Luke T. Maud

# Updates to ALMA Site Properties:
using the ESO-Allegro Phase RMS database
ALMA Memo 624

Luke T. Maud  ESO Headquarters, Karl-Schwarzchild-Str 2 85748 Garching,
Germany. Email<EMAIL_ADDRESS>Andrés F. Pérez-Sánchez  Allergro - ALMA ARC
node, Leiden Observatory, Leiden University, PO Box 9513.png, 2300 RA Leiden,
The Netherlands  Yoshiharu Asaki  Joint ALMA Observatory, Alonso de Córdova
3107, Vitacura, Santiago, 763 0355, Chile  National Astronomical Observatory
of Japan, Alonso de Córdova 3788, Office 61B, Vitacura, Santiago, Chile
National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo
181-8588, Japan  Felix Stoehr  ESO Headquarters, Karl-Schwarzchild-Str 2 85748
Garching, Germany. Email<EMAIL_ADDRESS>Bill Dent  Joint ALMA Observatory,
Alonso de Córdova 3107, Vitacura, Santiago, 763 0355, Chile  María Díaz Trigo
ESO Headquarters, Karl-Schwarzchild-Str 2 85748 Garching, Germany. Email:
<EMAIL_ADDRESS>
###### Abstract

We present a long-term overview of the atmospheric phase stability at the
Atacama Large Millimeter/submillimeter Array (ALMA) site, using $>$5 years of
data, that acts as the successor to the studies summarized two decades ago by
Evans (2003). Importantly, we explore the atmospheric variations, the ‘phase
RMS’, and associated metadata of over 17000 accrued ALMA observations taken
since Cycle 3 (2015) by using the Bandpass calibrator source scans. We
indicate the temporal phase RMS trends for average baseline lengths of 500,
1000, 5000, and 10000 m, in contrast to the old stability studies that used a
single 300 m baseline phase monitor system. At the ALMA site, on the
Chajnantor plateau, we report the diurnal variations and monthly changes in
the phase RMS on ALMA relevant baselines lengths, measured directly from data,
and we reaffirm such trends in atmospheric transmission (via Precipitable
Water Vapour - PWV). We confirm that day observations have respectively higher
phase RMS and PWV in contrast to night, while the monthly variations show
Chilean winter (June - August) providing the best, high-frequency and long-
baseline observing conditions - low (stable) phase RMS and low PWV. Yet, not
all good phase stability condition occur when the PWV is low. Measurements of
the phase RMS as a function of short timescales, 30 to 240 s, that tie with
typical target source scan times, and as a function of baseline length
indicate that phase variations are smaller for short timescales and baselines
and larger for longer timescales and baselines. We illustrate that fast-
switching phase-referencing techniques, that allow short target scan times,
could work well in reducing the phase RMS to suitable levels specifically for
high-frequencies (Band 8, 9 and 10), long-baselines, and the two combined.
Understanding and counteracting atmospheric variations is fundamental for
interferometric synthesis arrays and we provide a forward look for improving
observing scenarios to use the conditions at the ALMA site most optimally in
order to maximize the science return. The Phase RMS database will be available
along with helper scripts on the ALMA science portal for public use.

##  1 Introduction

Since the ‘Site Properties and Stringency’ ALMA Memo 471 (Evans, 2003) there
has not been any global exploration of atmospheric phase stability, ‘phase
RMS’, conditions despite the many thousands of available ALMA datasets taken
since observations began. The Precipitable Water Vapour (PWV) content has been
explored in detail, as extracted from the APEX
telescope111http://archive.eso.org/wdb/wdb/asm/meteo_apex/form, measurements
at ALMA (using the Water Vapour Radiometer - WVR - system Nikolic et al. 2013)
and other site measurements (Otarola et al., 2019; Cortés et al., 2020) dating
from 2006. However, for interferometric arrays the PWV parameterises directly
only the transmission, and not the all important atmospheric phase stability
which is fundamental to being able to correlate signals from all antennas in
an array successfully.

There have been dedicated campaigns focused on e.g. long baseline conditions
(ALMA Partnership et al., 2015; Asaki et al., 2016; Matsushita et al., 2017),
and those looking to offer the high frequency observing capability at the
longest baselines (Asaki et al., 2020a, b; Maud et al., 2020, 2022). The
latter studies specifically investigated the phase RMS conditions given the
critical nature in conducting such ‘difficult’ observations and the importance
of phase stability. Globally a study about phase stability conditions for ALMA
is lacking. ALMA does have a feedback loop in place where conditions are
checked during observing and from previous observations. This is generally
used in the context of the scheduling of observations, or to understand
whether the observation currently being or already taken meet certain quality
assurance (QA) parameters (See the ALMA Technical
Handbook222https://almascience.eso.org/documents-and-tools, and Petry et al.
2020). Table 1 shows the nominal PWV levels with respect to associated highest
observing bands, which are used as a reference for scheduling
observations333The nominal PWV values are not necessarily hard-limits for the
observing bands as the observing strategy can be adjusted when scheduling
dependent on other factors such as antenna number, or longer time on source in
higher (worse) PWV at a given band., while Table 2 shows the phase RMS, as
path length variation in $\mu$m (see Section 2.2), for a limit of 30∘. A phase
RMS of 30∘ can be considered as a ‘very good’ to ‘ideal’ value (see also
Section 4.1).

Table 1: ALMA PWV octiles, the nominal PWV values for each octile and
associated highest observing bands.

Octile |  Nominal PWV (mm) |  Associated Bands
---|---|---
1 | 0.472 | Band 5a, 9, 10
2 | 0.658 | Band 8b, 9
3 | 0.913 | Band 7, 8c
4 | 1.262 | Band 7
5 | 1.796 | Band 5d, 6
6 | 2.748 | Band 4
7 | 5.186 | Band 3

aBand 5 around the 183 GHz water line.
bBand 8 at the upper end of the band, $>$430 GHz.
cBand 8 at the lower end of the band, $<$430 GHz.
dBand 5 away from the 183 GHz water line.

The ESO-Allegro Phase RMS database development study, of which this ALMA memo
presents the key results, was undertaken to make a retrospective systematic
analysis of all 12 m main array data taken from Cycle 3 to Cycle 7444The study
is still ingesting data taken after 2019 and is planning to continue.. Using
the Bandpass source scan of each observation, a snapshot of the phase RMS
conditions as a function of short timescales ($<$5-10 min) and baseline length
can be established from each observing run. Combining over 17000 EBs
(including some from 2020 and 2021), standardised to certain baseline lengths
and with measurements over a range of timescales, allows for an investigation
of the actual phase stability conditions at the ALMA site in recent history
and how they vary diurnally and monthly, or correlate with other metadata
(e.g. PWV, wind speed, temperature). The harvested phase RMS parameters can
also be used to investigate how changing observation strategies for e.g. long-
baselines and high-frequencies using fast-switching (or dynamic) phase
referencing, could be utilized to optimally use the conditions at the ALMA
site (Section 4.3), and also to remedy a common misconception often held that
low PWV means conditions are always good and that successful high frequency
observations can be made (Section 3.3.1).

##  2 Background

###  2.1 Chajnantor Plateau and overview of the Evans 2003 Memo

ALMA is situated on the Chajnantor plateau at an altitude of 5050 m in the
Andes of northern Chile. It is one of, if not the best, site for ground based
sub-millimeter wavelength astronomy. The ALMA site is high and dry. The
majority of studies on weather conditions or site parameters that discussed
long-term (years) atmospheric phase stability, as also noted in the Evans
(2003) memo (using data from 1995 to 2002), are from pre-construction surveys
and investigations that used ad-hoc monitoring systems at fixed locations on
the plateau rather than tied with actual ALMA antenna positions. In short,
these studies present both opacity/PWV data and phase RMS measurements using a
dedicated short, 300 m, baseline two element phase monitoring system555The
ALMA memo series is where tens of phase RMS specific memos are stored:
https://library.nrao.edu/alma.shtml. In brief, diurnal and seasonal variations
in opacity and phase RMS are observed (e.g. Holdaway & Matsushita, 1997;
Radford et al., 2001; Butler et al., 2001, and references therein). In the
summer666Throughout this memo, unless stated, we broadly use ‘summer’ and
’winter’ only related to December to March, and April to November,
respectively. months (starting December and through into March in Chile) there
is the so-called ‘Altiplanic winter’ (see, Otarola et al., 2019, for a
meteorological explanation) where opacity/PWV is significantly elevated as
moist air is drawn over the Andes. Generally, conditions in and around
February are so bad that ALMA does not observe and uses this month for
maintenance tasks (see the ALMA Proposer’s
Guide777https://almascience.eso.org/proposing/proposers-guide). The winter
months (broadly April through to November, and specifically June, July and
August) are those with notably lower opacity/PWV despite being modulated with
diurnal variations, where day time has higher values than the night (see also,
Otarola et al., 2019; Cortés et al., 2020).

Table 2: ALMA bands, the frequency range of the bands, the frequency used to
calculate the path length variations for a phase RMS of 30∘, and the path
length variation in $\mu$m for the phase RMS of 30∘.

Band |  Frequency Range |  Frequency |  Path Length Variation ($\mu$m)
---|---|---|---
|  (GHz) |  (GHz) |  for 30∘ phase RMS
Band 10 | 787-950 | 850 | 29
Band 9 | 602-720 | 650 | 38
Band 8 | 385-500 | 440 | 57
Band 7 | 275-373 | 320 | 78
Band 6 | 211-275 | 240 | 104
Band 5 | 163-211 | 185 | 135
Band 4 | 125-163 | 140 | 178
Band 3 | 84-116 | 100 | 250
Band 1∗ | 35-50 | 40 | 624

∗Band 1 is offered for ALMA Cycle 10.

Similarly, the phase monitor system showed that the phase RMS on a 300 m
baseline follows closely the pattern of sun rise and sun set, in that
$\sim$00:00 to 13:00 UTC (night) exhibits the lowest phase RMS, while a clear
hump begins to emerge at $\sim$13:00 UTC and peaks around 19:00 UTC
(day/afternoon), see Evans (2003, Figure 5). As Evans (2003) note, the phase
RMS from their 10 min data samples indicates that the atmosphere is only
stable enough to conduct short baseline or low frequency observations for the
majority of the time without any phase compensation. They indicate that only
10 % of time could be used for e.g. $\sim$500 GHz observations (ALMA Band 8,
with a 30∘ phase RMS limit). Although discussed, the statistics presented did
not incorporate phase compensation, i.e. phase referencing or a WVR system,
which act to lower the phase RMS and would allow higher frequency and longer
baseline observations for a larger proportion of time.

