Evaluation of New Submillimeter VLBI Sites for the Event Horizon Telescope

Figure 4 compares the 225 GHz opacity calculated with the am code using MERRA-2 data against the logged tipping radiometer measurements made at three different EHT sites. The tipping radiometer data sets are each multiyear: 1995–2004 for ALMA/APEX ⁹ , 2013–2017 for LMT (Ferrusca & Contreras 2014), and 2009–2014 for SMA (Radford & Peterson 2016). The tipper data were minimally flagged for ${\tau }_{225}$ extremes, and more than 95% of entries were kept for each site. The am calculation is for the same dates as the tipper entries except for APEX, which is done for our nominal 10 year period ending on the first day of 2019. The agreement between the medians of the calculations and field measurements supports our methods. The calculation reproduces the wide range of seasonal opacities between median ${\tau }_{225}=0.04$ at APEX in July to ${\tau }_{225}=0.47$ at LMT. Seasonal features, like the dip in July/August opacity at the LMT, are also reproduced. Figure 4 confirms that the calculation methods accurately reflect ensemble observing conditions at geographically varied sites.

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Figure 5 plots the PWV statistics throughout the year at existing and candidate new sites. The northern sites (top row) generally exhibit minimum PWV values during December and January. Southern sites in the bottom row exhibit minimum PWV values during July and August. Historically, EHT observations are performed in March or April, when the northern sites still have reasonably dry atmospheres and ALMA has a median PWV column of 1–2 mm. All of the existing EHT sites have a median PWV column in March and April that is less than 5 mm. Most of the sites we analyze have comparable PWV statistics in those months.

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The PWV averages we report, which are derived from the MERRA-2 data, agree with measurements available in the literature for both the 2021 array sites (plus ALMA) and for the candidate new sites. At the South Pole, which is presently the driest site in the array, radiosonde measurements collected over several decades show PWV ranges from about 0.25 mm in July to just below 0.8 mm in January (Chamberlin 2001). The medians we derive for the SPT site are 0.24 mm in July and 0.8 mm in January. At Kitt Peak, multiyear infrared measurements done in the 1980s found median PWVs ranging from about 4 mm in winter to 27 mm in August during monsoon season (Wallace & Livingston 1984). We find 3.8–4.2 mm in winter and about 23 mm in August. Thus, for the driest and wettest sites in the EHT array, we find that the interpolated MERRA-2-based PWV agrees with what has been measured in the field.

PWV field measurements have also been made at many of the candidate new sites, and in most of those cases, we also find that the MERRA-2 PWV values are reliable. At Dome A and Dome C, the yearly median PWV values reported from satellite data from 2008 to 2010 are 0.21 and 0.28 mm, respectively (Tremblin et al. 2012). We find yearly medians of 0.19 and 0.29 mm for those sites, which are in good agreement as expected since the satellite data used would have been assimilated into MERRA-2. Ground-based radiometer measurements between 2009 and 2014 (Ricaud et al. 2015) observed mean seasonal PWV values of about 0.3 mm during June–August and about 0.7 mm in December–February. We find a similar range: 0.2 mm in June–August and 0.6 mm in December–February.

Precipitable water vapor measurements for Teide and Roque de los Muchachos Observatory in the Canary Islands were made using Global Positioning System path delays and radiosondes (Castro-Almazán et al. 2016). For the years 2012 and 2013, monthly median PWV values at CI ranged from about 2 mm in February to about 9 mm in August compared with our 10 year medians of 2.3 mm and 7.9 mm in February and August, respectively.

The European Southern Observatory performed a multi-instrument campaign involving optical, far-infrared, and radiosonde measurements at Paranal and La Silla (Querel et al. 2010). The study concluded that between 2005 and 2009, those sites had mean PWV columns of 2.3 ± 1.8 and 3.4 ± 2.4 mm, respectively. Those values are close to the mean of the monthly medians we obtain from interpolating MERRA-2 data: 2.6 mm at PAR and 3.6 mm at LAS. Both the Querel et al. (2010) result and our value agree with a two-year field measurement made using a 183 GHz radiometer (Kerber et al. 2015), which found 3.0 mm.

While the agreement with the literature is good for most of the sites we analyze, there are a few cases where the agreement is not as close. Far-infrared radiometer measurements made on intervals between 1984 and 1987 at Pico Veleta (Quesada 1989) returned median PWV values of 1.2 mm in January up to 4.1 mm in September. We find slightly more water for IRAM-30 m: 2.5 mm in January and 6.7 mm in September. At JELM, field measurements beginning in the late 1970s found 1.4 mm of water vapor in winter up to 6.8 mm in August (Grasdalen et al. 1985). We find about 3.0 mm in winter and almost 12 mm in August. In these cases, discrepancies could be caused by local effects that the MERRA-2 profiles do not resolve. Future field measurements will be needed to determine if such anomalies exist at particular sites.

As we have already established, cloud liquid water also affects submillimeter opacity. In Figure 6, the LWP and PWV values at the existing EHT sites are plotted for each 3 hr bin in the MERRA-2 data set, and the median of each axis is marked with a red line. The correlation between the LWP and PWV variables ranges from weak to strong depending on the site, with the Pearson coefficient varying from about 0.3 to a little more than 0.7, and the maximum LWP values range from 50 μm at the South Pole to approximately 200 μm at several of the sites. Figure 7 shows the same information but for the candidate new sites. The LWP/PWV correlation coefficients have a similar range as the existing sites: approximately 0.3 to 0.75 with the exception of CAS. At the BAN, BGA, BGK, NOR, NZ, and SPX sites, there are a significant number of days when the vapor content is less than 5 mm, but the liquid content is approaching 100 μm.

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At some of the sites in Figures 6 and 7 there is only moderate correlation between the LWP and PWV statistics. The frequency of appreciable cloud cover is therefore important in its own right. In Table 3, we show the number of days per month with at least 50 μm of LWP column on a bimonthly basis, which corresponds to a 0.13 and 0.18 opacity increase above the clear-sky conditions at 230 and 345 GHz, respectively. In March, the existing EHT sites have an average of five or fewer days each month with heavy cloud cover. Twenty-five of the candidate new sites have a comparable frequency of clouded days and would therefore be similarly reliable for observing.

