Explosive volcanic eruptions are typically associated with the injection into the atmosphere of large numbers of particles (known as tephra) dispersed over long distances depending on their size, shape and density. In this thesis, we present the MPI parallel Eulerian-Lagrangian Tephra Transport and Deposition Model (TTDM) Tetras. We build on this model a flexible multiscale TTDM, coupled using MUSCLE-HPC. This model accounts for processes at multiple temporal and spatial scales, such as fast rising of particles in the volcanic column, aggregation of particles and transport of particles by wind over very long range. We propose as well a new family of models called Spatially Extended Exit Rate (SEER) models to improve agreement with field data of proximal deposit compared to Tetras modelling strategy. We propose four SEER based models, ranging from an analytical expression to a compute intensive Lagrangian MPI parallel model. Finally, we investigate new inversion strategies based either on a semi analytical SEER model and metaheuristics or on Tetras coupled with the parallel approximate Bayesian computation framework ABCpy. For this, we had to develop a nested parallelism technique to integrate an MPI model with ABCpy.