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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

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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

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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

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Salinity Control Forum Salinity Control efforts in place removed 634 Ktons from the system in 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)

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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

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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

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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

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RiverWare Workspace

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Problems Found in CRSS Historic calibration –quantified the over-prediction throughout the basin –can not replicate extreme events Limited uncertainty analysis –future hydrology

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Calibration

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Extreme Events

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Limited Uncertainty Analysis Natural variability of flows Index sequential modeling generates synthetic streamflow that exactly match the historical record, shifted in time

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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

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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 Comparison of parametric and nonparametric model

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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

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Nonparametric (cont’d) Markov process for resampling Lall and Sharma (1996)

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Nearest Neighbor Resampling 1. D t (x t-1 ) d =1 (feature vector) 2. determine k nearest neighbors among D t using Euclidean distance 3. define a discrete kernel K(j(i)) for resampling one of the x j(i) as follows 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 Where v tj is the jith component of D t, and w j are scaling weights. Lall and Sharma (1996)

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Bivariate Probability Density Function

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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 –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)

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Exploratory Data Analysis (Climate Diagnostics) Search for climate indicator related to flows in the Upper Colorado River basin –USGS gauge : 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

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

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Sea Surface Temperate Sea Level Pressure

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

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high - low flow years

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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

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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

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Straight Bootstrap not conditioned on climate K-NN model conditioned on climate (Sep-Oct lag(1) correlation is not preserved

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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

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Salinity Model in RiverWare Subbasin of the upper Colorado Basin –above USGS gauge (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)

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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.

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