://doi.org/10.5194/angeo-36-1037-2018© Author(s) 2018. This work is distributed underthe Creative Commons Attribution 4.0 License.

An optimal tropospheric tomography approach with the supportof an auxiliary areaQingzhi Zhao1, Yibin Yao2,3, Wanqiang Yao1, and Pengfei Xia41College of Geomatics, Xi’an University of Science and Technology, Xi’an, China2School of Geodesy and Geomatics, Wuhan University, Wuhan, China3Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan, China4GNSS Research Centre, Wuhan University, Wuhan, China

Correspondence: Qingzhi Zhao ([email protected])

Received: 10 November 2017 – Revised: 15 May 2018 – Accepted: 18 July 2018 – Published: 31 July 2018

Abstract. Among most current tropospheric tomographystudies, only the signals crossing out from the top bound-ary of the tomographic area are used for reconstructing thethree-dimensional water vapour field, while signals pene-trating from the side faces of the tomographic body are ig-nored as invalid information. Such a method wastes the valu-able Global Navigation Satellite System (GNSS) observa-tions and decreases the utilisation efficiency of GNSS rays.This is the focus of this paper, which tries to effectivelyuse signals penetrating from the side faces of the tomo-graphic body for water vapour reconstruction. An optimisedtropospheric tomography method is proposed using an aux-iliary area. The top height of the tomography body is de-termined based on the average water vapour distribution de-rived from the Constellation Observing System for Meteo-rology, Ionosphere, and Climate (COSMIC) radio occulta-tion (RO) products. In addition, the coefficients of a nega-tive exponential function between the adjacent layers for ver-tical constraints are fitted using the COSMIC RO profiles.Thirteen GPS stations are selected in the CORS Networkof Texas to perform the tomographic experiment and vali-date the performance of the proposed method at 00:00 and12:00 UTC daily using the radiosonde data for a period of15 days. Compared to the conventional method, the accuracyof the reconstructed water vapour information derived fromthe proposed method is increased by 14.37 % and 16.13 %,respectively, in terms of mean root mean square (rms) andmean absolute error (MAE). The tomographic results ob-tained from the proposed method are further validated withthe slant water vapour (SWV) data derived using the GAMIT(GNSS processing software package). Results show that the

rms and MAE accuracy of SWV values has been improvedby 18.18 % and 27.62 %, respectively, when compared to theconventional method.

Keywords. History of geophysics (atmospheric sciences)

1 Introduction

Water vapour is one of the most important factors affectingatmospheric dynamics, evolution of weather systems, andglobal climate change. Therefore, knowledge of the watervapour distribution at a high spatio-temporal resolution isa vital prerequisite for the prediction of medium- to small-scale weather events as well as the monitoring of climatechange (Zhang et al., 2015). Traditionally, radiosonde andmicrowave radiometers have been used for acquiring watervapour information at a low spatio-temporal resolution withhigh costs and the techniques do not work in all weatherconditions (Wan, 2014). To overcome the drawbacks of theconventional methods, an improved method to detect atmo-spheric water vapour using Global Navigation Satellite Sys-tem (GNSS) technology has emerged with a high spatio-temporal resolution and low cost.

Since the concept of GNSS meteorology was first pro-posed by Bevis et al. (1992), various validations and appli-cations have been reported across the globe and a root meansquare (rms) error of integrated water vapour (IWV) of 1 to2 mm using ground-based GNSS observations was achieved(e.g. Rocken et al., 1993; Duan et al., 1996; Emardson etal., 2000; Niell et al., 2001; Gendt et al., 2004; Smith etal., 2007; Raja et al., 2008; de Haan et al., 2009; Lee et al.,

Published by Copernicus Publications on behalf of the European Geosciences Union.

1038 Q. Zhao et al.: An optimal tropospheric tomography approach

2013). However, to acquire three-dimensional water vapourinformation, the tropospheric tomography technique was in-troduced by taking advantage of SWV values crossing thearea of interest (Flores et al., 2000; Hirahara, 2000; Bi et al.,2006; Notarpietro et al., 2011). Such a technique was firstproposed in the area of medicine (Bramlet, 1978), and hasbeen widely applied in many areas, such as geology (Bour-jot and Romanowicz, 1992), earthquake analysis (Kissling etal., 1994), ionosphere modelling (Hajj et al., 1994; Rius etal., 1997), and wind analysis (Gao et al., 1999).

