7-1 

7 Hanford 300 Area 

7.1 Introduction 

This report is an exercise demonstrating the application of the Advanced Environmental 

Solutions, LLC (AES) Strategy to a highly transmissive, near surface aquifer in the 

Northwestern United States. This exercise is for testing the functionality for the Strategy 

only. Data utilized in this evaluation are based on readily available information. Most of 

this chapter is a recapitulation of Hanford data. An alternative to the current Conceptual 

Site Model of ground water flow is offered in section 7.3. 

The Hanford Site borders the Columbia River and covers 1,517 square kilometers (586 

square miles) just north of the city of Richland, Washington. In this case study, the AES 

Strategy provides a structured approach for studying the relationship between 

groundwater flow in the Hanford 300 Area, which is located in the southeast portion of 

the Hanford site, and the Columbia River. An accurate understanding of the 300 Area 

groundwater flow pattern will, in turn, aid in understanding the distribution and migration 

of contaminants, particularly hexavalent uranium, in the 300 Area. A map depicting the 

Hanford Site, including the 300 Area, is presented in Figure 7-1. 

The ground water beneath the 300 Area has been contaminated by liquid effluent 

discharges from 3 main waste sites: the 300 area, 618-11 burial ground, and the 316-4 

cribs/618-10 burial ground. These releases occurred from the late 1940s through the mid1980s. Since the end of fuel fabrication activities, contaminated discharges have largely 

ceased, although discharges of uncontaminated effluent continued until 1994. Remedial 

actions have been completed that removed the structures and contaminated soil 

associated with most of these disposal sites. However, residual amounts of some 

contaminants remain in the underlying vadose zone, and their presence is indicated in 

ground water monitoring results. 
7-2 

Figure 7-1. Hanford Site map including the 300 Area (DOE, 1999) 

7.2 Compilation of Available Data 

7.2.1 Geologic Setting 

The Hanford Site lies within the Pasco Basin, a structural depression that has 

accumulated a relatively thick sequence of fluvial, lacustrine, and glaciofluvial 

sediments. Local geology as well as the regional geology play a strong role in 

contaminant transport. 

7.2.2 Regional Geologic Information 

Figure 7-2 and Figure 7-3 show the surface geology and major structural features of the 

area, respectively. The Pasco Basin initially developed on the underlying Columbia 

River Basalt Group, a sequence of continental flood basalts covering more than 160,000 

km2

 (Vermeul et al., 2003). 
7-3 

Figure 7-2. Hanford Site regional geologic setting (Vermeul et al., 2003) 
7-4 

Figure 7-3. Structural geologic features of the Hanford Site within the Pasco Basin (Vermeul et al., 

2003) 

Overlying the basalt within the Pasco Basin are fluvial and lacustrine sediments of the 

Ringold Formation (Figure 7-4) (Lindsey et al., 1992). The ancestral Columbia River and 

its tributaries flowed into the Pasco Basin, depositing coarse-grained sediments in the 

migrating river channels and fine-grained sediments (silt and clay) primarily as overbank 

flood deposits. On at least two occasions, these river channels were blocked, forming 

lakes in the Pasco Basin and depositing extensive layers of fine-grained lacustrine 

sediments within the Ringold Formation. 

7.2.3 Site-specific Geologic Information 

The major geologic units in the Hanford Site area are the Miocene Columbia River Basalt 

Group (CRBG) and intercalated sedimentary rocks of the Ellensburg Formation. These 

are overlain by younger (Mio-Pliocene) sedimentary rocks of the Ringold Formation, the 

early “Palouse” soil/Plio- Pleistocene Unit, and the Pleistocene cataclysmic flood 

deposits of the Hanford Formation (Figure 7-4). 
7-5 

Figure 7-4. Major geological units at the Hanford Site (DOE, 1999) 

The Plio-Pleistocene Unit is made up of sandy gravels that separate the Hanford 

Formation and the Ringold Formation in the east-central Cold Creek syncline and at the 

east end of the Gable Mountain anticline (east and south of the 200 East Area). These 

gravels are up to 25m (75 feet) thick. Along the western margin of the site, the “Palouse” 

soil separates the two formations. The Hanford Formation consists of pebble to boulder 

sized gravel, fine to coarse-grained sand, and silts of unconsolidated deposits from ice 

age flooding. The Hanford Formation generally lies above the water table throughout 

most of the Hanford Site, except in the 100 and 300 Areas (DOE, 1998). 

7.2.4 Site-specific Hydrogeologic Information 

Geologic descriptions are available from 67 boreholes in the 300 Area. All of these 

boreholes are deep enough to penetrate the contact between the Hanford and Ringold 

stratigraphic formations. EarthVision geologic modeling and visualization software was 

used to interpolate unit contacts between borehole locations and to create a threedimensional model of the hydrogeologic framework. Figure 7-5 provides an index to the 

three cross sections shown in Figure 7-6, Figure 7-7, and Figure 7-8, which are drawn 

through the model to illustrate the framework (Peterson, 2005). 

Highly transmissive Hanford formation gravels are found below the water table across 

portions of the 300 Area. The extent and thickness of saturated Hanford formation 

gravels vary as a consequence of changes in water-table elevation, which are caused by 

changes in the Columbia River stage. The saturated thickness of the Hanford formation 

in the 300 Area varies from 0 to 15 meters (0 to 49 feet). Aquifer pumping tests at five 

boreholes within the 300 Area reveal an average hydraulic conductivity of approximately 
7-6 

14,000 meters (45,932 feet) per day for saturated Hanford formation gravels. This 

indicates a highly transmissive hydrologic unit. The value is significantly higher than the 

average hydraulic conductivity for Hanford formation gravels elsewhere on the Hanford 

Site (i.e., approximately 2,000 meters (6,562 feet) per day (Peterson, 2005). 

Extrapolating from the known geology indicates that there is a high likelihood that zones 

of high permeability are present and are highly variable in their spatial distribution. 

Ringold Formation gravels below the water-table range in thickness from 15 to 50 meters 

(49 to 164 feet). Aquifer pumping tests at seven boreholes in the 300 Area suggest an 

average hydraulic conductivity of approximately 125 meters (410 feet) per day, which is 

again higher than the average values for Ringold gravels elsewhere on the Hanford Site 

but considerably less transmissive than the overlying Hanford unit. Relatively higher 

conductivities may exist in the upper part of the Ringold Formation (i.e., Unit E gravel), 

where most pumping tests have been performed (Peterson, 2005). 

Figure 7-5. Index map to cross sections shown in Figures 6, 7, and 8 (Peterson, 2005) 
7-7 

Figure 7-6. West to east cross section along flow path from 300 Area process trenches to the 

Columbia River (Peterson, 2005) 

Figure 7-7. North to south cross section along shoreline wells (Peterson, 2005) 

Figure 7-8. West to east cross section through central portion of 300 Area (Peterson, 2005) 
7-8 

7.2.5 Vadose Zone Data 

The sediments beneath waste sites at Hanford are highly heterogeneous (for example, 

sediments include interbedded sand, silts, gravels, and boulders). Temporal and spatial 

variations in net water infiltration through current and past liquid discharges, water line 

leaks, and variable chemical interactions complicate description and understanding of 

contaminant transport, and lead to uncertainty in the evaluation of transport at 

contaminated sites. A number of knowledge gaps—including an insufficient 

understanding of source terms, geological and hydrologic properties, preferential flow, 

and chemical interactions–make current modeling of contaminant transport in the 

Hanford vadose zone unreliable. 

Figure 7-9 presents three potential types of preferential flow models in the Hanford 

vadose zone: (1) fingering, (2) funnel flow, and (3) flow associated with clastic dikes or 

poorly sealed borehole annular space. Funnel flow can enhance lateral migration, and 

horizontal layering will tend to stabilize fingered flow, whereas cross-bedding 

concentrates and coalesces fingers. Flow through clastic dikes and poorly sealed wellannular spaces could exhibit a hysteretic Effect, which may appear during infiltration 

events (such as large rainfall events), and there may be flow impediments during drying 

(Faybishenko, 2000). 

In the 300 Area, the vadose zone is relatively thin, ranging from about 1 to 30 m in 

thickness. It is generally composed of recent surficial deposits and portions of the 

Hanford formation and/or Ringold Unit E. Sediments from the upper strata of the Ringold 

Formation within the 300 Area is characterized by complex interstratified beds and lenses 

of sand and gravel. Ringold Formation deposits are generally more cemented and better 

sorted than those from the Hanford formation. Ringold strata typically contain a lower 

percentage of angular basaltic detritus than Hanford formation deposits. The Hanford 

formation is characterized by dark grayish-brown to dark olive-gray sandy gravel, typical 

of the gravel-dominated facies, with some silt and local sand stringers. The upper portion 

of the unit generally exhibits a pebble to boulder gravel, which becomes finer with depth, 

to a very fine-to-medium pebble gravel (DOE, 1998). 
7-9 

Figure 7-9. Conceptual model of fluid flow beneath single shell tanks at Hanford Site showing 

fingering, funnel flow, and flow associated with clastic dikes or poorly sealed borehole annular space 

(Faybishenko, 2000) 

7.2.6 Hydrologic Data 

Ground water flow beneath the 300 Area is generally directed toward the southeast. 

Ground water appears to converge beneath the 300 Area, with flow coming into the 300 

Area from the northwest, west, and southwest. The uppermost aquifer (Hanford 

formation) is highly transmissive because of open framework gravelly sediment, thus 

leading to high flow velocities (i.e., meters per day). However, because the hydraulic 

gradient that drives the flow varies with Columbia River stage, actual movement paths of 

water can be variable when viewed on short time scales, such as days or weeks. When 

viewed over seasons and years, however, the net flow and movement of contaminant 

plumes follows the generally southeasterly course (Peterson, 2005). 

It is not clear exactly what influence the Columbia River has on the overall ground water 

flow direction. Data indicates that the aquifer is in communication with the river and that 

the stage of the river does impact the lateral movement of water into and out of the 

aquifer. What is less clear is what influence the river has on the flow of ground water 

within the aquifer locally at the aquifer/ river interface. Improving our understanding of 

the relationship between the river and Area 300 groundwater through the implementation 

of the AES Strategy is the primary focus of this exercise. 
7-10 

7.2.7 Seasonal Variability in Water-Table Conditions 

To better understand how the dynamic hydrologic system in the 300 Area influences the 

dispersal pattern of contaminant plumes, hourly hydraulic head data were analyzed to (a) 

determine the predominant ground water flow directions, and (b) assess variability in 

flow directions during the various seasons. The analysis used hourly measurements of 

hydraulic head made at 30 wells in the 300 Area during the period of March 1992 

through February 1993, using pressure transducers. Water-table elevation contour maps 

were prepared for March, May, June, September, and December 1992 (Figure 7-10, 

Figure 7-11, Figure 7-12, Figure 7-13, and Figure 7-14, respectively). The contours were 

based on 22 wells deemed most representative of unconfined aquifer (i.e., water table) 

conditions. The values contoured were averages of all hourly measurements made during 

a particular month. The water-table maps for the various months reveal that the shape of 

the water table and, therefore, the inferred long-term ground water flow pattern, appears 

to show little variation from season to season. The overall elevation of the water table is 

higher during the seasonal high river discharge that occurs in May and June. The aquifer 

apparently equilibrates rapidly to changes in river stage, which is expected given the high 

transmissibility of the stratigraphic units (Peterson, 2005). 

Figure 7-10. 300 Area water-table elevation, 

March 1992 (averaged hourly) (Peterson, 

2005) 

Figure 7-11. 300 Area water-table elevation, 

May 1992 (averaged hourly) (Peterson, 2005) 
7-11 

Figure 7-12. 300 Area water-table elevation, 

June 1992 (averaged hourly) (Peterson, 2005) 

Figure 7-13. 300 Area water-table elevation, 

September 1992 (averaged hourly) (Peterson, 

2005) 

Figure 7-14. 300 Area water-table elevation, 

December 1992 (averaged hourly) (Peterson, 

2005) 
7-12 

The fluctuating river stage causes corresponding fluctuations in water-table elevations. 

Typically, lines of equal topographic elevation result in flow in a parallel fashion from an 

unconfined aquifer into the adjacent stream. Water table contour shapes in the preceding 

Figure 7-10 through Figure 7-14 cannot be adequately explained by either topography or 

river infiltration into the aquifer. Contours at all seasons indicate that there could be an 

influence on the direction of ground water flow by the impinging river on the bank of the 

river. Consequently, dispersal of contaminants from a particular source may have a 

deflected path over the course of several years. 

The water-table maps indicate that the ground water flow direction in the vicinity of the 

300 Area process trenches, the last liquid waste disposal facility to receive uraniumbearing effluent, is generally to the south-southeast for all seasons (Peterson, 2005). 

Periodic reversal of the hydraulic gradient (i.e., directed inland from the river) occurs 

near the river when the stage is high, but this change is not readily apparent in the 

monthly averaged data. Based on hydraulic gradients, Figure 7-10 through Figure 7-14 

suggest that along the shoreline to the south of the process trenches, river water may be 

continually entering the aquifer, flowing south along the shore, and then discharging back 

to the river. The highly transmissive Hanford unit is thicker along this section of 

shoreline, which would possibly enhance this exchange (see cross section in Figure 7-7). 

The implication of having a fairly consistent long-term orientation of flow direction is 

that plume boundaries can be more accurately anticipated, especially when the source of 

the contaminant is also accurately known (Peterson, 2005). If however the flow direction 

is changing, then any conceptual site model and any monitoring program must take this 

into account. 

Because of the highly transmissive character of much of the uppermost hydrologic unit 

beneath the 300 Area (Hanford formation), the water table elevation responds quickly to 

fluctuations in stage of the adjacent Columbia River. Consequently, the hydraulic 

gradient steepness and orientation may vary dramatically over the short time periods 

associated with daily river fluctuations. (Peterson, 2005).

7.2.8 300 Area Uranium Plume 

The ground water beneath the 300 Area has been contaminated by liquid effluent 

discharges to a variety of disposal sites during a period of operations that extends from 

the late 1940s through the mid- 1980s. Since the end of fuel fabrication activities, 

contaminated discharges have largely ceased, although discharges of uncontaminated 

effluent continued until 1994. Remedial actions are underway and the structures and 

contaminated soil associated with most of these disposal sites have been removed. 

However, residual amounts of some contaminants remain in the underlying vadose zone, 

and their presence is indicated in ground water monitoring results (Peterson, 2005). 

Various ground water monitoring locations are provided in Figure 7-15. 

The longevity of the 300 Area ground water uranium plume, despite attempted source 

term removal and copious water flow through the aquifer to the Columbia River, 

prompted an investigation into the processes controlling the release and transport of 

uranium at this site. The mildly alkaline pH and relatively high carbonate concentrations 

of the 300 Area porewaters are conditions that normally suppress hexavalent uranium 
7-13 

(U(VI)) adsorption on iron oxide-poor sediments as exist below the 300 Area; however, 

significant sorbed U(VI) concentrations (up to 250 mg kg-1 of uranium) are observed in 

the vadose zone. This sorbed U(VI) is believed to sustain the ground water plume 

through desorption as meteoric water infiltrates the vadose zone from above and as 

seasonal river stage fluctuations cycle ground water into the lower vadose zone from 

below. The lack of understanding of the distribution coefficient (Kd) for U(VI) makes 

modeling of the movement and mobility of uranium difficult. 

The desorption or dissolution of uranium from capillary fringe sediments due to 

fluctuations in the water table controlled by changes in the adjacent river levels results in 

periodic pulsing of uranium into the ground water. This makes detailed characterization 

of the nature and extent of the contaminant plume within both the Vadose Zone and 

aquifer, along with compiling the detailed associated hydrogeologic and geologic 

conditions, paramount. 
7-14 

Figure 7-15. 300 Area ground water monitoring locations (Peterson, 2005) 

7.2.9 Monitoring Considerations 

Critical monitoring parameters to be considered in this type of environment include the 

collection frequency of water levels and ground-water samples. Annual monitoring of 

water-table levels would not likely show the short-term pulsing of the water table due to 

the changes in river levels. Fluctuations in the river stage not only occur seasonally, but 

hourly. 
7-15 

In addition, uranium concentrations in ground water from seeps collected at the edge of 

the Columbia River, near the point where ground water with the highest concentrations of 

uranium should discharge, were considerably lower than uranium concentrations 

collected from the river. This implies that there is a discharge of ground water through 

preferential pathways, potentially upwelling below the seep lines of the river or the 

uranium concentrations are coming from another source, possibly upstream. The concept 

of preferential pathways or the influence of river stage and pressure impact on the aquifer 

has not come into consideration in past ground-water models for the 300 Area. The 

geology consists of mostly river gravels of the Hanford Formation a highly variable 

formation with a likely potential for preferential pathways. 

Development of semi-confined hydraulic heads due to infiltration of river water into the 

water table due to fluctuations in the river level could result in localized hydraulic 

pumping of ground water into the river. This condition may only exist for short periods 

of time during river level changes (Catalano et al., 2006). 

Figure 7-16 provides a hydrogeologic conceptual model for movement of contaminants 

within the vadose zone and ground water below the 300 area in relation to changes in 

river stage (DOE, 2002). 

