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© K.Fedra DSS for Integrated Water Resources Management (IWRM) DM under uncertainty DDr. Kurt Fedra ESS GmbH, Austria Environmental Software & Services A-2352 Gumpoldskirchen DDr. Kurt Fedra ESS GmbH, Austria Environmental Software & Services A-2352 Gumpoldskirchen

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© K.Fedra IWRM: Integrated Water Resources Management Problems: Not enough, too much Wrong time and place Insufficient quality Unused potential, inefficiency Conflicts Problems: Not enough, too much Wrong time and place Insufficient quality Unused potential, inefficiency Conflicts

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© K.Fedra IWRM: Integrated Water Resources Management How much water is/will be available where and when, of which quality, at which cost ? How could anybody possibly know for sure ? HOW SURE do we need to be ? How much water is/will be available where and when, of which quality, at which cost ? How could anybody possibly know for sure ? HOW SURE do we need to be ?

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© K.Fedra EpistemiologyEpistemiology How do we know ? Induction, empiricism (from observations to generalisation, from generalisation to forecast) (Neo)positivism (objective reality) Constructivism (reality is social construct) How do we know ? Induction, empiricism (from observations to generalisation, from generalisation to forecast) (Neo)positivism (objective reality) Constructivism (reality is social construct)

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© K.Fedra Knowledge and uncertainty... The Logic of Scientific Discovery (K.Popper, 1959): Uncertainty: see Hypothesis The problem of induction: from singular statements (observations) to universal statements (hypotheses, theories, models)from singular statements (observations) to universal statements (hypotheses, theories, models) … difficulties of inductive logic … are insurmountable.

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© K.Fedra Knowledge and uncertainty... Alternative approach: Hypothetico-deductive: Formulate a hypothesis (model) and test (against data, information) INCLUDING the effect on the decision (robustness)

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© K.Fedra Knowledge and uncertainty... Reichenbach (Erkenntnis, 1930) … for it is not given to science to reach either truth or falsity (quoted in Popper, op.cit) … for it is not given to science to reach either truth or falsity (quoted in Popper, op.cit) Wittgenstein (Tractatus, 1918) Alles was wir überhaupt beschreiben können, könnte auch anders sein. Xenophanes (6 th cent BC) … But as for certain truth, no man has known it. For all is but a woven web of guesses.

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© K.Fedra Risk and uncertainty Uncertainty: inability to measure or forecast with some (specified) precision Measurement uncertainty: Principle element (Heisenberg) Practical element (methodological) Uncertainty: inability to measure or forecast with some (specified) precision Measurement uncertainty: Principle element (Heisenberg) Practical element (methodological)

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© K.Fedra Risk and uncertainty How to decide rationally with –Partial information ( some elements are simply unknown ) –Uncertainty ( probabilistic information, elements are known as PDF, probability density function, or frequency distribution of observations ) How to decide rationally with –Partial information ( some elements are simply unknown ) –Uncertainty ( probabilistic information, elements are known as PDF, probability density function, or frequency distribution of observations )

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© K.Fedra Representation of uncertainty Ranges, interval arithmetic Fuzzy sets, fuzzy logic Frequency and probability distributions Scenarios and ensembles Qualitative reasoning, expert systems Ranges, interval arithmetic Fuzzy sets, fuzzy logic Frequency and probability distributions Scenarios and ensembles Qualitative reasoning, expert systems

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© K.Fedra Interval mathematics Every number is an interval 5 = 4 Every measurement is described by an interval (how do you measure ?) Precision depends on scale or resolution (world is fractal) Every number is an interval 5 = 4 Every measurement is described by an interval (how do you measure ?) Precision depends on scale or resolution (world is fractal)

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© K.Fedra Interval mathematics [a,b] + [c,d] = [a + c, b + d] [a,b] − [c, d] = [a − d, b −c] [a,b] × [c,d] = [min (ac, ad, bc, bd), max (ac, ad, bc, bd)] [a,b] / [c,d] = [min (a/c, a/d, b/c, b/d), max (a/c, a/d, b/c, b/d)] [a,b] + [c,d] = [a + c, b + d] [a,b] − [c, d] = [a − d, b −c] [a,b] × [c,d] = [min (ac, ad, bc, bd), max (ac, ad, bc, bd)] [a,b] / [c,d] = [min (a/c, a/d, b/c, b/d), max (a/c, a/d, b/c, b/d)]

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© K.Fedra Interval mathematics Ranges, interval arithmetic X = 5 Y = 3 X*Y = 15 X = [4,6]Y = [2,4] X*Y = [8,24] Ranges, interval arithmetic X = 5 Y = 3 X*Y = 15 X = [4,6]Y = [2,4] X*Y = [8,24]

