A Streamflow Generation Technique Under Climate Change Using Paleo and Observational Data for Colorado River Balaji Rajagopalan, Kenneth Nowak University of Colorado, Boulder, CO James Prairie USBR Ben Harding Amec, Boulder Marty Hoerling ESRL/NOAA Hydrology Days, 2008

UC CRSS stream gauges LC CRSS stream gauges Lees Ferry

Recent conditions in the Colorado River Basin Below normal flows into Lake Powell 2000-2004 62%, 59%, 25%, 51%, 51%, respectively 2002 at 25% lowest inflow recorded since completion of Glen Canyon Dam Some relief in 2005 105% of normal inflows Not in 2006 ! 73% of normal inflows Current 2007 forecast 130% of normal inflows Colorado River at Lees Ferry, AZ Explain the use of paleo flows – note that the recent drought is not unprecendented in paleo flows. Has occurred five times in the past. 5-year running average

Paleo Reconstructions observed record Woodhouse et al. 2006 Stockton and Jacoby, 1976 Basic methodology for tree ring reconstruction. Sites, Cores, Chronology, Regression fit on observed period. Proxy information - trees are an integrating variable. Species and location are important to provide appropriate integrators. Over observational period a regression model is fit (typically linear). Then the model is used to project flows into the past. An excellent fit would capture about 80% of the variability. An good reconstruction explains 50% of the variability. Ours explains 84% of the variability Based on this there is variety in reconstructed magnitudes. Lead to a hesitancy in water managers directly using these data. Since it is a discrete variable we require Markov chain. Further the variability over time requires a nonhomogeneous Markov chain, which can capture non stationary TPs Hirschboeck and Meko, 2005 Hildalgo et al. 2002

Paleo reconstructions indicate Past Flow Summary Paleo reconstructions indicate 20th century one of the most wettest Long dry spells are not uncommon 20-25% changes in the mean flow Significant interannual/interdecadal variability Rich variety of wet/dry spell sequences All the reconstructions agree greatly on the ‘state’ (wet or dry) information How will the future differ?

IPCC 2007 AR4 Projections Wet get wetter and dry get drier… Southwest Likely to get drier 6

IPCC 2007 Southwest North America Regional Findings Annual mean warming likely to exceed global mean Western NA warming between 2C and 7C at 2100 In Southwest greatest warming in summer Precipitation likely to decrease in southwest Snow season length and depth very likely to decrease Less agreement on the upper basin climate – important for water generation in the basin Stuff and m 7

National Geographic, Feb 2008 Science, February 1, 2008 8

Colorado River Climate Change Studies over the Years Early Studies – Scenarios, About 1980 Stockton and Boggess, 1979 Revelle and Waggoner, 1983* Mid Studies, First Global Climate Model Use, 1990s Nash and Gleick, 1991, 1993 McCabe and Wolock, 1999 (NAST) IPCC, 2001 More Recent Studies, Since 2004 Milly et al.,2005, “Global Patterns of trends in runoff” Christensen and Lettenmaier, 2004, 2006 Hoerling and Eischeid, 2006, “Past Peak Water?” Seager et al, 2007, “Imminent Transition to more arid climate state..” IPCC, 2007 (Regional Assessments) Barnett and Pierce, 2008, “When will Lake Mead Go Dry?” National Research Council Colorado River Report, 2007 Over 10 studies during last 30 years. One of the most highly studied areas in the country. 2 around 1980 4 in the 1990s and 5 since 2004 plus the NRC report on the Colorado River Stuff and m 9

Study Climate Change Technique (Scenario/GCM) Flow Generation Technique (Regression equation/Hydrologic model) Runoff Results Operations Model Used [results?] Notes Stockton and Boggess, 1979 Scenario Regression: Langbein's 1949 US Historical Runoff- Temperature-Precipitation Relationships +2C and -10% Precip = ~ -33% reduction in Lees Ferry Flow   Results are for the warmer/drier and warmer/wetter scenarios. Revelle and Waggoner, 1983 Regression on Upper Basin Historical Temperature and Precipitation +2C and -10% Precip= -40% reduction in Lee Ferry Flow +2C only = -29% runoff, -10% Precip only = -11% runoff. Nash and Gleick, 1991 and 1993 Scenario and GCM NWSRFS Hydrology model runoff derived from 5 temperature & precipitation Scenarios and 3 GCMs using doubled CO2 equilibrium runs. +2C and -10% Precip = ~ -20% reduction in Lee Ferry Flow Used USBR CRSS Model for operations impacts. Many runoff results from different scenarios and sub-basins ranging from decreases of 33% to increases of 19%. Christensen et al., 2004 GCM UW VIC Hydrology model runoff derived from temperature & precipitation from NCAR GCM using Business as Usual Emissions. +2C and -3% Precip at 2100 = -17% reduction in total basin runoff Created and used operations model, CRMM. Used single GCM known not to be very temperature sensitive to CO2 increases. Hoerling and Eischeid, 2006 Regression on PDSI developed from 18 AR4 GCMs and 42 runs using Business as Usual Emissions. +2.8C and ~0% Precip at 2035-2060 = -45% reduction in Lee Fee Flow Christensen and Lettenmaier, 2006 UW VIC Hydrology Model runoff using temperature & precipitation from 11 AR4 GCMs with 2 emissions scenarios. +4.4C and -2% Precip at 2070-2099 = -11% reduction in total basin runoff Also used CRMM operations model. Other results available, increased winter precipitation buffers reduction in runoff. 10

