Uncertainty & Variability Water Resource Risk Analysis Davis, CA 2009

Learning Objectives At the end of this session participants will be able to: Explain the differences between variability and uncertainty. Identify reasons for separating the two. Categorize uncertainty by type and cause.

The Point There are lots of things we don’t know in an analysis Do we not know because things are –Uncertain? –Variable? Be able to distinguish the two

There are facts in this world… …we just don’t always know them Mean daily flow on a stream Amount of rock in a channel bottom Average value of a house Mean lock time Mean strength of materials

Uncertainty When there exists a constant or knowable fact unknown by us, this is uncertainty –Sometimes called epistemic uncertainty

There Is Variation in the World Seismic Risk Stream Flow Susquehanna River Hurricane Tracks

Variability Variation in values due to variability in system, a natural characteristic of system Effect of chance –Sometimes called aleatory uncertainty Can’t be reduced through study or measurement Sometimes you can change the system to reduce the variability

Variability and Uncertainty 8 Model Structure Model Detail Model Boundaries Model Precision and Accuracy Calibration Validation Extrapolation Model Resolution Stressor Pathways Exposed Populations Sources Activity Patterns Boundaries Spatial considerations Temporal considerations SCENARIOMODEL INPUTS VariabilityUncertainty

Uncertainty and Variability When we’re not sure, we’re uncertain Uncertainty represented by probability distributions Can often be reduced by throwing money at it Differences inherent in the system—chance Variability represented by probability distributions Cannot be reduced by throwing money at it

We use probability distributions

What is Uncertain? Knowledge Model Uncertainty Quantity Uncertainty-current focus –Parameters –Empirical quantities Decision-Rule Uncertainty Natural Variability

Quantity Uncertainty Different kinds of quantities –Some have a “true” parameter value It may be known or uncertain –Some have a “best” or “appropriate” value Different sources of uncertainty for each Treatment of uncertainty depends on the quantity and cause of uncertainty

Input/Quantity Uncertainty Empirical quantities –Only quantity with true parameter value, uncertainty and true value possible here –Mean daily flow, mean strength of materials, value of a house, time –Full range of treatments Defined constants –Certain by definition, no reason for uncertainty, look it up –Sq. ft./acre, gallons in an acre-foot of water, π

Quantity Uncertainty Decision variables –Decision makers exercise direct control over these kinds of values No true value Can be uncertain over best value –Reasonable incremental cost, mitigation goals, factors of safety –Parametric variation

Quantity Uncertainty Value parameters –Represent aspects of decision makers’ preferences No true value –Discount rate, value of statistical life –Parametric variation Index Variables –Identify a location or cell in time or space A particular year in multi-year model, a geographic grid in a spatial model –Parametric variation No true value

Quantity Uncertainty Model Domain Parameters –Specify & define scope of system modeled –Study area, industry segment, planning horizon –Parametric variation No true value Outcome Criteria –Measure or rank desirability of model outcomes –HUs, costs, probability, reliability index, BCR –Depends on inputs

Sources of Uncertainty in Empirical Quantities Random Error & Statistical Variation –Sample error Systematic Error & Subjective Judgment –Calibration of equipment, feels like an 8 Linguistic Imprecision (ambiguity) –Fill to -1 Variability –Chance-some fish die

Sources of Uncertainty in Empirical Quantities Randomness & Unpredictability –Natural events, outbreaks Disagreement or Ambiguity –Partners, experts Approximation –Past conditions

Practical Approaches Lists are your friend—make them –Uncertain knowledge, models and quantities Identify those that can be easily addressed Address them Identify the most important ones not easily addressed Develop plan for addressing them

Variation Variation = Variability+Uncertainty Both are sometimes present The two are not always distinguished They are sometimes confused Would like to keep them separate when possible –Can it be done? –Can you do it?

Context There are 2 components contributing to variation in outputs Uncertainty is reducible Variability is not reducible, it is an objective characteristic of system

More Money Means Variability –Better description of chance –Better understanding of its nature –No reduction in variability Uncertainty –Better description of uncertainty –Reduction of uncertainty –Handling uncertainty

Take Away Points Variability is chance and can’t be reduced. Uncertainty is ignorance and often can be reduced. Better risk assessments separate the two but it is not always easy. Separating the two is becoming more important for risk management.

Charles Yoe, Ph.D. Questions?