AgendaCALVIN: Optimization of Californias Water Supplies29 November 200110:00am 4:00 pm744 P St., Sacramento, CA; AuditoriumCALVIN is an optimization model which suggests operations of Californias inter-tied water supply system which would maximize statewide economic benefits to agricultural and urban water users within environmental flow requirements. Morning sessions will focus on technical aspects, with the afternoon sessions on results, policy, and management implications. Project descriptions, details, and results can be found at: http://cee.engr.ucdavis.edu/faculty/lund/CALVIN/Tentative Workshop Agenda10:00Overview of CALVIN Model (Jay Lund)10:30Economic Valuation of Water Uses (Richard Howitt, Mimi Jenkins)11:00 Managing Data and Model Outputs (Ken Kirby) Model engineering and economic outputs and how they are used Data Management and Databases 11:30Model Calibration (Mimi Jenkins)12:00Limited Foresight and Carryover Storage (Andy Draper)12:30Lunch1:30Limitations of Model and Data (Jay Lund)1:45Results and Implications (Various speakers) Alternatives Examined (Randy Ritzema) Delivery & Economic Performance with Optimized Operations (Randy Ritzema) Willingness-to-Pay for Additional Water (Richard Howitt) Water Transfers and Exchanges (Richard Howitt)2:30Break2:45Results and Implications (continued) Economic Values for Facility Expansion (Stacy Tanaka) Economic Costs of Environmental Flows (Stacy Tanaka) Conjunctive Use (Mimi Jenkins) Other operational changes (Mimi Jenkins)3:30Implications for State Water Policy and Planning (Jay Lund and Richard Howitt)3:45Continuing Work (Jay Lund)Conclusions4:00End

CALVINEconomic-Engineering Optimization for Californias Water SuppliesProfessor Jay R. LundCivil & Environmental Engineering, UC Davis Professor Richard E. HowittAgricultural & Resource Economics, UC DavisWeb site:cee.engr.ucdavis.edu/faculty/lund/CALVIN/

Real work done byDr. Marion W. JenkinsDr. Andrew J. DraperDr. Kenneth W. KirbyMatthew D. Davis Kristen B. Ward Brad D. Newlin Brian J. Van Lienden Stacy Tanaka Randy Ritzema Guilherme MarquesSiwa M. Msangi Pia M. Grimes Jennifer L. Cordua Mark LeuMatthew EllisDr. Arnaud Reynaud

Funded byCALFED Bay Delta Program State of California Resources AgencyNational Science FoundationUS Environmental Protection AgencyCalifornia Energy CommissionUS Bureau of ReclamationLawrence Livermore National Laboratory

Overview1) California Water Problems2) What is CALVIN?3) Modeling Approach and Data4) What is Optimization?5) Results6) Innovations and Uses7) Major Themes

California Water ProblemsCalifornia: an often dry place with a good climate

Wetter winters, very dry summers.

Water in north/mountains, demands in south, central and coast.

Groundwater is 30-40% of supply.

Competition for water:Agriculture, urban, environment

Motivation for Project Californias water system is huge and complex.Water is controversial and economically important.Major changes are being considered.

Can we make better sense of this system?Understanding from data and analysisInsights from resultsReduce reliance on narrow perspectivesHow could system management be improved?What is user willingness to pay for additional water and changes in facilities & policies?

These are not back of the envelope calculations.

What is CALVIN?Entire inter-tied California water systemSurface and groundwater systemsEconomics-driven optimization model Economic Values for Agricultural and Urban UsesFlow Constraints for Environmental UsesPrescribes monthly system operation

Approacha) Develop schematic of sources, facilities, & demands.b) Develop explicit economic values for agricultural & urban water use for 2020 land use and population.c) Identify minimum environmental flows.d) Reconcile estimates of unimpaired 1922-1993 inflows, & identify problems therein.e) Develop databases, metadata, and documentation for more transparent and flexible statewide analysis.

Approach (continued)f) Apply economic-engineering optimization to combine this information and suggest: 1) promising capacity expansion & operational solutions, 2) economic value of additional water to users, 3) costs of environmental water use, and 4) economic value of changes in capacities and policies.

Model Schematic

Over 1,200 spatial elements 51 Surface reservoirs 28 Ground water reservoirs 24 Agricultural regions 19 Urban demand regions 600+ Conveyance Links

CALVINs Demand Coverage

Economic Values for WaterWillingness to payAgriculturalUrbanOperating Costs

Agricultural Water Use Values010,00020,00030,00040,00050,00060,00070,000050100150200250300350400Deliveries (taf)Benefits ($ 000)MarchAugustJuneJulyMayAprilSeptemberOctober01,0002,0003,00051015OctoberFebruaryJanuary

Urban Water Use Values05,00010,00015,00020,00025,00030,00035,00040,00045,00050,000202530354045505560Deliveries (taf)Penalty ($000)WinterSummerSpring

Operating CostsFixed head pumpingEnergy costsMaintenance costsGroundwater recharge basinsWastewater reuse treatmentFixed head hydropowerUrban water quality costs

Environmental Flow Constraints Minimum instream flows Rivers and lakes Delta outflows Wildlife refuge deliveries

Sources: DWRSIM PROSIM - CVPIA Various local studies

Hydrology Surface & Groundwater 1921 - 1993 historical period: Monthly unimpaired inflows Surface inflows from State & Federal data Groundwater from Federal & local studies

Need to reconcile conflicting data!

Policy Constraints

All Cases Environmental flows Flood control storage Current Policy Base Case DWRSIM surface operations CVGSM pumping and deliveries Unconstrained economic case Only environment & flood control

Model Inputs Schematic and facility capacities Agricultural water values Environmental Flow Constraints Urban water values Operating costs Hydrology: Surface & ground water Policy Constraints

Data Flow for the CALVIN Model

Database and InterfaceTsunami of data for a controversial systemPolitical need for transparent analysisPractical need for efficient data managementDatabases central for modeling & managementMetadata and documentationDatabase & study management softwarePlanning & modeling implications

What is Optimization?Finding the best decisions within constraints.Best implies performance objective(s).Constraints limit the range and flexibility of decisions.Some constraints are physical.Other constraints are policy.Optimization can identify promising solutions.

Network Optimization In Words

Decisions: Water operations and allocations

Best performance: (1) Minimize sum of all costs over all times

Subject to some constraints: (2) Conservation of mass (3) Maximum flow limits (4) Minimum flow limits

Network Flow with Gains - MathMinimize: (1) Z = cij Xij, Xij is flow from node i to node jSubject to: (2) Xji = aij Xij + bj for all nodes j (3) Xij uijfor all arcs (4) Xij lijfor all arcs

cij = economic costs (ag. or urban)bj = external inflows to node jaij = gains/losses on flows in arcuij = upper bound on arclij = lower bound on arc

Some ResultsDelivery, Scarcity, and Cost PerformanceWillingness to payWater transfers and exchangesEconomic Value of Facility ChangesCosts of Environmental FlowsConjunctive Use and other Operations

CALVINs Innovations

1) Statewide model 2) Groundwater and Surface Water 3) Supply and Demand integration 4) Optimization model 5) Economic perspective and values 6) Data - model management 7) Supply & demand data checking 8) New management options

ThemesEconomic scarcity should be a major indicator for Californias water performance.Water resources, facilities, and demands can be more effective if managed together, especially at regional scales. The range of hydrologic events is important, not just average and drought years.Newer software, data, and methods allow more transparent and efficient management.

More Information ...Web site:cee.engr.ucdavis.edu/faculty/lund/CALVIN/

The Economic Valuation of Agricultural and urban Water supplies

Richard E. Howitt, Mimi Jenkins, Siwa M. Msangi,

Arnaud Reynaud, and Kristin B. Ward.

Water Demand FunctionsUrban demands are generally demands for direct consumption.Agricultural demands are derived demands that depend on the cost of other inputs and the value of the output.Environmental demands are represented by constraints.The elasticity of demand measures the responsiveness of the quantity demanded to changes in the price ( cost ) of water. An elastic demand has an elasticity greater than one, and is relatively responsive to price changes.Direct statistical estimation of demands is prevented by the absence of price variation in Californian agricultural or urban water

Calvins Economic RequirementsCalvin needs a stepped Penalty function for each delivery node on the schematic.The penalty is the cost of not having a quantity of water and is the inverse of the demand function that measures the value of having water.The continuous economic demand functions are divided into discrete steps for linear solution.The agricultural and urban demand functions must be calibrated so that the marginal value of the observed deliveries is equal to the observed water price.

Data Base for the SWAP Model The Statewide Agricultural Production Model ( SWAP ) models the regional adjustment of profit maximizing farmers allocating water over the range of crops currently grown in the region.The base year for calibrating SWAP is 1992 Base costs, prices, yields and input quantities are largely based on CVPM data.SWAP crop acreages were extrapolated to 2020 levels using forecasts from DWR Bulletin 160-98

Economic Model Comparison

CVPM

SWAP

Regions

21 Central Valley

21 Central Valley & 3 Southern California

Production Costs

Quadratic PMP costs by crop & region*

Market prices for inputs with shadow values for constrained inputs

Production Technology

Fixed yield per acre.

