A Streamflow Generation Technique A Streamflow Generation Technique Under Climate Change Using Paleo Under Climate Change Using Paleo

and Observational Data for Colorado and Observational Data for Colorado RiverRiver

Balaji Rajagopalan, Kenneth NowakBalaji Rajagopalan, Kenneth NowakUniversity of Colorado, Boulder, COUniversity of Colorado, Boulder, CO

James PrairieJames PrairieUSBRUSBR

Ben HardingBen HardingAmec, BoulderAmec, Boulder

Marty HoerlingMarty HoerlingESRL/NOAAESRL/NOAA

Hydrology Days, 2008Hydrology Days, 2008

UC CRSS stream gauges

LC CRSS stream gauges

Lees Ferry

Colorado River at Lees Ferry, AZ

Recent conditions in the Recent conditions in the Colorado River BasinColorado River Basin

Below normal flows into Below normal flows into Lake Powell 2000-2004Lake Powell 2000-2004 62%, 59%, 25%, 51%, 62%, 59%, 25%, 51%,

51%, respectively51%, respectively 2002 at 25% lowest 2002 at 25% lowest

inflow recorded since inflow recorded since completion of Glen completion of Glen Canyon DamCanyon Dam

Some relief in 2005 Some relief in 2005 105% of normal inflows105% of normal inflows

Not in 2006 !Not in 2006 ! 73% of normal inflows73% of normal inflows

Current 2007 forecastCurrent 2007 forecast 130% of normal inflows130% of normal inflows

5-year running average

observed record

Woodhouse et al. 2006

Stockton and Jacoby, 1976

Hirschboeck and Meko, 2005

Hildalgo et al. 2002

Paleo Reconstructions

Past Flow SummaryPast Flow Summary

Paleo reconstructions indicatePaleo reconstructions indicate 2020thth century one of the most wettest century one of the most wettest Long dry spells are not uncommonLong dry spells are not uncommon 20-25% changes in the mean flow20-25% changes in the mean flow Significant interannual/interdecadal variabilitySignificant interannual/interdecadal variability Rich variety of wet/dry spell sequencesRich variety of wet/dry spell sequences

All the reconstructions agree greatly on the ‘state’ All the reconstructions agree greatly on the ‘state’ (wet or dry) information(wet or dry) information

How will the future differ?How will the future differ?

IPCC 2007 AR4 ProjectionsIPCC 2007 AR4 Projections Wet get wetter and dry get drier…Wet get wetter and dry get drier… Southwest Likely to get drierSouthwest Likely to get drier

IPCC 2007 Southwest North IPCC 2007 Southwest North America Regional FindingsAmerica Regional Findings

Annual mean warming likely to exceed Annual mean warming likely to exceed global meanglobal mean

Western NA warming between 2C and 7C at Western NA warming between 2C and 7C at 21002100

In Southwest greatest warming in summerIn Southwest greatest warming in summer Precipitation likely to decrease in southwestPrecipitation likely to decrease in southwest Snow season length and depth very likely to Snow season length and depth very likely to

decreasedecrease Less agreement on the upper basin climate – Less agreement on the upper basin climate –

important for water generation in the basinimportant for water generation in the basin

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Science, February 1, 2008

National Geographic, Feb 2008

Colorado River Climate Change Colorado River Climate Change Studies over the Years Studies over the Years

Early Studies – Scenarios, About 1980Early Studies – Scenarios, About 1980 Stockton and Boggess, 1979 Stockton and Boggess, 1979 Revelle and Waggoner, 1983*Revelle and Waggoner, 1983*

Mid Studies, First Global Climate Model Use, 1990sMid Studies, First Global Climate Model Use, 1990s Nash and Gleick, 1991, 1993Nash and Gleick, 1991, 1993 McCabe and Wolock, 1999 (NAST)McCabe and Wolock, 1999 (NAST) IPCC, 2001IPCC, 2001

More Recent Studies, Since 2004More Recent Studies, Since 2004 Milly et al.,2005, “Global Patterns of trends in runoff”Milly et al.,2005, “Global Patterns of trends in runoff” Christensen and Lettenmaier, 2004, 2006Christensen and Lettenmaier, 2004, 2006 Hoerling and Eischeid, 2006, “Past Peak Water?”Hoerling and Eischeid, 2006, “Past Peak Water?” Seager et al, 2007, “Imminent Transition to more arid climate state..”Seager et al, 2007, “Imminent Transition to more arid climate state..” IPCC, 2007 (Regional Assessments)IPCC, 2007 (Regional Assessments) Barnett and Pierce, 2008, “When will Lake Mead Go Dry?”Barnett and Pierce, 2008, “When will Lake Mead Go Dry?”

