Atmospheric chemistry is a tool for researchers in studying the earth's atmosphere. It finds its application in various areas, such as weather forecasting or the study of climate change. The Modular Earth Submodel System MESSy is a software framework enabling researchers to use various mathematical models to run numerical simulations to predict weather changes or analyze climate change effects. With such numerical simulations, extensive data is produced, which demands considerable hard drive space. We solve this problem by applying lossy data compressing using adaptive mesh coarsening. For this, we develop a coupling interface between MESSy and the software library t8code, which specializes in adaptive mesh management. We further develop criteria for compressing chemical species and evaluate them on the greenhouse gasses.  Finally, we present our results of a benchmark study with the greenhouse gasses.