Lagrangian methods were used in the past for dispersion modelling, air quality studies and climate-chemistry simulations, because they have a good representation of tracer transport. Here we show that air density inconsistencies between the Lagrangian representation and the model’s core grid can lead to substantial discrepancies. They affect any process calculation related to tracers on the model’s grid, both box and column processes, such as chemistry, photolysis, radiation, and sedimentation. This discrepancies can be resolved by using consistently Lagrangian methods for the core and (implicitely) for the tracer transport. Here we regard two Lagrangian methods, which divide the atmosphere by mass and present a transformation for these methods to derive a partitioning of the atmosphere in disjunct volumes and masses, which is a necessary pre-requisite to calculate any box or column process.