Multivariate Techniques for Modeling Storm Hydrographs in the HJA Experimental Forest - PowerPoint PPT Presentation

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Multivariate Techniques for Modeling Storm Hydrographs in the HJA Experimental Forest

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  1. Multivariate Techniques for Modeling Storm Hydrographs in the HJA Experimental Forest Melissa Martin and Julia Jones, PhD. Oregon State University

  2. The Watersheds

  3. The Hydrograph

  4. Objectives • Compare peak discharge and precipitation for WR, DR, WRS events for each watershed • Examine relationship of hydrograph variables to intensity/timing of precipitation, under the three soil conditions listed above for each watershed • How are these different across the watersheds?

  5. Principal Component Analysis • Why consider PCA? • What is PCA? - Explains variance-covariance structure - Good for data reduction • The ith PC is given by • Proportion of total population variance due to the kth PC is equal to

  6. Example: PCA for WS2 • Examine the 10 hydrograph variables for normality

  7. Obtain the coefficients of the PC’s

  8. How many PC’s to choose? • Four PC’s are included in all principal component analyses

  9. Biplots: A 2-dimensional representation

  10. Storm event type for WS2

  11. PCA results for WS2, WS8, WS9, and event type

  12. Normality assumptions • Not good for WS9 • Not good for WS8

  13. Areas for future research • Statistical models: Factor analysis, two-way MANOVA, blocking, restricted date ranges, PCA regression • Hydrograph properties: Getting more storm events for WS8 (GetPQ), creating software for HJA

  14. References • Slide 1: Photograph courtesy of Julia Jones. • Slide 3: HJ Andrews Experimental Forest figure from Perkins and Jones, Snow and physiographic controls, 1997. - Information about the watersheds and event classification: Perkins and Jones, Snow and physiographic controls, 1997. • Slide 4: Hydrograph figure from Perkins and Jones, Snow and physiographic controls, 1997. • Slide 6: The result quoted is Result 8.1, found in Johnson, Richard A. and Wichern, Dean W. Applied Multivariate Statistical Analysis, 2002. Fifth edition, Prentice Hall, Upper Saddle River, New Jersey. Page 428.

  15. Thank You • Desiree Tullos for creating the EISI program • Julia Jones and Tom Dietterich for mentoring help on this research project • Reed Perkins for running GetPQ to create the hydrograph data set • The entire HJA staff • Fellow EISI participants