An improved pixel-based water vapor tomography model

Abstract. As an innovative use of Global Navigation Satellite System (GNSS), the GNSS water vapor tomography technique shows great potential in monitoring three-dimensional water vapor variation. Most of the previous studies employ the pixel-based method, i.e., dividing the troposphere space into finite voxels and considering water vapor in each voxel as constant. However, this method cannot reflect the variations in voxels and breaks the continuity of the troposphere. Moreover, in the pixel-based method, each voxel needs a parameter to represent the water vapor density, which means that huge numbers of parameters are needed to represent the water vapor field when the interested area is large and/or the expected resolution is high. In order to overcome the abovementioned problems, in this study, we propose an improved pixel-based water vapor tomography model, which uses layered optimal polynomial functions obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) by adaptive training for water vapor retrieval. Tomography experiments were carried out using the GNSS data collected from the Hong Kong Satellite Positioning Reference Station Network (SatRef) from 25 March to 25 April 2014 under different scenarios. The tomographic results are compared to the ECMWF data and validated by the radiosonde. Results show that the new model outperforms the traditional one by reducing the root-mean-square error (RMSE), and this improvement is more pronounced, at 5.88 % in voxels without the penetration of GNSS rays. The improved model also has advantages in more convenient expression.

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A Regional Zenith Tropospheric Delay (ZTD) Model Based on GPT3 and ANN

Remote Sensing ◽

10.3390/rs13050838 ◽

2021 ◽

Vol 13 (5) ◽

pp. 838

Author(s):

Fei Yang ◽

Jiming Guo ◽

Chaoyang Zhang ◽

Yitao Li ◽

Jun Li

Keyword(s):

Satellite System ◽

Reference Station ◽

Tropospheric Delay ◽

Neutral Atmosphere ◽

Zenith Tropospheric Delay ◽

Satellite Positioning ◽

Proposed Model ◽

Radio Signals ◽

Global Navigation Satellite ◽

Gnss Data

The delays of radio signals transmitted by global navigation satellite system (GNSS) satellites and induced by neutral atmosphere, which are usually represented by zenith tropospheric delay (ZTD), are required as critical information both for GNSS positioning and navigation and GNSS meteorology. Establishing a stable and reliable ZTD model is one of the interests in GNSS research. In this study, we proposed a regional ZTD model that makes full use of the ZTD calculated from regional GNSS data and the corresponding ZTD estimated by global pressure and temperature 3 (GPT3) model, adopting the artificial neutral network (ANN) to construct the correlation between ZTD derived from GPT3 and GNSS observations. The experiments in Hong Kong using Satellite Positioning Reference Station Network (SatRet) were conducted and three statistical values, i.e., bias, root mean square error (RMSE), and compound relative error (CRE) were adopted for our comparisons. Numerical results showed that the proposed model outperformed the parameter ZTD model (Saastamoinen model) and the empirical ZTD model (GPT3 model), with an approximately 56%/52% and 52%/37% RMSE improvement in the internal and external accuracy verification, respectively. Moreover, the proposed method effectively improved the systematic deviation of GPT3 model and achieved better ZTD estimation in both rainy and rainless conditions.

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An Adaptive Non-Uniform Vertical Stratification Method for Troposphere Water Vapor Tomography

Remote Sensing ◽

10.3390/rs13193818 ◽

2021 ◽

Vol 13 (19) ◽

pp. 3818

Author(s):

Hao Wang ◽

Nan Ding ◽

Wenyuan Zhang

Keyword(s):

