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Wasantha Lal

Some Previous Work On Model Sensitivity Analysis and Uncertainty Analysis at SFWMD successes, challenges and disappointments. Wasantha Lal. Initial Purpose of Sensitivity/Uncertainty Analysis.

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Wasantha Lal

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  1. Some Previous Work OnModel Sensitivity Analysis and Uncertainty Analysis at SFWMDsuccesses, challenges and disappointments Wasantha Lal

  2. Initial Purpose of Sensitivity/Uncertainty Analysis • To make sure that model outputs (eg. NSM and SFWMM) are used appropriately when making important decisions • To understand which parameters are most critical for the model output • To understand implications of model resolution (eg. 2x2)

  3. What causes uncertainty of model output forecasting uncertainty Operational uncertainty

  4. In addition to output uncertainty, what else may affect decision making

  5. How uncertainty analysis can be used in decisionmaking

  6. Examples of decision making under uncertainty(from other disciplines) • Steel/concrete design codes using factors of safety – ACI, API • Standards for water/air quality - EPA • Flood risk assessment - FEMA

  7. Model Unc. Work done at SFWMD • Uncertainty workshop, Louks and Stedinger, 1994 • First order method • (Monte Carlo) Latin Hypercube sampling method Report suggesting first order and LHS methods

  8. Model Unc. Work done at SFWMD (cont.. 2) • NSM sens/uncert analysis- Lal • First order method • Rosenblueth method • Factorial design method • Latin Hypercube method (LHS) • Singular Value Decomposition (SVD) Sensitivity and uncertainty analysis of Natural System Model NSM 4.2, 1994 (report) Sensitivity and uncertainty analysis of a regional simulation model for the Natural System in South Florida, Proc. XXVII IAHR/ASCE Conf , 1997, San Francisco

  9. First order method Sensitivity matrix

  10. Regional distribution of parameters

  11. parameters observations

  12. Sensitiviy matrix

  13. Sensitivity to ground elevation

  14. Sensitivity of daily values

  15. Input parameter uncertainties

  16. Model output uncertainties – first order method

  17. Singular Value Decomposition A=sensitivity matrix U,V=orthonornal mat Lambda=diagonal mat of singular values

  18. U^T V^T

  19. Parameter resolution Parameter correlation

  20. Parameter covariance

  21. Factorial design method for sensitivity

  22. Sensitivities derived fro factorial design

  23. Sensitivity from factorial design method

  24. Rosenblueth method Variance of the output

  25. Uncertainty bands

  26. Uncertainty bandwidth

  27. Uncertainty bandwidth for discharge

  28. Bandwidth of the duration curve

  29. Latin Hypercube Sampling

  30. Statistics for LHS

  31. Parameter rankings based on significance

  32. Model Unc. Work done at SFWMD (Cont.. 3) • Evaluation of NSM output uncertainty using SFWMM model results – Lal • Regression analysis • Spectral analysis • Other statistics of SFWMM output Evaluation of the NSM output uncertainty using SFWMM results

  33. Error bands

  34. Error statistics

  35. Error distribution

  36. Variation of error during the year

  37. Variation of error bands throughout the year

  38. Model Unc. Work done at SFWMD (Cont.. 4) • Numerical errors of overland flow and groundwater flow models – Lal • Discretization errors • Computational errors Performance comparison of overland flow algorithms, ASCE (HY) 124(4) Numerical errors in groundwater and overland flow models, Water Resources Research, 36(5), 2000

  39. Numerical ErrorLal, WRR 36(5), 2000

  40. Error-run time curveLal, ASCE HY 124(4), 1998

  41. Model Unc. Work done at SFWMD (cont.. 5) • SFWMM sensitivity/uncert analysis – Paul Trimble • First order method • SVD • Error analysis statistics Paul Trimble, An evaluation of the certainty of system performance measures generated by the South Dlorida Water Management Model, Masters Thesis, FAU, 1995

  42. Model Unc. Work done at SFWMD (Cont.. 6) • Uncertainty and Sensitivity of Phosphorous Deposition, Ahn and James • Sensitivity analysis of the ELM, Fitz et al. • Uncertainty of spatial data for landscape modeling, Sklar • Numerous other works

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