The biogeochemical model, PnET-BGC, has been used to evaluate the long-term acid-base response of surface waters to changes in atmospheric acid deposition. We propose a methodology to identify the input factors of greatest model sensitivity and propagate uncertainty of input factors to model outputs. The quantified model uncertainty enabled application of an "exceedance probability" approach to determine allowable atmospheric deposition in the form of Total Maximum Daily Loads (TMDLs) for twelve acid-impaired streams in Great Smoky Mountains National Park. Results indicate that acidification of surface water resulting from acidic deposition has been substantial. Even if current atmospheric deposition is reduced to pre-industrial levels, only one of the twelve impaired streams might be recovered to its site-specific standard by 2050. Our sensitivity analysis indicates that the model is most sensitive to precipitation quantity, air temperature and calcium weathering rate, and suggests further research to improve characterization of these inputs. (C) 2017 Elsevier Ltd. All rights reserved.