Water Vapor ◽

Exponential Distribution ◽

Weather Prediction ◽

Satellite System ◽

Vertical Stratification ◽

Reference Station ◽

Specific Calculation ◽

Satellite Positioning ◽

Stratification Method ◽

Global Navigation Satellite

Global Navigation Satellite System (GNSS) water vapor tomography provides a four-dimensional (4-D) distribution of water vapor in the atmosphere for weather monitoring. It has developed into a widely used technique in numerical weather prediction (NWP). Vertical stratification is essential in discretizing the tomographic region. Traditional discretization methods divide the tomographic area into regular voxels with an equal height interval, which ignores the dynamic exponential distribution of water vapor. In recent years, non-uniform stratification methods have been widely validated by tomographic experiments. However, such experiments have not proposed a specific calculation method for stratification thickness. Therefore, in this paper, we introduced an adaptive non-uniform stratification method that follows the exponential distribution of water vapor in the tomographic region and presented the process of iterative calculation to acquire the optimal stratification interval. The proposed approach was applied based on the exponential decreasing trend in water vapor with increasing altitude. Moreover, it could adaptively calculate the interval of stratification height according to water vapor content. The tomographic experiments were performed using Global Positioning System (GPS) data from 19 ground-based stations in the Hong Kong Satellite Positioning Reference Station Network (SatRef) from 1 to 31 August 2019. The results indicated that, compared to the traditional stratification method, the root mean square error derived from the proposed approach was reduced by 0.26 g/m3. Additionally, severe weather can negatively affect the accuracy of the tomographic results. The results also showed that the accuracy of the tomographic results was reduced with increasing altitude. Moreover, the performance of the tomographic water vapor fields below 3000 m was improved by the proposed approach.

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Subsidence determination in the Central Valley, California

Reports on Geodesy and Geoinformatics ◽

10.2478/rgg-2018-0012 ◽

2018 ◽

Vol 106 (1) ◽

pp. 35-42 ◽

Cited By ~ 1

Author(s):

Marcelo Romero ◽

Mike Mustafa Berber

Keyword(s):

Central Valley ◽

Satellite System ◽

Geodetic Survey ◽

Reference Station ◽

National Geodetic Survey ◽

The North ◽

Elevation Changes ◽

System Data ◽

Global Navigation Satellite ◽

Gnss Data

Abstract Twenty four hour GNSS (Global Navigation Satellite System) data acquired monthly for 5 years from 8 CORS (Continuously Operating Reference Station) stations in Central Valley, California are processed and vertical velocities of the points are determined. To process GNSS data, online GNSS data processing service APPS (Automatic Precise Positioning Service) is used. GNSS data downloaded from NGS (National Geodetic Survey) CORS are analyzed and subsidence at these points is portrayed with graphics. It is revealed that elevation changes range from 5 mm uplift in the north to 163 mm subsidence in the southern part of the valley.

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A Tropospheric Tomography Method with a Novel Height Factor Model Including Two Parts: Isotropic and Anisotropic Height Factors

Remote Sensing ◽

10.3390/rs12111848 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1848 ◽

Cited By ~ 2

Author(s):

Wenyuan Zhang ◽

Shubi Zhang ◽

Nan Ding ◽

Qingzhi Zhao

Keyword(s):

Water Vapor ◽

Factor Model ◽

Traditional Approach ◽

Satellite System ◽

Spatiotemporal Variability ◽

Radiosonde Data ◽

Key Factor ◽

Improved Model ◽

Global Navigation Satellite ◽

Height Factor

Global Navigation Satellite System (GNSS) tomography has developed into an efficient tool for sensing the high spatiotemporal variability of atmospheric water vapor. The integration of GNSS top signals and side rays for tropospheric tomography systems using a novel height factor model (HFM) is proposed and discussed in this paper. Within the HFM, the sectional slant wet delay (SWD) of inside signals (the part of the side signal inside the tomography area), which is considered a key factor for modeling side rays, is separated into isotropic and anisotropic components. Correspondingly, two height factors are defined to calculate the isotropic and anisotropic part of tropospheric delays in the HFM. In addition, the dynamic tomography top boundary is first analyzed and determined based on 30-year radiosonde data to reasonably divide signals into top and side rays. Four special experimental schemes based on different tomography regions of Hong Kong are performed to assess the proposed HFM method, the results of which show increases of 33.42% in the mean utilization of rays, as well as decreases of 0.46 g/m3 in the average root mean square error (RMSE), compared to the traditional approach, revealing the improvement of tomography solutions when the side signals are included in the modeling. Furthermore, compared with the existing correction model for modeling side rays, the water vapor profiles retrieved from the proposed improved model are closer to the radiosonde data, which highlights the advantages of the proposed HFM for optimizing the GNSS tomography model.

