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(eng): In several hours of a calm meteorological situation, a relatively significant level of radioactivity may accumulate around the source. When the calm situation expires, a wind-induced convective movement of the air immediately begins. Random realisations of the input atmospheric dispersion model parameters for this CALM scenario are generated using Latin\nHypercube Sampling scheme. The resultant complex random radiological trajectories, passing through both calm and convective stages of the release scenario, represent the necessary prerequisite for the prospective uncertainty analysis (UA) and the sensitivity analysis (SA). The novel approximation-based (AB) solution replaces the non-Gaussian sum of individual puffs at the end of the calm period with one Gaussian ‘‘super-puff’’ distribution. This substantially accelerates generation of a sufficiently large number of random realisations for the radiological trajectories, thus facilitating the subsequent UA and SA. Both of these procedures exploit a common mapping between the pairs of calculated output fields on the one hand and the realisation vectors of the associated random input parameters on the other hand. This paper presents the necessary technical background, as well as the idea of the AB solution and its use. Examples of 2-D random trajectories of deposited 137Cs are presented in a graphical form. Global sensitivity analysis based on random sampling methods is outlined and improved feasibility o f the originally long-running computation is demonstrated.