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Characterization of uncertainty associated with transport-transformation models is often of critical importance, as for example in cases where environmental and biological models are employed in risk assessment. However, uncertainty analysis using conventional methods such as standard Monte Carlo or Latin Hypercube Sampling may not be efficient, or even feasible, for complex, computationally demanding models. This work introduces a computationally efficient alternative method for uncertainty propagation, the Stochastic Response Surface Method (SRSM). The SRSM approximates uncertainties in model outputs through a series expansion in normal random variables (polynomial chaos expansion). The unknown coefficients in series expansions are calculated using a limited number of model simulations. This method is analogous to approximation of a deterministic system by an algebraic response surface. Further improvements in the computational efficiency of the SRSM are accomplished by coupling the SRSM with ADIFOR, which facilitates automatic calculation of partial derivatives in numerical models coded in Fortran. The coupled method, SRSM-ADIFOR, uses the model outputs and their derivatives to calculate the unknown coefficients. The SRSM and the SRSM-ADIFOR are general methods, and are applicable to any model with random inputs. The SRSM has also been implemented as a black-box, web-based tool for facilitating its easy use. The SRSM and the SRSM-ADIFOR have been applied to a set of environmental and biological models. In all the case studies, the SRSM required an order of magnitude fewer simulations compared to conventional methods, and the SRSM-ADIFOR required even fewer simulations. In addition to their computational efficiency, these methods directly provide sensitivity information and individual contributions of input uncertainties to output uncertainties; conventional methods require substantially larger numbers of simulations to provide such information. Thus, the SRSM and the SRSM-ADIFOR provide computationally efficient means for uncertainty and sensitivity analysis. Finally, this research addresses uncertainties associated with model structure and resolution with application to photochemical air quality modeling. A three dimensional version of the regulatory Reactive Plume Model (RPM), RPM-3D, has been developed and applied to understand model uncertainty.