1 Reservoir Yield R&D Unit Reservoir Yield R&D Unit Water Supply Workshop Water Supply Workshop June 2, 2009 June 2, 2009 Beth Faber Beth Faber PhD, PE PhD, PE Hydrologic Engineering Center Hydrologic Engineering Center USACE USACE Outline Outline • Determination of Yield, Sizing Reservoirs Determination of Yield, Sizing Reservoirs – Storage / Yield Relationship Storage / Yield Relationship – Simple Yield Computation Methods Simple Yield Computation Methods – Alternatives to Critical Period Analysis Alternatives to Critical Period Analysis – Reliability Reliability • Water Supply Contracts Water Supply Contracts – different question different question – Firm Yield R&D Firm Yield R&D – Methods in the Field Methods in the Field – Yield in Yield in ResSim ResSim
OutlineOutline•• Determination of Yield, Sizing ReservoirsDetermination of Yield, Sizing Reservoirs
–– Storage / Yield RelationshipStorage / Yield Relationship–– Simple Yield Computation MethodsSimple Yield Computation Methods–– Alternatives to Critical Period AnalysisAlternatives to Critical Period Analysis–– ReliabilityReliability
•• Water Supply Contracts Water Supply Contracts –– different questiondifferent question–– Firm Yield R&DFirm Yield R&D–– Methods in the FieldMethods in the Field–– Yield in Yield in ResSimResSim
2
Redistribution of WaterRedistribution of Water
The function of a reservoir system is to redistribute The function of a reservoir system is to redistribute the natural occurrence of water in time and place.the natural occurrence of water in time and place.
–– Formerly, people settled near rivers and used water as Formerly, people settled near rivers and used water as it arrived.it arrived.
–– Then we built reservoirs to accumulate and release Then we built reservoirs to accumulate and release water to improve the distribution in time...water to improve the distribution in time...
store it when it comes, release as needed store it when it comes, release as needed (supply) or at non(supply) or at non--damaging rate (after flood)damaging rate (after flood)
–– ...and conveyance to improve the distribution in space...and conveyance to improve the distribution in space
Distribution of Water in TimeDistribution of Water in Time
•• WithinWithin--year Reservoir Storageyear Reservoir Storage–– Reservoir stores wet Reservoir stores wet seasonseason water for use in the dry water for use in the dry
–– Reservoir stores wet Reservoir stores wet yearyear water for use in dry years water for use in dry years or extended droughtor extended drought
•• Evaluation of current and future demand and local Evaluation of current and future demand and local hydrology will determine if withinhydrology will determine if within-- or overor over--year is year is needed, and the required size of reservoir.needed, and the required size of reservoir.
3
Within-year and Over-year Reservoir Storage and Yield
0
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Inflo
w, R
elea
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f/mon
th)
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Res
ervo
ir St
orag
e (a
f)
DemandInflow
Reservoir Storage
Storage / Yield of a ReservoirStorage / Yield of a Reservoir
•• YIELD = amount of water that can be provided on a YIELD = amount of water that can be provided on a regular basis (yield regular basis (yield ≤≤ average flow)average flow)
•• The most basic evaluation is the atThe most basic evaluation is the at--site Storage / Yield site Storage / Yield relationship.relationship.
•• In a study, there are 2 ways build the relationship: In a study, there are 2 ways build the relationship:
–– PlanningPlanning: For a given demand, how large must : For a given demand, how large must the reservoir at that location be?the reservoir at that location be?
–– Reassessment/OperationsReassessment/Operations: For a given : For a given reservoir, what is the annual yield?reservoir, what is the annual yield?
Fix one variable, vary the otherFix one variable, vary the other
–– Supply Contract Supply Contract –– what volume needed in existing what volume needed in existing reservoir to supply needed yield? (...share of inflow)reservoir to supply needed yield? (...share of inflow)
•• There are various methods for determining the There are various methods for determining the relationship between reservoir storage and yieldrelationship between reservoir storage and yield–– Simplified MethodsSimplified Methods (Planning)(Planning)
•• RipplRippl Mass Diagram Mass Diagram (cum. inflow (cum. inflow vsvs cum. demand)cum. demand)•• Sequent Peak Algorithm Sequent Peak Algorithm (cum. net inflow)(cum. net inflow)
–– Sequential Reservoir RoutingSequential Reservoir Routing (Operations)(Operations)–– simulation of realistic reservoir operation over a multiple simulation of realistic reservoir operation over a multiple
year periodyear period–– more complex demand patterns and sources can be more complex demand patterns and sources can be
evaluated, as well as lossesevaluated, as well as losses
5
Input Data Needed...Input Data Needed...
