Precipitable Water Vapor Measurement using GNSS Data in the Atacama Desert for Millimeter and Submillimeter Astronomical Observations

Precipitable water vapor (PWV) strongly affects the quality of data obtained from millimeter-and submillimeter-wave astronomical observations, such as those for cosmic microwave background (CMB) measurements. Some of these observatories have used radiometers to monitor PWV. In this study, PWV was measured from April 2021 to April 2022 using Global Navigation Satellite System (GNSS) instruments in the Atacama Desert, Chile, where several millimeter and submillimeter-wave telescopes are located. We evaluated the accuracy of these measurements by comparing them to radiometer measurements. We calculated the PWV from GNSS data using Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP), an online software package. When using GNSS data alone, the estimated PWV showed a systematic offset of + 1 . 08 mm. When combining GNSS data with data from a barometer which was co-located with the GNSS receiver, the estimated PWV showed a lower systematic offset of − 0 . 14 mm. The GNSS PWV showed a statistical error of 0.52 mm with an averaging time of an hour. Compared to other PWV measurement methods, GNSS instruments are robust in bad weather conditions, have sufficient time resolution, and are less expensive. By demonstrating good accuracy and precision in low PWV conditions, this paper shows that GNSS instruments are valuable tools for PWV measurements for observing site evaluation and data analysis for ground-based telescopes.

Thompson 2009 ).In particular, Cerro Toco hosts several CMB experiments, including the Atacama Cosmology Telescope (Swetz et al. 2011 ), the Atacama B-mode Search (ABS; Kusaka et al. 2018 ), the POLARBEAR experiment (Kermish et al. 2012 ), the Simons Array (SA; Suzuki et al. 2016 ), and the Cosmology Large Angular Scale Surv e yor (Essinger-Hileman et al. 2014 ).Planned experiments for this location include the Simons Observatory (Ade et al. 2019 ) and CMB-S4 (Abazajian et al. 2019 ).CMB experiments use PWV measurements for the selection of observation sites and data analysis.Since these experiments have observation time-scales of several years, the PWV estimation method must be robust and continuous o v er years.
The Global Navigation Satellite System (GNSS) is one of the tools that are used to measure PWV.GNSS is a general term used to describe satellite-based positioning systems such as Global Positioning System (GPS), Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS), Galileo, BeiDou, Navigation with Indian Constellation (NavIC), and Quasi-Zenith Satellite System (QZSS).Estimation of PWV using GPS was first reported in 1992 (Bevis et al. 1992 ), and a number of studies have shown that GNSS data can be used to estimate PWV as accurately as other methods (e.g.Schneider et al. 2010 ).Estimating PWV in dry climates using GNSS data is known to be more challenging than in humid climates, but papers have reported successful estimations in dry regions such as Antarctica (Suparta et al. 2007(Suparta et al. , 2009 ; ;V ázquez B & Grejner-Brzezinska 2013 ;Negusini et al. 2016Negusini et al. , 2021 ; ;Ding, Chen & Tang 2022 ), Northern Sweden (Buehler et al. 2012), the Himalayas (Jade et al. 2004 ;Jade & Vijayan 2008 ;Joshi et al. 2013 ;Ningombam et al. 2016 ;Ningombam, Jade &Shrungeshwara 2018 ), andCanary Islands (Garc ía-Lorenzo et al. 2010 ;Schneider et al. 2010 ).
There are several other instruments that can measure PWV, such as radiometers, radiosondes, and the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard satellites.Ho we ver, instruments that can continuously and accurately observe PWV are limited.Radiometer measurements are easily distorted by the presence of liquid water and may significantly o v erestimate PWV (Shangguan et al. 2015 ).Observations should be excluded around precipitation events to a v oid this error, b ut this results in periods of downtime.
Radiosondes are e xpensiv e to operate for long periods of time.MODIS can only measure PWV twice per site per day and is known to o v erestimate PWV in dry weather (Li, Muller & Cross 2003 ;Vaquero-Mart ínez et al. 2017 ;He & Liu 2019 ;Sam Khaniani, Nikraftar & Zakeri 2020 ).
In contrast, GNSS instruments are ine xpensiv e these days and stable in bad weather conditions, making them suitable for supporting observatories.Wood-Vasey, Perrefort & Baker ( 2022 ) used GPS measurements of PWV to support photometric calibrations in the red optical and near-infrared wavelengths in their optical observations.In this study, GNSS measurements of PWV were e v aluated to support millimetre/submillimetre astronomical observatories, especially CMB experiments.Using GNSS data, continuous estimates of PWV at Cerro Toco o v er a year with sufficient accuracy and sampling rate are presented.This paper is organized as follows.Section 2 describes the calculation of PWV from GNSS data.Section 3 describes the instruments, location, and systems used to collect data.Section 4 describes the software and data processing flow for the PWV estimation.Section 5 discusses the performance of the GNSS-derived PWV compared to the radiometer.Section 6 discusses the uncertainties of the GNSSderived PWV.Section 7 discusses the quality of GNSS-derived PWV estimates in the context of data analysis and site e v aluation for CMB observatory.Section 8 summarizes the results and conclusions.

