# 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 |