Table 3. Days with at Least 50 μm LWP

Site	Jan.	Mar.	May	Jul.	Sep.	Nov.
ALMA/APEX	${1}_{0}^{2}$	${0}_{0}^{1}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
GLT	${2}_{1}^{4}$	${2}_{1}^{4}$	${9}_{8}^{11}$	${10}_{9}^{13}$	${13}_{12}^{16}$	${7}_{6}^{9}$
IRAM-30 m	${2}_{2}^{4}$	${4}_{3}^{6}$	${3}_{2}^{5}$	${0}_{0}^{0}$	${2}_{2}^{4}$	${4}_{3}^{6}$
JCMT/SMA	${1}_{1}^{2}$	${3}_{2}^{5}$	${1}_{1}^{3}$	${0}_{0}^{1}$	${2}_{1}^{3}$	${2}_{2}^{4}$
KP	${2}_{2}^{4}$	${1}_{0}^{2}$	${0}_{0}^{1}$	${9}_{8}^{11}$	${4}_{3}^{6}$	${1}_{1}^{2}$
LMT	${0}_{0}^{1}$	${2}_{1}^{3}$	${7}_{6}^{10}$	${10}_{9}^{12}$	${15}_{14}^{18}$	${2}_{2}^{4}$
NOEMA	${4}_{3}^{5}$	${5}_{4}^{7}$	${10}_{9}^{12}$	${6}_{5}^{8}$	${6}_{5}^{8}$	${5}_{4}^{7}$
SMT	${2}_{1}^{3}$	${1}_{1}^{2}$	${1}_{0}^{2}$	${10}_{9}^{12}$	${6}_{5}^{8}$	${1}_{1}^{2}$
SPT	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
BAJA	${1}_{1}^{3}$	${0}_{0}^{1}$	${0}_{0}^{1}$	${3}_{2}^{4}$	${2}_{2}^{4}$	${0}_{0}^{1}$
BAN	${6}_{5}^{8}$	${11}_{9}^{13}$	${13}_{11}^{15}$	${16}_{15}^{19}$	${11}_{9}^{13}$	${9}_{7}^{11}$
BAR	${1}_{0}^{2}$	${1}_{1}^{2}$	${3}_{2}^{5}$	${3}_{3}^{5}$	${1}_{1}^{2}$	${0}_{0}^{1}$
BGA	${3}_{2}^{4}$	${6}_{5}^{8}$	${13}_{12}^{15}$	${10}_{9}^{12}$	${7}_{6}^{9}$	${3}_{2}^{5}$
BGK	${23}_{22}^{25}$	${23}_{21}^{25}$	${19}_{18}^{22}$	${16}_{15}^{18}$	${22}_{21}^{24}$	${22}_{21}^{24}$
BLDR	${2}_{1}^{4}$	${3}_{3}^{5}$	${7}_{6}^{9}$	${7}_{6}^{9}$	${5}_{4}^{6}$	${2}_{1}^{3}$
BMAC	${10}_{9}^{13}$	${8}_{6}^{10}$	${2}_{1}^{4}$	${1}_{0}^{2}$	${1}_{1}^{2}$	${4}_{3}^{6}$
BOL	${17}_{15}^{19}$	${13}_{12}^{16}$	${5}_{4}^{7}$	${3}_{2}^{4}$	${8}_{7}^{10}$	${10}_{9}^{12}$
BRZ	${13}_{12}^{16}$	${17}_{15}^{19}$	${7}_{6}^{9}$	${3}_{3}^{5}$	${5}_{4}^{7}$	${16}_{15}^{18}$
CAS	$2{6}_{26}^{28}$	$2{3}_{22}^{26}$	$1{9}_{17}^{21}$	$1{7}_{16}^{19}$	$1{8}_{17}^{21}$	$2{4}_{23}^{26}$
CAT	${5}_{4}^{7}$	${6}_{5}^{8}$	${9}_{8}^{12}$	${8}_{7}^{10}$	${8}_{7}^{10}$	${8}_{7}^{10}$
CNI	${1}_{1}^{2}$	${2}_{1}^{3}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{1}$	${2}_{2}^{4}$
Dome A	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
Dome C	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
Dome F	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
ERB	${5}_{4}^{7}$	${7}_{6}^{9}$	${3}_{3}^{5}$	${0}_{0}^{0}$	${0}_{0}^{1}$	${5}_{4}^{7}$
FAIR	${3}_{3}^{5}$	${3}_{2}^{4}$	${12}_{11}^{14}$	${19}_{18}^{22}$	${10}_{9}^{13}$	${4}_{3}^{6}$
FUJI	${1}_{0}^{2}$	${2}_{2}^{4}$	${4}_{3}^{6}$	${10}_{9}^{12}$	${7}_{6}^{9}$	${2}_{2}^{4}$
GAM	${8}_{7}^{10}$	${7}_{6}^{9}$	${0}_{0}^{1}$	${0}_{0}^{0}$	${0}_{0}^{1}$	${1}_{1}^{2}$
GARS	${22}_{21}^{24}$	${21}_{20}^{24}$	${18}_{16}^{20}$	${14}_{13}^{17}$	${15}_{14}^{17}$	${21}_{20}^{23}$
GLT-S	${0}_{0}^{0}$	${0}_{0}^{0}$	${1}_{0}^{2}$	${1}_{1}^{2}$	${1}_{1}^{3}$	${0}_{0}^{1}$
HAN	${0}_{0}^{1}$	${1}_{1}^{2}$	${3}_{2}^{5}$	${7}_{6}^{10}$	${4}_{3}^{5}$	${0}_{0}^{1}$
HAY	${9}_{7}^{11}$	${10}_{9}^{13}$	${13}_{11}^{15}$	${11}_{10}^{13}$	${8}_{7}^{10}$	${9}_{7}^{11}$
HOP	${2}_{2}^{4}$	${1}_{0}^{2}$	${0}_{0}^{1}$	${12}_{11}^{15}$	${6}_{5}^{8}$	${1}_{1}^{2}$
JELM	${2}_{1}^{3}$	${3}_{2}^{5}$	${7}_{6}^{9}$	${6}_{5}^{8}$	${4}_{3}^{6}$	${2}_{1}^{4}$
KEN	${4}_{3}^{6}$	${9}_{7}^{11}$	${10}_{9}^{12}$	${11}_{10}^{14}$	${8}_{7}^{10}$	${15}_{14}^{18}$
KILI	${5}_{4}^{7}$	${9}_{8}^{12}$	${4}_{3}^{6}$	${0}_{0}^{0}$	${1}_{0}^{2}$	${11}_{10}^{13}$
KVNYS	${4}_{3}^{5}$	${5}_{4}^{7}$	${6}_{5}^{8}$	${13}_{11}^{15}$	${7}_{6}^{9}$	${8}_{7}^{10}$
LAS	${0}_{0}^{0}$	${0}_{0}^{1}$	${1}_{1}^{3}$	${1}_{0}^{2}$	${0}_{0}^{1}$	${0}_{0}^{0}$
LLA	${5}_{4}^{7}$	${2}_{1}^{3}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
LOS	${2}_{1}^{3}$	${2}_{1}^{3}$	${3}_{2}^{4}$	${9}_{8}^{11}$	${6}_{5}^{8}$	${2}_{1}^{3}$
NOB	${5}_{4}^{7}$	${9}_{8}^{11}$	${10}_{9}^{12}$	${19}_{18}^{21}$	${16}_{14}^{18}$	${10}_{9}^{12}$
NOR	${4}_{3}^{6}$	${6}_{5}^{8}$	${8}_{7}^{10}$	$1{6}_{14}^{18}$	$1{1}_{9}^{13}$	${4}_{3}^{6}$
NZ	${12}_{10}^{14}$	${9}_{8}^{11}$	${11}_{10}^{13}$	${10}_{8}^{12}$	${11}_{10}^{14}$	${12}_{11}^{14}$
ORG	${4}_{3}^{6}$	${8}_{6}^{10}$	${7}_{6}^{9}$	${1}_{1}^{2}$	${2}_{2}^{4}$	${5}_{4}^{7}$
OVRO	${3}_{2}^{4}$	${3}_{2}^{5}$	${4}_{3}^{6}$	${4}_{3}^{5}$	${1}_{1}^{3}$	${2}_{1}^{3}$
PAR	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{1}$	${0}_{0}^{0}$	${0}_{0}^{0}$	${0}_{0}^{0}$
PIKE	${1}_{0}^{2}$	${1}_{1}^{3}$	${3}_{3}^{5}$	${8}_{7}^{10}$	${3}_{3}^{5}$	${0}_{0}^{2}$
SAN	${2}_{1}^{3}$	${1}_{0}^{2}$	${1}_{0}^{2}$	${3}_{2}^{5}$	${1}_{1}^{3}$	${0}_{0}^{1}$
SGO	${1}_{0}^{2}$	${0}_{0}^{1}$	${2}_{1}^{3}$	${1}_{1}^{3}$	${1}_{1}^{3}$	${0}_{0}^{1}$
SOC	${2}_{1}^{3}$	${2}_{1}^{3}$	${2}_{2}^{4}$	${11}_{10}^{13}$	${8}_{6}^{10}$	${1}_{1}^{3}$
SPX	${2}_{2}^{4}$	${3}_{3}^{5}$	${12}_{10}^{14}$	${12}_{11}^{14}$	${7}_{5}^{9}$	${3}_{2}^{4}$
SUF	${4}_{3}^{5}$	${6}_{5}^{8}$	${9}_{8}^{11}$	${1}_{1}^{2}$	${0}_{0}^{2}$	${3}_{2}^{5}$
YAN	${19}_{17}^{21}$	${20}_{19}^{23}$	${9}_{8}^{11}$	${4}_{3}^{6}$	${9}_{8}^{11}$	${12}_{10}^{14}$
YBG	${0}_{0}^{0}$	${0}_{0}^{1}$	${4}_{3}^{6}$	${16}_{14}^{18}$	${10}_{9}^{12}$	${0}_{0}^{0}$

Note. Sub/superscripts are 25/75th percentiles, respectively.

