Stochastic Nonparametric Framework for Basin Wide Streamflow and Salinity Modeling

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Stochastic Nonparametric Framework for Basin Wide
Streamflow and Salinity Modeling Application to
Colorado River basin Study Progress
Meeting James R. Prairie August 17, 2006
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Recent progress

• Stochastic streamflow conditioned on Paleo Flow
• Non homogenous Markov Chain with Kernel Smoothing
• Estimate lag-1 two state transition probabilities
  for each year using a Kernel Estimator
• Generate Flow State
• Conditionally Generate flow magnitude
• Colorado River Basin Wide flow simulation
• Modify the nonparametric space-time disagg
  approach
• to generate monthly flows at all the 29 stations
  simultaneously
• Flow simulation using Paleo recontructions

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Masters Research Single site Modified K-NN
streamflow generator Climate Analysis Nonparametri
c Natural Salt Model
Stochastic Nonparametric Technique for Space-Time
Disaggregation
Basin Wide Natural Salt Model
Incorporate Paleoclimate Information Streamflow
conditioned on Flow States from Paleo
reconstructions
Policy Analysis Impacts of drought Hydrology Water
quality
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Proposed Methods
Block bootstrap resampling of Paleo flows
Nonhomogeneous Markov model Markov Chain on a
30-yr window
Nonhomogeneous Markov model with smoothing
or
or
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Datasets

• Paleo reconstruction from Woodhouse et al. 2006
• Water years 1490-1997
• Observed natural flow from Reclamation
• Water years 1906-2003

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Addressing previous issues

• Determined order of the Markov model
• used AIC (Gates and Tong, 1976)
• Indicated order 0 (or 1) - we used order 1
• Subjective block length and window for estimating
  the Markov Chain Transition Probabilities
• Nonhomogeneous Markov Chain with Kernel Smoothing
  alleviates this problem (Rajagopalan et al., 1996)

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

• 2 state, lag 1 model chosen
• wet (1) if flow above annual median of observed
  record dry (0) otherwise.
• AIC used for order selection (order 1 chosen)
• TP for each year are obtained
• using the Kernel Estimator

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

• K(x) is a discrete quadratic Kernel (or weight
  function)
• h is the smoothing window obtained objectively
  using
• Least Square Cross Validation

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TPMs without smoothing
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TPMs with smoothing
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Window length chosen with LSCV
3 states
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Simulation Algorithm

• Determine planning horizon
• We chose 98yrs (same length as observational
  record)
• Select 98 year block at random
• For example 1701-1798
• Generate flow states
  for each year of the resampled block using
  their respective TPMs estimated earlier NHMC
• Generate flow magnitudes for each year by
  resampling observed flow using a conditional K-NN
  method
• Repeat steps 2 through 4 to obtain as many
  required simulations

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Advantages over block resampling

• No need for a subjective window length
• i.e., 30 year window was used to estimate the TP
• Obviates the need for additional sub-lengths
  within the planning horizon
• i.e., earlier 3 30-yr blocks were resampled
• Fully Objective in estimating the TPMs for each
  year

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No Conditioning

• ISM
• 98 simulations
• 98 year length

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No Conditioning

• ISM
• 98 simulations
• 60 year length

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Paleo Conditioned

• NHMC with smoothing
• 500 simulations
• 98 year length

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Paleo Conditioned

• NHMC with smoothing
• 500 simulations
• 60 year length

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Drought and Surplus Statistics
Surplus Length
Surplus volume
flow
Drought Length
Threshold (e.g., mean)
time
Drought Deficit
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No Conditioning

• ISM
• 98 simulations
• 98 year length

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Paleo Conditioned

• NHMC with smoothing
• 2 states
• 500 simulations
• 98 year length

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Paleo Conditioned

• Markov chain length
• 31 years
• 2 states
• 500 simulations
• 98 year length

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Sequent Peak Algorithm

• Determine required Storage Capacity (Sc) at
  various demand levels given specified inflows.
• Evaluate risk of not meeting the required Sc

y inflow time series (2x) d demand level S
storage S0 0
if positive
otherwise
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No Conditioning

• ISM
• 98 simulations
• 98 year length

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No Conditioning

• Traditional KNN
• 98 simulations
• 98 year length

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Paleo Conditioned

• NHMC with smoothing
• 500 simulations
• 98 year length

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Paleo Conditioned

• PDF of 16.5 boxplot
• Red hatch represents risk of not meeting 16.5
  demand at a 60 MAF storage capacity

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Paleo Conditioned

• PDF of 16.5 boxplot

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Paleo Conditioned

• NHMC with smoothing
• 500 simulations
• 98 year length

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Paleo Conditioned

• PDF of 13.5 boxplot
• Red hatch represents risk of not meeting 13.5
  demand at a 60 MAF storage capacity

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Paleo Conditioned

• CDF of 13.5 boxplot

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Storage Capacity Firm Yield function

• What is the maximum yield (Y) given a specific
  storage capacity (K) and flow sequence (Qt)?
• Mathematically this can be answered with
  optimization

Maximize Y Subject to
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Paleo Conditioned

• NHMC with smoothing
• 500 simulations
• 98 year length

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• Basic Statistics
• Preserved for observed data
• Note
• max and min constrained in observed

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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
• More variety block bootstrap reconstructed
  streamflows
• Most variety nonhomogeneous Markov chain
• TPM provide flexibility
• Homogenous Markov chains
• Nonhomogenous Markov chains
• Use TPM to mimic climate signal (e.g., PDO)
• Generate drier or wetter than average flows

