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Real Options, Optimisation Methods and Flood Risk Management Michelle Woodward - HR Wallingford and Real Options, Optimisation Methods and Flood Risk Management Michelle Woodward - HR Wallingford and Exeter University Ben Gouldby – HR Wallingford Zoran Kapelan – Exeter University Soon-Thiam Khu – Exeter University

Objective of Ph. D Title: Real options based optimum selection of flood risk mitigation Objective of Ph. D Title: Real options based optimum selection of flood risk mitigation options Objective: To investigate optimum flood risk intervention strategies taking into account the possible effects of climate change Page 2

Presentation outline • Overview of Risk Analysis tool • Calculating Benefits of interventions • Presentation outline • Overview of Risk Analysis tool • Calculating Benefits of interventions • Optimisation Techniques • Evolutionary Algorithms • Dynamic Programming • Real Options • Valuing flexibility for climate change adaptation strategies • Outline of computational framework Page 3

Background to RASP Risk Assessment for System Planning Research Project funded by the UK Background to RASP Risk Assessment for System Planning Research Project funded by the UK Environment Agency (2001 -2004) Page 4

RASP is a framework for flood risk analysis National Level National justification, regional prioritisation, RASP is a framework for flood risk analysis National Level National justification, regional prioritisation, long term outlook Common database (NFCDD) Catchment / Coastal Cell Level Strategic planning Development regulation Common input/output Site / System Level Scheme appraisal Page 5

Conceptual model Utilises a structured definition of the flood system Page 6 Conceptual model Utilises a structured definition of the flood system Page 6

The system model Determining flood systems” • Recognises that levees behave as “defence depth The system model Determining flood systems” • Recognises that levees behave as “defence depth versus probability The system model: • A flood depth versus probability distribution is established by considering multiple combinations of storm loading and possible levee failure Page 7

All inundation scenarios A new super fast inundation model (HR RSFM) enables 10000 s All inundation scenarios A new super fast inundation model (HR RSFM) enables 10000 s of inundation scenarios to be realised Runtime: <0. 1 sec Model has been compared to hydrodynamic models like Infoworks-RS 2 D Page 8

The system model 1. Depth damage curves are used Estimatingdamages to assess the flood The system model 1. Depth damage curves are used Estimatingdamages to assess the flood Three steps are used to calculate risk associated with each possible flood scenario 2. By combining the scenario damage with the probability of the scenario occurring a scenario risk is estimated 3. By integrating across all scenarios the expected annual damages (risk) is determined Source: Flood Hazard Research Centre, 2003 Page 9

Investigating intervention strategies Page 10 Investigating intervention strategies Page 10

Optimisation Techniques -Dynamic Programming Enumerative Scheme -Evolutionary Algorithms Inspired by Darwin’s theory of evolution Optimisation Techniques -Dynamic Programming Enumerative Scheme -Evolutionary Algorithms Inspired by Darwin’s theory of evolution Survival of the fittest Genetic operators § Reproduction (crossover) § Mutation § Selection Page 11

Structure of a Simple Genetic Algorithm START Generate initial population Evaluate objective function Application Structure of a Simple Genetic Algorithm START Generate initial population Evaluate objective function Application Model Are optimisation criteria met? Best individual Generate new population RESULT Mutation Page 12 Crossover Selection

Genetic Algorithm Operators 5 2 4 6 7 1 6 9 3 1 4 Genetic Algorithm Operators 5 2 4 6 7 1 6 9 3 1 4 2 Two Parent Chromosomes 8 0 5 2 4 6 4 2 0 6 9 3 1 7 1 8 Crossover 5 2 4 6 4 2 0 Mutation 6 Page 13 9 9 1 7 1 8 Two new Offspring

Multi-objective optimisation • Multi objective optimisation methods seek solutions that are “optimum” with respect Multi-objective optimisation • Multi objective optimisation methods seek solutions that are “optimum” with respect to all objectives. • Invariably a set of optimal solutions is discovered (known as a Pareto set) Page 14

The Pareto Front Page 15 The Pareto Front Page 15

The Pareto Front Page 16 The Pareto Front Page 16

The Pareto Front Page 17 The Pareto Front Page 17

Optimisation Problem Objectives: Maximise Benefit: EADwithout interventions – EADwith interventions n Minimise total cost: Optimisation Problem Objectives: Maximise Benefit: EADwithout interventions – EADwith interventions n Minimise total cost: ∑Ci intervention Ci = costs per i=1 Subject to: Realistic and available intervention options Page 18

Multi-objective optimisation Identification of transition, where significantly more investment yields little benefit (incremental benefit Multi-objective optimisation Identification of transition, where significantly more investment yields little benefit (incremental benefit cost) Identification of costs associated with specified benefit level The Pareto Front Benefit (£’s) Identification of most appropriate option/s given fixed budget Cost (£’s) Page 19

Real options overview “A Real Option is a choice that becomes available through an Real options overview “A Real Option is a choice that becomes available through an investment opportunity or action” Page 20

Real Option Overview Plausible range of future extreme water levels Maximum height increase for Real Option Overview Plausible range of future extreme water levels Maximum height increase for widened defence Maximum height increase for current defence Present Day extreme water level Current Defence Page 21 Widening of Base

Framework for Optioneering Features include • Analysis of Real Options • Automated option searching Framework for Optioneering Features include • Analysis of Real Options • Automated option searching techniques using evolutionary optimization processes (multiobjective optimization) • Automated option cost generation • Economic discounting of benefits and costs • Temporally evolving risk analysis (a fast. RASP) – risk is a function of future climate change scenario, future socio-economic scenarios • Range of decision making methods Page 22

Overview of framework Decision variables include: Standard of maintenance Raise crest level (Each defence) Overview of framework Decision variables include: Standard of maintenance Raise crest level (Each defence) Widen defence (each defence) Non structural measures (flood proofing) Page 23

Thank you for listening m. woodward@hrwallingford. co. uk b. gouldby@hrwallingford. co. uk Page 24 Thank you for listening m. [email protected] co. uk b. [email protected] co. uk Page 24