Modeling the Effects of Acid Deposition: Uncertainty and Spatial Variability in Estimation of Long‐Term Sulfate Dynamics in a Region

The choice of appropriate parameter values for mathematical models that are meant to describe long-term (decades or longer) changes in hydrochemical catchment response to atmospheric deposition is difficult because long time series of observations are generally unavailable. Some information about the range (or distribution) of stream chemistry variables across a given region is often available, however, and this should provide useful guidance in selecting allowable values for parameters for regional application of the model. We develop a method for using data that describe the present-day distribution of stream water chemistry in a region to constrain allowable ranges of parameters in a mathematical model and to infer particular parameter combinations that are inconsistent with observations. We apply the method to a simple model of catchment sulfate dynamics using measured sulfate concentrations from several streams in Shenandoah National Park, Virginia. Acceptable parameter combinations for this case are well defined by a single linear axis. Extrapolation of the distribution of sulfate concentrations into the future using these acceptable parameter combinations suggests that a shift in mean sulfate concentration in the southwest section of the park would be detectable with 90% certainty 8 to 10 years hence, assuming that atmospheric deposition remains constant.