Introduction
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.
GPS tomographic approach
Tomography model
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:
SWV=1ρw⋅∫sρsds,
where SWV is the slant water vapor; ρw is the density of liquid
water; s is the slant path that GNSS signals pass through troposphere; ρ(s) is the water vapor density. After being discretized by the fourth-order
Newton–Cotes formula, the equation can be expressed as (Schwarz, 1997; Stoer
and Bulirsch, 1980)
SWV=1ρw⋅190⋅∑i=1m∑j=04Cij4ρsji=Sρ+ΔSWV,
where Cij(4) is the fourth-order coefficients of the jth segment
point within the ith grid; ρ(sji) is the corresponding water
vapor density values; m denotes the number of the grids which the signals
pass through; S represents the distance that the GPS signals span the voxels;
ΔSWV is the noise.
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 Π (Song, 2004):
SWV=Π⋅SWD,
where Π is the humidity conversion factor, which is geographically
dependent and varied from location to location.
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
ρh=ρC⋅e-h-h0hz2,
where ρ(h) denotes the water vapor density at the height of h;
hzrepresents the height index of water vapor; ρC is a
constant value of water vapor density; h0 is a constant. ρC and h0 may be determined using radiosonde or COSMIC products. Based
on Eq. (), Eq. () is used as the vertical constraint to establish the
relationship between water vapor density in adjacent vertical layers:
ρi,j,k+1ρi,j,k=ehk-hk+1⋅hk+hk+1-2h0hz2,
where the subscripts “i”, “j” and “k” denote the index of voxel in the east–west,
north–south and vertical directions, respectively; hk is the
height of the kth voxel.
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. (). It is similar to the
horizontal temperature interpolation, but the vertical temperature is
interpolated by computing the temperature decay rate using radiosonde
products. After the temperature and relative humidity are obtained, the
water vapor density of all the voxels can be computed using the temperature
and relative humidity and utilized as the prior values in the tomography
(Hardy, 1998; Song, 2004).
ZHD computation
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 () shows how to calculate the ZHD using the
radiosonde products and GPS radio occultation products (Liu et al., 2000):
ZHDd=10-6⋅∑n=I0Ihn+1-hnNdn+1+Ndn2Nd=k1PdT1+Pd57.97⋅10-81+0.52T-9.4611⋅10-4tT2,
where I denotes the height of the atmosphere whose pressure is less than
0.02 hPa; I0 denotes the initial height of computing the ZHD; h is the
geopotential height; Nd is the dry air refractivity; t and T are the
temperature in degrees Celsius and kelvin, respectively; Pd
denotes the dry pressure. Via the stepwise regression analysis, we find that
the offsets of Saastamoinen-derived and radiosonde-derived ZHD mainly
correlate with the temperature and pressure. In order to improve the
accuracy of the ZHD, we compensate the Saastamoinen-derived ZHD with a model
at a similar form to the Black formula (Black, 1978).
ΔZHD=c(T-d)PT,
where ΔZHD is the ZHD corrections; P is pressure; c and d are two
parameters of the calibration model to be determined by radiosonde and
COSMIC profile historical data.
Humidity conversion factor
The humidity conversion factor Π varies in different areas and seasons, and
it can be expressed as a function of the tropospheric weighted mean
temperature Tm (Bevis et al., 1994):
Π=106ρw⋅Rmw⋅k3Tm+k2-mwmd⋅k1
Tm=∫0∞PwT⋅dh∫0∞PwT2⋅dh=∑h2-h1PwT∑h2-h1PwT2,
where ρw is the density of liquid water; k1, k2 and
k3 are constants as k1= 77.6 K hPa-1, k2= 70.4 K hPa-1 and
k3= 3.739 × 105 K hPa-1 (Bevis et al., 1994); md and mw are the molar
masses of dry atmosphere and water vapor, respectively; R indicates universal
gas constant; Pw means water vapor pressure whose unit is hPa.
The parameter conversion factor Π mainly depends on Tm.