Figure 7-16. Hydrogeologic conceptual model of contaminant movement below the Hanford 300 

Area (DOE, 2002) 

7.3 Application of Ground Water Monitoring Performance 

Strategy 

It is well documented that the 300-Area water table elevation changes in relation to the 

river stage. It is also well documented that a portion of a stream’s flow may move 

through permeable materials adjacent to the stream. The USGS offers a stream transport 

simulator (OTIS) that includes inflow and storage in bank and bed materials. (Figure 

7-17). 
7-16 

Figure 7-17. Transient storage mechanisms (Runkel, 1998) 

Significant portions of the river flow may move through the coarse gravel of the 

streambed and, more importantly, the porous areas within the stream bank (Figure 7-17, 

Diagram B). 

Modeling of river-ground-water interaction including surface water momentum is not 

generally done and requires computational hydrodynamic codes. 

In the case of the Hanford 300 Area, transient migration of water into the bank of the 

outside bend of the adjacent Columbia River may have resulted in the downstream 

migration of contamination within Water Table Aquifer. As proposed in Figure 7-18, 

flow in the Columbia River adjacent to the 300 Area impacts the western bank (cutbank) 

just north of the 300 Area (north of the 618-5 Burial Ground Facility). 
7-17 

Figure 7-18. Alternative conceptual model of Hanford 300 Area showing potential infiltration and 

downstream flushing of formation 

The arrows pointing from left to right across Figure 7-18 represent the movement of 

ground water towards the Columbia River. The bold arrow at the top of Figure 7-18 

suggests the dominant intrusion and lateral movement of surface water from the 

Columbia River into the water table aquifer. The other arrows in the Columbia River 

follow general surface water flow. The curved line presents the conceptualized extent of 

surface water intrusion into the water table aquifer. 
7-18 

It is well documented that the water table in the 300 Area rises and falls with the changes 

in the river stage. The outside of bends in the river may also be impacted as well by water 

forced into the formation. The impact of the river on the water table may not be limited 

just to a simple lateral moving in and out of the formation. The water being forced into 

the formation can produce a “flushing effect” resulting in a downstream component of 

flow within the formation. Based on the geometry of the river, this flushing effect would 

be expected in the 300 Area in two locations: one at the upstream point where the river 

turns southeasterly and impacts the west river bank and adjacent to the 307 Trench, 

where river flow around the island adjacent to the 618-5 Burial Ground would impact the 

west river bank. 

Figure 7-19 shows the actual extent of forced water intrusion and its effect on nitrate 

concentrations in ground water from 2002 (represented by the curved colored (teal) line). 

The shape of the contact between higher and lower nitrate concentrations mimics the 

shape of the water forced into the formation by the river, as proposed in Figure 7-18. 

Downstream movement of water within the formation would also result in the 

downstream migration of contaminants as indicated for uranium in Figure 7-20 below. 

Figure 7-19. Extent of river water intrusion as estimated from nitrate concentrations in 

2002(Yabusaki et al, 2004) 
7-19 

Figure 7-20. 300 Area Ground-Water Uranium Concentrations, August 1997 

7.3.1 Performance Indicators and FEPs 

Performance indicators and features, events, or processes (FEPs) for the Hanford 300 

Area uranium plume include, but are not limited to: 

The primary system performance indicators in our analysis of the Hanford 300 area are 

the shapes of the published uranium and nitrate contaminant plumes. 

River stage is incorporated in all recent Hanford flow and transport modeling, but so far 

as we can determine, hydrodynamic effects of flow impinging on the cutbank of the 

Columbia River have not been incorporated in the CSM. 

Re-analysis of existing monitoring data from wells in and near the 300 Area may provide 

insight into the distribution of river water components that could be related to 

hydrodynamic effects. 

Additionally pressure measurements along the river bank might be possible. 
7-20 

7.4 Monitoring Strategy Application Conclusions 

By applying the Strategy, we were able to perform a thorough compilation of the 

available geologic and hydrogeologic data for the Hanford 300 Area and gain a better 

understanding of the interaction of the Columbia River System with ground water. 

Transient migration of water into the bank of the adjacent Columbia River at the 300 

Area may produce a component of movement that can produce a “flushing effect” 

resulting in the downstream migration of contamination within the formation containing 

the Water Table Aquifer. 

Thus, we have proposed an alternative to the 300 Area conceptual model that may 

improve the explanation of contaminant flow and transport at the Hanford 300 Area. 

Performance Indicators suggesting this revision to the conceptual model included the 

shape of the uranium plume and the position of the 300 Area on the cut bank of the 

Columbia River. 

Hydrodynamic modeling should be evaluated as a means of evaluating the potential for a 

bidirectional component of contaminant movement in the water table. 

Water-table monitoring collection frequencies could be adjusted to show the short-term 

pulsing of the water table due to the changes in river levels. Fluctuations in the river 

stage not only occur seasonally, but hourly. In addition, detailed changes in the river 

stage need to be documented. By evaluating these fluctuations in the water table in 

relation to the changes in river stage, conclusions can be drawn on the effects of transient 

migration of river water within the formation and subsequent movement of uranium. 

In addition, the concept of preferential pathways could be further explored. 
7-21 

7.5 Hanford References 

Catalano, J. G., et al. “Changes in Uranium Speciation through a Depth Sequence of 

Contaminate Hanford Sediments.” Environmental Science and Technology 

Magazine. 2006. 

Department of Energy (DOE). DOE/RL-98-48, Rev. 0, Volume II. “Ground 

water/Vadose Zone Integration Project Background Information and State of 

Knowledge.” U.S. Department of Energy: Richland, Washington. 1998. 

DOE. DOE/EIS-0222-F. “Hanford Comprehensive Land-Use Plan Environmental Impact 

Statements.” U.S. Department of Energy: Richland, Washington.1999. 

DOE. DOE/RL-2002-11, Rev. 0. “300-FF-5 Operable Unit Sampling and Analysis 

Plan.” Prepared by CH2M HILL Hanford, Inc. for the U.S. Department of Energy: 

Richland, Washington. 2002. 

DOE. Site Transition Plan for the Rocky Flats Environmental Technology Site, Office of 

Legacy Management and Office of Environmental Management, DOELM&EM/GJ-662-2005, March 2005. 

Faybishenko, B. “Vadose Zone Characterization and Monitoring” in: Looney, B and 

Falta, R, Vadose Zone Science and Technology Solutions, Vol. 1.pp. 133-509. 2000. 

Lindsey, K. A., et al. WHC-SD-EN-TI-012, Rev. 0 “Geology Setting of the 200 East 

Area: An Update.” Westinghouse Hanford Company: Richland, Washington.1992. 

Peterson RE (ed.). PNNL-15127. “Contaminants of Potential Concern in the 300-FF-5 

Operable Unit:” Expanded Annual Ground water Report for Fiscal Year 2004. 

Pacific Northwest National Laboratory: Richland, Washington. 2005. 

Runkel, R.L. “One-Dimensional Transport with Inflow and Storage (OTIS): A Solute 

Transoprt Model for Streams and Rivers.” U.S Geological Survey, WaterResources Investigations Report 98-4018. 1998. 

Vermeul, V.R., et al. PNNL-14398. “Transient Inverse Calibration of the Site-Wide 

Groundwater Flow Model (ACM-2).” FY 2003 Progress Report. September 2003. 

Yabusaki, S., et al. Powerpoint Presentation: “Objectives and Tentative Scientific 

Approach for Uranium Reactive transport Modeling in the 300 Area.” PNNL. May 

10-11, 2004. 
8-1 

8 Analysis of Characterization and Monitoring 

Data 

8.1 Introduction 

Accurate analysis of site characterization and monitoring data is a crucial, and often 

challenging, part of development of a sound ground-water monitoring strategy. This 

Chapter overviews data analysis methods that may aid development and implementation 

of the Integrated Ground-Water Monitoring Strategy, and offers suggestions for avoiding 

common pitfalls related to review of environmental data. While this is not a 

comprehensive discussion of all the issues, it focuses on lessons learned through review 

of site data from around the DOD, DOE, and NRC complex. 

Development of an optimized ground-water monitoring strategy requires an adequate 

understanding of flow, transport, and risk. In some cases, careful review of existing data 

yields sufficient information to understand flow and transport, and thereby to choose a 

confirmation monitoring scheme. In other cases, additional characterization may be 

necessary to reduce model uncertainty in order to optimize the monitoring approach. In 

either case, the concepts in this chapter are intended to help you maximize the value of 

the data available to you. Topics covered include: 

• Data types 

• Basic statistical analysis 

• Methods for identifying data errors and outliers 

• Quality control charts and the T-Test 

• Mann-Kendall Test – lessons learned 

• Rainfall data – methods of analysis and sources of uncertainty 

• Finding correlation between monitoring well data 

• Water level measurements 

• Unmixing of multimodal data 

• Cluster Analysis 

• Factor Analysis 

• Methods for analyzing mapped data, and 

• Quality assurance 

In addition to these topics, we would like to emphasize the value of 3D conceptual 

modeling of spatial data in understanding flow and transport. In Chapters 1-7 numerous 

modeling examples are provided, along with modeling software recommendations. In our 

experience, this sort of visualization can tremendously aid in understanding a subsurface 

system. 

8.1.1 Data Types – Characterization versus Monitoring 

Generally speaking, characterization and monitoring entail different sorts of measurement 

activities. Specifically, characterization includes measurement of intrinsic properties of a 

site. Also, characterization measurements at a given point may be made only once, 

although some site characteristics like rainfall, response of wells to rainfall, response of 
8-2 

wells to tides, or establishing a water quality baseline could require extensive periods of 

observation. Characterization and monitoring data will have geographic and time 

coordinates (x, y, z, t) and may vary across the site in 4-dimensional space. 

Monitoring is often measurement of something that is expected to change, with the 

change meaning something in terms of risk-related processes such as plume movement. 

Monitoring data are acquired to evaluate progress of some ongoing process, or to alert the 

site operator to an off-normal situation. Monitoring data are generally acquired at a fixed 

point in space, so vary only in time. These would include results from sampling from a 

device such as a lysimeter or a well that has been placed in one point. Results may derive 

from field measurements (e.g., pH, alkalinity, conductivity, turbidity radon ...) or may 

derive from measurements on a sample sent to a laboratory (e.g., anion content, organic 

content, cation content, radionuclide content...). Establishing baseline values for 

measurements to be made at a monitoring point, (x, y, z, t) is part of characterization, and 

detecting changes in the baseline are part of monitoring effort. 

Much of the uncertainty in estimating risk from subsurface contamination can be traced 

to uncertainty in site characterization and monitoring design. For example, it does not 

matter if a ground-water sample is analyzed to femto-Curie levels of Sr-90 if the 

sampling point is not chosen appropriately. Similarly, it does not matter if a flow and 

transport model is built and forced to calibrate if features in the site geology that control 

flow are not characterized adequately. 

In addition, selection of appropriate chemical methods is important. It does no good to 

monitor for a given constituent of concern if the method detection limit is not below 

regulatory requirements or other action levels (Example: method detection limit is 10 

mg/L and the MCL is 1 mg/L). Ideally methods should be chosen to provide quantitative 

data for all analytes at their ambient levels, with very few “below detection” results. 

Missing values, or truncated data sets, limit one’s ability to glean understanding of the 

system being tested. 

An Integrated Ground-Water Monitoring Strategy does not include site characterization 

and pre-operational monitoring, but must include review and evaluation of 

characterization data and existing monitoring data in order to select critical monitoring 

points within the system. If characterization is adequate, and if the characterization has 

been used correctly in flow, transport, and risk models, then the task of confirmation 

monitoring design is simplified. 

If characterization is not adequate, then selection of monitoring points is more difficult. 

The site manager must decide whether the risk associated with the remaining 

uncertainties is acceptable or not, and take appropriate action. This action could mean rerunning a Performance Assessment (PA) model, and could also include filling gaps in 

characterization if the PA indicates unacceptable risk. Reducing model uncertainty by 

installing monitoring systems could be called characterization. 

8.1.2 Data Evaluation versus Statistical Analysis 

The distinction between data analysis and statistical hypothesis testing is important. 

Many of the data analysis techniques violate assumptions made in formal statistics, but 
8-3 

produce useful results; likewise, many formal statistical tests may provide useful insight 

even when the data tested (e.g., log-normal data) violate the test assumptions. 

Data evaluation is the process of looking for associations, trends, patterns, or outliers in 

the data. The purpose is to alert an investigator to something in the data structure that 

may have implications about a process or anything that might have meaning to the 

investigator. Multivariate data analysis has recently been popularized as “data mining.” 

Statistical analysis of data is the process of testing a data point against some hypothesis 

about the data. Classically this comes from quality control in a production operation or 

manufacturing setting. Section 8.1.3, below contains a more detailed discussion on 

quality control analysis using the T-Test. 

Below are several recommended sources for additional reading about data evaluation and 

statistical analysis: 

Velleman, Paul F., article in The American Statistician (1993) 47:1, 65-72 (and its 

discussion in various internet sources) presents an enlightening discussion of this topic. 

EPA (2003, 2004), in their Guidance for Monitoring at Hazardous Waste Sites, discusses 

some of the objectives of data analysis and statistical testing. Their discussion is from a 

different viewpoint than that presented here, but the common feature is that the purpose 

of the data analysis is to provide a person or team with a basis for making a decision 

either about the monitoring system or about what the data are telling in terms of risk so 

that a decision can be made. 

NIST (2004) has an online statistical handbook that goes into depth on data analysis. 

They list the objectives of data analysis: 

1. Maximize insight into a data set; 

2. Uncover underlying structure; 

3. Extract important variables; 

4. Detect outliers and anomalies; and 

5. Test underlying assumptions. 

They also point out that there is no prescription for data analysis. The operator must 

understand the philosophy of data analysis and apply this to the problem at hand. 

8.2 Univariate data 

Univariate means basically that we consider one variable at a time. In nature we often 

find that the population from which we draw samples is formed from the mixing of 

several sources. For example, copper in soil samples may be ascribed to underlying 

bedrock, or two types of bedrock and to atmospheric deposition from a smelter. Even 

contaminants, such as TCE, in a given water sample may be present from leaking tanks at 

multiple upgradient areas. 

Sometimes it is obvious that there are multiple sources for a given analyte, and we can 

estimate how to partition the data so as to better understand the sources. Sometimes the 

underlying chemical or geochemical processes leading to the observed values produce a 
8-4 

time-varying distribution – for example, a spill or burial may dissipate with time. This 

might result in monitoring observations that fit an exponential function. 

Univariate populations may fit the familiar so-called normal or Gaussian distribution. 

Sometimes taking the logs of the data may produce an apparent fit to the normal curve. 

A number of distribution types have been recognized by statisticians, and statistical tests 

have been developed for each. Most familiar statistical terms such as the Pearson 

product-moment correlation coefficient assume a Gaussian distribution and lose meaning 

for strongly skewed data sets. 

Statistical tests that do not depend on the population or sample distribution have been 

developed. Generally these are based on ranking the numbers and using ranks rather than 

values. (c.f. Kendall, 1975; Siegel, 1956) This chapter only provides a glimpse at some 

practical issues so that the data problem holder will seek expert help for data analysis. 

8.2.1 Basic Statistical Analysis 

Basic univariate analysis includes the computation of the mean (Equation 1), standard 

deviation (Equation 2), variance (square of the standard deviation), coefficient of 

variation (standard deviation divided by the mean), and identification and possible 

rejection of extreme observations (discussed in Section 8.2.2 below). 

 Equation 1. Mean Equation 2. Standard deviation 

1

1 N

i

i

m H

N =

= ∑ 

2

1

( )

1

N

i

i

H m

N

σ =

−

= −

∑

In the above equations, m is the sample mean of the observations, N is the number of 

observations, H is the observed values, σ is the standard deviation of the observations. 

For time-series data sets, trend analysis with the Mann-Kendall test provides us more 

information about the temporal variation of the water heads and concentrations. The 

Mann-Kendall test is discussed in detail in Section 8.2.4 below. 

8.2.2 Identification of Outlier Points 

An important part of data analysis is identification and assessment of potentially 

erroneous data points. A measurement may be read, recorded, or transcribed wrongly, or 

a mistake may be made in the way in which a treatment was applied for this 

measurement. A major error greatly distorts the mean, the standard deviation, the 

variance, and the coefficient of variation, and affects conclusions about the trends and 

correlations. The principal safeguards are vigilance in carrying out the operating 

instructions in the measuring and recording process, and eye inspection of the 

observation data. 
8-5 

If a figure in the data to be analyzed looks suspicious, an inquiry about this observation 

sometimes shows that there was a gross error. If no explanation of an extreme 

observation is discovered, we may consider rejecting it. The discussion of rules for the 

rejection of observations began well over a century ago in astronomy and geodesy. Most 

rules have been based on something like a test of significance (Snedecor and Cochran, 

1976). The investigator computes the probability that a residual as large as the suspect 

would occur by chance if there is no gross error. If this probability is sufficiently small, 

the suspect is rejected. Anscombe and Tukey (1963) present a rule that rejects an 

observation whose residual has the value of d if |d| > Cs, where C is a constant to be 

determined with the following equation which is obtained from Snedecor and Cochran 

(1976), and s is the standard deviation of the observations calculated from Equation 2. 

Equation 3. Anscombe and Tukey significance test 

2 2 1 1

4( 1)

1.4 0.85

K N C K

N N

K z

⎛ ⎞ − − = − ⎜ ⎟ ⎝ ⎠ −

= +

In Equation 3, N is the number of the observations, z is corresponding to the one-tailed 

probability value of N 1 P

N

− in the normal distribution, where P is the small premium 

which is involved in a rejection rule, say 2.5% or 5%. 

