DSS for Integrated Water Resources Management IWRM DM

DSS for Integrated Water Resources Management (IWRM) DM under uncertainty DDr. Kurt Fedra kurt@ess. co. at ESS Gmb. H, Austria http: //www. ess. co. at Environmental Software & Services A-2352 Gumpoldskirchen 1 © K. Fedra 2007

IWRM: Integrated Water Resources Management Problems: • Not enough, too much • Wrong time and place • Insufficient quality • Unused potential, inefficiency • Conflicts 2 © K. Fedra 2007

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 ? 3 © K. Fedra 2007

Epistemiology How do we know ? • Induction, empiricism (from observations to generalisation, from generalisation to forecast) • (Neo)positivism (objective reality) • Constructivism (reality is social construct) 4 © K. Fedra 2007

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) … difficulties of inductive logic … are insurmountable. 5 © K. Fedra 2007

Knowledge and uncertainty. . . Alternative approach: Hypothetico-deductive: Formulate a hypothesis (model) and test (against data, information) INCLUDING the effect on the decision (robustness) 6 © K. Fedra 2007

Risk and uncertainty Uncertainty: inability to measure or forecast with some (specified) precision Measurement uncertainty: • Principle element (Heisenberg) • Practical element (methodological) 8 © K. Fedra 2007

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) 9 © K. Fedra 2007

Representation of uncertainty • Ranges, interval arithmetic • Fuzzy sets, fuzzy logic • Frequency and probability distributions • Scenarios and ensembles • Qualitative reasoning, expert systems 10 © K. Fedra 2007

Interval mathematics Every number is an interval 5 = <6, >4 Every measurement is described by an interval (how do you measure ? ) Precision depends on scale or resolution (world is fractal) 11 © K. Fedra 2007

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)] 12 © K. Fedra 2007

Interval mathematics Ranges, interval arithmetic X X*Y 13 =5 = 15 = [4, 6] = [8, 24] Y=3 Y = [2, 4] © K. Fedra 2007

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 = very big 14 © K. Fedra 2007

Fuzzy sets, fuzzy logic • Membership function: 15 © K. Fedra 2007

Uncertainty 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” 16 © K. Fedra 2007

Uncertainty 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) 17 © K. Fedra 2007

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. 18 © K. Fedra 2007

Game theory Cooperative games: Payoffs are calculated for coalitions (groups) of players that coordinate their strategies, assuming: Transferable utilities (sharing of benefits) 19 © K. Fedra 2007

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 ? 20 © K. Fedra 2007

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 21 © K. Fedra 2007

Game theory Zero sum games: • How to divide the cake ? Non-zero sum games: • How to make a BIGGER cake ! • win – win solutions 22 © K. Fedra 2007

Non-zero sum games Prisoners dilemma (10 or 1 year …) A is silent A betrays 23 B is silent B betrays 6 months each (win-win) A 10 years B goes free A goes free 5 years each B 10 years © K. Fedra 2007

Formal decision making Decision Table: other prisoner (unknown !) Decision is silent be silent 0. 5 10 0 5 betray What do you do ? Minimize your maximum cost ! 24 © K. Fedra 2007

Formal decision making Safe rational decision: Minimize your maximum cost is sub-optimal. Missing element: communication, coordination ! 25 © K. Fedra 2007

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) 26 © K. Fedra 2007

Decision making processes Handbook of OR (B. E. Gillet, 1976): • • Formulation of the problem Construction of a mathematical model Derive solution from model Testing model and solution • Establish control over the solution • Put it to work (implementation) 27 © K. Fedra 2007

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 ? ) 28 © K. Fedra 2007

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 …. ) 29 © K. Fedra 2007

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). 30 © K. Fedra 2007

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 …. . 31 © K. Fedra 2007

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 ? 32 © K. Fedra 2007

Sensitivity and robustness Assume a hydroelectric project: Building costs 28 Power benefits 2 Life time 25 Discount rate 8 Project NPV - 3. 5 28 M $ 2 M $/year 25 years 6% 3. 5 M $

Sensitivity and robustness Assume a hydroelectric project: Building costs Power benefits Life time Discount rate Project NPV 30 2. 5 30 8 0. 3 30 M$ 2. 5 M$/a 30 years 6 % 6. 5 M $

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)

Uncertainty: Climate Change • Increases in: – – – average temperature precipitation intensity extreme events • Decrease in –average precipitation

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

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

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).