Stochastic Nonparametric Framework for Basin Wide Streamflow and Salinity Modeling Application to Colorado River basin Boulder Dendro Workshop James R. Prairie May 14, 2007

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 50% of normal inflows Colorado River at Lees Ferry, AZ 5-year running average Explain the use of paleo flows – note that the recent drought is not unprecendented in paleo flows. Has occurred five times in the past.

Continuing pressures in the basin Evidence of shift in annual cycle of precipitation Regonda et al. 2005; Cayan et al. 2001 Mote, 2003 Links with large-scale climate Hoerling and Kumar, 2003 Trends indicated increased drought conditioned Andreadis and Lettenmaier, 2006 Increasing population growth Growing water demand by M&I Further development of allocated water supply

Motivation How unusual is the current dry spell? How can we simulate stream flow scenarios that are consistent with the current dry spell and other realistic conditions? Key question for this research is how to plan for effective and sustainable management of water resources in the basin? a robust framework to generate realistic basin-wide streamflow scenarios a decision support model to evaluate operating policy alternatives for efficient management and sustainability of water resources in the basin.

Can we provide answers? What is currently possible ISM : captures natural variability of streamflow Only resamples the observed record Limited dataset How can we improve ? Improve stochastic hydrology scenarios Incorporate Paleoclimate information

How do we accomplish this? Proposed framework Robust space-time disaggregation model central component of all these sections. Incorporating Paleoclimate Information Combine observed and paleostreamflow data Colorado River decision support system Colorado River Simulation System (CRSS) Provides means policy analysis

Flowchart of study Streamflow Generation Combining Observed And Paleo Reconstructed Data Nonparametric Space-Time Disaggregation Decision Support System

Flowchart of study Streamflow Generation Combining Observed And Paleo Reconstructed Data Nonparametric Space-Time Disaggregation Decision Support System

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

Simulation flowchart Nonhomogeneous Markov model Generate system state Generate flow conditionally (K-NN resampling)

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

Nonhomogenous Markov model with Kernel smoothing (Rajagopalan et al 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)

Window length chosen with LSCV

Paleo Conditioned NHMC with smoothing 500 simulations 60 year length

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

No Conditioning ISM 98 simulations 60 year length

Paleo Conditioned NHMC with smoothing 2 states 500 simulations 60 year length

Conclusions Combines strength of Reconstructed paleo streamflows: system state Observed streamflows: flows magnitude Develops a rich variety of streamflow sequences Generates sequences not in the observed record Generates drought and surplus characteristic of paleo period TPM provide flexibility Nonhomogenous Markov chains Nonstationary TPMs Use TPM to mimic climate signal (e.g., PDO) Generate drier or wetter than average flows

Flowchart of study Streamflow Generation Combining Observed And Paleo Reconstructed Data Nonparametric Space-Time Disaggregation Decision Support System

UC CRSS stream gauges LC CRSS stream gauges

Disaggregation scheme Colorado River at Glenwood Springs, Colorado Colorado River near Cameo, Colorado San Juan River near Bluff, Utah Colorado River near Lees Ferry, Arizona 1 2 3 4 5 6 7 8 9 100 11 122 17 18 19 20 temporal disaggregation annual to monthly at index gauge spatial disaggregation monthly index gauge to monthly gauge Index gauge Lees Ferry

Proposed Methodology Resampling from a conditional PDF With the “additivity” constraint Where Z is the annual flow X are the monthly flows Or this can be viewed as a spatial problem Where Z is the sum of d locations of monthly flows X are the d locations of monthly flow Annual stochastic flow modified K-NN lag-1 model (Prairie et al., 2006) 500 annual simulations Joint probability Marginal probability Prairie et al., 2006

Lees Ferry intervening

Cross Correlation Total sum of intervening

Probability Density Function Lees Ferry Intervening

Probability Density Function Lees Ferry Total sum of intervening

Conclusions A flexible, simple, framework for space-time disaggregation is presented Eliminates data transformation Parsimonious Ability to capture any arbitrary PDF structure Preserves all the required statistics and additivity Easily be conditioned on large-scale climate information Can be developed in various scheme to fit needs View nonparametric methods as an additional stochastic view of data set Adds to ISM and parametric methods

Flowchart of study Streamflow Generation Combining Observed And Paleo Reconstructed Data Nonparametric Space-Time Disaggregation Decision Support System

Colorado River Simulation System (CRSS) Requires realistic inflow scenarios Captures basin policy Long-term basin planning model Developed in RiverWare (Zagona et al. 2001) Run on a monthly time step

Hydrologic Sensitivity Runs 4 hydrologic inflow scenarios Records sampled from a dataset using ISM Observed flow (1906-2004) 99 traces Paleo flow (1490-1997) (Woodhouse et al., 2006) 508 traces Other Paleo conditioned (Prairie, 2006) 125 traces Parametric stochastic (Lee et al., 2006) 100 traces All 4 inflow scenarios were run for each alternative Describe the basics of each alternative. Will give more detail in slides to come.