After rejecting the outlier points, we carry out the statistical analysis with the treated data 

sets. The results are compared with those obtained with the original observation data sets. 

8.2.3 Quality Control Charts: the T-Test 

A classic example of statistical analysis is ‘Student’s T-Test’. This test is often used to 

analyze monitoring well results and other types of univariate analysis. Originally, 

William Sealy Gossett developed this test to detect off-normal conditions in the 

production of Guinness beer. In this case, a new measurement (e.g., sugar content, 

specific gravity...) can be compared with historical data representing “normal” 

conditions. The result is a confirmation or rejection of a hypothesis that the new 

measurement is drawn from the normal population. Because any introductory statistics 

text will include the T-test, we will not discuss it further here. 

The results of a T-test can be expressed graphically in the form of a “control chart” for 

process monitoring on which the target value is plotted as a horizontal line against time 

with parallel lines at the uppermost and lowermost “normal” bounds (at some confidence 

level for acceptance of the “is normal” hypothesis) (Figure 8-1). 
8-6 

Figure 8-1. Example control chart 

A version of this method is typically used in ground-water monitoring programs to spot 

anomalous results as they are returned from the lab. Characterization, or pre-operation 

monitoring is used to establish an expected range for some variable – say pH, or water 

level. This expected range is used to bound ‘normal’ values for the variable – and 

periodic measurements are compared to the normal value, commonly by displaying them 

on a chart. Visual inspection of the chart or a computerized notice alerts the operator to 

an off-normal condition. The operator then decides on an action. In the case of a plant 

producing thousands of items per hour, this may mean an immediate adjustment of 

operating conditions. In the case of a ground-water monitoring result, the action might 

include a recheck of the analysis, and following that, possible re-sampling of the field 

site. All off-normal results should be referred to technical experts for evaluations – the 

job of inspecting control charts is often assigned to technicians who may not have the 

perspective to fully evaluate the potential meaning of an off-normal observation.. 

If the off-normal condition is confirmed, then its meaning must be determined so that any 

possible risk implications can be judged. This may mean re-running a computer 

simulation, it may mean revising a conceptual model. It could indicate a release of 

contamination, or the impending approach of an unknown plume. It could point to an 

analytical or sampling problem. It may trigger a regulatory reporting requirement. 

Interpretation is the responsibility of the individual investigator in the context of 

extensive site-specific knowledge. 

Time-trends are also revealed with the control chart method. Changes in variance or 

upward or downward trends in the mean will be revealed in such a chart. This is 

especially important in judging behavior of a contaminant plume, or for tracking progress 

of a remediation process. 
8-7 

The methods of univariate data analysis and statistics have been developed mainly since 

the 18th century: Gauss, Bayes onward. The reader is referred to basic statistics texts for 

information. My favorite is: Peatman, John G., (1936, ’41, ’47) “Descriptive and 

Sampling Statistics.” 

Guidance 

When preparing a control chart: 

• Plot all measurements against time. 

• Watch for changes in variance. 

• Watch for data outside the expected range. 

8.2.4 Applying the Mann-Kendall Test

To evaluate the presence of trends in the time-series observations at individual 

monitoring wells in this report, we applied the Mann-Kendall test, which is commonly 

reliable in the interpretation of environmental data (Helsel and Hirsch, 2002; Soderberg 

et al., 2005). This test is often applied on data sets from monitoring wells to assess the 

stability of a contaminant plume and it is an important tool in the decision making 

process that relates to ground-water monitoring network design. 

The Mann-Kendall test is non-parametric and therefore does not assume an underlying 

distribution in the data sets. It can address missing data values and be modified to 

account for seasonality or predictable fluctuations (Soderberg et al., 2005). In the MannKendall test, a statistical parameter S is valuated with Equation 4 by comparing each data 

point to the data points that occur after it in the time series (Gilbert, 1987). 

Equation 4. Mann-Kendall test 

1

1 1

1, If >0

sgn( ), sgn( ) 0, If =0

1, If <0

j i N N

ji ji ji

i ji

j i

H H

S HH HH HH

H H

−

= =+

⎧ − ⎪ = − −= − ⎨

⎪− − ⎩

∑ ∑

In Equation 4 above, H indicates observed values, and the sign of S indicates the 

direction of the trend (i.e. positive S indicates an upward trend, negative indicates a down 

trend and 0 value indicates flat or no trend). S and N are then used to read a p-value from 

a statistic table (Gilbert, 1987), and the p-value is a measure of the significance of the 

trend. When N < 10, a two-tailed test is used to test for both upward and downward 

trends in a single alternative hypothesis. 

For large data set (N > 10), S can be modified to be approximated by a normal 

distribution. Another statistical parameter, Z, is calculated by Equation 5: 
8-8 

Equation 5. Z calculation 

1

( 1) / If S > 0

0 If S = 0

( 1) / If S < 0

( 1)(2 5) ( 1)(2 5)

18

s

s

N

i

i

s

S

Z

S

N N N Ti i i

σ

σ

σ =

⎧ − ⎪ = ⎨

⎪

⎩ +

− +− − +

=

∑

In the above equation, T is the number of tied values. With a calculated Z value we can 

compute a p-value from the normal distribution to evaluate the significance of the trend 

found from S value. 

The example in Figure 8-2 below illustrates how simple the Mann-Kendall test really is. 

The next few figures illustrate that use of this simple test may, in some cases, actually 

obscure information that should be gleaned from the data. We provide this as an example 

to make the reader more aware of possible sources for misinterpretation when applying 

this test. 

Simple Mann-Kendall trend example

Data Analysis and Visualization, 11/30/05 19

N (number of data points) = 4 (6 comparisons)

from initial data point -- +3 +3

from second data point -- 0 -2

from third data point -- -1 -1

S (sum of sgns) = +2 0

0

20

40

60

80

100

120

140

1/1/84 1/1/88 1/1/92 1/1/96 1/1/00

Figure 8-2. Mann-Kendall Example 
8-9 

Figure 8-3, labeled “Seasonal Kendall Slope Estimator,” shows PCE concentrations over 

several years at a monitoring well. For each sampling point a determination is made as to 

whether the subsequent sampling events result in a higher of lower concentration. The 

plotted data in Figure 8-3 yield a -18 value – or a strong downward trend. 

Figure 8-3. Published figure indicating declining PCE concentrations in ug/L (DOE, 2006) 

A simple linear regression evaluation of the data provided in Figure 8-3 is represented in 

Figure 8-4. This simple regression evaluation also shows an overall reduction in PCE 

concentrations over time. However, a closer examination of the data reveals a steep 

downward trend over six sampling events, followed by an upsurge and gradual decline 

over the next six sampling events, and finally an increasing concentration trend for five 

sampling events. 

n=16 

Slope = -0.5457 units per year 

Z=-0.7794 

Conf. Table Significant

80% 1.282 No 

90% 1.645 No 

95% 1.960 No 
8-10 

Graph of PCE in Well 90399

0

2

4

6

8

10

12

14

Feb-00 Nov-02 Aug-05

Date

PCE ug/

Series1

Linear

(Series1)

Figure 8-4. Linear regression fit to PCE data from MS-EXCEL 

Figure 8-5 shows the data broken into three groups with trend lines for each. It is 

possible that the three slopes represent some hydrogeological phenomenon such as 

contaminant release from a pool or from the vadose zone as a function of infiltration or 

water level. We discuss a similar example at Rocky Flats elsewhere in this document. 

The line equations are of the form y=mx+b, where m is the slope and b the intercept. 

Excel uses Julian dates which are around 30,000, but displays dates as days, months, and 

years, thus the slope is a very small number even though the line plots as a steep line. 
8-11 

Graph of PCE in Well 90399

y = -0.001x + 43.79

y = -0.0277x + 1027.7

y = -0.004x + 156.09

y = 0.0081x - 303.44

0

2

4

6

8

10

12

14

16

Feb-00 Nov-02 Aug-05

Date

PCE ug/

Figure 8-5. Parsing time series data into three groups. 

The simple determination that there is an overall downward concentration with time at 

this observation point is correct. Unfortunately, presenting only this conclusion may 

obscure the fact that the ground water / contaminant system is displaying complex 

behavior that might indicate future non-compliant excursions of contaminant 

concentrations. 

An example based on monitoring of VOCs at the DOE Rocky Flats Site is discussed in 

Chapter 5 above. In the example monitored results decline and remain low for long 

periods of time until an unusual weather event seems to flush contaminant from a 

bedrock pool into the water table flow system. This example provides insight into the 

issue of when to stop monitoring. Weather, including decade-long precipitation cycles 

may control apparent trends in contaminant amounts. 

8.3 Rainfall Data – Sources of Uncertainty for Infiltration 

Infiltration rates and permeability are two key variables controlling the accuracy of 

ground-water flow and transport models. Infiltration comes from rainfall and from 

engineered features such as leaking water systems and disposal or retention ponds. This 

section provides background for understanding uncertainty in infiltration. It specifically 

Linear fit from Figure 8-4 
8-12 

illustrates the importance of exploring all possible water sources when developing a 

conceptual model, and the importance of verifying that rain station data matches 

observed site conditions. 

8.3.1 Consider All Water Infiltration Sources 

Often the amount of leakage from water supply systems is poorly known. It can be 

estimated by shutting off the water supply to and from storage tanks and measuring loss 

over a period of time. A forty year old water system at the Savannah River Site in a nonindustrial area – i.e. where drinking, sanitary supply, and fire suppression were the only 

water lines in about a five-acre area – was shown to leak almost 100 gpm, which would 

have gone undetected had the supply well not been turned off in support of aquifer 

performance testing (ref. personal knowledge). That was about one gallon per square 

foot per day. Because the leakage was underground in a grassy or paved area, most of 

this water moves downward as infiltration. By way of contrast, infiltration from rainfall 

was on the order 15” of rain per year or one cubic foot per square foot per year. That was 

7.5/365 gallons per square foot per year or 0.02 gallons per square foot per day. Thus 

infiltration from leaking water lines was much greater than natural infiltration in this area. 

This case illustrates the importance of identifying all known water sources, natural and 

man-made, that could influence a system, and assessing the impact that these sources 

could have on the water table and infiltration. 

8.3.2 Ensure Rain Station Data Match Facility-Specific Gauging 

Infiltration is often estimated from rain gauging stations and estimates of the balance 

between evaporation, runoff, and infiltration. In the next few paragraphs, tables and 

figures will illustrate that facility-specific gauging should be done if local rainfall is to be 

known with any precision. 

The Savannah River Site has a number of weather and rain gauging stations. We are 

grateful to the DOE Savannah River Operations Office for access to daily rainfall data. 

The raw data from the five rain gauging stations presented in Figure 8-6 include 8000 

records taken over 22 years. Visual presentation of data points in scatter plots by month 

reveals that while winter rainfall patterns are relatively uniform over a large area, summer 

rainfall varies significantly even at short distances. Figure 8-7 compares rainfall data 

from the mid-1980’s through 2002 at Stations F and H, which are located just two miles 

apart. In this graph, Station F data is on the Y axis and Station H is on the X axis. 

Perfectly correlated data would group along a single line. As we can see from the data in 

July, rainfall measurements are quite scattered indicating that rainfall at one station is not 

indicative of the same intensity of rainfall at the other due in part to frequent isolated 

thundershowers. January data is more tightly grouped and is representative of data seen 

in the winter months due in part to the passage of large weather systems. 
8-13 

Savannah River

Site

Savannah

River

## NPM-1

NPM-19A

#

NPN-4

#

P-13D

# P-15D

#

P16-D

# P-18D

#

P-19 # P-24D

8 0 8 16 Miles

A S

C

F H

Savannah River

Site

Savannah

River

## NPM-1

NPM-19A

#

NPN-4

#

P-13D

# P-15D

#

P16-D

# P-18D

#

P-19 # P-24D

8 0 8 16 Miles

Savannah River

Site

Savannah

River

## NPM-1

NPM-19A

#

NPN-4

#

P-13D

# P-15D

#

P16-D

# P-18D

#

P-19 # P-24D

8 0 8 16 Miles

A S

C

F H

Figure 8-6. SRS rain gauging station and well locations. Rain stations are located under respective 

station identifier A, C, F, H, and S. Well locations are denoted by black dots. Adapted from Jones, 

1990. 

Figure 8-7. Rain data for Stations F and H, which are only two miles apart, show that particularly in 

summer, rainfall patterns are highly variable, even over short distances. 
8-14 

Figure 8-8 compares 17 years of rainfall data at Stations C and S. The Figure illustrates 

that at a distance of seven miles, rainfall readings vary significantly. In July, for 

example, it is not uncommon to see a variation of more than an inch between stations. 

In Figure 8-9, data from all five stations was used to show the correlation as a function of 

distance. As shown in the Figure, summertime rainfall patterns are significant, and vary 

much more than winter rainfall. Another possible factor is the azimuthal relation 

between gauging stations. Winter or summer, most weather systems move from west to 

east in this area. Station H is almost due east of station F, whereas station S is almost due 

north of station C. 

Figure 8-8. Rain Gauges C and S are about 7 miles apart and show significant variation in observed 

rainfall. 
8-15 

Figure 8-9. Correlation of rainfall as a function of distance in July and January. 

This case illustrates the need to ensure that rain measurements used in conceptual 

modeling match actual observations. A surprisingly short distance can make a large 

difference in the amount of rainfall received. Further, the correlation between rainfall 

and distance to the station can vary significantly by season. Site managers should be 

aware of this phenomenon if observed data do not closely match modeled contaminant 

movement. 

8.4 Correlations between different wells 

To interpret the relationship between data in different monitoring wells, we can compute 

the correlation coefficients among them. Understanding the correlation between wells 

can help us to analyze the hydrogeologic conditions and build the conceptual site models. 

For example, the correlations between two wells which are located in two aquifers 

separated by a confining layer, may give us information about the continuation of the 

confining layer and the hydraulic connections of the two aquifers. The correlation 

coefficient (ρij) is computed by Equation 6 below. 

Equation 6. Correlation coefficient 

( ) ij i j i j

ij

ij ij

C E H H mm

ρ

σσ σσ

− = =

where Cij is the covariance. H indicates the observed value, E is the expected frequency, 

and m is the mean. Considering the significance of the correlation, we define: 

If ρij > 0.9, Hi and Hj are positively correlated; 

If ρij < -0.9, Hi and Hj are negatively correlated; 

If -0.1< ρij < 0.1, Hi and Hj are not correlated, or independent. 

A real data set from Savannah River Site, South Carolina, is used to test the statistical 

methodology introduced above. In this data set, there are water head observations from 
8-16 

137 monitoring wells, in which each well includes about 16 time-series water head 

observations. The computer code developed here is used to compute the mean, variance, 

standard deviation, coefficient of variation, and the Mann-Kendall trend parameter for 

each well. To evaluate the significance of the trends, we also compute the p-value for 

each trend analysis. Finally, the correlation coefficients between different monitoring 

wells are calculated to help us to evaluate the conceptual site models for ground-water 

flow and transport modeling. The results of the first 10 wells of this data set are listed in 

Table 8-1. Fortran 90 code for the computations is included as Appendix B to this 

chapter. 

Figure 8-10 presents selected water head curves to demonstrate the results from statistic 

analysis. Wells P-15D and P-18D, P-15D and P-19TD, P-15D and P-25TA, and P-19TD 

and P-25TA are positively correlated, P-15D and P-22D are negatively correlated, and P22D has a downward trend but all others have an upward trend. An outlier point was 

removed from P-18D, P-19TD and P-25TA. 

0 2 4 6 8 10 12 14 16 18

170

180

190

200

210

220

230

Water Heads (ft)

 P-15D

 P-18D

 P-19TD

 P-25TA

 P-22D

Cumulative Time (month)

Rejected 

outlier point

Figure 8-10. Rejection of outliers 

The three outlier points shown in Figure 8-10 are on the same date at widely-spaced 

wells. On this same date, other wells do not show unusual water levels. It is very likely 

that a sampling error was made, and that no-one checked the data before they became 

part of the permanent database. 

Laboratory analytical data for this database are always compared to trends from the 

previous three results, and a deviation calculated. When the deviation is greater than a 

certain portion of the average deviation of previous measurements or exceeds a 

regulatory limit, the new point is flagged for human review. This simple QA check can 

and should be implemented as data from field measurements are entered into any 

database. 

