Many engineering systems represent challenging classes of complex dynamic systems. Lacking information about their systems properties leads to model uncertainties up to a level where quantification of uncertainties may become the dominant question in modeling, simulation andapplication tasks. Uncertainty quantification is the prerequisite for probabilistic risk assessment and related tasks. The current work will present recent approaches for these challenges based on response surface techniques, which reduce massively the initial complex model. The reduction is achieved by a regression-like analysis of model output with orthonormal polynomials that depend on the model input parameters. This way, the model response to changes in uncertain parameters, design or control variables is represented by polynomials for each model prediction of interest. This technique is known as polynomial chaos expansion (PCE) in the field of stochastic PDE solutions. The reduced model represented by the response surface is vastly faster than the original complex one, and thus provides a promising starting point for follow-up tasks: uncertainty quantification, model calibration and probabilistic risk assessment. Obviously, a response surface can be constructed in different ways. Methods for constructing the response surface can demand only a minimum number of model evaluations, but as well may ask for many model evaluations to achieve a better quality of the involved projection integrals. The scope of the current work is to test and compare different integration rules, i.e., methods to choose the sets of parameter values for which the model has to be evaluated. To test and compare the different methods, their accuracy in uncertainty quantification, model calibration and risk assessment will be measured against brute-force reference computations based on the original model. As illustrative example, we consider a study from the field of CO2 storage in the subsurface.