Long-Term Salinity Prediction with Uncertainty Analysis: Application for Colorado River Above Glenwood Springs, CO

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Long-Term Salinity Prediction with Uncertainty
AnalysisApplication for Colorado River Above
Glenwood Springs, CO

• James Roger Prairie
• Dept. of Civil, Architectural, and Environmental
  Engineering
• Masters Defense
• Spring 2002

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Motivation

• Colorado River Basin
• arid and semi-arid climates
• irrigation demands for agriculture
• Law of the River
• Mexico Treaty Minute No. 242
• Colorado River Basin Salinity Control Act of 1974

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Motivation

• Salinity Control Forum
• Federal Water Pollution Control Act Amendments of
  1972
• Fixed numerical salinity criteria
• 723 mg/L below Hoover Dam
• 747 mg/L below Parker Dam
• 879 mg/L at Imperial Dam
• review standards on 3 year intervals
• Develop basin wide plan for salinity control

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Salinity Damages and Control Efforts

• Damages are presently, aprox. 330 million/year
• As of 1998 salinity control projects has removed
  an estimated 634 Ktons of salt from the river
• total expenditure through 1998 426 million
• Proposed projects will remove an additional 390
  Ktons
• projects additional expenditure 170 million
• Additional 453 Ktons of salinity controls needed
  by 2015

Data taken from Quality of Water, Progress Report
19, 1999 Progress Report 20,2001
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Existing Colorado River Simulation System (CRSS)

• Includes three interconnected models
• salt regression model
• USGS salt model
• stochastic natural flow model
• index sequential method
• simulation model of entire Colorado River basin
• implemented in RiverWare

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Existing Salt Model Over-Prediction
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Research Objectives

• Investigate and improve generation of natural
  salt associated stochastic natural flow
• Investigate and improve modeling natural
  hydrologic variability (stochastic natural flow)
• Apply modifications to a case study in the
  Colorado River Basin

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Case Study Area

• Historic flow from 1906 - 95
• Historic salt from 1941 - 95

USGS gauge 09072500 (Colorado River near Glenwood
Springs, CO)
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Stochastic Simulation

• Simulate from the conditional probability
  function
• joint over the marginal densities

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Index Sequential Method

• Current stochastic hydrology model utilized by
  the USBR

Adapted from Ouarda, 1997
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Parametric PAR(1)

• Periodic Auto Regressive model (PAR)
• developed a lag(1) model
• Stochastic Analysis, Modeling, and Simulation
  (SAMS) (Salas, 1992)
• Data must fit a Gaussian distribution
• Expected to preserve
• mean, standard deviation, lag(1) correlation
• skew dependant on transformation
• Gaussian probability density function

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Traditional K-NN Model

• K- Nearest Neighbor model (K-NN) (Lall and
  Sharma, 1996)
• No prior assumption of datas distribution
• no transformations needed
• Resamples the original data with replacement
  using locally weighted bootstrapping technique
• only recreates values in the original data
• Expected to preserve
• all distributional properties
• (mean, standard deviation, lag(1) correlation and
  skewness)
• any arbitrary probability density function

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K-NN Algorithm
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Modified Nonparametric K-NN Natural Flow Model

• Improvement on traditional K-NN
• keeps modeling simple yet creates values not seen
  in the historic record
• perturbs the historic record within its
  representative neighborhood
• allows extrapolation beyond sample

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Local Regression
4.5
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Local Regression
alpha 0.3 or 27 neighbors
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Residual Resampling
yt yt et
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Model Evaluation

• Natural flow 1906 to 1995
• Basic Statistics
• mean,standard deviation, autocorrelation,
  skewness
• Higher Order Statistics
• probability density function
• conditional probability
• Minimum and Maximum Flows

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Conditional PDF
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Summary

• Comparison of 3 stochastic hydrology models
• ISM, PAR(1), modified K-NN
• Modified K-NN addresses limitations of both the
  ISM and PAR(1) models
• generates values and sequences not seen in the
  historic record
• generates a greater variety of flows than the ISM

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Climate Links

• Search for climate indicator in Northern
  Hemisphere related to flows in the Upper Colorado
  River basin
• USGS gauge 09163500 Colorado River at
  Utah/Colorado stateline
• represents flow in Upper Colorado River
• climate indicators
• sea surface temperature, sea level pressure,
  geopotential height 500mb, vector winds 1000mb,
  out going long wave radiation, velocity
  potential, and divergence
• Correlations
• search DJF months
• only present in certain regions
• Composites
• identify climate patterns associated with chosen
  flow regimes
• high, low, high minus low

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USGS gauge 09163500 (Colorado River at
Utah/Colorado Stateline) climate and flow data
available from 1951 to 1995
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Low flow
Composites
High minus Low flow
High flow
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USGS Salt Model

• 12 monthly regressions
• based on observed historic flow and salt mass
  from water year 1941 to 1983
• historic salt f (historic flow, several
  development variables)
• natural salt f (natural flow, development
  variables set to zero)

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Statistical Nonparametric Model for Natural Salt
Estimation

• Based on calculated natural flow and natural salt
  mass from water year 1941-85
• calculated natural flow observed historic
  flow total depletions
• calculated natural salt observed historic
  salt - salt added from agriculture salt
  removed with exports
• Nonparametric regression (local regression)
• natural salt f (natural flow)
• Residual resampling

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Nonparametric Salt Model and USGS Salt Model
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Comparison with Observed Historic Salt
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Natural Salt Mass from Nonparametric Salt Model
and USGS Salt Model
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USGS Salt Model and New Salt Model with K-NN
Resampling Comparison
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Summary

• The new nonparametric salt model removed the
  over-prediction seen with the USGS salt model
• Provides uncertainty estimates
• Can capture any arbitrary relationship (linear or
  nonlinear)