M E T H O D O L O G Y
The method of deriving PWV information from GPS data was established by Bevis et al. ( 1992 ).As electromagnetic signals from satellites propagate through the troposphere, they are delayed, which depends on the index of refraction along the propagation path.The tropospheric delay in the zenith direction is called the zenith total delay (ZTD) and is expressed in metres.ZTD is estimated by observing dual frequency signals from multiple GNSS satellites.ZTD can be written as the sum of the zenith hydrostatic delay (ZHD) and the zenith wet delay (ZWD; Davis et al. 1985 ): (1) ZHD is the dry component of the delay, while ZWD is a wet component and is proportional to the PWV.ZHD is typically of the order of 1.25 m on the Atacama Desert and accounts for almost all of ZTD.ZHD is accurately modelled using meteorological parameters.ZWD is estimated through two steps: ZTD measurement from GNSS data and ZHD estimation from meteorological parameters.Since ZWD is of the order of millimetres and varies rapidly, it has not been modelled as well as ZHD.ZHD is modelled by Davis et al. ( 1985 ) as a function of the surface pressure P : where k 1 = 77.604K hPa −1 is the refractivity constant for dry air, R d = 287.04J K −1 kg −1 is the specific gas constant for dry air, and g m is the mean gravity: where ρ( z) and g ( z) are air density and gravity acceleration, respectively, as a function of zenith height z.We estimate g m with the Bosser et al. ( 2007 ) model parametrized by latitude, surface ele v ation, and time.
ZWD is converted to PWV as follows: The conversion factor is known to have an approximate value of 1/6.5 ∼ 0.15 (Bevis et al. 1992 ;Rocken et al. 1993 ).More accurately, is estimated as a function of the weighted mean temperature T m : where ρ ∼ 1000 (kg m −3 ) is the density of liquid water, R ν ∼ 461 (J kg −1 K −1 ) is the specific gas constant for water vapour, and k 3 ∼ 3 .7 × 10 5 (K 2 h Pa −1 ) and k 2 ∼ 22 (K h Pa −1 ) are physical constants related to atmospheric refractivity (Askne & Nordius 1987 ;Bevis et al. 1994 ). is expected to vary only by 4 per cent in the Atacama Desert.Thus, for simplicity, is considered constant at its typical value of = 0.151 in this research.Alternatively, T m at each time can be estimated from our data set, as discussed in Appendix A .

GNSS antenna and weather station
GNSS data were acquired at the SA experiment site at Cerro Toco (22 • 57 S, 67 • 47 W, 5200 m a.s.l.).Fig. 1 shows a map of the SA   It outputs the surface pressure every minute with a resolution of 0.1 hPa and accuracy of 1.0 hPa, and its range is 540-1100 hPa.A small percentage of the data fell below this range.

GNSS recei v er system
Fig. 3 shows a block diagram of the GNSS receiver system.The raw GNSS signal from the antenna is transmitted through a coaxial cable 1 https:// www.tallysman.com/product/ vsp6037l-verostar-full-gnss-antennal-band 2 https:// www.davisinstruments.com/pages/ vantage-pro2 to a GNSS receiver inside the equipment container.A multiband GNSS receiver (u-blox ZED-F9P3 ) was employed, which supports the major GNSS systems, including GPS, GLONASS, Galileo, and BeiDou.In this paper, we only used GPS and GLONASS observation data for the analysis.
The receiver was configured to output raw GNSS data for later post-processing with software.A single-board computer (Raspberry Pi 4B4 ) receives raw GNSS data from the receiver module and streams them to a data storage computer using the Transmission Control Protocol (TCP) server functionality of rtkrcv in the RTKLIB5 software package.Raw GNSS data are converted to the Receiver Independent Exchange (RINEX) format using convbin in the RTKLIB package.The receiver was also configured to output National Marine Electronics Association (NMEA) messages and a pulse-per-second signal so that the single-board computer can synchronize its system clock to GNSS-referenced time.

