Prepared in cooperation with the

U.S. DEPARTMENT OF ENERGY

Preliminary Evaluation of the Importance of Existing 

Hydraulic-Head Observation Locations to AdvectiveTransport Predictions, Death Valley Regional Flow 

System, California and Nevada

U.S. Department of the Interior

U.S. Geological Survey

Water-Resources Investigations Report 00-4282

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

Model column number

Model row number

Las Vegas

Nevada

Test Site

Least important observation locations
Preliminary Evaluation of the Importance of Existing

Hydraulic-Head Observation Locations to AdvectiveTransport Predictions, Death Valley Regional Flow

System, California and Nevada

By Mary C. Hill1, D. Matthew Ely2, Claire R. Tiedeman3,

Grady M. O’Brien4, Frank A. D’Agnese4, and Claudia C. Faunt5

U.S. GEOLOGICAL SURVEY

Denver, Colorado

2001

Prepared in cooperation with the

U.S. DEPARTMENT OF ENERGY

Water-Resources Investigations Report 00-4282

1 U.S. Geological Survey, Boulder, CO

2 U.S. Geological Survey, Tacoma, WA

3 U.S. Geological Survey, Menlo Park, CA

4 U.S. Geological Survey, Tucson, AZ

5 U.S. Geological Survey, San Diego, CA
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

CHARLES G. GROAT, Director

Any use of trade, product, or firm names in this publication is for descriptive

purposes only and does not imply endorsement by the U.S. Government

For additional information write to:

Regional Research Hydrologist

U.S. Geological Survey

Box 26046, Mail Stop 413

Denver Federal Center

Denver, CO 80225-0046
CONTENTS III

CONTENTS

Abstract.................................................................................................................................................................................. 1

Introduction............................................................................................................................................................................ 2

The Death Valley Regional Ground-Water Flow System ..................................................................................................... 4

Methods of Evaluation........................................................................................................................................................... 7

Predictions of Interest ................................................................................................................................................ 7

Statistics for Evaluating Observation Locations ........................................................................................................ 9

Prediction standard deviation—Measure of prediction uncertainty ............................................................... 9

Increased uncertainty statistic......................................................................................................................... 10

Dimensionless scaled sensitivity .................................................................................................................... 10

Using the statistics .......................................................................................................................................... 11

Grouping of Observations .......................................................................................................................................... 11

Results of Evaluation............................................................................................................................................................. 12

Omission of Individual Observations......................................................................................................................... 12

Is an observation important to any of the predictions?................................................................................... 12

How does observation importance vary with advective transport direction?................................................. 16

What is the breadth of each observation's importance?.................................................................................. 16

How does observation importance vary on a site-specific basis? .................................................................. 18

Omission of Observation Groups............................................................................................................................... 20

Is a group important to any of the predictions and how does group importance vary with 

transport direction? ................................................................................................................................... 20

What is the breadth of each group’s importance? .......................................................................................... 20

How does observation group importance vary on a site-specific basis? ........................................................ 23

Omission of a Set of 100 Low-Importance Individual Observation Locations ......................................................... 24

Summary and Conclusions .................................................................................................................................................... 25

References Cited.................................................................................................................................................................... 25

Appendix A: Graphs showing the importance of individual observation locations to advective transport 

simulated from 14 UGTA sites ....................................................................................................................................... 27

Appendix B: Graphs showing the importance of groups of observation locations to advective transport 

simulated from 14 UGTA sites ....................................................................................................................................... 45

FIGURES

1. Location of the Death Valley regional ground-water flow system and the boundary 

of the three-layer ground-water model, Nevada and California.............................................................................. 5

2. Locations of hydraulic-head observations used to calibrate the three-layer model of 

the Death Valley regional ground-water flow system............................................................................................. 8

3. Areal view of a particle path simulated from an UGTA site using the ADV Package ........................................... 9

4. Maps of (A) shallow and (B) intermediate and deep observation locations and observation groups..................... 13

5. Is the observation location important to any of the predictions? ............................................................................ 15

6. Is the observation location important to any of the predictions in each of the coordinate directions? ................... 17

7. How pervasively is the observation location important? ........................................................................................ 19

8. Largest percent increase in the uncertainty of advective transport in the east–west, 

north–south, or vertical directions, at any of the 15 sites (14 UGTA sites and Yucca Mountain).......................... 19
IV Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

9. Number of origins (of the 14 UGTA sites and Yucca Mountain) for which the mean 

uncertainty increases (a) more than or equal to 10 percent with the omission of the 

observation group, (b) more than or equal to 5 percent but less than 10 percent with 

the omission of the observation group, and (c) more than or equal to 1 percent but less 

than 5 percent with the omission of the observation group..................................................................................... 21