Traditionally, Tm is determined by a single means such as ECMWF
(European Centre for Medium-Range Weather Forecasts), NCEP, radiosonde
sounding and so on. Compared to the radiosonde technique, the accuracies of
the ECMWF and NCEP are relatively lower. However, the temporal resolution of
the radiosonde is low and the distribution of radiosonde stations is
sparse. In this case, we jointly use the radiosonde and COSMIC products to
estimate the Tm for the purpose of improving its temporal resolution.
The conversion factor Π is then determined using the Tm.
Tomography grid division
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.
Interpolation function inside each voxel
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. () is proposed for the vertical interpolation, as shown in
Eq. ().
ρkih=hk+1-hhk+1-hkeh+hk-2h0hk-hhz2ρkihk+h-hkhk+1-hkeh+hk+1-2h0hk+1-hhz2ρk+1ihk+1,
where ρki(h) denotes the water vapor density in the “kth”
voxel; i represents the “ith” GPS ray; hk and hk+1 denote the
corresponding height of the bottom and top of the kth voxel,
respectively; ρki(hk) and ρk+1i(hk) represent the water vapor density on the bottom
and top of the “kth” voxel, respectively.
Processing results and analysis
Data description
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 (www.cosmic.ucar.edu). The post-processed profiles that are available in
6-week latency are used for this study. As one type of the post-processed
data products, “wetPrf” profile offers water vapor pressure, temperature
and refractivity, which are almost evenly distributed around the globe.
Radiosonde measurement has a high accuracy, high vertical resolution,
long-term stability and all-weather capability for obtaining water vapor
density, pressure and temperature in the troposphere and lower stratosphere.
However, these measurements are only distributed in the limited areas where
there are the radiosonde stations. Particularly, they are rare in the
Southern Hemisphere and cannot cover the oceans.
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 ∘C, respectively. For
the humidity sensor, the total uncertainties in sounding and repeatability
are 5 and 2 %, respectively (www.vaisala.com). The COSMIC RO uses a
compact, low-power and low-cost sensor, which provides the high-accuracy
meteorological elements with averaged profiles temperature of less than
0.1 K. (http://www.cosmic.ucar.edu/ro.html) .
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 + GNSS receivers are equipped at all 12 stations with a data
sampling rate of 5s. One-month GPS datasets on 1–28 February 2014 were
collected in Hong Kong. In addition, the “wetPrf” profiles whose address is
the same as Hong Kong and radiosonde products at the
“45004th” station in February of 2007–2013 were
used as historical data to optimize the tomography solutions. There are 81
“wetPrf” profiles during this period of time. The quality flags of all
“wetPrf” profiles are examined and the flags indicate “bad = 0”,
suggesting that these profiles have passed quality control successfully.
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).
ZHD calibration
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
(http://apps.ecmwf.int/datasets/data/interim-full-daily) to obtain
atmosphere element above the height of 30km. The radiosonde-derived ZHD is
used as references to obtain the ZHD offsets for the computation of c and d in
Eq. (). The established ZHD model can be expressed as
ZHD=ZHDs-0.0014(T-0.5009)PT,
where ZHDs is derived from the Saastamoinen model.
In order to assess the feasibility of Eq. (), the correlation between the
ZHD offsets (ΔZHD) and the pressure and temperature are displayed in
Table 1, respectively.
Correlation coefficients between the ZHD offset and temperature and
pressure.
Parameter
Temperature T
Pressure P
P/T
ΔZHD
-0.83
-0.79
0.85
As seen in Table 1, the ΔZHD are highly correlated to T, P and
P/T, which explains why we express the ΔZHD as a function of the T, P and
P/T in Eq. (). Using the established model of Eq. (), the calibration effect
is assessed using datasets in February 2014.
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.
Date
2014/02/01
2014/02/02
2014/02/03
2014/02/04
Time
00:00
12:00
00:00
12:00
00:00
12:00
00:00
12:00
Π
0.161
0.163
0.162
0.163
0.162
0.163
0.162
0.162
Date
2014/02/05
2014/02/06
2014/02/07
Time
00:00
12:00
00:00
12:00
00:00
12:00
Π
0.161
0.162
0.160
0.162
0.160
0.158
Humidity conversion factor determination
According to Eqs. () and (), if the conversion accuracy is better than 1 mm,
the precision of the weighted mean temperature Tm must be less than
3 K. Since Tm varies with seasons and region, we combine radiosonde
product and COSMIC “wetPrf” profile to calculate Tm based on Eq. ()
using measurements in February from 2007 to 2013. Then, we fit the
relationship between Tmand the surface temperature T as follows:
Tm=0.73⋅T+71.34.
