Models and uncertainty

Models and Uncertainty NGWA Environmental Law Conference Dublin, Ohio July 25, 2007 Todd R. Crawford Crawford Independent Analysts Dr. Willem A. Schre üder Principia Mathematica

Uncertainty ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Models ,[object Object],[object Object],[object Object],[object Object],[object Object]

Monte Carlo ,[object Object],[object Object],[object Object],[object Object],[object Object]

NGWA Environmental Law Conference 2006 – Review ,[object Object],[object Object],[object Object],[object Object]

Using Equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

A Deterministic Approach ,[object Object],[object Object],[object Object],[object Object],[object Object]

The Observed Values are predicted by the J&E Model

What’s the Most Likely Result? ,[object Object],[object Object]

Getting Reasonable Values for α ,[object Object],[object Object],[object Object]

Reasonable Inputs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Reasonable Distributions? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Monte Carlo Simulation in Excel ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Random Numbers in Excel – example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

α for TCE at 5 m in dry, sandy soil

Summary Statistics for α ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Using the results ,[object Object],[object Object],[object Object],[object Object]

Your results may/should differ ,[object Object],[object Object],[object Object],[object Object],[object Object]

To Do List ,[object Object],[object Object],[object Object]

Models and uncertainty

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