During several hours of the calm meteorological situation, a relatively significant level of radioactivity can be accumulated around the source. At the second stage, the calm situation is assumed to terminate and convective movement of the air induced by wind immediately starts. Random realisations of the input atmospheric dispersion model parameters for the CALM scenario are generated using LHS (Latin Hypercube Sampling) scheme. The resultant complex random radiological trajectories passing through both calm and convective stages of the release scenario represent inevitable prerequisite for prospective uncertainty analysis (UA) and sensitivity analysis (SA). Novel concept of Approximate Based (AB) solution approximates non-Gaussian sum of individual puffs at the end of the calm period by only one Gaussian “superpuff” distribution. Substantial acceleration of generation of sufficiently large number of random realisation makes further UA and SA feasible. Both procedures come from common mapping of the pairs of matrix random dependant output fields and vector of random input parameters realisations. Examples of 2-D random trajectories of deposited 137Cs are presented. Global sensitivity analysis utilising random sampling methods is outlined.