Water Resources Systems Modeling for Planning and Management An Introduction to the Development and Application of Optimization and Simulation Models for Aiding in Water for Resources Planning, Management and for Addressing Operational Issues and Problems.

A River Basin System Water for: Water Supply (M,I,A) Recreation Nature Hydropower Pollution Control Navigation

A River Basin System Infrastructure: Reservoirs, wells, pumps Diversion canals, pipelines Recreation facilities Hydropower plants Water & Wastewater Treatment Plants Navigation locks Flood Control Res. & Levees Distribution/Collection Sys. Infrastructure: Reservoirs, wells, pumps Diversion canals, pipelines Recreation facilities Hydropower plants Water & Wastewater Treatment Plants Navigation locks Flood Control Res. & Levees Distribution/Collection Sys.

A River Basin System Why Model : What to do or design? Where to do or design it? How much or how big and how to operate? When to implement? Why? What are the Hydrologic, Economic, Ecosystem, and Social Impacts? Why Model : What to do or design? Where to do or design it? How much or how big and how to operate? When to implement? Why? What are the Hydrologic, Economic, Ecosystem, and Social Impacts?

A River Basin System When to Model : There exists a problem or opportunity. A decision is to be made. Many alternatives. Best alternative not obvious. Quantitative aspects.

A System – Interdependent Components River Basin : Lakes, Reservoirs, Wetlands, River, Aquifers, wells, Pumps, Treatment Plants, Diversions, M, I, & A Users, Hydropower Plants

A System – Interdependent Components Municipality : Water Treatment, Water distribution network, Aquifers wells, Pumps, Storage tanks, Sewerage collection network, Wastewater treatment.

A System – Interdependent Components Irrigation: Diversion canals, Drainage system, Crop areas, Equipment, Labor, Fertilizer, Pesticides, etc.

A System – Interdependent Components THE SYSTEM INPUTS OUTPUTS COMPONENTS FOCUS: Performance of System not necessarily of its individual components.

A System – Interdependent Components THE SYSTEM INPUTS OUTPUTS COMPONENTS GOAL: Maximize System Performance.

Water Resources Systems

Water Resources Systems Engineering Topics: Modeling Approaches &Applications Shared Vision Modeling System Performance Criteria Integrating Hydrology and Aquatic Ecosystems – a Case Study

Water Resources Systems Modeling A Model : A mathematical description of some system. Model Components : Variables, parameters, functions, inputs, outputs. A Model Solution Algorithm : A mathematical / computational procedure for performing operations on the model – for getting outputs from inputs.

Water Resources Systems Modeling Model Types : Descriptive (Simulation) Prescriptive (Optimization) Deterministic Probabilistic or Stochastic Static Dynamic Mixed

Water Resources Systems Modeling Algorithm Types : Descriptive (Simulation) Prescriptive (Constrained Optimization) Mathematical Programming Lagrange Multipliers Linear Programming Non-linear Programming Dynamic Programming Evolutionary Search Procedures Genetic Algorithms, Genetic Programming

Water Resources Systems Modeling Simulation : Optimization : WATER RESOURCE SYSTEM System Inputs System Design and Operating Policy System Outputs WATER RESOURCE SYSTEM System Inputs System Design and Operating Policy System Outputs

Water Resources Systems Modeling Modeling Example Problem. Need a water tank of capacity  V. Performance Criterion. Cost minimization. Numerous alternatives. Shape, dimensions, materials. Best design not obvious.

Water Resources Systems Modeling H R Modeling Example Continued Consider a cylindrical tank  V. having radius R and height H. Average costs per unit area: C top C side C base

Modeling Example Continued Model: Minimize Total_cost (Objective) subject to: (Constraints) Volume = (  R 2 H)  V. Total_cost = $_Side+$_Base+$_Top $_Side = C side (2  RH) $_Base = C base (  R 2 ) $_Top = C top (  R 2 ) Water Resources Systems Modeling

Modeling Example Continued Solution: $_Side / Total_cost = 2/3 ($_Base+$_Top) / Total_cost = 1/3 No matter what shape and unit costs. Water Resources Systems Modeling

Modeling Example Continued Solution: a tradeoff between cost and volume. Water Resources Systems Modeling Total Cost Tank Volume

Other Modeling Examples Water Pollution Control Water Allocations to Competing Uses Water Resources Systems Modeling Tradeoffs!

Other Modeling Examples Water Quality – Aquatic Ecosystems Water Resources Systems Modeling Silt Acid Mine Drainage Point-Source Pollution Fish Kill Ecosystem Enhancement

Stakeholder Participation: Shared Vision Modeling

A multi-purpose river basin planning example: Shared Vision Modeling

Irrigation Urban area Levee protection Pumped storage hydropower Recreation Flood storage Gage A multi-purpose river basin planning example: Shared Vision Modeling

Water Resource Systems Engineering Planning & Management Objectives Types of Objectives or Measures of Performance: Physical Statistical Economic Environmental – Ecological Social Combinations Multi-objective analyses.

Why? How? Water Resource Systems Engineering Planning & Management Objectives Broad Goals  Aims  Objectives  Specific Strategies: National Security and Welfare. Self Sufficiency. Regional Economic Development. Public and Environmental Health. Economic Efficiency and Equity. Environmental Quality. Ecosystem Biodiversity and Health. System Reliability, Resilience, Robustness. Water supply: quantity, quality, reliability, cost. Flood protection, flood plain zoning. Energy and food production. Recreation, navigation, wildlife habitat. Water and wastewater treatment.

