A Bayesian approach for calculating variable total maximum daily loads and uncertainty assessment.

To account for both variability and uncertainty in nonpoint source pollution, one dimensional water quality model was integrated with Bayesian statistics and load duration curve methods to develop a variable total maximum daily load (TMDL) for total nitrogen (TN). Bayesian statistics was adopted to inversely calibrate the unknown parameters in the model, i.e., area-specific export rate (E) and in-stream loss rate coefficient (K) for TN, from the stream monitoring data. Prior distributions for E and K based on published measurements were developed to support Bayesian parameter calibration. Then the resulting E and K values were used in water quality model for simulation of catchment TN export load, TMDL and required load reduction along with their uncertainties in the ChangLe River agricultural watershed in eastern China. Results indicated that the export load, TMDL and required load reduction for TN synchronously increased with increasing stream water discharge. The uncertainties associated with these estimates also presented temporal variability with higher uncertainties for the high flow regime and lower uncertainties for the low flow regime. To assure 90% compliance with the targeted in-stream TN concentration of 2.0mgL(-1), the required load reduction was determined to be 1.7 × 10(3), 4.6 × 10(3), and 14.6 × 10(3)kg TNd (-1) for low, median and high flow regimes, respectively. The integrated modeling approach developed in this study allows decision makers to determine the required load reduction for different TN compliance levels while incorporating both flow-dependent variability and uncertainty assessment to support practical adaptive implementation of TMDL programs.