Probabilistic Scenario Analysis Institute for Water Resources 2009 Charles Yoe, PhD

Why Are Decisions Hard? Complex Inherent uncertainty Conflicting objectives Differences in perspectives, i.e., risk attitudes Scenarios can address these aspects Know what questions you’re trying to answer.

Bundle of Tools and Techniques Probabilistic scenario analysis is not scenario planning –Two different techniques for addressing uncertainty HEC FDA, Beach FX, Harbor Sim are all examples of PSA We’ll use event trees to better understand the idea

Scenarios Literally an outline or synopsis of a play Scenarios can be used to describe present Most often used to describe possible futures Corps scenarios –Without condition(s) –With conditions –Base year –Existing condition

Scenario Comparison HUsCost Without condition5,0000 With condition Plan A 7,500One Million Change due Plan A +2,500+1,000,000 With condition Plan B 25,000One billion Change due Plan B +20,000+1,000,000,000

Scenario Analysis Deterministic scenario analysis –Examine specific scenarios –Organize and simplify avalanche of data into limited number of possible future states of the study area or infrastructure Probabilistic scenario analysis –Characterize range of potential futures and their likelihoods

Some New Scenario Types As-planned scenario Failure scenarios Improvement scenarios

“As-Planned Scenario Surprise free scenario--free of any failures Risk free scenario--every feature of system functions as planned—no exposure to hazard Terrorist Attack on Infrastructure Plot Detected As planned Yes No Attack Foiled Structure Undamaged Successful Attack

Failure Scenarios Tell story how various elements of system might interact under certain conditions Challenge notion system will function as planned Any aspect of as-planned scenario may be challenged One common failure scenarios is “worst- case” scenario

Worst-Case Scenario Introduces conservatism into analysis--a deliberate error Given any worst case an even worse case can, paradoxically, be defined Possible is not necessarily probable Failure in the better than worst-case world is still possible

Improvement Scenarios Risk analysis often results in new risk management options to reduce risks Develop an improvement scenario for each management option considered –Used to evaluate risk management options –Used to select the best option.

Scenario Comparisons Most likely future condition absent risk management, –Status quo or "without condition“--basic failure scenario –Every new risk management option evaluated against this Most likely future condition with specific risk management option –“With condition“--improvement scenarios –Each option has its own unique with condition Compare "with" and "without" conditions for each new risk management option

Methods of Comparison Risk Effect of Interest Baseline Existing Future No Action Future with Option A Before & After Comparison With & Without Option Comparison TargetGap Analysis Time

Deterministic Limits Limited number can be considered Likelihoods are difficult to estimate Cannot address full range of outcomes

Scenario Tools Event trees –Forward logic Fault trees –Backward logic Decision trees –Decision, chance, decision, chance Probability trees –All branches are probabilities

Event Tree

Constructing Trees Keep it simple –Rainfall  Dam failure –Does that answer your questions? Don’t attempt complex model all at once Rapid iteration prototyping Analyze pros and cons of individual scenarios only after considering all alternatives –Avoid temptation to become enamored of one or a few scenarios early in the process

Constructing Trees (cont.) Use Yes and No branches when possible –Not always possible or desirable Separates elements of problem in structured way Different trees yield different insights

Variability and Uncertainty 19 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

What is Uncertain? Knowledge Model Uncertainty Quantity Uncertainty –Parameters –Empirical quantities Natural Variability

Many Scenarios Because of variability and uncertainty there are many possible scenarios It is not possible to describe them all Some may be important to the decision process Probability can be added to a scenario in a variety of ways –Monte Carlo process

Probability Is Not Intuitive Learn It Pick a door. What is the probability you picked the winning door? What is the probability you did not?

Data and Distributions

Checklist for Choosing a Distributions From Some Data 1.Can you use your data? 2.Understand your variable a)Source of data b)Continuous/discrete c)Bounded/unbounded d)Meaningful parameters e)Univariate/multivariate f)1 st or 2 nd order 3.Look at your data— plot it 4.Use theory 5.Calculate statistics 6.Use previous experience 7.Distribution fitting 8.Expert opinion 9.Sensitivity analysis

Model Uncertainty Help people understand your model Be the first to point out its weaknesses Don’t be afraid to be creative

Take Away Points PSA is a class of tools that relies on –Scenarios –Probabilities PSA’s take many forms –Most IWR tools are PSA’s –Event trees & fault trees –Process models & Flow diagrams PSA’s are very powerful and useful tools

Charles Yoe, Ph.D. Questions?