QA is discussed further below. 
8-17 

Table 8-1 . Statistical analysis of water head observations from Savannah River Site 

Original Statistic Analysis of the Observations 

WellNam AqNam ObNm MinVal MaxVal MeanV Varian Stand CoefV Mann ModM Trend p-val 

P-15D WT 16 225.27 234.90 228.34 8.83 2.97 0.013 58. 2.57 Uptrend 0.005 

P-16D WT 16 210.41 216.96 214.20 3.41 1.85 0.009 -39. -1.72 Downtren 0.044 

P-16TC uprK 16 220.15 221.50 220.74 0.11 0.33 0.002 11. 0.45 Uptrend 0.320 

P-17D WT 16 275.47 285.06 276.98 5.30 2.30 0.008 -24. -1.04 Downtren 0.153 

P-18D WT 16 191.44 223.06 217.63 47.61 6.90 0.032 27. 1.17 Uptrend 0.122 

P-19TD TD 16 176.65 186.80 178.46 5.20 2.28 0.013 73. 3.27 Uptrend 0.001 

P-19TC uprK 16 176.72 179.59 177.99 0.45 0.67 0.004 80. 3.56 Uptrend 0.000 

P-22D WT 16 169.98 182.62 179.35 17.77 4.22 0.024 -31. -1.37 Downtren 0.085 

P-24TA TA 16 180.85 184.34 183.11 0.69 0.83 0.005 0. 0.00 Flat 0.500 

P-25TA TA 16 172.25 213.12 175.69 93.77 9.68 0.055 63. 2.80 Uptrend 0.003 

Modified Statistic Analysis of the Observations (After rejecting the outlier points) 

WellNam AqNam ObNm MinVal MaxVal MeanV Varian Stand CoefV Mann ModM Trend p-val 

P-15D WT 16 225.27 234.90 228.34 8.83 2.97 0.013 58. 2.57 Uptrend 0.005 

P-16D WT 16 210.41 216.96 214.20 3.41 1.85 0.009 -39. -1.72 Downtren 0.044 

P-16TC uprK 16 220.15 221.50 220.74 0.11 0.33 0.002 11. 0.45 Uptrend 0.320 

P-17D WT 15 275.47 279.31 276.44 1.01 1.00 0.004 -19. -0.89 Downtren 0.189 

P-18D WT 15 218.12 223.06 219.37 2.02 1.42 0.006 26. 1.24 Uptrend 0.108 

P-19TD TD 15 176.65 179.69 177.90 0.59 0.77 0.004 74. 3.65 Uptrend 0.000 

P-19TC uprK 16 176.72 179.59 177.99 0.45 0.67 0.004 80. 3.56 Uptrend 0.000 

P-22D WT 16 169.98 182.62 179.35 17.77 4.22 0.024 -31. -1.37 Downtren 0.085 

P-24TA TA 16 180.85 184.34 183.11 0.69 0.83 0.005 0. 0.00 Flat 0.500 

P-25TA TA 15 172.25 174.45 173.19 0.40 0.63 0.004 64. 3.13 Uptrend 0.001 

Following Wells are Highly Positively Correlated: R > 0.95 

P-17D WT and P-18D WT 0.95 

P-19TD TD and P-19TC uprK 1.00 

Following Wells are Positively Correlated: 0.9 < R < 0.95 

P-15D WT and P-18D WT 0.90 

P-15D WT and P-19TD TD 0.92 

P-15D WT and P-25TA TA 0.91 

P-19TD TD and P-25TA TA 0.94 

P-19TC uprK and P-25TA TA 0.93 

Following Wells are not Correlated: -0.1 < R < 0.1 

P-16D WT and P-16TC uprK 0.02 

P-16D WT and P-17D WT 0.07 

Following Wells are Negatively Correlated: R < -0.9 

P-15D WT and P-22D WT -0.90 

All Correlation Coefficients of Water Head Between Wells 

 P-15D P-16D P-16TC P-17D P-18D P-19TD P-19TC P-22D P-24TA P-25TA 

 WT WT uprK WT WT TD uprK WT TA TA 

P-15D WT 1.000 -0.106 0.747 0.858 0.901 0.918 0.892 -0.902 -0.498 0.907 

P-16D WT -0.106 1.000 0.017 0.073 -0.157 -0.200 -0.122 0.125 0.103 -0.324 

P-16TC uprK 0.747 0.017 1.000 0.833 0.839 0.713 0.710 -0.601 -0.357 0.590 

P-17D WT 0.858 0.073 0.833 1.000 0.953 0.781 0.751 -0.868 -0.697 0.671 

P-18D WT 0.901 -0.157 0.839 0.953 1.000 0.874 0.850 -0.887 -0.656 0.788 

P-19TD TD 0.918 -0.200 0.713 0.781 0.874 1.000 0.997 -0.842 -0.432 0.941 

P-19TC uprK 0.892 -0.122 0.710 0.751 0.850 0.997 1.000 -0.805 -0.396 0.932 

P-22D WT -0.902 0.125 -0.601 -0.868 -0.887 -0.842 -0.805 1.000 0.574 -0.857 

P-24TA TA -0.498 0.103 -0.357 -0.697 -0.656 -0.432 -0.396 0.574 1.000 -0.320 

P-25TA TA 0.907 -0.324 0.590 0.671 0.788 0.941 0.932 -0.857 -0.320 1.000 
8-18 

8.5 Water Level Measurements 

Water level measurements are relied upon to estimate flow direction in aquifers. There is 

extensive literature on water level diurnal changes and response to rainfall. Typically, 

water levels are measured during quarterly sampling events. For special studies, an 

attempt may be made to measure all wells in a study area (e.g., model area) in a very 

short time span. In the Charleston Naval Weapons Station case described in Chapter 2, 

water levels change enough to suggest very different flow directions at different times. 

Figure 8-11 illustrates the variation of water level between sampling events as captured 

by a continuous recorder (see line starting at March 31, 2003). Note that a change of 

over ten feet was missed by the periodic sampling. 

P-13D 

215

220

225

230

235

240

245

250

04/01/9804/01/9903/31/0003/31/0103/31/0203/31/0303/30/0403/30/05

water level elevation (ft.)

Figure 8-11 Periodic and continuous water level measurements compared for SRS well P-13D. 

Courtesy Bill Jones, SRNL. 
8-19 

8.6 Unmixing of Multimodal Data 

Concentration data from different contaminant sources (or permeability measurements 

from different types of sediment facies) may present bi-modal or multimodal distribution. 

This section will introduce an inverse method to identify the individual modes or sources 

with statistical approaches. 

Previous studies assume that if the measurements from an individual source have a lognormal distribution (Sinclair, 1981; Gilbert, 1987), then, the density function of the whole 

data set can be represented by the linear combination of a number of separate log-normal 

probability density functions (Heslop et al., 2002); that is, a distribution curve is 

composed of a finite number of log-normal populations. Under this assumption, a mixture 

of N separate populations can be represented at a given field by the frequency function 

f(x), 

Equation 7 

2

2

1

( )

2

1

() ( , )

1 ( , ) exp 2

1

i

i

N

ii i i

i

x m

i ii

i

N

i

i

fx p m

m

p

σ

η σ

η σ

σ π

=

− −

=

=

=

=

∑

∑

where ( , ) ηi ii m σ corresponds to a log-normal probability density function with mean mi , 

standard deviation σ i and non-negative mixing proportion i p . 

Sampled frequency values are therefore a discrete realization of the continuous frequency 

function and as such should be considered as an incomplete data set. Fitting is normally 

performed on the mixture frequency distribution to identify the number of modes or 

sources and to estimate the unknown parameters including mean, standard deviation, and 

proportion of each mode. For two or three mode problems, an Excel macro can be used 

to estimate these parameters by trial and error method. Figure 8-12 presents an example 

for identifying the distributions of two contaminant sources. 
8-20 

14 16 18 20 22 24 26 28 30 32 34

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Frequency function

log concentration(mg/L)

 Sample

 Mode 1

 Mode 2

 Mixture

Figure 8-12. Unmixing bimodal data 

The two identified modes in Figure 8-12 represent the distribution of two contaminant 

sources. The first has a mean log concentration of 19.96 mg/L, standard deviation of 

2.15, proportion of 0.65, and the second has a mean log concentration of 26.16 mg/L, 

standard deviation of 2.76 and proportion of 0.35. 

For the more complex problem with more than three modes or sources, the expectationmaximization (EM) algorithm (Dempster et al., 1977, and Heslop et al., 2002) can be 

used for the inverse analysis. This algorithm uses the maximum likelihood estimation 

(MLE) to maximize the probability that the sample data fit well to the computed 

frequency function. A brief explanation of this equation is below, but the reader is 

referred to the sourced text for a more detailed description on the EM algorithm. 

Using a two-step procedure (expectation and maximization), the EM algorithm iteratively 

determines the MLE of the parameters that describe the mixture distribution of a given 

incomplete data set. Before EM iteration can begin, it is necessary to provide an initial 

estimation of the parameters. Expectation (E-step) is performed first, and involves the 

determination of the complete data log-likelihood constrained by the observed 

(incomplete) data and the previously made estimation of the parameters. MLE (the Mstep) is then performed for the estimated complete data log-likelihood (obtained during 

the E-step). From this maximization procedure, new estimates of parameters are 

determined. The E- and M-steps are repeated, with the new parameter-values produced 

during each M-step being utilized in the complete data likelihood determination in the 

subsequent E-step. By the stepwise improvement of the parameter vector the loglikelihood of the observed data is increased until a predefined convergence criterion is 

reached. More information on the algorithm and its application to finite mixture models 

can be found in Dempster et al. (1977); Jones & McLachlan (1990); McLachlan & Peel 

(2000) and Heslop et al. (2002). 
8-21 

Determining the number of modes (or components) contributing to the mixture 

distribution is not trivial, because the goodness of fit of a finite mixture model will 

always improve as the number of components in the mixture is increased. To assess the 

number of individual components that should be included in a model, we adopted the 

technique of Kruiver et al. (2001), which is based on a comparison of the residuals 

(calculated between the measured and modeled curves) for fits involving different 

numbers of components. The technique compares the variances and means of the residual 

arrays for two competing models. If the inclusion of an additional component does not 

significantly reduce the variance and mean of the residual array (assessed using an F-test 

and Student’s t-test, respectively) then the more complex (higher-component) model is 

unnecessary on a statistical basis. The use of the fitting procedure based on the EM 

algorithm provides an effective method for determining the contributions and 

characteristics of individual source populations. 

The statistics of a concentration data set from a synthetic site with three possible 

contaminant sources are shown in Figure 8-13 and Figure 8-14. The identified 

distributions of three sources and the estimated parameters are listed in Table 8-2. 

Table 8-2. The identified distributions of three sources and the estimated parameters 

Source Mean log 

concentration (mg/L) 

Standard deviation Proportion 

Mode 1 1.58 0.126 0.54 

Mode 2 2.08 0.122 0.32 

Mode 3 2.55 0.100 0.14 

Figure 8-13 presents the statistics of contaminant concentration data and the 

corresponding cumulative probability distribution whereas, Figure 8-14, presents this 

distribution for each of the three contaminant sources. 
8-22 

0.5

2

1 0

3 0

5 0

7 0

9 0

9 8

99.5

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

0

5

1 0

1 5

2 0

2 5

Counts

log concentration (log m g/L)

Cumulative Counts (%)

Figure 8-13. Probability plot 

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Frequency function

log concentration(mg/L)

 Sample

 Mode1

 Mode2

 Mode3

 Mixture

Figure 8-14. Tri-modal distribution 
8-23 

Dissecting plots of mixed population data has been used in exploration geochemistry for 

many years to distinguish mineralized from barren areas. The reader is referred to online 

sources starting with authors Sinclair, Miesch, and McCammon and the program 

Probplot, An Interactive Computer Program to Fix Mixtures of Normal (or Log Normal) 

Distributions with Maximum Likelihood Optimization Procedures, distributed by the 

Association of Applied Geochemists (www.appliedgeochemists.org). 

8.7 Multivariate Analysis Methods: Cluster and Factor 

Analysis 

Multivariate data analysis includes studies of cluster analysis, a method to show the 

closeness of relationships between samples or variables in n-space (where n is the 

number of variables), and correlations and structure of correlation matrices (factor 

analysis). (Samples in n-variable space (R-mode) or variables in n-sample space (Qmode).) 

Cluster analysis is a powerful method to examine data in part because its results can be 

presented in a simple graph. Analytical results containing a dozen variables can be 

flattened for quick review onto a plane. 

Results are often displayed as a tree that reduces n-dimensional data to a 2-dimensional 

display. These methods were developed largely in the 20th century – the term factor 

analysis first appearing in 1931 and cluster analysis in 1939. Their use requires many 

computations – for example cluster analysis requires the computation of n! distances 

between samples in n-space several times. Advent of the high-speed digital computer has 

made the methods commonplace. 

These methods are not really statistical tests – they are data analysis and presentation 

procedures, and they may be applied without concern for many of the assumptions 

underlying many statistical tests. (See NIST, 2004 and Tukey, 1977 for discussions of 

exploratory data analysis.) Readily available statistical packages such as SPSS and SAS 

are capable of performing all of these analyses. More recently, there are some shareware 

programs or add-ons for programs such as MS-EXCEL that will perform most of the 

needed multivariate data analyses. Some of these add-ons can be currently found at: 

http://statpages.org/javasta2.html#Excel. 

8.7.1 Case Study: Multivariate Data Analysis at Mill Tailing Site 

Let us go through a test case using ground-water monitoring data from a uranium mill 

tailings disposal site. The data were obtained from reports available in the NRC 

electronic reading room system. We will use factor analysis to look for structure in the 

data, and cluster analysis to examine a hypothesis about the possibility that the sampled 

wells draw from two different bodies of subsurface water. 

Figure 8-15 is a cross-section of the mill tailings site looking northeast. A steep change 

in the elevation of a clay layer dividing an upper from a lower water-bearing zone led us 

to propose an alternative conceptual model in which a fault cuts the layer, as shown in 

Figure 8-15. 
8-24 

Figure 8-15. Cross section showing concept of merged water bodies. Our study examines whether 

this water is separated into two isolated chambers. 

Chloride plumes exist at the site above the clay on the left of this figure, and below the 

clay on the right of the figure. This supported the conceptual site model in which there 

was no permeability barrier, and that the mapped plumes were really one. The water 

samples are designated as belonging to a West or Southwest “flow regime” in the site 

data report, which treats these regimes as separate water bodies. 

Cluster analysis using SPSS on the data shown in Appendix 8-A support the hypothesis 

that the West and Southwest regime samples have different chemistry, and so the water 

can be presumed to represent two zones. This supports the site data report’s position that 

the permeability barrier (clay layer) may be continuous, rather than faulted. Thus the 

proposed alternative CSM hypothesis is rejected. The Sections below explain in detail 

the methodology used to perform this multivariate analysis, and the rest of the results 

from this particular case study. 

8.7.1.1 Multivariate Analysis – Step by Step Guidance 

Step 1. Obtain the data electronically. 

In this case we downloaded pdf copies of tables and re-typed them into an EXCEL 

spreadsheet. 

Step 2. Data conditioning. 

This could include standardizing data to z-scores or ranks, or converting data to logs or 

roots in order to limit the range of magnitudes. It also includes deciding what to do with 
8-25 

truncated or censored data sets. It our case we eliminated about 15 of the samples 

because they were not analyzed for a number of constituents. We eliminated one analyte 

(Beryllium) because it was not detected in any samples, and we converted a lot of the 

non-detects for Arsenic into half the value reported as the detection limit. We also 

simplified the variable names to save space. 

We will not write step-by-step instructions for data conditioning because it should only 

be conducted by someone familiar with the process. 

Step 3. Develop hypotheses to be evaluated, or questions to be answered. 

In this case, questions to address included: 

• Do the data readily reveal any underlying controlling processes; and 

• Can we use water chemistry to substantiate or refute the hypothesis that that the 

wells represented two “flow regimes” – perhaps different aquifers? 

• Are there any outlier samples? (The operator must decide what these mean once 

they are identified.) 

Step 4. Decide what analysis to apply. 

• Factor analysis looks at correlations among all the variables. This method is 

typically ideal for discovering close associations or lack of associations between 

variables. 

• Cluster analysis can quickly reveal outliers and can show whether samples fall 

into natural groupings in variable space. 

Step 5. Use available software for the analysis. 

We used SAS and SPSS. Results are discussed below. 

8.7.1.2 Cluster Analysis Results 

SPSS was used to divide the 137 observations (from Appendix 8-A) into ten groups 

based on their proximity in variable space. The data were then examined using cluster 

analysis to help identify outlying data points and look for data trends, and factor analysis 

to identify correlations in the data. (Similar results were obtained with SAS, but are not 

presented here.) 

Figure 8-16 presents some of the cluster results discussed above in a “family tree” format 

called a dendrogram. It is clear that Observations 5 from well LA2, 64 from A8, 69 from 

DOMW1, and 115 from MW30 are outliers because these observations fell into clusters 

unique for their wells (see data table in Appendix 8-A). They are marked by decreased 

water quality that does not follow a trend across time, as the subsequent observations at 

the wells contain normal data for the wells. 
8-26 

 SW-LA2 11 òôòø ó ó ó ó

 SW-LA6 33 òú ó ó ó ó ó

 SW-LA6 34 òú ó ó ùòòò÷ ó

 SW-LA2 7 ò÷ ùò÷ ó ó

 SW-LA2 8 òòòú ó ó

 SW-LA2 10 òòò÷ ó ùòòòòòòòòòòòòòòòòòòòø

 SW-LA5 29 òø ó ó ó

 SW-LA5 31 òú ó ó ó

 SW-LA5 30 òôòòòòòø ó ó ó

 SW-LA5 28 ò÷ ùòòò÷ ó ó

 W-A8 66 òø ó ó ó

 W-A8 67 òôòòòòò÷ ó ó

 W-A8 65 ò÷ ó ó

 SW-PW7 55 òø ó ó

 SW-PW7 62 òú ó ó

 SW-PW7 58 òôòø ó ó

 SW-PW7 61 ò÷ ùòòòø ó ó

 SW-PW7 63 òòò÷ ó ó ó

 SW-PW7 52 òø ó ó ó

 SW-PW7 57 òú ùòø ó ùòø

 SW-PW7 54 òú ó ó ó ó ó

 SW-PW7 59 òú ó ó ó ó ó

 SW-PW7 53 òôòø ó ùòòòòòòòòò÷ ó ó

 SW-PW7 50 ò÷ ùòòò÷ ó ó ó

 SW-PW7 51 òòò÷ ó ó ó

 SW-PW7 56 òòòòòòòòò÷ ó ó

 W-MW76 122 òø ó ó

 W-MW76 125 òú ó ùòø

 W-MW76 118 òú ó ó ó

 W-MW76 119 òôòø ó ó ó

 W-MW76 121 òú ó ó ó ó

 W-MW76 123 ò÷ ó ó ó ó

 W-MW76 120 òòòôòòòòòòòòòòòòòòòòòòòòòòòòòòòòòø ó ó ùòòòø

 W-MW76 124 òòòú ùòòòòò÷ ó ó ó

 W-MW76 126 òòò÷ ó ó ó ó

 W-A8 64 òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷ ó ó ùòø

 W-MW30 116 òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷ ó ó ó

 SW-LA2 5 òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷ ó ó

 W-DOMW1 69 òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷ ó

 SW-LA8 47 òûòø ó

 SW-LA8 48 ò÷ ùòø ó

 SW-LA8 46 òòò÷ ùòòòø ó

 SW-LA8 45 òòòòò÷ ùòø ó

 SW-LA8 44 òòòòòòòòò÷ ùòòòòòòòòòòòòòø ó

 SW-LA8 49 òòòòòòòòòòò÷ ùòòòòòòòòòòòòòòòòòòòòòòò÷

 SW-LA8 43 òòòòòòòòòòòòòòòòòòòòòòòòò÷ 

Figure 8-16. Dendrogram (partial) of the clusters for the water analyses presented in Appendix 8-A. 

