Atmospheric retrieval, inverse-modelling, and data-assimilation workflows require transparent transport models that can be evaluated repeatedly and provide consistent sensitivities. We present TARSA v1.0, a lightweight regional three-dimensional Eulerian model for inert tracers and simplified aerosol applications under prescribed ERA5 meteorology. TARSA advances tracer mass mixing ratios with a conservative finite-volume core comprising monotonic advection, vertical turbulent diffusion, sedimentation, and parameterised dry and wet deposition. The default advection scheme uses a TVD-admissible, cubic-Hermite-regularised Koren limiter to reduce selected gradient-error roughness. Analytic, tangent-linear, discrete-adjoint, and automatic-differentiation gradients agree to single precision in a scalar emission-amplitude check. Numerical verification includes mass-conservation, analytical plume, and manufactured-solution tests. Independent evaluation against european and north-american regional experiments (ETEX-1, CAPTEX-1) shows agreement in plume timing and concentration amplitude, with performance broadly comparable to published transport-model results. A Saharan dust-column case during Fennec, driven by prescribed MERRA-2 emissions without externally prescribed dust initial or lateral boundary concentrations, shows moderate agreement with GRASP/POLDER coarse-dust column estimates. TARSA provides a reproducible forward operator for regional transport and observation-space studies, supporting future air-quality applications using satellite aerosol observations. Its prescribed process set and local sensitivity structure support future retrieval and inversion applications, while end-to-end inverse-modelling performance remains to be demonstrated.