Reconstructing missing data by comparing interpolation techniques: Applications for long-term water quality data

Abstract

Missing data are typical yet must be addressed for proper inferences or expanding datasets to guide our limnological understanding and management of aquatic systems. Interpolation methods (i.e., estimating missing values using known values within the dataset) can alleviate data gaps and common problems. We compared seven popular interpolation methods for predicting substantial missingness in a long-term water quality dataset from the Upper Mississippi River, U.S.A. The dataset included 80,000 sampling sites collected over 30 yr that had substantial missingness for total nitrogen (TN), total phosphorus (TP), and water velocity. For all three interpolated water quality variables, random forests had very high prediction accuracy and outperformed the methods of ordinary kriging, polynomial regressions, regression trees, and inverse distance weighting. TP had a mean absolute error (MAE) of 0.03 mg (L-TP)⁻¹, TN had a MAE of 0.39 mg (L-TN)⁻¹, and water velocity had a MAE of 0.10 m s⁻¹. The random forests' error rates were mapped and showed low spatiotemporal variability across the riverscape, indicating high model performance across many habitat types and large spatial scales. In the current era of “big data,” interpolation becomes an imperative step prior to ecological analyses yet remains unfamiliar and underutilized. Our research briefly describes the importance of addressing missingness and provides a roadmap to conduct model intercomparisons of other big datasets. We also share adaptable data analysis scripts, which allows others to readily conduct interpolation comparisons for many limnology applications and contexts.