ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-35-87-2017An improved troposphere tomographic approach considering the signals coming
from the side face of the tomographic areaZhaoQingzhiYaoYibinybyao@whu.edu.cnSchool of Geodesy and Geomatics, Wuhan University, Wuhan, ChinaKey Laboratory of Geospace Environment and Geodesy, Ministry of
Education, Wuhan University, Wuhan, ChinaCollaborative Innovation Center for Geospatial Technology, Wuhan,
ChinaYibin Yao (ybyao@whu.edu.cn)11January2017351879519October20168December20168December2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/35/87/2017/angeo-35-87-2017.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/35/87/2017/angeo-35-87-2017.pdf
The spatio-temporal distribution of atmospheric water
vapour information plays a crucial role
in the establishment of modern numerical weather forecast models and
description of the different weather variations. A troposphere tomographic
method has been proposed considering the signal rays penetrating from the
side of the area of interest to solve the problem of the low utilisation rate
of global navigation satellite system (GNSS) observations. Given the method
above needs the establishment of a unit scale factor model using the
radiosonde data at only one location in the research area, an improved
approach is proposed by considering the reasonability of modelling data and
the diversity of the modelling parameters for building a more accurate unit
scale factor model. The new established model is established using grid point
data derived from the European Centre for Medium-Range Weather Forecasts
(ECMWF) and evenly distributed in the tomographic area, which can enhance the
number of calculated initial water vapour density values with high accuracy.
We validated the improved method with respect to the previous methods, as
well as the result from a radiosonde using data from 12 stations from the
Hong Kong Satellite Positioning Reference Station Network. The obtained
result shows that the number of initial values estimated by the new model is
increased by 6.83 %, while the internal and external accuracies are 0.08
and 0.24 g m-3, respectively. Integrated water vapour (IWV) and water
vapour density profile comparisons show that the improved method is superior
to previous studies in terms of RMS, MAE, and bias, which suggests higher
accuracy and reliability.
Hydrology (water supply)Introduction
Atmospheric water vapour only accounts for a small proportion of total
atmospheric volume, but it plays an important role in the formation of clouds
and rainfall, as well as the evolution of weather systems (Liu et al., 2005;
Wang et al., 2014). Knowing precise information about the spatio-temporal
distribution of water vapour is a prerequisite for atmospheric research
(Emanuel et al., 1995; Park et al., 1999; Bauer et al., 2011; Ducroco et al.,
2002). With the rapid development of the global navigation satellite system
(GNSS), the GNSS troposphere tomographic technique has become a potentially
powerful method for obtaining three-dimensional distributions of water vapour
with high spatio-temporal resolution (Braun, et al., 1999; Flores et al.,
2000; Troller, et al., 2002; Nilsson and Gradinarsky, 2006; Perler et al.,
2011; Brenot et al., 2014; Yao and Zhao, 2016). In recent years, the
integration of GNSS data and NWP has given better results in the field of
GNSS meteorology (Douša and Václavovic, 2014; Douša et al., 2016;
Wilgan et al., 2016).
The concept of tropospheric tomography was first proposed with the use of
low-cost L1 observations (Braun et al., 1999) and realised by Flores et
al. (2000) with GPS dual-frequency observations, which marks the beginning of
tomographic techniques for GNSS and its applications to meteorology.
Tropospheric tomography is used to discretise the tomographic area into a
large number of voxels and established the integral equation using the signal
observations which cross the whole tomographic area (Flores et al., 2000). In
addition, some constraint conditions are also imposed on the tomographic
modelling so as to overcome the ill-posed problem caused by the unfavourable
geometric distribution of ground-based receivers as well as the constellation
of the GNSS satellites (Flores et al., 2000; Skone and Houle, 2005; Nilsson
and Gradinarsky, 2006; Bender and Raabe, 2007; Brenot et al., 2014).
Recently, some external information was exploited which tries to improve the
initial fields used in tomographic modelling. The initial water vapour fields
calculated from COSMIC radio occultation data were used as initial values to
enhance the accuracy of iterative algorithms (Xia et al., 2013). Several
studies also verified that the performance of tomographic results has been
improved by superimposing the 2-D images of integrated water vapour (IWV)
derived from interferometric synthetic aperture radar (InSAR) (Heublein et
al., 2015; Benevides et al., 2015); however, only the observed signal rays
penetrating from the top boundary of the area of interest were used to build
the observation equation in previous studies for the most previous studies.