•• The The supplysupply data used can be either data used can be either –– the historical record, or a critical dry period within the the historical record, or a critical dry period within the
record record -- be careful defining single critical periodbe careful defining single critical period
–– a synthetic drought event or data seriesa synthetic drought event or data series
•• The The demanddemand requirements can be eitherrequirements can be either–– 100% of actual or forecasted demand100% of actual or forecasted demandconstant or varied, depending on the methodconstant or varied, depending on the method
–– Partial demand, or demand met with some frequency Partial demand, or demand met with some frequency or reliabilityor reliability
demand need demand need notnot be constant...be constant...
specify reservoir size
Critical Period AnalysisCritical Period Analysis
•• These methods looked at historical These methods looked at historical critical periodscritical periodsof low streamflow and determined demand that of low streamflow and determined demand that could be met without failure (could be met without failure (““worst caseworst case”” analysis)analysis)–– only one particular duration and magnitude only one particular duration and magnitude ---- many other many other
drought options are possibledrought options are possible–– can be subject to can be subject to sampling errorsampling error with a short data setwith a short data set–– also leads to also leads to false confidencefalse confidence about reliabilityabout reliability
•• Alternatives to critical period are probabilistic Alternatives to critical period are probabilistic descriptions and synthetic data sets... descriptions and synthetic data sets...
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Alternatives to Critical PeriodAlternatives to Critical Period
•• Probabilistic description of droughtProbabilistic description of drought
–– define a drought with a particular exceedance define a drought with a particular exceedance probability and durationprobability and duration
–– for this method, need to assume that annual for this method, need to assume that annual volumes are independent...volumes are independent...
•• Specification of system reliabilitySpecification of system reliability
0
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2,000,000
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10,000,000
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Annu
al F
low
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ume
(af)
Annual Flow Volume, Feather River, Oroville, CAAnnual Flow Volume, Feather River, Oroville, CA
serial correlation = 0.24
12
0
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35,000,000
40,000,000
020406080100
Probability of Non-Exceedance
Tota
l Flo
w V
olum
e (a
f)
4 years3 years2 years1 year
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2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
012345
Frequency of Drought Volume for Various DurationsFrequency of Drought Volume for Various Durations
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Annu
al F
low
Vol
ume
(af)
balanced 1, 2, 3, 4 yr 1%drought 10%drought
Annual Flow Volume, Feather River, Oroville, CAAnnual Flow Volume, Feather River, Oroville, CA
balanced droughts, similar to balanced
hyetograph
13
Statistics Issues...Statistics Issues...•• For the creation of probabilistic balanced droughts, For the creation of probabilistic balanced droughts,
we assumed that annual volumes are we assumed that annual volumes are independentindependent, , which in many cases is not accuratewhich in many cases is not accurate
•• This assumption allowed frequency analysis on This assumption allowed frequency analysis on annual flow volume to determine volumes with 1% annual flow volume to determine volumes with 1% exceedenceexceedence probprob, or 5%, etc, or 5%, etc
•• The same assumption can not be made on reservoir The same assumption can not be made on reservoir levels in an overlevels in an over--year systemyear system–– ieie, annual minimum elevations are NOT independent, annual minimum elevations are NOT independent
Alternatives to Critical PeriodAlternatives to Critical Period
•• Probabilistic description of droughtProbabilistic description of drought•• Specification of system reliabilitySpecification of system reliability
–– use use stochastic streamflow modelstochastic streamflow model to generate many to generate many years of synthetic flowyears of synthetic flow
–– simulate reservoir operation with current demand, simulate reservoir operation with current demand, determine frequency of failuredetermine frequency of failure
–– determine a demand (yield) that provides certain determine a demand (yield) that provides certain probability of failure, probability of failure, ieie 0.1%, 1%, 5%...0.1%, 1%, 5%...
questionquestion: do we need 100% reliability?: do we need 100% reliability?
