View source for Atmospheric model verification using BICEP/Keck data

''September 23, 2020 - Colin Bischoff and Reijo Keskitalo''


=Introduction=

In this post we study atmospheric noise correlations in two scansets (approximately 55 minutes) of Keck array data acquired with five co-positioned cameras observing at 100, 150 and 220 GHz.

It is expected, that as CMB-S4 SAT:s integrate down the instrumental noise across large numbers of detectors, the dominant noise component in the final analysis will have an atmospheric origin.  For that reason, it is exceptionally important to forecast the extent to which the atmospheric noise in various detectors is statistically independent. The rate at which we acquire these independent measurements of the atmosphere will dictate our mapping speed.

Dataset like the BICEP/Keck data of concern here has never been used to verify the TOAST atmospheric simulation module before. Compared to earlier verification campaigns with POLARBEAR, ACT and SPT, these data uniquely offer
* detector line-of-sights separated by up to 16 degrees
* small aperture telescope with resulting near-field geometry
* multiple co-positioned cameras


=Focalplane=

Each array of detectors has a square layout of single frequency detectors. Two arrays observe at 100 GHz, one at 150GHz and two at 220GHz. The deck angle around the boresight is different between the two studied observations, 20150614C06_dk023 and 20150714B04_dk338:

[[File:fpgeom.20150614C06_dk023.png|800px]]

[[File:fpgeom.20150714B04_dk338.png|800px]]

Holes in the grids are left by the ad hoc data cuts implemented in this analysis.


=Time-ordered data=

The calibrated but unfiltered timestreams show prominent correlations across all frequencies:

[[File:tod_20150614C06_dk023.pairsum_unfiltered.png|800px]]

Interestingly enough, the 150 and 220GHz data above seem to decouple somehow at around 2000 seconds.

[[File:tod_20150714B04_dk338.pairsum_unfiltered.png|800px]]

The dominant features of the above plots are long time scale fluctuations that are typically filtered out early in the data processing. Here we show the same TOD after filtering each half-scan with a 2nd order polynomial and each scanset with a 10th order ground-synchronous polynomial.

[[File:tod_20150614C06_dk023.pairsum_filtered.png|800px]]

[[File:tod_20150714B04_dk338.pairsum_filtered.png|800px]]


=Detector correlations=

We will use the filtered TOD to measure the detector-detector correlations as a function of detector separation and time lag.  Two cases of detector pairs are considered: in-scan offset where the cross-scan separation of the detectors is no larger than 0.1 degrees on different cameras or 0.3 degrees on the same camera. The reason for the more relaxed definition of the pairs on the same camera is required to render a sufficient sample of in-scan separations: on the same camera the separations are very quantized.  Similarly, we define cross-scan offset pairs of detectors with the same tolerances.

Here is a plot of the dimensionless correlation function (top row) between 220 GHz detectors on the same camera:

[[File:cov_20150614C06_dk023_220GHz_x_220GHz.same_camera.pairsum.png|800px]]

The cross-scan panel (top right) shows that detectors that are separated by less than a degree are highly correlated up to a lag of about 1 s. The azimuthal scan rate (2.8 deg/s) translated on-sky is 1.6 deg/s.  Even detectors separated by more than 10 degrees exhibit measurable correlations that survive the polynomial filtering.

The in-scan panel (top left) shows that the peak correlation between detectors occurs at a lag that matches the time to scan their angular separation. Green correlation functions in the plot peak at approximately 3 seconds while the boresight travels the 6 degrees separating the detectors in 3.75 seconds. All correlation peaks are expected to tilt towards zero lags due to the correlation strength slowly weakening as the atmosphere itself changes.  The atmospheric changes also explain why the height of the peak correlation drops with increasing detector separation.

If we consider pairs of detectors on different cameras, located eight feet apart on the mount, we find a very similar correlation structure:

[[File:cov_20150614C06_dk023_220GHz_x_220GHz.different_camera.pairsum.png|800px]]

This is a very important result for the 3-shooter design baselined for CMB-S4 SATs. Co-positioned SAT cameras on the same mount do not render independent observations of the field but rather the atmospheric noise component is highly correlated.

Correlations across frequency bands are equally prominent. Here we pair 150 and 220GHz detectors across two cameras:

[[File:cov_20150614C06_dk023_150GHz_x_220GHz.different_camera.pairsum.png|800px]]

While the atmospheric noise at 100GHz is notably fainter:

[[File:cov_20150614C06_dk023_100GHz_x_100GHz.different_camera.pairsum.png|800px]]

For completeness, here is the 220GHz correlation measured from the other scanset:

[[File:cov_20150714B04_dk338_220GHz_x_220GHz.different_camera.pairsum.png|800px]]


=Simulations=

We then used the TOAST simulation facilities to synthesize data with the same scanning pattern and focalplane.  To allow for comparison, we simulated uncorrelated instrumental noise and atmospheric noise.  The resulting correlation patterns are similar to what we find in the BICEP/Keck data at 220GHz:

[[File:cov_20150614C06_dk023_220GHz_x_220GHz.same_camera.sim.pairsum.png|800px]]

[[File:cov_20150714B04_dk338_220GHz_x_220GHz.same_camera.sim.pairsum.png|800px]]

The dominant difference between real data and the simulation is the height of the in-scan offset bump.  It suggests that the simulated atmosphere does not change quite as fast as the one observed in the two real scansets.  At least three potential explanations exist:
1. Our static, wind-driven atmospheric model fails to account for turbulent evolution of the water vapor distribution in the atmosphere
2. The simulated wind speeds, based on historical distributions 10 meters above ground, are too low.
3. The assumed water vapor distribution is incorrect.  If the water vapor is closer to the telescope, same wind speeds would have a larger effect.
Our model also slightly underestimates the level of atmospheric correlations, but that is easily to calibrate.