10. The 100 least significant shallow and intermediate hydraulic-head observation

locations that were removed to evaluate the importance of observations at these locations.................................. 24

TABLES

1. Parameter values and standard deviations used to evaluate hydraulic-head observation locations........................ 6

2. Observation location group name and number of observation locations in each group. ........................................ 14

3. Observation locations where the maximum uncertainty in any coordinate direction increases 

by one percent or more with omission of the observation location. ....................................................................... 18

4. Importance of observation groups categorized by the percent increase in uncertainty with 

omission of the observation group. ......................................................................................................................... 22

CONVERSION FACTORS

Multiply By To obtain

meter (m) 3.28 foot

cubic meter per day (m3/d) 35.31 cubic foot per day

kilometer (km) 0.62 mile

Temperature: Degrees Celsius (°C) can be converted to degrees Fahrenheit (°F) by using the formula °F = [1.8(°C)] + 32. 

Degrees Fahrenheit can be converted to degrees Celsius by using the formula °C = 0.556(°F − 32).

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929, formerly called “Sea-Level 

Datum of 1929”), which is derived from a general adjustment of the first-order leveling networks of the United States and Canada.
ABSTRACT 1

Preliminary Evaluation of the Importance of Existing

Hydraulic-Head Observation Locations to AdvectiveTransport Predictions, Death Valley Regional Flow

System, California and Nevada

By Mary C. Hill, D. Matthew Ely, Claire R. Tiedeman, Grady M. O’Brien, Frank A. D’Agnese,

and Claudia C. Faunt

ABSTRACT

When a model is calibrated by nonlinear

regression, calculated diagnostic statistics and

measures of uncertainty provide a wealth of

information about many aspects of the system.

This report presents a method of ranking the

likely importance of existing observation locations using measures of prediction uncertainty.

It is suggested that continued monitoring is warranted at more important locations, and unwarranted or less warranted at less important

locations. The report develops the methodology

and then demonstrates it using the hydraulichead observation locations of a three-layer

model of the Death Valley regional flow system

(DVRFS). The predictions of interest are subsurface transport from beneath Yucca Mountain and

14 Underground Test Area (UGTA) sites. The

advective component of transport is considered

because it is the component most affected by the

system dynamics represented by the regionalscale model being used. The problem is addressed using the capabilities of the U.S. Geological Survey computer program MODFLOW2000, with its ADVective-Travel Observation

(ADV) Package, and an additional computer

program developed for this work.

The methods presented in this report are used

in three ways:

(1) The ratings for individual observations

are obtained by manipulating the measures of prediction uncertainty, and do not

involve recalibrating the model. In this

analysis, observation locations are each

omitted individually and the resulting

increase in uncertainty in the predictions

is calculated. The uncertainty is quantified as standard deviations on the simulated advective transport. The increase in

uncertainty is quantified as the percent

increase in the standard deviations caused

by omitting the one observation location

from the calculation of standard deviations. In general, observation locations

associated with larger increases are rated

as more important.

(2) Ratings for largely geographically based

groups are obtained using a straightforward extension of the method used for

individual observation locations. This

analysis is needed where observations are

clustered to determine whether the area is

important to the predictions of interest.

(3) Finally, the method is used to evaluate

omitting a set of 100 observation locations. The locations were selected because they had low individual ratings and

were not one of the few locations at

which hydraulic heads from deep in the

system were measured.

The major results of the three analyses, when

applied to the three-layer DVRFS ground-water
2 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

flow system, are described in the following paragraphs. The discussion is labeled using the numbers 1 to 3 to clearly relate it to the three ways

the method is used, as listed above.

(1) The individual observation location

analysis indicates that three observation

locations are most important. They are

located in Emigrant Valley, Oasis Valley,

and Beatty. Of importance is that these

and other observations shown to be important by this analysis are far from the

travel paths considered. This displays the

importance of the regional setting within

which the transport occurs, the importance of including some sites throughout

the area in the monitoring network, and

the importance of including sites in these

areas in particular.

The method considered in this report

indicates that the 19 observation locations that reflect hydraulic heads deeper

in the system (in model layers 1, 2, and

3) are not very important. This appears to

be because the locations of these observations are in the vicinity of shallow observation locations that also generally are

rated as low importance, and because the

model layers are hydraulically well connected vertically. The value of deep observations to testing conceptual models,

however, is stressed. As a result, the deep

observations are rated higher than is consistent with the results of the analysis

presented, and none of these observations

are omitted in the scenario discussed under (3) below.