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0
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Annu
al F
low
Vol
ume
(af)
aggregate monthly data into annual volume...aggregate monthly data into annual volume...
disaggregate annual volume into monthly...disaggregate annual volume into monthly...
generate annual data with appropriate statistics generate annual data with appropriate statistics using stochastic streamflow model AR(1)using stochastic streamflow model AR(1)
100 years
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0
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7,000,000
8,000,000
9,000,000
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Ann
ual F
low
Vol
ume
(af)
0
1,000,000
2,000,000
3,000,000
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5,000,000
6,000,000
7,000,000
8,000,000
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Ann
ual F
low
Vol
ume
(af)
0
1,000,000
2,000,000
3,000,000
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5,000,000
6,000,000
7,000,000
8,000,000
9,000,000
10,000,000
Ann
ual F
low
Vol
ume
(af)
Synthetic Annual Volume Series for Feather River 1000 years
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ervo
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F)
Release = 100,000 AF/mono failures in 1000 years
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Res
ervo
ir Vo
lum
e (A
F)
Reliability is 99.9% (“1” in 1,000)Volume = 1,500,000 AF
changes to 1,200,000 AF if 1 failure and 1 on “edge”
average flow need storage = 6,000,000 af to yield average flow
need storage = 13,000,000 af to yield average flow
Storage / Yield Relationship for 1000 year seriesStorage / Yield Relationship for 1000 year series
Water Supply contract volumesWater Supply contract volumes•• Question: In an existing reservoir, what volume is Question: In an existing reservoir, what volume is
needed for user with demand of X needed for user with demand of X mgdmgd??–– users seeking water supply will contract for a certain users seeking water supply will contract for a certain
volumevolume in the reservoir for their usein the reservoir for their use–– the important aspect is that the user is one of several the important aspect is that the user is one of several
users of the conservation poolusers of the conservation pool–– Some important questions are Some important questions are
•• ““what access does the new user have to inflow...?what access does the new user have to inflow...?””•• ““what accounting is made for water returned to the what accounting is made for water returned to the
reservoir?reservoir?””
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First develop storage/yield relationshipFirst develop storage/yield relationship
Evaluate user storage Evaluate user storage ““accountaccount”” = % of Pool= % of Pool
assume X% of pool receives X% of inflow
most contracts are down here....most contracts are down here....
Iterative computation, must propose %-of-pool and then resolve to that %
Notice, having half Notice, having half of a 400,000 AF of a 400,000 AF conservation pool is conservation pool is not the same as not the same as having all of a having all of a 200,000 AF 200,000 AF conservation pool. conservation pool. The difference is The difference is that only get half of that only get half of the inflow.the inflow.
910
675
More complex than More complex than this under this under Prior Prior Appropriation Appropriation DoctrineDoctrine
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Water Supply / Firm Yield R&D UnitWater Supply / Firm Yield R&D Unit
•• Survey the methods in use to compute firm yield for Survey the methods in use to compute firm yield for water supply contractswater supply contracts
•• Evaluate methodsEvaluate methods•• Investigate Investigate ““consistentconsistent”” method that could apply in all method that could apply in all
or most cases, and build tools to implementor most cases, and build tools to implement•• So far, feedback from:So far, feedback from:•• NWW, LPR, LRN, LRL, LRH, POD, SPL, SWL, SWTNWW, LPR, LRN, LRL, LRH, POD, SPL, SWL, SWT
Methods in the FieldMethods in the Field•• ThereThere’’s another method in use to answer the question s another method in use to answer the question
““how much volume does X how much volume does X mgdmgd need?need?””
•• The method simulates the reservoir without the new The method simulates the reservoir without the new use, notes the lowest storage in the POR or critical use, notes the lowest storage in the POR or critical period, then adds the new use, find new lowest storage.period, then adds the new use, find new lowest storage.
•• Difference between lowest storages = volume neededDifference between lowest storages = volume needed
•• This method seems correct, but makes implicit This method seems correct, but makes implicit assumptions that are not obvious or correct...assumptions that are not obvious or correct...
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Additional Drawdown after adding Water Supply
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50,000
100,000
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350,000
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Diff
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rage
Lev
el (a
f)
Total Reservoir Storage, without and with water supply
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500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
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Res
ervo
ir St
orag
e in
AF
with WSwithout WS
900 mgd out750 mgd back
150 mgd
250,000 AF265,000 AF
Additional Drawdown after adding Water Supply
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
1951
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Diff
eren
ce in
Sto
rage
Lev
el (a
f)
Total Reservoir Storage, without and with water supply
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
1951
1953
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1957
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1961
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1965
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Res
ervo
ir St
orag
e in
AF
with WSwithout WS
900 mgd out750 mgd back
150 mgd
250,000 AF265,000 AF
low is at 250,000 AF
low is at 265,000 AF
22
Methods in the FieldMethods in the Field•• The outcome of this computation is the new use draws The outcome of this computation is the new use draws
directly from storage for the entire withdrawal, and only directly from storage for the entire withdrawal, and only refills its refills its ““accountaccount”” when the reservoir completely fillswhen the reservoir completely fills
•• Implicit assumptions:Implicit assumptions:–– The added useThe added use’’s account has no access to inflow s account has no access to inflow
other than surplus (when reservoir is full)other than surplus (when reservoir is full)–– The added use is given 100% credit for its return flowThe added use is given 100% credit for its return flow
•• Is this correct?Is this correct? ...not in riparian water law states...not in riparian water law states
–– In Riparian states, more appropriate to allocate inflow In Riparian states, more appropriate to allocate inflow in proportion with % of pool.in proportion with % of pool.
