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 One common failure scenarios is “worst- case” scenario Corps “without condition”

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. Corps “with condition”

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

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

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

Event Tree

Tree Symbols Trees are composed of nodes and branches –Circles=>chance or probability nodes –Squares=>decision nodes –Triangles=>endpoints

Tree Time Nodes represent points in logical time –Decision node=>time when decision maker makes decision –Chance node=>time when result of uncertain event becomes known –Endpoint=>time when process is ended or problem is resolved Time (logic) flows from left to right –Branches leading into a node have already occurred –Branches leading out of or following a node have not occurred yet

Temporal Logical

Branches Branches from chance node are possible outcomes of uncertain events –You have no control over these Branches from decision node are the possible decisions that can be made –You can control these Branches have values –Probabilities are listed on top They are conditional on all preceding events! They must sum to one. –Quantitative values are listed on bottom

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

Endpoints Mutually exclusive Collectively exhaustive Endpoints define sample space, i.e., all possible outcomes of interest Value/units of measure –Be consistent throughout model Can be multiple objectives (payoff matrix)

1. Identify all possible endpoints of interest. 2. Collect relative endpoints to get desired information.

Constructing Trees Rapidly Know the question Know relevant endpoints Keep it simple –Rainfall  Dam failure –Does that answer your questions? Don’t attempt complex model all at once Rapid iteration prototyping Make sure all possible endpoints and important paths are included Analyze pros and cons of details only after considering alternatives –Avoid temptation to become enamored of one or a few endpoints early in the process

5 Steps to Event Tree ID the problem –Write down the question(s) model is to answer –Endpoints define sample space ID major factors/issues to address—details! ID alternatives for each factor/issue Construct tree portraying all important alternative scenarios, start with “as-planned” scenario Collect evidence to quantify model

How Much Detail? You need all possible relevant endpoints and all important pathways to those endpoints How much detail in the pathways is the question=>more detail=more pathways Will more complex model change outcome values that much? Will extra detail mean extra insight? Do you want a model enabling a good choice or a model of reality?

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

Monte Carlo Simulation Simulation model that uses the Monte Carlo process Deterministic values replaced by distributions Values randomly generated for each probabilistic variable & calculations completed Process repeated desired # times

Some Language Simulation-- technique for calculating a model output value many times with different input values. Purpose is to get complete range of all possible scenarios. Iteration--one recalculation of the model during a simulation. Uncertain variables are sampled once during each iteration according to their probability distributions.

Monte Carlo Simulation X = Simulation Iteration

How Many Iterations? Means often stabilize quickly (10 2 ) Estimating probabilities of outcomes (10 3 ) Defining tails of output distribution (10 4 ) If extreme events are important (10 5 )

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?