Application of statistics to correlate groundwater chemistry with land use on O‘ahu, Hawai‘i

Abstract

This study compiles commonly available groundwater chemistry data from the Pearl Harbor Sole Source Aquifer (SSA), Hawai‘i—O‘ahu’s primary drinking water source—and applies hierarchical clustering analysis (HCA), principal component analyses (PCA), piper diagrams, and box plots with geospatial analysis to better define groundwater regions and correlate groundwater chemistry in those regions with land use. Groundwater in this aquifer recharges and flows through chemically similar soil and rocks, such that anthropogenic activities are a primary influence on the chemical variability of the aquifer’s differing regions. Our analyses link specific chemical species in groundwater to land use/cover categories: urban, agriculture, and natural and anthropogenically-induced saline water intrusion. To create distinct statistical groupings with different groundwater chemistry compositions, it was important that the suite of parameters used in the statistical analysis do not covary. In our case, Cl⁻ covaried with several major ions; however, by including F⁻, alkalinity, and SiO_x that do not covary with Cl⁻ in the covariance matrix, we produced improved spatial grouping of HCA clusters and stronger affinities to land use designations. Results show that dominant groundwater chemistry changes with land use along flow paths. These results pertain to areas where groundwater flows from conservation land in high recharge areas of O‘ahu’s mountain ranges to urban and agricultural land use regions: groundwater retains its source characteristics until about 3–6 km into agricultural and urban zoned lands. Ultimately, this study outlines a simple method for water quality regulators to use groundwater chemistry to identify risks of target contaminants based on land use.

Appendices

Appendix 1. Discussion of the method

A.1 Multiple samples from the same well

Samples used in this study were collected at different times and by different organizations and were analyzed by different laboratories; several sampling locations have multiple samples over time. We recognize that this diversity may affect the robustness of the results and the conclusions drawn. It is a key part of our study to demonstrate the utility of existing data for regional evaluations, thus removing the need for expensive field sampling for each new hydrologic investigation. Additionally, it is important to note that, for this study, our priority was to capture substantial differences in groundwater composition across broad gradients. Therefore, we completed this analysis with all available data that met our vetting process. It was necessary to include datasets from multiple studies, as no single past project had a broad enough reach to meet our needs. Having duplicate samples from different time intervals allowed for greater insight into the results of the coupled HCA-PCA approach as it showed how local groundwater composition can vary through time due to changes in pumping, climate variations, anthropogenic contamination, and other external stressors. We then investigated how those processes affect groundwater chemistry and resulting relationships to other regional groundwater compositions.

A.2 Statistical approach

Considering the two data management methods to prepare the HCA-PCA pipelines, the approach that incorporated F⁻ and SiO_x into the log-normalized ion data to produce HCA2 and PCA2 appears to be more robust (Fig. 13). HCA1, which utilized the % meq/L data input for the Piper diagram showed six clusters at a Euclidean distance of 100 (Fig. 2). In contrast, HCA2 using the log-normalized ion data and included SiO_x and F⁻ showed six clusters at a Euclidean distance of 9 (Fig. 4). The shorter Euclidean distance suggests a greater general similarity between the log-normalized data points. The difference of essentially an order of magnitude between the Euclidean distances could be due in part to data management, as HCA1 data was normalized on a percent scale, where HCA2 data was normalized on a log scale. Additionally, there could be some improved clustering results from the separation of the Na⁺-K⁺ parameter and inclusion of the SiO_x and F⁻ variables in HCA2.

Both PCA1 and PCA2 demonstrate a general geochemistry for O‘ahu groundwater. In PCA1, PCA1-1 accounts for the majority of explained variance (0.471) with Na⁺-K⁺, Ca²⁺, and Mg²⁺ being the most important features to PCA1-1 (0.536, 0.501, and 0.453, respectively). SO₄²⁻, alkalinity, and Cl⁻, are secondary features in PCA1-1 (0.332. 0.290, and 0.249, respectively). PCA1-2 of PCA1 accounts for only 0.347 of explained variance, but Alkalinity (0.597) and Cl⁻ (0.596) are the key features. The variance in PCA1-1 implies that there is a general variance among the chemical composition of groundwater across the study area, attributable to a variety of common ion concentrations. The variance in PCA1-2 attributable to alkalinity and Cl⁻, key components of seawater, show that a somewhat secondary driver to the differences seen in groundwater compositions across O‘ahu is the presence of saltwater intrusion. It could be argued that PCA1-1 of PCA1 is a measurement of general groundwater chemistry variability, whereas PCA1-2 is a metric of seawater contamination.

PCA2 continues the narrative of a general chemistry for local groundwater, as Ca²⁺, Mg²⁺, Na⁺, K⁺, and Cl⁻ all carried similar weight (between 0.380 and 0.402) for PCA2-1, which accounted for 0.662 of the data variance. PCA2 also showed the importance of incorporating SiO_x, alkalinity, and F⁻ into the analysis, as they were by far the most important variables of PCA2-2 (0.685, 0.565, and 0.387). The implication from PCA2-2 of PCA2 is that SiO_x alkalinity, and F⁻ could be important measurements for differentiating local regions of groundwater on O‘ahu as the other ion concentration variables often co-vary. The differentiations offered by these additional parameters indicates a robustness for the HCA2-PCA2 dataset and approach.

When small-batch PCAs were run for each cluster of HCA2 with the log-normalized ions including SiO_x and F⁻, the majority of variance was explained for each by their PC1s, with the majority of parameters covarying together. One exception was cluster 2a, in which 0.733 of variance was explained by PCA2-1; within that PCA2-1, SiO_x had a weight of 0.998. It seems that for cluster 2a, SiO_x concentrations were the defining variable.

HCA2 clusters 2b and 2a appear to be the most unique. Cluster 2a has higher alkalinity, while cluster 2b has higher F⁻ concentrations, although there is a large range of F⁻ concentrations for all clusters. Cluster 2b and 2a both have higher Ca²⁺, Mg²⁺, Cl⁻, Na⁺, K⁺, and SO₄²⁻, although cluster 2b is always higher than cluster 2a. Again, the PCA partnered with its HCA, in this case, PCA2, shows agreement with the box plot chemistry: clusters 2b and 2a are plotted in distinct and separate regions from the rest of the clusters, which otherwise plot adjacent to one another (Fig. 5). Interestingly, the upper and lower quartile boundaries for each cluster defined by HCA2 are generally closer together than in those clusters defined by HCA1. This could imply that the grouping is more robust for HCA2 and more accurately groups samples that are similar to one another, as discussed earlier in reference to the Euclidean distances and inclusion of additional variables.

Appendix 2. Piper diagrams

Fig. 12

Piper diagram 1—color-coded based on HCA with no combined pairs in Piper diagram data (HCA1). Six clusters. Piper diagram completed with %meq/L data for all parameters. Points color-coded based on the groups they formed in the previously described HCA methods

Fig. 13

Piper diagram 2—color-coded based on HCA with log-normalized ion data including F‾ and SiO_x (HCA2). Six clusters. Points color-coded based on the groups they formed in the previously described HCA methods