29SOLA, 2014, Vol. 10, 29−33, doi:10.2151/sola.2014-007

AbstractA procedure for estimating the precipitable water vapor (PWV)

distribution around ground-based stations of the global navigation satellite system (GNSS) on a scale of several kilometers is pre-sented. This procedure utilizes the difference between the zenith total delay above a GNSS station and the zenith mapped slant path delay (SPD). This difference can be used to estimate the PWV gradient in each SPD direction by assuming an exponential distri-bution for the horizontal water vapor gradient.

The procedure was tested using an estimation of the PWV variation associated with the parent storm of an F3 Fujita scale tornado that occurred in Ibaraki prefecture on 6 May, 2012. Differential reflectivity observed by a dual-polarimetric radar indi-cated the existence of a developed parent cloud approximately 1h before the tornado occurred. A high-resolution numerical weather model simulation suggested the existence of a strong PWV gra-dient around the parent cloud, made evident by the co-existence of a strong updraft and downdraft within an approximately 5-km radius. The PWV gradient, calculated using the GNSS observation network with an average spacing of approximately 17 km, could not detect such a small-scale, strong PWV gradient. The PWV gradient estimated using the proposed procedure revealed a strong PWV gradient and its enhancement. In this case, a higher-order inhomogeneity component of each SPD played a critical role.

(Citation: Shoji, Y., H. Yamauchi, W. Mashiko, and E. Sato, 2014: Estimation of local-scale precipitable water vapor distribu-tion around each GNSS station using slant path delay. SOLA, 10, 29−33, doi:10.2151/sola.2014-007).

1. Introduction

In Japan, the Geospatial Information Authority of Japan (GSI) operates a nationwide permanent global navigation satellite system (GNSS) called the Earth Observation Network (GEONET) with an average spacing of 17 km. It is regarded as one of the densest GNSS networks in the world and covers all of Japan. Several studies have attempted to use GNSS-derived precipitable water vapor (PWV) measurements to monitor heavy rainfall (e.g., Kanda et al. 2000; Niimura et al. 2000; Inoue and Inoue 2007). These studies have confirmed the validity of measuring GNSS- derived PWV and its variation to monitor heavy rainfall. However, as vertically integrated water vapor, PWV does not provide verti-cal profile information; therefore, monitoring PWV with a 17-km spacing alone does not always provide sufficient information on precursors of severe storms.

Shoji et al. (2004) developed a retrieval procedure for signal delay along each ray path (slant path delay (SPD)). They decom-posed the SPD into three components: an isotropic component, a first-order gradient, and a higher-order inhomogeneity. Shoji (2013) proposed two new indices using decomposed components of the gradient and higher-order inhomogeneity: the water vapor concentration (WVC) index, which represents the spatial con-centration of water vapor 2 to 3 km above ground, and the water vapor inhomogeneity (WVI) index, which expresses the degree of water vapor variation around each GNSS station on a scale of

several kilometers. Using SPD values derived from the procedure of Shoji et al. (2013), Kawabata et al. (2013) considered the impact of SPD assimilation on the reproduction of small-scale convective precipitation. Sato et al. (2013) compared PWV values measured by radiosonde with those derived from the GNSS SPD and found that the SPD closest to the radiosonde path exhibited better agreement than the estimated zenith total delay (ZTD). The WVI index is based on the standard deviation of the SPDs mea-sured at a GNSS station, so directional information for each SPD is neglected. However, the results of Kawabata et al. (2013) and Sato et al. (2013) clearly demonstrate that the slant path direction does provide practical information.

This article presents a new approach for utilizing SPD to monitor severe storms. In Section 2, we describe a procedure for analyzing the PWV gradient around GNSS stations. Section 3 introduces application results for the F3 scale tornado which occurred in Japan on 6 May, 2012, and a summary and discussion are presented in Section 4.

2. Procedure for estimating PWV gradient around GNSS sites

The procedure for estimating the PWV distribution around GNSS stations can be divided into the following three steps.

2.1 Retrieval of ZTD and SPD at each GNSS stationThe procedure for this step was identical to that described

by Shoji (2013), except for the precise orbit and satellite clock correction data. The ZTD and SPD at each station were estimated by adopting the precise point positioning method (Zumberge et al. 1997) with GIPSY-OASIS II (Webb and Zumberge 1993) Version 6.1.