Notarpietro et al. (2011) propose a method to calculate the value of signal
slant water vapour (SWV) outside the tomographic area with ECMWF data, while Benevides et
al. (2014) propose the geometric linear method using the empirically
exponential negative function. Chen and Liu (2016) estimate the slant wet
delay (SWD) outside the modelling area with the help of numerical weather
prediction (NWP) profile data. Yao et al. (2016) proposed a method which also
considers the signals penetrating from the side face of the research area by
introducing the unit scale factor model, while the unit scale factor refers
to the proportion between the value of signal SWV inside the tomographic area
and the total value of this signal SWV. This method proposed above enhanced
the utilisation rate of signal observations as well as the number of voxels
crossed by satellite rays. To improve the accuracy of the method proposed
above, a more sophisticated unit scale factor model is reconstructed from the
point of selection of modelling data and modelling parameters. The
experimental results show that the tomographic result using the new unit
scale factor model is superior to those methods outlined in previous studies.
An improved method for tropospheric tomography
In this section, an improved method of using the signals penetrating from the
side face of the area of interest was introduced. According to a previous
study (Yao et al., 2016), the values of the unit scale factor of each voxel
in every layer was first calculated using existing radiosonde data in the
first 3 days of the tomographic epoch and SWV signals penetrating from
the top of research area. As shown by the green voxels in Fig. 1, the unit
scale factor of each voxel for the location of the radiosonde station was
calculated based on the formula
γpk=ρijk0SWVp,
where γpk is the unit scale factor of the kth layer for
signal p, ρijk0 represents the initial water vapour value
calculated using radiosonde data in the first three days of the tomographic
epoch, and SWVp is the total slant water vapour content of ray p.
Then, the unit scale factor model of every voxel for the location of the
radiosonde station can be expressed and regarded as thus establishing the
model as the new representation of the whole layer:
γelek=a1k+a2k⋅sin(ele),
where γelek is the established unit scale factor model for
the kth layer based on the data calculated in Eq. (1); a1 and a2 are
the coefficients of the unit scale factor model, which are estimated by the
least squares method; and “ele” denotes the elevation angle of the signal
ray. Finally, the average initial water vapour density value of voxels in
which the radiosonde station is not located can be obtained.
Schematic of the improved method for building the unit scale factor
model.
However, there are two points worth noting about the proposed method.
(a) From Eq. (1), only those data from the location of the radiosonde station
were considered as being modelling data. For some cases, the established
model may offer good accuracy because the atmospheric water vapour is
relatively stable within a small research area (Rius et al., 1997); however,
if the radiosonde station is located at the side of the area of interest, the
accuracy of the established unit scale factor model may not be suitable for
the whole tomography area and, even worse, the method proposed above cannot be
used if the radiosonde data are unavailable or there are no radiosonde
stations within the tomographic area. In addition, the temporal resolution of
radiosonde data is low, as it is only obtained at 00:00 and 12:00 UTC.
(b) It can be seen from Eq. (2) that only the elevation angle was considered
in previous studies, which may not be able to reflect the characteristics of
the unit scale factor in its entirety.
Therefore, the research here was designed to overcome such deficiencies. To
solve the first problem, the data from the European Centre for Medium-Range
Weather Forecasts were introduced: this can provide global reanalysis data for
variables such as temperature and pressure. In our study, the
modelling data derived from the radiosonde were replaced by the layered data
derived from ECMWF with a minimum spatial resolution of 0.125∘×0.125∘, while the temporal resolution was four times per day
at 00:00, 06:00, 12:00, and 18:00 UTC, respectively. It can be observed from
Fig. 1 that the ECMWF grid points are evenly distributed across the
tomographic area, which will guarantee the accuracy of the unit scale factor
model for the whole area. In addition, the temporal resolution is higher than
that of the radiosonde data, the latter being obtained only twice a day. For
the second issue, by analysing Eq. (1), we found that the unit scale factor
was also subjected to SWV. In addition, the travel distances of SWV rays are
different for different voxels. Therefore, the improved unit scale factor
model is proposed and expressed as
γk=a1k+a2k⋅sin(ele)+a3k⋅(1/SWVp)+a4k⋅(1/dijkp),
where a1k-a4k are the coefficients of unit scale factor
model and dijkp is the distance of signal p in voxel (i,j,k).
For the satellite rays crossing from the top of the tomographic area, the
observation equation can be expressed in linear form:
SWV=∑dijk⋅xijk,
where dijk is the distance travelled by the signal ray in voxel
(i,j,k), which can be calculated based on the intersections between the
satellite ray and the two side faces of voxel (i,j,k), and xijk is
the water vapour density of voxel (i,j,k).
