Spatio-Temporal Analysis of Water Quality Parameters in Machángara River with Nonuniform Interpolation Methods

Water quality measurements in rivers are usually performed at intervals of days or months in monitoring campaigns, but little attention has been paid to the spatial and temporal dynamics of those measurements. In this work, we propose scrutinizing the scope and limitations of state-of-the-art interpolation methods aiming to estimate the spatio-temporal dynamics (in terms of trends and structures) of relevant variables for water quality analysis usually taken in rivers. We used a database with several water quality measurements from the Machángara River between 2002 and 2007 provided by the Metropolitan Water Company of Quito, Ecuador. This database included flow rate, temperature, dissolved oxygen, and chemical oxygen demand, among other variables. For visualization purposes, the absence of measurements at intermediate points in an irregular spatio-temporal sampling grid was fixed by using deterministic and stochastic interpolation methods, namely, Delaunay and k-Nearest Neighbors (kNN). For data-driven model diagnosis, a study on model residuals was performed comparing the quality of both kinds of approaches. For most variables, a value of k = 15 yielded a reasonable fitting when Mahalanobis distance was used, and water quality variables were better estimated when using the kNN method. The use of kNN provided the best estimation capabilities in the presence of atypical samples in the spatio-temporal dynamics in terms of leave-one-out absolute error, and it was better for variables with slow-changing dynamics, though its performance degraded for variables with fast-changing dynamics. The proposed spatio-temporal analysis of water quality measurements provides relevant and useful information, hence complementing and extending the classical statistical analysis in this field, and our results encourage the search for new methods overcoming the limitations of the analyzed traditional interpolators