The GNSS-derived PWV at each station was converted from an estimated ZTD using the proportionality coefficient Π (Askne and Nordius 1987). ZTD is the integrated refractivity (N ) of the atmosphere in the zenith direction, where the refractivity is a func-tion of temperature (T ), partial dry-air pressure (Pd), and partial vapor pressure (Pw):

ZTD=∞

∫ N z dz( ) ,0

(1)

N n K PT

K PT

K PT

d w w= − ⋅ = + +( ) ,1 106 1 2 3 2 (2)

where n is the refractive index and K1, K2, and K3 are constants that have been determined theoretically or by fitting to the ob-served atmospheric data.

Using Eq. (2), the contribution of dry atmosphere (Ndry) and water vapor (Nwet) can be derived as follows.

N K PT

N K PT

K PT

d w wdry wet= = +1 2 3 2, . (3)

As described by Shoji (2013), the relationship between ZTD and SPD is

SPD ZTDEST( , ) ( ) ( cot ( cos sin ))θ φ θ θ φ φ ε= ⋅ + + +m G GN E

(4)

where ZTDEST is the ZTD value estimated from the GNSS anal-ysis. ZTDEST can be regarded as a representative value of ZTD

Estimation of Local-scale Precipitable Water Vapor Distribution Around Each GNSS Station Using Slant Path Delay

Yoshinori Shoji, Hiroshi Yamauchi, Wataru Mashiko, and Eiichi SatoMeteorological Research Institute, Ibaraki, Japan

Corresponding author: Yoshinori Shoji, Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan. E-mail: yshoji@mri-jma.go.jp. ©2014, the Meteorological Society of Japan.

30 Shoji et al., Estimation of Precipitable Water Distribution Using GNSS Slant Path Delay

Here, the second term of the right side denotes the contribution of gwet.

Following Ruffini et al. (1999), we acquire the following rela-tionship:

( ( ) ) ,g z z dz Hwet ZTD⋅ = ⋅∇∞

∫0 (8)

where ÑZTD is the horizontal gradient of the ZTD distribution.According to Askne and Nordius (1987), PWV is proportional

to the delay in the zenith direction caused by water vapor (Zenith Wet Delay: ZWD). In this study, we assume that the difference between ZTDEST and ZTDSPD is due to the several-kilometer hori-zontal gradient of water vapor refractivity (Nwet) alone. Therefore, combining Eqs. (7) and (8) gives

∇ = ⋅∇ ≈ ⋅∇ = ⋅−⋅

PWV ZTD ZWD ZTD ZTDSPD ESTΠ Π ΠH cot ( )

,q

(9)

where Π is the proportionality coefficient. The horizontal gradient of PWV is expressed as a function of the ZTD difference, eleva-tion angle, and scale height. In this study, we used the following relationship between water vapor scale height (Hw) and PWV, which was determined by the statistical comparison of Shoji (2013).

Hw = 8.64679 ·PWV + 1657.91. (10)

2.3 Analysis of PWV distribution around GNSS stations using retrieved PWV and PWV gradient

We can more finely estimate the PWV distribution around each GNSS station by using the several-kilometer PWV gradient described in Section 2.2. In this procedure, ZTD in the azimuth direction of each SPD is expressed as a function of distance from each GNSS station (Fig. 1):

ZTD ZTD ZTD

ZTD ZTD ZTDEST

ESTSPD EST

( )

cot ( )

d d

dH

= + ⋅∇

= + ⋅−⋅ q

(11)

Thus, ZTD(d ) becomes equal to ZTDSPD when d is H cot (q), the distance at which the slant path reaches the scale height H. Hereinafter, we refer to this distance as dH. Furthermore, accord-ing to Shoji (2013), ÑPWV is most affected by the Nwet gradient at its scale height H assuming an exponential distribution of the Nwet gradient in the vertical direction.

The assumptions we made in Section 2.2 are approximate, so we need to refrain from excessive use of the estimated gradient. In this study, we set a virtual GNSS station around each GNSS station in each slant path direction at a distance dH and set the ZTDSPD as the virtual station’s ZTD for convenience. Virtual GNSS stations were not set when dH exceeded 5 km. By applying this qualification, SPDs of 20° elevation or less were excluded in this analysis. For more precise study, the applicability of the above restrictions should be investigated further. PWV at each virtual station was converted from ZTDSPD multiplied by Π at the actual GNSS station. PWVs at both actual and virtual GNSS stations were interpolated into a 2.5 × 2.5 km2 grid space using Cressman’s objective analysis (Cressman 1959). Hereinafter, we refer to PWVs at virtual GNSS points as PWVSPD.