Although the signals coming out from the side of the research area were used,
some voxels remained uncrossed by satellite rays due to the influence of the
geometric distribution of receivers as well as the constellation of the GNSS
satellites. Therefore, constraint conditions between the voxels for
horizontal and vertical directions are still needed (Flores et al., 2000;
Troller et al., 2002; Bender and Raabe, 2007). In our study, the
Gauss-weighted function was used to describe the relationship of voxels
aligned in a horizontal direction based on the knowledge that the water
vapour density is relatively stable within a small area (Rius et al., 1997;
Song et al., 2004). The empirical negative exponential function was exploited
to restrict the values of voxels aligned in a vertical direction (Flores et
al., 2000). Consequently, the final tomographic modelling of the improved
method can be expressed as
yl1×1ρl2×10l3×10l4×1=Al1×n1Asl2×n1Hl3×n1Vl4×n1⋅Xn1×1,
where l1–l4 are the number of observation equations, initial water
vapour density equation, horizontal equation, and vertical equation,
respectively; n1 is the number of voxels in the tomography area; H
and V are the coefficient matrices of horizontal and vertical
constraints, respectively; and As is the coefficient matrix
representing the initial equation. The initial values which cannot be
calculated in Eq. (3) are then set to a value of zero.
Geographic distribution of ground-based GPS, and radiosonde,
stations in the research area.
Geographic coordination of ECMWF grid points located in the research
area.
NumberLongitude (∘)Latitude (∘)NumberLongitude (∘)Latitude (∘)B1L1113.87522.250B2L3114.12522.375B1L2114.00022.250B2L4114.25022.375B1L3114.12522.250B3L1113.87522.500B1L4114.25022.250B3L2114.00022.500B2L1113.87522.375B3L3114.12522.500B2L2114.00022.375B3L4114.25022.500Experiment and analysisExperiment description and data-processing strategy
The improved, proposed method was validated using the data from 12 stations
(as shown by the black triangles in Fig. 2) from the Hong Kong Satellite
Positioning Reference Station Network (SatRef) for the period of 25 March to
25 April 2014. The tomographic range is from 113.87 to 114.35 and 22.19 to
22.54 in longitude and latitude directions, respectively, while the
tomography height is selected as 8 km. The steps of longitude, latitude, and
height are 0.06∘, 0.05∘, and 0.8 km, respectively.
Therefore, a total of 7×8×10 voxels are discretised for the
tomographic area. As shown by the black circle in Fig. 2, there is a
radiosonde station (45004) located in the research
area for which the sounding balloon is launched twice a day at 00:00 and
12:00 UTC, respectively. In addition, as shown by the black rectangles in
Fig. 1, there are 12 ECMWF grid points evenly distributed in the area of
interest: further geographical information is given in Table 1.
In the present study, the GPS data were processed using GAMIT/GLOBK (v. 10.5)
(Herring et al., 2010) software at a sampling interval of 30 s. The wet
Niell mapping function was used (Niell, 1996) to project the SWD. The intervals of zenith total delay (ZTD) and wet horizontal gradients
were estimated as being 0.5 and 2 h, respectively. To obtain the absolute
tropospheric parameters, three International GNSS Service (IGS) stations
(SHAO, LHAZ, and BJFS) were also used in GPS data resolution (Rocken et al.,
1995; Yao and Zhao, 2016). During the conversion from SWD to SWV (Bevis et
al., 1992), the weighted mean tropospheric temperature was calculated based
on the empirical formula proposed by Chen et al. (2007) using the observed
surface temperature.
To compare the performance of the improved method, three methods are used in
this tomographic modelling.Method 1:
only using the signals penetrating from the top of research area
to build the observation equation, and superimposing the horizontal and
vertical equations mentioned in Sect. 2.
Method 2:
apart from the tomographic modelling established by method 1, the
signals crossing from the side face of the tomographic area were also used
with the old unit scale factor model established from radiosonde data to
build the initial equation.
Method 3:
apart from the tomographic modelling established by method 1, the
signals crossing from the side face of the tomographic area were also used
with the new unit scale factor model established in this paper based on
ECMWF grid points data to build the initial equation.
Analysis of the new unit scale factor model
It can be seen from Figs. 3 and 4 that the number of signals used and the
number of voxels crossed by satellite rays are the same for methods 2 and 3,
while that for method 1 is relatively small for the tested period, with an
interval of 30 min used throughout. When the signals crossing the side face
of the area were used, the signal utilisation rate was increased by
32.84 %, while the number of voxels traversed by rays was improved by
14.09 %, from 64.65 to 78.74 %. However, by comparing the number of
initial water vapour density values (see Fig. 5) which we can calculate for
methods 2 and 3, we found that the number of initial values calculated of
water vapour density from method 2 is less than that of method 3. This is
because not all the unit scale factor model data can be established for every
layer of the tomographic area based on the old model using radiosonde data.
