Fitted dust (top panel) and (bottom panel) amplitudes (A^EE and A^BB) at ℓ = 80, in μK² for the 400 deg² patches as a function of their mean ⟨I₃₅₃⟩. The empirical scaling law, A^EE,BB ∝⟨I₃₅₃⟩^1.9, adjusted in amplitude to the data points, is overplotted as a red line. The ± 3σ statistical error on this relation from Monte Carlo simulations of Planck inhomogeneous noise (see Appendix C.1) is represented as a light blue shaded area and the total ± 3σ error, including statistical noise plus Gaussian sample variance, is represented as a light red shaded area. Points are computed for all 352 patches, but we note that, as described in Sect. 3.3.2, the patches overlap and so their properties are not independent.