TMDLs and Statistical Models

Kenneth H. Reckhow

Duke University

TMDL Applications

Forecast and establish initial pollutant allocation

Forecasting

The problem with water quality forecasting is that we’re not terribly good at it.

Result: prediction uncertainty is high

N Reductions Relative to 1991-95

0

5

10

15

20

25

-70-60-50-40-30-20-100

Sta

ndar

d V

iola

tions

(%

)

90% Predictive Interval90% Predictive Interval

““Margin of Safety”Margin of Safety”

Target ReductionTarget Reductionwith 95% Confidencewith 95% Confidence

TMDL Applications

Forecast and establish initial pollutant allocation

Update and modify through adaptive implementation

• 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).

Prior (model forecast)

Sample(monitoringData)

Posterior (integrating modelingand monitoring)

Adaptive Implementation: Bayesian Analysis

Criterion Concentration

Bayes (Probability) Networks

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

Oxygen is Oxygen is depleteddepleted in in the bottom the bottom

water.water.

Oxygen is Oxygen is depleteddepleted in in the bottom the bottom

water.water.

Algae die and Algae die and accumulateaccumulate on the bottom where they on the bottom where they are are consumedconsumed by bacteria. by bacteria.

Algae die and Algae die and accumulateaccumulate on the bottom where they on the bottom where they are are consumedconsumed by bacteria. by bacteria.

Under calm wind Under calm wind conditions, density conditions, density

stratificationstratification occurs.occurs.

Under calm wind Under calm wind conditions, density conditions, density

stratificationstratification occurs.occurs.

Nitrogen Nitrogen stimulatesstimulates the growth of algae.the growth of algae.

Nitrogen Nitrogen stimulatesstimulates the growth of algae.the growth of algae.

Fish and Fish and shellfish may shellfish may diedie

or become or become weakened weakened and and vulnerable to vulnerable to

disease.disease.

Fish and Fish and shellfish may shellfish may diedie

or become or become weakened weakened and and vulnerable to vulnerable to

disease.disease.

The Negative Effects of Excessive

Nitrogen inan Estuary

The Negative Effects of Excessive

Nitrogen inan Estuary

NitrogenInputs Cause and Effect

RelationshipsCause and Effect

Relationships

Frequency of Hypoxia

Duration of Stratification

HarmfulAlgal Blooms

Carbon Production

SedimentOxygenDemand

RiverFlow

AlgalDensity

ChlorophyllViolations

Number ofFishkills

FishHealth

ShellfishAbundance

SedimentOxygenDemand

Duration of Stratification

RiverFlow

AlgalDensity

Carbon Production

Frequency of Hypoxia

Cross-System Cross-System ComparisonComparison

Simple Simple MechanisticMechanistic

Expert Expert ElicitationElicitation

Number ofFishkills

NitrogenInputs

FishHealth

ChlorophyllViolations

HarmfulAlgal Blooms

ShellfishAbundance

Empirical ModelEmpirical Model

Seasonal RegressionSeasonal Regression

Site-Specific ApplicationSite-Specific Application

Survival ModelSurvival Model

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.