water resources systems modeling for planning and management an introduction to the development and...

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 SystemA River Basin System

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

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


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.


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.

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

River Basin:• Lakes, Reservoirs,• Wetlands, River,• Aquifers, wells, • Pumps,• Treatment Plants,• Diversions, • M, I, & A Users,• Hydropower Plants


Municipality:• Water Treatment,• Water distribution network,• Aquifers wells, • Pumps, • Storage tanks,• Sewerage collection network,• Wastewater treatment.


Irrigation:• Diversion canals,• Drainage system,• Crop areas,• Equipment, • Labor, • Fertilizer,• Pesticides, etc.


THE SYSTEM

INPUTS OUTPUTS

COMPONENTS

FOCUS: Performance of System

not necessarily of its individual 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.


Model Types:

• Descriptive (Simulation)

• Prescriptive (Optimization)

• Deterministic

• Probabilistic or Stochastic

• Static

• Dynamic

• Mixed


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


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


Modeling Example

• Problem.

Need a water tank of capacity V.

• Performance Criterion. Cost minimization.

• Numerous alternatives.

Shape, dimensions, materials.

• Best design not obvious.


H

R

Modeling Example Continued

Consider a cylindrical tank V.

having radius R and height H.

Average costs per unit area:

Ctop

Cside

Cbase


Model:

Minimize Total_cost (Objective)

subject to: (Constraints)

Volume = (R2H) V.

Total_cost = $_Side+$_Base+$_Top

$_Side = Cside(2RH)

$_Base = Cbase(R2)

$_Top = Ctop(R2)



Solution:

$_Side / Total_cost = 2/3

($_Base+$_Top) / Total_cost = 1/3

No matter what shape and unit

costs.



Solution: a tradeoff between cost and volume.


TotalCost

Tank Volume

Other Modeling Examples

Water Pollution Control

Water Allocations to Competing

Uses


Tradeoffs!

Other Modeling Examples

Water Quality – Aquatic Ecosystems


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

RecreationFlood storage

•Gage

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

Water Resource Systems EngineeringPlanning & Management Objectives

Types of Objectives or Measures of Performance:

• Physical

• Statistical

• Economic

• Environmental – Ecological

• Social

• Combinations

• Multi-objective analyses.

Why? How?

Water Resource Systems EngineeringPlanning & 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.


Mean

Time

Failure threshold

System Performance Measure

Time series of system performance values:


Mean

Time

Failure threshold


Same: Mean and Variance

Different: Reliability, Resilience and Vulnerability


Mean

Mean

Failure threshold


Time

Failure threshold


Compare Reliabilities, Resiliences, Vulnerabilities.


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.


Economic objectives:

Maximize Net Revenue (Private):Marginal Revenue = Marginal cost

Maximize Net Social Benefits (Public):Unit Price = Marginal cost

Unit price = Po – bQ

Marginal cost = c

Q

Po

2b b Marginal revenue = Po – 2bQ P*pri.

P*pub.

Q*pri. Q*pub.

Private:Consumer’s surplus

Producer’s surplus

Public: All consumer surplus.


Decision Making with Multiple Objectives:

ALTERNATIVE PROJECTS

AL

TE

RN

AT

IVE

OB

JEC

TIV

ES

Relative impact.

Relative importance.

Alternative Codes:

1-10, ++ + 0 - --, A B C D, S F.

22 $3 57 Sat



Other Multi-objective Methods:• Satisficing• Dominance• Lexicography• Indifference Analyses• Obj. Weights or Obj. Constraints• Goal Attainment and Programming• Compromise Programming• Interactive Methods



Multi-objective Methods:

• Satisficing (setting improving targets for objectives that are functions of decision variables in vector

X.)OBJ2(X)

OBJ1(X)

A C

E

DB

Second Iteration: C

First Iteration: C, D, F.

Alternatives Considered: A, B, C, D, E, F.

•

•

•

•

•

•F




• Dominance (eliminating alternatives that are inferior with respect to all

objectives.)OBJ2(X)

OBJ1(X)

A C

E

DB


•

•

•

•

•

•F A dominated by C and F

B dominated by C, D, F

D dominated by C




• Lexicography (rank objectives from most important to least important. If a tie go to next most important objective, etc.)

OBJ2(X)

OBJ1(X)

A C

E

DB


•

•

•

•

•

•F If OBJ1 is most

important, pick E.

If OBJ2 is most important, pick F.




• Objective Weights (identify Pareto efficiency frontier by varying weights associated with each objective.)

Maximize {w1• OBJ1(X) + w2• OBJ2(X)}

Subject to model constraints gi(X) bi i

OBJ2(X)

OBJ1(X)

••

•

FC

E

Changing weights in objective space identifies dominant solutions on efficiency frontier.




• Objective Weights (identify Pareto efficiency frontier by varying weights associated with each objective.)

Maximize {w1• OBJ1(X) + w2• OBJ2(X)}

Subject to model constraints gi(X) bi i

OBJ2(X)

OBJ1(X)

••

•

FC

E

Changing weights in objective space identifies dominant solutions on convex efficiency frontier. It misses others.•




• Objective Constraints (include all objectives but one as constraints having bounds. Vary bound values

to identify Pareto efficiency frontier.)

Maximize OBJ1(X)

Subject to:

gi(X) bi i

OBJ2(X) L2 OBJ1(X)

•OBJ2(X)•

•

FC

E

L2

Discrete frontier




• Objective Constraints (include all objectives but one as constraints having bounds. Vary bound values

to identify Pareto efficiency frontier.)

Maximize OBJ1(X)

Subject to:

gi(X) bi i

OBJ2(X) L2 OBJ1(X)

•OBJ2(X)•

•

FC

E

L2

Continuous frontier




• Goal Attainment (minimize maximum weighted deviation from preselected targets for each objective. Vary weight values to identify efficiency frontier.)

Minimize D

Subject to:

gi(X) bi i

wk•{Tk – OBJk(X)} D k OBJ1(X)

•

OBJ2(X)

•

•

FC

E

T2

T1




• Goal Programming (minimize sum of weighted deviations from preselected targets for each objective. Vary weight values to identify efficiency frontier.)

Minimize k [wdk(Dk) + we

k(Ek)]

Subject to:

gi(X) bi i

OBJk(X) = Tk – Dk + Ek k OBJk(X)Tk

Ek

Dkwe

k(Ek)

wdk(Dk)




• Compromise Programming (minimize nth root of weighted sum of deviations from best value for each objective raised to the nth power. Vary weights and n to identify portion of efficiency frontier.)

Minimize { k wkn[Zk - OBJk(X)]n}1/n

Subject to:

gi(X) bi i

Zk = Max. feasible value of OBJk k

OBJ2(X)

Z2

OBJ1(X) Z1

n=2n=




• Interactive Methods (user(s) involved in defining improvements in all objectives, as desired.)

OBJ1(X)

OBJ2(X)

OBJ1(X)

OBJ2(X)

Iterating along efficiency frontier.

Iterating toward the efficiency frontier.

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water resources systems modeling for planning and management an introduction to the development and...

Documents

river basin system water

performance of system

drainage system

model components

water supply

case study slide

water distribution network

individual components