A Comparison of Linear and Non-linear Machine Learning Techniques (PCA and SOM) for Characterizing Urban Nutrient Runoff

Urban stormwater runoff represents a significant challenge for the practical assessment of diffuse pollution sources on receiving water bodies. Given the high dimensionality of the problem, the main goal of this study was the comparison of linear and non-linear machine learning (ML) methods to characterize urban nutrient runoff from impervious surfaces. In particular, the principal component analysis (PCA) for the linear technique and the self-organizing map (SOM) for the non-linear technique were chosen and compared considering the high number of successful applications in the water quality field. To strengthen this comparison, these techniques were supported by well-known linear and non-linear methods. Those techniques were applied to a complete dataset with precipitation, flow rate, and water quality (sediments and nutrients) records of 577 events gathered for a watershed located in Southern Italy. According to the results, both linear and non-linear techniques can represent build-up and wash-off, the two main processes that characterize urban nutrient runoff. In particular, non-linear methods are able to capture and represent better the rainfall-runoff process and the transport of dissolved nutrients in urban runoff (dilution process). However, their computational time is higher than the linear technique (0.0054 s vs. 15.24 s, for linear and non-linear, respectively, in our study). The outcomes of this study provide significant insights into the application of ML methods for the water quality field.