CES trade-off between cost and water use

Variable yield with ME quadratic production function in land, water & capital cost by crop & region

Output price

Prices change with total production

Fixed price with regional differences

Water Use

Yearly

Monthly

SWAP Model Regions

21

Palo Verde

Imperial Valley

SAN JOAQUIN VALLEY REGIONS

SOUTHERN CALIFORNIA REGIONS

SACRAMENTO VALLEY REGIONS

Coachella Valley

20

18

15

19

3

2

1

5

7

6

17

14

13

10

12

16

11

9

8

4

Swap Agricultural Regions

CVPM/ SWAP Region

Description

1

CVP Users: Anderson Cottonwood, Clear Creek, Bella Vista, Sacramento River miscellaneous users.

2

CVP Users: Corning Canal, Kirkwood, Tehama, Sacramento River miscellaneous users.

3

CVP Users: Glenn Colusa ID, Provident, Princeton-Cordora, Maxwell, Colusa Basin Drain MWC, Orland-Artois WD, Colusa County, Davis, Dunnigan, Glide, Kanawha, La Grande, Westside WD, and Tehama Colusa Canal Service Area.

4

CVP Users:Princeton-Cordora-Glenn, Colusa Irrigation Co., Meridian Farm WC, Pelger Mutual WC, Reclamation Districts 1004 and 108, Roberts Ditch, Sartain M.D., Sutter MWC, Swinford Trac IC, Tisdale Irrigation, Sacramento River miscellaneous users.

5

Most Feather River riparian and appropriative users.

6

Yolo and Solano Counties, CVP users: Conaway Ranch, and Sacramento River miscellaneous users.

7

Sacramento Company north of the American River, CVP Users: Natomas Central MWC, Pleasant Grove-Verona, San Juan Suburban, Sacramento River Miscellaneous users.

8

Sacramento County south of the American River, San Joaquin Company

9

Delta Regions. CVP users: Banta Carbona, West Side, Plainview.

10

Delta Mendota Canal. CVP Users:

11

Stanislaus River water rights: Modesto ID, Oakdale ID, South San Joaquin ID.

12

Turlock ID.

13

Merced ID, CVP Users: Madera, Chowchilla, Gravley Ford.

14

CVP Users: Westlands

15

Tulare Lake Bed. CVP Users: Fresno Slough, James, Tranquility, Traction Ranch, Laguna, Reclamation District 1606.

16

Eastern Fresno Company, CVP Users: Friant-Kern Canal, Fresno ID, Garfield, International.

17

CVP Users: Friant-Kern Canal, Hills Valley, Tri-Valley Orange Grove.

18

CVP Users: Friant-Kern Canal, County of Fresno, Lower Tule River ID, Pixley ID

19

Kern Co. SWP service area

20

CVP Users: Friant-Kern Canal, Shafter-Wasco, South San Joaquin.

21

CVP Users: Cross Valley Canal, Friant-Kern Canal, Arvin Edison

22

Imperial ID

23

Coachella Valley WD

24

Palo Verde ID

Agricultural Crop Descriptions

Crop Category

Description of Included Crops

Cotton

Cotton

Field

Field Corn

Fodder

Alfalfa hay, Pasture, Miscellaneous Grasses

Grain

Wheat

Grapes

Table, Raisin, and Wine Grapes

Pasture

Irrigated Pasture

Orchard

Almonds, Walnuts, Prunes, Citrus and Peaches

Tomatoes

Fresh Market and Processing Tomatoes

Rice

Rice

Sugarbeets

Sugarbeets

Subtropical

Avocado, Olives, Figs, and Pomegranates

Truck

Melons, Onions, Potatoes, and Miscellaneous Vegetables

Source: CVPIA, 1997, Technical Appendix Volume Eight; Various Counties Agricultural Crop and Livestock Report, Various Years

Agricultural Response to Changes in the Price and Quantity of Water Changes at the Extensive MarginChanges in the total Area of Irrigated cropsAdjustments in the regional cropping mix.

Changes at the Intensive MarginA change in crop input use per acreChanges in Water application efficiency due to technology and management.

The CES Isoyield function is as follows:

= 1

Where A1 is a scale parameter

B1 is a share parameter for the CES function obtained from the CVPM.

EFFC is the measure of water use efficiency, for each crop and region, and is obtained by taking the ratio of applied water to the Evapotranspiration of Applied Water (AW/ETAW).

_994874632.unknown

Efficiency-Cost Trade-offs. Orchards Sacramento Valley

Chart1

150

132

110

107

115

100

110

92

80

82

52

62

38

$/AC/YR

Fitted CES fcn

AW/ETAW

$/Acre/Year

Orchard - CES Fcn

Data Points Plotted from Data Eyeballed from CVPIA 1997, Technical Appendix Vol 2, pg B-8

Orchard Irrigation Technologies for Sacramento Valley

dataAW/ETAW$/AC/YRpredicted LHSRHS(LHS-RHS)(LHS-RHS)^2

1.11500.98716439971-0.01283560030.0001647526

1.151320.98197456271-0.01802543730.0003249164

1.251100.98642895661-0.01357104340.0001841732

1.261070.9836652071-0.0163347930.0002668255

1.291151.021978712610.02197871260.0004830638

1.351001.01079909310.0107990930.0001166204

1.371101.051459145910.05145914590.0026480437

1.38921.000015952610.00001595260.0000000003

1.4800.96635978791-0.03364021210.0011316639

1.5821.020842943510.02084294350.0004344283

1.58520.90939145231-0.09060854770.0082099089

1.78621.044402128610.04440212860.001971549

2.22381.013925002310.01392500230.0001939057

CES regression

solved valuesCVPIA values

a0.13509693440.114

b0.50801718930.422

rho-0.1801748899-0.266

objective0.0161298517

Orchard - CES Fcn

150

132

110

107

115

100

110

92

80

82

52

62

38

$/AC/YR

Fitted CES fcn

AW/ETAW

$/Acre/Year

Orchard isoquant

CES Isoquant generated with parameters estimated from regression on Orchard in Sac Valley

Observed dataGenerated Data

AW/ETAW$/AC/YRObserved EfficCapital Costspredicted LHSRHS(LHS-RHS)(LHS-RHS)^2

1.11501.1156.40090084490.99897708551-0.00102291450.0000010464

1.151321.15141.23629723671.001461459410.00146145940.0000021359

1.251101.25115.16308610141.000139046510.00013904650.0000000193

1.261071.26112.95555764870.99989469981-0.00010530020.0000000111

1.291151.29106.80160324810.9993529531-0.0006470470.0000004187

1.351001.3596.4462259890.99955776891-0.00044223110.0000001956

1.371101.3793.47053066580.99995962341-0.00004037660.0000000016

1.38921.3892.05029622261.000186725910.00018672590.0000000349

1.4801.489.31867179471.000630621410.00063062140.0000003977

1.5821.576.85309231870.99979174821-0.00020825180.0000000434

1.58521.5869.07226320531.000038112210.00003811220.0000000015

1.78621.7854.57673252880.99999951161-0.00000048840

2.22382.2236.59888088261.000000159710.00000015970

CES parameters

a0.1350969344

b0.5080171893

rho-0.1801748899

objective0.0000043059

Orchard isoquant

00

00

00

00

00

00

00

00

00

00

00

00

00

observed values

Fitted CES Isoquant

AW/ETAW

$/Acres/Year

Sheet3

Sheet4

Sheet5

Calibrating Regional Crop Production FunctionsRegional data available- acres, average yields, input quantities, crop price, input cash cost, resource constraintsOptimize a constrained problem to obtain shadow values on binding constraints.Define the form of the production function- in this case, a quadratic function of three inputs.Use maximum entropy methods, marginal and average product conditions to estimate the production function coefficient values.Use the ME coefficient values to define a production model that calibrates to the base year, but is only constrained by the resource constraints.

The production function is written, in general form, as:

The specific quadratic used in the SWAP model has the form:

EMBED Equation.3

EMBED Equation.3

_1029588593.unknown

_1068388169.unknown

_1068388190.unknown

_994874683.unknown

The total problem defined over G regions and i crops in each region for a single year is :

EMBED Equation.3

EMBED Equation.3

_1029247073.unknown

_1068388257.unknown

_1068388304.unknown

_1068388080.unknown

_963516148.unknown

Linking Annual Cropping Decisions to Monthly Water UseAssume that crops require water in a predetermined monthly pattern based on ET requirements.Farmers can make small water reallocations between months.Any changes in the total applied water due to technology or stress irrigation are allocated are allocated proportionally across months

The water constraints in the model for i crops and a single region G are:

_1029254734.unknown

_1068388487.unknown

SWAP-Derived Agricultural Water demands020040060080010000204060Water Availability in KAFWillingness to Pay in $/AFJuly DemandApril Demand

Agricultural Water Use Values010,00020,00030,00040,00050,00060,00070,000050100150200250300350400Deliveries (taf)Benefits ($ 000)MarchAugustJuneJulyMayAprilSeptemberOctober01,0002,0003,00051015OctoberFebruaryJanuary

Tomato production-Yolo countyWaterLand

Calibrated Production Surface for Grapes, Fresno

Urban DemandsResidential demands are based on comprehensive survey of estimated price elasticities. The demand function is fitted through the observed 1995 price and quantity demanded with the function slope determined by the elasticity. The 2020 demand are obtained by scaling the 1995 quantities by population growth.Commercial is assumed proportional to the population and is added to the residential demand.Industrial are based on a 1991 survey of shortage induced production losses in 12 counties, and scaled to 2020.

