Optimizing the flow adjustment of constituent concentrations via LOESS for trend analysis

Trend analysis of stream constituent concentrations requires adjustment for exogenous variables like discharge because concentrations often have variable relations with flow. To remove the influence of flow on stream water quality data, an accurate characterization of the relationship between the constituent and streamflow is needed. One popular method, locally weighted regression (LOESS), provides an effective means for flow-adjusting concentrations. The LOESS fit can be tailored to the data via the smoothing parameter (f), so that the user can avoid overfitting or oversmoothing the data. However, it is a common practice to use a single f value when flow-adjusting water quality data for trend analysis. This study provides a robust, automated method for determining the optimal f value (f_opt) for each dataset via an iterative K-fold cross-validation procedure that minimizes prediction error in LOESS. The method is developed by analyzing datasets of seven different constituents across 17 sites (119 datasets total) from a stream monitoring program in northwest Arkansas (USA). We recommend using 10 iterations of 10-fold cross-validation (10 × 10 CV) in order to select f_opt when flow-adjusting water quality data with LOESS. The use of a default f value did not produce different trend interpretations for the data used here; however, the proposed approach may be helpful in other water quality studies which employ similar statistical fitting methods. Additionally, we provide an implementation of the method in the R statistical computing environment.