###  2.2 The Phase RMS database

For every observation execution block (EB) observed on the 12 m main array
listed as a Quality Assurance level 2 (QA2) semi-pass or pass we obtain the
raw (ASDM) data of the Bandpass calibrator source along with the WVR
information. The ASDMs are imported to Measurement Sets as per typical data
reduction using casa (CASA Team et al., 2022). We extract and store
metadata888The PWV is always reported with respect to Zenith, while all
metadata are extracted for the entire observing time, not just the Bandpass
scan length., such as PWV, wind speed, temperature and also extract
information about the calibrators and targets, such as source names and
elevation. All parameters are stored in an SQL database which is described
further in the Appendix. WVR phase corrections are applied to all datasets
using the wvrgcal command, such that we have two parallel phase-time streams
of data, with and without WVR correction. Subsequently, the Bandpass phase
solutions are obtained on an integration timescale (typically between 3-6 s
for the ALMA 12 m main array observations). Integration based solutions are
possible because the Bandpass calibrators are all point-like strong sources
with high signal-to-noise ratios (SNR). Using the gaincal command in this
process also means that automatic flags are produced for any bad or corrupted
integration(s) or antenna(s). From the antenna based phase gaintables the
baseline based phase-time streams are reconstructed and the phase RMS values
are then calculated (for all baselines) and as a function of time.

For all EBs we calculate the phase RMS for timescales of 30 s, 45 s, then 60 s
to 240 s, in 30 s steps which is possible given that the Bandpass observations
are at least 5 min long. The minimum of 30 s is chosen as this relates closely
with realistic target scan times that could be used at ALMA (see also Section
4.2). Specifically, we extract the phases for numerous overlapping samples of
a given timescale from the phase-time stream as we move from the start to the
end of the data by one integration, shifting the sampling window each time,
while calculating the phase RMS999In practice we use the standard deviation
which avoids having to make an additional solution to offset each phase-time
stream to an average zero-degrees phase, as is required when calculating the
RMS. The RMS, when using a sample with zero mean is exactly the same as the
standard deviation. per sampled window. The final phase RMS stored, for a
given baseline and timescale, is the average from all of the sampling windows.
In recent works the phase RMS measured as a function of timescale in this
manner is shown to be a reasonable proxy for establishing the amount of phase
RMS that likely remains in the science target source scans after phase
correction using phase-referencing on that timescale (Maud et al., 2020,
2022)101010There is much discussion in the various Holdaway ALMA memos that
the timescale should be half the phase referencing cycle time. However in Maud
et al. (2022) this would result in overly optimistic values of phase RMS from
their ALMA observations, while Carilli & Holdaway (1999) note that the factor
2 is appropriate for self-calibrated data where the phase solution is at the
mid-point of the timescale of a target scan.. We also store the residual phase
RMS which are measured after the application of an ideal phase gain solution
made on a given timescale, and the so-called D-phase, that is the difference
between the phase gain solutions themselves (see the Appendix for further
details). These are not used nor discussed in this memo.

Importantly, the phase RMS is stored as a frequency independent
parameter111111If the EB was taken in Band 3 (100 GHz) and achieved 10∘ phase
RMS, this is equivalent to $\sim$83 $\mu$m, which, for example then relates to
a Band 6 (250 GHz) phase RMS of $\sim$25∘., ‘Path Length’ variation in units
of microns, irrespective of the observing band (frequency) used. The path
length variation ($\ell$, in $\mu$m) can be established from $\sigma_{\phi}$
(radians), the phase RMS of the phase, $\phi$, for a given observing frequency
($\nu_{obs}$, in Hz) via:

$\ell=\frac{\sigma_{\phi}.c}{2\pi.\nu_{obs}}\quad(\mu m),$ (1)

where $c$ is the speed of light (in $\mu$m s-1)121212Excluding possible
atmospheric dispersion effects around deep atmospheric absorption lines that
can alter the path length within a given band (see Curtis et al., 2009,
although subsequent, unpublished, ALMA testing found these result could be a
factor of 2 worse than in reality).. Our sample is not limited only to the
best conditions, in terms of phase RMS, just because the conditions in some
cases allowed higher frequency bands to be used. The variations in path length
for a given observation are simply a property of the atmospheric fluctuations
at that time. Some low frequency observations were made in conditions that
could have been used for higher frequencies, especially when there were no
high frequency projects at a given time during the day or night. As we report
the phase RMS in microns we can always calculate what the highest possible
observing frequency could have been. The caveat of our sample is that we are
limited to ‘better’ conditions, in terms of PWV and likely phase RMS, as we
use data that was suitable for ALMA to observe in. For example, ALMA does not
observe in February when the PWV can exceed $>$10 mm (see Section 3.1) and
hence we clearly miss such high PWVs in our sample as compared to continual
monitoring (Otarola et al., 2019; Cortés et al., 2020). We have no phase RMS
measures from February to compare with. It is not critical that we miss the
very worst conditions as ALMA would not be able to observe, although it must
be remembered that our presented statistics are therefore percentages or
fractions based upon the time when ALMA can observe, and are not referenced to
time available in a calendar year.

####  2.2.1 Making a Comparable Phase RMS Sample

As ALMA is a reconfigurable interferometer there is a broad spread in baseline
length between ‘Compact’ and ’Extended’ arrays with $<$500 m and $>$10 km
maximal baseline lengths. We therefore produce ‘Summary’ phase RMS values for
500, 1000, 5000 and 10000 m baseline lengths (at all timescales). These are
chosen to maximise the overlap with baselines in various ALMA array
configurations. If these baseline lengths exist in a given EB (see also Figure
1), then an average phase RMS from baseline lengths about the summary value
are calculated and stored ($\pm$100, $\pm$200, $\pm$1000, $\pm$2000 m for the
four baseline lengths, respectively). In cases where any of the four summary
baseline lengths do not exist in the EB, an extrapolation is made from the
summary values that do exist131313In the case of the shortest baseline
configuration ($<$500 m longest baseline) we scale to the 500 m Summary value
using the phase RMS calculated from the longest 20 percent of baselines.. We
use the scaling values from the long baseline Spatial Structure Function (SSF)
investigations of Matsushita et al. (2017) following $b^{0.65}$ and $b^{0.22}$
for data without WVR correction applied, and $b^{0.60}$ and $b^{0.29}$ for
data with WVR correction141414Using WVR corrected data we scale the phase RMS
value at the 500 m summary baseline length by $\sim$1.51 to establish the
value at 1000 m, and thereafter we scale the 1000 m value by $\sim$1.59 to
calculate the 5000 m value, and finally we use a factor of $\sim$1.22 to scale
from 5000 to 10000 m. for baselines, $b$, $<$1 km and those $>$1 km,
respectively. There are 66 %, 48 %, 12 % and 8 % of the EBs with baselines
covering 500, 1000, 5000 and 10000 m respectively. We identify a possible
caveat here that for longer baseline observations and short timescales,
$<$60-90 s, the phase RMS can flatten from $\sim$1000-5000 m (Figure 1, Asaki
et al. 2020a, see also Figures 9 and 10 in, and Maud et al. 2022, Figure 9 in)
and thus the baseline based scaling from shorter summary baselines could
overestimate the phase RMS when projecting out to $\geq$5000 m.

The Bandpass source observations from which the phase RMS are calculated cover
a range of observing elevations, from 21∘ to 88∘, where the median elevation
of all observations is 58∘ (there are only 15 observations with elevation
$<$30∘). Figure 2 shows the distribution of the Bandpass source elevations as
well as the line indicative of the scaling factor that would be required to
normalize the phase RMS values to an elevation of 60∘ (using the ratio of
sin(elevation)/sin(60∘), see Holdaway & Ishiguro 1995). If we were to scale
everything to a 60∘ elevation, there are 3711 observations with an elevation
$<$47∘ where the phase RMS would be reduced by more than 15 %, while there are
only 93 observations $>$85∘ elevation where the phase RMS would be increased
by $>$15 %. Considering this, the phase RMS values as directly measured from
the data are higher, on average, than those we would obtain if we were to
scale everything to a 60∘ elevation. Therefore, throughout the memo we present
the phase RMS as measured under the premise that the distribution of
elevations provides a more realistic representation of how science sources are
observed on the sky at varying elevations.

Figure 1: Typical plot of the phase RMS after WVR corrections are applied (in
degrees) as calculated on 240 s (grey) and 60 s (red) timescales against
baseline length for the Bandpass source scan of a long baseline observation.
The slopes, as fitted using baselines $>$1500 m, indicate that the 60 s
timescale is shallower than the 240 s timescale (that matches closely
Matsushita et al. 2017). Hypothetically, if this observation did not have
baselines $>$5000 m then scaling the 60 s, 5000 m phase RMS to 10000 m using
the Matsushita et al. (2017) slope of 0.29 then we would overestimate the
phase RMS by $\sim$5 % as compared to the fitted slope. In reality we would
not know the slope for a short baseline observation. The bars at the bottom of
the plot indicate the ranges used for establishing the ‘Summary’ baseline
phase RMS values. Figure 2: Histogram of the Bandpass source elevations. The
orange line indicates the scaling factor that would be needed to scale the
phase RMS at the plotted elevations to a normalized 60∘ elevation. The phase
RMS of low elevation observations would decrease, while those at high
elevation would marginally increase. There are only 15 observations below 30∘
elevation which cannot be seen on the plot due to the y-axis scale.

####  2.2.2 Summary of Main Points

  * •

The database stores various metadata about each EB along with phase RMS values
for a range of timescales for each baseline of the EB, and as established on
summary baseline lengths of 500, 1000, 5000 and 10000 m.

  * •

The phase RMS are recorded and presented as a frequency (Band) independent
path length variation in units of microns. These values are irrespective of
the band the observation itself was conducted in.

  * •

The phase RMS as used throughout the report are the averages of the phase RMS
values taken over a range of baseline lengths and from multiple overlapping
time samples of the phase-time stream for each of those baselines using the
Bandpass source scan.

  * •

Extrapolating the short-baseline phase RMS values to longer baselines
($\geq$5000 m) using the fixed baseline based power-law scaling could act to
overestimate the phase RMS for shorter timescales ($<$60-90 s).

  * •

We miss the very worst conditions where observations, even at Band 3, could
not be successfully made. In particular we are likely to report lower PWV
values (at quartiles, percentiles and cumulatively) as compared to historic
continual measurements.

  * •

All percentages or fractions presented are relative to time in which ALMA can
observe.

Figure 3: Cumulative distribution function for day (solid) and night (dashed)
PWV measurements from all data of years 2015 to 2019 inclusive (colours).
Night time provides more lower PWV time for higher frequency bands to the
order of $\sim$10 %. The grey markers indicate the various nominal PWV levels
(Table 1).

##  3 Results

###  3.1 Precipitable Water Vapour

####  3.1.1 Overall Results

For completeness we briefly report on the changes in PWV, but for further
detailed analyses we direct the reader to Otarola et al. (2019); Cortés et al.
(2020). The PWV level directly translates to the transmission at ALMA and is
used to determine which observing band can be used. Figure 3 shows the
cumulative distribution function for the PWV of the data ingested from years
2015 to 2019 inclusive (colours) for day (solid line) and night (dashed line).
In all years the night time always offers lower PWV conditions overall.
Comparing the top octiles, corresponding to nominal PWV values of $<$0.472,
0.658, 0.913 and 1.262 mm PWV respectively, night time offers 5, 10, 11 and 11
% more ‘time’ than the day (averaged over all years and months). From the
conditions of the observations taken since Cycle 3, we indicate that the Band
7 nominal PWV level was met roughly $\sim$50-55 % of the time during the
night, and $\sim$40-45 % of the time during the day. Observations with nominal
Band 3 PWV conditions or better occurred $>$95% of the time when ALMA observed
on the sky. Year by year variations are of a few percent, but we do not have
an extensive sample as compared to Otarola et al. (2019); Cortés et al.
(2020). We also reiterate that the reported percentages are based on the
observations made, i.e. none during the high-PWV month of February.