Residential Price Elasticities

Study / Report

Location and Sector

Season

Long-run or Short-run

Elasticity

Howe 1982

Western United States, single- family residential

Summer

long

-0.43

Weber 1989

East Bay Municipal Utility District, aggregated residential

Winter

Annual

long

-0.08 to 0.2

-0.1 to -0.2

CCWD 1989

Contra Costa Water District, residential

Annual

Winter

Summer

long

long

long

-0.2 to -0.4

very small

-0.35

DWRb 1991

California, residential

Annual

long

-0.2 to -0.5

Dziegielewski and Optiz 1991

MWD of Southern California, single-family residential

multiple-family residential

overall weighted urban average

combined commercial/industrial

Winter

Summer

Winter

Summer

Annual

Annual

long

-0.24

-0.39

-0.13c

-0.15c

-0.22

-0.28d

Renwick et al. 1998

Bay Area and Southern California, 8 agencies, single-family residential

Average

Summer

long

long

-0.16

-0.20

a compiled from Dziegielewski and Optiz (1991), USBR (1997) , DWR (1991, 1998a), and Baumann et al. (1998).

b California Department of Water Resources

c appears more inelastic than single-family residential because many multiple-family users do not pay the price of water and therefore appear insensitive to price changes

d may appear more elastic than residential due to impacts of wastewater discharge requirements period

Estimating Residential DemandsResidential price elasticities1995 retail water prices1995 population x pcu1+2+3 = 1995 Demand Curve1995 demand curve scaled by 2020 population4 = 2020 Demand Curve

Calibrating Residential Demands to the 2020 Population

Converting Residential demands to Urban Loss FunctionsIntegrate the 2020 residential demand functionAdd a constant level of 2020 commercial useFind the quantity that drives the demand price ( or loss of not having water) to zeroPlot the loss function against monthly delivery.

Residential Loss Functions for 2020

Industrial Values1991 production losses due to water shortages 12 counties1995 industrial use scaled by population to 20201+2 = 2020 Industrial Loss Function

1995 Urban Residential Water Prices in California

ConclusionsWater demand functions must reflect rational adjustments to changing scarcity by usersDemand functions need to be specified by use, region and monthUrban demands can be estimated on a regional basis using published elasticities and base year dataAgricultural demand functions can be estimated using regional production data and ET requirements.

Managing Data in CALVINModel, Database, Documentation, and Post-processing SOFTWARE

CALVIN Physical OutputsFlows across all linksEOM Storage Levels at all storage nodesEvaporation at all storage nodesDeliveries to all demand nodesFlowStorage

CALVIN Economic OutputsScarcitiesCost of scarcitiesMarginal WTP for more water

Shadow values on constraints (Lagrange Multiplier)Marginal value of water at each nodePost-processed by intersecting deliveries with economic water loss functions for Ag & UrbanProduced directly by HEC-PRM Optimization

SWAP Post-Processed OutputsIrrigation efficienciesCrop acreagesCrop yieldsGross revenueNet revenue

Ag annual deliveries by water source from CALVINSWAP Model

Data Management Design PrinciplesTransparent model assumptionsEasily modified model inputsObject oriented data managementDocumentation of input values = metadataMetadata attached to each piece of data

RELATIONAL DATABASETime series stored in DSSPaired data stored in DSSModel definition file in ASCIIOutput in DSSHEC-PRM Requirements

CALVIN Data Storage & SoftwareData StorageSoftware

Region 3 Schematic

Network Component Listing

Node Properties

Metadata

SummaryMetadata is essentialRelational databases and software allow modeling of complex systems in more detail than otherwise possibleData management eliminates majority of input file errors (especially related to syntax)More work to be done

Hydrologic and Agricultural Demand CalibrationIntegrate DWRSIMs surface hydrology with CVGSMs groundwater hydrologyReconcile DWR agricultural water demand assumptions with deliveries in the CVPIA PEISProduce a model consistent with established representations of Californias hydrology and demandsIdentify data problems and regions than cannot be fully reconciled

Calibration ProceduresImpose Base Case diversions, deliveries, and operations on CALVINAdjust agricultural demands to match BC deliveries Adjust agricultural return flows and reuse rates to calibrate groundwater to CVGSM NAARun CALVIN Base Case and adjust streamflows to match DWRSIM 514a at 15 matching control pointsVerify scarcity results with similar estimates

Configuration of Physical and Calibration Links

Agricultural demands increased by about 10% (1.9 MAF)Reuse rates reduced in a few regionsSW return flows eliminated in much of Tulare BasinGW calibration successful in Sac Valley (top chart)Problems with GW calibration in Tulare Basin, esp. CVPM region 14, 18, 19, and 21GW Calibration ResultsSacramento Valley GWSJ Valley & Tulare Basin GW

Net addition of 38 taf/year calibration flowsBiggest monthly imbalances on Sac R. (below Colusa BD) & Feather R. (incl. Yuba+Bear), > +/- 1 MAFLargest annual imbalances on Sac R. +620 taf/yr, Lower SJR -434 taf/yr, and in-Delta CU (- 380 taf/yr)Largest net additions of SW in CALVIN Region 1 and 4; net removals in CALVIN Region 2 and 3SW Calibration ResultsSac R.Colusa BDSac R.HoodIn-DeltaCU

What we learnedCalibration is necessary and longHydrologic data needs improvement:more explicit and separate GW & SW hydrologic databetter estimates (methods) for local accretions/depletionsAgricultural water use uncertainty is significantVery weak data for modeling Tulare Basin:conjunctive use operationsgroundwater-surface water interactionsLarge discrepancy in in-Delta CU estimates

A Limited Foresight Modelandthe Value of Carryover Storage

Perfect Foresightor the Model that Knew too MuchMulti-year optimization too omniscientOver valuation of existing facilitiesUnder valuation of new facilitiesExcessive carryover storage prior to droughtsSingle-year optimization too short sighted How to construct model with limited foresight to:Reflect imperfect knowledge of probability distribution of inflowsBalance present and future water needs

Sequential Annual RunsUse one year time period (Oct Sep)72 consecutive model runs for period-of-analysis 1922-1993Model runs linked by ending/carryover storageCarryover storage value functions limit drawdownSystem performance sum of 72 year costs excluding carryover storage penalties

Iterative SolutionRun HEC-PRM for one yearyr=72?BOP Oct = EOP SepSet yr=1, read initial conditionsSTOPDefine initial carryover storage penalty functionSTARTSignificantimprovementYesNoyr = yr +1Revise carryover storage penalty functionCalculate total penaltiesIteration n=1Iteration n=1?YesNoIteration n= n + 1Yes

Model Run TimesRun times remain an obstacle for analyzing complex systemsSolver times proportional to cube of number of constraintsSolver times proportional to number of variablesRun time as a function of years of analysis found to be approx. quadraticLimited foresight model exploits rapid increase in run times

Case StudiesThree case studies used as proof of conceptSingle reservoir operationIntegrated two reservoir operationSingle reservoir operated conjunctively with groundwaterReservoirs operated for water conservation and flood controlObjective function to minimize economic cost of shortage associated with d/s agricultural deliveriesNetwork flow solver (HEC-PRM)

Case (a): Application to a Single ReservoirFour separate models developed:New Don Pedro Reservoir, Tuolumne RiverLake McClure, Merced RiverPine Flat Reservoir, Kings RiverLake Berryesssa, Putah Creek

Case studies to provide a framework for the presentation of ideas rather than a realistic operation of each stream-reservoir system.Value functions developed for agricultural deliveries

Valuing Carryover StorageAssume quadratic penaltyP = a + bS + cS2P|S=K = 0dP/dS is -ve, d2P/dS2 is +vedP/dS between reasonable limits

Grid SearchSimple to implementEnsures global optimumResponse surface mapped-outComputationally inefficientAccuracy limited by grid spacingCoarse grid search starting point for more efficient methods

Nelder-Mead Simplex MethodUnconstrained minimization of several variablesZero-order search methodGlobal optimum not guaranteed

New Don Pedro ReservoirAverage Annual Shortage Cost as a Function of Pmin and Pmax

Lake McClureAverage Annual Shortage Cost as a Function of Pmin and Pmax

Pine Flat ReservoirAverage Annual Shortage Cost as a Function of Pmin and Pmax

Lake BerryessaAverage Annual Shortage Cost as a Function of Pmin and Pmax

New Don Pedro Reservoir Operation under Perfect Foresight

New Don Pedro Reservoir Operation under Limited Foresight

New Don Pedro Reservoir Carryover Storage for Different Levels of Information

Reservoir Operating Rules

Case (b): Integrated Two-Reservoir System

Flood Control & Carryover Storage

Balancing Storage Between Reservoirs in ParallelObjectives:Equalize refill potentialMinimize EV(spills)Avoid inefficient conditions

Carryover Storage Penalty Functions

Carryover Storage: New Don Pedroand New Exchequer Reservoirs

Case (c): Conjunctive Use

Groundwater MiningFor perfect foresight model groundwater mining prevented by applying constraint to ending groundwater storageFor limited foresight model linear penalty attached to end-of-year storageInitial value of penalty set equal to shadow value on groundwater mining constraint from perfect foresight runPenalty iteratively raised until no groundwater mining occurs

Comparison of Groundwater Storage under Perfect and Limited Foresight Models

Conclusions: Perfect ForesightPerfect foresight may significantly distort reservoir operation where reservoirs are used for over-year storage, and where multi-year droughts occur.The impacts of perfect foresight revealed bylack of hedging under average hydrologic conditionsaggressive hedging during the initial years of an extended drought.The perfect foresight models can substantially under estimate shortages and shortage costsAs system storage increases the effects of perfect foresight are diminished.