Precise point positioning
Precise point positioning (PPP) is one of the GNSS analysis techniques for achieving fine-tuned positioning in the centimetre or millimetre range.PPP does not require nearby reference stations, unlike other GNSS positioning techniques such as real-time kinematic or differential GNSS.Instead, the precise satellite products, which correct the satellite orbit and clock errors, are used to assist in the positioning.Our ZTD estimation was performed using CSRS-PPP (Canadian Spatial Reference System PPP), a free online PPP service, since it has high accuracy compared to other software (Guo 2005 ;Mendez Astudillo et al. 2018 ;V ázquez-Ontiveros et al. 2023 ).
The CSRS-PPP o v erview is described in T étreault et al. ( 2005 ), and recent updates are provided on its website.6CSRS-PPP computes ZTD from uploaded GNSS data in RINEX format along with the precise satellite products from the International GNSS Service and Natural Resources Canada (NRCan).Among their 'ultra-rapid', 'rapid', and 'final' data product options, 'final' products are used in the calculations.Only GPS and GLONASS observations are processed, as other satellites are not yet supported by this software.Satellites with ele v ations less than 7.5 • are also excluded from the analysis to reduce multipath errors.
CSRS-PPP also calculates ZHD using gridded Vienna Mapping Function 1 (VMF1).Therefore, it is capable of estimating PWV from GNSS data alone.Ho we v er, as discussed in Section 5 , the accurac y of the PWV estimation can be impro v ed with data from a barometer co-located with the GNSS instrument.Thus, ZWD was calculated by two methods: one using the barometerderived ZHD (denoted as ' w/ barometer ') and the other using VMF1derived ZHD (denoted as ' w/o barometer ').ZWD was converted to PWV using equation ( 4 ).

Radiometer data for comparison
To e v aluate the accuracy of the GNSS-deri ved PWV measurements, they were compared with PWV measurements obtained by a groundbased microwave radiometer that is used in APEX. 7Their estimated systematic uncertainty is less than 3 per cent (Cort és et al. 2020 ).
The distances between APEX and SA are 6 km horizontally and 150 m vertically, which lead to statistical and systematic differences in PWV, respectively.In the Atacama Desert, the spatial inhomogeneity of PWV causes a path-length variation of the order of 200-300 μm between points that are 6 km apart, with an average time of 10 s (ALMA Partnership 2015 ; Matsushita et al. 2017 ).This corresponds to PWV variation of the order of 0.05 mm, assuming = 0.15.This is a small enough difference that can be ignored in this study, as discussed in Section 5 .APEX is situated at an altitude of 5050 m, while the SA experiment is at 5200 m.We correct for this vertical difference using the relationship given by Ot árola et al. ( 2010): where PWV APEX is the PWV measured by the APEX radiometer, and PWV RM is the estimated radiometer PWV value for the SA site.

R E S U LT S
The accuracy of our GNSS-derived PWV ( PWV GNSS ) was e v aluated through comparison to the radiometer-derived PWV ( PWV RM ).The analysis was done using 1 yr of GNSS data at the SA experimental site from 2021 April 18 to 2022 April 30.Fig. 5 shows the time series of the w/ barometer PWV GNSS and PWV RM .The 34 per cent of APEX radiometer data are missing because the radiometer shutter closes when bad weather is predicted, as well as during austral summer from January to March every year.The GNSS PWV data co v er almost a full year aside from where the pressure data are missing or reached the lower limit of the barometer range (3 per cent in total).This downtime can be further reduced by adopting a barometer with a wider range.The PWV GNSS follows the trend of PWV RM while having nearly zero downtime.estimate, hence the small offset.Hereafter, w/ barometer PWV GNSS is just denoted as PWV GNSS .
Fig. 7 shows the distribution of PWV GNSS − PWV RM for different time averages of the PWV timestreams (15 min, 1 h, and 4 h).The statistical fluctuation is almost independent of the PWV values.The standard deviation (STD) of PWV GNSS − PWV RM is 0.64, 0.52, and 0.37 mm for the average time of 15 min, 1 h, and 4 h, respectively.These are dominated by the statistical uncertainty of PWV GNSS , since the statistical uncertainty of PWV RM is less than 0.05 mm (see Section 4.3 ).