Figure 4: Reproduction of the ALMA Proposer Guide Figure 2 (left) and our version as replicated using the PWV metadata stored in the Phase RMS database (right). At low PWV percentiles of 10 % and 25 % we indicate similar values, however our sample is biased to the conditions ALMA observed in and hence do not include the ‘worst’ PWV. The horizontal lines indicate the nominal PWV values for different bands. Table 3: PWV level (in mm) for all months at 10, 25, 50 and 75 th percentiles. February is excluded as there are no data. Percentile |  Jan. |  Mar. |  Apr. |  May |  June |  July |  Aug. |  Sep. |  Oct. |  Nov. |  Dec.
---|---|---|---|---|---|---|---|---|---|---|---
75 % | 4.65 | 3.27 | 2.52 | 1.45 | 1.30 | 1.53 | 1.06 | 1.56 | 1.54 | 2.14 | 2.97
50 % | 3.05 | 2.03 | 1.51 | 0.98 | 0.88 | 0.82 | 0.70 | 0\. 92 | 0.94 | 1.29 | 1.64
25 % | 1.86 | 1.23 | 0.90 | 0.64 | 0.64 | 0.58 | 0.48 | 0\. 58 | 0.63 | 0.69 | 0.94
10 % | 1.12 | 0.75 | 0.60 | 0.43 | 0.51 | 0.43 | 0.37 | 0.45 | 0.47 | 0.46 | 0.62

####  3.1.2 Seasonal Variation

Figure 4 (left panel) is a reproduction of Figure 2 from the ALMA Proposer’s
Guide that presents the PWV percentiles of 10, 25, 50 and 75 % as a function
of months. The right panel is a replicated version using the PWV metadata from
the Phase RMS database, excluding the month of February. Comparing to the
Proposer’s Guide figure, we show similar trends and similar values at the 10 %
and 25 % levels, however, as we are limited to conditions when ALMA observed
we report lower PWV values at the 50 % and 75 % levels, i.e. we indicate a
larger fraction of ‘better’ conditions. Our replicated figure is more
representative in indicating the percentiles for data that are taken and
therefore more tied with the conditions that the users can expect. However,
the global view, as shown in the ALMA Proposer’s Guide is the best
representation in terms of total time and hence for planning how many hours
ALMA could observe. In the months from May through to November the 50th
percentile level indicates Band 8 nominal PWV conditions (Table 3).

Figure 5: PWV at 25, 50 and 75 percentile levels per month over a 24 hour
period averaged over all years. The summer months, particularly December,
January and March are the worst, while the winter months June, July, August
offer $\sim$1 mm conditions approximately 50 % of the time. The time axis is
shown in UTC while the yellow band indicates sun-up and sun-set for the
various months.

####  3.1.3 Diurnal Changes

Over a 24 hour timescale the 25, 50 and 75 percentiles do not fluctuate
significantly (Figure 5). On average the maximum to minimum PWV level changes
by a factor of 2.2, 1.9 and 1.8 respectively at each quartile. The day time
generally shows an increase in PWV from $\sim$11-13 UT while the night time
hours have the lowest PWV. During the winter the increase in PWV during day
time is lower than that occurring in the summer months.

Figure 6: The percentage of time available for various bands using PWV from the Phase RMS database presented in the style of Figure 3 from the ALMA Proposer’s Guide. The box-spread are 25 and 75 % while the whiskers are the 9 and 95 % levels considering the time available per year as measured using the observations since 2015. Day time uses the UTC range 1100-2300, otherwise observations are associated with night time. Note that Band 5 at 183 GHz is paired with Band 9 and 10 as it requires very good transmission, while Band 1 can be conducted in Band 3 conditions that define the time availability in that panel. Table 4: Median percentage of time available (based on ALMA time on-sky) for each month, during day/night with cuts at the nominal PWV levels, 5.19, 2.75, 1.80, 0.91, 0.66 and 0.47 mm PWV |  Jan. |  Mar. |  Apr. |  May |  June |  July |  Aug. |  Sep. |  Oct. |  Nov. |  Dec.
---|---|---|---|---|---|---|---|---|---|---|---
5.19 | 77/79 | 91/95 | 98/98 | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 | 98/97
2.75 | 35/45 | 50/66 | 73/84 | 94/99 | 99/99 | 93/95 | 99/100 | 96/91 | 90/96 | 92/96 | 69/70
1.80 | 18/32 | 19/48 | 54/67 | 82/89 | 97/92 | 84/87 | 91/92 | 77/79 | 78/84 | 78/87 | 44/57
0.91 | 3/7 | 7/22 | 13/38 | 23/41 | 66/55 | 54/59 | 74/73 | 33/57 | 43/59 | 32/59 | 16/29
0.66 | 2/4 | 5/11 | 4/23 | 21/23 | 39/33 | 36/38 | 50/59 | 17/35 | 21/31 | 22/35 | 5/15
0.47 | 0/0 | 1/3 | 2/9 | 9/7 | 6/5 | 16/19 | 26/38 | 9/12 | 9/14 | 7/14 | 1/5

####  3.1.4 Impact on observing

Figure 6 shows the day (we use 1100 to 2300 UTC, or 7 am to 7 pm where Chilean
local time = UTC - 4) and night time percentages of time available where the
PWV falls below the nominal PWV octiles for the associated bands, as shown in
each panel, in the style of Figure 3 from the ALMA proposer guide. For the
conditions in which ALMA made observations, Band 3 (and therefore Band 1)
could have been conducted essentially at all times. For all bands there is the
clear trend for both day and night in that the summer months November to April
have the lowest percentage of ‘low’ PWV time. The winter months June through
to September provide the ‘best’ low PWV conditions, primarily in the night,
although the day median time available typically indicate only 5-10 % less
time. It is clear that higher frequency observations are most possible in
winter with Band 10 nominal PWV conditions averaging about 17 % of the time
from July to October inclusive (day and night averaged). Table 4 lists the
median percentages of time available.

###  3.2 Phase RMS

####  3.2.1 Overall Results

The Phase RMS is a main driver of the accuracy of any interferometric
observation and can be the main limiting factor. The phase RMS must to be low
enough during the scans of a particular science target after calibration as to
allow accurate and reliable image reconstruction (see also Section 4.1). As
outlined in Section 2.2, unlike previous studies (e.g. Evans, 2003; Holdaway &
Owen, 1995; Butler et al., 2001), we measure the phase RMS of ALMA data on a
range of timescales that are relevant to phase referencing cycle times,
essentially providing a proxy for the phase RMS that would remain in the scans
of a target (see also Maud et al., 2022) after phase calibration, and for ALMA
relevant baseline lengths. ALMA observations follow different observing
strategies using a range of cycle times for changing array configurations and
observing bands that we discuss further in Section 4.2, here we provide the
overall view of the measured phase RMS parameters for comparisons.

Figure 7: Cumulative distribution functions for the phase RMS ‘Summary’ values
with increasing timescale moving left to right (60, 120, 180, 240 s) and
increasing baseline length moving top to bottom (500, 1000, 5000, 10000 m).
Black and grey indicate the with and without WVR corrections applied, while
the dashed and solid lines are night and day (1100-2300 UTC). For all
baselines and timescales the night time with WVR correction provides the
largest amount of low phase RMS conditions. The orange dotted lines indicate
the levels of 30∘ phase RMS (as a path length variation in $\mu$m) for Band 9,
7 and 3 from left to right in each panel.

Figure 7 shows the night (dashed) and day (solid) cumulative distribution
functions combining all years of data using the phase RMS summary values for
baseline lengths 500, 1000, 5000, 10000 m (top to bottom) and timescales 60,
120, 180, 240 s (left to right). The black and grey represent the phase RMS as
measured with and without the WVR corrections applied, respectively, while the
orange lines indicate the Band 9, 7 and 3 phase RMS of 30∘ (as a path length
variation). The WVR system significantly improves the phase RMS and,
interestingly, when applied pushes the day time observing to lower phase RMS
as compared to night time conditions without the WVR corrections. As the WVR
corrections are significant, and they generally improve all observations, most
subsequent phase RMS plots and discussion relates to WVR applied values (see
Section 3.4 for WVR statistics). Overall, the shorter baselines and short
timescales provide more low phase RMS conditions, while long baseline and long
timescales do not provide low enough phase RMS for the highest frequency bands
(9 and 10).

Figure 8: Cumulative distribution function for the phase RMS at 120 s on the
1000 m summary baseline with WVR corrections applied. The dashed and solid
lines are night and day (1100-2300 UTC) while the colours indicate the
different complete years 2015 to 2019. The grey markers indicate the 30∘ phase
RMS as a path length variation for the various bands (Table 2). Generally at
night there is $\sim$10 % variation in different years, and thus $\pm$5 % as
compared with the cumulative function for all years. During the day the spread
is roughly doubled. Overall the same trends hold for the other baselines and
timescales.

For short baselines there is less differentiation between timescales as
compared to the longer baselines. For the 500 m baseline length at night time
with WVR correction the 30∘ Band 7 limit (see Table 2) is achieved 74, 78, 83
and 90 % of the time for moving from the longest to shortest timescales, 240,
180, 120 and 60 s. For the longest 10000 m baselines there is almost a factor
of 6 increase in the amount of time, 7, 11, 19, 41 %, that conditions meet the
same band 7 limit moving from 240 s to 60 s (see also Section 4.2). This
finding is tied with the atmospheric structure, in that the spatially large
turbulent atmospheric cells providing the most phase variations are common to
both antennas on short baselines. Interferometers are sensitive to turbulent
cells of the order (of a few) of the scale of the baseline lengths as they
move over the array. For short baselines the phase RMS saturates at timescales
of a few minutes as many small-scale cells pass over the antennas creating the
maximum variation whereas the spatially larger cells remain common to the
antenna pairs and are not ‘seen’. The phase RMS can only be notably reduced
for short baselines if moving to very short timescales, although this is
pragmatically inefficient (cf. Masson, 1994) and short baselines anyway have
intrinsically better phase RMS when measured on the same timescales as
compared to longer baselines (as shown in Figure 7). On the contrary, longer
baselines are sensitive to the spatially larger turbulent cells and so the
phase RMS increases as a function of time as many of the increasingly larger
cells pass over the array that are not common to either antenna of a given
baseline. Saturation of the phase RMS takes some tens of minutes to hours
until the largest cells have completely crossed the array (cf. Matsushita et
al., 2017). The positive aspect is that in moving to shorter timescales (10s
of seconds) there can be significant improvements (reduction) in the phase RMS
for long baselines.

Figure 9: Phase RMS levels before WVR correction (upper) and after WVR
corrections (lower), shown as path length variations in $\mu$m at the 10, 25,
50, 75 and 90 percentiles as a function of month for the various baseline and
timescales. Moving left to right and top to bottom shows timescales of 60,
120, 180, 240 s and baseline lengths of 500, 1000, 5000, 10000 m respectively.
Winter months provide more stable conditions, as do shorter baselines and
shorter timescales.