Water Resource Systems Engineering Planning & Management Objectives Overall measures of system performance: Mean – average or expected value. Variance – average of squared deviations from the mean value. Reliability – Prob(satisfactory state). Resilience – Prob(sat. state following unsat. state). Robustness – adaptability to other than design input conditions. Vulnerability – expected magnitude or extent of failure when unsatisfactory state occurs.

Water Resource Systems Engineering Planning & Management Objectives Mean Time Failure threshold System Performance Measure Time series of system performance values:

Water Resource Systems Engineering Planning & Management Objectives Mean Time Failure threshold System Performance Measure Same: Mean and Variance Different: Reliability, Resilience and Vulnerability

Water Resource Systems Engineering Planning & Management Objectives Mean Failure threshold System Performance Measure Time Failure threshold System Performance Measure Compare Reliabilities, Resiliences, Vulnerabilities.

Water Resource Systems Engineering Planning & Management Objectives Objectives expressed as functions to be maximized or minimized or as constraints that have to satisfied. Economic objectives: Maximize benefits: improvement in income, welfare, or willingness to pay. Minimize costs: benefits forgone, opportunity costs, adverse externalities. Maximize net benefits: benefits less losses and costs. Minimize inequity: differences in distributions of net benefit among stakeholders.

Water Resource Systems Engineering Planning & Management Objectives Economic objectives: Maximize Net Revenue (Private): Marginal Revenue = Marginal cost Maximize Net Social Benefits (Public): Unit Price = Marginal cost Unit price = P o – bQ Marginal cost = c Q P o 2b b Marginal revenue = P o – 2bQ P* pri. P* pub. Q* pri. Q* pub. Private: Consumer’s surplus Producer’s surplus Public: All consumer surplus.

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: ALTERNATIVE PROJECTS ALTERNATIVE OBJECTIVES Relative impact. Relative importance. Alternative Codes: 1-10, , A B C D, S F. 22$357Sat

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Other Multi-objective Methods: Satisficing Dominance Lexicography Indifference Analyses Obj. Weights or Obj. Constraints Goal Attainment and Programming Compromise Programming Interactive Methods

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Satisficing (setting improving targets for objectives that are functions of decision variables in vector X.) OBJ 2 (X) OBJ 1 (X) A C E D B Second Iteration: C First Iteration: C, D, F. Alternatives Considered: A, B, C, D, E, F. F

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Dominance (eliminating alternatives that are inferior with respect to all objectives.) OBJ 2 (X) OBJ 1 (X) A C E D B Alternatives Considered: A, B, C, D, E, F. F A dominated by C and F B dominated by C, D, F D dominated by C

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Lexicography (rank objectives from most important to least important. If a tie go to next most important objective, etc.) OBJ 2 (X) OBJ 1 (X) A C E D B Alternatives Considered: A, B, C, D, E, F. F If OBJ 1 is most important, pick E. If OBJ 2 is most important, pick F.

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Objective Weights (identify Pareto efficiency frontier by varying weights associated with each objective.) Maximize {w 1 OBJ 1 (X) + w 2 OBJ 2 (X)} Subject to model constraints g i (X)  b i  i OBJ 2 (X) OBJ 1 (X) F C E Changing weights in objective space identifies dominant solutions on efficiency frontier.

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Objective Weights (identify Pareto efficiency frontier by varying weights associated with each objective.) Maximize {w 1 OBJ 1 (X) + w 2 OBJ 2 (X)} Subject to model constraints g i (X)  b i  i OBJ 2 (X) OBJ 1 (X) F C E Changing weights in objective space identifies dominant solutions on convex efficiency frontier. It misses others.

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Objective Constraints (include all objectives but one as constraints having bounds. Vary bound values to identify Pareto efficiency frontier.) Maximize OBJ 1 (X) Subject to: g i (X)  b i  i OBJ 2 (X)  L 2 OBJ 1 (X) OBJ 2 (X) F C E L2L2 Discrete frontier

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Objective Constraints (include all objectives but one as constraints having bounds. Vary bound values to identify Pareto efficiency frontier.) Maximize OBJ 1 (X) Subject to: g i (X)  b i  i OBJ 2 (X)  L 2 OBJ 1 (X) OBJ 2 (X) F C E L2L2 Continuous frontier

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Goal Attainment (minimize maximum weighted deviation from preselected targets for each objective. Vary weight values to identify efficiency frontier.) Minimize D Subject to: g i (X)  b i  i w k {T k – OBJ k (X)}  D  k OBJ 1 (X) OBJ 2 (X) F C E T2T2 T1T1

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Goal Programming (minimize sum of weighted deviations from preselected targets for each objective. Vary weight values to identify efficiency frontier.) Minimize  k [w d k (D k ) + w e k (E k )] Subject to: g i (X)  b i  i OBJ k (X) = T k – D k + E k  k OBJ k (X) TkTk EkEk DkDk w e k (E k ) w d k (D k )

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Compromise Programming (minimize n th root of weighted sum of deviations from best value for each objective raised to the n th power. Vary weights and n to identify portion of efficiency frontier.) Minimize {  k w k n [Z k - OBJ k (X)] n } 1/n Subject to: g i (X)  b i  i Z k = Max. feasible value of OBJ k  k OBJ 2 (X) Z2Z2 OBJ 1 (X) Z1Z1 n=2 n= 

Water Resource Systems Engineering Planning & Management Objectives Decision Making with Multiple Objectives: Multi-objective Methods: Interactive Methods (user(s) involved in defining improvements in all objectives, as desired.) OBJ 1 (X) OBJ 2 (X) OBJ 1 (X) OBJ 2 (X) Iterating along efficiency frontier. Iterating toward the efficiency frontier