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Multivariate Analysis of Variance for Stream Classification in Texas

Multivariate Analysis of Variance for Stream Classification in Texas. Eric S. Hersh CE397 – Statistics in Water Resources Term Project Cinco de Mayo, 2009. Can we quantitatively regionalize the streams of Texas?.

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Multivariate Analysis of Variance for Stream Classification in Texas

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  1. Multivariate Analysis of Variancefor Stream Classification in Texas Eric S. Hersh CE397 – Statistics in Water Resources Term Project Cinco de Mayo, 2009

  2. Can we quantitatively regionalize the streams of Texas?

  3. Hersh, E.S., Maidment, D.R., and W.S. Gordon. “An Integrated Stream Classification System to Support Environmental Flow Analyses in Texas.” J. Am. Water Res. Assoc. Submitted November 2008.

  4. Revisited - the question posed Can we improve the way in which we perform the regionalization and thus (potentially) increase its classification strength?

  5. Analysis of Variance ANOVA Purpose: test whether group means are different Purpose: ANOVA with several dependent variables MANOVA Multivariate Analysis of Variance

  6. The Model • Multiple metric dependent variables (n=18) • Based on categorical (non-metric) independent variables (n=5 regions) • Manipulate independent variables to determine effect on dependent variables using SAS PROC GLM (general linear model) Region = DO ± Temp ± TSS ± pH ± Cond ± AirTemp ± Precip ± PET ± MAQ ± MAV ± BFI ± ZeroQ ± IQR ± Slope ± Substrate ± Sand ± Silt ± Clay

  7. ANOVA MANOVA = = … = where: p = parameter (dependent variable) k = factor (independent variable)

  8. Data Gaps • Total number of subbasins in Texas = 205 • Number with complete data = 103 Uh oh! This test is going to lose a lot of value. Unless… • Can we fill in the gaps somehow?

  9. Data Gaps • Some of the subbasins in Texas have no rivers. • Many have no gages. • Many have no WQ sampling stations. • Synthetic data would be difficult and poor. • But, the MANOVA test requires complete matrices. • Solution: fill in gaps with parameter means • Dilutes strength of classification (regions tend toward others)

  10. Hypothesis Test • Null Hypothesis: (vectors of) the group means are equal Of course not! That’s preposterous! There would be no regionalization! But… we don’t care.

  11. West (PRISM, 1971-2000) East

  12. Evaluating the Model • Pillai’s trace considered most robust • S.S. Pillai, 1901-1950, Indian mathematician

  13. Revision Methodology • Identify bordering subbasins (n=50, but 10 border multiple, so 60 trials total) • Switch one subbasin, check for increase in test stat, record and reset (21 deemed beneficial) • Rank by improvement • Implement changes in order, discard if decline (18 kept) • View in geographic context, apply decision rules (no islands or peninsulas, 15 kept)

  14. OLD NEW SWITCHED

  15. Possible Future Work • Write final report

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