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

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.