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Unlike PWV statistics, which have a seasonality that depends strongly on hemisphere, the seasonality of cloud cover is more regional. For example, the sites in the southwestern United States have increased cloudiness in late summer because of the North American monsoon. Except for NOEMA, which does not exhibit much seasonal variation to begin with, none of the existing EHT sites has its greatest number of clouded days in March. This supports the idea that March and April are good months for EHT observations. Of the candidate new sites, some, like BGK and YAN, probably have a prohibitive number of clouded days throughout the year. Other sites show remarkable seasonal dependence. For example, GAM goes from eight clouded days in January to zero days throughout June and August. If the EHT eventually moves from once-per-year, campaign-style observations to remotely controlled observations that target the optimal conditions for each source, then it may be possible to capitalize on such variability.

While PWV and LWP are good indicators of observing conditions, radiative transfer at a particular site also depends on local vertical properties of moisture and temperature (Paine 2019) and must therefore be calculated. Table 4 presents the zenith 230 GHz opacity. Opacities are calculated using the local thermodynamic conditions above each site. Neither March nor April are extreme seasons for the 230 GHz zenith opacity. Of the candidate new sites, 21 of them have median zenith opacity of less than 0.2 during either of those months. The sites with median opacity below 0.10 (Dome A, Dome C, Dome F, FUJI, GLT-S, LLA, NOR, and PIKE) have interquartile ranges that vary from less than 0.01 at Antarctic sites to 0.2 elsewhere. A second tier of sites have opacities between 0.1 and 0.15 (BAJA, BAR, HAN, PAR, SGO, SPX, and YBG).