Tropospheric tomography requires that the area of interestbe discretised into many voxels and using those satellite rayscrossing the voxels therein (Yao and Zhao, 2016); however,many voxels are not crossed by a signal ray due to the in-fluence of the geometric distribution of the constellation ofGNSS satellites as well as the ground-based GNSS receivers(Flores et al., 2000), which leads to a problem of inversion inthe tomographic resolution (Bender et al., 2011a). Normally,some constraints, such as the horizontal constraints and ver-tical constraints, are imposed in tomographic modelling soas to overcome rank deficiency problems (Flores et al., 2000;Bi et al., 2006; Troller et al., 2006; Rohm and Bosy, 2011;Chen and Liu, 2014; Rohm et al., 2014). Ding et al. (2018)proposed a node parameterisation approach using a combina-tion of three meshing techniques to dynamically adjust boththe boundary of the tomographic region and the position ofnodes. It must be noted that the satellite rays used in the con-ventional tomography method refer to signals crossing outfrom the top side of the tomographic body, while the sig-nals penetrating from the side faces are ignored as “unus-able” information (Yao et al., 2016). To maximise the usageof the signals penetrating from the side faces of the tomo-graphic body, some studies have been carried out in recentyears. A ray-tracing water vapour model has been appliedby Rohm and Bosy (2011) to estimate the outer part of theGNSS signal rays using the UNB3m model. Notarpietro etal. (2011) proposed a method to obtain the values of GNSSsignals inside the tomography area by extracting the valuesoutside the area, where the values outside the area are esti-mated with the support of the CIRA-Q wet atmospheric cli-matologic model or the ECMWF reanalysis data. The watervapour content inside the tomography area is estimated bygeometrical linear estimation using an exponential negativefunction (Benevides et al., 2014). Yao et al. (2016) proposeda method using signals crossing out from the side faces ofthe tomographic body by introducing the water vapour unitindex which was further improved using a more sophisti-cated model and additional data resources (Zhao and Yao,2017). Chen and Liu (2016) used numerical weather predic-tion (NWP) profile data to calculate the water vapour contentoutside the tomographic sides and then obtained the value ofwater vapour content inside the tomographic body. However,the methods mentioned above require the availability of spe-cific external information, which restricts the application ofthose methods.

In this paper, a new tropospheric tomography method isproposed by introducing an auxiliary area into the tomo-graphic process. The introduced auxiliary area can be used toincorporate the contribution of satellite rays crossing the sidefaces of a tomographic body into the tomographic results.In addition, the COSMIC (Constellation Observing Systemfor Meteorology, Ionosphere, and Climate) radio occultationproducts are also used for determining the top height of thetomography body as well as the coefficients of a vertical con-straint formula. The proposed method is capable of using allsatellite rays with a given elevation angle for water vapourreconstruction. This paper is organised as follows: Sect. 2presents a tropospheric tomography method with the supportof an auxiliary area; data processing and the determinationof the top height of the tomographic body are covered inSect. 3; in Sect. 4, the tomographic results are analysed tovalidate the proposed method with radiosonde data, and thediscussion and conclusions are presented in Sect. 5.

2 An optimal tropospheric tomography method withan auxiliary area

2.1 Tomographic principles

Generally, two classes of tropospheric parameters estimatedfrom ground-based GNSS observations are used for the re-construction of the water vapour field. The first kind of inputinformation is slant wet delay (SWD), which can be used toobtain the atmospheric wet refractivity (Flores et al., 2000;Hirahara, 2000; Skone and Hoyle, 2005; Rohm and Bosy,2009; Notarpietro et al., 2011). The second kind of input in-formation is slant water vapour (SWV), which can be used toreconstruct the three-dimensional water vapour density field(Champollion et al., 2005; Bi et al., 2006; Chen and Liu,2014). The corresponding output parameters from those twomethods can be mutually interconverted with the help of at-mospheric temperature information (Bender et al., 2011a).In our study, the more sophisticated SWV parameters are se-lected as input information for a tropospheric tomographyexperiment.