However, the improved method enabled the new unit scale factor model
to be established for every layer by using the data from ECMWF grid points.
The number of signals used for different methods in the experiment.
The number of voxels crossed by rays for different methods in the
experiment.
The number of initial water
vapour density values derived from methods 2
and 3 in the experiment.
Internal accuracy of the unit scale factor models used for methods 2
and 3 in the experiment.
External accuracy of the unit scale factor models used for methods 2
and 3 in the experiment.
To validate further the new unit scale factor model, a comparison of the
accuracy comparison of methods 2 and 3 was performed below. On the one hand,
the RMS errors in water vapour density differences derived from the old/new
unit scale factor mode established above and radiosonde/ECMWF data used to
build the unit scale model were calculated to evaluate the internal accuracy
of the two models. On the other hand, the external accuracies of two models
were also calculated, the initial water vapour density values calculated from
the old unit scale factor model was compared with that from radiosonde data
of the tomographic epoch at 00:00 and 12:00 UTC every day, while the new unit
scale factor model was compared with that from ECMWF data of the tomographic
epoch at 00:00, 06:00, 12:00, and 18:00 UTC on each day. Figures 6 and 7
show the internal accuracy and external accuracy for both unit scale factor
models used in methods 2 and 3 throughout the experiment. It can be seen that
the new unit scale factor model of the improved method has a higher
internal/external accuracy than that of the old unit scale factor model in
the previous study. Numerical results show that the average RMS errors of
internal/external accuracy for the old/new unit scale factor models were
0.34/0.08 and 1.64/0.24 g m-3, respectively. Table 2 lists the
statistical result of accuracy evaluation for the old/new unit scale factor
models.
Statistical result of RMS error for the old/new unit scale factor
models used by the conventional and improved methods in the experiment
(g m-3).
MethodInternal accuracy External accuracy MeanMaxMinMeanMaxMin20.341.260.071.642.500.7830.080.570.040.240.580.22Comparison with water vapour information derived from the
radiosonde
As mentioned by previous studies, the radiosonde can provide accurate water
vapour density profiles at different altitudes (Niell, 2001; Adeyemi and
Joerg, 2012; Liu et al., 2013), which makes it suitable for use as a
reference against which to assess the accuracy of the tomographic result. The
integrated water vapour (IWV) value for the location of the radiosonde
station was calculated using the water vapour density of voxels derived from
different tomographic results and compared with that from the radiosonde data
at 00:00 and 12:00 UTC, respectively. It can be seen (Fig. 8) that the IWV
time series derived from the three tomographic methods matched the radiosonde
data. The statistical results from the experimental period revealed that the
RMS/mean absolute error (MAE)/bias values for three tomographic methods were
5.82/3.42/4.95, 5.02/2.40/4.16, and 4.91/2.62/4.13 mm, respectively.
Comparison of IWV time series derived from radiosonde and
different tomographic methods in the experiment.
The water vapour density profile for the location of radiosonde was analysed
for heights of up to 5 km because the largest atmospheric water vapour
content is included in this height range. Figure 9 shows the RMS error and
MAE of water vapour density differences between radiosonde and different
tomographic methods: the accuracies of methods 2 and 3 are superior to that
of method 1, which is because more observed data points were imposed onto the
tomographic model. Table 3 also lists the statistical results of RMS, MAE, and bias
for the three tomographic methods. The numerical results show that the
RMS/MAE/bias values of the three tomographic methods were 2.48/2.01/-0.18, 2.24/1.81/-0.16, and 1.67/1.34/-0.11 g m-3, respectively.
RMS error and MAE of water vapour density differences between
radiosonde and three tomographic methods in the experiment.
Statistical result of RMS, MAE, and bias for three tomographic
methods at height from 0 to 5 km in the experiment (g m-3).
MethodRMS MAE Bias MeanMaxMinMeanMaxMinMeanMaxMin12.484.791.052.013.760.83-0.180.93-0.8622.244.620.931.817.700.73-0.160.87-0.8031.674.130.261.343.440.20-0.110.81-0.76
In addition, the water vapour density profile comparison was also compared
again for heights of up to 8 km. Figures 10 and 11 show the histograms of
RMS and MAE for the three tomographic methods used. Table 4 lists the
statistical results (RMS, MAE, and bias) for the three tomographic methods. It can
be seen from Figs. 10 and 11 that the accuracy of the improved method is the
best, while that of method 2 was second best, thus showing that the new unit
scale factor model of the improved method is better than the old model used
by method 2. Numerical results reveal that the RMS/MAE/bias values for the three
tomographic methods were 1.79/1.16/-0.77, 1.61/1.04/-0.53, and
1.19/0.76/-0.26 g m-3, respectively.
