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Incorporating Climate Information in Long Term
Salinity Prediction with Uncertainty Analysis
James Prairie(1,2), Balaji Rajagopalan(1), and Terry Fulp(2)
1. University of Colorado at Boulder, CADSWES
2. U.S. Bureau of Reclamation
Motivation
Colorado River Basin
“Law of the River”
Mexico Treaty Minute No. 242
assured water received by Mexico will have an average salinity of no more than 115 ppm +/- 30 ppm above the average annual salinity at Imperial Dam
Colorado River Basin Salinity Control Act of 1974
ensure that United States obligation to Mexico under Minute No. 242 is met
authorized construction of desalting plant and additional salinity control projects
Motivation
• Salinity Control Forum
– Created by Basin States in response to Federal Water Pollution Control Act Amendments of 1972
Developed 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 Control Forum
Salinity Control efforts in place removed 634 Ktons from the system in 1998. This accounted for 9% of the salt mass at Imperial Dam
total expenditure through 1998 $426 million
Proposed projects should remove an additional 390 Ktons
projects additional expenditure $170 million
• Projected additional 453 Ktons of salinity controls needed by 2015
(data taken from Quality of Water, Progress Report 19, 1999)
Colorado River Simulation System (CRSS)
First implemented in Fortran in the early 1980’s
Basin wide model for water and salinity
CRSS model was an essential tool for decision support
– model is used to determine required long-term (20 years) salt removal to maintain salinity criteria
CRSS
The Fortran version of CRSS was replaced by a policy model in RiverWare in 1996
New model was verified to old model
Recent attempts to verify the new CRSS against historic salinity data from 1970 to 1990 indicated a bias (over-prediction) and the inability to replicate extreme periods
CRSS
• Salt modeled as a conservative substance• Reservoirs modeled fully mixed• Monthly timestep
– results typically aggregated to annual
• Salt can enter the system from two sources– from natural flows
– additional salt loading (predominately agriculture)
• Model is used to predict future salt removal necessary to maintain salinity criteria– under future water development scenarios
• “human-induced salt loading”
– under future hydrologic uncertainty• “natural salt loading”
• Historical data is separated into natural and human-induced components
Problems Found in CRSS
• Historic calibration– quantified the over-prediction
throughout the basin
– can not replicate extreme events
• Limited uncertainty analysis– future hydrology
Gauge Station 42949: Colorado River above Imperial Dam AboveImperialDamColoradoR Outflow Salt Concentration (mg/l)
0
100
200
300
400
500
600
700
800
900
1000
Dec-70
Dec-72
Dec-74
Dec-76
Dec-78
Dec-80
Dec-82
Dec-84
Dec-86
Dec-88
Time
Ab
ove
Imp
eria
lDam
Co
lora
do
R O
utf
low
Sal
t C
on
cen
trat
ion
(m
g/l
)
Historic Salt Concentration
Salinity Standard
No Calibration
879 mg/L
Calibration
Gauge Station 1805: Colorado River near Cisco, UTUT_COStatelinetoColorado Outflow (acre-feet/month summed over the year)
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
Dec-70Dec-72
Dec-74Dec-76
Dec-78Dec-80
Dec-82Dec-84
Dec-86Dec-88
Time
UT
_CO
Sta
teli
ne
toC
olo
rad
o O
utf
low
(a
cre
-fe
et/
mo
nth
su
mm
ed
ove
r th
e y
ea
r)
Modeled Flow
Historic Flow
Average difference for modeled minus historical flow = 76,000 acre-ft/month
Extreme Events
Gauge Station 1805: Colorado River near Cisco, UTUT_COStatelinetoColorado Outflow Salt Concentration (mg/l)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Dec-70Dec-72
Dec-74Dec-76
Dec-78Dec-80
Dec-82Dec-84
Dec-86Dec-88
Time
UT
_CO
Sta
teli
ne
toC
olo
rad
o O
utf
low
Sa
lt C
on
cen
tra
tio
n (
mg
/l)
Modeled Salt Concentration
Historic Salt Concentration
No Calibration
Gauge Station 1805 Colorado: River near Cisco, UTUT_COStatelinetoColorado Outflow Salt Mass (tons)
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
Dec-70Dec-72
Dec-74Dec-76
Dec-78Dec-80
Dec-82Dec-84
Dec-86Dec-88
Time
UT
_CO
Sta
teli
ne
toC
olo
rad
o O
utf
low
Sa
lt M
ass
(to
ns)
Modeled Salt Mass
Historic Salt Mass
No Calibration
Average difference for modeled minus historical salt mass = -1,242 tons
Limited Uncertainty Analysis
• Natural variability of flows
• Index sequential modeling generates synthetic streamflow that
exactly match the historical record,
shifted in time
Graph #1 - Percentiles and PoliciesSlot14: AboveImperialDamColoradoR Outflow (acre-feet/month summed over the year)
5,000,000
7,000,000
9,000,000
11,000,000
13,000,000
15,000,000
17,000,000
19,000,000