The SWV can be described as a total water vapour contentfrom satellite to receiver antenna along the propagation path,and can be expressed by

SWV= 10−6 ·∫ρ(s)ds, (1)

where ρ(s) is the water vapour density (unit: g m−3) and dsis the distance travelled by a satellite ray. According to tro-pospheric tomography theory, the research area is discretisedinto many voxels under the assumption that the water vapourdensity value of each voxel is unchanged during a given pe-riod. Therefore, many satellite rays with different azimuthangles and elevation angles can be used to build the obser-vation equation governing the tomographic modelling. The

Ann. Geophys., 36, 1037–1046, 2018 www.ann-geophys.net/36/1037/2018/

Q. Zhao et al.: An optimal tropospheric tomography approach 1039

Figure 1. Schematic diagram of satellite signals crossing the tomography area (a) and their front view (b), where signals P1–P4 are crossedfrom the side of the tomography area.

relationship between SWV and water vapour density can beexpressed in the matrix form below:

y = A · x, (2)

where y represents a column vector with many SWV valuesand A is a coefficient matrix of distances crossed by satelliterays, while x denotes the unknown parameter which refers tothe water vapour density in our study.

Apart from the observation equation, some additional con-straint equations are required to solve the rank deficiency is-sue arising from the inversion algorithm (Flores et al., 2000;Bender et al., 2011b; Rohm and Bosy, 2011). Usually, twodifferent classes of constraints, the horizontal and verticalconstraints, are employed in tropospheric tomography (Flo-res et al., 2000; Bi et al., 2006; Troller et al., 2006; Benderet al., 2001b; Rohm and Bosy, 2011; Chen and Liu, 2014).In our study, a horizontal constraint equation is establishedbased on the assumption that the water vapour in a certainvoxel is a weighted mean value of its horizontally near neigh-bours (Yao et al., 2017). As for the vertical constraint equa-tion, the exponential negative function is introduced to re-flect the relationship between two adjacent voxels vertically.The coefficients of the exponential negative function are fit-ted based on the average water vapour distribution at differ-ent altitudes derived from the COSMIC RO “wetPrf” profilesfor the period of 2006 to 2016 (see Sect. 3.2). After the vari-ous constraints are combined with the observation equation,the conventional tomographic model can be obtained as AH

V

· x = y0

0

, (3)where H and V represent the coefficient matrices of horizon-tal and vertical constraints, respectively.

2.2 An improved tropospheric tomography method

For most current tropospheric tomography studies, onlythose signals passing through the entire tomographic area are

used, while the signals crossing out from the side faces of thetomographic body are ignored. Such behaviour not only ne-glects the valuable observations, but also decreases the num-bers of satellite rays usable and voxels crossed by rays. Asshown in Fig. 1, blue rays P1–P4 which cross the side facesof the tomographic body cannot be used for water vapour to-mography based on the conventional methods.

To incorporate the value of rays crossing the side facesof a tomography body, a novel method is proposed by in-troducing an auxiliary area. The main idea is that, when thetomography area is extended in latitudinal and longitudinaldirections over a certain distance, the satellite rays whichpenetrate from the side faces of the tomographic body arecrossing out from the top boundary of the surrounding area(called the auxiliary area). Therefore, the rays crossing outfrom the side faces of the tomographic body can be used forthe reconstruction of the water vapour field. For the originaltomographic area, the reconstructed water vapour density us-ing the auxiliary area can be used as the initial water vapourfield. The specific steps are presented as follows.

1. Determine the horizontal distance of horizontal exten-sion. As shown in Fig. 2, the blue rectangle marks theresearch area selected for tomography, while the redrectangle is the auxiliary area. Therefore, the distancebetween the research area and auxiliary area is first re-quired to be determined. Assuming that one station islocated on the border of the research area, as shown byN in Fig. 3, the extended distance can be calculated us-ing the following formula:

d =H/ tan(α), (4)

where d is the extended distance, H is the height of thetomography area, and α is the satellite cut-off elevationangle.

2. Reconstruct the water vapour field of the auxiliaryarea: according to the tomographic model established inEq. (3), the water vapour information for the auxiliary

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Figure 2. Geographical distribution of CORS stations (black trian-gles) selected in the tomography area which corresponds to the bluerectangle and the radiosonde station (black circle). The blue rect-angle is the original area, while the red rectangle is the auxiliaryregion.

area can be obtained using GNSS measurements withelevation angles greater than α.

