Stochastic calibration of riverine water quality models

Though commonly used, the suitability of deterministic calibration criteria for stochastic model calibration and uncertainty analysis is unclear. The purpose of this paper is to examine the suitability, relative benefits, and substantial disadvantages of "deterministic-optimization" approaches, such as root mean square error (RMSE), in stochastic contexts. Three alternate calibration strategies that are suitable for stochastic modeling of water quality under uncertainty are proposed and then demonstrated. The three alternate strategies are the absolute relative error (ARE), weighted relative error, and stochastic exceedance calibration strategy. The findings suggest that potential improvements can be made to current calibration paradigms. The alternate calibration strategies, all of which are based on relative error, were found to match or exceed RMSE calibration strategies, in terms of overall performance, with the enhancement of superior model surface-response characteristics. Additionally, the application of more stringent ARE criteria offered greater improvement in the stochastic calibration response than increasing the RMSE threshold criteria. Several qualitative benefits of ARE and related metrics also were shown. Because many environmental systems and almost all water quality models are subject to substantial uncertainty, approaches such as those proposed hold substantial, widely applicable benefits.