Long-Term Salinity Prediction with Uncertainty Analysis:

Application for Colorado River Above Glenwood Springs, CO

James PrairieWater Resources Division, Civil, Architectural, and Environmental Engineering Department, and U.S. Bureau of Reclamation, University of Colorado, Boulder

Balaji RajagopalanWater Resources Division, Civil, Architectural, and Environmental Engineering Department, University of Colorado, Boulder

Terry FulpU.S. Bureau of Reclamation, University of Colorado, Boulder

2nd F

eder

al I

nter

agen

cy

Hyd

rolo

gic

Mod

elin

g C

onf.

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

Salinity Control Forum

Existing Salt Model Over-Prediction

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 yt

t t t p

t t t t p

t t t p

1 2

1 2

1 2, , . . . ,

( , , , . . . , )

( , , . . . , )

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

year

(month)season

,11,,1, yy

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

yt-1

yt*et*

Residual Resampling

yt = yt* + et

*

Conditional PDF

June

May

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

Comparison with Observed Historic Salt

Comparison With Calculated Natural Salt

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

Annual Model With Resampling

• Based on 1941-1995 natural flow

• 1941-1995 annual salt model

• Simulates 1941-1995

• 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 Mass

Policy AnalysisHistoric Simulation

> 650,000 tons salt

> 350 mg/L salt concentration

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

Conclusion

• Developed a modeling framework for long-term salinity with uncertainty in the Colorado River– modified nonparametric K-NN natural flow

model– statistical nonparametric natural salt model– validation of historic record– demonstrated future projection

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