(2) The geographic grouping of the observations found one major area of importance

not identified by the individual observation analysis. Five of the 49 groups are

categorized as most highly important.

The most important groups were those

that, when omitted, produced mean increases greater than 10 percent at any

UGTA site or Yucca Mountain. Four of

the five groups were dominated by one

individual observation. However, one

group, located in Ash Meadows, had no

individual observations ranked of high

importance but collectively, when omitted, increased uncertainty substantially.

Other groups also located in Ash Meadows, including intermediate depth observations, consistently ranked as more

important than all other groups.

(3) To demonstrate the importance of omitting a set of low-rated observations, one

scenario is considered in which the 100

individually lowest-rated shallow and

intermediate-depth observation locations

are omitted. The measure of overall prediction uncertainty increased by just 0.59

percent, indicating that the wells associated with these observations probably

could prudently be measured less frequently.

INTRODUCTION

Construction of an accurate and defensible

ground-water model requires information, such as

hydraulic head and flows, that provides insight to the

overall flow system. Constraints on time, accessibility, and financial resources limit the amount of data

that can be collected in the field. When a calibrated

model of the system is available, data collection

effectiveness and efficiency can be improved by

evaluating the importance of measurement locations

in the context of the modeling objectives, using the

calibrated model to relate the measurement locations

and the predictions of interest. This report, prepared

in cooperation with the U.S. Department of Energy

(DOE), describes a method by which such an analysis can be conducted.

To demonstrate its use, the method is applied to

the three-layer, steady-state Death Valley Regional

Flow System (DVRFS) ground-water model described by D’Agnese and others (1997, 1999). Along

with spring-flow observations, 501 hydraulic-head

observations were used to calibrate the model. This

report evaluates the importance of the 501 hydraulichead observation locations using the calibrated threelayer model. Some observation locations represent

more than one well (D’Agnese and others, 1997, p.

86), so evaluating an observation location does not

directly evaluate a specific monitor-ing site. Evaluat-
INTRODUCTION 3

ing the observation locations, however, provides

substantial guidance for determining which wells in

the monitoring network are most and least important.

The three-layer DVRFS model was calibrated

under steady-state conditions, and the predictions

calculated in this report are simulated under steadystate conditions. The system is simulated using

MOD-FLOW-2000 (Harbaugh and others, 2000; Hill

and others, 2000); the predictions are simulated using

MODFLOW-2000’s ADVective-Transport Observation (ADV) Package (Anderman and Hill, 1997).

In the results presented, the same values of recharge

and pumpage are used for both calibration and predictive conditions. The methodology developed is

very general and can be adapted to any combination

of the model calibration and predictions being simulated with steady-state and transient models, and the

stresses imposed need not be the same under calibration and predictive conditions. As presently coded,

there is a restriction because the ADV Package has

only been developed for steady-state flow fields, and

this restriction would need to be addressed if predictions for a transient flow field were desired. The

present capabilities of the ADV Package, however,

could be used to evaluate an alternate steady-state

flow field for prediction conditions.

In this report, the DVRFS and the three-layer,

steady-state model are briefly described. Next, the

predictions of concern and their representation are

discussed. This is followed by a description of a

method for evaluating the importance of measurement locations in the context of predictions of interest. Results from applying the method to the DVRFS

model are presented that address the following questions.

• Is an observation important to any prediction?

• How does observation importance vary with

transport direction?

• What is the breadth of the observation importance?

• How does observation importance vary on a

site-specific basis?

Following the assessment of individual observations, observation groups are evaluated to determine

geographic areas of importance in the monitoring

network. To do so, the four questions given above

are addressed in the context of observation groups

instead of individual observations. Finally, the results

for individual locations are used to define a set of

100 observation locations, and the importance of this

set of observations on the predictions of interest is

evaluated.

Monitoring network design has been the topic of

several recent studies, including those by Loaiciga

and others (1992), James and Gorelick (1994), Meyer

and others (1994), Wagner (1995), Storck and others

(1997), and others referenced by Sun (1994). Those

studies mostly address contaminant plume detection.

The goal of this report, evaluating the importance of

observations to model predictions of interest, has

been considered by McLaughlin and Wood (1988),

Sun and Yeh (1990) and Sun (1994), and others

referenced by Sun (1994). None of the methods presented in those works were computationally feasible

given the execution times of models of interest to

DOE; thus, development of a new method was necessary for the present study.

