An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

Abstract

An indirect simulation-optimization model framework with enhanced computational efficiency and risk-based decision-making capability was developed to determine optimal total maximum daily load (TMDL) allocation under uncertainty. To convert the traditional direct simulation-optimization model into our indirect equivalent model framework, we proposed a two-step strategy: (1) application of interval regression equations derived by a Bayesian recursive regression tree (BRRT v2) algorithm, which approximates the original hydrodynamic and water-quality simulation models and accurately quantifies the inherent nonlinear relationship between nutrient load reductions and the credible interval of algal biomass with a given confidence interval; and (2) incorporation of the calibrated interval regression equations into an uncertain optimization framework, which is further converted to our indirect equivalent framework by the enhanced-interval linear programming (EILP) method and provides approximate-optimal solutions at various risk levels. The proposed strategy was applied to the Swift Creek Reservoir's nutrient TMDL allocation (Chesterfield County, VA) to identify the minimum OPEN ACCESSWater 2015, 7 6635 nutrient load allocations required from eight sub-watersheds to ensure compliance with user-specified chlorophyll criteria. Our results indicated that the BRRT-EILP model could identify critical sub-watersheds faster than the traditional one and requires lower reduction of nutrient loadings compared to traditional stochastic simulation and trial-and-error (TAE) approaches. This suggests that our proposed framework performs better in optimal TMDL development compared to the traditional simulation-optimization models and provides extreme and non-extreme tradeoff analysis under uncertainty for risk-based decision making.

Impaired Water Hazard Zones: Mapping Intersecting Environmental Health Vulnerabilities and Polluter Disproportionality

“…First, surface water CAWMHS only includes industrial surface water toxic releases from the U.S. EPA RSEI database. In addition, surface water CAWMHS does not account for the fate and transport of pollutants as found in a number of hydrological analyses used for assessing total maximum daily loads (TMDL) for U.S. waterways [24][25][26][27][28][29]. Accordingly, questions remain regarding the unequal spatial distribution of a broader set of point and non-point-sources (NPS) in the region.…”

Development and Application of Exceedance Model for Surface Water Quality Parameters

“…The source of water pollution was also identified where a specific treatment was needed. The use of probability to illustrate water quality is applied in studies [34][35][36][37][38]. The various exceedance models were used for finding exceedance water quality parameters to decide some useful water management strategies around the world [35][36][37][38].…”

A Stochastic Multi-Objective Chance-Constrained Programming Model for Water Supply Management in Xiaoqing River Watershed

“…Previously, many uncertain analysis approaches were developed for dealing with watershed-scale water resource management issues, including stochastic mathematical programming (SMP) [3][4][5][6][7], fuzzy mathematical programming (FMP) [8][9][10][11] and interval mathematical programming (IMP) [12,13], as well as their combinations [14][15][16][17][18]. Among them, stochastic chance-constrained programming (SCCP) was extensively applied in water resource management due to its capacity in evaluating the trade-offs between realization of system objectives and satisfaction degrees of model constraints [19][20][21][22].…”