Multivariate Analysis of Streamwater Quality Data

Presented during Stable Isotope Hydrology and Biogeochemistry
in Watershed Science Shortcourse

March 1, 2001


Click here to start

Table of Contents

Multivariate Analysis of Streamwater Quality Data

Outline of Lecture


Time Series

Solute Mixing Space

Mixing Models

Hydrograph Separation

Graphical Separation

Tracer Separation (Temporal)


Process Inference


Why Tracers?

Assumptions for Tracers

Example: Temporal Hydrograph Separation

End-member Mixing Analysis

EMMA Terminology

Quick Review

Matrix Definition

Matrix Algebra-Transpose

Matrix Multiplication

Matrix Multiplication Example


More Definitions

Matrix Inverse

Why would anyone do this?

Principal Components Analysis

A picture might help...

Geometry of PCA

Covariance Matrix

Correlation Matrix

Problem Set #1: Geometry of Mixing

Part A. Determining pold using two different tracers

Answers to Part A

Class Excercise 1B, Part 1

Exercise 1B: Answers, Part 1

Exercise 1B, Part 2

Exercise 1B: Answers, Part 2

Exercise 1C, Part1

Exercise 1C, Answers Part 1

Exercise 1C, Part 2

Exercise 1C, Answers Part 2

Exercise 1C, Part 3

Exercise 1C Answers Part C

Exercise 2: Answers

Application of EMMA


Inverse Problem


Soil Solution Caveats

EMMA Notation

Problem Statement

Overdetermined System of Equations

Constrained Solution


Mixing Diagram: Panola

Mixing Diagram 2: Panola

End-Member Composition

Author: Rick Hooper (U.S. Geological Survey, Northborough, Mass.)

Results: Predicting Solute Concentration

Groundwater Composition

Solute Time Series

Annual Hydrograph Separation

Event Hydrograph Separation

Birkenes Mixing Diagram

Birkenes Mixing Diagram

Solute Predictions

Solute Predictions

Orthogonal Projections

A Picture might help

Huh? This is backwards

Steps in EMMA


Step 1: Mixing Diagrams

Example: Stream K1L

Stream + Springs

Mixing Diagram Diagnostics

Computer Tips

Step 2: Perform PCA

Which matrix to factor?

Standardization issues

Results from Panola and Birkenes

PCA Computer Tips

S-Plus Commands

Step 3: Project into new coordinate system

Project Potential End Members

Panola U-Space

Step 4. Screen end members

Results for Panola

Results for Birkenes

Computer Tips for Projection

Step 5. Calculate predicted streamwater chemistry

Results: Original and Projected End Members

EMMA vs. Watershed Simulation Models

From Mixing to Predictive Models


Annual "Average" Routing

Streamwater Chemistry

Soilwater Sulfate Chemistry

Soil Base Saturation

Event Chemistry for 2 Storms

Summer Thunderstorm

Winter Frontal Storm

Results from Acidification Model

Testable Hypotheses

Testing End-Members

Ca/SO4 Mixing Diagram

Additional Field Data

Slide 108


Hillslope/Riparian Mixing



Next Steps

Advantages of EMMA