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

Calibration

Gauge Station 42949: Colorado River above Imperial Dam AboveImperialDamColoradoR Outflow Salt Concentration (mg/l)

1000 900 800 700 600 500 400 300 200 100 0 De c-7 0 De c-7 2 De c-7 4 De c-7 6 De c-7 8 De c-8 0

Time

De c-8 2 De c-8 4 De c-8 6 De c-8 8 879 mg/L Historic Salt Concentration Salinity Standard No Calibration

Extreme Events

Gauge Station 1805: Colorado River near Cisco, UT UT_COStatelinetoColorado Outflow (acre-feet/month summed over the year)

12,000,000 Average difference for modeled minus historical flow = 76,000 acre-ft/month 10,000,000 8,000,000 Modeled Flow Historic Flow 6,000,000 4,000,000

Gauge Station 1805 Colorado: River near Cisco, UT UT_COStatelinetoColorado Outflow Salt Mass (tons)

2,000,000 0 De c-7 0 De c-7 2 De c-7 4 De c-7 6 De c-7 8 De c-8 0

Time

De c-8 2 De c-8 4 De c-8 6 De c-8 8 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000 Average difference for modeled minus historical salt mass = -1,242 tons Modeled Salt Mass Historic Salt Mass No Calibration De c-7 0 De c-7 2 De c-7 4 De c-7 6 De c-7 8 De c-8 0

Time

De c-8 2 De c-8 4 De c-8 6 De c-8 8

Gauge Station 1805: Colorado River near Cisco, UT UT_COStatelinetoColorado Outflow Salt Concentration (mg/l)

2000 1800 1600 1400 1200 1000 800 600 400 200 0 De c-7 0 De c-7 2 De c-7 4 De c-7 6 De c-7 8 De c-8 0

Time

De c-8 2 De c-8 4 De c-8 6 De c-8 8 Modeled Salt Concentration Historic Salt Concentration No Calibration

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 Policies Slot14: AboveImperialDamColoradoR Outflow (acre-feet/month summed over the year)

19,000,000 17,000,000 15,000,000 13,000,000 11,000,000 9,000,000 7,000,000 5,000,000 1970 1972 1974 1976 1978 1980

Time

1982 1984 1986 1988 Historical flow 70to90ForAnalysis.xls.xls-5% 70to90ForAnalysis.xls.xls-50% 70to90ForAnalysis.xls.xls-95%

Graph #1 - Percentiles and Policies Slot15: AboveImperialDamColoradoR Outflow Salt Concentration (mg/l)

1100 1000 900 800 700 600 500 1970 1972 1974 1976 1978 1980

Time

1982 1984 1986 1988 879 mg/L historical salinity salinity standard 70to90ForAnalysis.xls.xls-5% 70to90ForAnalysis.xls.xls-50% 70to90ForAnalysis.xls.xls-95%

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

Research Topics Interconnection

Comparison of parametric and nonparametric model Exploratory Data Analysis (Climate Diagnostics) Climate Indicators Stochastic Flow Model K-NN and AR(1) Investigation of CRSS model and data Natural Salt Model Nonparametric regression (lowess) Salinity Model in RiverWare replacement for CRSM Compare Model Results compare salt mass pdf

Comparison of parametric and nonparametric model Parametric

• Periodic Auto Regressive model (PAR) – developed a lag(1) model

y

n , t = m t n t =

year

=

season

+

j

å =

p

1 F

j

, t (

y

n , t -

j

m t -

j

) + S n , t – 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

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

Nonparametric (cont’d) • Markov process for resampling

Lall and Sharma (1996)

Nearest Neighbor Resampling

1. D t (x t-1 ) d =1 (feature vector) 2. determine k nearest neighbors among D t using Euclidean distance

r it

= å åå

j d

å = 1

w j

(

v ij

-

v tj

) 1 / 2 å åå Where v tj and w j is the jith component of D are scaling weights.

t , 3. define a discrete kernel K(j(i)) for resampling one of the x j(i) as follows

K

= 1

j

å =

k

1 1

j j

4. using the discrete probability mass function K(j(i)), resample x j(i) and update the feature vector then return to step 2 as needed 5. Various means to obtain k – GCV – Heuristic scheme

k

=

N

Lall and Sharma (1996)

