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Precipitable water vapor (PWV) is an important parameter for climate research and a crucial factor to achieve high accuracy in satellite geodesy and satellite altimetry. Currently Global Navigation Satellite System (GNSS) PWV retrieval using static Precise Point Positioning is limited to ground stations. We demonstrated the PWV retrieval using kinematic Precise Point Positioning method with shipborne GNSS observations during a 20‐day experiment in 2016 in Fram Strait, the region of the Arctic Ocean between Greenland and Svalbard. The shipborne GNSS PWV shows an agreement of ~1.1 mm with numerical weather model data and radiosonde observations, and a root‐mean‐square of ~1.7 mm compared to Satellite with ARgos and ALtiKa PWV. An improvement of 10% is demonstrated with the multi‐GNSS compared to the Global Positioning System solution. The PWV retrieval was conducted under different sea state from calm water up to gale. Such shipborne GNSS PWV has the promising potential to improve numerical weather forecasts and satellite altimetry. Atmospheric water vapor retrieval using GNSS kinematic Precise Point Positing technique is demonstrated with shipborne GNSS data collected during a 20‐day cruise in Fram Strait (~80°N), the area in the Arctic Ocean between Greenland and Svalbard. An accuracy of ~1 mm is achieved compared to ERA‐Interim precipitable water vapor (PWV) and radiosonde data, and an agreement of ~2 mm is demonstrated between shipborne GNSS PWV and satellite altimetry PWV observation. The contribution of multi‐GNSS is addressed, and efforts are also made to investigate the PWV spatial resolution in order to include more data for comparison. Static Precise Point Positioning method is widely used at ground‐based GNSS stations in climate research and weather forecasting. However, it is still limited to land. Shipborne GNSS PWV retrieval could fill in the vast ocean with high temporal/spatial resolutions. Shipborne GNSS PWV could cover open sea, coastal, and polar regions (e.g., in this study) where regular meteorological observations are rare. Shipborne GNSS PWV retrieval in real time is feasible and could provide additional information for weather predictions. Moreover, shipborne GNSS PWV retrieval provides a potential method for satellite altimetry calibration, the major technique measuring sea surface height for sea level monitoring. Shipborne GNSS PWV retrieval is demonstrated with an accuracy of 1 mm, and an agreement of 1.7 mm with satellite altimetry PWVThe multi‐GNSS solution shows an RMS improvement of ~10% compared to the GPS solution in oceanwide PWV retrieval using kinematic PPP methodShipborne GNSS PWV retrieval could expand GNSS meteorology to ocean and improve NWM, satellite altimetry, and weather forecasting

With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.

Very Long Baseline Interferometry (VLBI) intensive (INT) sessions are critical for the rapid determination and densification of Universal Time 1‐Coordinate Universal Time (UT1‐UTC), which plays an important role in satellite geodesy and space exploration missions and is not predictable over longer time scales. Due to the limited observation geometry of INT sessions with two to three stations observing about 1 hr, tropospheric gradients cannot be estimated, which degrades the UT1‐UTC precision. We investigate the impact of tropospheric ties at Global Navigation Satellite Systems (GNSSs) and VLBI co‐located stations in INT sessions from 2001 to 2021. VLBI and GNSS observations are combined on the observation level. The results are evaluated by using both UT1‐UTC and Length of Day (LOD) from consecutive sessions. We demonstrate a better agreement of 10%–30% when comparing the derived LOD to GNSS LOD for INT1, INT2, and VGOS‐2 sessions; whereas, the agreement is not improved when directly comparing UT1‐UTC to the IERS Earth Orientation Parameters (EOPs) product, potentially because INT sessions also contribute to IERS EOP products. The major impact comes from tropospheric gradient ties, whereas applying zenith delay ties does not improve or even deteriorate UT1‐UTC agreement. Gradient ties also introduce systematic biases in UT1‐UTC by around −3 to −5 μs, except for the Russian INT sessions. Regression analysis shows that the east gradient introduces systematic effects in UT1‐UTC for sessions involving Germany and USA (Hawaii), whereas for Germany–Japan and Russian sessions, the north gradient also contributes systematically. Universal Time 1‐Coordinate Universal Time (UT1‐UTC) gives the time difference of UT1, defined by Earth's rotation, and UTC, defined by atomic clocks. UT1‐UTC is essential for real‐time navigation and space exploration. The variation of the first‐order negative time derivative of UT1‐UTC, Length of Day (LOD), is induced by mass redistribution, including tides of the solid Earth and oceans, the liquid core of the Earth and atmospheric variation, and climate events such as El Niño. Very Long Baseline Interferometry (VLBI) observing active galactic nuclei is the only space geodetic technique that can determine UT1‐UTC unambiguously. The 1‐hr intensive (INT) sessions, designed for the rapid determination and densification of UT1‐UTC, are performed daily with two VLBI radio telescopes. Due to the limited observation geometry, tropospheric gradients cannot be modeled in INT sessions, deteriorating UT1‐UTC estimates. We demonstrate an improvement of 10%–30% in LOD by applying tropospheric ties at VLBI and Global Navigation Satellite Systems co‐locations, especially the tropospheric gradients ties. Tropospheric gradient ties also introduce a systematic effect of −3 to −5 μs on UT1‐UTC, especially the east gradient. Our study shows that tropospheric ties should be adopted in future VLBI analysis for optimal UT1‐UTC products. Tropospheric ties are applied in a Global Navigation Satellite System–Very Long Baseline Interferometry (GNSS–VLBI) integrated solution analyzing VLBI intensive (INT) sessions from 2001 to 2021Length of Day (LOD) of IVS INT sessions shows a better agreement by 10%–30% when compared to GNSS LOD product, mainly due to gradient tiesGradient ties, especially the east one, introduce systematic biases of −3 to −5 μs in Universal Time 1‐Coordinate Universal Time of IVS INT sessions Tropospheric ties are applied in a Global Navigation Satellite System–Very Long Baseline Interferometry (GNSS–VLBI) integrated solution analyzing VLBI intensive (INT) sessions from 2001 to 2021 Length of Day (LOD) of IVS INT sessions shows a better agreement by 10%–30% when compared to GNSS LOD product, mainly due to gradient ties Gradient ties, especially the east one, introduce systematic biases of −3 to −5 μs in Universal Time 1‐Coordinate Universal Time of IVS INT sessions