Histogram of RMS error for different tomographic areas in the
experiment.
Histogram of MAE for different tomographic areas in the experiment.
RMS and relative error change with height for three tomographic
methods from 25 March to 25 April 2014.
Statistical result of RMS, MAE, and bias for three tomographic
methods at heights from 0 to 8 km in the experiment (g m-3).
MethodRMS MAE Bias MeanMaxMinMeanMaxMinMeanMaxMin11.792.820.821.162.000.59-0.772.20-2.5421.612.750.751.041.900.56-0.532.13-2.4831.192.390.580.761.280.42-0.261.72-1.74
Linear regression of water vapour density derived from radiosonde
and three tomography methods in the experiment.
The water vapour density profiles at different altitudes were also compared
to investigate the relationship between the different tomographic model
errors and height. The average RMS error and relative error at different
layers for three tomographic models were calculated for the period from
25 March to 25 April 2014. Fig. 12 shows the RMS and relative error changes
with height throughout the experimental period. It can be seen from Fig. 12
that the RMS error, in general, decreased with altitude, while the relative
error showed the opposite trend. The RMS error and relative error of the
improved method, in general, were smaller than those of methods 1 and 2,
which also demonstrated that the new unit scale factor model in the improved
method was superior to the previous version.
The water vapour density values were sampled randomly over the test period of
32 days and then compared with values calculated using radiosonde data. In
our study, 300 sampled values were determined for each of the three
tomographic methods. Figure 13 shows the linear regression on the water
vapour density for the three methods. From the sampled data it may be
concluded that the improved method proposed in this paper showed the best
regression result compared to that of methods 1 and 2. The RMS errors of
water vapour density differences of method 1-radiosonde, method 2-radiosonde,
and method 3-radiosonde for the sampled data were
2.23, 2.03, and 1.52 g m-3, respectively.
Conclusions
A new unit scale factor model was proposed using the layered data provided by
ECMWF, which considered the reasonability of selecting modelling data as well
as the modelling parameters. We analysed the accuracy of this new unit scale
factor model and validated the tomographic result of the improved method. The
GPS observations from 12 stations forming the Hong Kong Satellite
Positioning Reference Station Network were used for the period of 25 March to
25 April 2014. By analysing the initial water vapour density values, which
were calculated by the unit scale factor model, we found that the new model
proposed in this paper enhanced the number of initial values estimated by
6.83 %. The internal/external accuracies of the new unit scale factor
model were analysed: the new model was superior to the model used in a
previous study. Comparing the IWV time series with that from radiosonde data,
it was found that the RMS, MAE, and bias of the improved method were
4.91, 2.62, and 4.13 mm, respectively, which were smaller than those of previous methods. The
statistical results of water vapour density between radiosonde and different
tomographic methods over the 32-day test period also showed that the improved
method offered an improved performance. In addition, the RMS error and
relative error showed completely opposite trends with changing height.
Overall, the improved tomography method using the new unit scale factor model
has enhanced the accuracy of tomographic result by 33.5 and 26.1 %,
respectively, when compared to the previous studies (methods 1 and 2). With
the continuous improvement of the GNSS network, more satellite signals will
be used and more voxels will be crossed by rays. Furthermore, some other
observations derived from interferometric synthetic aperture radar (InSAR) or
COSMIC radio occultation data can also be used for the troposphere tomography,
either directly or indirectly. It is expected that tropospheric tomography
with higher-quality water vapour information will be obtained in the near
future.
Data availability
The GPS observation and meteorological data can be download from the Lands
Department of HKSAR (https://www.geodetic.gov.hk/smo/index.htm). The
radiosonde data sets and ECMWF grid data sets are available from the websites
of ftp://ftp.ncdc.noaa.gov/pub/data/igra/ and
http://apps.ecmwf.int/datasets/, respectively.
Acknowledgements
The authors would like to thank IGAR and ECMWF for providing access to the
web-based IGAR and layered meteorological data. The Lands Department of HKSAR
is also acknowledge for providing GPS data from the Hong Kong Satellite
Positioning Reference Station Network (SatRef). This research was supported
by the National Key Research and Development Program of China
(2016YFB0501803) and the National Natural Science Foundation of China
(41574028). The topical editor,
M. Salzmann, thanks J. Bosy and one anonymous referee for help in evaluating
this paper.
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