E₂ as a function of R_conv/R for H-rich stars at different metallicities. Black dotted line corresponds to the formula from Yoon et al. (2010); red dashed line refers to the free fitting; green solid line refers to the fitting data with the fixed exponent of R_conv/R = 8.0, cyan dotted line refers to the fitting data with all three different metallicities. Different color bar points correspond to the weights of E₂ defined in Eq. (A.5). Left panel: Z_⊙, middle panel: 0.1 Z_⊙, right panel: 0.01 Z_⊙.