A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products

Accurate tropospheric delay (TD) and weighted mean temperature (Tm) are important for Global Navigation Satellite System (GNSS) positioning and GNSS meteorology. For this purpose, plenty of empirical models have been built to provide estimates of TD and Tm. However, these models cannot resolve TD and Tm variations at synoptic timescales since they only model the average annual, semi-annual, and/or daily variations. As a result, the existed empirical models cannot perform well under extreme weather conditions. To address this limitation, we propose to estimate Zenith Hydrostatic Delay (ZHD), Zenith Wet Delay (ZWD), and Tm directly from the stratified numerical weather forecasting products of the mesoscale version of the Global/Regional Assimilation and PrEdiction System (GRAPES_MESO) of China. The GRAPES_MESO forecasting data has a temporal resolution of 3 h, which provides the opportunity to resolve the synoptic variation. However, it is found that the estimated ZWD and Tm exhibit apparent systematic deviation from in situ observation-based estimates, which is due to the inherent biases in the GRAPES_MESO data. To solve this problem, we propose to correct these biases using a linear model and a spherical cap harmonic model. The estimates after correction are termed as the “CTropGrid” products. When validated by the radiosonde data, the CTropGrid product has biases of 1.5 mm, −0.7 mm, and −0.1 K, and Root Mean Square (RMS) error of 8.9 mm, 20.2 mm, and 1.5 K for ZHD, ZWD, and Tm. Compared to the widely used GPT2w model, the CTropGrid products have improved the accuracies of ZHD, ZWD, and Tm by 11.9%, 55.6%, and 60.5% in terms of RMS. When validating the Zenith Tropospheric Delay (ZTD) products (the sum of ZHD and ZWD) using the IGS ZTD data, the CTropGrid ZTD has a bias of −0.7 mm and an RMS of 35.8 mm, which is 22.7% better than the GPT2w model in terms of RMS. Besides the accuracy improvements, the CTropGrid products well model the synoptic-scale variations of ZHD, ZWD, and Tm. Compared to the existing empirical models that only capture the tidal (seasonal and/or diurnal) variations, the CTropGrid products capture well the non-tidal variations of ZHD, ZWD, and Tm, which enhances the tropospheric delay corrections and GNSS water vapor monitoring at synoptic timescales. Therefore, the CTropGrid product is an important progress in GNSS positioning and GNSS meteorology.

A New GPT2w Model Improved by PSO-LSSVM for GNSS High-Precision Positioning

Tropospheric delay is an important error affecting GNSS high-precision navigation and positioning, which will decrease the precision of navigation and positioning if it is not well corrected. Actually, tropospheric delay, especially in the zenith direction, is related to a series of meteorological parameters, such as temperature and pressure. To estimate the zenith tropospheric delay (ZTD) as accurately as possible, the paper proposes a new fused model using the least squares support vector machines (LSSVM) and the particle swarm optimization (PSO) to improve the precision and temporal resolution of meteorological parameters in global pressure and temperature 2 wet (GPT2w). The proposed model uses the time series of meteorological parameters from the GPT2w model as the initial value, and thus, the time series of the residuals can be obtained between the meteorological parameters from meteorological sensors (MS) and the GPT2w model. The long time series of meteorological parameters is the evident periodic signal. The GPT2w model describes its dominant frequency (harmonics), and the residuals thus can be seen as the short-period signal (nonharmonics). The combined PSO and LSSVM model (PSO-LSSVM) is used to predict the specific value of the short-period signal. The new GPT2w model, in which the meteorological parameter value is obtained by combining the estimated meteorological parameters residuals and the GPT2w-derived meteorological parameters, can be acquired. The GNSS network stations in Hong Kong throughout 2017-2018 are processed by the GNSS Processing and Analysis Software (GPAS), which is developed by the Chinese Academy of Surveying & Mapping, to estimate the zenith tropospheric delay and station coordinates using the new GPT2w model. Statistical results reveal that the accuracy of the new GPT2w model-derived ZTD was improved by 60% or more compared with that of the GPT2w-derived ZTD. In addition, the positioning accuracy of the GNSS station has been effectively improved up to 44.89%. Such results reveal that the new GPT2w model can greatly reduce the influence of nonharmonic components (short-period terms) of the meteorological parameter time series and achieve better accuracy than the GPT2w model.

A Refined Regional Model for Estimating Pressure, Temperature, and Water Vapor Pressure for Geodetic Applications in China

Pressure, temperature, and water vapor pressure are basic meteorological parameters that are frequently required in Global Navigation Satellite System (GNSS) positioning/navigation and GNSS meteorology. Although models like Global Pressure and Temperature (GPT) and Global Pressure and Temperature 2 wet (GPT2w) were developed for these demands, their spatial resolutions are lower than 0.75° and temporal resolutions are below 6 h, which limits their achievement. The publication of European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 hourly 0.25° × 0.25° data offers the opportunity to lift this limitation. In this work, the ERA5 surface data are used to evaluate the temporal variabilities of pressure, temperature, and water vapor pressure in the area of China. We characterize their diurnal variations using hourly data and take into account their geographical variations by 0.25° × 0.25° grids. In addition, we improve the height corrections for the three parameters employing the ERA5 pressure level data. Through these efforts, we build a new regional model named Chinese pressure, temperature, and water vapor pressure (CPTw), which has the advanced resolution of 0.25° × 0.25° and temporal resolution of 1 h. We evaluate the performance using ERA5 data and radiosonde data compared with the approved GPT2w model. Results demonstrate that the accuracies of the new model are superior to the GPT2w model in all meteorological parameters. The validation with the radiosonde data shows RMS for pressure, temperature, and water vapor pressure of the CPTw model is reduced by 14.1%, 25.8%, and 4.8%, compared with that of the GPT2w model. The new model catches especially well the diurnal changes in pressure, temperature, and water vapor pressure, which have never been realized before. Since the CPTw model can provide accurate empirical pressure, temperature, and water vapor pressure for any time and location in China and its surrounding areas, it can not only meet the need of empirical meteorological parameters in real-time geodetic applications like GNSS positioning and navigation, but it is also useful for GNSS meteorology.