At higher frequencies the lowest phase RMS, or path length variations, are
required. Even on the shortest 500 m baseline, at night with WVR applied, the
cumulative distribution is increasing rapidly below $\sim$100 $\mu$m. At the
30∘ Band 9 limit (38 $\mu$m) there is notable difference when moving to
shorter times, from 240 to 60 s, where conditions meet the limit for 18, 24,
34 and 56 % of the time. For the longest baselines, again at night with WVR
applied, there is $\sim$4.5 % of time available with a low enough phase RMS at
the 60 s timescale to meet the Band 9 limit, and effectively zero time
available for longer timescales (also see Section 4.2). On the other hand, the
longest baselines at night with WVR applied can be conducted in Band 3 $>$80 %
of the time as it has the least strict phase RMS requirement except Band 1
which can essentially be conducted 100 % of the time at night, irrespective of
the timescale (60 s to 240 s).

In Figure 8 we present the yearly cumulative distribution for the summary 1000
m baseline and 120 s timescale with WVR correction applied. Overall each year
of data shows the same general trend with $\pm$5 % variation from the all year
average at night, and $\pm$10 % for the day. The 500 m baseline spread is
reduced by a factor of $\sim$2, the 5000 m baseline is very similar to the
1000 s baseline as shown, while the 10000 m baseline has a spread larger by a
factor of $\sim$2.

####  3.2.2 Seasonal Variation

The above cumulative values provide a rather pessimistic view on the
possibility of long baseline and high frequency observations, one of ALMA’s
key capabilities as outlined since before construction (Richer, 2005; Wootten
& Thompson, 2009). In Figure 9 we show the phase RMS, as path length
variations, before (upper panels) and after WVR application (lower panels) at
the 10, 25, 50, 75 and 90 percentile levels as a function of month in each
panel, while left to right is for the 60, 120, 180 and 240 s timescale and the
top to bottom shows baseline lengths of 500, 1000, 5000 and 10000 m
(separately for observations before and after WVR correction). Globally the
winter months (June, July, August) provide the greatest proportion of low
phase RMS conditions, although the increase of the various percentiles is
typically a factor of 2 moving to summer months ($>$3-4 for phase RMS without
WVR correction). Considering the months that ALMA can observe in, January is
by far the worst month in terms of phase stability where the percentiles
change is $>$2-3 as compared to winter months for WVR corrected phase RMS. For
Solar mode observations at ALMA the WVR system cannot be used and so the
significant yearly variations in phase RMS without WVR corrections must be
accounted for in scheduling. Note that any diurnal variations are averaged out
here.

Comparing with PWV only, as shown in Figure 4, the nominal Band 8 ($<$0.913
mm) condition is achievable in terms of transmission at the $\sim$50 % level
from May through to October, but in terms of phase RMS (after WVR application)
the short baselines indicate Band 8 conditions at the 50-75 % level while the
longest baselines show Band 8 conditions consistent with only 10-25 %,
depending on the timescale used. For the longer baselines the shortest
timescales provide a notably larger fraction of observations with low Phase
RMS conditions, of the order 2-3 times more. The PWV alone is too optimistic
in estimating when the ‘most difficult’ observations at higher frequencies and
longer baselines could be taken, but on the contrary it is the limiting factor
for shorter baselines where the phase RMS limits can be met more easily.

(a) Without WVR corrections

(b) With WVR corrections applied

Figure 10: Variation of the median phase RMS without (left) and with WVR
(right) correction as a function of month for years 2015 to 2019 inclusive.
February has no data, nor June 2017. The median phase RMS can be scaled to
longer or shorter baselines using the related power function from Section
2.2.1, i.e. 1000m to 10000m with WVR applied scales the phase RMS by (10000
m/1000 m)0.29 = 1.95. Note the change of y-axis scale between the panels.

In Figure 10 we show the median phase RMS values per month for all years 2015
to 2019 inclusive without and with WVR corrections applied for the summary
1000 m baseline length and a 120 s timescale. As noted above, there is
typically a factor of 2 change between the best and worst months (January
excluded) when WVR corrections are applied but over a factor of 4 without WVR
correction, although these median phase RMS values per month average out any
diurnal changes (see below). The median phase RMS values shown can be scaled
to longer (or shorter) baselines using the power scales indicated in Section
2.2.1, which would result in a scaling of $\sim$1.95 from the 1000 m to the
10000 m baseline using the WVR corrected data.

Figure 11: 25, 50, 75 percentiles of phase RMS, as path length variations in
$\mu$m, for the summary 1000 m baseline and 120 s timescale after WVR
corrections. The yellow bar indicates the range of sun-up and sun-down for
each month. There are clear diurnal trends, with the summer showing more
significant changes compared to the winter months. Like Figure 10, the phase
RMS can be scaled to longer or shorter baselines using the related power
function from Section 2.2.1. The horizontal grey lines are the 30∘ limits for
each band. There are no observations February.

####  3.2.3 Diurnal Changes

Figure 11 shows the phase RMS at the 25, 50 and 75 percentiles for data from
all years binned into hourly groups for all months using the summary 1000 m
baseline and 120 s timescale. The diurnal variation are much more significant
for the phase RMS as compared to those in PWV (Figure 5). In the summer months
the variation in phase RMS can change significantly, by over a factor of 7,
from the night time minima to the day time peak, whereas during winter the
change is less extreme with factors typically below 3. The day time in winter
months typically has a similar phase RMS as compared with the night time in
summer months. It is evident that the Band 9 phase RMS limit is at the 25
percentile during the night time for winter months.

Figure 12: The percentage of time when the phase RMS variability is $<$30∘
(shown as a path length variation in $\mu$m) at the various bands for the
summary 1000m baseline and as measured over a 120s timescale. The y-axis
indicates the phase RMS as a path length variation in microns. Between 1100
and 2300 UTC, equivalent to 7 am to 7 pm local Chilean time, is considered to
be "Day" time. The horizontal line within the box indicates to median, while
the box-spread are the 25th and 75th percentiles. The whiskers show the
minimum and maximal values for the best and worst year. Note, a similar plot
is presented in the ALMA Proposer’s Guide.

####  3.2.4 Implications for observations

Figure 12 is a plot following the style of the ALMA Proposer’s Guide Figure
3151515The Cycle 10 ALMA Proposer’s Guide also includes a similar version of a
phase RMS plot but where some bands are grouped together. (also see Figure 6)
showing the percentage of time available for a given observing condition,
however crucially here the observing conditions are based on the phase RMS
levels (as path length variations) using the summary 1000 m baseline and 120 s
timescale values. The limits are equivalent to $<$30∘ phase RMS for each band.
Note that, unlike Figure 6 that shows PWV (i.e. transmission), where Band 5
(183 GHz) is associated with Bands 9 and 10, here, in setting the phase RMS
limits only the frequency of the observations matters (Equation 1), and hence
Band 5 is presented separately161616Atmospheric dispersion can affect the path
length within given bands (Curtis et al., 2009), but we do not need to
consider it in calculating the representative path length variability limits
per band..

Table 5: Median percentage (to nearest percent) of time available (based on ALMA time on-sky) for each month, during day/night based on the phase RMS, as a path length variation in $\mu$m, on the summary 1000 m baseline as measured over 120 s. The path length cuts for the bands converts to $<$30∘ phase RMS per band Band |  Path Len. |  Jan. |  Mar. |  Apr. |  May |  June |  July |  Aug. |  Sep. |  Oct. |  Nov. |  Dec.
---|---|---|---|---|---|---|---|---|---|---|---|---
|  ($\mu$m) |  |  |  |  |  |  |  |  |  |  |
1 | 624 | 91/95 | 96/99 | 94/99 | 95/100 | 99/100 | 97/99 | 99/99 | 100/99 | 100/100 | 100/100 | 98/99
3 | 250 | 49/93 | 69/98 | 88/98 | 92/99 | 98/99 | 94/97 | 95/97 | 98/98 | 93/98 | 97/99 | 75/97
4 | 178 | 27/87 | 47/96 | 75/96 | 78/96 | 95/97 | 88/93 | 91/93 | 92/96 | 82/97 | 81/98 | 55/95
5 | 135 | 19/77 | 33/92 | 57/94 | 73/94 | 88/92 | 83/90 | 82/88 | 81/91 | 66/93 | 62/94 | 42/89
6 | 104 | 13/61 | 27/84 | 40/85 | 51/87 | 72/88 | 68/83 | 66/86 | 64/84 | 47/85 | 49/89 | 27/79
7 | 78 | 8/34 | 15/71 | 25/70 | 36/75 | 55/77 | 55/70 | 45/75 | 40/70 | 32/75 | 29/75 | 13/64
8 | 57 | 3/8 | 6/41 | 11/40 | 20/47 | 34/57 | 33/53 | 25/53 | 19/47 | 14/53 | 12/48 | 4/34
9 | 38 | 1/2 | 1/9 | 2/11 | 5/21 | 15/22 | 12/25 | 10/20 | 5/12 | 3/14 | 2/11 | 1/7
10 | 29 | 0/0 | 1/1 | 0/3 | 1/9 | 6/11 | 5/10 | 3/4 | 1/2 | 1/1 | 0/2 | 0/0

For all bands below and including Band 7 the night time indicates a flat
availability of time as a function of month (excluding January), while the day
time shows a notable decrease in the summer months, December thorough to March
inclusive. For Bands 8, 9 and 10 both the day and night indicate a peak in
time available for the winter months. The median percentages of time available
are listed in Table 5. Band 1 observation can essentially be conducted all the
time (except January), while Band 3 observations can typically be conducted
$>$90 % of the time. At the highest frequency bands Band 9 and 10, at best,
can be conducted $\sim$20-30 % and $\sim$10-15 % of the time, respectively,
only in the winter months during the night time when considering the 30∘ phase
RMS limit. At Band 10 a 40∘ phase RMS limit corresponds to $\sim$38 $\mu$m,
and hence the time available would be exactly as shown for Band 9.

For baselines $<$1000 m there is a few percent increase in the time available
when decreasing to the shorter, 60 s timescale, while on the contrary there is
a few percent decrease in time available moving to the longest 240 s
timescale. With respect to baseline length, for the longest summary baseline,
10000 m, the time available reduces by $\sim$10-20 % for Bands 1 to 5 and by
$\sim$20-30 % for Bands 6 and 7. At Band 8 the time available is reduced down
to a maximum of 10 % at night in the winter months, while time available at
Band 9 and 10 is effectively 0 %. As ALMA changes the observing scenario for
different array configuration and frequencies, we discuss the changing
timescales for the longer baseline lengths in Section 4.2. Overall, the time
available for any given Band can be limited by either the PWV or by the phase
RMS, and which of these dominates depends on the ALMA array configuration. The
time available based on phase RMS for the 1000 m baseline length and 120 s
(Figure 12) or 180 s timescales are well balanced with that available due to
the PWV conditions. However, it is also not necessarily true that both the PWV
and phase RMS criteria are met at the same time.

###  3.3 Correlations and Trends

We highlight here that the metadata used to compare with the phase RMS are
averages or standard deviations of the parameters from the entire duration of
the science observations, not just over the length of the Bandpass source
scan.

