Stratospheric emissions from aircraft or rockets are important sources of chemical perturbations. Small-radius high-aspect-ratio plumes from stratospheric emissions are smaller than global Eulerian models' grid cells. To help global Eulerian models resolve subgrid plumes in the stratosphere, a Lagrangian plume model, comprising a Lagrangian trajectory model and an adaptive-grid plume model with a sequence of plume cross-section representations (from a highly resolved 2-D grid to a simplified 1-D grid based on a tradeoff between the accuracy and computational cost), is created and embedded into a global Eulerian (i.e., GEOS-Chem) model to establish a multiscale Plume-in-Grid (PiG) model. We compare this PiG model to the GEOS-Chem model based on a 1-month simulation of continuous inert tracer emissions by aircraft in the stratosphere. In the PiG results, the final injected tracer is more concentrated and approximately 1/3 of the tracer is at concentrations 2–4 orders of magnitude larger compared to the GEOS-Chem results. The entropy of injected tracer in the PiG results is 6% lower than the GEOS-Chem results, indicating less tracer mixing. The total product mass from a hypothetical second-order process (applied to the injected tracer) in the PiG results is 2 orders of magnitude larger than the GEOS-Chem results. Increasing the GEOS-Chem model's horizontal resolution 4-fold is insufficient to resolve this product difference, while requiring over seven times the computational resources of the PiG model. This paper describes the PiG model framework and parameterization of plume physical processes. Chemical and aerosol processes will be introduced in the future.