3. Select the water vapour density of voxels located in thetomographic area and consider those values initial con-straints for the reconstruction of the water vapour fieldtherein. Given this, a novel tomographic model for theproposed method can be established as

AHVI

· x =

y

00ρo

, (5)where I is the unit matrix of the initial constraint equa-tion, while ρo is the initial water vapour density valueof each voxel derived from the tomographic result inStep (2).

4. Singular value decomposition is used to solve Eq. (5),and the general inverse matrix can be obtained (Ran andGe, 1997). In this way, the contribution of satellite rayswhich penetrate from the side faces of the tomographicbody can be incorporated into the water vapour recon-struction process.

3 Data processing and determination of the topboundary

3.1 Data collection and processing

In the present study, the data from 13 ground-based stations(N in Fig. 2) derived from the CORS Network in Texas

are selected for the period of 11 to 25 May 2015. One ra-diosonde station (• in Fig. 2) is located in this area, whereradiosonde balloons are launched twice per day at 00:00 and12:00 UTC, respectively. The space-based COSMIC post-processed “wetPrf” profiles provided by the University Cor-poration for Atmospheric Research/COSMIC Data Analy-sis and Archival Center (UCAR/CDAAC) are also used forthe period 2006 to 2016 (http://www.cosmic.ucar.edu/, lastaccess: September 2017). “wetPrf” profiles include the lat-itude and longitude of the perigee point, refractivity, tem-perature, pressure, and mean sea level altitude from the sur-face to 40 km (Hudnut et al., 2007). The parameters providedby “wetPrf” profiles are interpolated at altitude intervalsof 100 m and calculated by the non-standard 1DVar (one-dimensional variational) technique (Hudnut et al., 2007).

The research area is divided as follows: latitude rangesfrom 32.1 to 33.3◦ N in steps of 0.2◦ and longitude rangesfrom 96.5 to 98.3◦W in steps of 0.3◦. The top height ofthe tomographic body is at an elevation of 10 km with stepsof 1 km, which is determined based on the average watervapour variations with altitude from COSMIC “wetPrf” pro-files. Consequently, there is a total of 6× 6× 10 voxels ob-tained in our study. The satellite cut-off elevation angle is se-lected as 10◦; therefore, the auxiliary area can be determinedbased on the method proposed in Sect. 2.2 with a latituderange from 31.7 to 33.7◦ N, a longitude range from 96.2◦Wto 98.6◦W, and a total of 10× 8× 10 voxels.

The ground-based GPS observations for the experimentperiod of 15 days are processed with GAMIT/GLOBK(v10.5) (Herring et al., 2010). The zenith total delay (ZTD)parameter and wet delay gradients in the east–west andnorth–south directions are estimated at intervals of 0.5 and2 h, respectively. In the GPS data processing, four Interna-tional GNSS Service (IGS) stations (INEG, NIST, NLIB,and PIE1) with a baseline length larger than 500 km are alsoused (see Fig. 2) to reduce the strong correlation of tropo-spheric parameters caused by the similar propagation pathsof signals between satellites and stations in the local area(Rocken et al., 1995). The accurate zenith hydrostatic de-lay (ZHD) is calculated based on the Saastamoinen model(Saastamoinen, 1972) using the interpolated pressure param-eters derived from the ECMWF ERA-Interim products with aresolution of 0.125◦× 0.125◦. The zenith wet delay (ZWD)can be obtained by extracting ZHD from ZTD. Therefore,the SWDs of satellite rays with various azimuth and ele-vation angles are obtained using the wet mapping function(Niell et al., 2001). The weighted mean temperature, which ishighly related to the specific area and season, can be obtainedby statistical analyses of a large number of radiosonde pro-files (Bevis et al., 1992). Here, Tm is calculated based on theempirical formula (Tm = 70.20+ 0.72Ts) proposed by Beviset al. (1992) using the interpolated surface temperature (Ts)from ERA-Interim products. Therefore, the SWV can be ob-tained using the calculated conversion factor with Tm (Beviset al., 1992).


http://www.cosmic.ucar.edu/


Figure 3. The schematic diagram of the calculating distance of the auxiliary region.