Table 4. Zenith Opacity at 230 GHz

Site	Jan.	Feb.	Mar.	Apr.	May	Jun.	Jul.	Aug.	Sep.	Oct.	Nov.	Dec.
ALMA/APEX	${0.13}_{0.06}^{0.26}$	${0.15}_{0.07}^{0.31}$	${0.08}_{0.04}^{0.16}$	${0.06}_{0.03}^{0.11}$	${0.04}_{0.03}^{0.07}$	${0.04}_{0.03}^{0.06}$	${0.03}_{0.02}^{0.06}$	${0.03}_{0.03}^{0.05}$	${0.04}_{0.03}^{0.06}$	${0.04}_{0.03}^{0.06}$	${0.04}_{0.03}^{0.07}$	${0.07}_{0.04}^{0.15}$
GLT	${0.16}_{0.13}^{0.26}$	${0.15}_{0.12}^{0.25}$	${0.15}_{0.13}^{0.24}$	${0.21}_{0.16}^{0.31}$	${0.37}_{0.29}^{0.58}$	${0.65}_{0.53}^{0.94}$	${0.84}_{0.69}^{1.17}$	${0.82}_{0.62}^{1.27}$	${0.53}_{0.39}^{0.82}$	${0.37}_{0.24}^{0.60}$	${0.24}_{0.17}^{0.40}$	${0.17}_{0.13}^{0.30}$
IRAM-30 m	${0.14}_{0.08}^{0.24}$	${0.13}_{0.07}^{0.24}$	${0.15}_{0.08}^{0.29}$	${0.20}_{0.12}^{0.34}$	${0.24}_{0.14}^{0.37}$	${0.30}_{0.20}^{0.43}$	${0.26}_{0.16}^{0.40}$	${0.33}_{0.21}^{0.49}$	${0.29}_{0.19}^{0.45}$	${0.26}_{0.15}^{0.42}$	${0.19}_{0.11}^{0.36}$	${0.15}_{0.08}^{0.27}$
JCMT/SMA	${0.06}_{0.04}^{0.12}$	${0.08}_{0.04}^{0.17}$	${0.08}_{0.04}^{0.20}$	${0.08}_{0.05}^{0.16}$	${0.08}_{0.05}^{0.16}$	${0.09}_{0.06}^{0.15}$	${0.11}_{0.06}^{0.17}$	${0.09}_{0.06}^{0.21}$	${0.08}_{0.05}^{0.17}$	${0.11}_{0.06}^{0.22}$	${0.09}_{0.05}^{0.21}$	${0.07}_{0.04}^{0.17}$
KP	${0.21}_{0.13}^{0.40}$	${0.21}_{0.13}^{0.36}$	${0.24}_{0.15}^{0.37}$	${0.25}_{0.16}^{0.37}$	${0.29}_{0.20}^{0.43}$	${0.45}_{0.26}^{0.78}$	${1.47}_{1.11}^{1.77}$	${1.31}_{0.97}^{1.66}$	${0.92}_{0.54}^{1.31}$	${0.40}_{0.25}^{0.65}$	${0.26}_{0.16}^{0.42}$	${0.24}_{0.14}^{0.40}$
LMT	${0.09}_{0.05}^{0.15}$	${0.09}_{0.05}^{0.16}$	${0.13}_{0.06}^{0.21}$	${0.19}_{0.12}^{0.33}$	${0.25}_{0.15}^{0.45}$	${0.40}_{0.20}^{0.63}$	${0.37}_{0.22}^{0.56}$	${0.39}_{0.26}^{0.58}$	${0.49}_{0.31}^{0.69}$	${0.26}_{0.11}^{0.46}$	${0.14}_{0.07}^{0.27}$	${0.09}_{0.05}^{0.16}$
NOEMA	${0.16}_{0.09}^{0.29}$	${0.16}_{0.09}^{0.30}$	${0.19}_{0.12}^{0.33}$	${0.27}_{0.17}^{0.45}$	${0.37}_{0.22}^{0.62}$	${0.46}_{0.31}^{0.71}$	${0.48}_{0.31}^{0.69}$	${0.45}_{0.29}^{0.67}$	${0.39}_{0.24}^{0.60}$	${0.29}_{0.16}^{0.51}$	${0.25}_{0.14}^{0.45}$	${0.17}_{0.09}^{0.31}$
SMT	${0.12}_{0.07}^{0.20}$	${0.11}_{0.06}^{0.19}$	${0.13}_{0.07}^{0.20}$	${0.15}_{0.09}^{0.22}$	${0.17}_{0.12}^{0.26}$	${0.30}_{0.16}^{0.51}$	${0.82}_{0.60}^{1.05}$	${0.73}_{0.51}^{0.99}$	${0.48}_{0.29}^{0.73}$	${0.19}_{0.12}^{0.34}$	${0.13}_{0.07}^{0.22}$	${0.13}_{0.07}^{0.21}$
SPT	${0.06}_{0.05}^{0.07}$	${0.05}_{0.05}^{0.06}$	${0.05}_{0.04}^{0.05}$	${0.04}_{0.04}^{0.05}$	${0.04}_{0.04}^{0.05}$	${0.04}_{0.03}^{0.04}$	${0.04}_{0.03}^{0.04}$	${0.04}_{0.03}^{0.04}$	${0.04}_{0.03}^{0.04}$	${0.04}_{0.04}^{0.05}$	${0.04}_{0.04}^{0.05}$	${0.06}_{0.05}^{0.07}$
BAJA	${0.13}_{0.07}^{0.25}$	${0.11}_{0.06}^{0.20}$	${0.12}_{0.07}^{0.21}$	${0.13}_{0.07}^{0.21}$	${0.14}_{0.09}^{0.21}$	${0.19}_{0.12}^{0.39}$	${0.67}_{0.40}^{0.94}$	${0.56}_{0.31}^{0.82}$	${0.34}_{0.16}^{0.62}$	${0.16}_{0.09}^{0.27}$	${0.13}_{0.07}^{0.21}$	${0.13}_{0.07}^{0.22}$
BAN	${0.24}_{0.14}^{0.42}$	${0.20}_{0.12}^{0.37}$	${0.27}_{0.16}^{0.45}$	${0.30}_{0.20}^{0.49}$	${0.43}_{0.29}^{0.65}$	${0.62}_{0.45}^{0.89}$	${0.69}_{0.51}^{0.99}$	${0.65}_{0.49}^{0.94}$	${0.48}_{0.33}^{0.73}$	${0.36}_{0.22}^{0.58}$	${0.27}_{0.16}^{0.46}$	${0.21}_{0.13}^{0.36}$
BAR	${0.11}_{0.05}^{0.17}$	${0.08}_{0.05}^{0.14}$	${0.11}_{0.06}^{0.16}$	${0.12}_{0.07}^{0.19}$	${0.16}_{0.11}^{0.25}$	${0.19}_{0.12}^{0.29}$	${0.29}_{0.16}^{0.48}$	${0.21}_{0.13}^{0.37}$	${0.17}_{0.11}^{0.27}$	${0.14}_{0.08}^{0.21}$	${0.11}_{0.06}^{0.16}$	${0.09}_{0.05}^{0.16}$
BGA	${0.15}_{0.09}^{0.26}$	${0.16}_{0.11}^{0.27}$	${0.19}_{0.11}^{0.33}$	${0.25}_{0.14}^{0.43}$	${0.37}_{0.24}^{0.60}$	${0.46}_{0.29}^{0.73}$	${0.42}_{0.27}^{0.67}$	${0.39}_{0.26}^{0.58}$	${0.36}_{0.21}^{0.58}$	${0.26}_{0.13}^{0.45}$	${0.21}_{0.12}^{0.33}$	${0.15}_{0.08}^{0.26}$
BGK	${0.58}_{0.34}^{0.94}$	${0.54}_{0.31}^{0.89}$	${0.51}_{0.29}^{0.87}$	${0.54}_{0.30}^{0.94}$	${0.62}_{0.37}^{1.08}$	${0.76}_{0.51}^{1.20}$	${0.89}_{0.65}^{1.39}$	${0.92}_{0.63}^{1.47}$	${0.89}_{0.54}^{1.43}$	${0.73}_{0.43}^{1.17}$	${0.60}_{0.34}^{1.02}$	${0.53}_{0.29}^{0.92}$
BLDR	${0.21}_{0.13}^{0.30}$	${0.20}_{0.14}^{0.33}$	${0.24}_{0.16}^{0.36}$	${0.31}_{0.24}^{0.48}$	${0.46}_{0.33}^{0.63}$	${0.54}_{0.39}^{0.76}$	${0.84}_{0.62}^{1.11}$	${0.73}_{0.54}^{0.99}$	${0.53}_{0.37}^{0.76}$	${0.36}_{0.25}^{0.51}$	${0.24}_{0.15}^{0.34}$	${0.20}_{0.13}^{0.30}$
BMAC	${0.63}_{0.40}^{0.99}$	${0.62}_{0.36}^{1.02}$	${0.49}_{0.29}^{0.76}$	${0.30}_{0.16}^{0.53}$	${0.22}_{0.13}^{0.39}$	${0.12}_{0.07}^{0.24}$	${0.13}_{0.07}^{0.22}$	${0.16}_{0.08}^{0.29}$	${0.21}_{0.12}^{0.39}$	${0.30}_{0.17}^{0.51}$	${0.37}_{0.22}^{0.60}$	${0.49}_{0.30}^{0.80}$
BOL	${0.39}_{0.27}^{0.51}$	${0.42}_{0.29}^{0.54}$	${0.34}_{0.22}^{0.49}$	${0.24}_{0.14}^{0.40}$	${0.15}_{0.08}^{0.29}$	${0.12}_{0.05}^{0.24}$	${0.09}_{0.05}^{0.20}$	${0.11}_{0.05}^{0.22}$	${0.17}_{0.08}^{0.34}$	${0.27}_{0.14}^{0.43}$	${0.27}_{0.16}^{0.43}$	${0.37}_{0.25}^{0.51}$
BRZ	${0.71}_{0.34}^{1.35}$	${0.63}_{0.36}^{1.14}$	${0.97}_{0.54}^{1.47}$	${0.63}_{0.31}^{1.14}$	${0.43}_{0.21}^{0.76}$	${0.33}_{0.15}^{0.58}$	${0.24}_{0.11}^{0.46}$	${0.22}_{0.09}^{0.45}$	${0.36}_{0.13}^{0.69}$	${0.71}_{0.36}^{1.17}$	${0.94}_{0.49}^{1.47}$	${0.94}_{0.54}^{1.51}$