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Towards operational multi-GNSS tropospheric products at GFZ Potsdam

Atmospheric Measurement Techniques ◽

10.5194/amt-15-21-2022 ◽

2022 ◽

Vol 15 (1) ◽

pp. 21-39

Author(s):

Karina Wilgan ◽

Galina Dick ◽

Florian Zus ◽

Jens Wickert

Keyword(s):

Positive Impact ◽

Satellite System ◽

Three Solutions ◽

Satellite Systems ◽

Weather Forecasts ◽

Preparation Step ◽

Global Navigation Satellite ◽

Gnss Data ◽

The Impact ◽

Comparable Quality

Abstract. The assimilation of global navigation satellite system (GNSS) data has been proven to have a positive impact on weather forecasts. However, the impact is limited due to the fact that solely the zenith total delays (ZTDs) or integrated water vapor (IWV) derived from the GPS satellite constellation are utilized. Assimilation of more advanced products, such as slant total delays (STDs), from several satellite systems may lead to improved forecasts. This study shows a preparation step for the assimilation, i.e., the analysis of the multi-GNSS tropospheric advanced parameters: ZTDs, tropospheric gradients and STDs. Three solutions are taken into consideration: GPS-only, GPS–GLONASS (GR) and GPS–GLONASS–Galileo (GRE). The GNSS estimates are calculated using the operational EPOS.P8 software developed at GFZ. The ZTDs retrieved with this software are currently being operationally assimilated by weather services, while the STDs and tropospheric gradients are being tested for this purpose. The obtained parameters are compared with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis. The results show that all three GNSS solutions show similar level of agreement with the ERA5 model. For ZTDs, the agreement with ERA5 results in biases of approx. 2 mm and standard deviations (SDs) of 8.5 mm. The statistics are slightly better for the GRE solution compared to the other solutions. For tropospheric gradients, the biases are negligible, and SDs are equal to approx. 0.4 mm. The statistics are almost identical for all three GNSS solutions. For STDs, the agreement from all three solutions is very similar; however it is slightly better for GPS only. The average bias with respect to ERA5 equals approx. 4 mm, with SDs of approx. 26 mm. The biases are only slightly reduced for the Galileo-only estimates from the GRE solution. This study shows that all systems provide data of comparable quality. However, the advantage of combining several GNSS systems in the operational data assimilation is the geometry improvement by adding more observations, especially for low elevation and azimuth angles.

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Reconstruction of Wet Refractivity Field Using an Improved Parameterized Tropospheric Tomographic Technique

Remote Sensing ◽

10.3390/rs12183034 ◽

2020 ◽

Vol 12 (18) ◽

pp. 3034

Author(s):

Biyan Chen ◽

Wujiao Dai ◽

Pengfei Xia ◽

Minsi Ao ◽

Jingshu Tan

Keyword(s):

Water Vapor ◽

Optimal Algorithm ◽

Satellite System ◽

Hunan Province ◽

Homogeneous Distribution ◽

Nonparametric Model ◽

Negative Effects ◽

Parameterized Model ◽

Improved Model ◽

Global Navigation Satellite

In most previous studies of tropospheric tomography, water vapor is assumed to have a homogeneous distribution within each voxel. The parameterization of voxels can mitigate the negative effects of the improper assumption to the tomographic solution. An improved parameterized algorithm is proposed for determining the water vapor distribution by Global Navigation Satellite System (GNSS) tomography. Within a voxel, a generic point is determined via horizontal inverse distance weighted (IDW) interpolation and vertical exponential interpolation from the wet refractivities at the eight surrounding voxel nodes. The parameters involved in exponential and IDW interpolation are dynamically estimated for each tomography by using the refractivity field of the last process. By considering the quasi-exponential behavior of the wet refractivity profile, an optimal algorithm is proposed to discretize the vertical layers of the tomographic model. The improved parameterization algorithm is validated with the observational data collected over a 1-month period from 124 Global Positioning System (GPS) stations of Hunan Province, China. Assessments by GPS, radiosonde, and European Centre for Medium-Range Weather Forecasts (ECMWF) ReAnalysis 5 (ERA5) data, demonstrate that the improved model outperforms the traditional nonparametric model and the parameterized model using trilinear interpolation. In the assessment by GPS data, the improved model performs better than the traditional model and the trilinear parameterized model by 54% and 10%, respectively. Such improvements are 31% and 10% in the validation by radiosonde profiles. In comparison with the ERA5 reanalysis, the improved model yields a minimum overall root mean square (RMS) error of 8.94 mm/km, while those of the traditional and trilinear parametrized models are 10.79 and 9.73 mm/km, respectively. The RMS errors vertically decrease from ~20 mm/km at the bottom to ~5 mm/km at the top layer.

