# Sequential optimal monitoring network design and iterative spatial estimation of pollutant concentration for identification of unknown groundwater pollution source locations

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- Received:
- Accepted:

DOI: 10.1007/s10661-012-2971-8

- Cite this article as:
- Prakash, O. & Datta, B. Environ Monit Assess (2013) 185: 5611. doi:10.1007/s10661-012-2971-8

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## Abstract

One of the difficulties in accurate characterization of unknown groundwater pollution sources is the uncertainty regarding the number and the location of such sources. Only when the number of source locations is estimated with some degree of certainty that the characterization of the sources in terms of location, magnitude, and activity duration can be meaningful. A fairly good knowledge of source locations can substantially decrease the degree of nonuniqueness in the set of possible aquifer responses to subjected geochemical stresses. A methodology is developed to use a sequence of dedicated monitoring network design and implementation and to screen and identify the possible source locations. The proposed methodology utilizes a combination of spatial interpolation of concentration measurements and simulated annealing as optimization algorithm for optimal design of the monitoring network. These monitoring networks are to be designed and implemented sequentially. The sequential design is based on iterative pollutant concentration measurement information from the sequentially designed monitoring networks. The optimal monitoring network design utilizes concentration gradient information from the monitoring network at previous iteration to define the objective function. The capability of the feedback information based iterative methodology is shown to be effective in estimating the source locations when no such information is initially available. This unknown pollution source locations identification methodology should be very useful as a screening model for subsequent accurate estimation of the unknown pollution sources in terms of location, magnitude, and activity duration.

### Keywords

Optimal monitoring networkGroundwater pollutionGeostatistical spatial interpolationOptimizationPollution source locations identification### Notations

- d
*x*,d*y* Size of the grid in the

*i,j*direction, respectively*k*Maximum permissible number of monitoring wells that can be placed in the study area including the existing ones in the current design stage

*ε*_{min}Average of the measured concentration from the initial and implemented well locations

*ε*_{max}A very high value of concentration

*m*Total number of monitoring wells already existing at the beginning of each design iteration

*f*_{i,j}Decision variable that can have integer values, 0 or 1

- itr
Variable representing iteration number

- ITR
Current iteration number

*i,j*Grid location co-ordinates

*M*^{int}Total number of initially available wells

*M*^{imp}Number of implemented monitoring wells

*M*^{eli}Total number of wells eliminated

*M*_{ITR}Total number of wells in a field before the current iteration ITR

- C
_{obs} Initially observed pollutant concentration data from arbitrary observation wells

- C
_{obs}\( {{{M_{\mathrm{ITR}}}}}\) Current observed pollutant concentration

- \( {C_{{\mathrm{avg}_{{{M_{\mathrm{ITR}}}}}^{\mathrm{ITR}}}}} \)
Average concentration for current iteration ITR

- \( {C_{{\mathrm{krig}_{i,j}^{\mathrm{ITR}}}}} \)
Kriged concentration values at all grid locations

*i,j*for current iteration ITR- \( \mathrm{Var}_{i,j}^{\mathrm{ITR}} \)
Variance of Gaussian noise distribution at all the nodes

*i,j*, for current iteration ITR- ∀
For all

- Є
Belongs to