GNSS-based water vapor estimation and validation during the MOSAiC expedition

Abstract. Within the transpolar drifting expedition MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate), the Global Navigation Satellite System (GNSS) was used among other techniques to monitor variations in atmospheric water vapor. Based on 15 months of continuously tracked GNSS data including GPS, GLONASS and Galileo, epoch-wise coordinates and hourly zenith total delays (ZTDs) were determined using a kinematic precise point positioning (PPP) approach. The derived ZTD values agree to 1.1 ± 0.2 mm (root mean square (rms) of the differences 10.2 mm) with the numerical weather data of ECMWF's latest reanalysis, ERA5, computed for the derived ship's locations. This level of agreement is also confirmed by comparing the on-board estimates with ZTDs derived for terrestrial GNSS stations in Bremerhaven and Ny-Ålesund and for the radio telescopes observing very long baseline interferometry in Ny-Ålesund. Preliminary estimates of integrated water vapor derived from frequently launched radiosondes are used to assess the GNSS-derived integrated water vapor estimates. The overall difference of 0.08 ± 0.04 kg m−2 (rms of the differences 1.47 kg m−2) demonstrates a good agreement between GNSS and radiosonde data. Finally, the water vapor variations associated with two warm-air intrusion events in April 2020 are assessed.


, and is an important input parameter for numerical weather models (NWM).
In the generally dry Arctic, atmospheric moisture intrusions from lower latitudes affect the snow and sea ice cover by increased longwave radiation (Woods and Caballero, 2016). The estimation of ZTDs and the subsequent conversion into precipitable water vapor (PWV) or integrated water vapor (IWV) is done operationally for many hundred land-based GNSS-stations and is 25 confirmed to agree with conventional meteorological observations (e.g., Gendt et al., 2004;Shangguan et al., 2015;Steinke et al., 2015). According to Ning et al. (2016) the accuracy of GNSS-based IWV is at a level of 1-2 kg m −2 . However, with a few exceptions continuous and long-term GNSS-based water vapor time series over oceans are not available but are highly important for climate investigations. In the past, several authors investigated shipborne PWV retrieval and reported an agreement at the 2 mm level compared to radiosondes (Fujita et al., 2008) and at the 3 mm level compared to radiometer data (Rocken 30 et al., 2005). Boniface et al. (2012) investigated the ability to determine mesoscale moisture fields from shipborne GNSS data over four months. Wang et al. (2019) studied a 20-day ship cruise in the Fram Strait and reported an agreement for the PWV of 1.1 mm compared to weather models and radiosondes. Based on the four-months ship campaign, Shoji et al. (2017) reported the practical potential of kinematic precise point positioning (PPP) for water vapor monitoring over oceans worldwide with particular challenges during high-humidity conditions. Based on the large-scale EUREC 4 A campaign, Bosser et al. (2020) presented 35 IWV solutions derived from GNSS receivers on-board the research vessels RV Atalante, RV Maria S. Merian, and RV Meteor.
Overall, they reported a good agreement with biases of ±2 kg m −2 with respect to numerical weather models and terrestrial GNSS stations. For this study, we derived a 15 months zenith total delay and water vapor time series between summer 2019 and autumn 2020 observed by a GNSS receiver installed on-board the German research vessel RV Polarstern (Alfred Wegener Institute, 2017) as part of the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition. 40 The main objective of the MOSAiC expedition was to investigate the complex climate processes of the Central Arctic for improving global climate models. RV Polarstern departed on September 20, 2019 in Tromsø, Norway and started the transpolar drift on October 4 at 85 • N, 137 • E. Interrupted for around four weeks due to a supply trip to Svalbard in May and June 2020, RV Polarstern ended the drift on August 9, 2020 at 79 • N, 4 • E. For the second part of the expedition, RV Polarstern returned to the Central Arctic in mid of August 2020 to observe the sea ice in its onset and early freezing phase. RV Polarstern finally returned to Bremerhaven on Oct. 12, 2020. The GNSS receiver was a continuously operational instrument within the ship-based atmosphere monitoring system. It was provided by the GFZ German Research Centre for Geosciences with the main motivation to derive water vapor variations continuously from ground and to allow a comparison for the radiosonde data.

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Following this introduction, the GNSS installation on RV Polarstern and data availability is discussed in Sect. 2. The processing strategy applied in this study is summarized in Sect. 3 while Sect. 4 discusses the derived kinematic coordinates. In Sect. 5, the ZTD solution is assessed with respect to ERA5-based ZTDs and ZTDs derived from land-based GNSS and VLBI (Very Long Baseline Interferometry). Subsequently derived IWV values are discussed in Sect. 6 in comparison to preliminary radiosonde data. The paper closes with a summary and conclusions in Sect. 7.