An approach that could have been taken in this

report to identify important observation locations in

the context of predictions is to undertake a jackknife

procedure (Seber and Wild, 1989, p. 206–214; Efron,

1982). Jackknife procedures designed to evaluate

model bias and calculate parameter standard deviations commonly are used in multiple linear regression, and involve recalibrating the model by

estimating parameters by regression using sets of

observations in which one or more of the observations used in model calibration are omitted. The

extension required for use in the present report is that

the parameter values resulting from the jackknife

procedure would be used to simulate predictions. If

one observation was removed at a time, the procedure could be used to evaluate the importance of the

observation based on the amount the predictions

changed. The purpose of jackknife methods is to

evaluate not only the observation location, but also

the value of the observation. Observations are considered to have substantial influence if their omission

has a substantial effect on the prediction.

Application of jackknifing methods to the

DVRFS model would be a very effective way to

evaluate the observations. The required jackknife

procedure is, however, very computationally intensive. To rate each observation individually, as is done

in this report, would require a number of regressions

equal to the number of observations. If there are 501

observations and a regression run takes even just

three hours, at least 1,503 hours, or 62 days, of execution time would be required. In contrast, the methods suggested for this report are much less compu-
4 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

tationally intensive, and the ratings are consistent

with the concept of leverage. Observations are considered to have substantial leverage if they are located such that their omission could have a

substantial effect on the prediction. The set of observations with large influence, which would be detected by a jackknife procedure, generally is a subset

of the observations with large leverage, which would

be detected using the method presented in this report.

It is highly likely that observation locations that rate

as important by a jackknife procedure will be rated as

important in the present analysis. A jackknife procedure likely would show that some of the locations

that rate highly in the present analysis were not as

important as indicated. Thus, given the objectives

stated by DOE and the timeframe involved, the

methodology presented in this report was proposed,

and is developed and demonstrated here.

A possible subsequent step that could be pursued

is to perform jackknife calculations on the observations that are rated as important using the methods

presented here. This step was not, however, pursued

as part of this report.

The demonstration presented in this report does

not consider how the ratings of observations would

change given different, feasible sets of parameter

values and alternate conceptual models. Here, feasible means that all models considered need to respect

all that is known about the system equally well. All

ground-water models are non-unique, so that many

feasible alternatives exist. Given adequate information about a system, all feasible models will be

tightly constrained so are likely to produce similar

predictions, and the issue of non-uniqueness probably

would be of little concern (Hill and others, 1998). It

is unlikely that any model of the large, complex

DVRFS will be so well constrained, and it would be

prudent to repeat the calculations described here

using alternate feasible models. This could be made

practical by designing a limited number of alternate

models that reflected the expected range of variation

between possible models.

THE DEATH VALLEY REGIONAL

GROUND-WATER FLOW SYSTEM

Yucca Mountain in southern Nevada (fig. 1) is

being studied as a potential site for a high-level radioactive waste repository. Also, sites located on the

nearby Nevada Test Site were used for underground

testing of nuclear devices. Possible transport of contaminants from these sites is of concern, prompting

DOE to investigate the underlying ground-water

system. At a regional scale, the system of concern is

the DVRFS, and this regional system is considered in

this report.

The DVRFS encompasses nearly 80,000 square

kilometers and extends from immediately west of Las

Vegas, Nevada, to Death Valley National Park, California. Water levels in the region range from more

than 1,500 meters (m) above to 86 m below sea level.

The hydrology of the region is the result of both arid

climatic conditions and complex geology. Groundwater flow generally can be described as dominated

by interbasin flow and may be conceptualized as

having two main components: a series of relatively

shallow and localized flow paths that are superimposed on deeper regional flow paths. A significant

component of the regional ground-water flow is

through a thick sequence of Paleozoic carbonate rock

that generally occurs at depth. Structural features,

such as faults and fractures, probably control regional

ground-water flow. Faults result in abrupt juxtaposition of geologic units with contrasting hydraulic

properties; extensive and prevalent fracturing results

in locally enhanced or decreased permeability. Water

discharges from the system as evapotranspiration by

plants, evaporation from playa surfaces, and flow to

springs and wells. Water recharges the system mostly

as infiltration of precipitation in highlands such as

the Spring Mountains and Pahute Mesa. The flow

system is hydrogeologically complex and very heterogeneous, with possible local values of hydraulic

conductivity ranging over 14 orders of magnitude

and hydraulic gradients ranging from nearly zero to

over 2 percent.

