Table of Contents
Multivariate Analysis of Streamwater Quality
Data
Outline of Lecture
Overview
Time Series
Solute Mixing Space
Mixing Models
Hydrograph Separation
Graphical Separation
Tracer Separation (Temporal)
Contradiction
Process Inference
Terminology
Why Tracers?
Assumptions for Tracers
Example: Temporal Hydrograph Separation
Endmember Mixing Analysis
EMMA Terminology
Quick Review
Matrix Definition
Matrix AlgebraTranspose
Matrix Multiplication
Matrix Multiplication Example
Questions
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 p_{old }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
References
Inverse Problem
Problems
Soil Solution Caveats
EMMA Notation
Problem Statement
Overdetermined System of Equations
Constrained Solution
Application
Mixing Diagram: Panola
Mixing Diagram 2: Panola
EndMember 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
EMMA and PCA
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
SPlus Commands
Step 3: Project into new coordinate system
Project Potential End Members
Panola USpace
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
MAGIC
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 EndMembers
Ca/SO_{4} Mixing Diagram
Additional Field Data
Slide 108
Hypotheses
Hillslope/Riparian Mixing
Huh?
Implication
Next Steps
Advantages of EMMA