ISM-Based Flows Historic natural flow (1906-2004) : averages 15.0 MAF Paleo reconstruction (1490-1997) : averages 14.6 MAF Lees B from Woodhouse et al., 2006 5-year running average Indicate 5 times increase in data from paleo reconstruction. Improves frequency analysis of drought occurrence. Current 5 year drought unprecedented in historic observed natural flow

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

Alternate Stochastic Techniques Paleo conditioned Combines observed and paleo streamflows Generates Observed flow magnitudes Flow sequences similar to paleo record Parametric Fit observed data to appropriate model (i.e., CAR) Flow magnitudes not observed Flow sequences similar to observed record Describe basics. Paleo conditioned flow aims to pull strengths from the observed and paleo records. Strengths: Can easily explain this method. Preserves the data distribution of the NF yet generates both drought and surplus sequences longer than those in the observed record. Can reproduce non-Normal distributions Weakness: can not generate values beyond those in the observed record. Move to next slide which shows weakness of reconstructions (magnitudes) and strengths (system state).

CRSS Modeling Assumptions – Alternate Hydrologic Sequences Index Sequential Method & Alternate Stochastic Techniques Alternate Hydrologic Sequences & Results

Boxplots of Basic Statistics Observed Direct Paleo Paleo Conditioned Parametric Point out differences among methods when viewing the basic statistics.

Annual Natural Flow at Lees Ferry No Action Alternative Years 2008-2060 Flow duration curve of natural flow at Lees Ferry. Point out what was seen in the previous boxplots with actual data in present plot. PS has the highest flows (much higher than any others) while the DP has the lowest flows followed closely by PS. NPC follows closely with observed as these exhibit the same data distribution.

Lake Powell End of July Elevations No Action Alternative 10th, 50th and 90th Percentile Values Longest droughts and surplus are generated by the nonparametric paleo conditioned. This accounts for the lower elevations in the initial years (2014-2027). Increased variability of percentiles at the 10% level is due to sensitivity of inflows when the reservoir is a low elevations versus less sensitivity when reservoir is at higher elevations. DNF has highest mean flow, while DP has lowest mean flow as seen in 10th percentile. The variability observed in the NPC and PS is due to sample variability which is greatly reduced in ISM based methods because each trace only varies by on year of data. Increase sample sizes, on the order of possible 500 traces would smooth out the variability seen in NPC and PS.

Lake Mead End of December Elevations No Action Alternative 10th, 50th and 90th Percentile Values Note the 10th percentile has lower variability than observed at Powell. This results from the minimum objective release providing a flow of 8.23 at least 10 percent of the time and Shortage criteria is absolutely protecting Mead at 1000 ft.

Glen Canyon 10-Year Release Volume No Action Alternative Years 2008-2060 Largest release from the PS method followed by the NPC while the NPC showed the lowest release followed by the PS. This slide exhibits the influence of flow sequence. Even though the NPC does not have the lowest flows in any given year (DP does) it does have the ability to generate the greatest variability in sequences exhibits how sequences of low flow.

Final statements Integrated flexible framework Simple Robust Parsimonious Easily represents nonlinear relationship Effective policy analysis requires use of stochastic methods other than ISM Presented framework allows an improved understanding for operation risks and reliability Allows an understanding of climate variability risks based on paleo hydrologic state information

Future direction Alternate annual simulation models (parametric, semi parametric) Include correlation from first month and last month Apply hidden Markov model Explore additional policy choice. Optimization framework to include economic benefits Can easily consider climate change scenarios using climate projections to simulate annual flow

Major Contributions Prairie, J.R., B. Rajagopalan, U. Lall, T. Fulp (2006) A stochastic nonparametric technique for space-time disaggregation of streamflows, Water Resources Research, (in press). Prairie, J.R., B. Rajagopalan, U. Lall, T. Fulp (2006), A stochastic nonparametric approach for streamflow generation combining observational and paleo reconstructed data, Water Resources Research, (under review). Prairie, J.R., et al. (2006) Comparative policy analysis with various streamflow scenarios, (anticipated).

Additional Publications Prairie, J.R., B. Rajagopalan, T.J. Fulp, and E.A. Zagona (2006), Modified K-NN Model for Stochastic Streamflow Simulation, ASCE Journal of Hydrologic Engineering, 11(4) 371-378.

Acknowledgements To my committee and advisor. Thank you for your guidance and commitment. Balaji Rajagopalan, Edith Zagona, Kenneth Strzepek, Subhrendu Gangopadhyay, and Terrance Fulp Funding support provided by Reclamation’s Lower Colorado Regional Office Reclamation’s Upper Colorado Regional Office Kib Jacobson, Dave Trueman Logistical support provided by CADSWES Expert support provided from Carly Jerla, Russ Callejo, Andrew Gilmore, Bill Oakley