The left-most column is the well name and the right column indicates the observation number. 

Once the outliers have been identified through cluster analysis, the data can be evaluated 

to determine what causes these samples to stand out. Before rejecting or removing these 

outliers, it is critical to evaluate results of other constituents from the same well during 

the same sampling period or from other wells in the same sampling period to determine if 

the results represent potential sampling errors or real pulses of contaminants. 

Examination of Figure 8-16 reveals the following: 
8-27 

• Out of 4 observations from well A8, 3 fell in Cluster 1. Observation 64 stands out 

as an outlier (single-member cluster 7). Examination of the data table reveals this 

sample has higher gross-alpha and radium than other samples from that well. 

• Out of 15 observations from well MW30 all fell in Cluster 1, with the exception 

of observation 115, which fell in Cluster 9. A very high sulfate analysis was 

reported for this sample. This could represent a bad analysis, or the passage of a 

plume not otherwise observed in the semi-annual sampling. 

• 14 of 15 Samples (observations) from well LA2 fell in cluster 3. Observation 5 

again represents a single-member cluster (number 2) and reference to the data 

table reveals a Th230 analysis that is out of line with the entire data table, 

suggesting a typographical error in recording data. 

• 6 of 7 observations from well DOMW1 clustered together. Observation 69 is 

identified as an outlier, and is high in sulfate, chloride and total dissolved solids 

relative to other samples from this well. 

• Not all wells sampled have odd observations, for example all 9 observations from 

well MW76 fell in Cluster 10, 

Water chemistry data further supports dividing the wells into two major groups. The 

majority of the wells screened in the Southwest flow regime falling into Clusters 1 and 3 

and the majority of wells screened in the West flow regime falling only into Cluster 1 

thus, supporting the hypothesis that the West and Southwest flow regimes are separated 

into two isolated water bodies. 

Please note that there is abundant material on cluster analysis and cluster dendrograms on 

the Internet. These materials should be consulted for further general information. 

8.7.1.3 Factor Analysis Results 

Next, a factor analysis was performed on the data in Appendix 8-A to determine 

relationships between samples or variables in n-space. Factors are not presented here, but 

results of correlation coefficients are presented in Table 8-3. 
8-28 

Table 8-3. Correlations between monitoring data variables 

 as Cl galpha pb210 ra Ra226 ra228 so4 tds u th230 

 as 1.00000 -0.24668 0.22502 0.03648 0.06288 0.07260 -0.00517 0.12385 0.10167 0.11758 0.01139 

 cl -0.24668 1.00000 0.27811 -0.07228 0.14136 0.05518 0.42869 0.41603 0.41539 0.29323 0.16194 

 galpha 0.22502 0.27811 1.00000 0.18202 0.06628 0.05021 0.10118 0.49497 0.60718 0.96203 0.24884 

 pb210 0.03648 -0.07228 0.18202 1.00000 0.49116 0.53849 0.04436 0.15358 0.09250 0.16585 0.07580 

 ra 0.06288 0.14136 0.06628 0.49116 1.00000 0.98053 0.57561 0.57808 0.54190 0.00793 -0.01624 

 ra226 0.07260 0.05518 0.05021 0.53849 0.98053 1.00000 0.40389 0.49020 0.44462 -0.00777 -0.05480

 ra228 -0.00517 0.42869 0.10118 0.04436 0.57561 0.40389 1.00000 0.65338 0.67449 0.07046 0.15290 

 so4 0.12385 0.41603 0.49497 0.15358 0.57808 0.49020 0.65338 1.00000 0.92958 0.45045 0.12761 

 tds 0.10167 0.41539 0.60718 0.09250 0.54190 0.44462 0.67449 0.92958 1.00000 0.57897 0.17896 

 u 0.11758 0.29323 0.96203 0.16585 0.00793 -0.00777 0.07046 0.45045 0.57897 1.00000 0.29619 

 th230 0.01139 0.16194 0.24884 0.07580 -0.01624 -0.05480 0.15290 0.12761 0.17896 0.29619 1.00000 

Correlations obtained in the factor analysis indicate: 

• Gross alpha correlates with uranium (R=.96) 

• Radium is highly correlated with Radium 226 (R=.98), but only moderately 

correlated with Radium 228 (R=.57) and lead 210 (R=.49) 

• Radium correlates with Sulfate (R=.58) and total dissolved solids (R=.54). 

• Radium does not correlate with Uranium (R=.008) 

• Uranium correlates with sulfate (R=.45) and total dissolved solids (R=.58). 

A possible interpretation is that Ra comes from the mill tailings in which it has been 

separated from U and that much of the observed U is natural. 

8.8 Analysis of Mapped (Spatial) Data 

This Section discusses data analysis of spatial data. Specifically, if focuses on a 

discussion of the following three topic areas: 

• Testing for outliers in mapped data; 

• Determining the distribution of uncertainty – the completeness transform; 

• Incongruity; 

Information learned in these three areas often provides useful insight about site 

performance, or rather, help locate areas of uncertainty at the site. The areas of 

uncertainty then become candidate areas for validation monitoring points. 

For characterization data, spatial statistical analysis methods developed within the mining 

industry for mine planning are often useful for determining whether a site has been 

adequately characterized. We did not include geostatistics in this analysis. 

Parameters being measured may fall into a number of classes that may vary across the 

site in different patterns. If we were developing a gold mine, we might only test core 

samples for gold. More generalized site characterization will include measurements for 

many things, but the general approach is similar for each. 
8-29 

8.8.1 Outliers in Mapped Data 

Generally, mapped data are presented in the form of contoured maps. Such maps may be 

produced with computers, but for data analysis it is best to hand contour the data. In the 

process of hand contouring, any points that cause problems in the drawing of smooth 

contours will become apparent. With computer contouring the operator has less 

opportunity to interact with the data, and thus less opportunity to spot outliers, but these 

may still produce contoured “bulls eyes.” Any bulls-eyes in contoured data, or deviations 

from smooth contours in a variable, such as water levels (piezometric surfaces) should be 

visited to determine whether the data point is valid and whether it represents an 

opportunity to re-evaluate the conceptual model. 

Characterization and monitoring data should be evaluated for outliers and trends that 

might suggest alternative conceptual models. Examples might include water levels that 

deviate from smoothed contour piezometric maps or trend surfaces. 

Guidance includes: 

• Hand contour spatial data to gain insight 

• Computer contouring is highly dependent on data point spacing and is accurate 

only for regularly spaced data 

• Question any closed contours (bulls eyes) in a piezometric or concentration map 

in the context of the site model. 

8.8.2 Uncertainty in Mapped Data 

Geostatistical methods were developed to quantify uncertainty in geologic measurements 

so that decisions about whether to proceed with mining in an area, or to determine 

whether additional drilling was needed to fill in data gaps before a risk-informed decision 

could be made. This is a very active field of research today, especially as applied to 

petroleum reservoirs. (Yarus and Chambers, 1994). 

This section presents case studies drawn from real data that illustrate site-specific 

conceptual model revisions required by anomalous data. In two cases the non-fitting data 

were first discarded, and only after subsequent analysis, were identified as clues leading 

to revision of the conceptual site model. 

For the purpose of preparing a map, a geologic variable such as a stratigraphic top, water 

level, or other parameters, can only be known with certainty at the control points. While 

there may be errors in measuring variables at control points, these are distinct from errors 

in estimating values between control points. 

The interrelationships between spatial autocorrelation of the surface, the spacing between 

control points, and the likely error of interpolated points are formalized in regionalized 

variable theory, a branch of statistics devised initially for the analysis of mining problems 

(Matheron, 1965). Under this statistical theory, geologic variables are considered to be 

composed of two components: 

1) a gentle regional trend or drift; and 

2) autocorrelated residuals or deviations from the drift. 
8-30 

Once the drift has been removed (by subtracting a series of trend surfaces or moving 

averages) the degree of similarity between points is given by the semivariance. This is the 

variance of the differences between all possible pairs of points on the map that are the 

same distance apart, and is closely related to the autocorrelation. A plot of semivariance 

vs distance is called a semivariogram, and rises from zero at zero distance to a maximum 

value equal to the total variance around the drift. The distance at which the semivariance 

becomes a maximum is called the “range,” and is also the distance at which the 

autocorrelation of the mapped surface will drop to zero. The value at which the 

autocorrelation reaches maximum on the semivariogram is called the “sill”. The 

autocorrelation (y axis) of a semivariogram plot may not always start at zero. This is due 

to the “nugget effect”, which represents inherent variability plus sampling variability at 

zero distance for the database. 

Once the form of the semivariogram has been determined, it may be used in a surface 

estimation procedure called universal kriging (Matheron, 1965). Provided the drift has 

been properly removed, this procedure provides a contoured surface with the smallest 

errors possible with any estimation procedure. Kriging also yields an estimate, in the 

form of a map, of the possible errors at all estimated points. This is a map of the +or– 

bounds on the mapped surface at every point within the map area. Areas of high 

estimation error then become the subject of additional characterization input. Estimation 

error could refer to a contoured map of pressure heads, to a contoured map of 

contaminant concentrations, or to patterns on a geologic map. 

A recent paper by Cumbest and others (Personal communication, 2004 – it remains 

unpublished in 2007) gives a refined technique to apply geostatistical methodology to 

evaluate the thoroughness of a geotechnical investigation relative to investigation design 

goals. The technique basically uses the spatial distribution of the model error to map the 

probabilities that the model estimation values are in exceedance of specified design 

values. This is accomplished by calculating the probability of exceedance using the 

probability density function ( ( , ) ηi ii m σ (Equation 7) for the standard normal variable. 

The standard normal variable in this case is defined as the difference between the 

estimated value and the specified design value. The resulting probabilities are then 

converted to thoroughness by using the complement to the binominal entropy function. In 

essence, in locations where the estimated model values are known to be in exceedance of 

the specified design value (i.e. probabilities very near 1 or very near 0) result in 

thoroughness of very near 100 percent. At locations where the model error is large 

relative to the difference between the estimated and design values the probabilities of 

exceedance are not well known (i.e. very near 0.5) are associated with a thoroughness 

very near zero. Other locations exhibit a continuum of thoroughness values depending on 

their assigned probabilities. 

Guidance 

• Areas of poor characterization coverage are areas where monitoring points are 

needed. 

• Kriged estimates of errors (see discussion in Section 8.8.2), or the geotechnical 

thoroughness transform may be useful. 
8-31 

8.8.3 Incongruity between Mapped Variables 

The investigator should visually compare all sets of mapped variables for a site. One 

obvious test of a computer flow model, for example, is to see if model flow directions are 

consistent with apparent plume movement from monitoring data. In Figure 8-17, below, 

water table gradients from a site flow model indicate a dominantly westward flow 

direction, but plumes suggest a northwestward flow direction, which is more consistent 

with regional geology. 

Figure 8-17. Map of chloride plume (blue) superimposed on a vector potentiometric data (arrows), 

and contoured hydraulic conductivity data (red). 

Figure 8-17 shows that the direction of plume flow is in good agreement with the zone of 

high hydraulic conductivity. This indicates that the hydraulic conductivity has a greater 

influence on plume migration direction than does the potentiometric surface. 
8-32 

Figure 8-18. Typical alluvial fan 

Published reports for the site in Figure 8-17 suggest that the environment of deposition 

was a series of alluvial fans. As shown in the photograph in Figure 8-18, alluvial fans are 

deposited by radial streams exiting from mountains onto a plain or valley. With the 

abrupt drop in stream gradient, sediments are deposited, the channel is choked and flow 

escapes to form another channel, resulting over time in a fan-shaped deposit. Before this 

channel switching occurs flooding may transport fine-grained sediment outside the 

channels, while coarser sediment remains in the channel bottom. From time to time lakes 

and swamps may fill the valley, resulting in deposition of fine grained and organic-rich 

sediments. The channel deposits will tend to be more permeable than the overbank 

sediments, and thus offer preferential flow directions to underground water. 
8-33 

Figure 8-19. Diagram of alluvial fans in Wyoming 

The site presented in Figure 8-17 is near the area of Figure 8-19 and has a similar 

geologic setting. Any high permeability zones at the site should follow trends suggested 

by the arrows on this figure. Permeability data for the site are presented in Table 8-4. 

Two companies performed aquifer testing on six wells, but used different aquifer 

thicknesses in computing hydraulic conductivity, K, from transmissivity results. We 

suspect that one company (referred to in this report as Company A) may have used screen 

lengths, while the other company (referred to in this report as Company B) used an 

estimate of total aquifer thickness of 240. We have used the screen length from 

Company B’s results to compute a column of K adjusted for screen length. 

It appears that there are two groups of hydraulic conductivity results– one set between 

about 0.1 and 1.0 ft/d and another ranging up to 6 ft/d. If we accept the alluvial fan 

conceptual model for deposition, then we should infer that the higher numbers represent 

in-channel measurements, and the lower numbers out-of-channel measurements. A 

revised flow and transport model incorporating high permeability zones might better 

represent the site. 
8-34 

Table 8-4. Hydraulic conductivity data 

Well ID Company Method Perm 

(ft/day)

Perm 

(ft/min.)

Trans Thickness Adjusted 

K 

MWC33 A Jacob 0.22 1.53E-04 53 240 0.53 

MWC33 B Theis 0.23 1.60E-04 22.7 100 0.227 

MWC33 B Jacob 0.45 3.13E-04 45.1 100 0.451 

MWC34 A Jacob 0.28 1.94E-04 67 240 0.279167 

MWC35 A Jacob 0.78 5.42E-04 187 240 1.87 

MWC35 B Theis 0.12 8.33E-05 12 100 0.12 

MWC36 A Jacob 1.23 8.54E-04 341 240 6.82 

MWC36 B Theis 2.1 1.46E-03 105 50 2.1 

MWC36 B Jacob 3.3 2.29E-03 163 50 3.26 

MWC37 B Jacob 2 1.39E-03 40.8 20 2.04 

MWC37 B Theis 2.7 1.88E-03 53.5 20 2.675 

MWC42 A Jacob 0.6 4.17E-04 165 240 1.833333 

MWC42 B Theis 1 6.94E-04 90 90 1 

MWC42 B Jacob 3.34 2.32E-03 301 90 3.344444 

8.9 Quality Assurance 

Most sources of error in ground-water data can be controlled through a good quality 

assurance (QA) program. This is easy to say, but the hard part comes from the fact that a 

good QA program can only be designed and implemented if the physical principles and 

processes leading to some numerical result are well understood. 

Error control in general can be approached using the principles of systems engineering. 

Each entity –feature or process – must be thought of as an assembly of components. 

Each component plays a role in meeting the requirements set forth for the whole system 

or process. Each is a link in a chain, and failure of any one leads to failure of the chain. 

Quality assurance requires a comprehensive plan that ensures data integrity through each 

step of the process. It is important to be aware of possible sources of error in every step. 

A ground-water monitoring system, for example, has a number of subsystems: 

• Sampling 

• Analysis 

• Data storage 

• Reporting 

Drilling down, each subsystem has a number of components which introduce possible 

sources of error as well. Sampling, for example includes: 

• Choice of monitoring point 
8-35 

• Access to monitoring point – usually a well 

• Sampling method – pump, bailer... 

• Sampling protocol – length of pumping, duplicates, transport of samples, 

documentation.. 

• Field measurements of pH, alkalinity, conductivity, temperature. 

8.9.1 Quality Assurance Case Studies

Let us examine a case study to illustrate QA analysis for just one component in a system: 

the well. Figure 8-20 is a diagram of a typical well along with some notes on well 

construction. The well is the one component in this system that is usually trusted to 

reliably yield water samples whose chemistry is representative of the water-bearing zone 

being sampled. Yet well construction often includes several reactive parts: 

• Bentonite, a clay with very high ion exchange capacity; 

• Portland cement – essentially calcium hydroxide, a strong base, and 

• (Usually) electrical wiring which may allow currents to flow between the ground 

surface and the zone being sampled. 

Voltages between about plus 1 and minus 1 have been measured between galvanized or 

copper clad ground rods at the well head, and the grounding wire to the submerged pump 

at wells at the DOE-SRS. To the best of my knowledge, no systematic study has ever 

been made of electrochemical or electrophoretic effects of monitoring wells. (Electrical 

methods are used to reduce fouling of screens in production wells.) 

