1. Multivariate Analysis of a Carbonate Chemistry Time-Series Study
Kellie Teague
Mars 6300
Spring 2018

2. Objective
Study A time-series observation of changes in carbonate chemistry parameters within 2 coral reefs off of Waimanalo, Oahu, Hawaii. Water samples were collected once per week (April 2010 – May 2011) at sunrise, solar noon, and sunset.
Goals
Identify any statistical patterns inherent in the carbonate chemistry data, particularly with respect to Total Alkalinity (TA) and Dissolved Inorganic Carbon (DIC).
Determine the driving environmental influences to changes in the carbonate system surrounding coral reefs.
Hypothesis:
Because the independent variables are highly cross-correlated, an ordination analysis should show a distinct gradient based on time of day and time of year sampled. Location should not have a strong role, as the sampling sites are quite close together and share the same source water.

3. Dataset Description 294 discrete water samples – 147 from each site
named by location (K or M), time of day (M, N, or E) and sampling date
Ex: K1.M
5 independent variables
Sea Surface Temperature, SST (℃)
Salinity (psu) pH
Total Alkalinity (TA), µmol kg-1
Dissolved Inorganic Carbon (DIC), µmol kg-1

4. Dataset Processing Row/Column Summary -1 < skewness < 1
0% empty cells
Initial Outlier Analysis
Relative Euclidean, + 2 SD
13 samples identified
None were omitted (all within 3 SD)
Relativization
General relativization (p = 1) was used to give all variables equal weight
Final Outlier Analysis
Euclidean Distance, + 3 SD
7 samples identified
None were omitted (in order to maintain an equal sample size across groups)
Results of the final outlier analysis, after data relativization

5. Dataset Exploration Cross-Correlations
pH strongly negatively correlated with TA and DIC
TA and DIC strongly correlated with each other
Temperature is moderately correlated with pH, TA, & DIC
Salinity is weakly correlated with the other variables
All pair-wise correlations were found to be significant

6. Dataset Analysis
This dataset has a normal distribution (according to the skewness values), no empty cells in the matrix, and a robust sample size. Therefore, it is ideally suited for a Principle Component Analysis (PCA) ordination.
Hypothesis Because the independent variables are highly cross-correlated, an ordination analysis should show a distinct gradient based on time of day and time of year sampled. Location should not have a strong role, as the sampling sites are quite close together and share the same source water.
Used covariance matrix with Euclidean distance

7. Results Interpretation

8. Results Interpretation
Stopping Rules
p-value : 1 axis
average eigenvalue: 1 axis
broken-stick eigenvalue: 1 axis
Axis 1 vs. Axis 2 – orthogonality = 100%
A 1-axis solution provides the best result and explains 81.4% of the variance

9. Results Interpretation
The strongest loadings for both Axis 1 and Axis 2 are from Temperature and DIC
Axis 1 – Temperature is stronger and the two variables oppose one another
Axis 2 – DIC is stronger and the two variables go together

10. Results Interpretation

11. Results Interpretation
Correlations with Temperature
Correlations with DIC
Correlations with temperature: Axis , Axis
Correlations with DIC: Axis , Axis

12. Discussion - The Method
The results of this PCA suggest that temperature has a strong influence on the various parameters of the carbonate chemistry system. The gradient along Axis 1 shows a clear distinction between samples taken in the morning (M), at solar noon (N), and in the evening (E).
Grouping the ordination results by location confirmed that sampling site did not play a major role in the gradient distribution.
As expected based on the cross-correlations, the eigenvectors for TA and DIC were very similar and pH showed an opposing trend.
This method was helpful in supporting suspected patterns within the dataset.

13. Discussion – Next Steps
For a re-analysis, I propose using a PerMANOVA to quantify the effect size of the different categorical variables (location, time of day, season of year).
PerMANOVA is the best way to compare the between group dissimilarity to the within group dissimilarity via the F statistic using a distance-based approach.
For a PerMANOVA analysis, the groups must be balanced (which is one reason no outliers were omitted from the original PCA).
The next steps for this study should include determining if temperature is a true driving force in the carbonate system of coral reefs, or if other influences like light availability and water residence time more strongly affect coral reef metabolic processes.

14. Questions?