Download Long-Term Salinity Prediction with Uncertianty Analysis

Hydrology Days 2002
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
Edith Zagona
Center for Advanced Decision Support for Water and Environmental Sysytems (CADSWES),
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
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
Conditional PDF
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
Future Work
• Extend the modified K-NN flow model to perform spacetime dissaggregation to simulate flow and salt over the
entire basin
• Move operational policy to an annual time step
• Further research into the relationship between salt loading
and land use
• Continue work to incorporate climate information in
streamflow generation
Acknowledgements
• Balaji Rajagopalan, Terry Fulp, 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
Extra Slides Follow
Conclusions
– developed and tested a new statistical
nonparametric natural salt model
– discussed nonparametric techniques
• flexible and easy to implement
• can preserve any arbitrary distribution
• conditioning with additional data
– validation of historic record
– preservation of historic salinity violations
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
Correlation
Sea Surface Temperature
Sea Level Pressure
Residual Resampling
Alpha = 0.4 or k = 18
yt = yt* + et*
yt*
e t*
yt-1
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
Future Salt Mass
Motivation
• Salinity Control Forum
– Federal Water Pollution Control Act
Amendments of 1972
– 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
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
Index Sequential Method
• Current stochastic hydrology model utilized
by the USBR
data wrapped from beginning
1906
1995
1st synthetic hydrology
1906
1931
90 extracted overlapping 25
year ISM sequences
2nd synthetic hydrology
1907
1932
89rd synthetic hydrology
1993
1929
90th synthetic hydrology
1994
Adapted from Ouarda, 1997
1930
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
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)
Policy Analysis
Historic Simulation
• > 350 mg/L salt concentration
Incorporates total depletion as a
function of natural flow
CRSS Simulation Model
for Future Prediction
synthetic natural flow
flow
associated synthetic natural salt mass
• Natural flows based on
1906-1995
salt
• Natural salt model based
on 1941-1995
future agriculture
consumptive use
irrigated
lands
agricultural
salt loadings
salt removed
with exports
future exports
future municipal and industrial
• Constant Ag salt loading
of 137,000 tons/year
• Constant salt removal
with exports of 100
mg/L/year
USGS stream gauge 09072500
simulated future flow
• Projected depletions
2002-2062
simulated future salt mass
Policy Analysis
Future Projections
> 750,000 tons salt
> 600 mg/L salt concentration