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Comparison of natural streamflows generated from a parametric and nonparametric stochastic model

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Title: Incorporating Climate Information in Long Term Salinity Prediction with Uncertainty Analysis Author: CADSWES Last modified by: james prairie – PowerPoint PPT presentation

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Title: Comparison of natural streamflows generated from a parametric and nonparametric stochastic model


1
Comparison of natural streamflows generated from
a parametric and nonparametric stochastic model
  • James Prairie(1,2), Balaji Rajagopalan(1) and
    Terry Fulp(2)
  • 1. University of Colorado at Boulder, CADSWES
  • 2. U.S Bureau of Reclamation

2
Motivation
  • Generate future inflow scenarios for decision
    making models
  • reservoir operating rules, salinity control
  • Estimate uncertainty in model output

Options
  • Parametric Techniques
  • AR, ARMA, PAR, PARMA
  • Nonparametric Techniques
  • K-NN, density estimator, bootstrap

3
Objective of Study
  • Compare nonparametric and parametric techniques
    for simulation of streamflows
  • at USGS stream gauge 09180500 Colorado River
    near Cisco, UT

4
Outline of Talk
  • Overview of parametric technique
  • Explain nonparametric technique
  • Compare various distribution attributes
  • mean
  • standard deviation
  • lag(1) correlation
  • skewness
  • marginal probability density function
  • bivariate probability
  • Conclusions

5
Parametric
  • Periodic Auto Regressive model (PAR)
  • developed a lag(1) model
  • Stochastic Analysis, Modeling, and Simulation
    (SAMS)
  • Data must fit a Gaussian distribution
  • log and power transformation
  • not guaranteed to preserve statistics after back
    transformation
  • Expected to preserve
  • mean, standard deviation, lag(1) correlation
  • skew dependant on transformation
  • gaussian probability density function

Salas (1992)
6
Nonparametric
  • K- Nearest Neighbor model (K-NN)
  • lag(1) model
  • No prior assumption of datas 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

7
Nonparametric (contd)
  • Markov process for resampling

Lall and Sharma (1996)
8
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

Where v tj is the jith component of Dt, and w j
are scaling weights.
Lall and Sharma (1996)
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Bivariate Probability Density Function
18
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)

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