National Research Council Colorado River Report, 2007National Research Council Colorado River Report, 2007

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StudyStudy Climate Climate Change Change Technique Technique (Scenario/GC(Scenario/GCM)M)

Flow Generation Technique Flow Generation Technique (Regression (Regression equation/Hydrologic model)equation/Hydrologic model)

Runoff ResultsRunoff Results Operations Model Operations Model Used [results?]Used [results?]

NotesNotes

Stockton Stockton and and Boggess, Boggess, 19791979

ScenarioScenario RegressionRegression: Langbein's 1949 US : Langbein's 1949 US Historical Runoff- Temperature-Historical Runoff- Temperature-Precipitation RelationshipsPrecipitation Relationships

+2C and -10% Precip = +2C and -10% Precip = ~ -33% reduction in ~ -33% reduction in Lees Ferry FlowLees Ferry Flow

   Results are for the Results are for the warmer/drier and warmer/drier and warmer/wetter warmer/wetter scenarios.scenarios.

     

Revelle and Revelle and Waggoner, Waggoner, 19831983

ScenarioScenario RegressionRegression on Upper Basin on Upper Basin Historical Temperature and Historical Temperature and PrecipitationPrecipitation

+2C and -10% Precip= +2C and -10% Precip= -40% reduction in Lee -40% reduction in Lee Ferry FlowFerry Flow

   +2C only = -29% +2C only = -29% runoff,runoff,

      -10% Precip only = -10% Precip only = -11% runoff.-11% runoff.

Nash and Nash and Gleick, 1991 Gleick, 1991 and 1993and 1993

Scenario and Scenario and GCMGCM

NWSRFS Hydrology modelNWSRFS Hydrology model runoff derived from 5 runoff derived from 5 temperature & precipitation temperature & precipitation Scenarios and 3 GCMs using Scenarios and 3 GCMs using doubled CO2 equilibrium runs.doubled CO2 equilibrium runs.

+2C and -10% Precip = +2C and -10% Precip = ~ -20% reduction in ~ -20% reduction in Lee Ferry FlowLee Ferry Flow

Used USBR CRSS Used USBR CRSS Model for operations Model for operations impacts.impacts.

Many runoff results Many runoff results from different from different scenarios and sub-scenarios and sub-basins ranging from basins ranging from decreases of 33% to decreases of 33% to increases of 19%. increases of 19%.

Christensen Christensen et al., 2004et al., 2004

GCMGCM UW UW VIC Hydrology modelVIC Hydrology model runoff derived from temperature runoff derived from temperature & precipitation from NCAR & precipitation from NCAR GCM using Business as Usual GCM using Business as Usual Emissions.Emissions.

+2C and -3% Precip at +2C and -3% Precip at 2100 = -17% reduction 2100 = -17% reduction in total basin runoffin total basin runoff

Created and used Created and used operations model, operations model, CRMM.CRMM.

Used single GCM Used single GCM known not to be known not to be very temperature very temperature sensitive to CO2 sensitive to CO2 increases. increases.

Hoerling Hoerling and and Eischeid, Eischeid, 20062006

GCMGCM RegressionRegression on PDSI developed on PDSI developed from 18 AR4 GCMs and 42 runs from 18 AR4 GCMs and 42 runs using Business as Usual using Business as Usual Emissions.Emissions.

+2.8C and ~0% Precip +2.8C and ~0% Precip at 2035-2060 = -45% at 2035-2060 = -45% reduction in Lee Fee reduction in Lee Fee FlowFlow

     

Christensen Christensen and and Lettenmaier, Lettenmaier, 20062006

GCMGCM UW UW VIC Hydrology ModelVIC Hydrology Model runoff using temperature & runoff using temperature & precipitation from 11 AR4 precipitation from 11 AR4 GCMs with 2 emissions GCMs with 2 emissions scenarios.scenarios.

