# Atmospheric validation

*March, 2019*

### Background

In this post we document our efforts to validate simulated time-domain data from the TOAST atmospheric turbulence module against experimental data from a number of telescopes covering a range of frequencies, apertures, and observing sites.

### How the TOAST simulation works

TOAST simulates the fluctuating atmospheric noise component of total detector time-ordered data (TOD) in intervals up to the duration of a constant elevation scan (CES), though a long CES is often split into disjoint intervals, typically 10-20 minutes long. Each realization generates the volume of atmosphere that will be observed through by the telescope during the interval, calculated from the focal plane field-of-view (FOV), the scan throw, the interval duration, and the sampled wind velocity (drawn from local weather records). The simulation volume is truncated at a fixed elevation, typically 4 km. Water vapor in the volume is distributed according to a preset 3-dimensional covariance matrix that encodes the 3D turbulent Kolmogorov spectrum and an altitude-driven exponential decay term. Once the total volume is simulated, it drifts across the telescope field of view with the wind vector. Detector data are then created by performing line-of-sight integrals through the atmosphere to evaluate the total thermal emission from turbulent water vapor.

The generated TOD are scaled by an absorption coefficient that is specific to the observing frequency (or bandpass) and the randomized temperature, pressure and PWV. The environmental parameters (T, p, PWV) are drawn from distributions derived from 10 years of MERRA-2 data. The absorption coefficient is evaluated using aatm.

We expect the work presented here to help set of the minimum and maximum length scales (the *injection* and *dissipation* scales) in the Kolmogorov spectrum, and the wind velocity distribution, which presently corresponds to MERRA-2 data 10m above ground. We also look for the optimal volume element size and the impact of splitting the full volume into independent slices to make the problem more computationally tractable.

### Large patch POLARBEAR data

We begin with a sample of half-wave plate-modulated data that are demodulated and downsampled to 8Hz. The scan is 30 degrees at a rate of 0.5 deg/s both in sky coordinates. We filter thermal common modes from the TOD by creating low frequency templates from the dark bolometer data and regress them out from the optical data.

Here is an example of observed detector-detector cross-correlation functions (top row) and PSD (bottom row):

The left column considers detectors that scan at the same elevation. The color of the curve identifies the in-scan offset ranging from 0 to 2.5 degrees. It is evident that the peak correlation between detectors occurs at a lag that depends on their separation. The right column considers pairs that scan at the same azimuth. These correlation functions all peak at zero lag and show a suppression of correlation by increasing separation.

We simulated the same scan using our atmospheric module and decorrelated the resulting TOD with the same thermal templates as the real data. We then measured the resulting detector correlations to find

The overall level of the simulation PSD had to be calibrated to match the real data. We also tried halving the volume element size (to support small-scale structures) in the simulation:

and doubling the injection scale (for greater correlation length):