Algorithm for Multi-Stage Spatial Sampling Design with Multiple Criteria M
The difficulties encountered in the remediation of Dense Nonaqueous Phase Liquid (DNAPL) contaminants in the subsurface have spawned numerous studies relating to evaluation of the benefits of DNAPL source zone depletion. Mass discharge, defined as the contaminant mass per unit time ([M/T]) migrating across a hypothetic control plane orthogonal to the mean groundwater flow, has been widely proposed as a potential metric to assess the impact of partial mass removal in DNAPL source zones. In the field, mass discharge estimates derived from relative sparse observations of contaminant concentration, hydraulic conductivity, and/or mass flux are always subject to uncertainty regardless of the technologies applied. However, the uncertainty is typically not quantified in field applications. An earlier Tufts invention (Tufts Ref. T001444) comprises an algorithm for the quantification of mass discharge uncertainty using multi-level measurements of contaminant concentration and hydraulic conductivity. This algorithm is, to all knowledge, the first one to quantify the uncertainty of mass discharge based on field measurements. Applications of this algorithm on numerically simulated control planes have suggested that one stage sampling design with a regular (rectangular) sampling pattern is not efficient (in terms of sampling density or cost) to accurately model the uncertainty, due to limitations in applying geostatistics to non-representative sample data.
This invention comprises a second algorithm for multi-criteria multi-stage spatial sampling design, which has been developed to optimize the sampling locations and to reduce the required sampling density for an accurate model of uncertainty. The spatial sampling algorithm combines methodologies from a number of disciplines including geostatistics and Multiple Criteria Decision Making (MCDM). It is capable of obtaining representative sample data in terms of the recognition of spatial pattern of contaminant concentration distribution through the identification and delineation of highly concentrated areas (hot spots). Evaluation of this algorithm on hypothetical control planes suggested that the required sampling density can be reduced by at least 50% in comparison with one stage sampling design with a regular sampling pattern.
This algorithm is different from other spatial sampling designs in that (1) neither the sampling density nor the sampling pattern is decided a priori; instead, the minimal sampling density is determined by the accuracy of the uncertainty model of mass discharge, and there is no pre-set sampling pattern; (2) more freedom is allowed in the selection of sampling criteria in that there is no requirement that the sample criteria should be mathematically formulated in terms of quantities that can be measured or computed in advance of real sampling; and (3) the weights for sampling criteria are objectively determined and automatically updated by data themselves.
US Patent 8,615,379, Issued December 24, 2013
Tufts University case T001445