CAS	${0.80}_{0.53}^{1.27}$	${0.76}_{0.48}^{1.24}$	${0.71}_{0.46}^{1.17}$	${0.60}_{0.37}^{1.02}$	${0.49}_{0.33}^{0.82}$	${0.48}_{0.31}^{0.78}$	${0.45}_{0.27}^{0.73}$	${0.46}_{0.29}^{0.76}$	${0.48}_{0.30}^{0.78}$	${0.54}_{0.34}^{0.89}$	${0.63}_{0.42}^{1.05}$	${0.73}_{0.48}^{1.14}$
CAT	${0.31}_{0.20}^{0.53}$	${0.34}_{0.20}^{0.58}$	${0.31}_{0.19}^{0.54}$	${0.29}_{0.15}^{0.54}$	${0.31}_{0.14}^{0.62}$	${0.30}_{0.15}^{0.54}$	${0.26}_{0.13}^{0.48}$	${0.29}_{0.13}^{0.54}$	${0.24}_{0.13}^{0.48}$	${0.27}_{0.15}^{0.49}$	${0.29}_{0.17}^{0.51}$	${0.31}_{0.20}^{0.58}$
CNI	${0.16}_{0.09}^{0.27}$	${0.13}_{0.08}^{0.25}$	${0.16}_{0.08}^{0.27}$	${0.16}_{0.11}^{0.29}$	${0.19}_{0.12}^{0.30}$	${0.22}_{0.15}^{0.37}$	${0.26}_{0.15}^{0.46}$	${0.39}_{0.20}^{0.60}$	${0.33}_{0.20}^{0.54}$	${0.30}_{0.17}^{0.53}$	${0.22}_{0.12}^{0.42}$	${0.17}_{0.09}^{0.34}$
Dome A	${0.03}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.02}^{0.03}$	${0.02}_{0.02}^{0.03}$	${0.02}_{0.02}^{0.03}$	${0.02}_{0.02}^{0.03}$	${0.02}_{0.02}^{0.03}$	${0.02}_{0.02}^{0.02}$	${0.02}_{0.02}^{0.02}$	${0.02}_{0.02}^{0.03}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.04}$
Dome C	${0.05}_{0.04}^{0.06}$	${0.04}_{0.04}^{0.05}$	${0.04}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.04}$	${0.04}_{0.03}^{0.04}$	${0.05}_{0.04}^{0.05}$
Dome F	${0.04}_{0.04}^{0.05}$	${0.04}_{0.03}^{0.04}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.02}^{0.03}$	${0.03}_{0.02}^{0.03}$	${0.03}_{0.02}^{0.03}$	${0.03}_{0.02}^{0.03}$	${0.03}_{0.03}^{0.03}$	${0.03}_{0.03}^{0.04}$	${0.04}_{0.03}^{0.04}$
ERB	${0.24}_{0.15}^{0.40}$	${0.27}_{0.15}^{0.43}$	${0.31}_{0.20}^{0.51}$	${0.42}_{0.27}^{0.62}$	${0.54}_{0.39}^{0.73}$	${0.48}_{0.33}^{0.65}$	${0.49}_{0.33}^{0.71}$	${0.46}_{0.31}^{0.63}$	${0.43}_{0.30}^{0.58}$	${0.45}_{0.29}^{0.67}$	${0.33}_{0.19}^{0.54}$	${0.26}_{0.15}^{0.46}$
FAIR	${0.21}_{0.11}^{0.34}$	${0.20}_{0.13}^{0.31}$	${0.17}_{0.11}^{0.29}$	${0.27}_{0.19}^{0.42}$	${0.49}_{0.36}^{0.78}$	${0.80}_{0.60}^{1.14}$	${1.02}_{0.78}^{1.43}$	${0.87}_{0.65}^{1.27}$	${0.56}_{0.39}^{0.84}$	${0.36}_{0.24}^{0.53}$	${0.20}_{0.13}^{0.36}$	${0.22}_{0.14}^{0.36}$
FUJI	${0.04}_{0.03}^{0.08}$	${0.05}_{0.03}^{0.13}$	${0.06}_{0.03}^{0.16}$	${0.08}_{0.04}^{0.22}$	${0.13}_{0.05}^{0.34}$	${0.29}_{0.12}^{0.63}$	${0.49}_{0.29}^{0.80}$	${0.49}_{0.29}^{0.76}$	${0.34}_{0.13}^{0.63}$	${0.13}_{0.05}^{0.39}$	${0.07}_{0.03}^{0.19}$	${0.04}_{0.03}^{0.11}$
GAM	${0.94}_{0.60}^{1.35}$	${1.02}_{0.60}^{1.51}$	${0.84}_{0.53}^{1.24}$	${0.56}_{0.34}^{0.82}$	${0.33}_{0.21}^{0.48}$	${0.19}_{0.11}^{0.29}$	${0.19}_{0.11}^{0.30}$	${0.20}_{0.12}^{0.33}$	${0.30}_{0.14}^{0.51}$	${0.42}_{0.21}^{0.63}$	${0.48}_{0.25}^{0.73}$	${0.62}_{0.39}^{0.94}$
GARS	${0.71}_{0.51}^{1.14}$	${0.76}_{0.51}^{1.20}$	${0.78}_{0.48}^{1.24}$	${0.60}_{0.34}^{1.05}$	${0.58}_{0.33}^{1.05}$	${0.53}_{0.27}^{0.94}$	${0.40}_{0.21}^{0.82}$	${0.40}_{0.21}^{0.82}$	${0.48}_{0.25}^{0.94}$	${0.58}_{0.34}^{1.05}$	${0.62}_{0.42}^{1.05}$	${0.67}_{0.48}^{1.05}$
GLT-S	${0.06}_{0.05}^{0.09}$	${0.06}_{0.05}^{0.08}$	${0.05}_{0.04}^{0.08}$	${0.06}_{0.05}^{0.11}$	${0.09}_{0.07}^{0.15}$	${0.13}_{0.09}^{0.20}$	${0.16}_{0.12}^{0.22}$	${0.15}_{0.12}^{0.24}$	${0.13}_{0.08}^{0.20}$	${0.08}_{0.06}^{0.14}$	${0.06}_{0.05}^{0.11}$	${0.05}_{0.04}^{0.08}$
HAN	${0.07}_{0.05}^{0.12}$	${0.11}_{0.07}^{0.15}$	${0.12}_{0.08}^{0.19}$	${0.17}_{0.12}^{0.25}$	${0.22}_{0.15}^{0.31}$	${0.30}_{0.21}^{0.43}$	${0.53}_{0.37}^{0.69}$	${0.56}_{0.37}^{0.71}$	${0.26}_{0.15}^{0.45}$	${0.12}_{0.08}^{0.16}$	${0.08}_{0.06}^{0.13}$	${0.07}_{0.05}^{0.11}$
HAY	${0.42}_{0.22}^{0.73}$	${0.45}_{0.26}^{0.82}$	${0.54}_{0.30}^{0.99}$	${0.78}_{0.48}^{1.35}$	${1.35}_{0.89}^{2.21}$	${1.77}_{1.20}^{2.66}$	${2.21}_{1.56}^{3.00}$	${2.04}_{1.43}^{2.81}$	${1.51}_{0.94}^{2.41}$	${1.05}_{0.65}^{1.83}$	${0.65}_{0.39}^{1.14}$	${0.53}_{0.31}^{0.97}$
HOP	${0.17}_{0.11}^{0.31}$	${0.17}_{0.11}^{0.30}$	${0.19}_{0.12}^{0.30}$	${0.21}_{0.14}^{0.31}$	${0.24}_{0.16}^{0.36}$	${0.42}_{0.25}^{0.73}$	${1.27}_{0.99}^{1.61}$	${1.14}_{0.87}^{1.51}$	${0.80}_{0.49}^{1.17}$	${0.33}_{0.20}^{0.56}$	${0.21}_{0.13}^{0.34}$	${0.19}_{0.11}^{0.33}$
JELM	${0.19}_{0.11}^{0.27}$	${0.17}_{0.12}^{0.30}$	${0.21}_{0.14}^{0.31}$	${0.27}_{0.20}^{0.42}$	${0.39}_{0.29}^{0.54}$	${0.45}_{0.31}^{0.60}$	${0.65}_{0.46}^{0.89}$	${0.58}_{0.42}^{0.80}$	${0.43}_{0.29}^{0.62}$	${0.30}_{0.21}^{0.45}$	${0.20}_{0.13}^{0.30}$	${0.17}_{0.11}^{0.27}$
KEN	${0.16}_{0.09}^{0.31}$	${0.17}_{0.09}^{0.34}$	${0.22}_{0.11}^{0.48}$	${0.46}_{0.26}^{0.71}$	${0.39}_{0.24}^{0.60}$	${0.33}_{0.20}^{0.54}$	${0.34}_{0.19}^{0.53}$	${0.31}_{0.16}^{0.53}$	${0.26}_{0.16}^{0.45}$	${0.34}_{0.21}^{0.54}$	${0.43}_{0.27}^{0.63}$	${0.30}_{0.17}^{0.51}$
KILI	${0.19}_{0.09}^{0.37}$	${0.17}_{0.09}^{0.39}$	${0.26}_{0.13}^{0.49}$	${0.37}_{0.21}^{0.58}$	${0.26}_{0.15}^{0.42}$	${0.15}_{0.08}^{0.24}$	${0.09}_{0.06}^{0.17}$	${0.12}_{0.06}^{0.21}$	${0.13}_{0.08}^{0.21}$	${0.17}_{0.09}^{0.33}$	${0.31}_{0.17}^{0.51}$	${0.31}_{0.17}^{0.51}$
