Transcript Long-Term Salinity Prediction with Uncertianty Analysis

2nd Federal Interagency
Hydrologic Modeling Conf.
Long-Term Salinity Prediction
with Uncertainty Analysis:
Application for Colorado River Above Glenwood
Springs, CO
James Prairie
Water Resources Division, Civil, Architectural, and Environmental Engineering
Department, and U.S. Bureau of Reclamation, University of Colorado, Boulder
Balaji Rajagopalan
Water Resources Division, Civil, Architectural, and Environmental Engineering
Department, University of Colorado, Boulder
Terry Fulp
U.S. Bureau of Reclamation, University of Colorado, Boulder
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
f ( yt , yt 1 , yt  2 ,..., yt  p )


y
f  t y , y ,..., y  
t 1
t 2
t p
f ( yt 1 , yt  2 ,..., yt  p )
– joint over the marginal densities
Parametric PAR(1)
• Periodic Auto Regressive model (PAR)
– developed a lag(1) model
y ,    1, y , 1   1    ,
  season(month)
  year
– 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
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
Residual Resampling
yt = yt* + et*
yt *
e t*
yt-1
June
Conditional PDF
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
calculated natural flow
flow
historic agriculture
consumptive use
estimated natural salt mass
Natural salt 1941-95
salt
irrigated
lands
agricultural
salt loadings
historic exports
Natural flow 1906-95
salt removed
with exports
historic municipal and industrial
Constant salinity pickup
137,000 tons/year
Exports removed
@ 100 mg/L
historic effects of off-stream
reservoir regulation
USGS stream gauge 09072500
simulated historic flow
simulated historic salt mass
Compare results to
observed historic
for validation
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 Salt Mass
• Based on 1906-1995 natural flows
• 1941-1995 monthly salt models
• Simulates 1941-1995
Policy Analysis
Historic 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 longterm 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 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