Simulations with well-calibrated models offer a unique way to predict the multifaceted behavior of environmental surface or subsurface systems. Due to the lack of available data and high computational costs of the numerical simulation, this class of problems is still very challenging for uncertainty quantification. However, prediction uncertainty must be quantified through stochastic simulations and parameter inference. We offer varies strategies (conventional, sparse and adaptive) based on arbitrary polynomial chaos to quantify uncertainty in environment systems incorporating the observation data.