####  3.3.1 PWV and Phase RMS

Figure 13 shows the plot of PWV against phase RMS on the 1000 m summary
baseline length and with a 120 s timescale (after WVR correction): the left
panel indicates PWV values $<$10 mm while the right panel zooms in to data
with $<$1.5 mm PWV. Overall there is considerable scatter but also an apparent
concentration of observations towards lower PWV, $<$2 mm, and lower phase RMS,
$<$150 $\mu$m. That said, low phase RMS can occur over a wide range of PWV
values: for the 1000 m baseline and 120 s timescale phase RMS values $<$50
$\mu$m were achieved in conditions with up to $\sim$5 mm PWV, although at the
very highest PWV values, $>$5 mm, the phase RMS does not typically go below
this. On the other hand, high phase RMS can be seen in observations with $<$1
mm PWV conditions (Figure 13). As has already been shown throughout this memo,
the night time phase RMS is notably lower, although it is not necessarily due
to the PWV being lower.

(a) PWV to 10 mm

(b) PWV to 1.5 mm

Figure 13: Plots of PWV against the phase RMS (as a path length variation) for the summary 1000 m baseline and 120 s timescale. The right panel indicates the zoom in to low ($<$1.5 mm) conditions. The day and night are plotted in orange and blue respectively. By-eye it is clear that night time provides lower phase RMS conditions, but that is not necessarily tied with low PWV. In panel (b) a line is drawn that could be considered to delineate the PWV - phase RMS limit, above which there are few ‘higher’ phase RMS observations. Table 6: The range of Spearman’s-rank-correlation coefficient for weather metadata, including PWV and $\Delta$PWV against the phase RMS before and after WVR correction, including all summary baselines and 60, 120, 180 and 240 s timescales. Note the p-values are all $\sim$0, i.e. any relationships are not by chance. Parameter |  All |  Day |  Night
---|---|---|---
PWV - Phase RMS (without WVR) | 0.57-0.61 | 0.50-0.54 | 0.63-0.66
$\Delta$PWV - Phase RMS (without WVR) | 0.62-0.67 | 0.60-0.65 | 0.59-0.65
Temperature - Phase RMS (without WVR) | 0.33-0.41 | 0.34-0.41 | 0.13-0.20
Wind-speed - Phase RMS (without WVR) | 0.30-0.38 | 0.27-0.33 | 0.02-0.11
$\Delta$Wind-speed - Phase RMS (without WVR) | 0.19-0.25 | 0.15-0.21 | 0.06-0.12
Humidity - Phase RMS (without WVR) | 0.35-0.39 | 0.38-0.42 | 0.57-0.60
PWV - Phase RMS (with WVR) | 0.40-0.45 | 0.45-0.50 | 0.36-0.42
$\Delta$PWV - Phase RMS (with WVR) | 0.45-0.48 | 0.50-0.53 | 0.34-0.37
Temperature - Phase RMS (with WVR) | 0.23-0.29 | 0.29-0.36 | (-)0.12-(-)0.06
Wind-speed - Phase RMS (with WVR) | 0.41-0.48 | 0.32-0.37 | 0.16-0.24
$\Delta$Wind-speed - Phase RMS (with WVR) | 0.20-0.29 | 0.17-0.26 | 0.06-0.15
Humidity - Phase RMS (with WVR) | 0.13-0.22 | 0.23-0.32 | 0.30-0.36

Table 6 indicates the ranges of the correlation coefficient parameter from a
Spearman’s-rank-correlation test for various weather parameters, including PWV
and $\Delta$PWV (shown in Figure 14), with the phase RMS data with and without
WVR corrections applied, for day and night time separately and combined. The
PWV based correlations with phase RMS can be considered as moderate. The
coefficients indicate that $\Delta$PWV correlations could be marginally
stronger, except at night time (particularly after WVR correction). This
possibly points to different atmospheric behaviour, such as solar heating
creating more turbulence during the day that is tied with a higher variability
in PWV, although a deeper investigation on the weather conditions is beyond
the scope of this memo. Evans (2003) reported a ‘significant’ correlation
between PWV and phase RMS despite a large scatter in the data. They noted that
when the transparency is better than the median the phase RMS was ‘twice as
good as otherwise’. This roughly ties with the phase RMS data without WVR
corrections in our sample. The median phase RMS is $\sim$200 $\mu$m (1000 m
baseline, 120 s timescale), whereas the median phase RMS of data below the
median PWV (1.24 mm) is $\sim$115 $\mu$m, i.e. almost twice as good. The same
holds for day and night independently, where the PWV medians are $\sim$1.4 mm
and $\sim$1.1 mm respectively, and the phase RMS ratios change by $\sim$1.6.
Note that irrespective of the phase RMS absolute value, dependent on the
baseline length and timescale, the trends are still the same as shorter
baselines and timescales simply have lower absolute phase RMS, while longer
baselines and timescales have higher absolute phase RMS values.

Overall, lower PWV does tend to provide a higher concentration of lower phase
RMS observations, however, it is still possible to have poor phase RMS while
the transmission is good. In Figure 13, more clearly in panel (b) - dotted
line, there is a possible upper limit to the phase RMS as a function of PWV as
can be delineated by a diagonal drawn from $\sim$0.1 mm PWV and 50 $\mu$m
phase RMS up to $\sim$0.8 mm PWV and 450 $\mu$m phase RMS. Above the line
there are very few high phase RMS observations. The limit does not help
particularly with ALMA high frequency observations where $<$79 $\mu$m is
required for Band 7 or higher because values above this can occur when PWV
$>$0.2 mm, well below the nominal Band 10 PWV value (Table 1). For longer
baselines the phase RMS of the observations, and the dotted line move to
larger values.

####  3.3.2 Weather parameters with Phase RMS

Figure 14: The six panels show the $\Delta$PWV, temperature, wind speed,
$\Delta$wind speed, humidity and pressure against the phase RMS, as a path
length variation, for the summary 1000 m baseline as measured over 120 s with
WVR corrections applied. Both lower temperatures and lower wind speeds tie
with lower phase RMS values and predominantly occur at night time.

In the six panels in Figure 14 we plot the $\Delta$PWV, temperature, wind
speed, $\Delta$wind speed, humidity and pressure metadata against the phase
RMS, again on the 1000 m baseline measured over a 120 s timescale. Here we
echo the weather trends seen by Evans (2003): lower phase RMS (with and
without WVR correction) is concentrated towards lower temperatures, of which
occur primarily at night and at lower wind speeds.

Making cuts to separate the observations with temperatures above and below the
median temperature of $-$1.527∘C, we find that there are approximately 1.5
times more observations below the limit. This is closely tied with the ratio
of day to night observations, although the cut does not separate day and night
exclusively as $\sim$20 % of the observations with temperatures $<-$1.527∘C
were made in the day time (1100-2300 UTC). The corresponding median phase RMS
values (with WVR correction applied) for observations below and above the
median are $\sim$70 $\mu$m and $\sim$110 $\mu$m respectively. Similarly, in
making cuts for wind speed below and above 10 m/s we find the median phase RMS
(after WVR correction) values are $\sim$70 $\mu$m and $\sim$140 $\mu$m
respectively, pointing to high winds linking with a more turbulent atmosphere.
Lower winds speeds also predominately occur at night, where there is obviously
no solar heating, although $\sim$85 % of the observations have a wind speed
$<$10 m/s.

Humidity also appears to have a larger concentration of low phase RMS
observations at lower humidity, $<$20-30 %. A stronger correlation is also
reported at night time as compared to the day. In examining the median values
of the phase RMS at night time, 67, 76, 79, 85, 85 $\mu$m for each 10 % bin up
to 50 %, there is only a slight increase with humidity.

Based on the Spearman’s-rank-correlation coefficients reported in Table 6 the
correlations range from none to weak/moderate, and slightly differ when
considering all the observations or sub-sets of day and night. We summarize
these below:

  * •

Temperature is weakly/moderately correlated with phase RMS for the full sample
and day time, likely due to solar heating and an increase in turbulence. There
is no significant trend at night time which is predominately limited to lower
temperatures all of which have lower phase RMS.

  * •

Wind is weakly/moderately correlated with phase RMS. The correlation is
stronger after WVR corrections are applied. Observations with lower wind
speeds, $<$10 m/s, do indicate a factor of two reduction in the median phase
RMS. Similar to temperature, night time observations consists of a sub-sample
of lower wind speeds that have lower phase RMS values - therefore weakening
the night time correlation. There is no trend with wind direction (not shown).

  * •

Humidity shows a weak correlation with phase RMS after WVR application. In
comparing the median phase RMS values there is a slight trend of increasing
values with increasing (binned) humidity, however the magnitude of the change
in median phase RMS is largely outweighed by the general spread of phase RMS.

  * •

There are no correlations with atmospheric pressure. The largest correlation
coefficient is 0.13 (not tabulated).

Ultimately, irrespective of the correlations we cannot directly use the
relationships to estimate the phase RMS of a given observation based solely on
the metadata.

####  3.3.3 Other Weather Correlation

For completeness we briefly compare the weather metadata as a whole with all
other metadata values. As reported by Evans (2003), we find westerly winds are
stronger than the easterly ones, but note that the wind is usually blowing
westerly for the majority of the observations. Furthermore, the humidity and
PWV parameters have an apparent correlation, naturally more humid conditions
point to a higher likelihood of high water vapour content. Wind speed and
$\Delta$wind speed are correlated, in that higher wind speeds have the
potential to be the most variable.

###  3.4 WVR correction

A significant update in this memo compared with Evans (2003) is that the water
vapour radiometer (WVR) system171717Also see ALMA memos 252 and 361. (Hills &
Richer, 2000; Hills et al., 2001; Hills, 2004; Nikolic et al., 2013) is no
longer theory, but has been a working system for over 10 years at ALMA. As
already noted earlier, the phase RMS values are significantly improved after
application and therefore it is assumed that the WVR corrections will be
applied during calibration181818The ALMA calibration pipeline investigates
whether the phase RMS is actually reduced when the WVR corrections are
applied. Typically there is always an improvement, but in rare cases where the
phase RMS does not improve the Pipeline does not apply the WVR solutions..

Figure 15: Left - Improvement factor for the phase RMS after applying the WVR
corrections. Right - Improvement factor as a function of PWV. Colour indicates
the observing band used. Note that the brown colour is due to the overlap of
Bands 3, 6 and 7. The vast majority of data ($>$96 %) have some improvement
after WVR application ($>$1), while those without improvement are mostly
related to Band 3. Generally, lower frequency bands, observed in higher PWV
conditions have a larger median improvement factor, although there is
considerable scatter in improvement factor against PWV, and some low PWV
observations can also exhibit a large correction, $>$2-3.

The left panel of Figure 15 shows the histogram of the Improvement Factor of
the phase RMS after application of the WVR correction when considering the
phase RMS from the 1000 m summary baseline length and as measured over 120 s.
The symbols are coloured as a function of the observing band. The distribution
of the improvement factors remain largely unchanged irrespective of the
summary baseline length or timescale used. Firstly, the vast majority of the
observations ($>$96 %) are improved by the WVR application and have
improvement factors $>$1; secondly, over half of the observations ($>$58 %)
show a phase RMS improvement of a factor of 2 or more; thirdly, the majority
of observations that did not improve after WVR application were at low
frequency bands, mainly Band 3, but also for those at Band 6. Within the
nearest percent there is no change in the number of observations improved by
WVR application for changing timescales, but there is a decrease to 92 % and
90 % of observations with an improvement factor $>$1 for 5000 m and 10000 m
summary baseline lengths, respectively.