D I S C U S S I O N S F O R T H E G N S S P W V U N C E RTA I N T Y
We e v aluated the GNSS PWV uncertainty in Section 5 .Here, we discuss the source of uncertainties of our GNSS PWV, and the accuracy of our GNSS PWV in comparison to the literature.
The systematic uncertainty of GNSS PWV is represented by the deviation of a from 1 and the deviation of b from 0. It is expected to result from instrument miscalibration and modelling inaccuracies.The barometer miscalibration of 1 hPa affects b by 0.3 mm.We also found that the choice of the ZHD estimation model described in Section 2 affects b by about 0.1 mm.We used the g m estimation model of Bosser et al. ( 2007 ) and obtained b = −0.05mm as shown in Section 5 .For example, using the Saastamoinen ( 1973 ) model instead changed b to −0.14 mm.The altitude correction of the radiometer PWV with equation ( 6) changed a from 0.945 to 0.996.
The statistical uncertainty of GNSS PWV is represented by the STD of PWV GNSS − PWV RM .It is expected to arise from the uncertainties in the pressure and ZTD measurements.The statistical uncertainty in the ZTD analysis is caused by the multipath error, the imperfection of the GNSS clock and orbit corrections, the ionosphere correction error, and the hardware noise.A pressure measurement uncertainty of 1 hPa would map to a PWV uncertainty of 0.3 mm, and a ZTD measurement uncertainty of 1 mm would map to a PWV uncertainty of 0.2 mm.
The uncertainties of our GNSS PWV are compared to other studies in Table 1 .In the table, STD represents the standard deviation of the difference between the GNSS PWV and the PWV estimated by the method being compared.Although rigorous comparison is difficult due to differences in PWV ranges between studies, this study has the least uncertainty by comparing the raw values of STD.

A P P L I C AT I O N S TO C M B E X P E R I M E N T S
PWV is used to assess the data quality in the CMB observations.Many of modern ground-based CMB experiments use transition edge sensor (TES) bolometer arrays for their detectors.High optical loading from high PWV may make a TES inoperable, or may cause significant non-linearity of TES, which leads to systematic uncertainties (see e.g.Takakura et al. 2017 ;Appel et al. 2022 ).In order to impro v e data quality, some CMB experiments remove data where PWV is higher than a threshold value, typically around 3 mm for experiments optimized for the Atacama Desert.For example, POLARBEAR experiment discards its observations if the PWV exceeds a threshold of 4 mm (The POLARBEAR Collaboration 2017 ), and ABS experiment used a threshold of 2.5 mm (Kusaka et al. 2018 ).PWV measurements are also used in the instrument characterization, calibration, and null testing for data validation (Essinger-Hileman et al. 2016 ;Simon et al. 2016 ;Qu et al. 2023 ).In the null testing, the CMB observation data are split into two subsets based on an environmental or instrumental variable that may influence systematics, and consistency between the two subsets is examined.PWV is one of such environmental variables, and a null test between high-PWV and low-PWV subsets is often included in a test suite.The threshold of this split is PWV ∼ 1 mm for experiments in the Atacama Desert (Choi et al. 2020 ).Thus, PWV measurements with good fractional accuracy in the 1-3 mm range have a variety of uses in CMB analysis.

