Lost Horizon: Quantifying the Effect of Local Topography on Global 21 cm Cosmology Data Analysis

We present an investigation of the horizon and its effect on global 21 cm observations and analysis. We find that the horizon cannot be ignored when modeling low-frequency observations. Even if the sky and antenna beam are known exactly, forward models cannot fully describe the beam-weighted foreground component without accurate knowledge of the horizon. When fitting data to extract the 21 cm signal, a single time-averaged spectrum or independent multi-spectrum fits may be able to compensate for the bias imposed by the horizon. However, these types of fits lack constraining power on the 21 cm signal, leading to large uncertainties on the signal extraction, in some cases larger in magnitude than the 21 cm signal itself. A significant decrease in uncertainty can be achieved by performing multi-spectrum fits in which the spectra are modeled simultaneously with common parameters. The cost of this greatly increased constraining power, however, is that the time dependence of the horizon's effect, which is more complex than its spectral dependence, must be precisely modeled to achieve a good fit. To aid in modeling the horizon, we present an algorithm and Python package for calculating the horizon profile from a given observation site using elevation data. We also address several practical concerns such as pixelization error, uncertainty in the horizon profile, and foreground obstructions such as surrounding buildings and vegetation. We demonstrate that our training-set-based analysis pipeline can account for all of these factors to model the horizon well enough to precisely extract the 21 cm signal from simulated observations.