+4.4C and -2% Precip +4.4C and -2% Precip at 2070-2099 = -11% at 2070-2099 = -11% reduction in total basin reduction in total basin runoffrunoff

Also used CRMM Also used CRMM operations model.operations model.

Other results Other results available, increased available, increased winter precipitation winter precipitation buffers reduction in buffers reduction in runoff. runoff.

A PDF A PDF of of model model outputs outputs is not a is not a PDF of PDF of the the future.future.

Models Precip and Temp BiasesModels Precip and Temp Biases

Models show Models show consistent errors consistent errors (biases)(biases)

Western North Western North America is too America is too cold and too wetcold and too wet

Weather models Weather models show biases, tooshow biases, too

Can be correctedCan be corrected

Christensen & Lettenmaier, 2006Christensen & Lettenmaier, 2006Colorado River Projections - Mean ResultsColorado River Projections - Mean Results

11AR 4 Models, 2 Scenarios B1(Low) & A2 (High)11AR 4 Models, 2 Scenarios B1(Low) & A2 (High) Very different results from C&L, 2004Very different results from C&L, 2004 Increased Winter Precipitation importantIncreased Winter Precipitation important Caveats: Does hydrology model understate Caveats: Does hydrology model understate

summer drying?summer drying? Means can be deceptiveMeans can be deceptive

  P1 = 2010-P1 = 2010-

20392039P2 = 2040-P2 = 2040-

20692069 P3 = 2070-2099P3 = 2070-2099   

   B1B1 A2A2 B1B1 A2A2 B1B1 A2A2 CommentsComments

TemperaturesTemperatures 1.281.28 1.231.23 2.052.05 2.562.56 2.742.74 4.354.35 in Cin C

PrecipitationPrecipitation -1%-1% -1%-1% -1%-1% -2%-2% -1%-1% -2%-2% Relative to Historic RunRelative to Historic Run

SWESWE -15%-15% -13%-13% -25%-25% -21%-21% -29%-29% -28%-28% Relative to Historic RunRelative to Historic Run

RunoffRunoff 0%0% 0%0% -7%-7% -6%-6% -8%-8% -11%-11% Relative to Historic RunRelative to Historic Run

Future Flow SummaryFuture Flow Summary Future projections of Climate/Hydrology in Future projections of Climate/Hydrology in

the basin based on current knowledge the basin based on current knowledge suggestsuggest

Increase in temperature with less uncertaintyIncrease in temperature with less uncertainty Decrease in streamflow with large uncertainty Decrease in streamflow with large uncertainty Uncertain about the summer rainfall (which forms a Uncertain about the summer rainfall (which forms a

reasonable amount of flow)reasonable amount of flow) Unreliable on the sequence of wet/dry (which is key Unreliable on the sequence of wet/dry (which is key

for system risk/reliability)for system risk/reliability)

The best information that can be used is The best information that can be used is the projected mean flow the projected mean flow

Temperature Precipitation

General Circulation

Model

Hypothetical Scenarios

Regression

Hydrology Models:NWSRFS

VICPRMS

CRSSCRMM

Reservoir storage Hydroelectric power

UB Releases

1.Climate Change

Data Source

2.Flow Generation

Technique

Wet / Dry Spell Sequence

3.Water Supply Operations

Model

OR

Progression of Data and Models in studies about the influence of climate change on streamflows in the Colorado River Basin

Streamflow

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MotivationMotivation• Recent Dry Spell not unusual, based on Paleo reconstructions• Colorado River System has enormous storage of approx 60MAF ~ 4 times the average annual flow - consequently,

• wet and dry sequences are crucial for system risk/reliability assessment

•Current climate change flow ensembles are poor at generating the wet/dry sequences, summer inflows, and temperature sensitive - using these flows as is leads to

• over estimation of ET• over estimation of demands• over estimation of system risk

•Streamflow generation tool that can generate flow scenarios in the basin that are realistic in

•wet and dry spell sequences•Magnitude

•Need for combining all the available information

Need for CombinationNeed for Combination(Paleo, Observational and Climate Change (Paleo, Observational and Climate Change

projection)projection) Paleo reconstructions arePaleo reconstructions are

Good at providing ‘state’ (wet or dry) informationGood at providing ‘state’ (wet or dry) information Poor with the magnitude informationPoor with the magnitude information

Observations are reliable with the state and magnitudeObservations are reliable with the state and magnitude

Climate change projections haveClimate change projections have Uncertain sequence and magnitude informationUncertain sequence and magnitude information Reasonable projections of the mean flowReasonable projections of the mean flow

Observed Annual average flow (15MAF) is used to define Observed Annual average flow (15MAF) is used to define wet/dry state.wet/dry state.