Evaluation of GNSS PWV for the data selection in CMB experiments
Here, we discuss the performance of GNSS PWV for CMB data analysis.The average time of PWV measurements is set to 1 h, which approximates the length of the basic unit of CMB data.As shown in Section 5 , hourly GNSS PWV shows a statistical uncertainty of 0.52 mm and a systematic offset of −0.05 mm.
Table 2 shows how accurately we can judge whether PWV is less than 3, 2, and 1 mm using the GNSS data.F or e xample, when data are split at PWV = 3 mm, GNSS PWV makes only a small percentage of error assuming that the radiometer PWV is the true value.Of the entire data, 1.7 per cent are misjudged as PWV GNSS > 3 mm while PWV RM < 3 mm, and 1.9 per cent are misjudged as PWV GNSS < 3 mm while PWV RM > 3 mm.Table 1.An o v erview of other published GNSS PWV comparison studies at dry places where the mean annual PWV is less than 5 mm.The parameter t is the average time of the GNSS PWV data; a and b are the linear fit parameters in equation ( 7); and STD is the standard deviation of the difference between the GNSS PWV and the compared PWV.PWV, and Fig. 8 (b) shows their cumulative plots.GNSS estimates the PWV distribution with good accuracy where PWV is higher than 1 mm.The seasonal distribution of GNSS PWV is shown in Fig. 9 .The fractions of time when PWV is less than 3, 2, and 1 mm for each month are shown in Fig. 10 .It is the advantage of GNSS instruments to continuously e v aluate site conditions throughout the year.

C O N C L U S I O N
This study focused on how accurately PWV can be measured using GNSS data at Cerro Toco in the Atacama Desert to support millimetre/submillimetre-wave astronomical observations.We used CSRS-PPP to compute ZTD from GNSS data from 2021 April to 2022 April.ZHD is estimated using two methods, one using the colocated barometer data and the other using VMF1 outputs instead of the barometer.By comparing the GNSS PWV with the radiometer PWV, we e v aluated the accuracy of the GNSS PWV.
GNSS PWV supported by the barometer data showed a small offset of −0.05 mm.Using the VMF1 outputs, GNSS PWV showed a larger offset.We assume that the offset strongly depends on the accuracy of ZHD estimation model.The statistical uncertainty of GNSS PWV is 0.52 mm with 1 h time average.The statistical uncertainty can be reduced by blocking multireflected GNSS signals, using multiple types of GNSS satellites (Li et al. 2015 ;Lu et al. 2017   hourly PWV with better than 1 mm accurac y, ev en in occasional adverse weather conditions at Cerro Toco.
GNSS PWV data have a wide range of applications in support of CMB experiments, including site e v aluation, data selection, instrument characterization, and null testing.GNSS instruments are reliable and easily accessible tools for PWV measurements and hold promise for improving future millimetre/submillimetre-wave observations.

A P P E N D I X A : M O D E L L I N G T H E R E G I O NA L W E I G H T E D M E A N T E M P E R AT U R E I N T H E ATAC A M A D E S E RT F RO M R A D I O M E T E R A N D G N S S DATA
In this appendix, we discuss the deri v ation of the relationship between the weighted mean temperature T m and the surface temperature T s from our GNSS and radiometer data.T m is a meteorological parameter used in equation ( 5) to estimate GNSS PWV.It is calculated as ) where e ( z) and T ( z) are the water vapour pressure and the temperature, respectively, as a function of zenith height z (Davis et al. 1985 ).
T m is usually estimated using radiosonde data of temperature and relative humidity (RH) at several altitudes.To enable the estimation of T m from the ground, the following empirical approximation is often used: The coefficients c and d are known to vary from region to region.
A number of studies have established the regional T m models, some of which are shown in Table A1 .In the arid re gions, howev er, it is difficult to measure T m using radiosondes because the dry bias on the RH measurement is not negligible (see e.g.Otarola, Querel & Kerber 2011 ).
Here, we estimated the regional T m model at the SA site, located in the Atacama Desert, with the ground-based instruments of GNSS and the radiometer.First, GNSS ZWD was calculated as described in Section 4 .Then, the data were divided into groups with respect to T s as shown in Fig. A1 .The slope of the dotted line represents 1/ for each T s bin.To estimate , we remo v ed data points with RH greater than 40 per cent, which amount to 15 per cent of the entire data set.High humidity can cause bias in PWV measurements,8 which is indeed seen in the top left panels in Fig. A1 .Since T s and RH are highly correlated, bias in the small subset can lead to significant systematics here.
The radiometer PWV and GNSS ZWD were linearly fitted and 1/ was obtained for each T s group.The relationship between T s , , and T m is shown in Fig. A2 . is converted to T m using equation ( 5).The best-fitting model of our data set is T m = 1 .15 T s − 48 .6 . (A3) The fit parameters are c = 1.15 ± 0.31 and d = −48.6 ± 84, with correlation coefficient of −1.0.Our result is consistent with other regional T m models.
The fractional variation of is given as With typical values in Atacama, equation ( A4 ) can be approximated as follows: The variation of T m in this study is about ±10 K, resulting in a variation of ∼4 per cent .Our PWV estimate in Atacama impro v es by a few per cent with the surface temperature data.This ground-based method to estimate the T m model is easier to conduct than the radiosonde measurements; it is less e xpensiv e, and it is not affected by the dry bias.By continuing measurements for  several years, the uncertainties of this T m model would decrease, potentially making the accuracy of this method competitive with that of other methods.