GNSS installation and data availablility
The GNSS equipment was installed on July 4, 2019 shortly after the end of RV Polarstern's previous expedition PS120 and at the beginning of a nearly six-week shipyard period. Consequently, GNSS data have been recorded during the stay at Bremerhaven, the expedition PS121 (Fram Strait), and the entire MOSAiC expedition (PS122). For logistical reasons, the receiver was switched off on October 3, 2020 at a position very close to Ny Ålesund, Svalbard. Therefore, we have 15 months of high-60 accuracy GNSS data which is very valuable for climate relevant studies. Figure 1 shows GFZ's GNSS equipment installed at the RV Polarstern's observation deck. A JAV_GRANT-G3T antenna without a choke-ring was used. To support reflectometry, the antenna was mounted on a cube-structure together with a sidelooking antenna (Semmling et al., 2021). The receiver equipment (geodetic JAVAD_TR_G3TH receiver) was stored in a cabinet mounted at the observation deck's railings. As visible in Fig. 1, the antenna location is not perfect as being subject to shadowing and strong multipath effects caused by the nearby radomes and the crow's nest. Due to limited data bandwidth during the cruise data transfer in real-time was not possible. Data post-processing started after the cruise at GFZ. The raw data were converted using the JPS2RIN converter software (version v.2.0.191). The derived RINEX files were spliced, sampled, and checked using gfzrnx (Nischan, 2016).

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The considerable large number of received observations, represented in Fig The Bernese GNSS Software 5.2 (Dach et al., 2015) was used for the data processing, which was performed as kinematic PPP (Zumberge et al., 1997) with epoch-wise estimated coordinates and hourly estimated zenith total delays among other parameters. The kinematic approach is needed to account for the traveling periods, height variations due to tides and waves, and the drift phases which showed an average speed of 12 km per day (corresponding to 4 m within the observation interval 80 of 30 s). For validation purposes, the shipyard period in Bremerhaven (i.e., the dry dock period) was processed consistently in kinematic mode. The resulting kinematic coordinates are studied in Sect. 4. Overall, 25 ZTD values are estimated per day together with 8640 kinematic coordinates, 2880 clock corrections, around 80 differential code biases, and around 280 ambiguities.
The piecewise-linear ZTD estimates are constrained relatively with 1 mm. Table 1 provides a summary of the modeling and parametrization strategy. According to the capabilities of the processing software, ambiguity fixing was not applied, therefore, 85 ambiguity parameters are estimated. Driven by the receiver's high latitude and the free horizon on the portside a low elevation cutoff angle of 3 • was chosen. An elevation-dependent observation weighting using cos 2 (z) was applied with z as zenith angle. modeling and a-priori information observations ionosphere free-linear combination formed by undifferenced GPS, GLONASS, and Galileo observations, sampled with 30s, elevation cutoff 3 • , elevation-dependent weighting using cos 2 (z) a priori products CODE MGEX orbits, clock corrections, Earth rotation parameters (Prange et al., 2020) tropospheric correction hydrostatic delay computed based on VMF, mapped with VMF (Böhm et al., 2006) ionospheric correction 1st order effect considered with ionosphere-free linear combination GNSS phase center igs14_2129.atx (Rebischung and Schmid, 2016)  Some general processing indicators are highlighted in Fig. 3. On average, 40'000 to 60'000 ionosphere-free observations remained after pre-cleaning for the daily processing, which is equivalent to 13-20 observations per epoch. As shown in the Sing. Epoch

Assessment of kinematic coordinates
In general, kinematic coordinates have to be estimated for a shipborne GNSS receiver to account for the ship's motion. Compared to static coordinates, kinematic coordinates cannot be assessed easily due to missing repetitions of positions (unlike the repeatability check for permanent stations) and the usual absence of any ground-truth information as for example, known 110 marker coordinates. Therefore, the assessment of kinematic coordinates is possible only during specific periods.
One specific period was during the shipyard stay in Bremerhaven, where RV Polarstern spent nearly four weeks in the dry dock and the antenna position could be assumed to be static and thus precisely assessed. Fig. 4 shows the coordinate variations between July 7 and August 3, 2019 for North, East, and Up direction. For the horizontal components, 79 % and 83 % of the 115 coordinates are within ±4 cm. A larger variation is expected for the height with 78 % of the coordinates being within ±8 cm.
The standard deviation of the derived horizontal coordinates is 4.8 and 5.7 cm for North and East, respectively. However, it has to be noted that during the shipyard stay multipath increased while the number of observations decreased significantly (see Fig.   3). This is most probably related to additional obstacles and reflections due to construction work. A mean ellipsoidal height of 61.49±0.01 m was determined. Using a geoid height of 39.58 m at Bremerhaven this corresponds to an antenna height of 120 21.91 m during the dry dock phases.
The second period for a coordinate validation is the harbor stay in Tromsø, Norway. Without a ship motion the ocean tides can be used as ground truth, thus, the correlation between observed height and tidal record provides a validation opportunity.  Overall, kinematic coordinates for nearly 1.3 Mio. epochs were estimated from kinematic PPP. Whereas 0.5 % of all epochs are singular (i.e., epochs with less than four satellites) and another 0.9 % are interpolated but not estimated (see also Fig. 3) 130 ensuring the high-quality of the data.

