Water Quality Sensing and Spatio-Temporal Monitoring Structure with Autocorrelation Kernel Methods

Abstract

Pollution on water resources is usually analyzed with monitoring campaigns, which consist of programmed sampling, measurement, and recording of the most representative water quality parameters. These campaign measurements yields a non-uniform spatio-temporal sampled data structure to characterize complex dynamics phenomena. In this work, we propose an enhanced statistical interpolation method to provide water quality managers with statistically interpolated representations of spatial-temporal dynamics. Specifically, our proposal makes efficient use of the a priori available information of the quality parameter measurements through Support Vector Regression (SVR) based on Mercer's kernels. The methods are benchmarked against previously proposed methods in three segments of the Machángara River and one segment of the San Pedro River in Ecuador, and their different dynamics are shown by statistically interpolated spatial-temporal maps. The best interpolation performance in terms of mean absolute error was the SVR with Mercer's kernel given by either the Mahalanobis spatial-temporal covariance matrix or by the bivariate estimated autocorrelation function. In particular, the autocorrelation kernel provides with significant improvement of the estimation quality, consistently for all the six water quality variables, which points out the relevance of including a priori knowledge of the problem.

Keywords: Mahalanobis kernel; autocorrelation kernel; pollution measurements; spatio-temporal interpolation; support vector regression; water quality.

Figure 1

Location of monitoring stations at Machángara (Stretches 1, 2, and 3) and San Pedro (Stretch 4) Rivers. The station names and numeric codes were provided by the Metropolitan Water Company.

Figure 2

Flowchart of smoothing/interpolation for river water quality parameters.

Figure 3

Dynamics of water quality variables for Stretch 3. From left to right (columns), results with k-NN, RBF-SVR, Ma-SVR, and Au-SVR algorithms, for the selected variables: (a–d) Q in m${}^3$/s; (e–h) T in ${}^{\circ }$C; (i–l) DO in mg/L; (m–p) BOD in mg/L; (q–t) COD in mg/L; and (u–x) COD/BOD ratio (dimensionless).

Figure 4

Residual analysis for DO in Stretch 2: (a–d) Bland-Altman plots; (e–h) Scatter plots; (i–k) $|\Delta AE|$ of $Au-SVM$ compared with the other methods.

Figure 5

Residual analysis for T in Stretch 2: (a–d) Bland-Altman plots; (e–h) Scatter plots; (i–k) $|\Delta AE|$ of $Au-SVM$ compared with the other methods.

Figure 6

Dynamics of water quality variables for Stretches 1, 2, 3, and 4 (from left to right), when they are smoothed with the Au-SVR algorithm in terms of the estimated autocorrelation of the available data: (a–d) Q in m${}^3$/s; (e–h) T in ${}^{\circ }$C; (i–l) DO in mg/L; (m–p) BOD in mg/L; (q–t) COD in mg/L; and (u–x) COD/BOD ratio (dimensionless).

Figure 7

Dynamics of water quality variables for Stretches 1, 2, 3, and 4 (from left to right), when they are smoothed with the Ma-SVR algorithm in terms of the Mahalanobis distance from data covariance: (a–d) Q in m${}^3$/s; (e–h) T in ${}^{\circ }$C; (i–l) DO in mg/L; (m–p) BOD in mg/L; (q–t) COD in mg/L; and (u–x) COD/BOD ratio (dimensionless).