KVNYS	${0.24}_{0.16}^{0.40}$	${0.29}_{0.17}^{0.49}$	${0.39}_{0.24}^{0.63}$	${0.65}_{0.42}^{1.05}$	${1.02}_{0.67}^{1.56}$	${1.97}_{1.43}^{2.53}$	${3.22}_{2.41}^{3.91}$	${3.00}_{2.21}^{3.91}$	${1.56}_{1.05}^{2.30}$	${0.80}_{0.53}^{1.24}$	${0.56}_{0.31}^{0.99}$	${0.29}_{0.17}^{0.53}$
LAS	${0.29}_{0.17}^{0.46}$	${0.27}_{0.17}^{0.42}$	${0.22}_{0.15}^{0.34}$	${0.19}_{0.13}^{0.29}$	${0.20}_{0.13}^{0.30}$	${0.16}_{0.11}^{0.26}$	${0.14}_{0.08}^{0.22}$	${0.14}_{0.09}^{0.22}$	${0.14}_{0.09}^{0.22}$	${0.15}_{0.11}^{0.24}$	${0.17}_{0.12}^{0.25}$	${0.20}_{0.13}^{0.29}$
LLA	${0.22}_{0.11}^{0.40}$	${0.26}_{0.12}^{0.46}$	${0.13}_{0.06}^{0.22}$	${0.07}_{0.04}^{0.13}$	${0.05}_{0.03}^{0.08}$	${0.04}_{0.03}^{0.06}$	${0.04}_{0.03}^{0.06}$	${0.04}_{0.03}^{0.06}$	${0.05}_{0.03}^{0.07}$	${0.04}_{0.03}^{0.07}$	${0.06}_{0.04}^{0.09}$	${0.12}_{0.06}^{0.25}$
LOS	${0.24}_{0.16}^{0.36}$	${0.26}_{0.17}^{0.36}$	${0.27}_{0.19}^{0.39}$	${0.34}_{0.24}^{0.46}$	${0.42}_{0.30}^{0.58}$	${0.56}_{0.34}^{0.87}$	${1.17}_{0.92}^{1.47}$	${1.08}_{0.80}^{1.35}$	${0.80}_{0.53}^{1.11}$	${0.43}_{0.29}^{0.63}$	${0.27}_{0.17}^{0.40}$	${0.25}_{0.16}^{0.37}$
NOB	${0.24}_{0.16}^{0.40}$	${0.25}_{0.16}^{0.48}$	${0.31}_{0.19}^{0.63}$	${0.46}_{0.27}^{0.89}$	${0.71}_{0.42}^{1.24}$	${1.35}_{0.89}^{2.12}$	${2.04}_{1.51}^{2.66}$	${2.12}_{1.61}^{2.81}$	${1.51}_{0.89}^{2.30}$	${0.73}_{0.43}^{1.43}$	${0.43}_{0.26}^{0.80}$	${0.29}_{0.19}^{0.49}$
NOR	${0.08}_{0.04}^{0.17}$	${0.08}_{0.04}^{0.21}$	${0.09}_{0.05}^{0.26}$	${0.14}_{0.06}^{0.37}$	${0.21}_{0.09}^{0.54}$	${0.48}_{0.22}^{0.99}$	${0.84}_{0.51}^{1.31}$	${0.87}_{0.53}^{1.35}$	${0.53}_{0.17}^{1.05}$	${0.16}_{0.06}^{0.53}$	${0.12}_{0.05}^{0.29}$	${0.09}_{0.05}^{0.21}$
NZ	${0.43}_{0.24}^{0.87}$	${0.40}_{0.24}^{0.76}$	${0.34}_{0.19}^{0.71}$	${0.34}_{0.17}^{0.69}$	${0.30}_{0.17}^{0.58}$	${0.24}_{0.13}^{0.48}$	${0.24}_{0.12}^{0.45}$	${0.29}_{0.14}^{0.53}$	${0.30}_{0.15}^{0.56}$	${0.34}_{0.17}^{0.62}$	${0.37}_{0.21}^{0.69}$	${0.43}_{0.24}^{0.82}$
ORG	${0.24}_{0.13}^{0.42}$	${0.24}_{0.15}^{0.40}$	${0.27}_{0.17}^{0.49}$	${0.30}_{0.20}^{0.49}$	${0.42}_{0.27}^{0.62}$	${0.46}_{0.33}^{0.65}$	${0.53}_{0.37}^{0.73}$	${0.51}_{0.37}^{0.69}$	${0.42}_{0.29}^{0.58}$	${0.36}_{0.22}^{0.51}$	${0.27}_{0.15}^{0.45}$	${0.24}_{0.13}^{0.43}$
OVRO	${0.42}_{0.24}^{0.69}$	${0.42}_{0.31}^{0.56}$	${0.49}_{0.33}^{0.65}$	${0.51}_{0.39}^{0.69}$	${0.67}_{0.48}^{0.89}$	${0.67}_{0.48}^{0.94}$	${0.97}_{0.60}^{1.43}$	${0.76}_{0.51}^{1.17}$	${0.67}_{0.48}^{0.97}$	${0.56}_{0.40}^{0.80}$	${0.45}_{0.31}^{0.65}$	${0.40}_{0.26}^{0.62}$
PAR	${0.20}_{0.12}^{0.33}$	${0.21}_{0.14}^{0.39}$	${0.16}_{0.12}^{0.26}$	${0.14}_{0.09}^{0.22}$	${0.13}_{0.09}^{0.21}$	${0.11}_{0.07}^{0.17}$	${0.09}_{0.06}^{0.14}$	${0.09}_{0.07}^{0.15}$	${0.09}_{0.06}^{0.15}$	${0.11}_{0.07}^{0.15}$	${0.11}_{0.08}^{0.15}$	${0.14}_{0.09}^{0.21}$
PIKE	${0.07}_{0.05}^{0.12}$	${0.07}_{0.04}^{0.11}$	${0.08}_{0.05}^{0.13}$	${0.12}_{0.07}^{0.19}$	${0.16}_{0.11}^{0.26}$	${0.20}_{0.13}^{0.31}$	${0.36}_{0.22}^{0.54}$	${0.31}_{0.21}^{0.48}$	${0.20}_{0.12}^{0.33}$	${0.12}_{0.07}^{0.19}$	${0.08}_{0.05}^{0.12}$	${0.07}_{0.05}^{0.11}$
SAN	${0.15}_{0.08}^{0.27}$	${0.13}_{0.07}^{0.22}$	${0.15}_{0.08}^{0.25}$	${0.16}_{0.11}^{0.26}$	${0.21}_{0.13}^{0.33}$	${0.21}_{0.13}^{0.36}$	${0.63}_{0.27}^{0.92}$	${0.48}_{0.26}^{0.78}$	${0.31}_{0.17}^{0.54}$	${0.20}_{0.12}^{0.33}$	${0.15}_{0.09}^{0.25}$	${0.15}_{0.08}^{0.26}$
SGO	${0.16}_{0.11}^{0.26}$	${0.15}_{0.09}^{0.25}$	${0.13}_{0.08}^{0.20}$	${0.12}_{0.07}^{0.19}$	${0.13}_{0.07}^{0.21}$	${0.11}_{0.06}^{0.19}$	${0.11}_{0.06}^{0.17}$	${0.11}_{0.06}^{0.19}$	${0.11}_{0.06}^{0.17}$	${0.12}_{0.07}^{0.19}$	${0.12}_{0.08}^{0.19}$	${0.13}_{0.08}^{0.20}$
SOC	${0.24}_{0.15}^{0.37}$	${0.25}_{0.16}^{0.37}$	${0.27}_{0.19}^{0.39}$	${0.31}_{0.22}^{0.45}$	${0.39}_{0.26}^{0.54}$	${0.56}_{0.34}^{0.89}$	${1.31}_{1.05}^{1.66}$	${1.24}_{0.94}^{1.56}$	${0.94}_{0.62}^{1.27}$	${0.45}_{0.30}^{0.69}$	${0.29}_{0.17}^{0.43}$	${0.26}_{0.16}^{0.42}$
SPX	${0.09}_{0.05}^{0.17}$	${0.09}_{0.05}^{0.17}$	${0.11}_{0.06}^{0.19}$	${0.15}_{0.08}^{0.27}$	${0.24}_{0.13}^{0.40}$	${0.30}_{0.16}^{0.49}$	${0.30}_{0.16}^{0.53}$	${0.29}_{0.16}^{0.51}$	${0.21}_{0.12}^{0.39}$	${0.15}_{0.08}^{0.27}$	${0.14}_{0.07}^{0.25}$	${0.09}_{0.06}^{0.19}$
SUF	${0.22}_{0.13}^{0.37}$	${0.25}_{0.13}^{0.43}$	${0.37}_{0.22}^{0.60}$	${0.46}_{0.29}^{0.71}$	${0.62}_{0.43}^{0.89}$	${0.65}_{0.49}^{0.87}$	${0.62}_{0.48}^{0.78}$	${0.54}_{0.40}^{0.73}$	${0.42}_{0.30}^{0.54}$	${0.36}_{0.22}^{0.54}$	${0.29}_{0.16}^{0.45}$	${0.20}_{0.11}^{0.36}$
YAN	${0.56}_{0.42}^{0.67}$	${0.60}_{0.48}^{0.71}$	${0.60}_{0.46}^{0.71}$	${0.49}_{0.34}^{0.63}$	${0.37}_{0.24}^{0.53}$	${0.29}_{0.19}^{0.43}$	${0.24}_{0.14}^{0.39}$	${0.27}_{0.16}^{0.42}$	${0.37}_{0.24}^{0.51}$	${0.43}_{0.29}^{0.56}$	${0.45}_{0.29}^{0.60}$	${0.53}_{0.39}^{0.65}$
YBG	${0.07}_{0.05}^{0.09}$	${0.08}_{0.06}^{0.12}$	${0.12}_{0.08}^{0.19}$	${0.17}_{0.12}^{0.26}$	${0.29}_{0.20}^{0.43}$	${0.58}_{0.36}^{0.80}$	${0.82}_{0.71}^{1.02}$	${0.78}_{0.63}^{0.94}$	${0.63}_{0.45}^{0.78}$	${0.20}_{0.14}^{0.33}$	${0.09}_{0.07}^{0.13}$	${0.07}_{0.06}^{0.09}$

