4/25/2016

University of , Davis Department of Land, Air and Water Resources

Introduction to Simulation Models

ESM-121 Water Science and Management

Samuel Sandoval Solis, PhD Assistant Professor

Presentation 4 of 10

Hoover Oroville Dam 158 m 159 m 230 m 35.2 Km3 5.6 Km3 4.4 Km3 4.2 bill. KWh 1.8 bill. KWh 2.2 bill. KWh $49M - 1936 $36M - 1945

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• Masonry - Arch • Gravity Dams • Embankment dams • Rock-fill and earth-fill dams • Spillways

St Q R t K t

Q t K

St

Rt

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Allocate release Rt to 3 users and provide instream flow Qt

Operating Policy Allocation Policy

• Simulation models: Predict response to given design • Optimization models: Identify optimal design or operation

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• Address “What if …” questions • What will likely happen • Include larger hyd, econ, Operating Policy and env. data • i.e. “evaluate change given a design or policy”

Allocation Policy

• Used for design: - “Maximize the Net Benefits …” or - “Minimize the shortages” • Look for the best (ideal) operation • Perfect foresight

Optimization model T 3 Objective Maximize  Bi (xit ) Benefits: Bi(xit ) t1 i1 x  x  x  R t 1, 2, Decision Variables: xit 1t 2t 3t t 

Constraints St1  St  It  Rt t 1, 2,

St  K t 1, 2,

Optimization model

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Reservoir operating policy Allocation policy

Rt 8

Release available x1 i 6 water x2 x3 4 Dt Release Release demand Allocation, Allocation, X demand + excess 2

0 Dt K Dt+K St+ Qt 0 2 4 6 8 10 12 14 16 Release, R Policies

g(x) Hydrologic h(y) Model time series output x y

Input System Output

Model

 Deterministic process  Stochastic process  Inputs assumed known.  Explicitly account for variability  Ignore variability and uncertainty  Assume inputs are well  Inputs are stochastic processes represented by average values.  Historic record is one realization  Over estimates benefits and of process. underestimates losses

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Reservoir operating policy Allocation policy

Rt 8

Release available x1 i 6 water x2 x3 4 Dt Release Release demand Allocation, Allocation, X demand + excess 2

0 Dt K Dt+K St+ Qt 0 2 4 6 8 10 12 14 16 Release, R Distribution of inputs

FX(x) FY(y) Policies X Generate multiple input sequences Compute h(y) statistics of g(x) outputs y Simulate each System h(y) g(x) x Input sequence Get multiple output sequences y x Model

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