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We present TARSA (Transport Aerosol model for Remote Sensing Applications), a lightweight three-dimensional Eulerian transport model designed for regional studies and tight integration with atmospheric remote-sensing frameworks. TARSA solves a linear conservation equation for generic tracers expressed as mass mixing ratios, including advection by prescribed winds, turbulence-driven vertical diffusion, gravitational settling, and parameterised dry and wet deposition. Nonlinear aerosol microphysics and radiative feedbacks are excluded from the prognostic core, so that all active processes can be written as linear operators acting on a common state vector. The model employs a finite-volume discretisation with first-order upwind advection and implicit time stepping on a structured grid, driven by meteorological fields from the ERA5 reanalysis. All tracers share the same numerical infrastructure, and physical processes can be switched on or off on a per-tracer basis. We verify and validate TARSA using a hierarchy of experiments. An idealised manufactured Gaussian plume test in a uniform flow demonstrates accurate reproduction of the analytical reference over many orders of magnitude in concentration and confirms near machine-precision mass conservation. A real-world simulation of the ETEX-1 field tracer experiment shows that TARSA captures the large-scale trajectory and arrival sequence of an inert gas over Europe, while reproducing station-wise peak concentrations and dosages within the range reported for established Eulerian models. A short-range consistency experiment against Copernicus Atmosphere Monitoring Service (CAMS) reanalysis fields for carbon monoxide and several aerosol species shows that, when initialised and bounded by reanalysis mixing ratios without additional emissions, TARSA preserves the main spatial patterns and vertical structures of realistic tracers over a synoptic (2–3 day) time scale. Finally, we demonstrate TARSA’s suitability for satellite-constrained inverse problems with a proof-of-concept retrieval of volcanic sulfur dioxide emissions. Using column SO₂ observations from a polar-orbiting sensor and a linear emission-rate parameterisation, we estimate time-varying source strength by minimising the mismatch between observed and simulated columns under Gaussian observation errors. The inferred emissions reproduce the observed plume timing and downwind structure and provide an end-to-end example of TARSA as a transparent, efficient forward operator for source inversion. Owing to its linear formulation, sparse implicit solver, and modest computational cost, TARSA is well suited for inverse problems and multi-sensor data assimilation; a companion study will describe the corresponding inverse framework in detail.