Generate flow conditionally(K-NN resampling)

),,( 11 tttt xSSxf

Generate system state )( tS

Nonhomogeneous Markov Chain Model on the observed & Paleo

data

Proposed ApproachProposed ApproachModification to Prairie et al. (2008, accepted, WRR)Modification to Prairie et al. (2008, accepted, WRR)

f (x_t | S_t)Threshold for

Re-sampling basedOn future mean flow

Projection

h

window = 2h +1Discrete kernal

function1for)1(

)41(3)( 2

2

xxh

hxK

Source: Rajagopalan et al., 1996

Nonhomogenous Markov model with Kernel Nonhomogenous Markov model with Kernel smoothing (Rajagopalan et al., 1996)smoothing (Rajagopalan et al., 1996)

TP for each year are obtained TP for each year are obtained using the Kernel Estimatorusing the Kernel Estimator

hh determined with LSCV determined with LSCV 2 state, lag 1 model was chosen2 state, lag 1 model was chosen

‘‘wet (1)’ if flow above annual median of wet (1)’ if flow above annual median of observed record; ‘dry (0)’ otherwise.observed record; ‘dry (0)’ otherwise.

AIC used for order selection (order 1 AIC used for order selection (order 1 chosen)chosen)

nd

i dw

d

ndw

i dw

dw

dw

htt

K

htt

KtP

i

i

1

1)( )(1)( tPtP dwdd

Transition ProbabilitiesTransition Probabilities

Flow Generation StepsFlow Generation Steps1.1. Nonhomogenous Markov Chain Nonhomogenous Markov Chain

Lag-1, 2-state, moving window Markov chain on the Paleo reconsLag-1, 2-state, moving window Markov chain on the Paleo recons Transition probability for each yearTransition probability for each year

2.2. Select a mean flow from the climate change projectionsSelect a mean flow from the climate change projections3.3. Generate 100-year state sequences from the NHMM transition Generate 100-year state sequences from the NHMM transition

probabilities (S_t)probabilities (S_t)4.4. Divide the observed streamflows into ‘wet’ and ‘dry’ states using this Divide the observed streamflows into ‘wet’ and ‘dry’ states using this

mean flow thresholdmean flow threshold5.5. Conditionally re-sample streamflows from the observations based on the Conditionally re-sample streamflows from the observations based on the

state – i.e., re-sample from the conditional PDF state – i.e., re-sample from the conditional PDF f(x_t | S_t)f(x_t | S_t)6.6. Repeat steps 3-5, 1000 times to generate multi-century ensemblesRepeat steps 3-5, 1000 times to generate multi-century ensembles7.7. Compute suite of statisticsCompute suite of statistics

Drought LengthDrought Length Surplus LengthSurplus Length PDF of simulated streamflowPDF of simulated streamflow Flow statistics (mean, standard deviation, skew, etc.)Flow statistics (mean, standard deviation, skew, etc.)

8.8. Using Water Balance model compute the statistics of system risk/reliabilityUsing Water Balance model compute the statistics of system risk/reliability

Water Balance ModelWater Balance ModelStorage in any year is computed as: Storage = Previous Storage + Inflow - ET- Demand •Upper and Lower Colorado Basin demand = 13.5 MAF/yr

• Lakes Powell and Mead are modeled as one 50 MAF reservoir

• Initial storage of 30 MAF (i.e., current reservoir content)

• Inflow values are natural flows at Lee’s Ferry, AZ

• ET computed using Lake Area – Lake volume relationship and an average ET coefficient of 0.436

Shortage EIS Criteria:

•When storage reaches less than 36% capacity, demand (release) is reduced by 5%

Combined A/V CurvePowell & Mead

y = 0.0052x + 59097

050000

100000150000200000250000300000350000400000

0 10000000 20000000 30000000 40000000 50000000 60000000

Volume, AF

Area

, Acr

es

Combined Area-volume RelationshipCombined Area-volume RelationshipET CalculationET Calculation

ET coefficients/month (Max and Min)0.5 and 0.16 at Powell0.85 and 0.33 at MeadAverage ET coefficient : 0.436

ET = Area * Average coefficient * 12

PDF of generated streamflows

8MAF 10MAF 12MAF

Threshold

(e.g., mean

15MAF)

Drought Length

Surplus Length

timeDrought Deficit

Drought and Surplus Drought and Surplus StatisticsStatistics

Surplus volumeflo

w

Drought Length Distribution(15MAF threshold)

8MAF 12MAF10MAF

Surplus Length Distribution(15MAF threshold)

8MAF

12MAF10MAF

Observed Paleo 12MAF

8MAF

Deficit/Shortage Over 100-year traces

Without Shortage Criteria

With Shortage Criteria

Without Shortage Criteria

With Shortage Criteria

Probability of Reservoir Drying Up (based on 10000 years of simulation)

Probability of Reservoir Drying in any year over a 100-yr period(including intervening flows)

Flow between Powell and Mead&

Flow below mead(1.07 MAF)

With 12MAF meanAre included in the water balance

Without Shortage Criteria

With Shortage Criteria

Years to first drying of the reservoir over a 100-yr period

Summary Statistics

8MAF 10MAF 12MAF AR-1 KNN12MAF +

interv water

Probability of running reservoir dry 55.574 43.415 22.429 3.142 4.159 7.24

Probability of not meeting full demand 55.574 43.415 22.429 3.142 4.159 7.24

Average Shortage (acre-ft) 5,883,910 4,293,914 3,238,019 3,151,605 3,070,025 2,513,477

For traces in which storage reaches 0; average number of years until first zero storage even occurs (yrs) 9.963 15.265 28.22672

46.1685446.37274 44.74899

Average Storage (acre-ft) 4,050,848 6,002,170 11,945,284 28,146,154 26,517,321 22,573,823

8MAF 10MAF 12MAF AR-1 KNN12+xtra water

Probability of running reservoir dry 51.791 38.442 18.184 2.279 3.198 5.367

Probability of not meeting full demand 71.21 59.857 35.17 6.329 8.175 12.794

Average Shortage 4,605,838 3,136,899 2,117,600 1,724,782 1,699,274 1,527,080

Average Shortage (beyond shortage reduction) 6,079,703 4,508,356 3,465,159 3,590,345 3,293,336 2,706,211

For traces in which storage reaches 0; average number of years until first zero storage even occurs 10.219 16.031 29.84061 48.09465 48.24071 47.18023

Average Storage 4,312,296 6,354,209 12,403,741 28,374,069 26,763,690 22,882,710

Percent of deficits beyond shortage 5% 72.72995 64 51.70316 36.00885 39.11927 41.94935

With Shortage Criteria

Without Shortage Criteria

Lake mead

Lake Powell

Lake Level Risks based on Scenarios from Prairie et al. (2008)With CRSS

SummarySummary A flexible, simple and robust framework to combine paleo, A flexible, simple and robust framework to combine paleo,

observed and climate projection information observed and climate projection information Streamflow scenarios generated have realistic wet/dry sequences Streamflow scenarios generated have realistic wet/dry sequences

– important for system risk/reliability estimation– important for system risk/reliability estimation Coupling these with simple water balance model indicate Coupling these with simple water balance model indicate

Increased system risk (reservoir drying, unable to meet demands etc.) Increased system risk (reservoir drying, unable to meet demands etc.) during the next centuryduring the next century

Consistent with estimates from Paleo and Observed data (Prairie et al., Consistent with estimates from Paleo and Observed data (Prairie et al., 2006) 2006)

Shortage criteria reduces the system risk for 20-30% reduction in Shortage criteria reduces the system risk for 20-30% reduction in mean flowmean flow

The scenarios need to be driven through full CRSS model for The scenarios need to be driven through full CRSS model for system wide risk/reliability estimationsystem wide risk/reliability estimation