The developing multi‐Global Navigation Satellite Systems (GNSS) constellations have the potential to provide accurate high‐resolution tropospheric gradients. Such data, closely linked to strong humidity gradients accompanying severe weather phenomena, are considered a new important data source for meteorological studies, e.g., nowcasting of severe rainfall events. Here we describe the development of a multi‐GNSS processing system for the precise retrieval of high‐resolution tropospheric gradients. The retrieved products were validated by using independent water vapor radiometer (WVR) observations and numerical weather model (NWM) data. The multi‐GNSS high‐resolution gradients agree well with those, derived from NWM and WVR, especially for the fast‐changing peaks which were mostly associated with synoptic fronts. Compared to GPS‐only gradients, the correlations with the validation data are significantly improved up to 20–35%. The new data product has significant potential to improve numerical weather prediction and to advance meteorological studies. Retrieving high‐resolution tropospheric gradients from multi‐GNSS observationsGradients agree well with weather models and other meteorological observationsCompared to GPS only, the correlation is improved significantly up to 20–35%

Accurate tropospheric delays from Numerical Weather Models (NWM) are an important input to space geodetic techniques, especially for precise real‐time Global Navigation Satellite Systems, which are indispensable to earthquake and tsunami early warning systems as well as weather forecasting. The NWM‐based tropospheric delays are currently provided either site‐specific with a limited spatial coverage, or on two‐dimensional grids close to the Earth surface, which cannot be used for high altitudes. We introduce a new method of representing NWM‐derived tropospheric zenith hydrostatic and wet delays. A large volume of NWM‐derived data is parameterized with surface values and additional two or three coefficients for their vertical scaling to heights up to 14 km. A precision of 1–2 mm is achieved for reconstructing delays to the NWM‐determined delays at any altitudes. The method can efficiently deliver NWM‐derived tropospheric delays to a broader community of space geodetic techniques. Precise positioning with microwave‐based space geodetic techniques, such as Global Navigation Satellite Systems (GNSS), requires accurate modeling of the atmospheric refraction. Numerical Weather Models (NWM) can provide tropospheric delays with an accuracy of 1–2 cm in zenith direction and are therefore useful for improving the data analysis. However, due to the large data volume to handle, NWM‐based products are typically provided only for selected sites, or on a global grid referring to a specific height. We provide an efficient method to represent the vertical profile of tropospheric delay from the Earth surface up to 14 km altitude with a precision of 1–2 mm. The method is used to preserve the precision of NWM‐derived tropospheric delays at the altitudes using three to four coefficients per geographic location (longitude, latitude) at the ground. This paves the way of applying the NWM‐based accurate tropospheric delays in space geodetic data analysis, especially for global augmentations of real‐time GNSS, which play a critical role in the rapid characterization and early warning of geohazards such as earthquake and tsunami, as well as kinematic platforms of high altitudes. New method for precise modeling of the zenith hydrostatic and wet delays from the Earth surface up to an altitude of 14 kmTropospheric delay vertical modeling precision of better than 3 mm is achieved on a global scaleThe method provides numerical weather model‐derived precise tropospheric augmentation correction for real‐time space geodetic techniques New method for precise modeling of the zenith hydrostatic and wet delays from the Earth surface up to an altitude of 14 km Tropospheric delay vertical modeling precision of better than 3 mm is achieved on a global scale The method provides numerical weather model‐derived precise tropospheric augmentation correction for real‐time space geodetic techniques

