The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay

Qiu, Cong; Wang, Xiaoming; Li, Zishen; Zhang, Shaotian; Li, Haobo; Zhang, Jinglei; Yuan, Hong

doi:10.3390/rs12010130

Cited by 25 publications

(15 citation statements)

References 72 publications

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“…Our results show similar error levels for the VMF1 mapping function and similar unmodeled seasonal signatures when compared to results from similar assessment studies of Niell Mapping Function (NMF), Global Mapping Function (GMF), and VMF mapping functions [20][21][22][23]. Unlike the significant leap seen between the NMF and the VMF1 mapping functions, however, there is no significant advantage to switch from the VMF1 to the VMF3 mapping functions, even though VMF3 adopts a more accurate atmosphere data source and fitting strategy.…”

Section: Discussionsupporting

confidence: 70%

“…Similar studies have been done to assess the accuracy of other mapping functions by comparison with ray-tracing results [20][21][22][23]. Qiu et al [23] showed that VMF1 corresponds to the ERA-I numerical weather model better than the Niell Mapping Function [24] and the Global Mapping Function [25] at low elevation angles. Other studies rely on positioning or baseline length accuracies [16,26].…”

Section: Introductionmentioning

confidence: 88%

“…A preliminary evaluation showed that the VMF3 improvements have little impact on GNSS positioning, with estimated station height changing at a merely 0.25 mm level [14]. Similar studies have been done to assess the accuracy of other mapping functions by comparison with ray-tracing results [20][21][22][23]. Qiu et al [23] showed that VMF1 corresponds to the ERA-I numerical weather model better than the Niell Mapping Function [24] and the Global Mapping Function [25] at low elevation angles.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

Feng

Yan

et al. 2020

Remote Sensing

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In this paper, we assess, in the framework of Global Navigation Satellite System (GNSS) meteorology, the accuracy of GNSS propagation delays corresponding to the Saastamoinen zenith hydrostatic delay (ZHD) model and the Vienna Mapping function VMF1/VMF3 (hydrostatic and wet), with reference to radiosonde ray-tracing delays over a three-year period on 28 globally distributed sites. The results show that the Saastamoinen ZHD estimates have a mean root mean square (RMS) error of 1.7 mm with respect to the radiosonde. We also detected some seasonal signatures in these Saastamoinen ZHD estimates. This indicates that the Saastamoinen model, based on the hydrostatic assumption and the ground pressure, is insufficient to capture the full variability of the ZHD estimates over time with the accuracy needed for GNSS meteorology. Furthermore, we found that VMF3 slant hydrostatic delay (SHD) estimates outperform the corresponding VMF1 SHD estimates (equivalent SHD RMS error of 4.8 mm for VMF3 versus 7.1 mm for VMF1 at 5° elevation angle), with respect to the radiosonde SHD estimates. Unexpectedly, the situation is opposite for the VMF3 slant wet delay (SWD) estimates compared to VMF1 SWD estimates (equivalent SWD RMS error of 11.4 mm for VMF3 versus 7.0 mm for VMF1 at 5° elevation angle). Our general conclusion is that the joint approach using ZHD models and mapping functions must be revisited, at least in the framework of GNSS meteorology.

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Section: Discussionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

Feng

Yan

et al. 2020

Remote Sensing

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“…where denotes the geopotential, and is a constant gravity value of 9.80665 m/s 2 . Second, ℎ was converted to the geometric height ℎ as follows [27,28]:…”

Section: B Conversion Of Height Systemmentioning

confidence: 99%

A New Four-Layer Inverse Scale Height Grid Model of China for Zenith Tropospheric Delay Correction

Zhang

Wang

et al. 2020

IEEE Access

Self Cite

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To reduce the convergence time in the real-time precise point positioning (PPP), the zenith tropospheric delay (ZTD) needs to be modeled with high accuracy and sent to the users to be introduced as a priori value. Because of the height difference between the model height and user's location, the ZTD at the model height must be converted to that at the user's height. Therefore, it is crucial to investigate an optimal method for this height correction of ZTD. It is normally assumed that the ZTD decreases exponentially with the altitude and an empirical decrease factor is adopted for depicting the ZTD variation with altitude. In this study, the performance of the commonly used single-layer model of the decrease factor was investigated. Based on the investigation of the single-layer model, a new four-layer grid model (0.25°×0.25°) over China was constructed with 10-year (from 2009 to 2018) ERA5 data, and its performance was validated. The results indicate that the newly constructed four-layer model has a better performance than the single-layer model with the bias and root mean square (RMS) of the determined ZTD reduced by 54.4% and 27.6%, respectively. With the four-and single-layer grid model and GNSS-derived ZTD, two ZTD models i.e. four-layer ZTD and single-layer ZTD were constructed over China. The experiment shows that the convergence time of PPP can be obviously reduced when introducing these two ZTD models and the four-layer ZTD model has a much better performance than the single-layer ZTD, especially at stations with a high altitude. INDEX TERMS ZTD vertical reduction, height correction, inverse scale height, four-layer model

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“…In regards to the mapping function, both the Neill mapping function (NMF) and global mapping function (GMF) [47,48] are available. As suggested by previous studies, although the Vienna mapping functions (VMF) have a better performance than the others, the difference among these commonly used mapping functions is quite small [49]. The gradient model parameters for the north and east are estimated together with the ZTD with the form proposed by Macmillan [50].…”

Section: Ztd Calculation With Gnssmentioning

confidence: 99%

The Impact of Different Ocean Tide Loading Models on GNSS Estimated Zenith Tropospheric Delay Using Precise Point Positioning Technique

Zhang

Wang

et al. 2020

Remote Sensing

Self Cite

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Global navigation satellite systems (GNSSs) have become an important tool to derive atmospheric products, such as the total zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) for weather and climate studies. The ocean tide loading (OTL) effect is one of the primary errors that affects the accuracy of GNSS-derived ZTD/PWV, which means the study and choice of the OTL model is an important issue for high-accuracy ZTD estimation. In this study, GNSS data from 1 January 2019 to 31 January 2019 are processed using precise point positioning (PPP) at globally distributed stations. The performance of seven widely used global OTL models is assessed and their impact on the GNSS-derived ZTD is investigated by comparing them against the ZTD calculated from co-located radiosonde observations. The results indicate that the inclusion or exclusion of the OTL effect will lead to a difference in ZTD of up to 3–15 mm for island stations, and up to 1–2 mm for inland stations. The difference of the ZTD determined with different OTL models is quite small, with a root-mean-square (RMS) value below 1.5 mm at most stations. The comparison between the GNSS-derived ZTD and the radiosonde-derived ZTD indicates that the adoption of OTL models can improve the accuracy of GNSS-derived ZTD. The results also indicate that the adoption of a smaller cutoff elevation, e.g., 3° or 7°, can significantly reduce the difference between the ZTDs determined by GNSS and radiosonde, when compared against a 15° cutoff elevation. Compared to the radiosonde-derived ZTD, the RMS error of GNSS-derived ZTD is approximately 25–35 mm at a cutoff elevation of 15°, and 15–25 mm when the cutoff elevation is set to 3°.

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The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay

Cited by 25 publications

References 72 publications

Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

A New Four-Layer Inverse Scale Height Grid Model of China for Zenith Tropospheric Delay Correction

The Impact of Different Ocean Tide Loading Models on GNSS Estimated Zenith Tropospheric Delay Using Precise Point Positioning Technique

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