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Masters Research Single site Modified K-NN
streamflow generator Climate Analysis Nonparametri
c Natural Salt Model
Stochastic Nonparametric Technique for Space-Time
Disaggregation
Basin Wide Natural Salt Model
Incorporate Paleoclimate Information Streamflow
conditioned on Paleo states Streamflow
conditioned with TPM
Policy Analysis Impacts of drought Hydrology Water
quality
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Full basin disaggregation

• Upper basin
• 20 gauges (all above Lees Ferry, including Lees
  Ferry)
• Annual total flow at Lees Ferry modeled with
  modified K-NN
• Disaggregate Lees Ferry nonparametric
  disaggregation
• Results in intervening monthly flows at CRSS
  nodes
• Store the years resampled during the temporal
  disagg
• Lower basin
• 9 gauges (all gauges below Lees Ferry)
• Select the month values for all sites in a given
  year based on the years stored above

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Nonparametric disagg
K-NN years applied
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Advantages

• Paleo-conditioned flows for entire basin
• Upper Basin
• Generate both annual and monthly flows not
  previously observed
• Produces 92 of annual flows above Imperial Dam
• Faithfully reproduces PDF and CDF for both
  intervening and total flows
• Lower Basin
• Produces 8 of annual flows above Imperial Dam
• Preserves intermittent properties of tributaries
• Faithfully reproduces all statistics
• Easily incorporate reconstructions at Lees Ferry

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Disadvantages

• Upper Basin
• Generates negative flows at rim gauges (7 out of
  10 gauges)
• Average of 1.5 negatives over all simulations
  (500 sims)
• Is this important?
• Two largest contributors only produce 2.2
• Can not capture cross over correlation
• (i.e. between last month of previous year and
  first month of the current year)
• Improved in recent run (added a weighted
  resampling)
• Can not generate large extremes beyond the
  observed
• Annual flow model choice
• Using Paleo flow magnitudes
• Lower Basin
• Can only generate observed flows

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• Lees Ferry
• intervening

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• Lees Ferry
• Total sum of intervening

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• Lees Ferry
• Total sum of intervening
• No first month current year with last month
  previous year weighting

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• Cisco
• Total sum of intervening

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• Green River UT
• Total sum of intervening

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• San Juan
• Total sum of intervening

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• San Rafael
• Total sum of intervening
• 1.2 of flow above Lees
• 6 negatives over 500 sims

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Lower Basin

• Resample observed months based on K-NN from Upper
  basin disaggregation

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• Abv Imperial Dam
• Total sum of intervening

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• Little Colorado
• Total sum of intervening

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• Cross Correlation
• Total sum of intervening

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• Cross Correlation
• Total sum of intervening

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• Probability Density Function
• Lees Ferry
• Total sum of intervening

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• Probability Density Function
• Lees Ferry
• Total sum of intervening

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• Probability Density Function
• Lees Ferry
• Intervening

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• Drought Statistics
• Lees Ferry
• Total sum of intervening

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• Drought Statistics
• Paleo Conditioned
• Lees Ferry
• Total sum of intervening

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• Drought Statistics
• Paleo Conditioned
• Imperial Dam
• Total sum of intervening

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Comments

• Handling negatives in total natural flow
• Continuing to explore reducing negatives in
  simulations
• Should we address base data (natural flow)?
• How does RiverWare handle negatives at rims?
• Min 10 constraint
• K-NN implementation in Lower basin
• Robust, simple
• Handles intermittent streams
• Faithfully reproduces statistics

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Next steps

• Incorporate salinity methods in EIS CRSS
• Generate stochastic data no conditioning
• Flow and salt scenarios
• Disaggregate data
• Generate paleo conditioned data for network
• Flow and salt scenarios
• Disaggregate data
• Drive decision support system
• Perform policy analysis
• Compare results from at least two hydrologies
• Paleo conditioned streamflows
• Index Sequential Method (current Reclamation
  technique)
• Possibly stochastic no conditioning

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Continued Steps

• Submitted revisions for WRR paper
• Finalize and submit Salt Model Paper
• Journal of Hydrology
• Complete Markov Paper
• Water Resources Research
• Complete Policy Analysis Paper
• ASCE Journal of Water Resources Planning and
  Management or Journal of American Water Resources
  Association
• Incorporate all into dissertation

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Additional Research Information

• http//animas.colorado.edu/prairie/ResearchHomePa
  ge.html

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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 Reclamations Lower
  Colorado Regional Office
• Logistical support provided by CADSWES

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Extra Slide Follow
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Incorporate paleo state information

• Magnitudes of Paleo data in question?
• Address issue, use observed data to represent
  magnitude and paleo reconstructed streamflows to
  represent system state
• Generate streamflows from the observed record
  conditioned on paleo streamflow state information

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Paleo Reconstructed Streamflow Data
Natural Streamflow Data
Choose one path
Block Bootstrap Data (30 year blocks)
Determine TPMs in smoothed window
Categorize natural flow data
Compute state information
Nonhomogeneous Markov model
Use KNN technique to resample natural flow
data consistent with paleo state information
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No Conditioning

• ISM
• 98 simulations
• 98 year length

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Disaggregation scheme
Index gauge
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No Conditioning

• ISM
• 98 simulations
• 60 year length

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Paleo Conditioned

• Markov chain length
• 8 yrs - 00 01 02
• 6 yrs - 10 11 12
• 7 yrs - 20 21 22
• 3 states
• 500 simulations
• 98 year length

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Paleo Conditioned

• NHMC with smoothing
• 2 states
• 500 simulations
• 60 year length

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Paleo Conditioned

• Markov chain length
• 31 years
• 2 states
• 500 simulations
• 60 year length