A simple Lagrangian stochastic (LS) dispersion model was used to investigate atmospheric dispersion in the lower atmospheric boundary layer, for near-surface sources. The sensitivity of ground-level concentration to numerical errors was revealed. Numerical treatments of inhomogeneous atmospheric turbulence and surface reflection in Lagrangian trajectory calculations may cause non-negligible overestimates of ground-level concentration for elevated sources, although these errors become trivial for surface sources and for concentrations above the ground-level. Using a numerical error-correction scheme, the LS model was evaluated against an analytical model. Close agreement was found between the two models in predicting ground-level concentrations for dispersions in the surface layer. LS simulations for an elevated source were also conducted. A scaling scheme was proposed to normalize the dispersion results, by including the source height as a scaling length. The relationships between the normalized surface concentration and downwind distance were distinguished by atmospheric stabilities. In the near-field, the distance of peak ground-level concentration was 0.5, 1.0, and 2.0 times z_s U/u_*, where z_s is the source height, U is the mean wind speed at height 10 m, and u_* is the friction velocity, for unstable, neutral and stable atmospheric stability conditions, respectively. In the far-field, the concentration approached approximately the "-3/2", "-1" and "-2/3" law for unstable, neutral and stable atmospheres respectively.