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© K.Fedra Fuzzy sets, fuzzy logic Every element in a set has a membership value (0,1) Membership in a class (set) is gradual, can be overlapping An object can be more or less big big * big = very big Every element in a set has a membership value (0,1) Membership in a class (set) is gradual, can be overlapping An object can be more or less big big * big = very big

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© K.Fedra Fuzzy sets, fuzzy logic Membership function:

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© K.Fedra UncertaintyUncertainty Frequency, probability of events: Hydrology: precipitation, runoff Repeated observations establishes a set of possible states and their relative frequency: BUT: statements in the frequency domain only apply to LARGE NUMBERS of events, not to “tomorrow” Frequency, probability of events: Hydrology: precipitation, runoff Repeated observations establishes a set of possible states and their relative frequency: BUT: statements in the frequency domain only apply to LARGE NUMBERS of events, not to “tomorrow”

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© K.Fedra UncertaintyUncertainty Multiple actors or decision makers: What will the others do ? The amount of water available at a given point depends NOT ONLY on hydrometeorology, but also on all other upstream users ! (regulatory framework, water rights) Multiple actors or decision makers: What will the others do ? The amount of water available at a given point depends NOT ONLY on hydrometeorology, but also on all other upstream users ! (regulatory framework, water rights)

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© K.Fedra Game theory Branch of applied mathematics, economics (von Neumann, Morgenstern 1944): Players, (agents, actors, stakeholders) choose Strategies that maximise their Payoff (return, gain net benefit) given the strategies of other agents. Branch of applied mathematics, economics (von Neumann, Morgenstern 1944): Players, (agents, actors, stakeholders) choose Strategies that maximise their Payoff (return, gain net benefit) given the strategies of other agents.

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© K.Fedra Game theory Cooperative games: Payoffs are calculated for coalitions (groups) of players that coordinate their strategies, assuming: Transferable utilities (sharing of benefits) Cooperative games: Payoffs are calculated for coalitions (groups) of players that coordinate their strategies, assuming: Transferable utilities (sharing of benefits)

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© K.Fedra Cooperative games: Assume water is used competitively by inefficient irrigation (farmer) high value (agro)industry Industry provides funds (bank loan) to farmer to improve irrigation efficiency (flooding drip), using the (future) revenues of the additional income from water saved (increased production value) water market ? Assume water is used competitively by inefficient irrigation (farmer) high value (agro)industry Industry provides funds (bank loan) to farmer to improve irrigation efficiency (flooding drip), using the (future) revenues of the additional income from water saved (increased production value) water market ?

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© K.Fedra Game theory Zero sum games: Finite resources independent of strategies (game only allocates) Sum of all players gains is zero Non-zero sum games: Some (cooperative) strategies can increase the resource base Sum of benefits greater zero Zero sum games: Finite resources independent of strategies (game only allocates) Sum of all players gains is zero Non-zero sum games: Some (cooperative) strategies can increase the resource base Sum of benefits greater zero

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© K.Fedra Game theory Zero sum games: How to divide the cake ? Non-zero sum games: How to make a BIGGER cake ! win – win solutions Zero sum games: How to divide the cake ? Non-zero sum games: How to make a BIGGER cake ! win – win solutions

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© K.Fedra Non-zero sum games Prisoners dilemma (10 or 1 year …) B is silentB betrays A is silent 6 months each (win-win) A 10 years B goes free A betraysA goes free B10 years 5 years each

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© K.Fedra Formal decision making Decision Table: other prisoner (unknown !) other prisoner (unknown !) Decision is silent betray be silent betray 0 5 What do you do ? Minimize your maximum cost ! Decision Table: other prisoner (unknown !) other prisoner (unknown !) Decision is silent betray be silent betray 0 5 What do you do ? Minimize your maximum cost !

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© K.Fedra Formal decision making Safe rational decision: Minimize your maximum cost is sub-optimal. Missing element: communication, coordination ! Safe rational decision: Minimize your maximum cost is sub-optimal. Missing element: communication, coordination !

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© K.Fedra Non-zero sum games Tragedy of the Commons (Harding, 1968) Shared, common resource Individual benefit, distributed loss (externality) will lead to collapse. Examples: Aquifer overexploitation Fisheries, air pollution Common pasture (Harding, 1968) Tragedy of the Commons (Harding, 1968) Shared, common resource Individual benefit, distributed loss (externality) will lead to collapse. Examples: Aquifer overexploitation Fisheries, air pollution Common pasture (Harding, 1968)

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© K.Fedra Decision making processes Handbook of OR (B.E.Gillet, 1976): Formulation of the problemFormulation of the problem Construction of a mathematical modelConstruction of a mathematical model Derive solution from modelDerive solution from model Testing model and solutionTesting model and solution Establish control over the solutionEstablish control over the solution Put it to work ( implementation )Put it to work ( implementation ) Handbook of OR (B.E.Gillet, 1976): Formulation of the problemFormulation of the problem Construction of a mathematical modelConstruction of a mathematical model Derive solution from modelDerive solution from model Testing model and solutionTesting model and solution Establish control over the solutionEstablish control over the solution Put it to work ( implementation )Put it to work ( implementation )