The right panel of Figure 15 shows the spread of improvement factors as a
function of PWV. For observations taken using Band 3 and 4 the improvement
factor median values are between 2.5 to 3.0 and 2.6 to 3.2 considering all
summary baselines from 500 m to 10000 m and 60 s to 240 s timescales,
respectively, while observations in all bands higher than Band 6 have median
improvement ratios $<$2.0 (see Table 7). Of course lower frequency bands can
be observed in higher PWV conditions, whereas higher frequency bands are
necessarily restricted to lower PWV. Observations in the lowest PWV conditions
do tend to have a lower improvement factor after WVR application, although
there is still a notable scatter and even data taken in 0.5-1.0 mm PWV can
have improvement factors $>$2.

There are roughly 4 % of all observations that do not improve after WVR
application (for the 1000 m summary baseline length and 120 s timescale), of
which only $\sim$2 % of those used Band 8, 9 or 10191919As noted in the
Appendix, the database is not 100 % complete and there are some tens of high
frequency observations that have not yet been ingested. However, we do not
expect the percentages to change significantly as low observing band
observations with higher PWV dominate those that do not improve after WVR
application.. The median PWV for these Band 8, 9 and 10 observations is 0.37
mm, with a maximum of only 0.55 mm, indicative of very good transmission
conditions as one would expect for high frequency observations. The median
phase RMS, as a path length variation, is $\sim$50 $\mu$m before WVR
corrections are applied (1000 m baseline, 120 s timescale) and point to the
best stability conditions. The median improvement factor for these
observations is 0.98, and hence the WVR application essentially has no effect,
rather than making the phase RMS noticeably worse.

On the contrary, the majority of observation for Band 3 to 6 that get worse,
some by more than a factor of 2 after WVR application, were taken in higher
PWV conditions ($>$1.5-2.0 mm). In these unique cases it has been found that
in the presence of clouds above ALMA the ‘continuum’ emission from liquid
water (hydrosols) dominates the WVR brightness temperature, which is used for
generating the phase corrections, and hence the WVR solutions are erroneous.
Software has since been developed, remcloud202020See the ALMA technical
handbook and the ALMA Knowledgebase Article:
https://help.almascience.org/kb/articles/what-is-remcloud-and-how-could-it-
reduce-phase-rms., that acts to remove the cloud continuum from the WVR
spectral windows and allows for a more optimal functioning of the WVR system.

Table 7: Range of quartiles of the WVR improvement ratio as a function of observing band considering baseline lengths between 500 m to 10000 m and 60 s to 240 s timescales. Note very high outlier phase RMS values beyond the 95th percentile are excluded, while improvement factors $<$1 are still included.  Quartile: |  25 |  50 |  75
---|---|---|---
Band 3 | 1.7-2.1 | 2.5-3.0 | 3.5-4.3
Band 4 | 1.8-2.1 | 2.6-3.2 | 3.6-4.4
Band 5 | 1.2-1.4 | 1.7-2.0 | 2.6-3.0
Band 6 | 1.3-1.6 | 2.0-2.4 | 3.0-3.6
Band 7 | 1.1-1.3 | 1.4-1.7 | 2.0-2.4
Band 8 | 1.0-1.2 | 1.3-1.5 | 1.6-1.9
Band 9 | 1.0-1.1 | 1.1-1.3 | 1.2-1.6
Band 10 | 1.0-1.3 | 1.1-1.3 | 1.2-1.5

##  4 Observations with ALMA

###  4.1 The Importance of Low Phase RMS

The level of the phase RMS that remains in a target source after all
calibration processes have been made will govern the quality and accuracy of
the final data, and images. With phase fluctuations remaining in the data
after calibration the coherence for interferometric visibilities (${\bf
V}={\bf V}_{0}e^{i\phi}$, where ${\bf V}_{0}$ represents the true visibilities
and $\phi$ are the phase fluctuations caused by the troposphere, Thompson et
al. 2017) can be calculated following:

$\langle{\bf V}\rangle=\langle{\bf V}_{0}\rangle\,\langle
e^{i\phi}\rangle=\langle{\bf V}_{0}\rangle\,e^{-\sigma^{2}_{\phi}/2},$ (2)

assuming Gaussian random phase fluctuations, $\phi$, with a Phase RMS of
$\sigma_{\phi}$ (in radians) and a zero degree mean phase. The parameter
$\sigma_{\phi}$ is the Phase RMS as we report throughout this memo as a path
length variation ($\ell$, in $\mu$m).

A 30∘ good-to-ideal phase RMS limit relates to a coherence value of 0.87, i.e.
87 % of the amplitude is correctly attributed to the target, the rest is
decorrelated flux, effectively spread around the image due to phase
errors212121If targets are strong enough and relatively compact phase self-
calibration can be performed that can correctly attribute the flux spread
around an image to the target as further phase corrections are possible
(Brogan et al., 2018; Richards et al., 2022).. For simplicity, for a point
source, the peak flux density will drop whereas the integrated flux over a
region around the source, larger than the synthesised beam size, would
typically recover the majority of the total flux of the source. The spreading
of flux, due to phase errors is effectively a ‘seeing’ for sub-millimeter
interferometers and thus worsening phase RMS means the expected resolution is
not actually achieved. Figure 16 shows scenarios where an ideal 1 Jy (total
flux) point source has been corrupted with simplistic Gaussian phase noise
peaking at 50∘, 70∘, 90∘ and 130∘ phase RMS at the longest baselines and where
phase RMS was increased as a function of baseline length (note that a phase
RMS of 50∘ can be considered as ‘adequate’ conditions, while $>$70∘ are very
poor). The figure illustrates the spreading of the source flux away from a
point-like structure and how the effective angular resolution is worse
(larger) than the associated synthesised beam. These corrupted images are
ideal cases where the emission is evenly spread due to the false Gaussian like
phase noise on all baselines, whereas true phase errors can include systematic
offsets and the stochastic variations caused by the atmosphere - we refer the
reader to Figure 5 of Carilli & Holdaway (1999), and Figure 5 of Maud et al.
(2022) where images of point sources are shown with worsening levels of real
phase errors.

Figure 16: Ideal 1 Jy flux point source as corrupted by simplistic Gaussian
phase noise peaking at 50∘, 70∘, 90∘ and 130∘ phase RMS levels on the longest
baselines, left to right, top to bottom. With increasing corruptions the flux
is spread further away from the source and the effective resolution of the
observations becomes worse. A point source should be unresolved within the
beam (bottom left), without any larger scale emission. The 50∘ phase RMS could
be considered as an ‘adequate’ observing condition. The black contours are the
5, 10, 20, 40, 60, 80 % levels of the same ideal point source corrupted with
$\sim$30∘ phase RMS for comparison. Peak flux densities of these images are
0.83, 0.69, 0.54 and 0.29 Jy/bm. The simulated observations use Band 6 long
baselines and have a synthesised beam of $\sim$30 mas.

Recently, investigations to open the long-baseline and high-frequency
observation capabilities of ALMA reported that 0.7 is a pragmatic image
coherence222222The peak flux density divided by the integrated flux, valid for
unresolved or point-like sources, this is also referred to as the fractional
peak flux recovered (e.g. Dodson & Rioja, 2009; Rioja & Dodson, 2011; Rioja et
al., 2015; Martí-Vidal et al., 2010) level (Asaki et al., 2020a, b; Maud et
al., 2020, 2022). For their point source test targets the image defects, away
from point-like structure (i.e. beyond the Gaussian shape of the synthesised
beam), are negligible to minimal for images with $>$0.7 image coherence. For
an image coherence below 0.5-0.6, the image defects and flux decorrelation at
significant levels, $>$3-5 sigma, are apparent. Considering the phase error
budget, that is the combination of atmospheric phase variations and the
systematic errors imparted due to the calibrator-to-target separation angle,
Maud et al. (2022) note that the phase RMS should ideally be $<$30-40∘ (good
atmospheric stability), along with the use of close phase calibrators
(reducing systematic errors), within a few degrees, as to achieve an image
coherence $>$0.7. Importantly, regardless of what array configuration is used,
or the phase referencing cycle time, the phase RMS should always meet the
required limit such that the target source is not excessively corrupted. As
already shown in Section 3.2, this is considerably easier for lower
frequencies where overall larger path length variations (Equation 1)
correspond to relatively small phase RMS levels.

###  4.2 ALMA’s current observing schemes

Because of intrinsic phase variations increasing with timescale, observing
frequency and to some extent also with baseline length232323As noted in
Section 2.2.1, for short timescales the phase RMS with baseline length does
not necessarily continue to increase moving to baselines $>$1000-5000 m. for
any given atmospheric condition, ALMA employs different observing strategies
as a function of array configuration and frequency. These are also continually
being updated, most recently for Cycle 10 at higher frequency bands (8, 9 and
10) in part from the results presented in this memo (see Section 4.3).

ALMA employs gradually faster cycle times, i.e. more frequent visits to the
phase calibrator, as a function of increasing observing bands and for
different array configuration groups. The following schemes are those used for
Cycle 9 observations (since October 2022). For the shortest baseline
configurations C-1 to C-4 ($<$784 m) the target scan time is reduced down from
10 min to 5 min for Band 3 to Band 10. Although we do not investigate
timescales $>$240 s in this memo, as described in Section 3.2.1, the phase RMS
for short baseline arrays essentially saturates as these configurations are
not sensitive to spatially larger turbulent atmospheric cells, meaning that
the phase RMS will not noticeably increase even when increasing the timescales
beyond 5-10 min at the lowest observing bands. It could be possible to
increase cycle times if phase stability is already good as to improve
efficiency (Section 4.3).

For mid-baseline length configurations, C-5 (1.4 km) and C-6 (2.4 km), the
target scan times are reduced from 5 min down to 3 min, again moving from Band
3 to Band 10. Note that the phase calibrator scan lengths are typically 30 s,
but can be 60 s for higher frequencies where sources are weaker and a
sufficient SNR is required for the calibrators. As an example, using the Phase
RMS database we compare 180 s (3 min) and 240 s (4 min) timescales and find
$\sim$5-10 % more time available (in winter months) for Band 9 and 10, in
terms of meeting the 30∘ phase RMS limit (i.e. the strategy of shorter cycle
times in ALMA operations is validated). If even faster cycle times were
possible, there would be a further increase in time available, although this
comes at the expense of higher overheads (Section 4.3).

Figure 17: The percentage of time when the phase RMS variability is $<$30∘
(shown as a path length variation in $\mu$m) at the various bands for the
summary 5000m baseline length and as measured over a 60 s timescale which
closely ties with the C-7 ALMA configuration and the 54 s target scan time
(compare with e.g. Figure 12). The y-axis indicates the phase RMS as a path
length variation in microns. Between 1100 and 2300 UTC is considered to be
"day" time. The horizontal line within the box indicates to median, the box-
spread are the 25th and 75th percentiles, and whiskers are the minimum and
maximum values per month considering all years.

