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IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATION HSPF – CBWM

IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATION HSPF – CBWM. Modeling Subcommittee Quarterly Review January 25, 2006. What a model does:-. Parameters p. M. Outputs o. Inputs i. x describes system configuration. o = M (x,p,i). The inverse problem:-.

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IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATION HSPF – CBWM

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  1. IMPLEMENTATION OF PEST TO THE PHASE 5 SEDIMENT AND WATER-QUALITY CALIBRATIONHSPF – CBWM Modeling Subcommittee Quarterly Review January 25, 2006

  2. What a model does:- Parameters p M Outputs o Inputs i x describes system configuration o = M (x,p,i)

  3. The inverse problem:- Parameters p M Measurements q Inputs i x describes system configuration p= M-1 (x,i,q)

  4. PEST • Parameter estimation: iterative process • Pest minimizes the weighted sum of squared differences between model predictions and measured data. • Gauss-Marquardt-Lavenberg algorithm • Singular Value Decomposition

  5. oi ri qi

  6. Heads (m) very different units Conc (mg/l * 10-3)

  7. Theoretically:- The weight pertaining to each observation should be proportional to the inverse of the standard deviation associated with each observation.

  8. Nonlinear parameter estimation …..

  9. Initial parameter estimate:- Initial estimates o0 = M( p0 ) Nonlinear model Model outcomes

  10. Using Taylor’s theorem Parameter vector o=o0 + J(p - p0 ) Jacobian matrix Model outcomes

  11. Jacobian matrix:- One model run (at least) per adjustable parameter to calculate derivatives using finite differences.  o1 /  p1  o1 /  p2 o1 /  p3 o1 /  p4  o2 /  p1  o2 /  p2 o2 /  p3 o2 /  p4  o3 /  p1  o3 /  p2 o3 /  p3 o3 /  p4  o4 /  p1  o4 /  p2 o4 /  p3 o4 /  p4  o5 /  p1  o5 /  p2 o5 /  p3 o5 /  p4  o6 /  p1  o6 /  p2 o6 /  p3 o6 /  p4  o7 /  p1  o7 /  p2 o7 /  p3 o7 /  p4  o8 /  p1  o8 /  p2 o8 /  p3 o8 /  p4 etc

  12. Iterative solution improvement:- p2 At least n+1 model runs per optimization iteration (n = no. of adjustable parameters) p1

  13. Regularization and Simultaneous Calibration…..

  14. Simultaneous calibration adjustable LZSN #3 Watershed #1 #2 #4 #5

  15. Simultaneous calibration with regularisation minimum deviation from estimated average adjustable LZSN #3 Watershed #1 #2 #4 #5

  16. writes model input files Input files PEST TSPROC Output files reads model output files

  17. Input files Input files PEST Model calibration conditions Default condition Output files Output files

  18. For the IRC parameter pi36 1.0 * log(irc1) - 1.0 * log(irc12) = 0.0 1.00 regulir pi37 1.0 * log(irc12) - 1.0 * log(irc23) = 0.0 1.00 regulir pi38 1.0 * log(irc23) - 1.0 * log(irc34) = 0.0 1.00 regulir pi39 1.0 * log(irc34) - 1.0 * log(irc45) = 0.0 1.00 regulir pi40 1.0 * log(irc45) - 1.0 * log(irc1) = 0.0 1.00 regulir For the UZSN parameter pi26 1.0 * log(uzsn1) - 1.0 * log(uzsn12) = 0.0 1.00 reguluz pi27 1.0 * log(uzsn12) - 1.0 * log(uzsn23) = 0.0 1.00 reguluz pi28 1.0 * log(uzsn23) - 1.0 * log(uzsn34) = 0.0 1.00 reguluz pi29 1.0 * log(uzsn34) - 1.0 * log(uzsn45) = 0.0 1.00 reguluz pi30 1.0 * log(uzsn45) - 1.0 * log(uzsn1) = 0.0 1.00 reguluz

  19. We may also have… pi55 1.0 * log(lzsn1) = 0.90308998699 1.00 regullz2 pi56 1.0 * log(lzsn12) = 0.90308998699 1.00 regullz2 pi57 1.0 * log(lzsn23) = 0.90308998699 1.00 regullz2 pi58 1.0 * log(lzsn34) = 0.90308998699 1.00 regullz2 pi59 1.0 * log(lzsn45) = 0.90308998699 1.00 regullz2

  20. Application to the Monocacy……

  21. Future Work……

  22. Evaluate the accuracy of the model predictions with regularization • Determine an optimum period of calibration/verification • Try additional criteria for the Objective function (i.e., rating curve for sediment calibration) • Evaluate/Eliminate insensitive parameters • Extend application to entire watershed

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