Note. Sub/superscripts are 25th / 75th percentiles, respectively.

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The opacities we report agree reasonably well with published field measurements. At the Greenland Summit site, a multiyear 225 GHz radiometer campaign beginning in 2010, found that the median opacity during the winter months was about 0.06 (Matsushita et al. 2017). We find a similar median opacity: 0.05 to 0.06. The median in July is also similar: 0.16–0.19 in the Matsushita et al. (2017) field measurement and 0.16 for our retrieval.

At the HAN site, 220 GHz tipping radiometer measurements beginning at the end of 1999 until the middle of 2001 have been published (Ananthasubramanian et al. 2002). The monthly median opacities reported are ${0.07}_{0.05}^{0.09}$ in January and ${0.37}_{0.26}^{0.46}$ in July. For 2009–2019, we calculate opacities of ${0.07}_{0.05}^{0.12}$ and ${0.53}_{0.37}^{0.69}$ in those months. The agreement in wintertime is excellent. In summer, additional field measurement data is needed to constrain the level of overlap between the experimental and model distributions.

The wintertime conditions at FUJI are very good and agree with previous 220 GHz radiometer measurements done 1994–1995 (Sekimoto et al. 1996). In December of 1994, an opacity of about 0.04 was measured, which matches exactly with the ${0.04}_{0.03}^{0.11}$ range from our calculation. The agreement in March is also within the statistical variation: 0.11 observed compared with ${0.06}_{0.03}^{0.16}$ from our 10 year average. Mount Fuji has good submillimeter conditions in winter.

Finally, our opacity calculations agree with the 225 GHz tipping radiometer measurements for 2001 September to November, reported by Marvil et al. (2006) for the BAR site. The median measured opacity was 0.11 over that time frame, which is similar to the 0.11 to 0.17 10 year median values we calculate for the same months.

The highest-frequency Fourier components ($\vec{u}$) sampled during the 230 GHz observation in 2017 of the M87* source were measured on the baseline between Hawaii and Spain (Event Horizon Telescope Collaboration et al. 2019a) and corresponded to 25 μas instrumental angular resolution defined by the fringe spacing λ/D, where λ is the observing wavelength and D is the projected baseline length to the source. There is interest in operating at 345 GHz or potentially higher frequencies at the stations with suitable conditions, which could improve the nominal resolution by 50% or more. Most of the 2021 EHT sites are capable of 345 GHz operation during at least part of the year, and the transmittances (${Tr}\,=\,-\mathrm{ln}\tau$) of each existing site during March and April are plotted in Figure 8. Although the transmittance threshold for 345 GHz capability depends on the telescope sensitivity and other details like the atmospheric coherence, we can make a reasonable estimate of the transmittance that is required. Consider the case of a 0.1 Jy correlated flux density at 45° elevation with two-bit digital efficiency, and a 345 GHz zenith transmittance of 0.6 (opacity of 0.5) and sky-brightness temperature of 150 K. Under those conditions, two stations with 10 m diameter antennas having 64 μm effective surface-accuracy apertures and 100 K receiver temperatures integrating for 100 s at 8 GHz fringe-finding bandwidth would achieve an S/N 3 detection. Stronger detections would be achieved on baselines to large apertures like ALMA or NOEMA.

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The existing sites in Chile, Hawaii, and the South Pole have median March 345 GHz transmittance of 0.75 or greater. The South pole, in particular, has excellent 345 GHz transmittance even at the 25th percentile. The SPT site also has relatively good transmittance at 410 GHz (above 70%). Zenith transmission spectra for the new sites are plotted in Figure 9. Of these, Dome A , Dome C, and Dome F have high-frequency conditions that are similar to the SPT site. The FUJI, GLT-S, HAN, LLA, and PIKE sites are similar to the ALMA/APEX and JCMT/SMA sites: more opaque than Antarctica and more variable. BAJA, BAR, NOR, SGO, SPX, and YBG have comparable 345 GHz transmittance to the LMT site and would probably be viable during a useful fraction of time.

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The high-frequency transmittances we calculate are in agreement with published values. At Dome C, the 345 GHz value for an atmosphere with the median PWV of 0.28 mm have been reported to be between 0.85 and 0.90 (Tremblin et al. 2012). At Dome A, that same study found 345 GHz transmittance in median conditions to be greater than 0.9. Both of those findings agree with the spectra we report specifically for March. At Yangbajing Observatory, for a median atmosphere containing 2.8 mm of water vapor, that same Tremblin et al. (2012) study concluded that YBG has 345 GHz transmittance of 55%–60%. In March, we derive a similar median PWV of 2.4 mm for the YBG site and correspondingly greater transmittance of about 0.67.