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CRSS Simulation Model for Historic Validation
Natural flow 1906-95 Natural salt 1941-95
Constant salinity pickup 137,000 tons/year
Exports removed _at_ 100 mg/L
Compare results to observed historic for
validation
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Model Validation Historic Flow

• 1941-1995 natural flow
• Subdued peak

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Model Validation Historic Salt Mass

• 1941-1995 natural flow
• 1941-1995 monthly and annual salt model

12 monthly regressions
1 annual regression
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Determining Salinity Concentration
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Model ValidationHistoric Salt Concentration

• 1941-1995 natural flow
• 1941-1995 monthly and annual salt model

12 monthly regressions
1 annual regression
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Natural Flow vs. Total Depletion
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Annual Model With Resampling

• Based on 1941-1995 natural flow
• 1941-1995 annual salt model
• Simulates 1941-1995

• Historic Flow and Concentration

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Modified and Existing CRSS Comparison Historic
Flow

• Based on 1906-1995 natural flows
• Simulates 1941-1995

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Modified and Existing CRSS Comparison Historic
Salt Mass

• Based on 1906-1995 natural flows
• 1941-1995 monthly salt models
• Simulates 1941-1995

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Policy Analysis

• Fictional Salinity Standards
• Colorado River near Glenwood Springs, CO
• Salinity standards
• mass remains below 650,000 tons
• salt concentration below 350 mg/L
• Standards occur in tails of distribution

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Policy AnalysisHistoric Simulation
gt 650,000 tons salt
gt 350 mg/L salt concentration
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CRSS Simulation Model for Future Prediction

• Natural flows based on 1906-1995
• Natural salt model based on 1941-1995
• Projected depletions 2002-2062
• Constant Ag salt loading of 137,000 tons/year
• Constant salt removal with exports of 100
  mg/L/year

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Stochastic Planning Runs Projected Future Flow
and Salt Mass

• Passing gauge 09072500
• Based on 1906-1995 natural flows
• 1941-1995 monthly salt models
• Simulating 2002 to 2062

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Policy Analysis Future Projections
gt 750,000 tons salt
gt 600 mg/L salt concentration
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Conclusions

• Developed a modified modeling system for the
  Colorado River Simulation System
• stochastic natural flow model
• modified nonparametric K-NN natural flow model
• salt regression model
• statistical nonparametric natural salt model
• simulation model in the Colorado River basin
• demonstrated on a case study for basin above USGS
  gauge 09072500

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Conclusions

• includes both flow and salt uncertainty
• improved representation of flow variability
• better representation of natural salt and flow
  relationship
• discussed nonparametric techniques
• flexible and easy to implement
• can preserve any arbitrary distribution
• conditioning with additional data
• validation of observed historic record
• demonstrated future projection

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Future Work

• Extend the modified K-NN flow model to perform
  space-time dissaggregation to simulate flow and
  salt over the entire basin
• Move operational policy to an annual time step
• Incorporate total depletions as a function of
  natural flow
• Further research into the relationship between
  salt loading and land use
• Continue work to incorporate climate information
  in streamflow generation

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Acknowledgements

• Dr. Balaji Rajagopalan, Dr. Terry Fulp, Dr. Edith
  Zagona for advising and support
• Upper Colorado Regional Office
• of the US Bureau of Reclamation,
• in particular Dave Trueman for funding and
  support
• CADSWES personnel for use of their
• knowledge and computing facilities

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Extra Slides Follow
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Case Study

• Colorado River above USGS gauge 09072500
  (Colorado River near Glenwood Springs, CO)
• flow data available from water year 1906-1995
• salt data available from water year 1941-1995
• model at a monthly timestep to accommodate the
  reservoirs operating policy in the simulation
  model

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Motivation

• Generating synthetic natural flow
• future variability
• Index Sequential Method (ISM)
• cannot produce values or traces that had not
  occurred in the past
• limited variability among traces

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ENSO response in Colorado River Basin

• Published by Cayan and Webb, 1992
• A weak response seen over Upper Colorado River
  Basin

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Sea Surface Temperature
Correlation
Sea Level Pressure
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Comparison with Calculated Natural Salt
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CRSS Simulation Model

• Receives data from the
• Modified Nonparametric K-NN Natural Flow Model
• Statistical Nonparametric Natural Salt Model
• Simulates flow, salt mass, and salt concentration
  at USGS gauge 09072500 (Colorado River near
  Glenwood Springs, CO)

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Model Validation Natural Flow

• 1941-1995 natural flow
• Utilizes subset of available record

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Model Validation Natural Flow

• 1906-1995 natural flow
• Utilizes entire available record

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Model Validation Natural Salt Mass

• 1941-1995 natural flow
• Utilizes subset of available record
• 1941-1995 monthly and annual salt model

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Model Validation Natural Salt Mass

• 1906-1995 natural flow
• 1941-1995 monthly salt models

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Annual model with no resampling

• 1906-1995 natural flow
• 1941-1995 annual salt model
• Historic Flow and Concentration

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Modified and Existing CRSS Comparison Historic
Salt Concentration

• Based on 1906-1995 natural flows
• 1941-1995 monthly salt models
• Simulates 1941-1995

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Policy AnalysisHistoric Simulation

• gt 350 mg/L salt concentration

Incorporates total depletion as a function of
natural flow
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Historic Salt Mass
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Future Salt Mass
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Modified Colorado River Simulation System (CRSS)

• Includes three interconnected models
• stochastic natural flow model
• modified nonparametric K-NN natural flow model
• salt regression model
• statistical nonparametric natural salt model
• simulation model of entire Colorado River basin
• demonstrated on a case study for basin above USGS
  gauge 09072500