Nowadays more and more high‐rate real‐time GPS data become available that provide a great opportunity to contribute to earthquake early warning (EEW) system in terms of capturing regional surface displacements, as an independent information source, useful for promptly estimating the magnitude of large destructive earthquake. In our study, we demonstrate the performance of the real‐time ambiguity‐fixed precise point positioning (PPP) approach using 5 Hz GPS data collected during El Mayor‐Cucapah earthquake (Mw7.2, 4 April 2010). The PPP‐based displacements show to agree with accelerometer‐based displacement at centimeter level. The key for successfully obtaining high precision displacements is the efficient ambiguity resolution. PPP with ambiguity fixing can result in correct permanent co‐seismic offsets and correct recovery of moment magnitude and fault slip inversion at levels comparable to post‐processing. Integer ambiguity fixing improve real‐time PPP displacementsDisplacements from PPP and accelerometers, displayed a high agreementreal‐time PPP can become complementary to seismic EEW methods

AbstractIt is well known that Thom–Boardman symbols are realized by nonincreasing sequences of nonnegative integers. A natural question is whether the converse is also true. In this paper we answer this question affirmatively, that is, for any nonincreasing sequence of nonnegative integers, there is at least one map-germ with the prescribed sequence as its Thom–Boardman symbol.

Real-time satellite orbit and clock estimations are the prerequisite for Global Navigation Satellite System (GNSS) real-time precise positioning services. To meet the high-rate update requirement of satellite clock corrections, the computational efficiency is a key factor and a challenge due to the rapid development of multi-GNSS constellations. The Square Root Information Filter (SRIF) is widely used in real-time GNSS data processing thanks to its high numerical stability and computational efficiency. In real-time clock estimation, the outlier detection and elimination are critical to guarantee the precision and stability of the product but could be time-consuming. In this study, we developed a new quality control procedure including the three standard steps: i.e., detection, identification, and adaption, for real-time data processing of huge GNSS networks. Effort is made to improve the computational efficiency by optimizing the algorithm to provide only the essential information required in the processing, so that it can be applied in real-time and high-rate estimation of satellite clocks. The processing procedure is implemented in the PANDA (Positioning and Navigation Data Analyst) software package and evaluated in the operational generation of real-time GNSS orbit and clock products. We demonstrated that the new algorithm can efficiently eliminate outliers, and a clock precision of 0.06 ns, 0.24 ns, 0.06 ns, and 0.11 ns can be achieved for the GPS, GLONASS, Galileo, and BDS-2 IGSO/MEO satellites, respectively. The computation time per epoch is about 2 to 3 s depending on the number of existing outliers. Overall, the algorithm can satisfy the IGS real-time clock estimation in terms of both the computational efficiency and product quality.

Die Laufzeitverzögerung der GPS-Signale in der Atmosphäre kann wertvolle meteorologische Informationen liefern. Insbesondere ist es möglich, die räumliche Wasserdampfverteilung in der Troposphäre aus den Laufzeitdaten zu rekonstruieren. Hierzu muß jedoch zunächst die Qualität der GPS-Daten durch Validierungs-Studien ermittelt werden. Hier werden zwei Studien beschrieben: In der ersten werden die GPS-Daten mit denen eines Wasserdampf-Radiometers verglichen, in der zweiten werden die Analysen eines numerischen Wettermodells genutzt, um die GPS-Signal-Laufzeiten zu berechnen und mit den Beobachtungen zu vergleichen. In beiden Fällen ergibt sich eine gute Übereinstimmung für größere Elevationen, bei niedrigen Elevationen treten jedoch größere Abweichungen auf. Insgesamt ergibt sich eine mittlere Abweichung von 1,18 mm und ein RMS von 6,0 mm zwischen den Zenitdelays aus Radiometerbeobachtungen und der GPS-Analyse und eine Abweichung von 3,3 mm mit einem RMS von 2,9 mm zu den Modelldaten.