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

2. Recent conditions in the Colorado River Basin
Below normal flows into Lake Powell
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.

3. 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

4. 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.

5. 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

6. 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

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

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

9. 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

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

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

12. 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)

13. Window length chosen with LSCV

14. Paleo Conditioned
NHMC with smoothing
500 simulations
60 year length

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

16. No Conditioning
ISM
98 simulations
60 year length

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

18. 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

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

20. UC CRSS stream gauges
LC CRSS stream gauges

21. 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

22. 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

23. Lees Ferry
intervening

24. Cross Correlation
Total sum of intervening

25. Probability Density Function
Lees Ferry
Intervening

26. Probability Density Function
Lees Ferry
Total sum of intervening

27. 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

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

29. 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

30. Hydrologic Sensitivity Runs
4 hydrologic inflow scenarios
Records sampled from a dataset using ISM
Observed flow ( )
99 traces
Paleo flow ( ) (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.

31. ISM-Based Flows Historic natural flow (1906-2004) : averages 15.0 MAF
Paleo reconstruction ( ) : 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

32. 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

33. 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).

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

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

36. 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.

37. 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 ( ). 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.

38. 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.

39. 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.

40. 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

41. 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

42. 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).

43. 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)

44. 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