3. Application for monitoring the development of the parent storm of the F3 tornado on 6 May, 2012, in Tsukuba, Japan

From 12:35 to 12:51 JST (Japan Standard Time: +9 UTC) on 6 May, 2012, an F3 scale tornado passed through the northern part of Tsukuba City (Fig. 2). The tornado caused extensive damage including one fatality, and 37 injuries.

within an inverted-cone-shaped space above the GNSS antenna. q(f) is the angle of elevation (azimuth), m(q) is the isotropic mapping function that describes the ratio of SPD to ZTD, GN (GE) is the delay gradient parameter in the north (east) direction, and e is the postfit phase residual. In this study, we used the global map-ping function proposed by Boehm et al. (2006) as the isotropic mapping function. Following Shoji et al. (2004), we used e as the higher-order inhomogeneity component after eliminating errors due to the satellite clock error and the reflected wave (multipath). According to Shoji et al. (2004), the horizontal scales of ZTDEST, GN (GE), and e are roughly 600 km, 60 km, and 2−3 km, respec-tively.

Shoji (2013) used final ephemerides provided by the Inter-national GNSS Service (IGS) and retrieved PWV values every 5 min. However, we used final ephemerides provided by the Jet Propulsion Laboratory (JPL) because JPL’s final ephemerides contain 30 s orbit/clock correction, which enabled us to retrieve ZTDEST and SPD every 30 s.

2.2 Estimation of PWV gradient using SPDsUsing Eq. (4), we mapped each SPD to the zenith direction.

We call this ZTDSPD to distinguish it from ZTDEST (Fig. 1).

ZTD SPD

ZTD

SPD

EST

=

= + + +

( , )( )

cot ( cos sin )( )

θ φθ

θ φ φεθ

mG G

mN E

(5)

We make the following three assumptions.(1) The horizontal gradient of dry refractivity (Ndry) is small

enough to be negligible.(2) The difference between ZTDEST and ZTDSPD is due to the

several-kilometer horizontal gradient of water vapor refractiv-ity (Nwet) alone.

(3) The horizontal Nwet gradient (gwet) decreases exponentially with height.

g z g zHwet wet( ) ( ) exp= ⋅ −

0 (6)

Here, gwet (z) is the horizontal water-vapor gradient at altitude z and H is the scale height of gwet.

In this study, we ignore height differences among the various GNSS stations for simplicity. ZTD and PWV depend heavily on the altitude of the observation site. Practical and/or more precise application may need careful consideration of height differences.

If the above assumptions are met, N along an SPD can be ex-pressed as a function of the refractivity at the GNSS site and gwet as schematically depicted in Fig. 1. ZTD is the integrated refrac-tivity (N ). Therefore, ZTDSPD can be expressed by the following equation.

ZTD

ZTD

SPD wet

EST wet

= ⋅ + ⋅ ⋅

= + ⋅

−∞

∫ { ( ) ( ) cot ( )}

cot (

N z g z z dz

g

10 6

0q

q (( ) )z z dz⋅∞

∫0 (7)

Fig. 1. Schematic diagram illustrating the difference in integrated refrac-tivity (N ) at height (Z ) between the zenith direction and signal direction. The difference between ZTDSPD and ZTDEST is assumed to be caused by the horizontal gradient of wet refractivity.

31SOLA, 2014, Vol. 10, 29−33, doi:10.2151/sola.2014-007

3.1 Parent storm track observed by a dual-polarized Doppler radar

During the Tsukuba tornado, a C-band polarimetric radar of the Meteorological Research Institute (MRI-C) observed both the parent storm and the vertical structure of the tornado at close range (13 to 17 km) (Yamauchi et al. 2013). According to Yama-uchi et al. (2013), this parent storm developed at the south end of a meso-β scale rainband. The storm moved northeast at a speed of 20 m s−1. The horizontal (vertical) scale of the storm was 20 (12 km). The storm lasted from 11:50 to 13:30 JST (1 h 40 min). The track of the parent storm was captured well by the differential reflectivity (Zdr) observed by the MRI-C (Fig. 2).

3.2 Numerical simulation of the parent cloudMashiko (2012) conducted a high-resolution numerical simu-

lation experiment using the Japan Meteorological Agency (JMA) nonhydrostatic model (NHM) (Saito et al. 2006, 2007). Down-scale experiments were performed using JMA mesoscale analysis (MANAL) data for 09:00 JST on 6 May, 2012 as the initial field. The horizontal grid spacing of MANAL is 5 km, and grid spacings of downscale experiments were set to 1 km, 250 m, and 50 m. In the 50 m resolution experiment (NHM50m), a hook-shaped precipitation system that entailed a mesocyclone was reproduced. The reproduced hook-shaped precipitation system was approxi-mately 30 min earlier and several kilometers northward from the event observed by the MRI-C radar. However, the tornado track and lifetime were well reproduced.

