Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads

Several sources of uncertainty are considered in using field data to perform mass balance calculations to estimate nonpoint source (NPS) loads of total dissolved solids (TDS) and selenium (Se) to two reaches along the Lower Arkansas River in Colorado. This approach renders stochastic models of the mass balance equations for each river reach, where the input variables and their associated parameters are treated as random variables described by probability distributions. A data set collected in an intensive field effort conducted over several years is used in developing the models. Monte Carlo simulation solves the stochastic mass balance equations to describe distributions of possible values of the NPS loads. Results indicate that uncertainty in these calculated loads is sizeable. Annual average coefficient of variation (CV) in calculated total NPS TDS loads for sample periods within the two reaches ranges between 0.15 and 2.76, averaging about 1.1. For the Se mass balance along the downstream reach, the average CV in calculated loads is 0.23. The 90% prediction interval width for total NPS TDS load averaged over the 58 sample periods along the upstream reach is 13,691 (kg/day)/km, compared to an overall average mean load of 8,383 (kg/day)/km. It is 8,545 (kg/day)/km averaged over the 61 sample periods downstream, compared to an overall average mean load of 11,183 (kg/day)/km. For the Se load, the overall average 90% prediction interval width is also substantial compared to the overall average mean: 0.028 (kg/day)/km compared to 0.038 (kg/day)/km. Change in stored solute mass within the river over sample periods is found to be a major contributing factor to the calculation of NPS loads. Also, sensitivity analyses are performed that yield information on the relative influence that the degree of uncertainty in each random parameter has on the uncertainty in the calculated solute loads.