Analysis of water quality measurements in the tributaries of the guayllabamba river with nonuniform interpolation methods

Abstract

Cities consume large amounts of water for human and industrial consumption and wastewater usually goes back to natural sources without any treatment and pollutes them. Therefore, actions of monitoring, control, and remediation of contaminated water sources are required. The mathematical treatment of these characteristics will make it possible to understand their spatio-temporal behavior and facilitate water remediation efforts. The objectives proposed in this thesis were: first, to analyze the most populated areas of Quito with greater discharges of wastewater flowing to the tributaries of the Guayllabamba River; second, to select the water quality monitoring stations of a tributary of the Guayllabamba River and establish a database; third, to analyze and compare deterministic interpolation methods and those that use statistical learning; fourth, to construct the interpolation surfaces and interpret spatio-temporal trends for a study area. The study area is located in Quito, Ecuador, located at a height of 2815 meters above sea level. The Municipal Drinking Water Company of Quito (EPMAPS) conducted 64 water quality monitoring campaigns for the Machángara and San Pedro River, from 2002 to 2007 through by traditional methods. Some monitoring stations located in agricultural, population and industrial areas were chosen, obtaining databases on which the interpolation methods were applied. An electronic prototype was constructed with electrochemical probes for water quality measurements in the San Pedro River and construct our database. The performance of each algorithm has been made based on the MAE, and the technique of cross-validation LOO (Leave One Out) that has served to find the optimal parameters. As results, we obtained interpolation surfaces for each variable and for each method used. The less smoothed interpolation surfaces were those obtained with Delaunay interpolation, then with better smoothing are kNN (k Nearest Neighbors) and SVM (Support Vector Machine) with Mahalanobis distance and autocorrelation core. The relative error of MAE interpolation in 15 analyzed variables was between 0.11 and 0.70 with an average of 0.32. Interpolation surfaces showed spatio-temporal trends of each variable and seasonal and spatial variability that will be very useful for water quality researchers. The constructed water quality measurement prototype allowed obtaining measurements with temporary resolutions of 35 seconds and of spatial resolutions adjustable to the support team. With the samples obtained with the prototype, it was possible to apply the interpolation algorithms and obtain interpolation surfaces and spatio-temporal trends of each region analyzed. On the other hand, learning based on the adjustment of free parameters involves computational costs that are susceptible to the search mode of minimum MAE errors. The search for optimal parameters based on grids has allowed us to obtain the parameters that better generalize water quality measurements and infer values for those moments and places where measurements were not possible. A contribution of this work is the constructed prototype with whose samples of water quality variables it was possible to build interpolation surfaces and determine spatio-temporal trends useful for water researchers.