For the C-7 (3.6 km) configuration a 54 s target scan time is used for all
bands. Observing efficiency is not reduced significantly compared to the
shorter baseline configurations because the scan time of the phase calibrator
is also reduced to maintain a reasonable duty cycle (18 s is used, so the
cycle times are $\sim$76 s including 2 s slewing242424Note that ‘slewing’
encompasses not only the antenna movement ($<$2 s), but antenna and software
stabilisation. to and 2 s slewing from the target). Using these short target
scan times means that ALMA can observe at long baselines $>$90 % of the time
for Band 3 to Band 5 at night in all months other than January and December,
and $>$70-80 % of the time during the day in winter months (Figure 17), based
upon the 30∘ phase RMS limit. For Bands 8 and 9 the time available based on
the phase RMS limit is reasonably coincident with that available based on
meeting the nominal PWV (compare with Figure 6), $\sim$40 % and $\sim$10-20 %
at night time in the winter months, respectively. Band 10 observations are the
most difficult to conduct given the short amount of time available that meets
the 30∘ limit. If however a 40∘ limit was acceptable (acknowledging the slight
drop in coherence) then the time available matches that for Band 9, that is
almost doubled from $\sim$5-7 % to $\sim$10-15 % at night time for winter
months (i.e. 38 $\mu$m $\sim$40∘ at Band 10). Recall that in Section 2.2.1 we
obtain the longer summary baseline phase RMS values by scaling from shorter
summary baseline lengths for most EBs, and hence we may overestimate the phase
RMS for the 60 s timescale and therefore we provide a more pessimistic view of
the time available.

At the longest baselines, configurations C-8 (8.5 km) to C-10 (16.2
km)252525Band 9 is limited to the C-8 and C-9 configurations, while Band 10 is
limited to the C-8 configuration as of Cycle 9 which offered all
configurations. C-9 and C-10 are not offered in Cycle 10, Bands 3 to 7 also
use a 54 s target scan time, while Band 8, 9 and 10 gradually decrease the
target scan times down to 30 s, i.e. fast switching at Band 10 (see below).
There is still $>$85-90 % of observing time available at Bands 3 to 5 at night
because the phase RMS does not increase significantly with baseline length
moving from 5000 m to 10000 m (see Section 2.2.1). At high frequencies($>$385
GHz) phase calibrators are weaker and fewer in number (see Asaki et al.,
2020a). This fact contravenes the requirement of fast cycle times for long
baselines, where short calibrator scans are required, because the SNR of
calibrators is not always sufficient for successful phase referencing. Only
since Cycle 9 have long baseline high frequency observations been offered to
the community, in part, as a result of the commissioning of the Band-to-Band
(B2B) mode (see Asaki et al., 2020a) that allows phase calibrators to be
observed at a lower frequency band while observing the target at a high
frequency band. In using the B2B technique the phase calibrators observed at
low frequencies are stronger, meaning that short scan times provide sufficient
SNR for phase solutions, and they are more closely located to a target on the
sky (see also the ALMA technical
handbook262626https://almascience.eso.org/proposing/technical-handbook). Using
the Phase RMS database, in Figure 18 we illustrate the moderate increase in
the observing time available from $\sim$5-10 % at night time in the winter
months to $\sim$10-15 % (up to a factor of 1.5 increase dependent on month) at
Band 9 and 10 when reducing the timescale from 60 s to 45 s, in the left and
right panels respectively. We use the phase RMS limit of 30∘ for Band 9 and
40∘ at Band 10, both equivalent to a path length variation of 38 $\mu$m. The
improvement means that the percentage of time available at the 45 s timescale
is constrained by that available when high frequency nominal PWV conditions
are met ($<$0.472 mm), whereas for the 60 s timescale the percent of observing
time available is otherwise limited by the phase RMS requirements and ALMA
would not be optimising the use of low PWV conditions should they arise.

Figure 18: The percentage of time when the phase RMS variability is $<$30-40∘
at Band 9/10 for the summary 10000m baseline length, that closely ties with
the C-8 to C-10 ALMA configurations, and as measured over a 60 s timescale
(left) and a 45 s timescale (right). The y-axis indicates the phase RMS as a
path length variation in microns. Between 1100 and 2300 UTC is considered to
be "day" time. The horizontal line within the box indicates to median, while
the box-spread are the 25th and 75th percentiles and whiskers the minimum and
maximum values per month considering all years. The circles represent the
median time available based on meeting the nominal PWV ($<$0.472) mm (Figure
6).

####  4.2.1 A note on ‘Fast-Switching’

Fast-switching phase referencing is a technique outlined for use at ALMA since
the early Holdaway memos (most recently Holdaway, 2001), and was also
summarized in Evans (2003). For ALMA, the fast-switching terminology can be
used to describe observations where the regular visits to phase calibrators
are made more frequently than $\sim$60 s272727For perspective, most
millimeter-to-radio wavelength interferometers use cycle times of the order
minute timescales, as does ALMA for the shortest baselines., and hence applies
to the longer baseline high frequency observations. The premise, as we have
also discussed above, is that we can achieve an overall lower phase RMS for
science target scans (bracketed by the phase calibrator) as the atmospheric
fluctuations are more frequently calibrated.

In the fast switching simulations by Holdaway (2001) the phase calibrator
scans times are reported to be shorter than 0.5 s, while slew times are $<$2
s. Considering the overall duty cycle (time-on-source / total cycle time) as
$\sim$0.9 we infer target scan times of $\sim$40 s. In their earlier
simulation work cycle times of $\sim$20 s are reported in trying to achieve a
30∘ phase RMS limit for an envisaged 3000 m baseline configuration (Table 4 in
Holdaway & Matsushita, 1997). In more recent work Asaki et al. (2014, 2016)
tested $\sim$20 s fast switching at ALMA, although the observations become
inefficient with a duty cycle $<$0.5.

Table 8: Simple estimates of the duty cycle for phase referencing using both
ALMA parameters and hypothetical setups. Slew times are assumed to be 2 s to,
and from, the phase calibrator to target.

Target Scan (s) |  Phase Cal Scan (s) |  Cycle Time (s) |  Duty Cycle
---|---|---|---
54a | 18 | 76 | 0.71
54 | 12 | 70 | 0.77
54 | 6 | 64 | 0.84
42 | 18 | 64 | 0.66
42b | 12 | 58 | 0.72
42 | 6 | 52 | 0.81
30c | 12 | 46 | 0.65
30 | 6 | 40 | 0.75
30 | 3d | 37 | 0.81
18 | 12 | 34 | 0.53
18 | 6 | 28 | 0.64
18 | 3d | 25 | 0.72

a setup for ALMA long baselines from Band 3 to 7 to nearest second
b setup for ALMA long baselines Band 9 to nearest second
c setup for ALMA long baselines Band 10 to nearest second
dassuming the integration time is also 3 s this does not sample the phase
calibrator more than once per scan.
Note: overall efficiencies (not calculated) would depend on other calibrations
as are required for general interferometric observations.

In their long baseline investigations Maud et al. (2022) report that the phase
RMS is roughly proportional to $\sqrt{\rm{time}}$, on average, such that a
factor of 4 reduction in cycle time (assumed as the target scan time when the
phase calibrator scan is considered negligible in length) can improve the
phase RMS by $\sim$2, e.g. reducing times from 120 s down to 30 s ‘fast
switching’. Holdaway & Matsushita (1997) note that they need to have 6 times
more cycles in their simulated phase referencing to improve the phase RMS from
45∘ to 20∘, also roughly following $\sqrt{\rm{time}}$. However, Maud et al.
(2022) also note that fast-switching will not necessarily improve all
observations, in terms of coherence, when the phase RMS is already good. As we
find from the work presented in this memo (above), ALMA can observe in Band 3
for over 90 % of the time while meeting the ideal 30∘ phase RMS limit,
corresponding to a maximal visibility coherence of 0.87 (Equation 2) when
considering only the atmospheric variability. Thus it is not necessary to
reduce cycle times by a factor of 4 to reduce the phase RMS to $\sim$15∘
because the coherence improvement is only $\sim$0.09 (to $\sim$0.96) while the
time on the target source per cycle would more than half, meaning a
considerable drop in efficiency and at least a twice as long total observing
time for very little gain (see also Table 8). For higher frequencies, where
the phase RMS in terms of path length variation needs to be as low as
possible, then faster cycle times can notably increase the observing time
available (e.g. Figure 18). Although the same scenario as above holds for
observing efficiency, if for example the phase RMS was $\sim$60∘ (coherence
0.57, Equation 2), then a reduction to 30∘ using 4 times faster cycle times
would provide a 0.3 improvement in coherence (up to 0.87), and would allow
previous unsuitable conditions, that would not have provided accurate
calibration or images, to be used. The reduction of cycle times from 76 s to
19 s however may not be pragmatically possible (see Section 4.3).

For ALMA operations there is a pragmatic limit and phase calibrator scans as
short as Holdaway (2001) intended are not really feasible: antennas need to
stabilise after moving; the software needs to initiate the scan sequences;
data should be recorded for a few integrations - that are typically 3 s long;
if using B2B mode the electronics must also stabilise due to the frequency
change; and the duty cycle should not drop so low as to lose efficiency, i.e.
when the observing time gained is primarily spent observing the calibrator or
slewing. In Table 8 we estimate the duty cycle for current ALMA long baselines
and theoretical phase calibration cycle times. We see that for ALMA’s current
long baseline parameters the duty cycle is only slightly reduced in the case
of Band 10, as compared to standard lower frequency long baselines observing,
but the cycle time and target scan times are almost halved. This reduction
offers a modest improvement in phase RMS by a factor 1.3 (following $\sqrt{\rm
time}$), and as presented above, boosts the time available by a factor $>$1.5.

###  4.3 Forward Look

A reduction in cycle times, specifically for the most stringent high frequency
observations, can provide notable increases in the observing time available.
From the Phase RMS database, using a timescale of 30 s indicates that the
median time available for high frequencies at long baselines can reach
$\sim$30 %, at night for the winter months, and exceeds what is possible based
on the nominal PWV values. For the future a more dynamic, or at least a choice
based system could be investigated. One could envisage that the ‘best’ cycle
time setup would be selected for the conditions at that specific time, on-the-
fly. The cycle time could be reduced for the most ‘difficult’ observations at
high frequencies where the PWV is met but the phase RMS might be borderline
using a standard setup. The dynamic process could also reduce cycle times for
lower frequency observations made during the day time in more unstable
conditions, or in reverse use longer cycle times that are more efficient if
the conditions are very stable. Of course the minimum cycle time would have to
be limited as to avoid losing efficiency, but that could easily be compared
with a preset pragmatic duty cycle ‘hard limit’. During the next decade ALMA’s
Wideband Sensitivity Upgrade (WSU, Carpenter et al. 2022) will quadruple the
available maximal bandwidth along with providing an improved sensitivity via
digital efficiency improvements. In light of these significant upcoming
modifications and based on the work presented in this memo, we would recommend
a thorough investigation into baseline length and cycle time optimisation,
including a fully dynamic system. Ultimately, such optimisations are the way
to maximise the science return and also allow more high frequency projects to
get on sky.