At 100GHz, the simulation shows an excess of correlated power:

[[File:cov_20150614C06_dk023_100GHz_x_100GHz.same_camera.sim.pairsum.png|800px]]

but this may simply be related to an issue in the absolute calibration of the data.  Currently, the data absolute calibration is based on a very ad hoc atmospheric loading template.


=Atmospheric loading=

TOAST includes facilities to estimate the smooth background loading from the atmosphere in the detector passband.  The loading is calculated using the `atm` code from ALMA.  The temperature is further modulated by the observing elevation.  This way TOAST can be used to simulate the el-nods that bookend the science scans.

Here is the el-nod in the June scanset:

[[File:elnod_20150614C06_dk023.start_pairsum_unfiltered.png|800px]]

Observe that the vertical ranges of the plots have been adjusted to match the frequency scaling of the el-nod signature (0.67:1:2.33).  That scaling is very different from the one used to plot water vapor-sourced fluctuations (0.25:1:5).

Here is the corresponding simulation:

[[File:elnod_20150614C06_dk023.start_pairsum_unfiltered.sim.png|800px]]

The ALMA atmospheric model was configured with typical South Pole weather for the season and convolved with the actual bandpasses.  While the simulated el-nod at 100 and 150GHz agrees very well with real data, the model seems to underestimate the amplitude of the modulation by 40% at 220GHz.  The total level of atmospheric loading varies quite a lot depending on the PWV, but it does not seem possible to create the kind of frequency scaling we see in the real data by chancing the parameters of the model.  The source of the mismatch remains unknown.


=Wind=

The scanset files include local weather station data.  The median values indicate very similar observing conditions:

{| class="wikitable"
! Scanset
! Temperature [C]
! Pressure [mBar]
! Relative humidity [%]
! Wind direction [deg]
! Wind speed [m/s]
! Boresight azimuth [deg]
! Wind/boresight angle [deg]
|-
| 20150614C06_dk023
| -59.2
| 682
| 39.2
| 73.9
| 7.04
| 63.8
| -10.1
|-
| 20150714B04_dk338
| -54.3
| 665
| 43.7
| 63.6
| 7.12
| -136.3
| -199.9
|}

According to the last column the scans are almost orthogonal to the wind direction at ground level.  Based on this information, we would anticipate few observable wind effects in the detector-detector correlations.  We tested this hypothesis by taking pairs of detectors offset in the in-scan direction and finding the lag that minimizes the difference between the two signal vectors.  We measured the lag separately for left and right-going scans and also considered a brief noise stare at the end of the scanset.  If the atmosphere remained completely still, the lag could be derived from the separation between the detectors using the azimuthal scan rate, 2.8 deg/s, translated to the observing elevation of each detector pair.

For the June scan set, the results are consistent with a gentle wind increasing the lag times in left-going scans and reducing them in the right-going scans.  For the July scan set the left-going scans experience much shorter lags than a stationary atmosphere would produce.  The fits for the right-going scans are inconclusive, potentially due to the scan rate almost matching the motion of the atmosphere.  The noise stares also lend evidence to the July scan set being subject to stronger wind.

{| class="wikitable"
! Scanset
! Left-going scan [s/deg]
! Right-going scan [s/deg]
! Stare [s/deg]
|-
| 20150614C06_dk023
| -0.77
| 0.58
| 2.97
|-
| 20150714B04_dk338
| -0.21
| n/a
| -0.67
|}

Based on a simple geometric model, the atmospheric fluctuations should move in front of the focalplane at an angular velocity that is the sum of the boresight motion and the wind.  Inverting the time delays gives us the effective scan rates:

{| class="wikitable"
! Scanset
! Left-going scan [deg/s]
! Right-going scan [deg/s]
! Stare [deg/s]
|-
| 20150614C06_dk023
| -1.30
| 1.72
| 0.34
|-
| 20150714B04_dk338
| -4.76
| n/a
| -1.49
|}

Here is a plot of the data for 20150614C06_dk023

[[File:lag_study_20150614C06_dk023_220.png|800px]]

Each data point is the measured lag for one 220GHz detector pair.  The gray area is the range of lags expected if the atmosphere was perfectly still.

Here are the 20150714B04_dk338 results:

[[File:lag_study_20150714B04_dk338_220.png|800px]]

The inconclusive results for the right-going scans complicated.  Likely there is no clear lag for detector pairs close by (less than 6 away).  As the separation increases,  some large scale near stationary component of the atmosphere takes over and the lags converge on the static model estimate.

Simulated results include a much more static atmosphere:

[[File:lag_study_20150614C06_dk023_220.sim.png|800px]]

There are three potential explanations:
# the randomized wind is too low
# the randomized wind is parallel with the bore sight
# the source of the emission is closer to the telescope than simulated.

We are thinking of how to narrow down the solution.

=Discussion=

If atmospheric noise is the dominant source of uncertainty in the CMB-S4 maps, it is critical that we maximize the number of independent observations of the atmosphere. The Keck array data analyzed in this post offers two insights:

# Atmospheric fluctuations on the sky are coherent over several degrees, severely limiting the statistical power of adjacent detectors.
# Co-positioned cameras sharing a mount sample the same atmospheric noise, offering little or no advantage in terms of atmospheric residual.

If atmospheric polarization is minimal or nonexistent, then the atmosphere only affects polarization through detector mismatch.  In this case, ensuring that the detector mismatch is randomized rather than systematic will greatly improve the statistical power of the experiment.