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A New GNSS-Derived Water Vapor Tomography Method Based on Optimized Voxel for Large GNSS Network

Remote Sensing ◽

10.3390/rs12142306 ◽

2020 ◽

Vol 12 (14) ◽

pp. 2306 ◽

Cited By ~ 1

Author(s):

Yibin Yao ◽

Chen Liu ◽

Chaoqian Xu

Keyword(s):

Water Vapor ◽

Conventional Method ◽

Three Dimensional ◽

Absolute Error ◽

Satellite System ◽

Tomographic Method ◽

Tomography Method ◽

Gnss Network ◽

Global Navigation Satellite ◽

Gnss Networks

The Global Navigation Satellite System (GNSS) tomographic technique can be used for remote sensing of the three-dimensional water vapor (WV) distribution in the troposphere, which has attracted considerable interest. However, a significant problem in this technique is the excessive reliance on constraints (particularly in large GNSS networks). In this paper, we propose an improved tomographic method based on optimized voxel, which only considers the voxels passed by GNSS rays. The proposed method can completely prevent the tomographic algorithm interference of constraints that originated from empirical functions. Experiments in Nanjing in the periods of day-of-year (DOY) 182–184, 2019, and 244–246, 2019, show that the mean absolute error (MAE) and root mean square error (RMSE) of the WV density profile obtained using the proposed method are 0.9 and 1.3 g/m3, while those obtained using the conventional method are 1.3 and 1.8 g/m3, respectively, with respect to the radiosonde (RS) method. The numerical results show that the proposed method is reliable and has a superior accuracy to that of the conventional method.

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A Case Study of the 3D Water Vapor Tomography Model Based on a Fast Voxel Traversal Algorithm for Ray Tracing

Remote Sensing ◽

10.3390/rs13122422 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2422

Author(s):

Heng Hu ◽

Min Liu ◽

Jiqin Zhong ◽

Xin Deng ◽

Yunchang Cao ◽

...

Keyword(s):

Water Vapor ◽

Ray Tracing ◽

Three Dimensional ◽

Satellite System ◽

Horizontal Distribution ◽

Observation Data ◽

Vapor Density ◽

Average Deviation ◽

Global Navigation Satellite ◽

Traversal Algorithm

A fast voxel traversal algorithm for ray tracing was applied to build a 4 × 4 × 20 tomography model using the observation data of 11 ground-based Global Navigation Satellite System (GNSS) meteorology (GNSS/MET) stations in Hebei Province, China. The precipitation water vapor (PWV) observed at 05 a.m. (Universal Time Coordinated: UTC) on 10 December 2019, was used to reconstruct three-dimensional (3D) water vapor density fields over the test area. The tomographic results (GNSS_T) show that the water vapor density above this area is mainly below 25 g/m3 and is concentrated between the first to the fourth layers. The vertical distribution conforms to the exponential characteristics, while the horizontal distribution shows a decreasing trend from southwest to northeast. In addition, the results of the 0.25° grid dataset generated by the Global Forecast System (GFS) of the National Center for Environmental Forecasting (NCEP) (GFS_L) were interpolated to the height of the tomographic grid, which is in good agreement with the tomographic results. GFS_L is larger than GNSS_T on the first floor at the surface, with an average deviation of 0.19 g/m3. In contrast, GFS_L from the second floor to the top of the model is smaller than GNSS_T, with the average deviations distributed between −0.08 and −0.15 g/m3.

