Comparison between numerical results based on smoothed maps of our model of the turbulent magnetic field (diamonds) and the application of our analytical expressions for the decrease in the rms of p (red) by depolarization (Eq. (F.62) with ω = 160′) and the increase in 𝒮 × p (black) with the resolution (Eqs. (F.53) and (F.45)). The fractional difference is less than 10% for 𝒮 × p. The dashed blue line represents the pencil beam value for the rms of p, as calculated from Eq. (F.63) based on the model taken at ω = 160′.