The 230 GHz Fourier coverage for each candidate new site is plotted in Figure 10 for M87* and in Figure 11 for Sgr A*. These coverages are based on the source position and array geometry; we have not flagged low S/N visibilities as we do in the subsequent Monte Carlo filling-factor calculations. The coverage is for a full 24 hr of observing including times when ALMA cannot observe the source. Tracks corresponding to baselines with ALMA are plotted in bold. The tracks of the 2021 EHT array are underlaid in gray for reference. The 2021 array with ALMA lacks coverage between about 4 and 7 Gλ in the north–south direction for both M87* and Sgr A*. Sgr A* also lacks mid-baseline coverage between 1 and 3 Gλ as well as long-baseline coverage in the east–west direction. In these plots, an elevation cutoff of 10° was specified, which is especially important for the very short tracks at large u-v spacing, e.g., for FUJI and SPX toward M87*.

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The number of new baselines is determined by the covisibility of the new site with the 2021 array with ALMA. For M87*, all of the considered sites that can observe that source form at least five new baselines. For Sgr A*, some sites form as few as two new baselines. The mean longitude of the 2021 EHT sites is 76° west. Sites near that longitude have significant covisibility with the existing EHT sites and with ALMA and therefore tend to make long u-v tracks.

Some site locations are more desirable than others because they sample obvious gaps in Fourier coverage. For M87*, the BOL, BRZ, CNI, BMAC, GAM, HAY, NZ, and YAN locations fill portions of the 4-7 Gλ gap in the north–south direction. The BMAC, CAS, CAT, GAM, GARS, NZ, SGO, and YBG sites extend the longest baselines. For Sgr A*, the 2021 coverage contains gaps between 4 and 7 Gλ in the north–south direction, which are filled by CAS, CAT, GARS, KEN, and KILI. Sites in central and southern Africa, e.g., KILI together with GAM, could significantly improve the resolution of the array in the east–west direction.

The geometric Fourier coverage contributed by a new site is important, but only if the weather conditions at that new site are adequate for making detections. The Monte Carlo incremental coverage, which flags intervals with low S/N values based on the probabilistic weather at each site, is presented in Figure 12 for a specific set of observing parameters: 10 m antennas at new stations, simultaneous 230 and 345 GHz frequency coverage, and 8 GHz bandwidth in each of two sidebands. For the simulations in Figures 12 and 13, the observing schedule is limited to times when ALMA can see the source, which is consistent with previous EHT schedules (Event Horizon Telescope Collaboration et al. 2019c). The bandwidth per frequency band is a projected doubling of the present-day EHT (Event Horizon Telescope Collaboration et al. 2019a) and helps compensate for some of the additional noise at 345 GHz. For M87*, an extended 500 μas FoV is specified, which is motivated by future efforts to connect horizon-scale structure with the M87* jet (Blackburn et al. 2019). For Sgr A*, a 150 μas FoV is used. We assume an observing time commensurate with the variability timescale of each source. M87* evolves slowly, so a full observation is specified to maximize the coverage on each baseline. Sgr A* evolves on a timescale of minutes (Event Horizon Telescope Collaboration et al. 2019a), so a 100 s snapshot observation is simulated, which truncates the Fourier coverage. Our approach to flagging low S/N scans accounts for the noise contributed by the physical temperature of the atmosphere. This is important at low-altitude polar sites like GLT and GARS, where the cold atmosphere compensates for marginal opacity.

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The Monte Carlo incremental filling factor is calculated in the following way. For the full observations, we report the Fourier filling of the augmented and fiducial arrays using the entirety of the Fourier coverage tracks, ${F}_{\mathrm{aug}}/{F}_{\mathrm{fid}}-1$. For the snapshot observations of Sgr A*, we vary the start time for the fiducial and augmented arrays independently to maximize the filling in each case: $\max \left({F}_{\mathrm{aug}}\right)/\max \left({F}_{\mathrm{fid}}\right)-1$. Depending on the coordinates of a new site, there might be no start times that produce greater snapshot Fourier filling than the fiducial array, which would make the incremental filling for that site zero. The maximum filling metric is a proxy for the best instantaneous coverage achievable by a new site.

The sites with the greatest incremental filling are added sequentially to the fiducial array as indicated beginning with the 2021 EHT sites. For M87*, SGO emerges as the site that adds the greatest Fourier coverage to the 2021 array with ALMA. Repeating the calculation for a 12 station array consisting of the 2021 EHT+SGO, CNI emerges as the next best site for increasing the Fourier coverage. Similarly for Sgr A* with a full observation, Dome A, KEN, BMAC, and Dome C yield the most incremental coverage. For Sgr A* with snapshot coverage, NZ adds the most coverage to the 2021 array, followed by Dome C, then CAT, and GARS. In general, the incremental coverage for a particular new site decreases as new sites are added to the fiducial array because there are fewer gaps in the Fourier coverage to fill. Our approach of adding the best locations in sequence makes the problem of selecting a group of sites computationally manageable and leads us to an array with excellent coverage. As the ngEHT develops, a comprehensive search for the global optimum array could lead to a different selection of sites.

The Fourier filling factor we present here is one metric for approaching VLBI array design. While we favor the filling metric for its simplicity, other considerations and metrics could prioritize a different set of new sites and should be vetted in future design efforts.

To demonstrate the improvement of horizon-scale imaging that would be possible with an expanded array under realistic meteorological conditions, we compare reconstructions made using the 2017, 2021, and an example ngEHT array. In the 2017 and 2021 arrays, we combine multiple 2 GHz-wide fringe-finding bands for an aggregate bandwidth over two polarizations of 16 GHz in 2017 and 32 GHz in 2021. For the ngEHT array, we assume the same parameters as the filling factor calculation: dual-frequency 230 and 345 GHz observing with an aggregate bandwidth of 128 GHz over two polarizations. The bandwidth of the EHT backend has increased at regular intervals (Doeleman et al. 2008; Fish et al. 2011; Doeleman et al. 2012; Johnson et al. 2015; Event Horizon Telescope Collaboration et al. 2019a), and it is reasonable to anticipate continued improvement on the timescale of array expansion (Blackburn et al. 2019). The image reconstructions are shown in Figure 13. The thermal noise used for these reconstructions are calculated under median conditions.

For M87*, the FoV is extended and the temperature scale is logarithmic to highlight the base of the low-brightness forward jet. For this particular source model with the 2017 and 2021 arrays, the jet base is not faithfully reconstructed. In contrast, the additional stations in the ngEHT array and the addition of the 345 GHz band reproduces the jet out to more than five shadow diameters, and the diffuse flux surrounding the jet is more tightly constrained. The sites in the ngEHT panel were primarily chosen based on the leading sites from the Monte Carlo incremental filling analysis in Figure 12: three or four sites each for M87* and snapshot Sgr A*. BAJA, GAM, LLA, OVRO, and NOR were also included either because they sample interesting Fourier components or because they have significant infrastructure already in place. The ngEHT Fourier coverage on M87* extends to approximately 12 Gλ under nominal meteorological conditions.

The Sgr A* reconstruction is shown in linear scale. We select a start time for the Sgr A* simulated observation when the Fourier filling is greatest. With 100 s snapshot observing, the Fourier tracks normally obtained through Earth-aperture synthesis become points. For the 2017 and 2021 arrays, the Fourier points are sparse, and the arrays and eht-imaging algorithms do not converge on the known structure; however, the large number of baselines in the ngEHT simulation fills a significant fraction of the Fourier plane even in snapshot mode. The ngEHT is capable of reconstructing the ring emission of Sgr A* including the morphology of the discontinuity in the left-hand site of the image. A full multifrequency reconstruction with scattering mitigation is an active research topic; however, these short-timescale reconstructions suggest that detailed movie-making of dynamical features at Sgr A* could be possible with the ngEHT.