The CoRoT and Kepler missions have provided high-quality measurements of the frequency spectra of solar-like pulsators, enabling us to probe stellar interiors with a very high degree of accuracy by comparing the observed and modeled frequencies. However, the frequencies computed with 1D models suffer from systematic errors related to the poor modeling of the uppermost layers of stars. These biases are what is commonly named the near surface effect. The dominant effect is thought to be related to the turbulent pressure that modifies the hydrostatic equilibrium and thus the frequencies. This has already been investigated using grids of 3D hydrodynamical simulations, however, the effect of metallicity has not been considered so far. We aim at studying the impact of metallicity on the surface effect, investigating its influence across the Hertzsprung–Russell diagram, and providing a relation between the frequency differences and global parameters. We computed a grid of 29 patched 1D stellar models with the stellar evolution code CESTAM in which poorly modeled surface layers have been replaced by averaged stratification computed with the 3D hydrodynamical code CO 5 BOLD. It allowed us to study the dependence of the surface effect on the metallicity. We found that a correct way of accounting for it is to consider the surface Rosseland mean opacity. It allowed us to give a physically-grounded justification as well as a scaling relation for the frequency differences at ν max as a function of T eff , log g and κ.