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A PDF of model outputs is not a PDF of the future. 12

Models Precip and Temp Biases Models show consistent errors (biases) Western North America is too cold and too wet Weather models show biases, too Can be corrected 13

Christensen & Lettenmaier, 2006 Colorado River Projections - Mean Results 11AR 4 Models, 2 Scenarios B1(Low) & A2 (High) Very different results from C&L, 2004 Increased Winter Precipitation important Caveats: Does hydrology model understate summer drying? Means can be deceptive   P1 = 2010-2039 P2 = 2040-2069 P3 = 2070-2099 B1 A2 Comments Temperatures 1.28 1.23 2.05 2.56 2.74 4.35 in C Precipitation -1% -2% Relative to Historic Run SWE -15% -13% -25% -21% -29% -28% Runoff 0% -7% -6% -8% -11% 14

The best information that can be used is the projected mean flow Future Flow Summary Future projections of Climate/Hydrology in the basin based on current knowledge suggest Increase in temperature with less uncertainty Decrease in streamflow with large uncertainty Uncertain about the summer rainfall (which forms a reasonable amount of flow) Unreliable on the sequence of wet/dry (which is key for system risk/reliability) The best information that can be used is the projected mean flow

Progression of Data and Models in studies about the influence of climate change on streamflows in the Colorado River Basin 1. Climate Change Data Source 3. Water Supply Operations Model 2. Flow Generation Technique Wet / Dry Spell Sequence General CirculationModel Regression CRSS CRMM Temperature Precipitation Streamflow OR Hydrology Models: NWSRFS VIC PRMS Reservoir storage Hydroelectric power UB Releases Hypothetical Scenarios Stuff and m 16

Motivation 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 Combination (Paleo, Observational and Climate Change projection) Paleo reconstructions are Good at providing ‘state’ (wet or dry) information Poor with the magnitude information Observations are reliable with the state and magnitude Climate change projections have Uncertain sequence and magnitude information Reasonable projections of the mean flow Observed Annual average flow (15MAF) is used to define wet/dry state.

Proposed Approach Modification to Prairie et al. (2008, accepted, WRR) Nonhomogeneous Markov Chain Model on the observed & Paleo data Generate system state Generate flow conditionally (K-NN resampling) f (x_t | S_t) Threshold for Re-sampling based On future mean flow Projection

Source: Rajagopalan et al., 1996 h window = 2h +1 Discrete kernal function Source: Rajagopalan et al., 1996

TP for each year are obtained using the Kernel Estimator Nonhomogenous Markov model with Kernel smoothing (Rajagopalan et al., 1996) TP for each year are obtained using the Kernel Estimator h determined with LSCV 2 state, lag 1 model was chosen ‘wet (1)’ if flow above annual median of observed record; ‘dry (0)’ otherwise. AIC used for order selection (order 1 chosen)

Transition Probabilities

Flow Generation Steps Nonhomogenous Markov Chain Lag-1, 2-state, moving window Markov chain on the Paleo recons Transition probability for each year Select a mean flow from the climate change projections Generate 100-year state sequences from the NHMM transition probabilities (S_t) Divide the observed streamflows into ‘wet’ and ‘dry’ states using this mean flow threshold Conditionally re-sample streamflows from the observations based on the state – i.e., re-sample from the conditional PDF f(x_t | S_t) Repeat steps 3-5, 1000 times to generate multi-century ensembles Compute suite of statistics Drought Length Surplus Length PDF of simulated streamflow Flow statistics (mean, standard deviation, skew, etc.) Using Water Balance model compute the statistics of system risk/reliability

Water Balance Model Storage 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 Area-volume Relationship ET Calculation ET coefficients/month (Max and Min) 0.5 and 0.16 at Powell 0.85 and 0.33 at Mead Average ET coefficient : 0.436 ET = Area * Average coefficient * 12

PDF of generated streamflows 8MAF 10MAF 12MAF

Drought and Surplus Statistics Surplus Length flow Surplus volume Drought Length Threshold (e.g., mean 15MAF) time Drought Deficit

Drought Length Distribution (15MAF threshold) 8MAF 10MAF 12MAF

Surplus Length Distribution (15MAF threshold) 8MAF Observed Paleo 12MAF 8MAF 10MAF 12MAF

Deficit/Shortage Over 100-year traces Without Shortage Criteria With Shortage Criteria

Without Shortage Criteria Probability of Reservoir Drying Up (based on 10000 years of simulation) Without Shortage Criteria With Shortage Criteria

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 mean Are included in the water balance

Years to first drying of the reservoir over a 100-yr period Without Shortage Criteria With Shortage Criteria

Without Shortage Criteria Summary Statistics Without Shortage Criteria 8MAF 10MAF 12MAF AR-1 KNN 12MAF + 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 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 46.16854 46.37274 44.74899 Average Storage (acre-ft) 4,050,848 6,002,170 11,945,284 28,146,154 26,517,321 22,573,823 With Shortage Criteria 8MAF 10MAF 12MAF AR-1 KNN 12+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

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

Summary A flexible, simple and robust framework to combine paleo, observed and climate projection information Streamflow scenarios generated have realistic wet/dry sequences – important for system risk/reliability estimation Coupling these with simple water balance model indicate Increased system risk (reservoir drying, unable to meet demands etc.) during the next century Consistent with estimates from Paleo and Observed data (Prairie et al., 2006) Shortage criteria reduces the system risk for 20-30% reduction in mean flow The scenarios need to be driven through full CRSS model for system wide risk/reliability estimation