Assessment of zenith total delay
The derived ZTDs are analyzed and the results are presented in this section. The assessment and validation process includes the comparison to numerical weather model data (Sect. 5.1), a comparison against ZTD derived for selected onshore GNSS

Comparison to onshore GNSS
The assessment of ZTDs determined for the GNSS receiver on-board RV Polarstern with respect to ZTDs derived for onshore GNSS receivers allows a second comparison option. A comparison between ship-based ZTD and land-based GNSS products 170 is in general possible for (1) harbor stays with a close-by GNSS station and (2) periods where the ship's distance to a terrestrial reference station does not exceed a few hundred kilometers under stable weather conditions. The first comparison approach can be applied for the shipyard stay in Bremerhaven (six weeks). Unfortunately, the harbor stay at Tromsø (one week) could not be used for a comparison due to the data restrictions. The second approach is challenging given the remote character of the MOSAiC expedition. However, during PS121, the re-supply trip at Svalbard and RV Polarstern's return trip, the distance 175 between the GNSS tracking stations at Ny Ålesund, Svalbard and RV Polarstern was shorter than 200 km for several days. The related ZTDs are thus compared to the onshore GNSS at Ny Ålesund. Reference ZTDs have been estimated within operational

GNSS processing system for meteorological applications, which is based on the GFZ Earth Parameter and Orbit determination
System (EPOS.P8) software (Gendt et al., 2004;Wickert et al., 2020).

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For the shipyard stay in Bremerhaven, a reasonable mean difference of 1.5±0.4 mm and an RMS of 9.9 mm was estimated between ZTDs for RV Polarstern and the German SAPOS station 0994. This station is located approx. 2.6 km from RV Polarstern and around 20 m above the ground like the GNSS antenna height at Polarstern. Therefore, no height correction was applied. Figure 9 shows   The comparison between the ZTDs derived for RV Polarstern and the GNSS station in Ny Ålesund, Svalbard is more challenging due to the larger distances, the ship's speed, and partly the performed ship operations. In addition, also the orographic setting might be a source for differences between the RV Polarstern measurements on open water and the measurements at the edge of a fjord surrounded by mountains in Ny Ålesund. The reference station (NYA2) is a GNSS station operated by GFZ  and observations and metadata are available within the IGS. Figure 10 shows Polarstern's ZTD 200 series and the ERA5-based ZTD values. In addition, the geometrical distance between RV Polarstern and NYA2 is indicated by the red line. Whereas the observed good agreement between the on-board estimates and ERA5 is expected, the differences regarding NYA2 are partly larger. Especially during the PS121 expedition (Fram Strait), time shifts between the ZTD series can be observed for some periods, e.g., for August, 26-28. For these particular dates the PS121 expedition report mentions a storm field close to Iceland affecting RV Polarstern with speeds of about 8 Bft (Metfies, 2020). During the re-supply stay 205 in June 2020, ZTDs are not permitted. However, less accurate ZTDs are expected for this period considering the drop in the processed phase observations (see Fig. 3) potentially caused by the logistic activities. For the arrival and departure periods the agreement is within the expected range. For the third interval, again, a good agreement is visible for October 2 and 3, 2020 but larger differences for the approaching period on October 1, 2020. While RV Polarstern approached Ny Ålesund closely with distances to NYA2 below 2 km, the corresponding values are, however, restricted by the research agreement and cannot be used