Conclusions: Limited ForesightThe limited foresight modelResults in an economically derived value of carryover storage.Prescribes more realistic reservoir operations.More likely to be acceptable to stakeholdersFacilitates the deduction of operating rulesCan quantify the over-achievement of perfect foresight models.

There exists a wide range of near-optimal carryover storage policies.

Differences between the limited and perfect foresight model are minor except prior and during drought conditions.

Conclusions: Conjunctive UseConjunctive use can substantially improve overall system reliability and reduce total costs Considerable benefits may accrue by explicitly adjusting surface reservoir operations to account for contingent groundwater supplies.The value of surface carryover storage rapidly diminishes with increasing groundwater supplies.Carryover storage rules determined without explicitly accounting for the presence of groundwater storage become economically very inefficient as groundwater supplies increase.Integrated conjunctive use greatly reduces the impact of perfect foresight.

LimitationsMajor sources of CALVINs limitations:Weak or unavailable input data from other sources.Limitations of HEC-PRM network solver.Lack of hydropower, flood control, and recreation benefits.

Major LimitationsSurface HydrologyValley floor inflowsDelta local suppliesSouthern CaliforniaGroundwater HydrologyWeak Tulare Basin dataSimplified stream-aquifer interaction1991-1993 groundwater extensionsCVGSM dataPumping capacities, costs, and use

Major Limitations (continued)Water Demands and DeliveriesYear-type variationLimited water qualityLimited understanding of agricultural flowsBase case delivery data from CVGSMRepresentation of local systemsEnvironmental RegulationsDelta representationOther pre-operated flow constraintsWater quality limitations

Major Limitations (continued)Perfect ForesightLess important with lots of groundwater storageProbably causes 5-10% of S. California benefitsNeed to be carefulLimited foresight methods under developmentValue of simulation modeling;Excluded Operating BenefitsHydropowerFlood ControlRecreation

Limitations ImplicationsData problems apply to ANY regional and statewide analysis.Use simulation models to refine and test optimization-based solutions.All models are wrong, but some are useful. G.E.P. Box (Like budget estimates?)

CALVIN Modeling AlternativesRandall Ritzema

How is water allocated now? Water rights and contracts+ Operating agreements+ Environmental regulations+ Water markets (sometimes)

= Complex institutional framework

Typically analyzed using simulation

Objective, in words:To quantify overall economic performance under flexible operations and allocations, within environmental requirements.

Performed by comparing current operations (Base Case) to flexible operations (Unconstrained Case).

Example Network OptimizationSWGWURBANENVIRONMENTALAGRICULTURALInflowLink, no economic valueLink, w/ economic value

Base CaseSWGWURBANENVIRONMENTALAGRICULTURALConstrained flowUnconstrained flow

BC Delivery ConstraintsSWGWURBANENVIRONMENTALAGRICULTURALConstrained flowUnconstrained flowDWRSIM Run 514, CVGSM NAA 1997DWRSIM Run 514, CVGSM NAA 1997

BC Operations ConstraintsSWGWURBANENVIRONMENTALAGRICULTURALConstrained flowUnconstrained flowCVGSM NAA 1997DWRSIM Run 514

Environmental ConstraintsSWGWURBANENVIRONMENTALAGRICULTURALConstrained flowUnconstrained flowMinimum Instream Flows(PROSIM NAA 1997)Refuges (Level 2)

Unconstrained CaseSWGWURBANENVIRONMENTALAGRICULTURALConstraints:Environmental flowsPhysical capacitiesReservoir flood control storage

Model AlternativesBase CaseBasis for ComparisonGoal: mimic simulation planning modelsCurrent water allocationsCurrent water operationsCurrent environmental flows

Model AlternativesBase CaseRegional UnconstrainedStatewide model is divided into 5 regionsSupplies re-operated and re-allocated within regions.Base Case inter-regional boundary flows

CALVIN Regions

Model AlternativesBase CaseRegional UnconstrainedStatewide UnconstrainedInter-regional boundary constraints removed

Delivery and Economic PerformanceComparison of Base Case, Regional Unconstrained, and Statewide Unconstrained AlternativesRandall Ritzema

Urban and Agricultural Deliveries (annual average, in taf)

Chart1

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Costs ($B)

Sheet1

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,481

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,821

Scarcity1,594890

Sheet2

Sheet3

Delivery Changes to Ag Sector (annual average, in taf)

Total Costs

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,606

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,946

Scarcity1,594890

Total Cost chart

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Costs ($B)

Deliveries

* Adapted from Table ES-3

Deliveries (taf/yr)AGBCRWMSWMRWM-BCSWM-BC

Demand RegionBCRWM-BCSWM-BCBCRWMSWM

CVPM 1153-10153152153Reg 1343434213577-13143

CVPM 26404757640687697Reg 254205428542888

CVPM 31543786154315501629Reg 352595259525900

CVPM 41098-660109810321098Reg 4954894579749-91201

CVPM 5173700173717371737Reg 5340630123013-394-393

CVPM 6104800104810481048270672657727026-490-41

CVPM 756500565565565

CVPM 889400894894894RWMSWM

CVPM 9117688117611841184Upper Sac-13143

CVPM 10169800169816981698Tulare Basin-91201

CVPM 1186700867867867Southern California-394-393

CVPM 1280300803803803

CVPM 13189100189118911891

CVPM 14149700149714971497URBANRWM-BCSWM-BC

CVPM 151983-65-11198319181972Reg 21818

CVPM 16498-5-2498493496Reg 31616

CVPM 17836-14-8836822828Reg 44240

CVPM 18193854222193819922160Reg 5597669

CVPM 19957-380957919957

CVPM 2067700677677677RWMSWM

CVPM 211162-230116211391162Tulare Basin318321

Palo Verde661-114-113661547548Southern California8781013

Coachella195-14-14195181181

Imperial2550-266-266255022842284

Total Agriculture27067-490-41270672657727026

Yuba5211525353

Napa-Solano1051010105115115

Contra Costa13500135135135

East Bay MUD29077290297297

Sacramento67900679679679

Stockton9500959595

San Francisco23266232238238

Santa Clara Valley6461010646656656

SB-SLO13900139139139

Fresno3384240338380378

Bakersfield26100261261261

Castaic Lake44757944119123

Antelope Valley1868791186273277

Coachella348104103348452451

Mojave*225127127225352352

San Bernardino27904279279283

Central MWD3534152197353436863731

E & W MWD7062634706732740

San Diego9542634954980988

Total Urban9246674744924699209990

Ag Delivery chart

-13143

-91201

-394-393

RWM

SWM

Urban Delivery chart

318321

8781013

RWM

SWM

Delivery Changes to Urban Sector (annual average, in taf)

Agricultural Scarcity Costs(annual average, in $ millions)

Total Costs

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,606

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,946

Scarcity1,594890

Total Cost chart

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Costs ($B)

