A fundamental understanding of the processes governing atmospheric dispersion of contaminants is essential for optimizing the emergency response following a biological incident. We present a mechanistic, vertically resolved atmospheric dispersion model that couples advection and diffusion in the atmosphere with surface deposition, resuspension and decay due to inactivation through a flux-exchange lower boundary. Air-clearance time is compared for two analytically solved reference cases, namely (i) perfect contaminant deposition and (ii) zero contaminant deposition. The model is applied to scenarios with constant turbulent diffusivity, a linear parameterization of turbulent diffusivity, and time-dependent resuspension, and compared to the reference cases. These scenarios are studied numerically. A non-monotonic dependence of the air-clearance time on the ratio of resuspension rate to deposition velocity is observed. We refer to the parameter region in which the air-clearance time exceeds that of reference case (ii) as the overshoot regime. This behaviour is associated with a slowly evolving air-surface exchange state with airborne contaminant. This regime is observed both for the scenarios assuming constant turbulent diffusivity and the linear parametrization of the turbulent diffusivity. The time-dependent resuspension is a logistic decay function which can be used to emulate scenarios with time intervals of high and low traffic. The model provides a simplified framework for investigating atmospheric persistence and air-surface exchange processes and may serve as a building block for more comprehensive atmospheric dispersion models.