3.2 Determination of the top boundary

As described in previous studies, a reasonable top height ofthe tomographic body is important for tropospheric tomog-raphy (Yao and Zhao, 2016, 2017). If the height is too high,the estimated water vapour density values are possibly neg-ative as more parameters near the altitude of the top bound-ary tend to zero. In contrast, a relatively large water vapourvalue is returned by the tomographic technique as some wa-ter vapour contents above the height of the top boundary areignored. In our study, the top boundary of the research areais determined using the COSMIC RO product which is fromthe selected 178 “wetPrf” profiles from the period of 2006 to2016. In addition, the water vapour density changes with al-titude are also obtained from radiosonde recordings at station72249 for the period from 2000 to 2015 to further verify theselected top boundary (Chen and Liu, 2014, 2016; Ye et al.,2016). Here, a principle is introduced to determine the finaltomographic height. The principle is that the water vapourdensity is less than 0.2 g m−3 over the certain height, whilethe standard deviation (SD) is less than 0.05 g m−3, whichhas been used by Yao and Zhao (2016, 2017).

Figures 4 and 5 show the vertical distribution of watervapour density with height in a single event (left) and thewater vapour distribution at different altitudes and exponen-tial fitting curves for the selected period (right) derived fromCOSMIC RO and radio-sounding, respectively. It can be seenfrom Figs. 4 and 5 that the water vapour density generally de-creases with the height increases, and the mean water vapourcontents for the corresponding periods are both close to zeroabove a height of 10 km. The calculated water vapour den-sity and SD for COSMIC RO and radiosonde aspects are0.13/0.040 and 0.17/0.044 g m−3 at the height of 10 km, re-spectively, which both satisfy the principle mentioned above.Therefore, the top height of the tomographic body in ourstudy was deemed to be 10 km.

In addition, a negative exponential function is introducedand the coefficients of the exponential model are estimatedusing the water vapour density from COSMIC “wetPrf” pro-files as

ρ = 10.5 · e(−0.437 h), (6)

where ρ represents the water vapour density while h refersto the geodetic height (unit of kilometres). This exponen-

tial model is used for establishing the vertical constraints be-tween the adjacent layers as described in Sect. 2.1.

4 Result validation and analysis

Based on the method proposed in Sect. 2, two schemes aredesigned to build the tomographic model and evaluate theperformance of the various tomographic results. The twomethods are presented as follows:

– Method 1: only using the signals crossing out from thetop side of the tomography area to reconstruct watervapour information based on the tomographic model(e.g. Eq. 3);

– Method 2: both the signals penetrating from the topand side faces of a tomography body are used to recon-struct water vapour information based on the tomogra-phy model proposed in this paper (e.g. Eq. (5).

4.1 Utilisation rate of signals and number of voxelscrossed by rays

If the satellite rays crossing the side faces of the tomogra-phy body are also used, the utilisation rate of signals and thenumber of voxels crossed by rays are expected to increase;therefore, the number of signals used and the number of vox-els crossed by rays are first analysed using data from 13 sta-tions derived from the CORS Network in Texas over a 15-day period. Figure 6 shows the number of signals used andthe number of voxels crossed by rays, from which it can beseen that the number of signals used and the number of vox-els crossed by rays of the proposed method are both largerthan those from the conventional method. Table 1 lists statis-tical results pertaining to the number of signals used as wellas the number of voxels crossed by rays for various condi-tions. The numerical result shows that the utilisation rate ofsatellite rays is increased by 21.06 %, while the number ofvoxels crossed by rays is improved by 1.53 %, from 81.39 %to 82.78 %, respectively.

4.2 Water vapour comparison with radiosonde data

It has been proven that radiosonde data can provide fairly ac-curate vertical profiles of tropospheric water vapour; there-



Figure 4. The vertical distribution of water vapour density in a single COSMIC RO event (a) and the 3-D water vapour distribution oftomography area and exponential fitting curve from 2006 to 2016 (b); the x axis shows the mean sea level (MSL) altitude.

Figure 5. The vertical distribution of water vapour density in a single sounding event (a) and the 3-D water vapour distribution of thetomography area and exponential fitting curve from 2000 to 2015 (b).

Table 1. Statistical result of the number of signals used and thenumber of voxels crossed by rays for the experiment period.

signal voxel

Method Mean Max. Min. Mean Max. Min.