Deliveries

* Adapted from Table ES-3

Deliveries (taf/yr)AGBCRWMSWMRWM-BCSWM-BC

Demand RegionBCRWM-BCSWM-BCBCRWMSWM

CVPM 1153-10153152153Reg 1343434213577-13143

CVPM 26404757640687697Reg 254205428542888

CVPM 31543786154315501629Reg 352595259525900

CVPM 41098-660109810321098Reg 4954894579749-91201

CVPM 5173700173717371737Reg 5340630123013-394-393

CVPM 6104800104810481048270672657727026-490-41

CVPM 756500565565565

CVPM 889400894894894RWMSWM

CVPM 9117688117611841184Upper Sac-13143

CVPM 10169800169816981698Tulare Basin-91201

CVPM 1186700867867867Southern California-394-393

CVPM 1280300803803803

CVPM 13189100189118911891

CVPM 14149700149714971497URBANRWM-BCSWM-BC

CVPM 151983-65-11198319181972Reg 21818

CVPM 16498-5-2498493496Reg 31616

CVPM 17836-14-8836822828Reg 44240

CVPM 18193854222193819922160Reg 5597669

CVPM 19957-380957919957

CVPM 2067700677677677RWMSWM

CVPM 211162-230116211391162Tulare Basin318321

Palo Verde661-114-113661547548Southern California8781013

Coachella195-14-14195181181

Imperial2550-266-266255022842284

Total Agriculture27067-490-41270672657727026

Yuba5211525353

Napa-Solano1051010105115115

Contra Costa13500135135135

East Bay MUD29077290297297

Sacramento67900679679679

Stockton9500959595

San Francisco23266232238238

Santa Clara Valley6461010646656656

SB-SLO13900139139139

Fresno3384240338380378

Bakersfield26100261261261

Castaic Lake44757944119123

Antelope Valley1868791186273277

Coachella348104103348452451

Mojave*225127127225352352

San Bernardino27904279279283

Central MWD3534152197353436863731

E & W MWD7062634706732740

San Diego9542634954980988

Total Urban9246674744924699209990

Ag Delivery chart

-13143

-91201

-394-393

RWM

SWM

Urban Delivery chart

318321

8781013

RWM

SWM

Sc. costs

Ag RegionBase CaseRegional UnconstrainedStatewide UnconstrainedUrban regionBase CaseRegional Water MarketsStatewide Water Markets

CVPM 100.20Regions 1 & 2

CVPM 23.50.20Yuba0.900

CVPM 33.12.90Napa2200

CVPM 402.10Contra Costa0.100

CVPM 5000East Bay MUD12.50.60.6

CVPM 6000Sacramento000

CVPM 7000Stockton0.100

CVPM 8000Regions 3 & 4

CVPM 90.200San Luis Obispo000

CVPM 10000San Francisco5.100

CVPM 11000Fresno17.700.7

CVPM 12000Bakersfield000

CVPM 13000Santa Clara Valley10.200

CVPM 14000Region 5: LA

CVPM 150.42.90.8Castaic Lake507.85.12.7

CVPM 1600.10San Bernardino3.52.20

CVPM 1700.40.2E & W MWD32.76.90

CVPM 1818.810.40Central MWD183.436.60.1

CVPM 1902.50Antelope Valley185.23.30

CVPM 20000Region 5: SD & Desert

CVPM 2101.40San Diego34.77.40

Palo Verde1.46.96.9Coachella367.4165166.1

Coachella00.90.9Mojave180.700

Imperial4.320.520.5

Total31.751.329.3Total1858.6227.1170.2

BCRWMSWMBCRWMSWM

US6.65.40LS35.60.60.6

LS0.200SJ15.300

SJ000Tu17.700.7

Tu19.217.71SC1495.4226.5168.9

SC5.728.328.3

ChangeBCRWMSWMChangeRWMSWM

Upper Sac Valley6.65.40Lower Sac Valley-35-35

Tulare Basin19.217.71Bay Area-15.3-15.3

Southern California5.728.328.3Tulare Basin-17.7-17

Southern California-1268.9-1326.5

Ag Scarcity chart

6.65.40

19.217.71

5.728.328.3

BC

RWM

SWM

Urb Scarcity Costs

-35-35

-15.3-15.3

-17.7-17

-1268.9-1326.5

RWM

SWM

Urban Scarcity Costs(annual average, in $ millions)

Total Costs

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,606

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,946

Scarcity1,594890

Total Cost chart

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Costs ($B)

Deliveries

* Adapted from Table ES-3

Deliveries (taf/yr)AGBCRWMSWMRWM-BCSWM-BC

Demand RegionBCRWM-BCSWM-BCBCRWMSWM

CVPM 1153-10153152153Reg 1343434213577-13143

CVPM 26404757640687697Reg 254205428542888

CVPM 31543786154315501629Reg 352595259525900

CVPM 41098-660109810321098Reg 4954894579749-91201

CVPM 5173700173717371737Reg 5340630123013-394-393

CVPM 6104800104810481048270672657727026-490-41

CVPM 756500565565565

CVPM 889400894894894RWMSWM

CVPM 9117688117611841184Upper Sac-13143

CVPM 10169800169816981698Tulare Basin-91201

CVPM 1186700867867867Southern California-394-393

CVPM 1280300803803803

CVPM 13189100189118911891

CVPM 14149700149714971497URBANRWM-BCSWM-BC

CVPM 151983-65-11198319181972Reg 21818

CVPM 16498-5-2498493496Reg 31616

CVPM 17836-14-8836822828Reg 44240

CVPM 18193854222193819922160Reg 5597669

CVPM 19957-380957919957

CVPM 2067700677677677RWMSWM

CVPM 211162-230116211391162Tulare Basin318321

Palo Verde661-114-113661547548Southern California8781013

Coachella195-14-14195181181

Imperial2550-266-266255022842284

Total Agriculture27067-490-41270672657727026

Yuba5211525353

Napa-Solano1051010105115115

Contra Costa13500135135135

East Bay MUD29077290297297

Sacramento67900679679679

Stockton9500959595

San Francisco23266232238238

Santa Clara Valley6461010646656656

SB-SLO13900139139139

Fresno3384240338380378

Bakersfield26100261261261

Castaic Lake44757944119123

Antelope Valley1868791186273277

Coachella348104103348452451

Mojave*225127127225352352

San Bernardino27904279279283

Central MWD3534152197353436863731

E & W MWD7062634706732740

San Diego9542634954980988

Total Urban9246674744924699209990

Ag Delivery chart

-13143

-91201

-394-393

RWM

SWM

Urban Delivery chart

318321

8781013

RWM

SWM

Sc. costs

Ag RegionBase CaseRegional UnconstrainedStatewide UnconstrainedUrban regionBase CaseRegional Water MarketsStatewide Water Markets

CVPM 100.20Regions 1 & 2

CVPM 23.50.20Yuba0.900

CVPM 33.12.90Napa2200

CVPM 402.10Contra Costa0.100

CVPM 5000East Bay MUD12.50.60.6

CVPM 6000Sacramento000

CVPM 7000Stockton0.100

CVPM 8000Regions 3 & 4

CVPM 90.200San Luis Obispo000

CVPM 10000San Francisco5.100

CVPM 11000Fresno17.700.7

CVPM 12000Bakersfield000

CVPM 13000Santa Clara Valley10.200

CVPM 14000Region 5: LA

CVPM 150.42.90.8Castaic Lake507.85.12.7

CVPM 1600.10San Bernardino3.52.20

CVPM 1700.40.2E & W MWD32.76.90

CVPM 1818.810.40Central MWD183.436.60.1

CVPM 1902.50Antelope Valley185.23.30

CVPM 20000Region 5: SD & Desert

CVPM 2101.40San Diego34.77.40

Palo Verde1.46.96.9Coachella367.4165166.1

Coachella00.90.9Mojave180.700

Imperial4.320.520.5

Total31.751.329.3Total1858.6227.1170.2

BCRWMSWMBCRWMSWM

US6.65.40Lower Sac Valley35.60.60.6

LS0.200Bay Area15.300

SJ000Tulare Basin17.700.7

Tu19.217.71Southern California1495.4226.5168.9

SC5.728.328.3

BCRWMSWMRWMSWM

Upper Sac Valley6.65.40Lower Sac Valley-35-35

Tulare Basin19.217.71Bay Area-15.3-15.3

Southern California5.728.328.3Tulare Basin-17.7-17

Southern California-1268.9-1326.5

Ag Scarcity chart

6.65.40

19.217.71

5.728.328.3

BC

RWM

SWM

Urb Scarcity Costs

35.60.60.6

15.300

17.700.7

1495.4226.5168.9

BC

RWM

SWM

Total Costs(annual average, in $ billions)4.182.852.78

Total Costs

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,606

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,946

Scarcity1,594890

Total Cost chart

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Deliveries

* Adapted from Table ES-3

Deliveries (taf/yr)AGBCRWMSWMRWM-BCSWM-BC

Demand RegionBCRWM-BCSWM-BCBCRWMSWM

CVPM 1153-10153152153Reg 1343434213577-13143

CVPM 26404757640687697Reg 254205428542888

CVPM 31543786154315501629Reg 352595259525900

CVPM 41098-660109810321098Reg 4954894579749-91201

CVPM 5173700173717371737Reg 5340630123013-394-393

CVPM 6104800104810481048270672657727026-490-41

CVPM 756500565565565

CVPM 889400894894894RWMSWM

CVPM 9117688117611841184Upper Sac-13143

CVPM 10169800169816981698Tulare Basin-91201

CVPM 1186700867867867Southern California-394-393

CVPM 1280300803803803

CVPM 13189100189118911891

CVPM 14149700149714971497URBANRWM-BCSWM-BC

CVPM 151983-65-11198319181972Reg 21818

CVPM 16498-5-2498493496Reg 31616

CVPM 17836-14-8836822828Reg 44240

CVPM 18193854222193819922160Reg 5597669

CVPM 19957-380957919957

CVPM 2067700677677677RWMSWM

CVPM 211162-230116211391162Tulare Basin318321

Palo Verde661-114-113661547548Southern California8781013

Coachella195-14-14195181181

Imperial2550-266-266255022842284

Total Agriculture27067-490-41270672657727026

Yuba5211525353

Napa-Solano1051010105115115

Contra Costa13500135135135

East Bay MUD29077290297297

Sacramento67900679679679

Stockton9500959595

San Francisco23266232238238

Santa Clara Valley6461010646656656

SB-SLO13900139139139

Fresno3384240338380378

Bakersfield26100261261261

Castaic Lake44757944119123

Antelope Valley1868791186273277

Coachella348104103348452451

Mojave*225127127225352352

San Bernardino27904279279283

Central MWD3534152197353436863731

E & W MWD7062634706732740

San Diego9542634954980988

Total Urban9246674744924699209990

Ag Delivery chart

-13143

-91201

-394-393

RWM

SWM

Urban Delivery chart

318321

8781013

RWM

SWM

Sc. costs

Ag RegionBase CaseRegional UnconstrainedStatewide UnconstrainedUrban regionBase CaseRegional Water MarketsStatewide Water Markets

