Water Resources Planning and Management Daene C. McKinney Simulating System Performance.

Water Resources Planning and Management

Daene C. McKinney

Simulating System Performance

Reservoir Management

• Important task for water managers around the world.

• Models used to– simulate or optimize

reservoir performance– design reservoirs or

associated facilities (spillways, etc.).

Operating Rules• Allocate releases among purposes, reservoirs, and time

intervals • In operation (as opposed to design), certain system

components are fixed:– Active and dead storage volume– Power plant and stream channel capacities– Reservoir head-capacity functions– Levee heights and flood plain areas– Monthly target outputs for irrigation, energy, water supply, etc

• Others are variable: Allocation of – stored water among reservoirs– stored and released water among purposes– stored and released water among time intervals

Standard Operating Policy

Qt

X2tK

StRt

X1t

Dt

KDQS

KDQSD

DQS

if

KQS

D

QS

R

ttt

tttt

ttt

tt

t

tt

t

Rt

Dt

Dt Dt+K St+ Qt

Release available water &

deficits occur

Release demand spill excess

Sufficient water to meet demands

Reservoir fills and demand met

Release demand &demand met

Demand

• Reservoir operating policy - release as function of storage volume and inflow

Rt = Rt(St,Qt)

Hedging Rule• Reduce releases in times of drought (hedging) to save water

for future releases in case of an extended period of low inflows.

hedging D

K

Done?No

System Simulation

• Create network representation of system• Need inflows for each period for each node• For each period:

Perform mass balance calculations for each node Determine releases from reservoirs Allocate water to users

Start

t = 0St = S0

St+1 = St +Qt -Rt

Stop

Yes

t = t + 1

Read Qt File

ComputeRt, Xit, i=1,…n

DataStorage

Qt

X3tK

St

RX2t

X1t

0

2

4

6

8

0 2 4 6 8 10 12 14 16Release, R

All

ocat

ion

, X

i x1

x2

x3

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Operating Policy Allocation Policy

Example

• Using unregulated river for irrigation• Proposed Reservoir

• Capacity: K = 40 million m3 (active)• Demand: D = 30 40 45 million m3

• Winter instream flow: 5 mil. m3 min.• 45 year historic flow record available

• Evaluate system performance for a 20 year period

• Simulate• Two seasons/year, winter (1) summer(2)• Continuity constraints• Operating policy

QtX2tK

St RX1t

DEMAND

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year

De

ma

nd

(1

0 m

illi

om

m3

)

Flow statistics

R2,t

Dt

Dt Dt+K S2,t+ Q2,tK

Release available water

Release demand

Release demand + excess

Summer Operating Policy

yyyy RQSS ,1,1,1,2

Storage at beginning of summer

KDQS

KDQSD

DQS

if

KQS

D

QS

R

yyy

yyyy

yyy

yy

y

yy

y

,2,2

,2,2

,2,2

,2,2

,2,2

,2

Performance Evaluation

• How well will the system perform?– Define performance criteria

• Indices related to the ability to meet targets and the seriousness of missing targets

– Simulate the system to evaluate the criteria– Interpret results

• Should design or policies be modified?

Performance Criteria - Reliability• Reliability – Frequency with which demand was satisfied

– Define a deficit as:

• Then reliability is:

• where n is the total number of simulation periods

Performance Criteria - Resilience

• Resilience = probability that once the system is in a period of deficit, the next period is not a deficit.

• How quickly does system recover from failure?

Performance Criteria - Vulnerability

• Vulnerability = average magnitude of deficits

• How bad are the consequences of failure?

Simulate the System

System

Policies

Input Output

x

g(x)

y

h(y)

0

2

4

6

8

0 2 4 6 8 10 12 14 16Release, R

All

ocat

ion

, X

i x1

x2

x3

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Reservoir operating policyAllocation policy

Hydrologictime series

Model output

Model

Uncertainty• Deterministic process

– Inputs assumed known. – Ignore variability – Assume inputs are well

represented by average values. – Over estimates benefits and

underestimates losses

• Stochastic process– Explicitly account for variability

and uncertainty– Inputs are stochastic processes – Historic record is one realization

of process.