1 662 676 655 293 307 2772 801 823 776 298 312 284

fore, the water vapour profiles derived from radiosonde dataare used as a reference to validate the tomographic resultsfrom various methods (Niell et al., 2001; Adeyemi and Jo-erg, 2012). The water vapour profiles for the location of ra-diosonde stations derived from various tomographic resultsare compared with that from radiosonde data at 00:00 and12:00 UTC daily for the experimental period of 15 days.Here, rms and MAE are introduced to quantify the qualityof the tomographic result. Figures 7 and 8 present the aver-age rms and MAE comparisons of tomographic results de-rived from two methods with radiosonde data during the ex-perimental period, respectively. The rms and MAE compar-isons clearly show that the accuracy of water vapour profiles

Table 2. Statistical information on the tomographic result comparedwith radiosonde data for the experimental period.

rms MAE

Method Mean Max. Min. Mean Max. Min.

1 1.74 2.93 0.55 1.24 2.14 0.422 1.49 2.75 0.43 1.04 1.97 0.34

from method 2 is superior to that from method 1. Statisticalresults for the experimental period (Table 2) show that themean rms/MAE values of the proposed method are 1.49 and1.04 g m−3, respectively, while the values using the conven-tional method are 1.74 and 1.24 g m−3, respectively.

In addition, water vapour profile comparisons for the spe-cific two epochs at 00:00 UTC, 14 May and 12:00 UTC, 19May are shown in Fig. 9. Those two times are selected be-cause they correspond to the minimum and maximum rmsvalues for the tested period. It can be seen from Fig. 9 thatthe water vapour density values derived from various to-mographic methods match the radiosonde data at most al-titudes. The statistical results show that the rms/MAE values



Figure 6. The number of signals used and the number of voxels crossed by rays for the experimental period.

Figure 7. The rms comparison of the tomographic result derivedfrom two methods with radiosonde data during the experimentalperiod.

Figure 8. The MAE comparison of the tomographic result derivedfrom two methods with radiosonde data during the experimentalperiod.

of method 2 are 0.43 and 2.75 g m−3, respectively, while thevalues of method 1 are 0.54 and 2.93 g m−3, respectively.

To investigate the relationship between water vapour pro-file error and altitude, a relative error is introduced and ex-pressed as

re(i)=|xref(i)− xtomo(i)|

xref(i), (7)

where xref is a reference value, which refers to the watervapour density derived from the radiosonde data, and xtomo

is the reconstructed water vapour information based on dif-ferent tomographic methods. For the selected period of 15days, there are two epochs at 00:00 and 12:00 UTC daily.Therefore, a total of 30 sets of data are compared. Figure 10presents the average water vapour profile comparison derivedfrom different tomographic methods and radiosonde data(left), rms changes with altitude (middle) and relative errorchanges with altitude (right) for the experimental period. Itcan be seen that the average water vapour profiles at differentaltitudes derived from the proposed method better matchedthat from the radiosonde data, while the rms error and relativeerror of the proposed method are less than those arising fromthe use of the conventional method at all layers. Such re-sults validate the superiority of the tomography method withan auxiliary area proposed in this paper. In addition, Fig. 10shows that the rms error generally decreases with increasingaltitude, while the relative error shows the opposite trend.This occurs because the water vapour is mainly concentratedin the lower layers and for the upper layers the water vapourdensity is very low; therefore, small differences between ra-diosonde and tomographic water vapour density values canlead to a large relative error.

4.3 SWV comparison

To validate the superiority of the proposed method, the datafor 4 days are selected to compare the SWV values derivedfrom the tomographic results and GAMIT 10.5. In this exper-iment, only 12 of 13 GPS stations in the research area partic-ipated in the reconstruction of the water vapour field, whilethe other station (TXSG) is regarded as a test station underthe condition that other settings remained unchanged. TheSWV values of the TXSG station calculated using the GPSobservations are considered to be the true value. The com-parison of SWV values derived from GPS-observed data andtomographic results of different methods is carried out witha tomography step of 0.5 h. Table 3 lists the average rms andMAE arising from the use of different tomographic meth-ods and the statistical results for the selected 4-day period.



Figure 9. Water vapour profile comparison derived from different tomographic methods and radiosondes at specific epochs, 14 May00:00 UTC (a) and 19 May 12:00 UTC (b).

Figure 10. Water vapour profile comparison derived from different tomographic methods and radiosonde (a), rms changes with altitude(b) and relative error changes with altitude (c) for the experimental period.