Comparison to VLBI
The geodetic fundamental site in Ny Ålesund also allows a comparison between the ZTDs determined for the GNSS antenna 215 on-board RV Polarstern and the ZTD observed by VLBI at the radio telescopes NYALES20 and NYALE13S 2 for a completely external validation. Very Long Baseline Interferometry is an interferometric technique measuring the time delay between the reception of signals transmitted by extragalactic radio sources at two or more antennas (Schuh and Behrend, 2012). Currently, VLBI sessions with global networks are not performed continuously but scheduled in twice weekly 24h sessions and provided within the International VLBI Service for Geodesy and Astrometry (IVS, Nothnagel et al., 2017). The high accuracy of VLBI-220 based troposphere estimates has been reported for example by Heinkelmann et al. (2007) and Balidakis et al. (2018). In the time span August 11 till September 12, 2019 in total nine 24h sessions with NYALES20, during May 20 and June 15, 2020 seven sessions with NYALES20 or NYALE13S, and during September 20 and October 4, 2020 another five sessions with NYALES20 were analyzed using PORT (Potsdam Open Source Radio Interferometry Tool). PORT is GFZ's VLBI analysis software and is based on VieVS (Vienna VLBI Software, Böhm et al., 2012, Nilsson et al., 2015. The derived  ZTDs are shown in orange in Fig. 10. First of all, it can be noted that the ZTDs of GNSS (NYA2) and VLBI agree well, which is expected due to the short horizontal distances between the stations 3 and the highly accurate space techniques GNSS and VLBI. Overall, a good agreement is visible also between the VLBI and the RV Polarstern ZTDs. However, a few VLBI-based ZTDs differ significantly in August 2019, while also the GNSS ZTDs showed some larger differences for these days as reported above. For June and October 2020, there were VLBI sessions each while RV Polarstern was close to Svalbard. However, during 230 these periods RV Polarstern was mainly within the territorial waters around Svalbard in which ZTDs are restricted. In June, one session with NYALES20 is within the restricted period, while a comparison is allowed for a session with NYALE13S. For This section discusses integrated water vapor values derived from the ZTD on-board RV Polarstern. The conversion between ZTD and IWV was performed applying Eq. 2 described in Bevis et al. (1994). The zenith wet delay was computed by subtracting the hydrostatic delay provided by ERA5 from the estimated ZTD values. The weighted mean temperature of the atmosphere T m was calculated from the ERA5 data using Eq. A18 given in Davis et al. (1985). To derive hourly IWV the 3-hourly ERA5 240 data are linearly interpolated.
From board RV Polarstern, radiosondes were launched every six hours during the entire MOSAiC expedition, and moreover every three hours for periods of specific interest. Based on the relative humidity data in the preliminary radiosonde dataset (Maturilli et al., 2021), vertically resolved specific humidity profiles were calculated applying Hyland and Wexler (1983) and 245 integrated over the atmospheric column to retrieve IWV. Measurements for which the radiosondes did not reach a height of at least 10'000 m are excluded in the following (0.9 %). for RV Atalante and RV Meteor, respectively. The majority of the absolute IWV values is below 5 kg m −2 as visible in Fig.   11. This result could be expected as driven by the low air temperatures, the amount of atmospheric water vapor was very low 255 during large parts of the transpolar drift. Consequently, IWV values observed by GNSS and radiosondes are below 5 kg m −2 from mid of October 2019 till end of April 2020 with only a few exceptions. One example for such rapid moisture increase occurred in April 2020 associated with two warm air intrusion events on April 16 and 19. According to Magnusson et al. (2020), the warm air was pushed to the northeast in front of a low pressure trough over Scandinavia in the first event. In contrast, the second event was driven by warm air transported northward on the western side of a high pressure ridge that developed over 260 Scandinavia. Both events on April 16 and 19 are well visible in the IWV time series shown in Fig. 12. For both events, the air temperature increased rapidly from around -20 • C to nearly 0 • C. Simultaneously the IWV observed by GNSS increased from below 5 kg m −2 to 8 and 13 kg m −2 for the two events. For both events, a nearly perfect agreement between GNSS-derived and radiosonde-based IWVs is visible.

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The MOSAiC expedition offered a unique opportunity to study polar environmental conditions during one full annual cycle.
Besides other techniques, an on-board GNSS receiver allowed to monitor the variations of atmospheric water vapor above RV Polarstern. Based on 15 months of continuously tracked GNSS data, a kinematic PPP approach including GPS, GLONASS,   and Galileo was used to determine epoch-wise coordinates and hourly zenith total delays. By assessing the GNSS data itself, a reliable number of observations was found, however, disturbed by multipath effects due to sub-optimal antenna location. Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. The authors want to thank IGS, IVS, CODE, and ECMWF for making the used data and products publicly available.

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We would also like to thank Thomas Gerber, Sylvia Magnussen, Markus Bradke, and the technical staff of RV Polarstern for all support during GNSS installation, operations, and data retrieval. Radiosonde data were obtained through a partnership between the leading Alfred Wegener Institute (AWI), the Atmospheric Radiation Measurement (ARM) User Facility, a U.S. Department of Energy facility managed by the Biological and Environmental Research Program, and the German Weather Service (DWD). Data used in this manuscript was produced as part of POLARSTERN cruise AWI_PS121 and of the international Multidisciplinary drifting Observatory for the Study of the Arctic