1. TMDLs and Statistical Models Kenneth H. Reckhow Duke University

2. TMDL Applications Forecast and establish initial pollutant allocation

3. Forecasting The problem with water quality forecasting is that we’re not terribly good at it. Result: prediction uncertainty is high

4. 90% Predictive Interval “Margin of Safety” Target Reduction with 95% Confidence

5. TMDL Applications Forecast and establish initial pollutant allocation Update and modify through adaptive implementation

6. TMDLs should be adaptive TMDL Implementation Modeling approaches need to be developed that integrate model forecasts with post-implementation monitoring (e.g., Bayesian analysis, Kalman filter, data assimilation).

7. Prior (model forecast) Sample (monitoring Data) Posterior (integrating modeling and monitoring) Adaptive Implementation: Bayesian Analysis Criterion Concentration

8. Bayes (Probability) Networks Conditional probability models that can be mechanistic, statistical, judgmental use probability to express uncertainty use Bayes theorem for adaptive implementation updating.

9. Oxygen is depleted in the bottom water. Algae die and accumulate on the bottom where they are consumed by bacteria. Under calm wind conditions, density stratification occurs. Nitrogen stimulates the growth of algae. Nitrogen stimulates the growth of algae. Fish and shellfish may die or become weakened and vulnerable to disease. The Negative Effects of Excessive Nitrogen in an Estuary The Negative Effects of Excessive Nitrogen in an Estuary

10. Nitrogen Inputs Cause and Effect Relationships Cause and Effect Relationships Frequency of Hypoxia Duration of Stratification Harmful Algal Blooms Carbon Production Sediment Oxygen Demand River Flow Algal Density Chlorophyll Violations Number of Fishkills Fish Health Shellfish Abundance

11. Sediment Oxygen Demand Duration of Stratification River Flow Algal Density Carbon Production Frequency of Hypoxia Cross-SystemComparison SimpleMechanistic ExpertElicitation Number of Fishkills Nitrogen Inputs Fish Health Chlorophyll Violations Harmful Algal Blooms Shellfish Abundance Empirical Model Seasonal Regression Site-Specific Application Survival Model

12. Research Opportunities This would allow more accurate assessment of the effectiveness of NPS controls, and targeting of BMP improvements. With SPARROW linked to a waterbody model, post-implementation monitoring could be designed for Bayesian updating.