Table 3. Statistical results of SWV comparison between differenttomographic methods and estimated SWV values for the selected 4days.

Method 1 2 1 2

Date rms (mm) MAE (mm)

2015-5-11 5.16 4.84 4.26 4.222015-5-15 5.91 3.91 5.55 2.682015-5-20 6.66 5.42 6.35 4.542015-5-24 2.52 2.38 1.93 1.63Mean 5.06 4.14 4.52 3.27

It can be seen that the rms and MAE values of the proposedmethod (4.14 and 3.27 mm, respectively) are less than thoseof the traditional method (5.06 and 4.52 mm, respectively),which indicates the high accuracy of the proposed method.

5 Conclusion

An optimised tomographic method is proposed in conjunc-tion with the concept of an auxiliary area for the inclusion ofthe signals crossing the side faces of the tomographic body.Both horizontal and vertical constraints are incorporated into

the tomographic model. The top height of the tomographybody is determined and the coefficients of the vertical con-straint equation are fitted using the average water vapour den-sity from the COSMIC “wetPrf” profiles for the period of2006 to 2016. The proposed method improves the utilisationrate of signals used (21.06 %) as well as the number of voxelscrossed by rays (1.53 %).

The proposed tomographic method is validated using thedata of 13 GPS stations from the CORS Network in Texasover a 15-day period. The water vapour profile compari-son with radiosonde data shows that the mean rms errorand MAE of the proposed method are decreased by 14.37 %and 16.13 %, respectively, when compared to the traditionalmethod. The water vapour profile error changes with altitudealso show that the rms and relative errors of the proposedmethod are less than that from the conventional method atdifferent heights, which indicates the superiority of the pro-posed method. The SWV comparison between the GAMIT-estimated and tomographic-derived values shows that the rmserror and MAE of the proposed method have been improvedby 18.18 % and 27.62 %, respectively, when compared to theconventional method, which further confirms its superiority.



Data availability. In this paper, we used (1) GNSS observationsand corresponding meteorological data, which can be downloadedfrom the Surveying and Mapping Office/Land Department (2018),Hong Kong (https://www.geodetic.gov.hk/smo/index.htm); (2) ra-diosonde data, which can be downloaded from the IGRA center (ftp://ftp.ncdc.noaa.gov/) (NOAA, 2018); and (3) COSMIC RO “wet-Prf” profiles, which can be downloaded from UCAR (2018) (http://www.cosmic.ucar.edu/).

Author contributions. QZ mainly contributed to this work. YY andWY conducted the analysis of the approach proposed, and theycontributed to the corrections and structure of this paper. PX con-tributed to the analysis of the COSMIC RO products. All the authorsparticipated in the writing and all commented on the paper.

Competing interests. The authors declare that they have no conflictof interest.

Special issue statement. This article is part of the special issue “Ad-vanced Global Navigation Satellite Systems tropospheric productsfor monitoring severe weather events and climate (GNSS4SWEC)(AMT/ACP/ANGEO inter-journal SI)”. It is not associated with aconference.

Acknowledgements. The authors would like to thank the Interna-tional GNSS Service (IGS) and National Geodetic Survey (NGS)for providing the GPS observations and the post-mission satelliteprecise products. The IGRA and ECMWF are also thanked for pro-viding the corresponding meteorological parameters. The Univer-sity Corporation for Atmospheric Research (UCAR) is thanked forproviding the COSMIC RO products. This research was supportedby the Key Laboratory of Geospace Environment and Geodesy,Ministry of Education, Wuhan University (17-01-02).

The topical editor, Petr Pisoft, thanks Chris Sioris, Kefei Zhang,and three anonymous referees for help in evaluating this paper.

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AbstractIntroductionAn optimal tropospheric tomography method with an auxiliary areaTomographic principlesAn improved tropospheric tomography method

Data processing and determination of the top boundaryData collection and processingDetermination of the top boundary

Result validation and analysisUtilisation rate of signals and number of voxels crossed by raysWater vapour comparison with radiosonde dataSWV comparison

ConclusionData availabilityAuthor contributionsCompeting interestsSpecial issue statementAcknowledgementsReferences

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An optimal tropospheric tomography approach with the support … · 2020. 6. 19. · years. A ray-tracing water vapour model has been applied by Rohm and Bosy (2011) to estimate the