One of the major systematic uncertainties in the measurement of Xmax from radio emission of EAS arises from variations of the refractive index in the atmosphere. The refractive index n varies with temperature, humidity and pressure, and the variations can be on the order of 10% for (n-1) at a given altitude. The effect of a varying refractive index on Xmax measurements is evaluated using CoREAS: a microscopic simulation of the radio emission from the individual particles in the cascade simulated with CORSIKA. We discuss the resulting offsets in Xmax for different frequency regimes, and compare them to a simple physical model. Under typical circumstances, the offsets in Xmax range from 4-11 g/cm2 for the 30-80 MHz frequency band. Therefore, for precise measurements it is required to include atmospheric data at the time and place of observation of the air shower into the simulations. The aim is to implement this in the next version of CoREAS/CORSIKA using the Global Data Assimilation System (GDAS), a global atmospheric model based on meteorological measurements and numerical weather predictions. This can then be used to re-evaluate the air shower measurements of the LOFAR radio telescope. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License (CC BY-NC-ND 4.0).