In the 250 m resolution experiment (NHM250m), an isolated area with a strong PWV gradient was formulated around the

southern-central part of Saitama Prefecture about 1 h before the tornado struck. The track of the strong PWV gradient area showed the key feature of the track of a high-Zdr area as observed by the MRI-C radar (Fig. 2).

The reproduced PWV gradient was enhanced as the system moved northeast (Fig. 3). This suggests that detection of a large PWV gradient can be an indicator of severe local storm devel-opment. However, as Fig. 3 also indicates, such a PWV gradient could not be observed by the GEONET due to insufficient hori-zontal resolution.

Figure 4 presents the reproduced horizontal distribution of PWV and the vertical cross-section of specific humidity when the reproduced PWV gradient reached its maximum. The significant PWV gradient is conspicuous due to the strong updraft and down-draft. The maximum PWV gradient at the time was 18.0 mm km−1 using 250 m grid resolution. Thinning out the grid interval reduces the expressed gradient. For example, the PWV gradient is 8.0 mm km−1 with 1-km grid resolution (blue line in Fig. 3).

3.3 Estimated PWV gradient around GNSS sitesFigure 5 plots the temporal variation of the PWV gradient

magnitude with time estimated at several GEONET stations near the parent storm track. The estimated PWV using ZTDEST (PWVEST) and that based on each ZTDSPD (PWVSPD) are also plotted. The time series graph of the estimated PWV gradient (blue lines) at each station indicates an abrupt change with the passing of the high-Zdr area. At station 0583 (Ishige), the largest PWV gradient of 8.1 mm km−1 was estimated at 12:36 JST (close to the tornado touchdown time). Also from this figure, we can see that the estimated gradient parameters, “GN (GE)” contribute little to the estimation of several-kilometer PWV distributions. This is understandable because the spatial scale of the gradient parameter is about 60 km.

Figure 6 presents the distribution of PWVSPD along with the strong radar echo region. PWVSPD clearly shows the spatiotem-poral variation of the PWV gradient due to strong convection passing. In these figures, large gradients are expressed at stations near the strong precipitation area. When we look closely at the distribution, PWVSPD tends to be larger in the direction toward the storm. This clearly demonstrates that GPS/GNSS SPD can express

Fig. 2. Distribution of differential reflectivity (Zdr) at 4km height ob-served by the MRI-C radar (middle right in (c)) at (a) 11:51, (b) 12:19, and (c) 12:35 JST. The large Zdr area is highlighted by white circles. White triangles with times are the maximum PWV gradient area expressed in NHM250m. Black thick contour lines represent 40 dBZ of radar echo intensity. Red crosses denote the locations of tornado-related vortices observed by the MRI-C radar at a 0.5° elevation angle. Red vectors are observed surface wind, and black dots are GNSS station positions. Topog-raphy is expressed by thin black contour lines every 100 m.

Fig. 3. Time series of magnitude of maximum PWV gradient expressed in NHM250m within the area covered in Fig. 2. The gradient was calculated by the centered difference. The red line represents the result of using the original 250 m grid. Other lines represent the result of using every other grid (green), every four grids (blue), and every 20 grids (pale purple).

Fig. 4. (a) Reproduced distribution of PWV by NHM250m at 12:12 JST. White vectors are surface winds. (b) Vertical cross section of specific humidity (color shade) along the white line of (a). Vectors represent wind parallel to the cross section. Black contours represent temperature.

32 Shoji et al., Estimation of Precipitable Water Distribution Using GNSS Slant Path Delay

a finer distribution of PWV than can be expressed by the network of GNSS stations.

Finally, Fig. 7 presents the PWV distribution before and after the tornado touchdown, (a) reproduced by NHM50m, (b) expressed by interpolation of PWVEST and PWVSPD, and (c) expressed by interpolation of only PWVEST. An area of large PWV contrast centered on strong precipitation implies a strong upward wind in front of and a strong downdraft behind the parent

Fig. 7. PWV fields before and after the tornado. (a) Reproduced by NHM50m. (b) Expressed using both PWVEST and PWVSPD. (c) Expressed by PWVEST only. Black lines in (a) are 40 mm h−1 rainfall intensity reproduced by NHM50m; those in (b) and (c) are the 40 dBZ echo intensity at the 0.5° elevation an-gle of the MRI-C. As described in Section 3.2, though the timing differs by about 30 minutes, the NHM simulation succeeded in reproducing the movement and development of the parent storm.