FY(y)

Simulate the System

Policies

Simulate each Input sequence

X

FX(x)

x

g(x)

y

h(y)

y

h(y)

Computestatistics of

outputs

System

Generate multiple input sequences

x

g(x)Get multiple

output sequences

0

2

4

6

8

0 2 4 6 8 10 12 14 16Release, R

All

ocat

ion

, X

i x1

x2

x3

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Rt

Dt

Dt Dt+K St+ QtK

Release available water

Release demand

Release demand + excess

Reservoir operating policyAllocation policy

Model

Distribution of inputs

The Simulation• Simulate reservoir operation

– Perform 23 equally likely simulations– Each simulation is 20 years long– Each simulation uses a different sequence of inflows

(realization)

Example – Realization 1Rmin 0.5 K 4

Realization 1

Winter SummerYear S1y Q1y S+Q R1y S2y Q2y S+Q D2y R2y Deficit1 0.000 4.740 4.740 0.740 4.000 1.805 5.805 3.000 3.000 0.0002 2.805 2.918 5.723 1.723 4.000 1.499 5.499 3.200 3.200 0.0003 2.299 2.747 5.045 1.045 4.000 1.548 5.548 3.400 3.400 0.0004 2.148 2.819 4.966 0.966 4.000 1.753 5.753 3.600 3.600 0.0005 2.153 3.871 6.023 2.023 4.000 2.229 6.229 3.800 3.800 0.0006 2.429 3.585 6.015 2.015 4.000 2.235 6.235 4.000 4.000 0.0007 2.235 4.736 6.971 2.971 4.000 2.984 6.984 4.100 4.100 0.0008 2.884 3.275 6.159 2.159 4.000 2.212 6.212 4.200 4.200 0.0009 2.012 3.188 5.200 1.200 4.000 2.666 6.666 4.300 4.300 0.00010 2.366 3.401 5.767 1.767 4.000 1.240 5.240 4.300 4.300 0.00011 0.940 3.811 4.750 0.750 4.000 2.371 6.371 4.400 4.400 0.00012 1.971 3.435 5.407 1.407 4.000 2.421 6.421 4.400 4.400 0.00013 2.021 2.460 4.481 0.500 3.981 1.317 5.298 4.400 4.400 0.00014 0.898 2.377 3.275 0.500 2.775 1.896 4.671 4.400 4.400 0.00015 0.271 3.692 3.963 0.500 3.463 1.831 5.293 4.500 4.500 0.00016 0.793 3.302 4.095 0.500 3.595 1.300 4.895 4.500 4.500 0.00017 0.395 2.548 2.944 0.500 2.444 2.047 4.491 4.500 4.491 -0.00918 0.000 2.454 2.454 0.500 1.954 1.658 3.612 4.500 3.612 -0.88819 0.000 3.139 3.139 0.500 2.639 2.768 5.407 4.500 4.500 0.00020 0.907 2.910 3.816 0.500 3.316 1.445 4.762 4.500 4.500 0.000

Deficit -0.897Number 2.000% 0.100

ResultsTotal # of Frequency

SimulationShortage Failures of Failure1 -1.031 2 0.1002 -10.050 8 0.4003 -0.516 1 0.0504 -0.184 1 0.0505 -1.159 2 0.1006 -10.747 8 0.4007 -4.627 6 0.3008 -1.134 4 0.2009 -1.446 4 0.20010 0.000 0 0.00011 -1.735 4 0.20012 -3.384 5 0.25013 -3.639 3 0.15014 0.000 0 0.00015 -0.067 1 0.05016 -1.561 3 0.15017 -3.586 6 0.30018 -0.223 1 0.05019 -1.347 1 0.05020 -0.977 2 0.10021 -4.758 0 0.25022 -4.966 5 0.25023 -3.641 4 0.200

Average -2.643 0.165Std. Dev. 2.93704 0.118163

0

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Simulation

# o

f F

ailu

res

Average failure frequency = 0.165Average reliability = 1- 0.165 = 0.835 = 83.5%Actual failure frequency [0, 0.40]Actual Reliability [100%, 60%]

Physical Environment Feedback Sub Model to FAV

Salinity

Temp

Surface, Subsurface

Light

FAVEstablishment

and Growth

FAVPatch

Local Physical Environment (tides, freshwater flow)

NutrientsHeavymetals

Riparian Vegetation

DO

Wind, Flow Velocity

Dispersal

SubstrateOrg Matter

Subsurface Light

-

Small SubstrateGrain Size

Understanding:

High – green arrow

Med – blue arrow

Low - red arrow

Importance:

High – thick line

Med – medium line

Low – thin line

Predictability:

High – solid line

Med – dashed line

Low – dotted line

Lars Anderson, UC DavisStuart Siegel, WWRMark Stacey, UCB

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