Methods in the FieldMethods in the Field•• Is this correct? Is this correct? ...not in riparian water law states...not in riparian water law states
–– In In RiparianRiparian states, more appropriate to allocate inflow states, more appropriate to allocate inflow in proportion with % of pool.in proportion with % of pool.
–– in in Prior AppropriationPrior Appropriation states, closer to correct, but states, closer to correct, but should account for water rightsshould account for water rights
•• To model this situation better, must track a storage To model this situation better, must track a storage account within the reservoir and explicitly model account within the reservoir and explicitly model useruser’’s inflow and removal.s inflow and removal.
•• Maximum deficit determines how large the volume Maximum deficit determines how large the volume must be (iterative if inflow = %must be (iterative if inflow = %--ofof--pool)pool)
23
What about competing uses?What about competing uses?•• Most of the methods demonstrated show water supply Most of the methods demonstrated show water supply
as the only use, and donas the only use, and don’’t capture the conflict or t capture the conflict or priority between usespriority between uses
•• Only last method really captures other uses, but it has Only last method really captures other uses, but it has other problems...other problems...
•• We need to simulate the reservoir realisticallyWe need to simulate the reservoir realistically–– add new use to existing reservoir system with other add new use to existing reservoir system with other
priorities and operationspriorities and operations–– track each users storage accounttrack each users storage account
What about multiWhat about multi--reservoir systems?reservoir systems?•• In the methods shown, multiple reservoirs serving the In the methods shown, multiple reservoirs serving the
same demand are only captured by combining volumessame demand are only captured by combining volumes
•• It would be better to model the complete reservoir It would be better to model the complete reservoir system... as well as the other uses and accountssystem... as well as the other uses and accounts
•• As a start, HECAs a start, HEC--ResSimResSim now has ability to do now has ability to do ““Reassessment/OperationsReassessment/Operations”” yield analysisyield analysis–– model existing reservoir or multimodel existing reservoir or multi--reservoir system, reservoir system,
increase yield iteratively until max the systemincrease yield iteratively until max the system–– next step, tracking water accounts for adding usersnext step, tracking water accounts for adding users
24
1 reservoir 1 reservoir system, system, want to find want to find yieldyield at at reservoir, reservoir, higher higher priority priority min flow min flow requirement requirement of 500 of 500 cfscfs at at confluenceconfluence
1 reservoir 1 reservoir system, system, want to find want to find yieldyield at at reservoir, reservoir, higher higher priority priority min flow min flow requirement requirement of 500 of 500 cfscfs at at confluenceconfluence
total diversion from resyield = 1015 cfs
downstream flow maintains min = 500 cfs
Reservoir elevation and flows
25
3 reservoir 3 reservoir system, all system, all reservoirs reservoirs contribute to contribute to supplying supplying demanddemanddiversion at diversion at confluenceconfluence
3 reservoir 3 reservoir system, all system, all reservoirs reservoirs contribute to contribute to supplying supplying demanddemanddiversion at diversion at confluenceconfluence
total flow at demand siteyield = 3110 – 500 = 2610 cfs
Reservoir elevation and flows
Reservoir elevation and flows
26
Not yet, but soon...Not yet, but soon...
•• This module doesnThis module doesn’’t account for individual user t account for individual user storage accounts yetstorage accounts yet
•• The computation is just full system yield, with the The computation is just full system yield, with the current reservoir and conservation pool sizescurrent reservoir and conservation pool sizes
•• Next step is the add storage accounting, so can Next step is the add storage accounting, so can show various fractions of the conservation poolshow various fractions of the conservation pool–– Would also need a tool for defining inflow belonging Would also need a tool for defining inflow belonging
to user, either % of total and userto user, either % of total and user--defined.defined.
