Transport schemes are an essential part of Numerical Weather Prediction (NWP) codes. Current simulation codes contain several of such schemes to be applied to different species present in the atmosphere. In weather and climate simulation models, the choice of the most efficient scheme is necessarily a trade-off between accuracy and computational efficiency. In this study, in order to illustrate the propagation of errors that occur in the process of numerical approximations the concepts that originate from the study of sinusoidal waves such as dispersion and diffusion were used. Furthermore the approximation quality has been investigated on the example of artificial solutions using convergence studies on the ICON (ICOsahedral Nonhydrostatic) model. The background of this study is to develop guidelines for the choice of the numerical scheme for a certain quality of the solution. For a real weather case, the differences between the advection schemes were investigated with a case study of pollen transport in La Chaux-de-Fonds and Davos. A difference in execution time could be demonstrated but the values obtained for the schemes are very similar. As part of a project for obtaining faster code with the emerging new supercomputing architectures (Graphics Processing Unit (GPU) based machines), the translation of the transport schemes in ICON has been continued in the domain specific language (DSL) contained in GridTools for Python (GT4Py). The implementations behave numerically identical to the original Fortran version of the code.