CVPM 100.20Regions 1 & 2

CVPM 23.50.20Yuba0.900

CVPM 33.12.90Napa2200

CVPM 402.10Contra Costa0.100

CVPM 5000East Bay MUD12.50.60.6

CVPM 6000Sacramento000

CVPM 7000Stockton0.100

CVPM 8000Regions 3 & 4

CVPM 90.200San Luis Obispo000

CVPM 10000San Francisco5.100

CVPM 11000Fresno17.700.7

CVPM 12000Bakersfield000

CVPM 13000Santa Clara Valley10.200

CVPM 14000Region 5: LA

CVPM 150.42.90.8Castaic Lake507.85.12.7

CVPM 1600.10San Bernardino3.52.20

CVPM 1700.40.2E & W MWD32.76.90

CVPM 1818.810.40Central MWD183.436.60.1

CVPM 1902.50Antelope Valley185.23.30

CVPM 20000Region 5: SD & Desert

CVPM 2101.40San Diego34.77.40

Palo Verde1.46.96.9Coachella367.4165166.1

Coachella00.90.9Mojave180.700

Imperial4.320.520.5

Total31.751.329.3Total1858.6227.1170.2

BCRWMSWMBCRWMSWM

US6.65.40Lower Sac Valley35.60.60.6

LS0.200Bay Area15.300

SJ000Tulare Basin17.700.7

Tu19.217.71Southern California1495.4226.5168.9

SC5.728.328.3

BCRWMSWMRWMSWM

Upper Sac Valley6.65.40Lower Sac Valley-35-35

Tulare Basin19.217.71Bay Area-15.3-15.3

Southern California5.728.328.3Tulare Basin-17.7-17

Southern California-1268.9-1326.5

Ag Scarcity chart

6.65.40

19.217.71

5.728.328.3

BC

RWM

SWM

Urb Scarcity Costs

35.60.60.6

15.300

17.700.7

1495.4226.5168.9

BC

RWM

SWM

Total Cost by Region(annual average, in $ millions)

Total Costs

BCRWMSWMBCRWMSWMBCSWM

Scarcity1596279200Scarcity1.600.280.20Surface Water23,26823,606

Operating258125682580Operating2.582.572.58Groundwater10,38510,531

Total417628472780Total4.182.852.78Groundwater recharge1,1181,381

Reuse / Reclamation2,3472,428

Total37,11837,946

Scarcity1,594890

RegionBCRWMSWM

Upper Sacramento Valley353429

Lower Sacramento & Delta212166166

San Joaquin and Bay Area394358333

Tulare Lake Basin461434415

Southern California307418551838

TOTAL417628472780

Total Cost chart

1.59572896532.5805772387

0.27872916822.5682313456

0.19964605152.5803197662

Scarcity

Operating

Deliveries

* Adapted from Table ES-3

Deliveries (taf/yr)AGBCRWMSWMRWM-BCSWM-BC

Demand RegionBCRWM-BCSWM-BCBCRWMSWM

CVPM 1153-10153152153Reg 1343434213577-13143

CVPM 26404757640687697Reg 254205428542888

CVPM 31543786154315501629Reg 352595259525900

CVPM 41098-660109810321098Reg 4954894579749-91201

CVPM 5173700173717371737Reg 5340630123013-394-393

CVPM 6104800104810481048270672657727026-490-41

CVPM 756500565565565

CVPM 889400894894894RWMSWM

CVPM 9117688117611841184Upper Sac-13143

CVPM 10169800169816981698Tulare Basin-91201

CVPM 1186700867867867Southern California-394-393

CVPM 1280300803803803

CVPM 13189100189118911891

CVPM 14149700149714971497URBANRWM-BCSWM-BC

CVPM 151983-65-11198319181972Reg 21818

CVPM 16498-5-2498493496Reg 31616

CVPM 17836-14-8836822828Reg 44240

CVPM 18193854222193819922160Reg 5597669

CVPM 19957-380957919957

CVPM 2067700677677677RWMSWM

CVPM 211162-230116211391162Tulare Basin318321

Palo Verde661-114-113661547548Southern California8781013

Coachella195-14-14195181181

Imperial2550-266-266255022842284

Total Agriculture27067-490-41270672657727026

Yuba5211525353

Napa-Solano1051010105115115

Contra Costa13500135135135

East Bay MUD29077290297297

Sacramento67900679679679

Stockton9500959595

San Francisco23266232238238

Santa Clara Valley6461010646656656

SB-SLO13900139139139

Fresno3384240338380378

Bakersfield26100261261261

Castaic Lake44757944119123

Antelope Valley1868791186273277

Coachella348104103348452451

Mojave*225127127225352352

San Bernardino27904279279283

Central MWD3534152197353436863731

E & W MWD7062634706732740

San Diego9542634954980988

Total Urban9246674744924699209990

Ag Delivery chart

-13143

-91201

-394-393

RWM

SWM

Urban Delivery chart

318321

8781013

RWM

SWM

Sc. costs

Ag RegionBase CaseRegional UnconstrainedStatewide UnconstrainedUrban regionBase CaseRegional Water MarketsStatewide Water Markets

CVPM 100.20Regions 1 & 2

CVPM 23.50.20Yuba0.900

CVPM 33.12.90Napa2200

CVPM 402.10Contra Costa0.100

CVPM 5000East Bay MUD12.50.60.6

CVPM 6000Sacramento000

CVPM 7000Stockton0.100

CVPM 8000Regions 3 & 4

CVPM 90.200San Luis Obispo000

CVPM 10000San Francisco5.100

CVPM 11000Fresno17.700.7

CVPM 12000Bakersfield000

CVPM 13000Santa Clara Valley10.200

CVPM 14000Region 5: LA

CVPM 150.42.90.8Castaic Lake507.85.12.7

CVPM 1600.10San Bernardino3.52.20

CVPM 1700.40.2E & W MWD32.76.90

CVPM 1818.810.40Central MWD183.436.60.1

CVPM 1902.50Antelope Valley185.23.30

CVPM 20000Region 5: SD & Desert

CVPM 2101.40San Diego34.77.40

Palo Verde1.46.96.9Coachella367.4165166.1

Coachella00.90.9Mojave180.700

Imperial4.320.520.5

Total31.751.329.3Total1858.6227.1170.2

BCRWMSWMBCRWMSWM

US6.65.40Lower Sac Valley35.60.60.6

LS0.200Bay Area15.300

SJ000Tulare Basin17.700.7

Tu19.217.71Southern California1495.4226.5168.9

SC5.728.328.3

BCRWMSWMRWMSWM

Upper Sac Valley6.65.40Lower Sac Valley-35-35

Tulare Basin19.217.71Bay Area-15.3-15.3

Southern California5.728.328.3Tulare Basin-17.7-17

Southern California-1268.9-1326.5

Ag Scarcity chart

6.65.40

19.217.71

5.728.328.3

BC

RWM

SWM

Urb Scarcity Costs

35.60.60.6

15.300

17.700.7

1495.4226.5168.9

BC

RWM

SWM

The importance of marginal values and spatial equilibriumMarginal changes in water allocation and management must be evaluated using marginal measures of value.Models of spatial equilibrium have conditions which balance the marginal profitability conditions of water between regions and usesIn CALVIN, the marginal values are measured in terms of the productive uses of water at each of the demand nodes. Underlying marginal values are production decisions which balance the marginal value productivity of water across crops and months.Optimal CALVIN runs are in spatial equilibrium since water cannot be reallocated without violating a constraint or reducing the overall economic value of Californias water.

