FOI has from SSM received a research grant to study uncertainties in observations and calculations with the goal to be able to better describe the effect of the combined uncertainty of all indata parameters in the resulting data. Generally results from dispersion modelling are presented as deterministic point estimates, i.e. the result from the dispersion calculation, a concentration of hazardous substance, is given only as a number. This has also been the practice at the Swedish Defence Research Institute. It should be mentioned, however, that we have always tried to consider several scenarios "a likely worst case", "a probable case" and "a likely favourable case", but the resulting concentrations have been presented in a form that looks like exact answers. At the heart of dispersion modelling lays the attempt to try to model the flow of air in the atmosphere as well as the, in reality partly stochastic, interaction between the released gas or particle and the atmosphere. It is therefore natural to consider the resulting concentration to be a random variable, and this was pointed out in the literature at an early stage (Lewellen and Syke, 1989). Since the concentration is a random variable it should also be presented in such language: mean, variance and probability distribution. There are several sources contributing to the uncertainty in the concentration, one is uncertainty in input to the dispersion model, another is uncertainties in the model itself, and from discrepancies between the model and reality. A third one is uncertainties arising from natural fluctuations in the real process. This report is focusing on characterising the uncertainty stemming from the input to the dispersion model. We present a review of methods (mainly numerical ones) that have been developed to aid in the estimation of uncertainty in the concentration estimates. Following that, we select a method (Latin hypercube sampling) and a dispersion model to make a case study of how to practically compute this type of uncertainty. The case study is a dispersion model of a hypothetical release of chlorine gas following a real accident with a derailed train in Kungsbacka. The purpose of the case study is to confirm that we have a functioning working method to handle uncertainties in the input, as well as give a flavour of how large the uncertainties actually are. The uncertainties are then presented in a number of ways, followed by a discussion and conclusion. One key observation is that following an accident it is not so much traditional statistical methods that are required, but rather statistics of extreme events