# Noise models and sky fractions for WAFTT

## Contents

- 1 Minimum elevation: 50 degrees
- 2 Minimum elevation: 40 degrees
- 3 Minimum elevation: 30 degrees
- 4 Inverse Variance Weighted Noise Results [from Joel, modified 1-30-2019]
- 5 Forecasts using Raphael's ILC [from Joel, modified 1-30-2019]
- 6 Depth Maps [from Matthew Hasselfield]
- 7 Observing schedules[from Reijo on 1-30-2019]

### Minimum elevation: 50 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 57 | 52 | 45 | 39 | |

Effective sky fraction for noise (in %) | 51 | 47 | 40 | 34 | |

Effective sky fraction for signal (in %) | 47 | 43 | 37 | 31 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 52.6 | 17.7 | 9.9 | 1.7 | 1.7 | 5.3 | 12.7 | |

ell knee TT | 449 | 409 | 378 | 1245 | 4440 | 4358 | 4397 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.5 | -3.5 | -3.0 | -2.3 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 74.4 | 25.0 | 14.0 | 2.4 | 2.4 | 7.6 | 18.0 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | |

Penalty (relative to f_sky scaling) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

### Minimum elevation: 40 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 68 | 63 | 55 | 48 | |

Effective sky fraction for noise (in %) | 63 | 58 | 51 | 44 | |

Effective sky fraction for signal (in %) | 59 | 54 | 47 | 41 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 58.0 | 19.6 | 10.9 | 1.8 | 1.9 | 6.1 | 14.6 | |

ell knee TT | 480 | 435 | 401 | 1327 | 4666 | 4519 | 4531 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.5 | -3.4 | -3.1 | -2.3 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 82.0 | 27.7 | 15.5 | 2.6 | 2.7 | 8.6 | 20.6 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | |

Penalty (relative to f_sky scaling) | 0.99 | 1.00 | 0.99 | 1.00 | 1.00 | 1.02 | 1.03 |

### Minimum elevation: 30 degrees

Galactic cut (in %) | 0 | 10 | 20 | 30 | |
---|---|---|---|---|---|

Sky fraction (in %) | 76 | 69 | 62 | 54 | |

Effective sky fraction for noise (in %) | 71 | 65 | 57 | 50 | |

Effective sky fraction for signal (in %) | 67 | 61 | 54 | 47 |

Frequency (GHz) | 20 | 27 | 39 | 93 | 145 | 225 | 280 | |
---|---|---|---|---|---|---|---|---|

white noise level TT (uK-arcmin) | 61.4 | 20.8 | 11.6 | 2.0 | 2.0 | 6.7 | 16.3 | |

ell knee TT | 517 | 465 | 429 | 1416 | 4853 | 4660 | 4639 | |

1/f exponent TT (uK-arcmin) | -3.5 | -3.4 | -3.4 | -3.1 | -2.4 | -3.4 | -3.4 | |

white noise level E/B (uK-arcmin) | 86.8 | 29.4 | 16.4 | 2.8 | 2.9 | 9.5 | 23.0 | |

ell knee E/B | 700 | 467 | 467 | 467 | 467 | 467 | 467 | |

1/f exponent E/B (uK-arcmin) | -1.4 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | -1.1 | |

Penalty (relative to f_sky scaling) | 0.99 | 1.00 | 1.00 | 1.00 | 1.02 | 1.07 | 1.09 |

### Inverse Variance Weighted Noise Results [from Joel, modified 1-30-2019]

### Forecasts using Raphael's ILC [from Joel, modified 1-30-2019]

### Depth Maps [from Matthew Hasselfield]

For this result, I used the hit maps "without elevation penalty" described by Reijo below. The noise model is the one described on Survey_Performance_Expectations, in Large-area Survey Performance Expectation 01, Lat-noise-181121.

The hit maps produced by Reijo were converted into depth maps as follows:

- Define the "survey time", T, as the number of seconds for which the LAT operates. This is specified in the noise model so its value doesn't matter here, but it's a useful parameter for describing the computations.
- The calibration between hit count and observing time was determined, by summing up the hits in all pixels and all elevation bins for the "cut=0" case. It was found that "one uncut survey" is equivalent to (350 * 86400 * 254) = 7.7e9 hits in these maps. So each hit corresponds to (T/7.7e9) of LAT time. Note this computation is done for the cut=0 case but the same conversion is applied to other cases (where galactic cut or other restrictions might yield a smaller total number of hits than in the cut=0 case... we are allowed to suffer inefficiency due to survey strategy).
- Consider a single frequency band, and a single value of "el_min" (the minimum allowed observing elevation):
- The maps of hits per pixel are combined with the pixel area to give maps of LAT time per unit area (in multiples of T).
- For each elevation bin, the el-dependent noise model is used to convert LAT time per unit area to depth (the sort of depth that has units of [uK arcmin]^-2).
- The per-elevation bin depth maps are summed. This produces a single depth map, units [uK arcmin]^-2, for this frequency and el_min.

- The above procedure is performed for each el_min and frequency band.
- Intra-tube correlations are captured by binning into cross-frequency depth maps (e.g. 90x150). (The mapping speed in off-diagonal elements comes from the off-diagonal elements of the inverse covariance matrix, which is provided by the noise model...)

- The above procedure is performed for the "white noise" limit, and also at ell=[1000,2000,3000].

The resulting noise maps can be found on NERSC, /global/cscratch1/sd/mhasse/cmb-s4/fskytaskforce/190103/:

- depth_el_min30.zip
- depth_el_min40.zip
- depth_el_min50.zip
- gal_masks_eq.zip (this archive contains Reijo's galactic masks, converted to same pixelization as the depth maps)

### Observing schedules[from Reijo on 1-30-2019]

We built the observing schedules using the opportunistic scheduler. First we tiled the sky in celestial coordinates with 10x20 degree (RAxDEC) tiles that overlap by half a tile in each direction. Then we ran the scheduler with three choices of minimum observing elevation: 30, 40 and 50 degrees. We required a 30-degree avoidance region around the Sun and the Moon. The three schedules were run with and without an additional "elevation penalty" which tells the scheduler to favor high elevation observations over low elevation observations.

Originally we tried adjusting the tile priority based on how much of the tile was embedded inside the galactic mask. This turned out to cause undesirable boundary effects, making the final hit distribution around the masked area very uneven. Instead, we ran the scheduler on the full sky and only masked pixels from the resulting hit maps. This approach lead to slightly lower overall observing time but higher effective sky fraction.

Here are the (masked) hit maps for all observing elevations when no elevation penalty is considered:

Here are the hit maps when the scheduler is told to penalize low elevation observations:

Here is the difference in observing elevations with and without the elevation penalty: