We present a variation of the recently updated Munich semi-analytical galaxy formation model, L-Galaxies, with a new gas stripping method. Extending earlier work, we directly measure the local environmental properties of galaxies to formulate a more accurate treatment of ram-pressure stripping for all galaxies. We fully re-calibrate the modified L-Galaxies model using a Markov Chain Monte Carlo (MCMC) method with the stellar mass function and quenched fraction of galaxies at $0leq zleq2$ as constraints. Due to this re-calibration, global galaxy population relations, including the stellar mass function, quenched fractions versus galaxy mass and HI mass function are all largely unchanged and remain consistent with observations. By comparing to data on galaxy properties in different environments from the SDSS and HSC surveys, we demonstrate that our modified model improves the agreement with the quenched fractions and star formation rates of galaxies as a function of environment, stellar mass, and redshift. Overall, in the vicinity of haloes with total mass $10^{12}$ to $10^{15}rm M_{odot}$ at $z=0$, our new model produces higher quenched fractions and stronger environmental dependencies, better recovering observed trends with halocentric distance up to several virial radii. By analysing the actual amount of gas stripped from galaxies in our model, we show that those in the vicinity of massive haloes lose a large fraction of their hot halo gas before they become satellites. We demonstrate that this affects galaxy quenching both within and beyond the halo boundary. This is likely to influence the correlations between galaxies up to tens of megaparsecs.
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