The Spatial information in CALVIN CALVIN explicitly defines the constraints and conveyance costs that constrain the movements of water across space. The shadow values measure the marginal cost of constraints. Calvin has the willingness-to-pay explicitly represented for each node.The gainers and losers from trades are clearly identified by location and sector

MARGINAL VALUES OF WATER

Mono-Owens is always high because of high value fixed head hydropower on the LAA system

Willingness-to-Pay

Practical Impediments to Water TradesThird party economic impacts in the exporting regionsDefining the tradeable quantities of water by the consumptive use of applied waterAvoiding negative environmental impacts from wheeling traded water or changing the type and location of use.

Using CALVIN to Measure Third party Economic Impacts CALVIN is optimized for a base condition, and an optimal trade condition.Urban benefits from trades are immediately shown by comparing the net benefits at urban nodes.Agricultural effects are measured by Post-optimality analysis using SWAP. CALVIN traded water allocations are fed back into SWAP which then estimates the change in regional crop production caused by the trade.Regional income and employment multipliers are used to measure the community effects of the change in production.

Defining Tradeable Water QuantitiesCALVIN tries to explicitly measure consumptive use and return flows.The net change in consumptive use by region and water use is calculated.CALVIN only proposes trades in which the change in return flows do not violate environmental constraints.

SCal trade

-114

-14

-266

75

87

104

127

0

152

26

26

TAF/ Yr

Regional Trade Quantities- S Cal

Trade2

-114

-14

-266

75

87

104

127

152

26

26

TAF/Yr

Quantities Traded - S California

Sheet1

CalvinS CalTrade

ExportersBase QTraded

Palo Verde661-114

Coachella-Ag195-14

Imperial2550-266

ImportersCastaic4475

Antelope18687

Coachella-Ur348104

Mojave225127

Central MWD3534152

E&W MWD70626

San Diego95426

Sheet2

Sheet3

Measuring Wheeling Costs and ConstraintsIn calculating the value of water trades, CALVIN accounts for wheeling costs and constraintsConstraints on wheeling water often limit trades, CALVIN shows the marginal shadow values of such constraints.In proposing trades, CALVIN not only identifies the buyer and seller, but shows how the water can optimally be wheeled between the buyer and seller in a particular month and for a water year type.

Conclusions on Marginal Value and TradeWater allocations and adjustments occur on the margin accordingly, marginal values- not average values- must be used to calculate efficient allocations.CALVIN optimal results suggest potentially valuable water trades that take into account all the costs and constraints on the system.By post optimality analysis CALVIN can measure and adjust for the main third party effects of water trades.

Conjunctive Use andOperational ChangesPresented by Mimi Jenkins

OverviewRole of GW in CaliforniaConjunctive Use Operations & Changes in CALVINOperational ChangesSacramento Valley Conjunctive Use Potential ImpactsSome LimitationsImplications

GW in California30-40% of Californias supplies in average yearsMore groundwater use in dry yearsTotal storage capacity = 850 MAF Largely unmanaged

GW in CALVINGW Resources:28 GW basinsFixed inflowsEconomic Drivers: Economic values for water useOperating costs of using water sourcesOperating Constraints:Ending storage set to Base Case (no additional mining)Pumping capacitiesOther capacities

Statewide Reliance on GW and CU

Average Monthly % GW Supply

Statewide Groundwater Storage

Operational Changes in CALVINQuality exchanges in Sac Valley, & between SJ River & Bay AreaSac Valley CU OperationsRegional operation of Bay Area resourcesReduced Delta exports with South-of-Delta re-operations (Region 3, 4 and 5)Increased Ag-Ag & Ag-Urban transfers in Tulare Basin to increase CU and eliminate scarcitiesMojave River Basin GW banking operationsSouthern California Ag-Urban & Urban-Urban transfers, increased CU operations

Sacramento Valley Conjunctive Use

Sacramento Valley Re-operationsPrincipal Demands:Upper Sacramento Valley Ag (CVPM 1-4)Lower Sacramento Valley Ag (CVPM 6-8)Lower Sacramento Valley Urban (Greater Sac Area)

Sacramento River Diversions

American River Diversions

Groundwater Pumping

Sac Valley CU Impacts & OutcomesSurplus Delta outflow up in drought years, slightly down in non-drought years, seasonal shift uncertainDrought year diversions down - 430 taf on Sac R., 228 taf on Amer. R.More flexibility to manage instream flows on Sac and American R. and in Delta Reduced opportunity costs of environmental flows$10 M/yr reduced operating costs (CVPM 7, 8 and Greater Sac Urban)$42 M/yr reduced scarcity costs

Some Limitations of ResultsMinimum GW pumping for Ag demandsCapacity for Folsom S. Canal supply to CVPM 8Dynamic stream-aquifer interactionsVariable head pumping costsYear-type variation in Ag & Urban demands

ImplicationsGW can serve both seasonal & drought demandsOptimized GW doesnt necessarily drain basinsEconomics & markets can help us better employ GWOptimization models can suggest promising conjunctive use solutionsConjunctive use can substantially reduce need dry year diversions from streamsConjunctive use can ease conflicts with environmental requirements and operations

Conclusions and Implications

Conclusions from ResultsSome qualitative policy conclusions:a) Regional or statewide markets have great potential to reduce water scarcity costs.b) Economically efficient local and regional management reduces demands for imports. c) Environmental flows have economic costs for agricultural, urban, & other activities. d) Economic values exist for expanded facilities.

e) Some scarcity is optimal.f) Economically optimal water reallocations are very limited, but reduce scarcity and scarcity costs considerably. g) Integrated local, regional, and statewide operation of water decreases competition with environmental uses.

Policy and Planning Implications

Optimization works and shows promise.

Significant new capabilities:Statewide and regional analysisEconomic and engineering analysisExplicitly integrated operationsTransparent operationsSuggests new management optionsTake the good, but remember the limitations.

Implications (continued)

Any regional & statewide analysis needs to:

Improve current dataCentral Valley hydrology and demandsAgricultural and urban water useTulare BasinModernize data management (software and institutions)Coordinate & extend data

Implications (continued)

CALVIN must graduate from the University.Most uses and data are outside the UniversityWere happy to help others use this capabilityModels shouldnt get tenure.

CALVIN is just a tool to help: Make better sense of a complex systemDevelop ideas for water management

Why do modeling? Need analytical ability to provide convincing ideas.

Uses for CALVIN?

Integrated statewide supply and demand accounting & data frameworkPreliminary economic evaluationLong-term statewide water planningPlanning & operations studies: Facility expansion, Joint operations, Conjunctive use, & Water transfers5) Suggest new management options6) No panacea, but a step along the way.

Continuing Work: CurrentClimate Change StudyEconomic costs and benefits of different Delta Export levelsAdd hydropower and flood control benefitsFaster, more flexible solverReasonable foresightFixing little things

Continuing Work: EnvisionedImprovements in economic water demandsImprovements in environmental demandsPolicy studies (catastrophe response, water transfers, new facilities, conjunctive use, environmental flows, etc. ...)More detailed regional studies (Bay Area)

ThemesEconomic scarcity should be a major indicator for Californias water performance.Water resources, facilities, and demands can be more effective if managed together, especially at regional scales. The range of hydrologic events is important, not just average and drought years.Newer methods, data, and software, including optimization, support more transparent and efficient management.

More Information ...Web site:cee.engr.ucdavis.edu/faculty/lund/CALVIN/

TIME SERIES of MONTHLY:

Objectives of the CALIBRATIONGeneral purpose was to reconcile data from disparate sources

More specifically are the points listed in slide.

Point 3 is: essentially makes CALVIN match groundwater in CVGSM NAA and surface water in DWRSIM Run 514 at the same time

NOTE: BASE CASE refers to a combination of CVPIA PEIS run NAA, and DWRSIM Run 514Isolate calibration parameters from more physically based parameters in the CALVIN modelDifference between CVGSM for Region 4 (Tulare Basin, CVPM 14-21) and CALVIN calibrated is about 450 taf/yr more long-term depletion of GW.- CVGSM NAA indicates 143 taf/yr avg. long-term recovery- our best calibrated results are 300 taf/yr avg. long-term depletion

Data problems in Region 4 (Tulare Basin) reduce confidence in CVGSM results and make this area particularly difficult to calibrate. the calibration exercise has identified fundamental and potentially significant inconsistencies and uncertainties in the available and commonly used hydrologic and water demand data. Such inconsistencies are not surprising given that most of these data were not developed to be consistent with active and integrated surface, groundwater, and water demand management. Additional hydrologic and modeling data development clearly is needed, as

BIG Uncertainty in modeling CU and GW in Tulare Basin discrepancy of over 500 taf/yr in estimates of long-term change in GW storage in the region.

identifying important data gaps and inconsistencies

IN MY PRESENTATION TODAY, ID LIKE TOSTART w/ some background on the role of GW and aquifers in California,

AND REVIEW how GW and CU are represented in CALVIN

2) THEN take a look at RESULTS FIRST AT the changes in CU that occur under the ECONOMICALLY-DRIVEN Unconstrained CALVIN RUNS, at both regional and statewide scales.

