Optimal redesign of coastal groundwater quality monitoring networks under uncertainty: application of the theory of belief functions

Abstract

This paper presents a new methodology for the optimal redesign of water quality monitoring networks in coastal aquifers. The GALDIT index is used to evaluate the extent and magnitude of seawater intrusion (SWI) in coastal aquifers. The weights of the GALDIT parameters are optimized using the genetic algorithm (GA). A SEAWAT-based simulation model, a spatiotemporal Kriging interpolation technique, and an artificial neural network surrogate model are then implemented to simulate total dissolved solids (TDS) concentration in coastal aquifers. To obtain more precise estimations, an ensemble meta-model is developed using the Dempster-Shafer’s belief function theory (D-ST) to combine the results obtained from the three individual simulation models. The combined meta-model is then used for calculating more precise TDS concentration. Some plausible scenarios are defined for variation of water elevation and water salinity at the coastline to incorporate uncertainty through the concept of value of information (VOI). Finally, the potential wells with the highest values of information are taken into consideration to redesign coastal groundwater quality monitoring network under uncertainty. The performance of the proposed methodology is evaluated by applying it to the Qom-Kahak aquifer, north-central Iran, which is threatened by SWI. At first, the individual and ensemble simulation models are developed and validated. Then, several scenarios are defined regarding the plausible changes in TDS concentration and water level at the coastline. In the next step, the scenarios, the GALDIT-GA vulnerability map, and the VOI concept are used for redesigning the existing monitoring network. The results illustrate that the revised groundwater quality monitoring network containing 10 new sampling locations outperforms the existing one based on the VOI criterion.

Appendices

Appendix 1

Table 7 The weights, rates, and ranges of the GALDIT parameters (Chachadi and Lobo-Ferreira 2001)

Appendix 2 Performance criteria used in PBAs

The performance criteria including correlation coefficient (CC), median absolute deviation (MAD), mean square error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and index of agreement (IOA) have been used in this paper according to the following equations:

Correlation coefficient (CC)

$$R=\frac{{\sum\nolimits _{i=1}^n}\left({x}_{i.a}-\overline{{x }_{a}}\right)({x}_{i.p}-\overline{{x }_{p}})}{\sqrt{{\sum\nolimits _{i=1}^n}{\left({x}_{i.a}-\overline{{x }_{a}}\right)}^{2}} \sqrt{\sum\nolimits _{i=1}^n{\left({x}_{i.p}-\overline{{x }_{p}}\right)}^{2}}}$$

(18)

Median absolute deviation (MAD):

$$MAD\left({x}_{a}.{x}_{p}\right)=median\left(\left|{x}_{1.a}-{x}_{1.p}\right|.\left|{x}_{2.a}-{x}_{2.p}\right|.\dots .\left|{x}_{n.a}-{x}_{n.p}\right|\right)$$

(19)

Mean square error (MSE):

$$MSE=\frac{1}{n}{\sum\nolimits_{i=1}^{n}({x}_{i.a}-{x}_{i.p})}^{2}$$

(20)

Root mean square error (RMSE):

$$RMSE=\sqrt{\frac{1}{n}{\sum\nolimits_{i=1}^{n}({x}_{i.a}-{x}_{i.p})}^{2}}$$

(21)

Mean absolute percentage error (MAPE):

$$MAPE=100\times \frac{1}{n}{\sum\nolimits _{i=1}^n}\frac{\left|{x}_{i.a}-{x}_{i.p}\right|}{{x}_{i.a}}$$

(22)

Index of agreement (IOA):

$$IOA=1-\frac{\sum\nolimits_{i=1}^{n}{({x}_{i.a}-{x}_{i.p})}^{2}}{\sum\nolimits_{i=1}^{n}{(\left|{x}_{i.p}-\overline{{x }_{a}}\right|+\left|{x}_{i.a}-\overline{{x }_{a}}\right|)}^{2}}$$

(23)

where ${x}_{i.a}$ and ${x}_{i.p}$ are actual and predicted TDS concentration values, respectively. n represents the number of data points. $\overline{{x }_{a}}$ and $\overline{{x }_{p}}$ are mean values of actual and predicted TDS concentration, respectively.