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Integrated water vapour content retrievals from ship-borne GNSS receivers during EUREC<sup>4</sup>A

Earth System Science Data ◽

10.5194/essd-13-1499-2021 ◽

2021 ◽

Vol 13 (4) ◽

pp. 1499-1517

Author(s):

Pierre Bosser ◽

Olivier Bock ◽

Cyrille Flamant ◽

Sandrine Bony ◽

Sabrina Speich

Keyword(s):

Water Vapour ◽

Satellite System ◽

Water Vapour Content ◽

Weather Forecasts ◽

Integrated Water Vapour ◽

Moderate Resolution ◽

Moderate Resolution Imaging Spectroradiometer ◽

Gnss Measurements ◽

Global Navigation Satellite ◽

Gnss Data

Abstract. In the framework of the EUREC4A (Elucidating the role of clouds–circulation coupling in climate) campaign that took place in January and February 2020, integrated water vapour (IWV) contents were retrieved over the open tropical Atlantic Ocean using Global Navigation Satellite System (GNSS) data acquired from three research vessels (R/Vs): R/V Atalante, R/V Maria S. Merian and R/V Meteor. This paper describes the GNSS processing method and compares the GNSS IWV retrievals with IWV estimates from the European Centre for Medium-range Weather Forecasts (ECMWF) fifth reanalysis (ERA5), from the Moderate Resolution Imaging Spectroradiometer (MODIS) infrared products and from terrestrial GNSS stations located along the tracks of the ships. The ship-borne GNSS IWV retrievals from R/V Atalante and R/V Meteor compare well with ERA5, with small biases (−1.62 kg m−2 for R/V Atalante and +0.65 kg m−2 for R/V Meteor) and a root mean square (rms) difference of about 2.3 kg m−2. The results for the R/V Maria S. Merian are found to be of poorer quality, with an rms difference of 6 kg m−2, which is very likely due to the location of the GNSS antenna on this R/V prone to multipath effects. The comparisons with ground-based GNSS data confirm these results. The comparisons of all three R/V IWV retrievals with MODIS infrared products show large rms differences of 5–7 kg m−2, reflecting the enhanced uncertainties in these satellite products in the tropics. These ship-borne IWV retrievals are intended to be used for the description and understanding of meteorological phenomena that occurred during the campaign, east of Barbados, Guyana and northern Brazil. Both the raw GNSS measurements and the IWV estimates are available through the AERIS data centre (https://en.aeris-data.fr/, last access: 20 September 2020). The digital object identifiers (DOIs) for R/V Atalante IWV and raw datasets are https://doi.org/10.25326/71 (Bosser et al., 2020a) and https://doi.org/10.25326/74 (Bosser et al., 2020d), respectively. The DOIs for the R/V Maria S. Merian IWV and raw datasets are https://doi.org/10.25326/72 (Bosser et al., 2020b) and https://doi.org/10.25326/75 (Bosser et al., 2020e), respectively. The DOIs for the R/V Meteor IWV and raw datasets are https://doi.org/10.25326/73 (Bosser et al., 2020c) and https://doi.org/10.25326/76 (Bosser et al., 2020f), respectively.

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Solving the Multilateration Problem without Iteration

Geomatics ◽

10.3390/geomatics1030018 ◽

2021 ◽

Vol 1 (3) ◽

pp. 324-334

Author(s):

Thomas H. Meyer ◽

Ahmed F. Elaksher

Keyword(s):

Three Dimensional ◽

Satellite System ◽

Simultaneous Equations ◽

Observation Equation ◽

Atmospheric Refraction ◽

Land Surveying ◽

Global Navigation Satellite ◽

Gnss Data ◽

Radio Beacon ◽

Taylor’S Series

The process of positioning, using only distances from control stations, is called trilateration (or multilateration if the problem is over-determined). The observation equation is Pythagoras’s formula, in terms of the summed squares of coordinate differences and, thus, is nonlinear. There is one observation equation for each control station, at a minimum, which produces a system of simultaneous equations to solve. Over-determined nonlinear systems of simultaneous equations are typically solved using iterative least squares after forming the system as a truncated Taylor’s series, omitting the nonlinear terms. This paper provides a linearization of the observation equation that is not a truncated infinite series—it is exact—and, thus, is solved exactly, with full rigor, without iteration and, thus, without the need of first providing approximate coordinates to seed the iteration. However, there is a cost of requiring an additional observation beyond that required by the non-linear approach. The examples and terminology come from terrestrial land surveying, but the method is fully general: it works for, say, radio beacon positioning, as well. The approach can use slope distances directly, which avoids the possible errors introduced by atmospheric refraction into the zenith-angle observations needed to provide horizontal distances. The formulas are derived for two- and three-dimensional cases and illustrated with an example using total-station and global navigation satellite system (GNSS) data.

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