Annual Water Year Natural Flow

USGS stream gauge 09180500 (Colorado River near Cisco, UT) 14000 12000 10000 8000 6000 4000 2000 0 19 06 19 09 19 12 19 15 19 18 19 21 19 24 19 27 19 30 19 33 19 36 19 39 19 42 19 45 19 48 19 51 19 54 19 57 19 60 19 63 19 66 19 69 19 72 19 75 19 78 19 81 19 84 19 87 19 90

Monthly Natural Flow

USGS stream gauge 09180500 (Colorado River near Cisco, UT) 4000 3500 3000 2500 2000 1500 1000 500 0 O ct 05 O ct 08 O ct 11 O ct 14 O ct 17 O ct 20 O ct 23 O ct 26 O ct 29 O ct 32 O ct 35 O ct 38 O ct 41 O ct 44 O ct 47 O ct 50 O ct 53 O ct 56 O ct 59 O ct 62 O ct 65 O ct 68 O ct 71 O ct 74 O ct 77 O ct 80 O ct 83 O ct 86 O ct 89

Bivariate Probability Density Function

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 PDF • Reproduction of bivariate probability density function – month to month PDF – PAR(1) gaussian assumption smoothes the original function – K-NN recreate the original function well • Additional research • nonparametric technique allow easy incorporation of additional influences to flow (i.e., climate)

Research Topics Interconnection

Comparison of parametric and nonparametric model Exploratory Data Analysis (Climate Diagnostics) Climate Indicators Stochastic Flow Model K-NN and AR(1) Investigation of CRSS model and data Natural Salt Model Nonparametric regression (lowess) Salinity Model in RiverWare replacement for CRSM Compare Model Results compare salt mass pdf

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

Published ENSO Response • Cayan, D.R., Webb, R.H., 1992.

Sea Surface Temperate Sea Level Pressure

CWCB natural flow Gauge 1635: @ CO-UT stateline (water year Oct to Sept) 12,000,000 10,000,000 8,000,000 6,000,000 4,000,000 2,000,000 0 19 09 19 12 19 15 19 18 19 21 19 24 19 27 19 30 19 33 19 36 19 39 19 42 19 45 19 48 19 51 19 54 19 57 19 60 19 63 19 66 19 69 19 72 19 75 19 78 19 81 19 84 19 87 19 90 19 93 19 96

high flow years - 1952, 1957, 1983, 1984, 1985, 1986, 1995 low flow years - 1955, 1963, 1977, 1981, 1990

high - low flow years

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

Research Topics Interconnection

Comparison of parametric and nonparametric model Exploratory Data Analysis (Climate Diagnostics) Climate Indicators Stochastic Flow Model K-NN and AR(1) Investigation of CRSS model and data Natural Salt Model Nonparametric regression (lowess) Salinity Model in RiverWare replacement for CRSM Compare Model Results compare salt mass pdf

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 • Conditioning the nonparametric model on large scale climate will improve the stochastic modeling of extreme events – probability of extreme events • Annual timestep

Research Topics Interconnection

Comparison of parametric and nonparametric model Exploratory Data Analysis (Climate Diagnostics) Climate Indicators Stochastic Flow Model K-NN and AR(1) Investigation of CRSS model and data Natural Salt Model Nonparametric regression (lowess) Salinity Model in RiverWare replacement for CRSM Compare Model Results compare salt mass pdf

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

900,000 800,000 700,000 600,000 500,000 400,000 300,000 19 70 19 71 19 72 19 73 19 74 19 75 19 76 19 77 19 78 19 79 19 80 19 81 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 historic NOT flow verified - USGS regression

Salt Mass above Gauge 0725

verified flow - adjust salinity pickup, lowess regression 900,000 800,000 700,000 600,000 500,000 400,000 300,000 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 flow verified - adjust salinity pickup, USGS regression historic verified flow - adjust salinity pickup, lowess regression

Research Topics Interconnection

Comparison of parametric and nonparametric model Exploratory Data Analysis (Climate Diagnostics) Climate Indicators Stochastic Flow Model K-NN and AR(1) Investigation of CRSS model and data Natural Salt Model Nonparametric regression (lowess) Salinity Model in RiverWare replacement for CRSM Compare Model Results compare salt mass pdf

Salinity Model in RiverWare • Subbasin of the upper Colorado Basin

– above USGS gauge 09072500 (Colorado River near Glenwood Springs, Colorado)

• Monthly timestep

– current CRSS rules

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.