## C.10 Study Question 10: Is the spatial coverage of the monitoring network appropriate (spatial optimization)?

Optimization and design of the monitoring program must assure sample independence while providing adequate spatial coverage of the site. This question addresses how to use statistical methods to optimize the spatial coverage of the site. Optimization can lead to decreasing or increasing the number of wells. The concepts of sufficiency and redundancy are related but different tools are available to determine if existing wells are redundant (that is, wells can be removed from monitoring) if there are sufficient wells (you may either add or remove wells). If the monitoring program is in the early stages, statistical design considerations and site investigation data can be used to establish a well network (Section 3.6). Statistical spatial optimization methods are most applicable for a site with existing large data sets. For an overview of temporal optimization methods, see Study Question 9. For effective optimization, you must establish the goal of the long-term monitoring program and identify an acceptable set of wells to determine a change.

This question can be relevant in all stages of the project life cycle: release detection, site characterization, remediation, monitoring, and closure; it is more likely that enough information exists to conduct optimization at later stages in the project life cycle.

Selecting and Characterizing the Data Set

Verify that the data set can support optimization techniques. Refer to Section 3.4: Common Statistical Assumptions for further discussion of how the following requirements may impact statistical analysis results.

- Check for the presence of outliers using box plots, probability plots, Dixon's test, and Rosner's test.
- Check for autocorrelation between successive sampling events.
- Check for significant temporal trends.
- Verify that the meanThe arithmetic average of a sample set that estimates the middle of a statistical distribution (Unified Guidance). and varianceThe square of the standard deviation (EPA 1989); a measure of how far numbers are separated in a data set. A small variance indicates that numbers in the dataset are clustered close to the mean. are stable over the data set (or subset) time.
- Verify that the data set exhibits normal distributionSymmetric distribution of data (bell-shaped curve), the most common distribution assumption in statistical analysis (Unified Guidance). or normalize it using transformation, determine a suitable method for handling nondetects.
- See also Section 4.1: Considerations for Statistical Analysis.

Statistical Methods and Tools

Using the results of the above plots and tests as a guide, you can use more sophisticated statistical methods to evaluate the redundancy or sufficiency of sample results among wells. The two approaches highlighted for this assessment are the redundancy or spatial uncertainty analyses. Spatial optimization is a challenging objective and an active area of research. Generally these methods require a lot of data and broad spatial coverage of the plume. Optimization results should be checked versus what is known or hypothesized about contamination using the conceptual site model (CSM)A living collection of information about a site which considers factors such as environmental and land use plans, site-specific chemical and geologic conditions, and the regulatory environment (ITRC 2007b).. Be aware that in some cases uncertainty can be high and additional sampling may be required. See Appendix D for software packages.

- This test analyzes a large data set and trims wells.
- If trends exist, then the performance metric is based on replicating these spatial trends (for example, maps of contaminant plumes) with the subset of wells.
- If there are no trends, then trimmed data are compared to the stationaryA distribution whose population characteristics do not change over time or space (Unified Guidance). summary statistics.

- Normality is not required, but some of the methods may be sensitive to highly skewed distributions.
- Some nondetectsLaboratory analytical result known only to be below the method detection limit (MDL), or reporting limit (RL); see "censored data" (Unified Guidance). are allowed, but use caution in applying these methods with frequent nondetects.
- You can use simple qualitative evaluations based on removing a single or multiple wells or more sophisticated analyses like slope factor analyses or genetic algorithms to search for optimal well reduction scenarios. These methods work better with more data, so are best applied in later project stages.

- This test calculates spatial uncertainty for a large data set. Areas of higher uncertainty warrant more wells and areas with lower uncertainty need fewer wells.
- If trends or seasonality exist, then these trends should be eliminated for some of these methods.

- These methods typically work best with normally distributed data or data that can be transformed to normality.
- Some nondetects are allowed, but use caution in applying this method with frequent nondetects.
- You cannot use this method when concentrations are trending with time (time series plots).
- These methods works better with more data, so it is best applied in later project stages.
- Spatial optimization methods generally employ geostatisticsA branch of statistics that focuses on the analysis of spatial or spatiotemporal data, such as groundwater data (Gilbert 1987). (for example, krigingA weighted moving-average technique to interpolate the data distribution by calculating an area mean at nodes of a grid (Gilbert 1987).). The current locations of wells and the error from the spatial model are used to identify where to place wells to improve estimates of contaminant concentrations. Detailed discussion of geostatistics is beyond the scope of this document.

Interpretation of Results and Associated Uncertainty

Optimizing groundwater monitoring well networks often works best when the network is evaluated as a unit. Therefore, greater potential for project benefits exists when both spatial and temporal information are considered. However, in some cases a project could benefit by eliminating redundant wells or by adding wells to reduce uncertainties. It is important that optimization be conducted such with regard to and consistent with what is known or hypothesized using the CSMconceptual site model.

Related Study Questions

Study Question 5: Is there a trend in contaminant concentrations?

Study Question 6: Is there seasonality in the concentrations?

Study Question 9: Is the sampling frequency appropriate (temporal optimization)?

Key Words: Optimization, Efficiency, Spatial Coverage, Release Detection, Site Characterization, Remediation, Monitoring, Closure

Publication Date: December 2013