A Global Model for Estimating Tropospheric Delay and Weighted Mean Temperature Developed with Atmospheric Reanalysis Data from 1979 to 2017

Precise modeling of tropospheric delay and weighted mean temperature (Tm) is critical for Global Navigation Satellite System (GNSS) positioning and meteorology. However, the model data in previous models cover a limited time span, which limits the accuracy of these models. Besides, the vertical variations of tropospheric delay and Tm are not perfectly modeled in previous studies, which affects the performance of height corrections. In this study, we used the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis from 1979 to 2017 to build a new empirical model. We first carefully modeled the lapse rates of tropospheric delay and Tm. Then we considered the temporal variations by linear trends, annual, and semi-annual variations and the spatial variations by grids. This new model can provide zenith hydrostatic delay (ZHD), zenith wet delay (ZWD), and Tm worldwide with a spatial resolution of 1° × 1°. We used the ECMWF ERA-Interim data and the radiosonde data in 2018 to validate this new model in comparison with the canonical GPT2w model. The results show that the new model has higher accuracies than the GPT2w model in all parameters. Particularly, this new model largely improves the accuracy in estimating ZHD and Tm at high-altitude (relative to the grid point height) regions.

Establishment and Assessment of a New GNSS Precipitable Water Vapor Interpolation Scheme Based on the GPT2w Model

With the development of Global Navigation Satellite System (GNSS) reference station networks that provide rich data sources containing atmospheric information, the precipitable water vapor (PWV) retrieved from GNSS remote sensing has become one of the most important bodies of data in many meteorological departments. GNSS stations are distributed in the form of scatters, generally, these separations range from a few kilometers to tens of kilometers. Therefore, the spatial resolution of GNSS-PWV can restrict some applications such as interferometric synthetic aperture radar (InSAR) atmospheric calibration and regional atmospheric water vapor analysis, which inevitably require the spatial interpolation of GNSS-PWV. This paper explored a PWV interpolation scheme based on the GPT2w model, which requires no meteorological data at an interpolation station and no regression analysis of the observation data. The PWV interpolation experiment was conducted in Hong Kong by different interpolation schemes, which differed in whether the impact of elevation was considered and whether the GPT2w model was added. In this paper, we adopted three skill scores, i.e., compound relative error (CRE), mean absolute error (MAE), and root mean square error (RMSE), and two approaches, i.e., station cross-validation and grid data validation, for our comparison. Numerical results showed that the interpolation schemes adding the GPT2w model could greatly improve the PWV interpolation accuracy when compared to the traditional schemes, especially at interpolation points away from the elevation range of reference stations. Moreover, this paper analyzed the PWV interpolation results under different weather conditions, at different locations, and on different days.

Development of time-varying global gridded <i>T</i>_s–<i>T</i>_m model for precise GPS–PWV retrieval

Water-vapor-weighted mean temperature, Tm, is the key variable for estimating the mapping factor between GPS zenith wet delay (ZWD) and precipitable water vapor (PWV). For the near-real-time GPS–PWV retrieval, estimating Tm from surface air temperature Ts is a widely used method because of its high temporal resolution and fair degree of accuracy. Based on the estimations of Tm and Ts at each reanalysis grid node of the ERA-Interim data, we analyzed the relationship between Tm and Ts without data smoothing. The analyses demonstrate that the Ts–Tm relationship has significant spatial and temporal variations. Static and time-varying global gridded Ts–Tm models were established and evaluated by comparisons with the radiosonde data at 723 radiosonde stations in the Integrated Global Radiosonde Archive (IGRA). Results show that our global gridded Ts–Tm equations have prominent advantages over the other globally applied models. At over 17 % of the stations, errors larger than 5 K exist in the Bevis equation (Bevis et al., 1992) and in the latitude-related linear model (Y. B. Yao et al., 2014), while these large errors are removed in our time-varying Ts–Tm models. Multiple statistical tests at the 5 % significance level show that the time-varying global gridded model is superior to the other models at 60.03 % of the radiosonde sites. The second-best model is the 1∘ × 1∘ GPT2w model, which is superior at only 12.86 % of the sites. More accurate Tm can reduce the contribution of the uncertainty associated with Tm to the total uncertainty in GPS–PWV, and the reduction augments with the growth of GPS–PWV. Our theoretical analyses with high PWV and small uncertainty in surface pressure indicate that the uncertainty associated with Tm can contribute more than 50 % of the total GPS–PWV uncertainty when using the Bevis equation, and it can decline to less than 25 % when using our time-varying Ts–Tm model. However, the uncertainty associated with surface pressure dominates the error budget of PWV (more than 75 %) when the surface pressure has an error larger than 5 hPa. GPS–PWV retrievals using different Tm estimates were compared at 74 International GNSS Service (IGS) stations. At 74.32 % of the IGS sites, the relative differences of GPS–PWV are within 1 % by applying the static or the time-varying global gridded Ts–Tm equations, while the Bevis model, the latitude-related model and the GPT2w model perform the same at 37.84 %, 41.89 % and 29.73 % of the sites. Compared with the radiosonde PWV, the error reduction in the GPS–PWV retrieval can be around 1–2 mm when using a more accurate Tm parameterization, which accounts for around 30 % of the total GPS–PWV error.