3) WE WILL then REVIEW some of the more promising operational changes that occur in CALVIN across the state

4) For the second half of the presentation, I WILL FOCUS ON the Sacramento Valley, and THE INTERESTING OPERATIONAL CHANGES that occur with increased conjunctive use management in this area

5) WE WILL ALSO EXAMINE some POTENTIAL impacts of this increased CU, PARTICULARLY for environmental demands on the American and SAC RIVERS, and in the Delta

6) THERE ARE SOME limitations PARTICULAR TO these results THAT I WILL POINT OUT7) FINALLY, WILL CONCLUDE with some implications

SO how does CALVIN manage CONJUNCTIVE USE and OPERATED GW???

CALVIN jointly OPERATES GW RESOURCES OVER THE 1922-93 HISTORIC PERIOD, TO OPTIMIZE PUMPINC AND RECHARGE DECISIONS IN CONJUNCTION WITH ALL OTHER WATER ALLOCATION AND STORAGE DECISIONS IN THE NETWORK.

GW OPERATIONS ARE DRIVEN BY ECONOMIC VALUES, considering the OPERATING COSTS and AVAILABILLTY of other resources IN THE MODEL. THESES DECISIONS are ALSO SUBJECT TO CAPACITY CONSTRAINTS and NO ADDITIONAL MINING BEYOND the BASE CASE.

GW Resources:FIXED INFLOWS consist of interbasin flows, various recharge sources, & stream-aquifer gainsAs explained this morning, GW resources are calibrated to CVGSM in Central Valley

Economic Drivers are the values for ag and urban water use

Operating costs for different water sources include pumping, treatment, local distribution, water quality,conveyance and other such costs of using different water sources

Other storage and conveyance capacities

Figure shows the frequency (ACROSS THE BOTTOM OF THE CHART) of different levels of groundwater use statewide (SHOWN IN % along the VERTICAL AXIS), comparing Base Case with the Regional and Statewide Unconstrained Alternatives.

Statewide, the median groundwater use is about 33% of total water deliveries for all THREE ALTERNATIVES.

In wet years, this can drop to as low as about 16-22%, and in dry years it can increase to as high as about 56%.

In GENERAL THE CHART SHOWS that economically-based operations tend to use GW far more conjunctively than in the Base Case, with greater variation in groundwater use between years.

WE can see that under water markets groundwater is used, in conjunction with surface water, for over-year storage to a greater extent than the Base Case.

THE DIFFERNCE is most pronounced between the BC and Regional WM case.

With a statewide water market, conjunctive use appears to increase only somewhat more.

On a monthly or seasonal basis (Figure), the regional water market decreases average groundwater pumping during the wet months of January and February and increases average pumping during the drier months (July and August).

This seasonal trend is somewhat greater with a statewide water market.

changes in surface and groundwater use improved supply reliability to users and/or decreased operating costs (related to delivery and urban water quality). There are examples of improved conjunctive use operations that involve urban and agricultural transfers as well as agricultural to agricultural transfers.

Here is a list of some of the more promising operational changes that come out of CALVIN.

Many more. THESE are some of the more interesting and significant operational changes that occur in the economically driven unconstrained CALVIN runs.

Under the statewide unconstrained alternative, the area of the state south of the Delta experiences significant changes in conveyance and reservoir operations. These changes are driven by both agricultural-to-urban transfers and through re-operation of the SWP and CVP facilities, which export water from the Delta to the Bay Area, agricultural users in the San Joaquin and Tulare Basin portion of the Central Valley, and urban areas of Southern California.

In concert with the changes in California Aqueduct operations, deliveries through the Mendota Pool and the Friant Kern Canal play a greater role in meeting Tulare Basin demands. Friant Kern Canal diversions from Millerton Lake increase by almost 350 taf/yr and Tulare Basin agricultural supplies from the Mendota Pool increase by 81 taf/yr. Since these increased flows reduce water to the San Joaquin River system, the Delta Mendota Canal increases supplies to San Joaquin River users through the Mendota Pool. Ultimately, about 440 taf/yr of California Aqueduct diversions to the Tulare Basin Region are replaced with water from the San Joaquin system.

THE * refers to the focus on the rest of this presentation, where I will present in more detail the interesting changes that occur with CU management in the Sac Valley.TOTAL PIE is about 5,300-5,400 taf/yearGW especially in GW-7 and GW-8Reducing ag and urban water supply operating costs for the Basin by $10-15 Million/yrNON-DROUGHT YEAR includes normal or wet yearsDROUGHT = 14 dry years spanning the 3 major droughts in CALIFORNIA

In wetter years, more surface water is used than for the Base Case, and in dry years more groundwater is used.

Exchanges of water sources to support the greater conjunctive use suggested by CALVIN are somewhat more extensive in some regions. Some of these exchanges also support urban water quality benefits for the Solano-Napa, Sacramento, Tulare, and Bay areas, as elaborated further in Chapter 4 and the appendices.

Greater conjunctive operation of local, regional, and statewide water resources decreases competition with environmental uses for limited streamflows. This is especially true under critical dry conditions when agricultural and urban reliance on surface flows is significantly reduced from Base Case levels. Under the statewide water market, total diversions from the Sacramento River are reduced on average by 429 taf during drought years with supplies made up by greater use of groundwater. Similarly, American River diversions during droughts are reduced by 228 taf/yr.The Sacramento and American Rivers not only have large minimum instream flow requirements, but also are major water sources shared by many local water users. Figure 4-17 illustrates increased conjunctive operation of Sacramento basin surface and groundwater resources under the statewide water market. The figure also compares Base Case and statewide water market use of the three sources in drought and non-drought years. In both the Base Case and statewide water market during non-drought years (normal and wet), the largest supply source is the Sacramento River, with groundwater pumping a close second and the American River a distant third. However, under optimized statewide operations, Sacramento River in-basin use in non-drought years is higher than in the Base Case, contributing over half of the supply (Table 4-8). Non-drought year diversions from the American River and groundwater pumping are lower than for Base Case operations. During drought years (14 out of the 72-year hydrologic period) the situation is markedly different. While the Base Case obtained a little more than half (53%) of its supply from groundwater during drought years (Figure 4-17), the statewide water market used significantly more groundwater, providing 64% of drought year supply. Simultaneously, withdrawals from the Sacramento and American Rivers drop respectively 430 taf and 228 taf, in the statewide water market compared to Base Case drought year operations (Table 4-8).An important limitation is that minimum groundwater pumping requirements are not imposed in CALVIN. In practice not all agricultural water users in a CVPM region have access to surface water, and some must pump groundwater. Every CVPM region has some minimum amount of groundwater pumping which may not be respected in the CALVIN results.

Overall under the statewide water market, diversions are reduced during drought periods by 1206 taf/yr from non-drought year averages, compared to only 330 taf/yr reduction in Base Case diversions from non- Changes in diversions from the Sacramento and American Rivers under the statewide water market re-operations can have significant consequences for the environmental concerns in the region. In the Base Case, diversions from both the Sacramento and American Rivers are fairly consistent across all years, even during critically dry periods (Figures 4-18 and 4-20). In contrast, under the greater basin-wide conjunctive operations of the statewide water market, diversions are much more variable, depending on hydrologic conditions. They frequently drop much lower than in the Base Case, especially during critically dry periods (Figures 4-19 and 4-21) and rise to higher levels during wet years. In the statewide water market, the Lower Sacramento urban area (Greater Sacramento) completely eliminated diversions from the Sacramento River.

In non-drought years, statewide water market allocations from the Sacramento River increase by 326 taf/yr, on average, over the Base Case while allocations from the American River and groundwater pumping decrease. . These changes in the inter-annual patterns of Sacramento and American River diversions may have other impacts for instream flow conditions (see Other Potential Benefits below).

. Surplus Delta outflow decreases by approximately 52 taf/yr in non-drought years and increase by 214 taf/yr in drought years (Table 4-12). On average surplus Delta outflows decrease by only 1 taf/yr in the statewide water market, . The same seasonal trend appears during drought years, except there is little to no surplus Delta outflow in summer and significantly higher outflow in winter. Thus the increased surplus Delta outflow presented in Table 4-12 in both non-drought and drought years is due to higher winter flows (Nov. to Mar.), rather than increased flow in all months (Figures 4-27 and 4-28).

reduces total exports from the Delta by an average of 360 taf/yr.

Changes in diversions from the Sacramento and American Rivers under the statewide water market re-operations can have significant consequences for the environmental concerns in the region. In the Base Case, diversions from both the Sacramento and American Rivers are fairly consistent across all years, even during critically dry periods (Figures 4-18 and 4-20). In contrast, under the greater basin-wide conjunctive operations of the statewide water market, diversions are much more variable, depending on hydrologic conditions. They frequently drop much lower than in the Base Case, especially during critically dry periods (Figures 4-19 and 4-21) and rise to higher levels during wet years.

These CALVIN model results are idealized in the sense of perfect foresight and do not reflect all considerations, such as hydropower, water temperature, and real time flood control operations. These results are interesting and useful, but not necessarily conclusive from the broader operating context. Aquifer suited for drought storageGroundwater mining has some economic valueGroundwater coordinated with other supplies and demands