Fig. 5. Time series of PWVEST (thick green line), PWVSPD of each observed satellite (thin gray lines along PWVEST), the magnitude of the PWV gradi-ent estimated from the gradient parameter (GN(GE)) (thick red line at the bottom of each graph), and the magnitude of the PWV gradient estimated by the difference between PWVSPD and PWVEST (thin blue lines at the bottom of each graph). The locations of stations 3011, 3008, and 0583 are plotted in Fig. 2.

Fig. 6. Distribution of PWVSPD (colored trian-gles) of each GNSS sta-tion at its virtual position described in Section 2.3. Red circles represent the high ZDR area, and thick black lines repre-sent 40 dBZ radar echo intensity at 4 km height. The locations vary with time depending on the GNSS satellite azimuth and elevation, and on the scale height of the water vapor gradient.

33SOLA, 2014, Vol. 10, 29−33, doi:10.2151/sola.2014-007

storm. Neither (b) nor (c) expresses such a strong PWV contrast. However, enhancement of the PWV contrast toward the tornado is expressed in (b). In Fig. 7c, no such PWV gradient is expressed at all. However, the gradient in (c) was weaker than the NWP simulation. In NHM simulation (a), the area of PWV less than 24 mm distributes westward of the storm. In our new analysis (b), decreasing PWV behind the storm is expressed rather more weakly than in NHM. The possible cause of this difference is discussed in the next section.

4. Summary and discussion

We have presented a procedure for estimating the PWV variation around GNSS ground-based stations on a scale of sev-eral kilometers. The procedure utilizes differences between the estimated ZTD (ZTDEST) and the zenith-mapped SPD (ZTDSPD). By assuming an exponential distribution for the horizontal water vapor gradient, this difference can be used to estimate the PWV gradient. Shoji (2013) proposed the WVI index, which is defined as the standard deviation of PWVSPD. The retrieved PWV gradient in this study can be regarded as another utilization of PWVSPD. The WVI index does not utilize ray-path direction data. The PWV gradient proposed in this paper utilizes both the deviation of PWVSPD and information on its direction.

The procedure was tested for the parent storm of the F3 tornado that struck on 6 May, 2012, in Tsukuba, Japan. During the tornado, both radar observation and high-resolution numer-ical weather prediction (NWP) model simulation revealed the existence of well-developed cumulus convection (the parent storm) at the southern tip of a line-shaped precipitation system approximately 1 h before the occurrence of the tornado. The NWP model simulation also revealed that the PWV gradient was enhanced as the storm approached the area where damage occurred. The Japanese nationwide dense GNSS network, with approximately 17 km spacing, cannot depict such a strong PWV gradient on a scale of several kilometers. Our estimated PWV gra-dient exhibited better agreement with the NWP model simulation. It was also confirmed that most of the improvement came from several-kilometer, higher-order inhomogeneity components.

However, the gradient was weaker than in the NWP simu-lation. This might be partly because of insufficient observation density. The horizontal scale of the higher-order inhomogeneity component of each SPD is several kilometers, and we adopted a distance cutoff of 5 km. In order to analyze several-kilometer PWV distributions, we need a denser GNSS network with at least 10-km horizontal spacing. Another possible reason for the weaker gradient may be the insufficient and inhomogeneous coverage of GPS satellites. As of 2012, from six to twelve GPS satellites could be observed simultaneously at each GNSS site in Japan. This might be insufficient for estimating the water vapor gradient in all directions. Also, we need to carefully check the quality of each SPD. In this study, we tried to eliminate the effects of the satellite clock error and multi-path (reflected-wave) error following Shoji (2013). However, it is difficult to distinguish atmospheric signals from these noises, especially under locally severe weather condi-tions.

The number of GNSSs has been increasing. As of December 2013, 24 satellites of the Russian GLONASS are in operation. The European Union’s GNSS (Galileo) is in the experiment phase, and China is developing an independent GNSS system named COMPASS. Furthermore, a number of space-based augmentation systems (e.g., Japan’s QZSS) and regional navigation satellite systems (e.g., the Indian Regional Navigation Satellite System, or IRNSS) will contribute further satellites and signals to the multi-constellation GNSS. In the next step of this study, we will assess the impact of the increased number of SPDs on multi-GNSS.

Acknowledgments

Part of this research was supported by the funds for integrated promotion of social system reform, research, and development of the Ministry of Education, Culture, Sports, Science and Technolo-gy (MEXT) of Japan.

For GPS analysis, we used the GIPSY/OASIS II software package, provided by JPL. The GSI kindly provided GEONET-ob-served RINEX data.

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Manuscript received 16 December 2013, accepted 31 January 2014SOLA: http://www. jstage. jst.go. jp/browse/sola/