Effects of detection limits on spatial modeling of water quality in lakes

Zhuoyan Song; Krista M Chomicki; Kenneth Drouillard; R Paul Weidman

doi:10.1016/j.scitotenv.2022.161052

Effects of detection limits on spatial modeling of water quality in lakes

Sci Total Environ. 2023 Mar 15:864:161052. doi: 10.1016/j.scitotenv.2022.161052. Epub 2022 Dec 22.

Authors

Zhuoyan Song¹, Krista M Chomicki², Kenneth Drouillard³, R Paul Weidman⁴

Affiliations

¹ Great Lakes Institute for Environmental Research, University of Windsor, Windsor, ON, Canada. Electronic address: zhuoyan@uwindsor.ca.
² Toronto and Region Conservation Authority, 101 Exchange Avenue, Vaughan, Ontario, Canada. Electronic address: krista.chomicki@trca.ca.
³ Great Lakes Institute for Environmental Research, University of Windsor, Windsor, ON, Canada. Electronic address: kgd@uwindsor.ca.
⁴ Great Lakes Institute for Environmental Research, University of Windsor, Windsor, ON, Canada. Electronic address: paul.weidman@uwindsor.ca.

PMID: 36566858
DOI: 10.1016/j.scitotenv.2022.161052

Abstract

Identifying sources and fate of nutrients and pollutants in lake waters is often difficult when key analytes (e.g., dissolved phosphate) are frequently below analytical detection limits (non-detects). One way of dealing with this problem in water quality data is to replace non-detects with "fill-in" values using imputation methods (IMs). While their performance for estimating descriptive statistics (e.g., mean and variance) has been evaluated comprehensively for many environmental variables, whether IMs can reconstruct spatial patterns using long-term water quality data with non-detects under different magnitudes of spatial variation remains under-studied. We developed an integrative framework, combining numerical simulations with univariate and multivariate approaches, to compare performance of nine IMs in recovering spatial patterns of water quality data with different degrees of spatial heterogeneity. We applied this framework to a 12-year water quality dataset sampled from the nearshore region of Lake Ontario near Pickering and Ajax to show the usefulness of IMs in estimating water quality spatial variation. Firstly, in the simplest modeling scenario, we found that most IMs reproduced spatial patterns of univariate data well with ≤30 % non-detects in the dataset. Secondly, when spatial patterns were heterogeneous (e.g., when weak water mixing in nearshore regions limited nutrient transport from input sources to offshore regions), most IMs also performed well by recovering spatial variation in multivariate data with ≤80 % non-detects. Thirdly, when spatial distributions were homogeneous (e.g., when strong water mixing increased transport of nutrients from input sources to other lake areas), only weighted quantile sum regression (WQSR) performed well in reconstructing spatial multivariate data trends with ≤10 % non-detects. Our study highlighted that IMs (especially WQSR) are useful for reconstructing spatial trends of water quality in large lakes. However, potential interactions between spatial heterogeneity and non-detect frequency must be considered when selecting an appropriate IM procedure to accurately model spatial patterns in water quality.

Keywords: Cladophora; Eutrophication; Great Lakes; Imputation methods; Non-detects; Phosphorus.