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988
Time
Slo
t14:
Ab
ove
Imp
eria
lDam
Co
lora
do
R O
utf
low
(ac
re-f
eet/
mo
nth
su
mm
ed o
ver
the
year
)
Historical flow
70to90ForAnalysis.xls.xls-5%
70to90ForAnalysis.xls.xls-50%
70to90ForAnalysis.xls.xls-95%
Graph #1 - Percentiles and PoliciesSlot15: AboveImperialDamColoradoR Outflow Salt Concentration (mg/l)
500
600
700
800
900
1000
1100
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988
Time
Slo
t15:
Ab
ove
Imp
eria
lDam
Co
lora
do
R O
utf
low
Sal
t C
on
cen
trat
ion
(m
g/l
)
historical salinity
salinity standard
70to90ForAnalysis.xls.xls-5%
70to90ForAnalysis.xls.xls-50%
70to90ForAnalysis.xls.xls-95%
879 mg/L
Research Objectives
Verify all data and recalibrate CRSS for both water quantity and water quality (total dissolved solids, or TDS)
Investigate the salinity methodologies currently used to model future water development and improve them as necessary for future predictions
Improve hydrologic uncertainty analysis
statistically preserve low flow events
incorporate climate information
Exploratory Data
Analysis
(Climate Diagnostics)
Stochastic Flow Model
Salinity Model in
RiverWare
Compare Model Results
Comparison of
parametric and
nonparametric model
Natural Salt
Model
Climate Indicators
K-NN and AR(1)
Nonparametric
regression (lowess)
replacement for
CRSM
compare salt mass
Research Topics Interconnection
Investigation of CRSS
model and data
Parametric• 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
( )å=
-- S+-F+=p
jjjj yy
1,,,, tnttntttn mm
season
year
==
tn
Comparison of parametric and nonparametric model
Nonparametric
• K- Nearest Neighbor model (K-NN)– lag(1) model
• 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
• augment using noise function• alternate nonparametric method
• Expected to preserve– all distributional properties
• (mean, standard deviation, lag(1) correlation and skewness)
– any arbitrary probability density function
Nearest Neighbor Resampling
1. Dt (x t-1) d =1 (feature vector)
2. determine k nearest neighbors among Dt using Euclidean distance
3. define a discrete kernel K(j(i)) for resampling one of the xj(i) as follows
4. using the discrete probability mass function K(j(i)), resample xj(i) and update the feature vector then return to step 2 as needed
5. Various means to obtain k– GCV– Heuristic scheme
( ) ÷÷ø
öççè
æ-= å
=
d
jtjijjit vvwr
1
2/1
Where v tj is the jith component of Dt, and w j are scaling weights.
( )( )å
=
=k
j
j
jijK
1
1
1
Lall and Sharma (1996)
Nk =
Annual Water Year Natural FlowUSGS stream gauge 09180500 (Colorado River near Cisco, UT)
0
2000
4000
6000
8000
10000
12000
14000
1906
1909
1912
1915
1918
1921
1924
1927
1930
1933
1936
1939
1942
1945
1948
1951
1954
1957
1960
1963
1966
1969
1972
1975
1978
1981
1984
1987
1990
flo
w (
1000
acr
e-fe
et/y
ear)
Monthly Natural FlowUSGS stream gauge 09180500 (Colorado River near Cisco, UT)
0
500
1000
1500
2000
2500
3000
3500
4000
Oct-05
Oct-08
Oct-11
Oct-14
Oct-17
Oct-20
Oct-23
Oct-26
Oct-29
Oct-32
Oct-35
Oct-38
Oct-41
Oct-44
Oct-47
Oct-50
Oct-53
Oct-56
Oct-59
Oct-62
Oct-65
Oct-68
Oct-71
Oct-74
Oct-77
Oct-80
Oct-83
Oct-86
Oct-89
flo
w (
1000
acr
e-fe
et/m
on
th)
Conclusions
• Basic statistics are preserved– both models reproduce mean, standard
deviation, lag(1) correlation, skew
• Reproduction of original probability density function– PAR(1) (parametric method) unable to
reproduce non gaussian PDF – K-NN (nonparametric method) does reproduce
• Reproduction of bivariate probability density function– PAR(1) gaussian assumption smoothes the
original function– K-NN recreate the original function well
• Drought Statistics• Additional research
• nonparametric technique allow easy incorporation of additional influences to flow (i.e., climate)
Exploratory Data
Analysis
(Climate Diagnostics)
Stochastic Flow Model
Salinity Model in
RiverWare
Compare Model Results
Comparison of
parametric and
nonparametric model
Natural Salt
Model
Climate Indicators
K-NN and AR(1)
Nonparametric
regression (lowess)
replacement for
CRSM
compare salt mass
Research Topics Interconnection
Investigation of CRSS
model and data
Exploratory Data Analysis(Climate Diagnostics)
• Search for climate indicator related to flows in the Upper Colorado River basin– USGS gauge 09163500: Colorado River at
Utah/Colorado stateline– represents flow in Upper Colorado River
• Correlations– search DJF months– only present in certain regions
• Composites– identify climate patterns associated with chosen
flow regimes• high, low, high minus low
– Climate indicators• sea surface temperature, sea level pressure,
geopotential height 500mb, vector winds 1000mb, out going long wave radiation, velocity potential, and divergence