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© K.Fedra Group decision making Multiple decision makers (multiple criteria, conflicting objectives) WHO can decide ? (legitimacy) WHO can implement the decision ? Conflict resolution: Reach agreement (convergency, e.g., Delphi method) on preference structure Bargain – trade off criteria Enforce decision rules (majority ?) Multiple decision makers (multiple criteria, conflicting objectives) WHO can decide ? (legitimacy) WHO can implement the decision ? Conflict resolution: Reach agreement (convergency, e.g., Delphi method) on preference structure Bargain – trade off criteria Enforce decision rules (majority ?)

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© K.Fedra Group decision making Same basic assumptions: Rational players maximizing their (perceived) benefit/utility Decision rules (pre-defined) –Plurality –Majority, simple, 2/3 … –Qualified votes (by some measure of entitlement, e.g., area, outflow, precipitation, existing water rights ….) Same basic assumptions: Rational players maximizing their (perceived) benefit/utility Decision rules (pre-defined) –Plurality –Majority, simple, 2/3 … –Qualified votes (by some measure of entitlement, e.g., area, outflow, precipitation, existing water rights ….)

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© K.Fedra Group decision making Satisficing approach: Every stakeholder can formulate any number of expectations, requirements, constraints for the optimization; If there is NO feasible solutions, these constraints must be relaxed; Relaxation is a group consensus building process, supported by the DSS (indicates which constraints are most restrictive). Satisficing approach: Every stakeholder can formulate any number of expectations, requirements, constraints for the optimization; If there is NO feasible solutions, these constraints must be relaxed; Relaxation is a group consensus building process, supported by the DSS (indicates which constraints are most restrictive).

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© K.Fedra Consensus building How to motivate a group of actors, DMs to cooperate: 1.Demonstrate the potential for an increase in overall net benefit (through optimization) 2.Demonstrate allocation of the net benefit in a win-win “cooperative game” 3.Use a DSS for that ….. How to motivate a group of actors, DMs to cooperate: 1.Demonstrate the potential for an increase in overall net benefit (through optimization) 2.Demonstrate allocation of the net benefit in a win-win “cooperative game” 3.Use a DSS for that …..

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© K.Fedra Decisions under uncertainty Remember min-max ? Minimize maximum costs Safe, but inefficient (sub-optimal) Design for robustness : –How much input uncertainty will make the result change ? Will the solution be feasible (non-dominated) over a range of (uncertain) input conditions ? Remember min-max ? Minimize maximum costs Safe, but inefficient (sub-optimal) Design for robustness : –How much input uncertainty will make the result change ? Will the solution be feasible (non-dominated) over a range of (uncertain) input conditions ?

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© K.Fedra 2007 Sensitivity and robustness Assume a hydroelectric project: Building costs 28 28M $ Power benefits 2 2 M $/year Life time 25 25years Discount rate 8 6% Project NPV M $

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© K.Fedra 2007 Sensitivity and robustness Assume a hydroelectric project: Building costs M$ Power benefits M$/a Life time years Discount rate 8 6 % Project NPV M $

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© K.Fedra 2007 Sensitivity and robustness Case 1: decision depends on (uncertain) future discount rate: high risk ! (6,8) Case 2: increased investment, leads to increased revenue (higher electricity production and life time) (more) robust solution (6,8)

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© K.Fedra 2007 Uncertainty: Climate Change Increases in:Increases in: – average temperature – precipitation intensity – extreme events Decrease inDecrease in –average precipitation

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© K.Fedra 2007 Uncertainty: Climate Change Consequences for the Nile basin: depending on the model and IPCC scenario chosen, resulting in:Consequences for the Nile basin: depending on the model and IPCC scenario chosen, resulting in: + 20% runoff - 80% runoff Extreme uncertainty !

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© K.Fedra 2007 Uncertainty: Climate Change Possible strategies: Reduce GHG emissions (too slow, little effect on a global scale)Reduce GHG emissions (too slow, little effect on a global scale) Sequestration (little capacity, too slow, little effect on a global scale)Sequestration (little capacity, too slow, little effect on a global scale) Adaptation (mitigation)Adaptation (mitigation)

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© K.Fedra 2007 Climate Change Adaptation DSS strategy: optimize the system (adaptation strategies) over several IPCC scenarios: a solution that is feasible (and pareto-optimal) for ALL CC scenarios is robust (effective). a solution that is feasible (and pareto-optimal) for ALL CC scenarios is robust (effective).

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