Figure 1 .
Figure 1.A map of the area around the SA experiment (Copyright 2023 Google; TerraMetrics, LLC -www.terrametrics.com ).The radiometer data at the APEX site were used for the reference values of PWV.

Figure 3 .
Figure 3. Block diagram of the GNSS antenna and receiver system.experimentsite.A GNSS antenna (Tallysman VSP6037L 1 ) was installed on an intermodal container in 2021 April, as shown in Fig.2.The surface pressure was measured by a barometer on a weather station (Davis Vantage Pro 2 2 ) co-located with the GNSS antenna.It outputs the surface pressure every minute with a resolution of 0.1 hPa and accuracy of 1.0 hPa, and its range is 540-1100 hPa.A small percentage of the data fell below this range.

Fig. 4
Fig.4illustrates how ZWD was derived.The raw GNSS data were converted to RINEX observation files and uploaded to the CSRS-PPP website.CSRS-PPP outputs both ZTD timestreams from the GNSS data and ZHD timestreams from the gridded VMF1.ZHD was also calculated using barometer data at the SA site and equation ( 2 ).

Figure 4 .
Figure 4. Block diagram of the ZWD estimation using GNSS with and without barometer data.

Figure 5 .
Figure 5. Hourly PWV time series.(a) PWV from radiometer estimate (top) and GNSS estimate (bottom).Time periods' missing data for more than 5 h are shown in bands.The radiometer data are missing when bad weather is predicted, as well as the shutdown period from January to March.The missing data from GNSS PWV occur where the barometer data are lost.(b) Time series of radiometer PWV and GNSS PWV o v er 15 d.Missing radiometer data are shown in grey bands.No GNSS PWV data are lost in this time range.

Fig. 6 Figure 6 .
Figure 6.Scatter plot of hourly PWV measured by GNSS versus PWV measured by the radiometer.Left: w/ barometer PWV GNSS versus PWV RM .Right: w/o barometer PWV GNSS versus PWV RM .Using the co-located barometer makes the offset small.The time range where the data are lost, shown in Fig. 5 , is not included in this plot.

Figure 7 .
Figure 7. Histogram of PWV GNSS − PWV RM with average time of 15 min, 1 h, and 4 h.The time range where the data are lost, shown in Fig. 5 , is not included in this plot.

PWVFigure 8 .
Figure 8.(a) Histograms of GNSS PWV and the radiometer PWV at the SA site from 2021 April to 2022 April.(b) Cumulative plots of GNSS PWV and radiometer PWV.

7. 2
Annual PWV trend at Cerro TocoHere, we demonstrate the site e v aluation for the millimetre/submillimetre-wave observatories using GNSS data.The data range from 2021 April to 2022 April as in Section 5 .Fig.8(a) shows the histograms of the GNSS PWV and radiometer

Figure 9 .
Figure 9. Histograms of GNSS PWV at the SA site by season from 2021 April to 2022 April.

Figure 10 .
Figure 10.Fractions of GNSS PWV at the SA site less than 3, 2, and 1 mm for each month.The data are from 2021 April to 2022 April.SA site had good atmospheric conditions from April to No v ember.

Figure A1 .
Figure A1.Scatter plot of hourly PWV versus ZWD for each surface temperature range in the Atacama Desert.The dashed line corresponds to the linear fit and the solid line corresponds to = 0.151.PWV was measured by the radiometer (Section 4.3 ) and ZWD was measured by the GNSS instruments.In the linear fit, data with RH greater than 40 per cent are remo v ed to mitigate the radiometer systematics due to the possible presence of liquid water or snow.

Figure A2 .
Figure A2.The relationship between the weighted mean temperature T m and the surface temperature T s in the Atacama Desert obtained from Fig. A1 .

Table 2 .
The fractions of PWV GNSS with respect to PWV RM split by a threshold of 3, 2, and 1 mm.

Table A1 .
The regional T m models established by previous studies and this study.