# Applying the Quadrant Method for Pumping‐Trace Metal Correlations in Variable Time, Low‐Data Systems

## TL;DR

This paper introduces a new method to study how groundwater pumping affects trace metal concentrations, especially when data is limited and samples are spaced far apart.

## Contribution

The paper introduces an interval-scaled pumping rate metric and applies the Quadrant method for analyzing pumping-trace metal correlations in low-data scenarios.

## Key findings

- The Quadrant method is more reproducible than Kendall's tau when samples are widely spaced and sample sizes are small (n ~ 4).
- Correlations between pumping and trace metal concentrations vary across the study area and depend on well-specific factors.
- The Quadrant method can be useful when traditional methods like Kendall's tau fail to produce significant correlations.

## Abstract

Due to increasing global demand for fresh water, it is increasingly necessary to understand how aquifer pumping affects groundwater chemistry. However, comprehensive predictive relationships between pumping and groundwater quality have yet to be developed, as the available data, which are often collected over inconsistent time intervals, are poorly suited for long‐term historical correlation studies. For example, we needed an adequate statistical method to better understand relationships between pumping rate and water quality in the City of Norman (OK, USA). Here we used the interval‐scaled change in mean pumping rate combined with the Quadrant method to examine correlations between pumping rates and changes in trace metal concentrations. We found that correlations vary across the study area and are likely dependent on a variety of factors specific to each well. Comparing the Quadrant method to the commonly used Kendall's tau correlation, which requires different assumptions about aquifer behavior, the methods produced similar correlations when sample sizes were large and the time interval between samples was relatively short. Sample sizes were then artificially restricted to determine correlation reproducibility. Despite being less reproducible overall, the Quadrant method was more reproducible when there were large time intervals between samples and very small sample sizes (n ~ 4), but not as reproducible as significant (p ≤ 0.1) Kendall's tau correlations. Therefore, the Quadrant method may be useful for further investigating the effects of pumping in cases where Kendall's tau does not produce significant correlations.

We introduce an interval‐scaled mean pumping rate metric and apply a Quadrant correlation method to quantify correlations between groundwater pumping rates and trace metal concentrations. Quadrant correlation of pumping and trace metal data helps particularly in cases of widely spaced sampling intervals and sample sizes less than 10.