CWCB natural flow Gauge 1635: @ CO-UT stateline(water year Oct to Sept)
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
1909
1912
1915
1918
1921
1924
1927
1930
1933
1936
1939
1942
1945
1948
1951
1954
1957
1960
1963
1966
1969
1972
1975
1978
1981
1984
1987
1990
1993
1996
flo
w (
acre
-fee
t/ye
ar)
high flow years - 1952, 1957, 1983, 1984, 1985, 1986, 1995
low flow years - 1955, 1963, 1977, 1981, 1990
Conclusions
• Found unique climate patterns for high and low flows
• High minus low displayed a difference for each flow regime– geopotential height at 500mb showed the
strongest signal
– climate signal similar to ENSO• influence by ENSO through teleconnections
• Time series analysis of Geopotential Height at 500mb– principal component analysis
• PC(1) structure
– develop relationship for flow dependant on climate
Exploratory Data
Analysis
(Climate Diagnostics)
Stochastic Flow Model
Salinity Model in
RiverWare
Compare Model Results
Comparison of
parametric and
nonparametric model
Natural Salt
Model
Climate Indicators
K-NN and AR(1)
Nonparametric
regression (lowess)
replacement for
CRSM
compare salt mass
Research Topics Interconnection
Investigation of CRSS
model and data
Stochastic Flow Model
• Natural flows will be determined from a multiple step process– nonparametric smooth bootstrap method to
develop an index of PC(1)– the k-nearest neighbor method uses locally
weighted resamples of the PC(1) for the current year to be simulated based on the index of PC(1) for the previous year
– the annual flow associated with the simulated PC(1) becomes the annual flow for the current year simulated
• Hypothesis:– Conditioning the nonparametric model on large
scale climate will improve the stochastic modeling of extreme events
• probability of extreme events
• Annual timestep
Straight Bootstrap not conditioned on climate
K-NN model conditioned on climate (Sep-Oct lag(1) correlation is not preserved
Exploratory Data
Analysis
(Climate Diagnostics)
Stochastic Flow Model
Salinity Model in
RiverWare
Compare Model Results
Comparison of
parametric and
nonparametric model
Natural Salt
Model
Climate Indicators
K-NN and AR(1)
Nonparametric
regression (lowess)
replacement for
CRSM
compare salt mass
Research Topics Interconnection
Investigation of CRSS
model and data
Natural Salt Model
• USGS natural salt model– uses least-squares regression to fit a
model of dissolved-solids discharge as a function of streamflow and several development variables
• Nonparametric regression– lowess regression between natural flow
and ''back-calculated'' natural salt • human-induced salt mass - historic salt
mass = ''back-calculate'' the natural salt mass
• a lowess regression is a robust, local smooth of scatterplot data
Salt Mass above Gauge 0725
300,000
400,000
500,000
600,000
700,000
800,000
900,000
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
Sa
lt M
as
s (
ton
s)
flow verified - adjust salinity pickup, USGS regression historic verified flow - adjust salinity pickup, lowess regression
Salt Mass above Gauge 0725
300,000
400,000
500,000
600,000
700,000
800,000
900,000
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
Sal
t M
ass
(to
ns)
historic NOT flow verified - USGS regression verified flow - adjust salinity pickup, lowess regression
Exploratory Data
Analysis
(Climate Diagnostics)
Stochastic Flow Model
Salinity Model in
RiverWare
Compare Model Results
Comparison of
parametric and
nonparametric model
Natural Salt
Model
Climate Indicators
K-NN and AR(1)
Nonparametric
regression (lowess)
replacement for
CRSM
compare salt mass
Research Topics Interconnection
Investigation of CRSS
model and data
Salinity Model in RiverWare
• Subbasin of the upper Colorado Basin – above USGS gauge 09072500 (Colorado River
near Glenwood Springs, Colorado)
• Monthly timestep
Compare Model Results
• Model results using natural flows and salt developed from– Nonparametric (K-NN)
– Parametric (PAR)
– Index Sequential Modeling (ISM)
Summary
• Our research incorporates four primary investigations:– comparison of parametric statistical techniques
with non-parametric statistical techniques for streamflow generation
– exploratory data analysis of relationships between streamflow and snow water equivalent in the Colorado River Basin with global climate indicators
– development of an algorithm that incorporates climate information and non-parametric statistical techniques in the generation of stochastic natural streamflow and salinity
– use of the generated natural streamflow and salinity in a river basin model that forecasts future flow and salinity values in the Upper Colorado river basin.