The filter sand, bentonite seal, and the cement grout are poured from the surface through 

a 2” pipe called a tremie. The bentonite is a slurry of dried clay pellets which absorb 

water and swell to make a tight seal between the well casing and the earth. Either the 

tremie pipe or a separate tag line is used to verify that the various layers are at the correct 

depth – but it is almost impossible to assure that the casing to earth annulus is uniformly 

filled. Another issue is pouring cement weighing about half again as much as water 

through a 2” pipe without creating a jet that eats through or around the bentonite seal. 

The tremie can be very long, depending on the depth of the well. Once the cement is 

poured, it is not possible to view details of the “as built” configuration. Only care in the 

installation can assure proper construction. One approach is to pour a small amount of 

cement (perhaps mixed in a bucket) and wait for it to cure before pouring the rest. 
8-36 

Ideal Monitoring Well

Drill Hole – walls are caked with mud

Insert casing with screen (slotted section)

Pour filter sand - get it right, like in the picture

Pour swelling clay seal pellets – wait until they 

swell – like in the picture

Pour cement in through a pipe. Do not jet 

a hole through the seal. 

Develop well – pump until all drilling mud 

is removed from screen zone 

Figure 8-20. Schematic of monitoring well with steps in installation. 

The next few figures show pH measurements for several wells at the DOE SRS. In well 

ASB8B, field pH results are relatively stable, varying in the range of about 4 to 6 pH 

units (see Figure 8-21). The actual range in the aquifer may be a little less. Sample 

aeration and possible calibration errors for field pH meters may account for the observed 

range of measurements. 
8-37 

Figure 8-21. pH with time for well ASB8B 

By contrast well ABP3 yields pHs between 12 and 3 (see Figure 8-22). Calcium 

hydroxide (cement) in water produces a pH of about 12.5. At this pH aluminum and zinc 

form soluble anions, and many transition metals are precipitated as hydroxides. Thus the 

disturbance in aquifer chemistry likely caused by poor well construction can render any 

effort to interpret metal chemistry useless. 

As shown in Figure 8-22, with time, the pH lowers. The steepest decline is in about 

1988, when sampling protocols were changed from pumping a fixed volume of water, to 

pumping until indicator parameters, including pH stabilized. The variation in pH is then 

about the same as observed in well ASB8 for a few years. Variance again increases at 

about the time that a change in sampling contractors went into effect. 

wel l =ASB8B

pH

0

1

2

3

4

5

6

7

8

9

10

11

12

13

COLLECTI ON_DATE

01JAN1980 01JAN1985 01JAN1990 01JAN1995 01JAN2000 01JAN2005
8-38 

Figure 8-22. pH with time for well ABP3 

Although wells are installed according to design specifications, it is almost impossible to 

inspect the as-built well. Acceptance criteria that include testing for well efficiency and 

for chemical parameters related to construction defects should be included in installation 

contracts. Training of samplers is important, but beyond this discussion. 

This leads our discussion back to QA issues. Several sources of error can be found 

throughout the sample/data handling process. When analyzing data or assessing data 

anomalies, it is important to carefully consider factors that could be introduced 

throughout the sample process. This case illustrates how factors such as well 

construction, can significantly impact sample quality, and result in misconceptions about 

site conditions. 

Obviously any geochemical understanding relying on accurate pH measurements from 

pumped wells could be clouded to the extent that the sampled values do not reflect 

aquifer conditions. Not only could pH be wrong, but concentrations of grout 

components, such as calcium, and concentrations of pH-sensitive chemicals – Zn, Al, to 

mention two - could be affected by highly alkaline conditions near the well. 

wel l =ABP3

pH

0

1

2

3

4

5

6

7

8

9

10

11

12

13

COLLECTI ON_DATE

26NOV1981 19MAY1987 08NOV1992 01MAY1998 22OCT2003 13APR2009
8-39 

Another issue with pH is the related to the chemicals that control ground-water pH. 

Commonly pH is controlled by calcium bicarbonate. When ground water is brought to 

the surface and exposed to the atmosphere, carbon dioxide can be gained or lost by 

exchange with the atmosphere. Figure 8-23 is taken from an unpublished report and 

shows results of pH and conductivity measured in the field and later in the laboratory. 

The samples are from an area underlain by limestone. Note that in every case pH 

decreases and conductivity increases between the field and the lab. There was no 

indication that the samples were acidified between collection and laboratory analysis, 

leading to the hypothesis that the observed changes are related to carbon dioxide 

exchange with the atmosphere. 

Figure 8-23 Field and laboratory measurements compared. 

8.10 References 

Anscombe, F.J. and J.W. Tukey. “Analysis of Residuals.” Technometrics. pp.141. 1963. 

Cumbest and others (Personal communication, 2004) 

Dempster, A.P., N.M Laird, and D.B Rubin. “Maximum Likelihood from Incomplete 

Data via the EM Algorithm.” J. R. statist. Soc. B. Vol. 39: 1–38.1977. 

Environmental Protection Agency (EPA). “Guidance for Monitoring at Hazardous Waste 

Sites: Framework for Monitoring Plan Development and Implementation.” OSWER 
8-40 

Directive No. 9355.4- 28, EPA. 2003. (access to this publication through www.cluin.org) 

Gilbert, R.O. Statistical Methods for Environmental Pollution Monitoring. New 

York:Van Nostrand Reinhold Company.1987. 

Helsel, D. R. and R. M. Hirsch. “Statistical Methods in Water Resources.” Chapter A3, in 

Water-Resources Investigations Report of U. S. Geological Survey, Book 4, 

Hydrologic Analysis and Interpretation. U. S. Geological Survey. 2002. 

Heslop, D., et al. “Analysis of Isothermal Remnant Magnetization Acquisition Curves 

Using the Expectation-Maximization Algorithm.” Geophys. J. Int. Vol.148: 58-64. 

2002. 

Jones, P.N. & G.J. McLachlan. “Algorithm AS 254: “Maximum Likelihood Estimation 

from Grouped and Truncated Data with Finite Normal Mixture Models.” Applied. 

Statistics. Vol. 39: 273–282. 1990. 

Kendall. M.G. Rank Correlation Methods. 4th ed. London: Charles Griffin & Company. 

pp. 202. 1975. 

Kruiver, P.P., M.J Dekkers,& D. Heslop. “Quantification of Magnetic Coercivity 

Components by the Analysis of Acquisition Curves of Isothermal Remnant 

Magnetization.” Earth Planet. Sci. Lett. VOl.189: 269–276. 2001. 

Matheron, G. Les Variables Regionalisees et Leur Estimation: Une Application de la 

Theorie des Fonctions Aleatoires Aux Sciences de la Nature. Paris: Masson et Cie, 

Editeurs. pp. 305. 1965. 

McLachlan, G. & D. Peel. Finite Mixture Models. New York: Wiley-Interscience. 2000. 

National Institute of Standards and Technology (NIST)/SEMATECH e-Handbook of 

Statistical Methods, http://www.itl.nist.gov/div898/handbook/, date. Date created: 

6/01/2003, Last updated: 7/18/2006 

Peatman, John G. Descriptive and Sampling Statistics. New York: Harper & Brothers. 

1936, ’41, ’47. 

Siegel, S. Nonparametric Statistics for the Behavioral Sciences. New York: McGrawHill. 312 p.1956. 

Sinclair, J. A. “Application of Probability Graphs in Mineral Exploration.” The 

Association of Exploration Geochemists, Special. Vol. 4: 95. 1981. 

Snedecor, G.W. and W.G. Cochran. Statistical Methods. Ames, Iowa: The Iowa State 

University Press. Sixth Ed. 593pp.1976. 
8-41 

Soderberg K., R. Hennet and C. Muffels. “Uncertainty and Trend Analysis for Radium 

in Groundwater and Drinking Water.” Proceeding of 2005 NGWR Naturally 

Occurring Contaminants Conference: Arsenic, Radium, Radon, and Uranium, 

Charleston, South Carolina. p30-43. February 24-25. 2005. 

Tukey, J. W. Exploratory Data Analysis. Massachusetts: Addison-Wesley, Reading. 

688p. 1977. 

Vanderbilt website control chart diagram 

(http://www.vanderbilt.edu/Engineering/CIS/Sloan/web/es130/quality/oldtool.htm#

control) 

Velleman, P.F. and L. Wilkinson. “Nominal, Ordinal, Interval, and Ratio Typologies are 

Misleading.” The American Statistician. Vol.47, No1: pp65-72. 1993. 

Yarus, J.M. and R.L Chambers. “Stochastic Modeling and Geostatistics, Principles, 

Methods, and Case Studies.” AAPG Computer Applications in Geology. No. 3: 

379p. 1994. 
8-42 

Appendix 8-A 

Monitoring Well Analyses from Mill Tailings Site with Results of Cluster Analysis 

Rads in pCi/l; non-rads and U in ppm. Galpha is gross alpha, which is a surrogate for radium plus 

uranium and other alpha-emitters. FL is West or Southwest flow direction – implied separate water 

