Effect of increasing noise in H i data on the HOG correlation with Faraday tomography structures for the case-study simulation along the mean field. Each panel displays the 98th percentile of the normalized Rayleigh statistic ${\tilde{V}}^{98\%}$ as a function of Faraday depth, ϕ, for the CNM and WNM phases. The different lines correspond to different levels of added Gaussian noise in the H i cubes, ranging from σ_EBHIS/5 to 10 × σ_EBHIS. While increasing noise decreases the overall correlation strength, the WNM remains more affected than the CNM, particularly at high velocities.