Long-Term Salinity Prediction with Uncertainty Analysis:

Application for Colorado River Above Glenwood Springs, CO

James Roger Prairie

Dept. of Civil, Architectural, and Environmental Engineering

Masters Defense

Spring 2002

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

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

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

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

Existing Salt Model Over-Prediction

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

USGS gauge 09072500

(Colorado River near Glenwood Springs, CO)

• Historic flow from 1906 - 95

• Historic salt from 1941 - 95

Case Study Area

Stochastic Simulation

• Simulate from the conditional probability function

– joint over the marginal densities

f yy y y

f y y y y

f y y y y dyt

t t t p

t t t t p

t t t t p t

1 2

1 2

1 2

, , . . . ,( , , , . . . , )

( , , , . . . , )

Index Sequential Method

• Current stochastic hydrology model utilized by the USBR

1906 1995

1906 1931

1907 1932

data wrapped from beginning

2nd synthetic hydrology

90th synthetic hydrology

89rd synthetic hydrology

1st synthetic hydrology90 extracted overlapping 25

year ISM sequences

1993 1929

1994 1930

Adapted from Ouarda, 1997

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

(month)season

year

,11,,1, yy

Traditional K-NN Model• K- Nearest Neighbor model (K-NN) (Lall and Sharma, 1996)

• No prior assumption of data’s 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

yt*

yt-1

K-NN Algorithm

990

Nk

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

Local Regression

4.5

Local Regression

alpha = 0.3

or 27 neighbors

yt-1

yt*et*

Residual Resampling

yt = yt* + et

*

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

Conditional PDF

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

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

USGS gauge 09163500

(Colorado River at Utah/Colorado Stateline)

climate and flow data available from 1951 to 1995

High flow

Low flow

High minus Low flow

Composites

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)

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

Nonparametric Salt Model and USGS Salt Model

Comparison with Observed Historic Salt

Natural Salt Mass from Nonparametric Salt Model and USGS Salt Model

USGS Salt Model and New Salt Model with K-NN Resampling Comparison

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)

CRSS Simulation Model for Historic Validation

saltflow

historic agriculture

historic exports

historic municipal and industrial

historic effects of off-stream

calculated natural flow estimated natural salt mass

simulated historic flow simulated historic salt mass

USGS stream gauge 09072500

consumptive useirrigatedlands

reservoir regulation

salt loadings

salt removedwith exports

agricultural

Constant salinity pickup 137,000 tons/year

Exports removed @ 100 mg/L

Compare results to observed historic for validation

Natural flow 1906-95

Natural salt 1941-95

Model Validation Historic Flow

• 1941-1995 natural flow

• Subdued peak

Model Validation Historic Salt Mass

• 1941-1995 natural flow

• 1941-1995 monthly and annual salt model

12 monthly regressions

1 annual regression

Determining Salinity Concentration

feet)-(acre volumeflow

735.29 (tons) masssalt (mg/L)ion concentratsalt

Model ValidationHistoric Salt Concentration

12 monthly regressions

1 annual regression

• 1941-1995 natural flow

• 1941-1995 monthly and annual salt model

Natural Flow vs. Total Depletion

Annual Model With Resampling

• Based on 1941-1995 natural flow

• 1941-1995 annual salt model

• Simulates 1941-1995

• Historic Flow and Concentration

Modified and Existing CRSS Comparison

Historic Flow

• Based on 1906-1995 natural flows

• Simulates 1941-1995

• Based on 1906-1995 natural flows

• 1941-1995 monthly salt models

• Simulates 1941-1995

Modified and Existing CRSS Comparison

Historic Salt Mass

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

Policy AnalysisHistoric Simulation

> 650,000 tons salt

> 350 mg/L salt concentration

CRSS Simulation Model for Future Prediction

saltflow

future agriculture

future exports

future municipal and industrial

synthetic natural flow associated synthetic natural salt mass

simulated future flow simulated future salt mass

USGS stream gauge 09072500

consumptive useirrigatedlands

salt loadings

salt removedwith exports

agricultural

• 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

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

Policy Analysis Future Projections

> 750,000 tons salt

> 600 mg/L salt concentration

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

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

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

Acknowledgements

• Dr. Balaji Rajagopalan, Dr. Terry Fulp, Dr. Edith Zagona for advising and support

• Upper Colorado Regional Officeof the US Bureau of Reclamation, in particular Dave Trueman for funding and support

• CADSWES personnel for use of their knowledge and computing facilities

Extra Slides Follow

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

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

ENSO response in Colorado River Basin

• Published by Cayan and Webb, 1992

• A weak response seen over Upper Colorado River Basin

Sea Surface Temperature

Sea Level PressureCor

rela

tion

Comparison with Calculated Natural Salt

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)

Model Validation Natural Flow

•1941-1995 natural flow

•Utilizes subset of available record

Model Validation Natural Flow

•1906-1995 natural flow

•Utilizes entire available record

Model Validation Natural Salt Mass

• 1941-1995 natural flow

• Utilizes subset of available record

• 1941-1995 monthly and annual salt model

Model Validation Natural Salt Mass

•1906-1995 natural flow

•1941-1995 monthly salt models

Annual model with no resampling

•1906-1995 natural flow

•1941-1995 annual salt model

•Historic Flow and Concentration

• Based on 1906-1995 natural flows

• 1941-1995 monthly salt models

• Simulates 1941-1995

Modified and Existing CRSS Comparison

Historic Salt Concentration

Policy AnalysisHistoric Simulation

Incorporates total depletion as a function of natural flow

• > 350 mg/L salt concentration

Historic Salt Mass

Future Salt Mass

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