bodies for wells. C is cluster number as assigned in SPSS 

Obs# Fl. C well Date ra226 ra228 ra th230 u pb210 G alpha so4 tds cl as 

1 SW 1 LA1 12/12/1996 7.2 6.0 13.2 0.050 0.029 0.60 49 851 1350 17.0 0.0005 

2 SW 1 LA1 9/2/1997 4.7 5.3 10.0 0.005 0.013 0.05 30 893 1380 19.0 0.0020 

3 SW 1 LA1 4/28/1998 4.1 4.6 8.7 0.010 0.006 0.20 36 875 1380 18.0 0.0005 

4 SW 1 LA1 6/24/1998 2.1 1.6 3.7 0.090 0.002 0.40 28 862 1380 17.0 0.0060 

5 SW 2 LA2 3/13/1996 11.0 11.0 22.0 20.000 0.074 1.80 51 770 1400 19.0 0.0005 

6 SW 3 LA2 6/12/1996 13.0 9.9 22.9 0.050 0.042 0.05 67 768 1480 21.0 0.0015 

7 SW 3 LA2 8/28/1996 14.0 7.0 21.0 0.200 0.059 0.40 55 760 1480 22.0 0.0010 

8 SW 3 LA2 10/28/1996 11.0 11.0 22.0 0.050 0.051 1.70 57 710 1370 22.0 0.0005 

9 SW 3 LA2 2/11/1997 10.0 9.6 19.6 0.100 0.051 0.80 62 704 1460 21.0 0.0030 

10 SW 3 LA2 6/6/1997 11.0 6.0 17.0 0.005 0.110 1.90 98 788 1420 24.0 0.0020 

11 SW 3 LA2 8/7/1997 21.0 9.2 30.2 0.150 0.008 0.50 81 812 1510 24.0 0.0030 

12 SW 3 LA2 11/3/1997 13.0 10.0 23.0 0.050 0.096 0.60 72 780 1400 24.0 0.0020 

13 SW 3 LA2 4/28/1998 13.7 9.7 23.4 0.100 0.078 0.10 84 818 1470 24.0 0.0015 

14 SW 3 LA2 6/23/1998 15.1 9.1 24.2 0.400 0.150 0.90 155 786 1500 23.0 0.0050 

15 SW 3 LA2 9/1/1998 14.9 9.7 24.6 0.020 0.075 0.30 84 792 1470 24.0 0.0040 

16 SW 3 LA2 11/17/1998 16.0 9.4 25.4 0.020 0.063 0.60 67 814 1490 22.0 0.0020 

17 SW 3 LA2 1/6/1999 12.7 9.6 22.3 0.050 0.073 0.40 48 834 1440 22.0 0.0060 

18 SW 3 LA2 8/25/1999 16.8 9.8 26.6 0.030 0.066 0.80 54 763 1440 21.0 0.0015 

19 SW 3 LA2 2/15/2000 14.0 8.8 22.8 0.500 0.063 0.67 74 780 1500 22.0 0.0015 

20 SW 1 LA3 12/12/1996 5.1 5.4 10.5 0.050 0.017 1.80 42 790 1290 6.0 0.0010 

21 SW 1 LA3 6/10/1997 3.8 6.8 10.6 0.100 0.420 0.40 356 831 1340 5.0 0.0020 

22 SW 1 LA3 9/2/1997 5.3 6.8 12.1 0.100 0.012 0.50 30 877 1220 6.0 0.0020 

23 SW 1 LA3 11/23/1997 5.0 5.8 10.8 0.050 0.020 0.30 29 890 1560 6.0 0.0005 

24 SW 1 LA3 4/21/1998 6.2 6.6 12.8 0.100 0.016 0.10 41 914 1380 6.0 0.0020 

25 SW 1 LA3 6/23/1998 7.8 7.6 15.4 0.200 0.032 0.20 46 836 1390 5.0 0.0050 

26 SW 1 LA5 6/10/1997 6.0 2.4 8.4 0.100 0.130 0.10 123 632 1120 4.0 0.0005 

27 SW 1 LA5 8/28/1997 14.0 3.5 17.5 0.100 0.040 0.10 58 677 1220 5.0 0.0030 

28 SW 3 LA5 11/22/1997 33.0 7.2 40.2 0.400 0.066 2.50 126 937 1670 5.0 0.0050 

29 3 LA5 4/21/1998 29.1 7.1 36.2 0.005 0.120 1.40 148 889 1610 5.0 0.0060 
8-43 

SW 

30 SW 3 LA5 6/23/1998 24.3 6.9 31.2 0.100 0.091 0.90 122 905 1700 5.0 0.0120 

31 SW 3 LA5 3/2/2000 26.0 7.8 33.8 0.240 0.073 1.40 150 890 1600 4.4 0.0040 

32 SW 3 LA6 12/12/1996 17.0 8.7 25.7 0.050 0.470 2.10 551 990 1570 21.0 0.0160 

33 SW 3 LA6 6/10/1997 15.0 7.7 22.7 0.100 0.053 0.90 74 962 1480 23.0 0.0160 

34 SW 3 LA6 9/2/1997 12.0 7.8 19.8 0.005 0.044 1.00 97 968 1560 24.0 0.0170 

35 SW 3 LA6 11/22/1997 18.0 8.4 26.4 0.500 1.200 1.70 906 1100 1830 20.0 0.0130 

36 SW 3 LA6 4/21/1998 18.8 8.9 27.7 0.530 0.800 1.30 791 1130 1700 20.0 0.0150 

37 SW 3 LA6 6/23/1998 18.3 9.8 28.1 0.800 0.830 0.80 865 1090 1760 20.0 0.0240 

38 SW 1 LA7 6/10/1997 1.7 3.3 5.0 0.050 0.010 0.10 15 302 616 6.0 0.0010 

39 SW 1 LA7 9/3/1997 2.0 3.1 5.1 0.005 0.005 0.20 10 497 910 11.0 0.0020 

40 SW 1 LA7 12/1/1997 1.1 1.6 2.7 0.050 0.003 0.20 8.6 308 562 7.0 0.0040 

41 SW 1 LA7 4/29/1998 2.7 2.3 5.0 0.050 0.006 0.10 14 323 604 7.0 0.0005 

42 SW 1 LA7 6/25/1998 0.6 1.1 1.7 0.100 0.001 0.25 13 361 674 7.0 0.0040 

43 SW 4 LA8 12/13/1996 12.0 7.3 19.3 0.400 4.400 6.40 2670 1480 2690 18.0 0.0150 

44 SW 5 LA8 6/9/1997 9.5 4.6 14.1 0.200 2.000 0.20 1380 1400 2480 19.0 0.0040 

45 SW 5 LA8 9/2/1997 6.1 3.8 9.9 6.900 4.100 1.10 2660 1180 2120 18.0 0.0030 

46 SW 5 LA8 11/21/1997 16.0 6.5 22.5 1.800 4.900 1.10 2080 1500 2770 20.0 0.0080 

47 SW 5 LA8 4/21/1998 11.6 4.4 16.0 1.180 3.300 1.20 2190 1580 2730 19.0 0.0060 

48 SW 5 LA8 6/23/1998 11.2 4.8 16.0 2.300 3.500 0.70 2220 1500 2760 20.0 0.0150 

49 SW 5 LA8 3/6/2000 10.0 6.4 16.4 8.200 3.600 3.30 1300 1400 2500 18.0 0.0015 

50 SW 6 PW7 3/11/1996 15.0 6.8 21.8 0.200 0.660 1.60 553 830 1290 3.0 1.0800 

51 SW 6 PW7 5/22/1996 19.0 5.0 24.0 0.800 0.730 0.90 757 850 1340 3.0 1.2600 

52 SW 6 PW7 9/4/1996 17.0 5.7 22.7 1.500 0.660 1.40 558 819 1350 3.0 0.8890 

53 SW 6 PW7 11/17/1996 14.0 5.4 19.4 2.700 0.700 2.30 509 860 1300 3.0 0.9460 

54 SW 6 PW7 3/12/1997 15.0 5.0 20.0 0.005 0.710 1.90 762 860 1360 3.0 0.8500 

55 SW 6 PW7 6/9/1997 12.0 5.1 17.1 0.200 0.640 1.80 621 814 1260 4.0 0.5130 

56 SW 6 PW7 8/5/1997 16.0 0.0 15.6 0.200 0.700 0.50 579 840 1330 3.0 0.8620 

57 SW 6 PW7 11/3/1997 15.0 5.4 20.4 0.300 0.600 0.80 638 859 1220 3.0 0.8120 

58 SW 6 PW7 3/10/1998 17.0 5.6 22.6 0.005 0.510 2.00 597 787 1310 3.0 0.4400 

59 SW 6 PW7 6/15/1998 15.0 6.5 21.5 0.300 0.560 1.70 480 692 1360 3.0 0.8100 

60 SW 1 PW7 9/22/1998 12.6 4.3 16.9 0.070 0.500 0.60 433 484 796 21.0 0.3380 

61 SW 6 PW7 12/8/1998 10.6 3.9 14.5 0.100 0.460 1.00 446 879 1200 3.0 0.3120 

62 SW 6 PW7 3/2/1999 13.2 5.2 18.4 0.050 0.490 1.30 460 764 1300 3.0 0.4550 

63 SW 6 PW7 2/15/2000 15.0 5.3 20.3 0.240 0.500 3.50 540 820 1400 2.5 0.4700 
8-44 

64 W 7 A8 7/8/1996 72.0 7.3 79.3 0.050 0.018 6.10 161 647 1160 8.0 0.0060 

65 W 3 A8 9/19/1996 40.0 2.6 42.6 0.005 0.023 0.10 96 796 1210 11.0 0.0010 

66 W 3 A8 9/8/1997 29.0 2.7 31.7 0.200 0.047 0.10 101 865 1370 13.0 0.0050 

67 W 3 A8 10/14/1998 26.0 3.8 29.9 0.200 0.067 0.60 94 900 1420 14.0 0.0020 

68 W 1 DOMW1 3/20/1995 0.5 0.5 1.5 0.100 0.006 1.30 0.5 133 441 4.6 0.0050 

69 W 8 DOMW1 6/29/1995 1.0 2.2 3.2 0.500 0.620 0.50 1.6 388 8571 33.0 0.0050 

70 W 1 DOMW1 8/23/1995 0.2 0.9 1.1 0.200 0.032 0.10 33 152 366 5.0 0.0010 

71 W 1 DOMW1 12/14/1995 7.1 0.6 7.7 0.005 0.006 1.40 11 145 452 4.0 0.0020 

72 W 1 DOMW1 3/22/1996 0.4 1.5 1.9 0.005 0.004 0.15 6.6 130 414 4.0 0.0010 

73 W 1 DOMW1 7/1/1996 0.3 0.4 0.7 0.005 0.004 0.30 5.7 128 398 4.0 0.0005 

74 W 1 DOMW1 11/11/1996 0.4 2.0 2.4 0.005 0.003 1.20 6.9 137 418 4.0 0.0005 

75 W 1 MW27 3/13/1996 8.1 6.2 14.3 0.005 0.004 2.90 20 450 738 6.0 0.0070 

76 W 1 MW27 6/11/1996 8.5 4.0 12.5 0.050 0.005 1.00 23 438 780 6.0 0.0050 

77 W 1 MW27 8/22/1996 8.5 3.1 11.6 0.900 0.005 0.50 18 433 702 6.0 0.0080 

78 W 1 MW27 10/11/1996 7.6 1.9 9.5 0.050 0.001 1.60 26 431 758 6.0 0.0080 

79 W 1 MW27 5/7/1997 7.4 4.0 11.4 0.005 0.003 1.00 24 398 726 5.0 0.0100 

80 W 1 MW27 7/28/1997 8.3 2.5 10.8 0.050 0.005 1.60 26 424 806 6.0 0.0120 

81 W 1 MW27 10/13/1997 6.3 4.2 10.5 0.050 0.004 1.10 22 408 746 5.0 0.0080 

82 W 1 MW27 2/4/1998 7.1 3.6 10.7 0.050 0.002 1.60 21 411 720 5.0 0.0060 

83 W 1 MW27 5/6/1998 8.7 3.9 12.6 0.020 0.004 1.40 19 407 746 9.0 0.0080 

84 W 1 MW27 7/29/1998 8.3 4.2 12.5 0.010 0.003 1.40 22 415 762 5.0 0.0110 

85 W 1 MW27 10/21/1998 7.0 3.8 10.8 0.050 0.004 2.60 9.6 390 728 5.0 0.0090 

86 W 1 MW27 1/6/1999 6.4 4.7 11.1 0.005 0.001 1.30 22 428 746 5.0 0.0120 

87 W 1 MW27 8/9/1999 5.1 3.3 8.4 0.030 0.001 1.50 17 378 760 5.0 0.0080 

88 W 1 MW27 1/20/2000 6.3 3.1 9.4 0.160 0.001 2.70 37 390 710 3.8 0.0065 

89 W 1 MW28 3/29/1996 9.2 5.8 15.0 0.005 0.003 1.20 26 380 688 5.0 0.0100 

90 W 1 MW28 6/5/1996 8.7 5.0 13.7 0.050 0.003 2.40 24 358 656 5.0 0.0080 

91 W 1 MW28 8/14/1996 7.5 3.8 11.3 0.005 0.001 0.50 29 386 670 5.0 0.0070 

92 W 1 MW28 10/28/1996 11.0 6.4 17.4 0.050 0.001 0.90 19 381 636 5.0 0.0060 

93 W 1 MW28 2/3/1997 11.0 3.8 14.8 0.100 0.004 1.40 51 359 678 4.0 0.0090 

94 W 1 MW28 4/30/1997 11.0 4.6 15.6 0.100 0.002 1.40 33 388 692 6.0 0.0090 

95 W 1 MW28 7/25/1997 6.6 4.4 11.0 0.050 0.003 1.10 20 374 688 5.0 0.0060 

96 W 1 MW28 10/8/1997 9.6 4.2 13.8 0.050 0.002 1.40 33 407 678 6.0 0.0090 

97 W 1 MW28 1/28/1998 10.0 4.5 14.5 0.200 0.002 1.00 30 435 748 6.0 0.0070 

98 W 1 MW28 4/28/1998 10.4 5.4 15.8 0.070 0.001 1.10 41 432 732 6.0 0.0040 

99 W 1 MW28 7/29/1998 12.3 7.1 19.4 0.010 0.002 0.20 32 445 798 6.0 0.0090 

100 W 1 MW28 10/20/1998 10.7 5.0 15.7 0.050 0.003 1.00 23 435 782 5.0 0.0100 

101 W 1 MW28 1/19/1999 10.3 4.0 14.3 0.100 0.004 1.20 27 479 818 6.0 0.0080 

102 W 1 MW28 1/20/2000 12.0 4.9 16.9 1.000 0.001 3.70 46 500 810 5.8 0.0078 

103 W 1 MW30 3/20/1996 15.0 1.7 16.7 0.005 0.056 2.00 60 250 540 3.0 0.0005 

104 W 1 MW30 6/17/1996 14.0 2.6 16.6 0.050 0.090 2.00 40 252 538 4.0 0.0050 

105 W 1 MW30 8/26/1996 18.0 2.3 20.3 0.200 0.053 1.80 73 264 478 4.0 0.0040 

106 W 1 MW30 10/29/1996 22.0 1.6 23.6 0.005 0.060 3.30 105 260 533 4.0 0.0040 

107 W 1 MW30 2/13/1997 31.0 3.0 34.0 0.005 0.062 3.90 69 256 590 6.0 0.0020 

108 W 1 MW30 5/7/1997 24.0 2.5 26.5 0.050 0.059 3.80 94 272 540 5.0 0.0060 

109 W 1 MW30 7/29/1997 12.0 4.0 16.0 0.005 0.019 1.50 58 284 606 2.0 0.0090 

110 W 1 MW30 10/22/1997 30.0 1.7 31.7 0.005 0.066 4.20 91 278 584 6.0 0.0050 

111 W 1 MW30 2/3/1998 14.0 4.0 18.0 0.100 0.061 1.90 50 283 610 5.0 0.0040 

112 W 1 MW30 6/16/1998 32.3 3.4 35.7 0.040 0.067 3.80 95 271 612 6.0 0.0070 

113 W 1 MW30 8/13/1998 25.6 2.8 28.4 0.010 0.063 2.10 94 288 614 6.0 0.0050 
8-45 

114 W 1 MW30 11/11/1998 35.1 2.3 37.4 0.050 0.075 3.40 114 259 618 8.0 0.0090 

115 W 1 MW30 1/7/1999 20.4 2.6 23.0 0.100 0.056 2.80 63 306 574 6.0 0.0080 

116 W 9 MW30 8/17/1999 20.3 3.5 23.8 0.030 0.070 4.10 142 1840 602 39.0 0.0015 

117 W 1 MW30 1/24/2000 28.0 3.5 31.5 1.000 0.065 4.60 180 310 620 6.5 0.0073 

118 W 10 MW76 6/6/1997 42.0 12.0 54.0 0.100 0.240 2.20 276 1710 2480 7.0 0.0680 

119 W 10 MW76 8/4/1997 35.0 9.8 44.8 0.005 0.200 2.20 380 1860 2570 8.0 0.0780 

120 W 10 MW76 11/4/1997 42.0 11.0 53.0 0.100 0.250 3.10 161 1830 2510 16.0 0.0830 

121 W 10 MW76 2/4/1998 36.0 11.0 47.0 0.100 0.260 3.00 355 1830 2610 7.0 0.0820 

122 W 10 MW76 5/5/1998 36.0 12.0 48.0 0.080 0.250 2.00 255 1880 2360 8.0 0.0890 

123 W 10 MW76 8/10/1998 42.8 9.8 52.6 0.100 0.230 1.70 220 1870 2710 7.0 0.0890 

124 W 10 MW76 10/14/1998 54.2 11.0 65.2 0.100 0.220 2.00 209 1780 2640 7.0 0.0920 

125 W 10 MW76 1/6/1999 39.0 11.0 50.0 0.100 0.220 2.30 249 1920 2600 6.0 0.0990 

126 W 10 MW76 1/24/2000 35.0 8.9 43.9 0.800 0.240 3.80 210 1900 2600 6.1 0.0740 

127 W 1 MW77 3/20/1997 4.2 5.4 9.6 0.050 0.003 0.90 16 444 730 0.5 0.0030 

128 W 1 MW77 6/6/1997 5.5 5.0 10.5 0.005 0.018 0.40 21 437 740 4.0 0.0050 

129 W 1 MW77 8/4/1997 5.7 4.9 10.6 0.005 0.001 0.80 24 442 714 4.0 0.0070 

130 W 1 MW77 11/4/1997 5.3 4.8 10.1 0.100 0.004 0.80 22 507 780 4.0 0.0080 

131 W 1 MW77 1/28/1998 6.3 5.4 11.7 0.005 0.001 0.60 11 511 798 4.0 0.0060 

132 W 1 MW77 4/29/1998 5.6 5.7 11.3 0.050 0.001 1.00 28 558 812 4.0 0.0050 

133 W 1 MW77 8/11/1998 6.8 5.6 12.4 0.020 0.005 0.30 26 573 876 4.0 0.0080 

134 W 1 MW77 11/3/1998 6.3 5.7 12.0 0.050 0.001 0.05 41 531 866 4.0 0.0070 

135 W 1 MW77 1/26/1999 5.2 6.4 11.6 0.040 0.001 0.70 30 560 878 4.0 0.0100 

136 W 1 MW77 8/9/1999 7.5 5.6 13.1 0.050 0.001 0.80 17 520 868 4.0 0.0070 

137 W 1 MW77 1/19/2000 6.7 5.4 12.1 6.200 0.001 1.20 43 590 900 3.2 0.0059 

Appendix 8-B Fortran 90 code for well-well correlations and for 

the Mann-Kendall test 

! program trend.for 

! Developed on March 8, 2005 by Zhenxue Dai 

! ****************************************************************** 

! This code carries out the basic statistic analysis of the observed data 

! including the water heads and the concentrations, as well as the other types of data. 

! It uses the Mann-Kendall test to evaluate the trends of the time series observations. 

! This code also calculate the water head correlations between different wells 

! from the observation data to identify the connections of the groundwater at 

! different aquifers or geological structures. 

! The input data format is: first well name, then water heads in this well 

! W123456 120, 122, 123,.... 

! W123457 120, 122, 123,.... 

! nw== number of observation wells 

! nt== number of observation points in each well 

! Wnam== wall name; WHH== water heads; ave== mean; Var==Variance 

! Stan== standard deviation; Cv== Coefficients of variation; Cov==Covariance 

! Trend== Uptrend, Downtrend, or Flat 

! Pval== p-value, p<0.1 trend test significant, p>0.1, test result uncertain 
8-46 

! Sman==Mann-Kendall statistic parameter in each well 

! Sz==modified Mann-Kendall statistic parameter in each well 

! Ssd==modified coefficient for each well. 

! Rela(k,i)== Correlation Coefficients between well k and well i. 

! alfa=1.68 for water head, and 1000 for concentrations 

! ****************************************************************** 

 parameter (nw=150,nt=20) 

 IMPLICIT DOUBLE PRECISION(A-H,O-Z),INTEGER(I-N) 

 dimension WHH(nw,nt),Var(nw),ave(nw), Stan(nw),Cv(nw) 

 dimension Rela(nw,nw),Cov(nw,nw),Hmin(nw),Hmax(nw),Pval(nw), 

 + Numt(nw),Sman(nw),Sz(nw),Ntie(nw),Ssd(nw) 

 character*8 Wnam(nw),trend(nw) 

 character*5 Waqu(nw) 

 character*80 str1 

 character*4 str2 

 character*8 out 

 alfa=1.0 

 write(*,*) "ENTER INPUT FILENAME (NO HEADER): " 

 read(*,'(a)')str1 

 write(*,*) "ENTER 4 CHARACTERS FOR OUTPUT FILENAME " 

 read(*,'(a)')str2 

 open(99,file=str1,status='old') 

 OUT=str2//'.out' 

 open(91,file=out,status='unknown') 

 write(*,*) " " 

 write(*,*) "THINKING... " 

 write(*,*) " " 

 num1 = 0 

 tranN0=0 

! BRING IN FIRST LINE OF INPUT FROM DATA FILE 

 read(99,*)Nww !=137, number of observation wells 

 read(99,*)Ntt !=16, max number of data at one well 

 do i=1,Nww 

 read(99,*) Wnam(i),Waqu(i),(WHH(i,j), j=1,Ntt) 

! if(id(i).eq.0) go to 50 (commented out by ZDai) 

 write(*,*) Wnam(i),Waqu(i) 

 end do 

 50 continue 
8-47 

 Iout=0 

499 continue 

 If(Iout.eq.0) Write(91,500) 

500 format(/,'Statistic Analysis of the Original Observations' 

 + ,/,'WellNam AqNam ObNm MinVal MaxVal ', 

 + 'MeanV Varian Stand CoefV ', 

 + 'Mann ModM Trend p-val') 

 If(Iout.eq.1) Write(91,801) 

801 format(/,'Statistic Analysis of the Observations', 

 + ' After Rejecting the Outlier Points', 

 + /,'WellNam AqNam ObNm MinVal MaxVal ', 

 + 'MeanV Varian Stand CoefV ', 

 + 'Mann ModM Trend p-val') 

! calculate mean, variance of water head in each well(Var(nw),ave(nw), Stan(nw)) 

 do 60 i=1,Nww 

 nwt=0 

 hhh=0 

 st=0 

 Hm=0 

 Hn=1.0e25 

 Sm=0 

 do j=1,Ntt 

 Ntie(j)=0 

 if(WHH(i,j).eq.-100) go to 62 

 nwt=nwt+1 

 hhh=hhh+WHH(i,j) 

 if(WHH(i,j).gt.Hm)Hm=WHH(i,j) !Max value 

 if(WHH(i,j).lt.Hn)Hn=WHH(i,j) !Min Value 

 do k=1,Ntt 

 if(k.gt.j.and.WHH(i,k).ne.-100)then 

 aa=WHH(i,k)-WHH(i,j) 

 if(aa.gt.0.0) Ms=1 

 if(aa.eq.0.0) then 

 Ms=0 

 Ntie(j)=Ntie(j)+1 

 end if 

 if(aa.lt.0.0) Ms=-1 

 Sm=Sm+Ms 

 end if 

 end do 

 

 62 continue 
8-48 

 end do 

 Numt(i)=nwt 

 Hmax(i)=Hm 

 Hmin(i)=Hn 

 Sman(i)=Sm 

 if(nwt.ne.0)ave(i)=hhh/nwt 

 Stie=0 

 do k2=1,ntt 

 Stie=Stie+Ntie(k2)*k2*(k2-1)*(2*k2+5) 

 end do 

 Ssd(i)=((Numt(i)*(Numt(i)-1)*(2*Numt(i)+5)-Stie)/18.0) 

 If(Ssd(i).gt.0.0) Ssd(i)=Ssd(i)**0.5 

 if(Sman(i).gt.0.0) then 

 if(ssd(i).ne.0.0) Sz(i)=(Sman(i)-1.0)/Ssd(i) 

 trend(i)=' Uptrend' 

 end if 

 if(Sman(i).eq.0.0) then 

 Sz(i)=0 

 trend(i)=' Flat' 

 end if 

 if(Sman(i).lt.0.0) then 

 if(ssd(i).ne.0.0)Sz(i)=(Sman(i)+1.0)/Ssd(i) 

 trend(i)='Downtren' 

 end if 

 Szz=abs(Sz(i)) 

 if(Szz.gt.5) Pval(i)=0.00000 

 if(Szz.gt.3.09.and.Szz.lt.5) 

 + Pval(i)=66.21327*exp(-szz/0.27834)-9.9998E-7 

 if(Szz.gt.1.96.and.Szz.lt.3.09) 

 + Pval(i)=2.59485*exp(-szz/0.42511)-0.00081 

 if(Szz.lt.1.96.and.Szz.gt.1.28) 

 + Pval(i)=0.8051*exp(-szz/0.66358)-0.01698 

 if(Szz.lt.1.28) Pval(i)=0.71701*exp(-szz/1.56831)-0.21701 

 do j=1,ntt 

 if(WHH(i,j).eq.-100) go to 63 

 st=st+(WHH(i,j)-ave(i))**2.0 

 63 continue 

 end do 

 if(nwt.ne.0.0)then 

 Var(i)=st/nwt 

 Stan(i)=(st/nwt)**0.5 

 end if 

 if(ave(i).ne.0.0)Cv(i)= stan(i)/ave(i) 

 if(nwt.eq.0)then 

 Write(91,901)Wnam(i),Waqu(i),Numt(i) 
8-49 

901 format(A8,1x,A5,I3,1x,'This well is deleted!') 

 go to 60 

 end if 

! Write(*,501) Wnam(i),Ave(i),Var(i),Stan(i),Cv(i) 

 Write(91,501)Wnam(i),Waqu(i),Numt(i),Hmin(i),Hmax(i),Ave(i), 

 + Var(i),Stan(i),Cv(i),Sman(i),Sz(i),Trend(i),Pval(i) 

 60 continue 

501 format(A8,1x,A5,I3,1x,3f7.2,F7.2,f6.2,f6.3,1x,f4.0,f6.2, 

 + 1x,A8,f6.3) 

 If(Iout.eq.1) go to 808 

! 