After obtaining Tm using Eq. (), the conversion factor Π can be
determined using Eq. (). In order to examine the improvement effect of
conversion factor, we compare the PWV in Hong Kong in February 2014 using
the different conversion factors obtained from the traditional method and
our improved method. In the traditional method, we use a constant value of
0.1538 as the conversion factor (Shi and Gao, 2009). The PWV derived from
the “45004th” radiosonde station (lat: 22.32; long: 114.16), which is close
to HKSC station (lat: 22.32; long: 114.14), is used as references.
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).
max
min
mean
rms
Traditional Π
4.97
0.23
1.79
2.22
Improved Π
4.36
0.16
1.47
1.97
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 Π method for humidity conversion factor computation.
Tomography grid division
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 × 10 km squares in horizon direction, as seen in Fig. 1. We
utilize the radiosonde and COSMIC historical data in February from 2010 to
2013 to determine the heights of DLVT and WVLT, and they are 3.88 and 3.61 km for the DLVT and 7.5 and 7.47 km for the WVLT, respectively. Then we
take their average values, which are 3.75 and 7.5 km as the final DLVT and
WVLT. Thus, we divide the vertical layers into two stages. The first stage
is from the ground to the DLVT (3.75 km). We divide it into 10 layers and
each layer height is 375 m. The second stage is from the DLVT (3.75 km) to the
WVLT (7.5 km). We divide it into five layers and each layer's height is 750 m.
Result validations
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. (), and the ZWD is obtained by deducting the ZHD
from the ZTD. The SWV is computed using Eq. () with optimized conversion
factors. Finally, we estimate the 3-D distribution of atmospheric water
vapor using parameterized approaches in which Eq. () is used for
interpolation in the vertical direction and Eq. () is applied as the
vertical constraints. Kalman filtering algorithm is used for tomography
solutions. In detail, the unknowns are the water vapor densities at the grid
points. The state transition matrix is a unit matrix. The process noise
matrix is acquired from the statistics of radiosonde-derived water vapor
densities. Figure 4 shows the 3-D distribution of atmospheric water vapor
density with a WVLT height of 7.5 km on 19 February 2014.
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.
Comparison of tomography-derived results and radiosonde-derived results
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):
PWV=1ρw∫0∞ρkdh.
Applying Eq. (14), the water vapor densities have been transferred to PWV.
Figure 5 shows the difference of PWV obtained from the radiosonde product
and tomography in the same region (latitude 22.31∘ and longitude
114.16∘).
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-3). “RD” represents the relative differences.
Height
Below 3.75 km
Above 3.75 km
Bias
RD
Bias
RD
Mean
Rad-Impr
-1.18
-15.25 %
0.44
23.47 %
Rad-Trad
-1.67
-21.58 %
0.64
34.14 %
rms
Rad-Impr
2.52
32.57 %
0.86
45.88 %
Rad-Trad
2.97
38.39%
0.98
52.27%
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.
Comparison of tomography-derived results and COSMIC-derived results
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.
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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-3). “RD” represents the relative differences.
Height
Below 3.75 km
Above 3.75 km
Bias
RD
Bias
RD
Mean
Rad-Impr
-0.59
-12.90 %
-0.55
-29.24 %
Rad-Trad
-0.89
-19.46 %
-0.77
-40.96 %
rms
Rad-Impr
1.24
26.09 %
0.72
38.28 %
Rad-Trad
1.46
30.72 %
0.89
47.32 %
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.
Conclusions
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-3 below and above 3.75 km, respectively, which is improved by
15 and 12 % compared to those of conventional method. Using the COSMIC
products as references, the results indicate that the water vapor density
rms is 1.24 and 0.72 g m-3 from our optimized method below
and above 3.75 km, respectively, which is improved by 15 and 19 % compared to
the conventional method.