A.5.5 Simulation Results for Scenario M3-C with Modified ISM (Quadrant Subdivision)

In the modified ISM, a DU is partitioned into several (≥3 to compute statistics) fairly homogeneous subparts, and ISM is applied to each of the subparts. Subdivision of a DU into fairly homogeneous subparts should be predicated on the CSM and/or results of a pilot study to extract information about the contamination distribution patterns. For simplicity in this example, equally sized quadrants are used.

In the modified ISM, at least one ISM replicate is collected from each subpart. The modified ISM may require more sampling effort than ISM applied to the entire DU (depending on the number of increments and replicates). The additional field effort is justified weighed against the potential to increase the information content of ISM and the needs of the site characterization.

This type of subdivision of a DU into subparts is also recommended by Pitard (1993). Unlike the reduced variability obtained from multiincrement sampling (MIS), the modified ISM provides a better estimate of overall DU variability, which can be used to compute a more accurate and rigorous 95% UCL by using direct statistical methods. The use of modified ISM may be particularly helpful under the following conditions: DU with large-scale DH and DU with mean concentration of the contaminant near the regulatory action level.

If the subparts have different areas, an area-weighted procedure can be used to estimate the DU mean and associated 95% UCL (see Section 4). Large DUs may require a greater number of subparts. For large DUs with many subparts, block kriging (Cressie 1993) may be used to characterize the DU contamination distribution.

Simulations using modified ISM were applied to Scenario M3-C DU shown in Figure A-20, with population parameters (including quadrants) summarized in Table A-18. Relevant statistics based on the modified ISM are summarized in Tables A-23 and A-24.

Table A-23. Summary statistics of modified ISM applied to M3-C using 1 ISM per quadrant,
each with no sample support (i.e., single points)

Statistics 25 Increments 36 Increments
Serpentine Systematic random Simple random Serpentine Systematic random Simple random
Minimum 722 719 707 728 740 741
Maximum 1396 1486 1608 1200 1251 1284
DU mean 829 851 858 830 842 857
Mean Q1 744 746 755 756 746 754
Mean Q2 860 900 905 854 893 910
Mean Q3 889 909 910 884 890 920
Mean Q4 825 848 861 826 840 846
Bias –19.0 2.3 9.4 –18.5 –6.0 9.2
Relative bias (FE) 0.02 <0.01 0.01 0.02 <0.01 0.01
Student's-t-UCL95 coverage 74% 81% 87.8% 75.8% 84.8% 88.3%
Student's-t-UCL95 (average) 983 1,036 1,068 9,78 1,000 1,043
Chebyshev UCL95 coverage 90% 96.3% 96.3% 97% 96.3% 97%
Chebyshev UCL95 (average) 1114 1194 1247 1104 1134 1200
RMSE 101 115 123 83 84 93
SD FE 0.119 0.136 0.145 0.098 0.099 0.110
CV Bar 0.15 0.17 0.19 0.14 0.15 0.17

Table A-24. Summary statistics of modified ISM applied to M3-C using 1 ISM per quadrant, each sample support of 0.05 units

Statistics 25 Increments 36 Increments
Systematic random Simple random Systematic random Simple random
Minimum 735 704 736 740
Maximum 1437 1337 1224 1300
DU mean 845 857 844 850
Mean Q1 755 748 754 749
Mean Q2 891 933 890 918
Mean Q3 910 909 888 892
Mean Q4 825 840 845 841
Bias –3.0 9.1 –3.9 1.4
Relative bias (FE) <0.01 0.01 <0.01 <0.01
Student's-t-UCL95 coverage 83.3% 85.8 84.8 88%
Student's-t-UCL95 (average) 1015 1059 1005 1022
Chebyshev UCL95 coverage 96% 98.25% 96% 98.8
Chebyshev UCL95 (average) 1159 1231 1142 1168
RMSE 98.3 105.6 86.5 88.5
SD of FE 0.116 0.124 0.102 0.104
CV Bar 0.158 0.185 0.151 0.162