! Reject the extremal observation points 

! 

 aSd=0.0 

 do i=1,nww 

 asd=asd+Stan(i) 

 end do 

 asd=asd/nww 

 do iw=1,nww 

 Sp=0.025 

 pp=(Numt(iw)-1)*Sp/Numt(iw) 

 if(pp.le.0.00003) zz=4 

 if(pp.gt.0.00003.and.pp.le.0.0062) 

 + zz=1.54688*exp(-pp/0.00117)+2.49239 

 if(pp.le.0.0688.and.pp.gt.0.0062) 

 + zz=1.41193*exp(-pp/0.02866)+1.36272 

 if(pp.gt.0.0688) 

 + zz=2.50842*exp(-pp/0.328)-0.54623 

 if(zz.le.0.0) zz=0.0 

! write(*,*)pp, zz 

 vk=1.4+0.85*zz 

 vc=vk*(1.0-(vk**2.0-2.0)/(4.0*(Numt(iw)-1.0))) 

 + *((Numt(iw)-1.0)/Numt(iw))**0.5 

 vCs=alfa*(vc*stan(iw))**2.0 

! write(*,*)Wnam(iw), vCs 

 do j=1,ntt 

 If(whh(iw,j).le.-100.0) go to 3721 

 vd=(whh(iw,j)-ave(iw))**2.0 

! vd=abs(whh(iw,j)-ave(iw))*(1.0-2*Sp) 

 if(vd.gt.vCs.or.vd.gt.100*alfa*asd)then 

 orig=whh(iw,j) 

 whh(iw,j)=-100 

! Numt(iw)=Numt(iw)-1 

 write(*,*)Wnam(iw),orig,'vd=',vd,'st=',vCs 

 end if 
8-50 

3721 continue 

 end do 

 end do 

 Iout=1 

 go to 499 

! LOOP calculate correlation coefficients between wells 

! 

808 continue 

 do 80 k=1,Nww 

 do 80 i=1,Nww 

 nwt=0 

 hhk=0 

 hhi=0 

 st=0 

 vari=0 

 vark=0 

 do j=1,Ntt 

 if(WHH(k,j).eq.-100.or.WHH(i,j).eq.-100) go to 82 

 nwt=nwt+1 

 hhk=hhk+WHH(k,j) 

 hhi=hhi+WHH(i,j) 

 82 continue 

 end do 

 if(nwt.ge.1)then 

 avek=hhk/nwt 

 avei=hhi/nwt 

 end if 

 do j=1,ntt 

 if(WHH(k,j).eq.-100.or.WHH(i,j).eq.-100) go to 83 

 st=st+(WHH(k,j)-avek)*(WHH(i,j)-avei) 

 vari=vari+(WHH(i,j)-avei)**2.0 

 vark=vark+(WHH(k,j)-avek)**2.0 

 83 continue 

 end do 

 if(nwt.ge.1)then 

 Cov(k,i)=st/nwt 

 Varii=(vari/nwt)**0.5 

 Varkk=(vark/nwt)**0.5 

 Rela(k,i)=Cov(k,i)/(Varkk*Varii) 

 end if 

 80 continue 

 Write(91,502) 

502 format(/,'Following Wells are Highly Positively Correlated:', 
8-51 

 + ' R > 0.95') 

 do k=1,Nww 

 do i=1,Nww 

 If(i.le.k) go to 21 

 If (Rela(k,i).ge.0.95) then 

 Write(91,503) Wnam(k),Waqu(k),Wnam(i),Waqu(i),Rela(k,i) 

503 format(A8,A5,'and ',A8,A5,f5.2) 

 end if 

21 continue 

 end do 

 end do 

 Write(91,602) 

602 format(/,'Following Wells are Positively Correlated:', 

 + ' 0.9 < R < 0.95') 

 do k=1,Nww 

 do i=1,Nww 

 If(i.le.k) go to 23 

 If (Rela(k,i).ge.0.9.and.Rela(k,i).lt.0.95) then 

 Write(91,603)Wnam(k),Waqu(k),Wnam(i),Waqu(i),Rela(k,i) 

603 format(A8,A5,'and ',A8,A5,f5.2) 

 end if 

23 continue 

 end do 

 end do 

 Write(91,604) 

604 format(/,'Following Wells are not Correlated:', 

 + ' -0.1 < R < 0.1') 

 do k=1,Nww 

 do i=1,Nww 

 If(i.le.k) go to 84 

 If (Rela(k,i).le.0.1.and.Rela(k,i).ge.-0.1) then 

 Write(91,605)Wnam(k),Waqu(k),Wnam(i),Waqu(i),Rela(k,i) 

605 format(A8,A5,'and ',A8,A5,f5.2) 

 end if 

84 continue 

 end do 

 end do 

 Write(91,504) 
8-52 

504 format(/,'Following Wells are Negatively Correlated:', 

 + ' R < -0.9') 

 do k=1,Nww 

 do i=1,Nww 

 If(i.le.k) go to 88 

 If (Rela(k,i).le.-0.9) then 

 Write(91,505)Wnam(k),Waqu(k),Wnam(i),Waqu(i),Rela(k,i) 

505 format(A8,A5,'and ',A8,A5,f5.2) 

 end if 

88 continue 

 end do 

 end do 

 Write(91,506) (Wnam(i), i=1,Nww) 

506 format(/,'All Correlation Coeff of Water Head Between Wells', 

 + /,15x,137(A7)) 

 Write(91,406) (Waqu(i), i=1,Nww) 

406 Format(15x,137(A5,2x)) 

 do k=1,Nww 

 Write(91,508) Wnam(k), Waqu(k),(Rela(k,i),i=1,Nww) 

508 format(A8,A5,137(f7.3)) 

 end do 

 CALL BEEPQQ(200,400) 

 CALL BEEPQQ(30,400) 

 CALL BEEPQQ(200,400) 

 CALL BEEPQQ(30,400) 

 CALL BEEPQQ(400,1500) 

 write(*,*) " DONE! " 

 stop 

 End 
G-1 

GLOSSARY 

Alluvium A general term for clay, silt, sand, gravel, or similar unconsolidated detrital 

material, deposited during comparatively recent geologic time by a stream or 

other body of running water, as a sorted or semi sorted sediment in the bed of 

the stream or on its floodplain or delta, as a cone or fan at the base of a 

mountain slope. 

Aquifer A geological formation capable of storing and yielding significant quantities of 

water. It is usually composed of sand, gravel, or permeable rock which lies 

upon a layer of clay or other impermeable material. 

Aquitard Less permeable beds, also saturated with water, from which water can't be 

produced through wells, but where the flow is significant enough to feed 

adjacent aquifers through vertical leakage. 

Becquerel (Bq) The International System (SI) unit of activity equal to one nuclear 

transformation (disintegration) per second. 1 Bq = 2.7x10-11 Curies (Ci) = 

27.03 picocuries (pCi). 

Colluvium A general term applied to any loose, mixed, and incoherent mass of soil 

material and/or rock fragments deposited by rainwash, sheetwash, or slow 

continuous downslope creep, usually collecting at the base of gentle slopes or 

hillsides. 

Comprehensive 

Environmental 

Response, 

Compensation, and 

Liability Act 

(CERCLA) 

Commonly referred to as “CERCLA” or “Superfund,” this federal statute was 

enacted by Congress in 1980 and was amended several times thereafter. 

CERCLA was designed to respond to situations involving past disposal of 

hazardous substances. CERCLA provides EPA the authority to clean up 

hazardous substance sites under “response” or “remedial” provisions of the 

National Contingency Plan (NCP) and other implementing regulations. 42 

U.S.C. §§ 9601 et seq.

Conceptual site model A qualitative description of the processes, geometry, and boundary conditions 

associated with a disposal site or site sub-system component (i.e., ground-water 

system, flow-through covers, source term, etc.). Conceptual model 

development includes abstracting system, or sub-system, descriptions into 

more simplified forms that can be mathematically modeled. 

Contaminant of 

Concern 

(COC) 

A contaminant or a chemical that poses potential public health risks. Potential 

contaminants of concern (PCOCs) are all chemicals that have been detected at 

the site. Only those contaminants retained for the risk assessment are referred 

to as COCs. 

Cuesta A ridge with a gentle slope on one side and a steep slope on the other. 

Curie (Ci) The customary unit of radioactivity. One curie (Ci) is equal to 37 billion 

disintegrations per second (3.7 x 1010 dps = 3.7 x 1010 Bq), which is 

approximately equal to the decay rate of one gram of 226Ra. 

Direct current 

electrical resistivity 

(DC-resistivity) 

A geophysical technique used to measure the resistance of a rock formation to 

an electric current. 
G-2 

Effluent Any substance, particularly a liquid, which enters the environment from a point 

source. Generally refers to wastewater from a sewage treatment or industrial 

plant. 

Erratics Boulders and other rock fragments transported by glacial ice from their place 

of origin to an area where the bedrock is different. 

Ground-penetrating 

radar (gpr) 

Geophysical exploration technique that utilizes pulses of electromagnetic 

radiation in the microwave band (UHF/VHF frequencies) of the radio 

spectrum, and reads the reflected signal to detect subsurface structures and 

objects without drilling, probing or otherwise breaking the ground surface. 

Half-life (t1/2) The time required for one-half of the radioactive isotopes in a sample to decay 

to radiogenic (daughter) isotopes or disintegrate. 

Hazardous Waste A category of waste regulated under RCRA. To be considered hazardous, a 

waste under RCRA must be a solid waste and must exhibit at least one of four 

characteristics described in 40 CFR 261.20 through 40 CFR 261.24 (i.e., 

ignitability, corrosivity, reactivity, or toxicity) or be specifically listed by EPA 

in 40 CFR 261.31 through 40 CFR 261.33. Hazardous waste does not include 

source, special nuclear, or by-product materials as defined by the AEA, nor 

material contained in point source discharges regulated under the Clean Water 

Act. 

Infiltration The net water intake into the native soils at the site or into a disposal unit(s) 

through the land or cover surface(s). 

Kd distribution coefficient. 

Kriging A geostatistical method of evaluating mine reserves based on a mathematical 

function known as a semivariogram. 

Lacustrine Of or applying to the sedimentary environment of a lake. 

Low-Level Waste 

(LLW) 

Radioactive waste that is not high level radioactive waste, spent nuclear fuel, 

transuranic waste, byproduct material (as defined in section 11e.(2) of the 

Atomic Energy Act of 1954, as amended), or naturally occurring radioactive 

material. [Adapted from Nuclear Waste Policy Act of 1982, as amended] 

Maximum 

Contaminant Level 

(MCL) 

Under the Safe Drinking Water Act, the maximum permissible level of a 

contaminant in water delivered to any user of a public water system. 

Non-Aqueous Phase 

Liquid 

(NAPL) 

Organic compounds or mixtures of such compounds that do not mix with 

water. A NAPL that is lighter than water is called light non-aqueous phase 

liquid (LNAPL) or a floater. A NAPL that is heavier than water is called dense 

non-aqueous phase liquid (DNAPL) or a sinker. 

Neutron probe A device used to measure the quantity of water present in soil. 

Ohm-m Unit of measure of electrical resistivity. 

Operable Unit (OU) A term given to large areas where remediation may be focused by grouping 

multiple units into a single management unit. 

Performance 

Assessment (PA) 

An analysis of a radioactive waste disposal facility conducted to demonstrate 

there is a reasonable expectation that performance objectives established for 

the long-term protection of the public and the environment will not be 

exceeded following closure of the facility. [DOE 435.1-1] 
G-3 

Petra Software developed by the GeoPLUS Corporation. It’s primary use is to store 

and provide tools for interpreting geologic data. 

Picocurie (pCi) A "picocurie" is one-trillionth of a curie. The same mass (one gram) of other 

radioactive elements may have an activity higher or lower than one curie. 

pCi/L Represents the number of picocuries in a liter of water. 

Plume A body of contaminated groundwater flowing from a specific source. 

Remediate To cleanup or decontaminate ground water or soil. 

Resource Conservation 

and Recovery Act 

(RCRA) 

A federal law enacted in 1976 to address solid waste and the treatment, storage, 

and disposal of hazardous waste. 42 U.S.C. §§ 6901-6992k. 

Semivariogram A key function in geostatistics used to fit a model of the spatial/temporal 

correlation of an observed phenomenon. 

Sorption coefficient 

(Kd) 

The ratio of the mass of solute on the solid phase per unit mass of solid phase 

to the concentration of solute in solution. The validity of this ratio requires that 

the reactions that cause the partitioning are fast and reversible (e.g., chemical 

equilibrium is achieved) and the sorption isotherm is linear. 

Stratigraphy The sequence or order of rock or soil layers in a geologic formation. 

Surface-based seismic 

surveys 

A geophysical technique to determine the detailed structure of rocks 

underlying a particular area by passing acoustic shock waves from the surface 

into the underlying strata and detecting and measuring the reflected signals. 

Surficial Of, relating to, or occurring on or near the surface of the earth. 

Thermocouple 

psychrometers (TCPs) 

Probes for determining soil water potential in situ. 

Till A mix of fine silt, sand, gravel, and large boulders, usually in a glacial setting. 

Tritium units One tritium unit is equal to one molecule of tritium per 1018 molecules of 

hydrogen and has an activity of 0.118 Bq/kg (3.19 pCi/kg or pCi/L). 

Vadose zone The horizon between the earth’s surface and the water table, also know as the 

“unsaturated zone”. Vadose zone wells installed by the USGS at the ADRS 

are designated with the prefix “UZB-x”. 
BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

NRC FORM 335

(9-2004)

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

 (Assigned by NRC, Add Vol., Supp., Rev.,

 and Addendum Numbers, if any.)

NUREG/CR-6948, Vol 2

3. DATE REPORT PUBLISHED

MONTH

November

YEAR

2007

4. FIN OR GRANT NUMBER

Y6020

2. TITLE AND SUBTITLE

Integrated Ground-Water Monitoring Strategy for NRC-Licensed Facilities and Sites: Case

Study Applications

5. AUTHOR(S)

Van Price, Tom Temples, Rex Hodges, Zhenxue Dai, David Watkins and Janice Imrich

6. TYPE OF REPORT

Technical

7. PERIOD COVERED (Inclusive Dates)

February 2003 - September 2007

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor,

Advanced Enivironmental Solutions, LLC

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type "Same as above"; if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

Division of Fuel, Engineering and Radiological Research

provide name and mailing address.)

and mailing address.)

10. SUPPLEMENTARY NOTES

T.J. Nicholson, NRC Project Manager

11. ABSTRACT (200 words or less)

This document discusses results of applying the Integrated Ground-Water Monitoring Strategy (the Strategy) to actual waste

sites using existing field characterization and monitoring data. The Strategy is a systematic approach to dealing with complex

sites. Application of such a systematic approach will reduce uncertainty associated with site analysis, and therefore uncertainty

associated with management decisions about a site. The Strategy can be used to guide the development of a ground-water

monitoring program or to review an existing one. The sites selected for study fall within a wide range of geologic and climatic

settings, waste compositions, and site design characteristics and represent realistic cases that might be encountered by the

NRC. No one case study illustrates a comprehensive application of the Strategy using all available site data. Rather, within each

case study we focus on certain aspects of the Strategy, to illustrate concepts that can be applied generically to all sites. The test

sites selected include:

- Charleston, South Carolina, Naval Weapons Station,

- Brookhaven National Laboratory on Long Island, New York,

- The USGS Amargosa Desert Research Site in Nevada,

- Rocky Flats in Colorado,

- C-Area at the Savannah River Site in South Carolina, and

- The Hanford 300 Area.

A Data Analysis section provides examples of detailed data analysis of monitoring data. 

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

conceptual site model

data management

geology

ground water 

monitoring

outlier

Performance Indicator

tritium

vadose

wells

14. SECURITY CLASSIFICATION

13. AVAILABILITY STATEMENT

unlimited

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER

407 West Main Street

Lexington, SC 29072

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001