For mid-baseline lengths, optimisation is already taking place for ALMA’s
current high frequency observing capabilities based on the results from the
Phase RMS database. The few minute long target scan times will be reduced down
to 90 s in Cycle 10. The Phase RMS database studies showed that going from
180-240 s timescales down to 90 s more than doubled the percent of time
available in the night time winter months for Bands 9 and 10, while the duty
cycle for phase referencing slightly improves as the phase calibrator scan
time is also reduced282828In Cycle 9 for high frequency observations the
target scan is 180 s and the phase calibrator scan is 60 s - duty cycle
$\sim$0.75. For Cycle 10, the target scan is 90 s and the phase calibrator
scan is 18 s - duty cycle $\sim$0.80. However, B2B mode costs an additional
overhead (see, Maud et al., 2020).. Further investigations based on extensions
of capabilities work (outlined recently by Maud et al., 2021) that forms part
of the ObsMode process (detailed in Takahashi et al., 2021) showed that the
reduction in phase calibrator scan time from 60 s to 18 s did not
significantly change the average calibrator separation distance from science
targets for Band 8, 9 and 10 observations. The close enough and strong enough
phase calibrators were still found when using the reduced scan times. Of
course the weaker phase calibrators that previously just met the SNR level are
no longer suitable, but since the B2B mode is now commissioned for mid-
baseline configurations (in Cycle 10), there are significantly more
calibrators available above the SNR limit when observing them at a lower
frequency, such that 18 s scans are more than sufficient.

The Phase RMS database will continue to be used to examine more closely
individual observations and to explore how the dynamic adjustment of cycle
times will affect observing times and efficiencies.

##  5 Summary

In this memo we report on ALMA site properties in terms of monthly, daily,
hourly variations of the phase RMS based on the examination of the Bandpass
source scans of over 17000 observations taken since the start of ALMA Cycle 3.
We also reaffirm trends seen for the PWV. In overview we find:

  * •

Notable variations of the phase RMS, and PWV, over the year with Chilean
summer (December - February/March) providing the worst conditions and winter
(June - August) offering the best.

  * •

That night time provides better conditions in offering the most stable phase
RMS, and lowest PWV:

    * –

The diurnal variations in phase RMS are significantly larger than those in
PWV.

    * –

The median phase RMS (per hour for all months and years) can change by up to a
factor of 7 between day and night time in summer months and by up to a factor
of 3 in winter months.

    * –

The median PWV fluctuates on average by a factor of 1.9 between night and day
averaged over all months. Summer and winter variations are slightly above and
below the average respectively.

    * –

The average observing time available during the day is $\sim$5-10 % lower than
at night time for any given nominal PWV/octile level.

  * •

The ‘complete’ 5 year sample, in both phase RMS and PWV is not long enough to
see any global year to year variations.

Importantly, we report on the variability of the phase RMS on summary baseline
lengths of 500, 1000, 5000 and 10000 m, that are relevant to ALMA array
configurations and for timescales closely related to the phase referencing
cycle times. Measuring the phase RMS on timescales between 30-240 s acts as a
proxy value of the expected phase errors remaining in any science target scans
after phase calibration and hence ties with the expected quality of the final
data. We also address bullet point 3 from Evans (2003) in now illustrating the
time available for ‘exciting science’ after phase correction would have been
applied. We find:

  * •

Application of the Water Vapour Radiometer corrections to the data provides a
phase RMS improvement in $>$96 % of the observations, and more than a factor
of 2 improvement for $\sim$57 % of the observations (referenced to the 1000 m
summary baseline and 120 s timescale).

  * •

Observations that do not improve with WVR application are mostly comprised of
Band 3, or low frequency observations ($<$Band 6), particularly where the PWV
is $>$1.5 mm and the solutions are affected by clouds.

  * •

ALMA’s use of faster cycle times for longer baselines can compensate for a
naturally increasing phase RMS with baseline length.

    * –

For short baseline, $\leq$1000 m, decreasing the timescales from 240 to 60 s
increases the percentage of time that high frequency observations can be made
in the available conditions from 18 to 56 % at Band 9, using the global
cumulative distributions. For $\leq$Band 7 the increase in available time is
at most 14 % when decreasing from 240 to 60 s timescales.

    * –

For long baselines, $\geq$5000 m, short timescales $\leq$60 s are required to
allow high frequency observations to be conducted in the conditions available,
otherwise the required phase RMS cannot be met.

    * –

Typically Band 3 to Band 5 can be observed in all configurations for $>$85-90
% of the time at night and $>$70-80 % of the time during the day in winter
months irrespective of the baseline length when considering ALMA’s current
observing scheme, using shorter timescales for the longer baseline
configurations.

    * –

Using the fast switching cycle times for ALMA high frequency long baselines
(46 s) aligns the time available where both the phase RMS and nominal PWV
criteria can be met, $>$10-15 % of the time available at night for winter
months for Bands 9 and 10 observations, when using a nominal PWV of $<$0.472
mm and $<$38 $\mu$m path length variation (phase RMS $<$30∘ for Band 9 and
$<$40∘ for Band 10).

We also find some moderate correlations between weather metadata parameters,
such as wind speed, humidity and the PWV and phase RMS. However, the general
scatter in parameter space prevents any accurate predictions of the phase RMS.
As also concluded by Evans (2003), we find that low PWV conditions do not
necessarily correlate directly to good atmospheric stability (low phase RMS).

We also suggest how faster, or slower, cycle times could be considered to
optimise observations given the observing conditions on a particular day/night
where dynamic changes could be made to ensure a low phase RMS was achieved.
However, such dynamic cycle time changes requires a deeper study as to trade
off any reduction in observing efficiency when using fast-switching compared
to the percent of observing time gained, and spent on-source. We recommend a
thorough investigation into baseline length and cycle time optimisation,
including a fully dynamic system in light of the upcoming Wideband Sensitivity
Upgrade.

The Phase RMS database will be available along with helper scripts on the ALMA
science portal for public use. Periodic updates are also planning to continue
ingesting new cycles of data.

## Appendix

### Database Contents

The Phase RMS database is built with an SQL architecture that is easily
portable and can be manipulated with various programming languages, such as
python. The database structure is not complex and consists of 8 tables in
which all EBs are indexed by their unique identification (UID). The tables and
a description of their contents are shown in Table 10 with column headings
indicated in Figure 19. The two ‘metadata’ tables are: the Source table
containing source information about the Bandpass, Phase calibrator, and the
target(s) and their minimum and maximal separation from the phase calibrator
and the phase referencing cycle time; and the Overview table storing UTC
observing time, total bandpass scan length, wind, temperature, pressure,
humidity, PWV and minimum and maximum baseline lengths. The table used
throughout this memo is the Summary table that holds the phase RMS values
(before and after WVR corrections) as extracted from the phase-time streams
for at the various timescales, 30 s, 45 s, then 60 s to 240 in 30 s steps and
the observing cycle-time292929For observations cycle times exceeding the
bandpass scan length the maximal phase RMS value calculated is over the
duration of the bandpass scan only. averaged for baseline lengths of 500,
1000, 5000 and 10000 m. There is also the Baseline table that stores the phase
RMS values per baseline from each observations on the above mentioned
timescales. The Baseline table was used to build the Summary table, and in
general individual outlier baselines are not ingested into the database.

Table 9: Total number of EBs in our lists to be ingested into the Phase RMS database Year |  Number |  Ingested |  Failed
---|---|---|---
2015 | 1889 | 1685 | 204
2016 | 3611 | 3250 | 357
2017 | 2732 | 2252 | 480
2018 | 4564 | 4054 | 510
2019 | 3975 | 3560 | 415
Total | 16771 | 14801 | 1966
Figure 19: Schematic of the Phase RMS SQL database tables and columns. Table
names are indicated at the top, and within the respective tables the column
headings are shown in grey. Not all columns are listed for the various
timescale measures but are noted by ‘all times’ and refer to 45, 60, 90, 120,
150, 180, 210 s times. ∗the Residual and Dphase Summary and Baseline tables
have the same structure as the Summary and Baseline tables.

At the time of generation (late 2021) for data from 2015 to 2019 inclusive
there are 16771 EBs in our list (see Table 9). As of the date of this memo
ingestion of 2020 and 2021 data has begun but is not complete. The database as
used for the memo is at a $\sim$87 % completeness level with $\sim$2000 EBs
that have not been correctly ingested for Cycle 3 (2015) to Cycle 7 (2019).
There are a total of 17532 observations ingested including years 2020 and
2021. Note also, there are a few tens of observations with corrupted metadata
that were not used in the correlations303030Updated database versions will
clean out such observations..

Table 10: Phase RMS database tables and description Table |  Description
---|---
Overview | Observing metadata and weather parameters
Source | Source metadata and parameters
Summary | Summary baseline length phase RMS values
Baseline | All baseline based phase RMS values
ResidualSummary | Summary of residual Phase RMS values
ResidualBaseline | All baseline based Residual Phase RMS values
DphaseSummary | Summary of pseudo D-phase values
DphaseBaseline | All baseline based pseudo D-phase values

Within the database there are also Residual and Dphase versions of the Summary
and Bandpass tables also storing the average baseline values and all baseline
values, however the phase RMS is calculated differently. For the Residual
tables, phase solutions are made for all given timescales by extracting
integration times within the Bandpass phase-time stream to act as ‘calibrator’
points, e.g for a 30 s timescale we take values at 0, 30, 60 … to $\sim$300 s
for a typical Bandpass scan. A gaintable is produced and applied back to the
Bandpass scan data which ‘corrects’ the phases to leave only the Residual
variations, for which we then measure the phase RMS from. The Dphase tables
present the value from the median difference of the aforementioned solutions,
although for timescales $>$90-120 s the values are not so robust as they can
consider only $<$3 points extracted from a typical Bandpass scan, e.g. the 120
s timescale can use only the median value from absolute phase solutions
recorded at 0, 120 and 240 s. We store these in the database for future
examination but do not discuss them further in the memo.

##### Data Availability:

All materials will be available on the ALMA science portal:
https://almascience.eso.org/tools/eu-arc-network.

##### Acknowledgments.

ALMA is a partnership between the European Southern Observatory (ESO), the
National Science Foundation (NSF) of the United States and the National
Institutes of Natural Sciences (NINS) of Japan in collaboration with the
Republic of Chile. ALMA is funded by ESO in representation of its member
states, by NSF in collaboration with the National Research Council (NRC) of
Canada and the National Science Council (NSC) of Taiwan, and by NINS in
collaboration with the Academia Sinica (AS) in Taiwan, and the Korea Astronomy
and Space Science Institute (KASI) of South Korea.

We are grateful for the discussions with, and hard work of, the Joint ALMA
Observatory staff including all of the people who make the observatory ‘run’
and are too many to list. The authors would particularly like to thank the
referees, Sergio Martín, Ruediger Kneissl, Eric Villard, Tony Mroczkowski, and
Carlos De Breuck for their helpful and detailed comments, in addition to John
Carpenter for his input on an earlier version and George Privon for
discussions about figures for the ALMA Proposer’s Guide.

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