The DVRFS was evaluated in D’Agnese and

others (1997, 1999) using a three-dimensional,

steady-state, finite-difference flow model, and that

model is used in this report. The flow-model grid has

163 rows, 153 columns, and 3 layers. The grid cells

are oriented north-south and are of uniform size, with

side dimensions of 1,500 m. The layers span depths

below the estimated water table of 0–500 m, 500–

1,250 m, and 1,250–2,750 m. In the model, 23 parameters are defined to represent essentially all

model quantities of interest, such as horizontal hydraulic conductivity, vertical anisotropy, recharge,

evapotranspiration, hydraulic connection to the

springs, and multipliers to represent the fraction of

water pumped from wells that is recharged back into

the ground-water system (table 1).
THE DEATH VALLEY REGIONAL GROUND-WATER FLOW SYSTEM 5

Figure 1. Location of the Death Valley Regional Flow System and the boundary of the three-layer ground-water

model, Nevada and California (from D’Agnese and others, 1997).

118°

38°

37°

36°

35°

117° 116° 115°
6 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

Table 1: Parameter values and standard deviations used to evaluate hydraulic-head observation locations

[Parameters in bold were estimated by regression with no prior information applied. The approximate confidence intervals were determined based on the

available, often scarce, information about the quantities involved. The listed standard deviations are used as input for the MODFLOW-2000 simulation;

if the parameter is log-transformed, the standard deviation relates to the log-transformed parameter value. Abbreviations: m/d, meters per day; m2

/d,

meters squared per day. Symbol: —, not applicable.]

Parameter

label Unit Description Parameter

value

Approximate 95

 percent confidence

interval in native space

Standard deviation

(on the logtransformed value

for all but EvtM,

Rch0 and Rch1)

K__1 m/d High hydraulic conductivity 0.269 — —

K__2 m/d Moderate hydraulic conductivity .445 x 10-1 — —

K__3 m/d Low hydraulic conductivity .557 x 10-2 — —

K__4 m/d Very low hydraulic conductivity .848 x 10-4 — —

K__5 m/d Very high hydraulic conductivity 19.9 — —

K__6 m/d Eleana Formation hydraulic conductivity .100 x 10-5 0.100 x 10-7 to .0001 2.3

K__7 m/d Fault hydraulic conductivity .100 x 10-3 .100 x 10-5 to 0.01 2.3

K__8 m/d Desert Range hydraulic conductivity .650 x 10-1 .650 x 10-3 to 6.5 2.3

K__9 m/d South Funeral hydraulic conductivity .157 — —

Anv1 — Vertical anisotropy for layers 1 and 2 1 1 to 100 1.15

Anv3 — Vertical anisotropy for layer 3 163 — —

EvtM — Maximum evapotranspiration rate factor 1 .5 to 2.0 0.375

Rch0 percent Area of no recharge potential 0 0 to .01 .0025

Rch1 percent Area of low recharge potential .100 x 10-1 0 to .02 .005

Rch2 percent Area of moderate recharge potential .299 x 10-1 — —

Rch3 percent Area of high recharge potential .226 — —

GHBa m2

/d Spring conductance for Ash Meadows 100 10 to 1,000 1.15

GHBg m2

/d Spring conductance for Grapevine Springs 11 1 to 50 .98

GHBo m2/d Spring conductance for Oasis Valley 1.7 1 to 10 .58

GHBf m2

/d Spring conductance for Furnace Creek 5 1 to 10 .58

GHBt m2

/d Spring conductance for Tecopa .1 .01 to 1 1.15

Qoth — Ground-water pumpage factor for all but Pahrump 1 .5 to 1.0 .125

Qpah — Ground-water pumpage factor for Pahrump Valley .25 .25 to 1.0 .188

Nine of the 23 parameters defined in the final

model had values that were estimated by inverse

modeling; the remaining 14 parameter values were

specified. In general, the specified parameters were

not well supported by the observations used in the

regression, as indicated by the composite scaled

sensitivities of 19 of the 23 parameter values reported

in D’Agnese and others (1999, fig. 12). For this report the estimated parameter values reported in table

1 are slightly different than those reported in

D’Agnese and others (1997, table 16) because the

regression was run with a tighter convergence criterion of 0.01. All changes resulting from this modification to the final regression run were very small.

In analyses based on uncertainty, such as the one

conducted for this report, it is important to consider

all the defined parameters to ensure that all possible

system characteristics are considered. This was

achieved by including all 23 of the defined parameters in the calculations.

A total of 501 hydraulic-head observations and

16 spring-flow observations were used to calibrate

the DVRFS model. For some of the hydraulic-head

observations, water levels at multiple locations in the

same grid cell were combined. The locations of the

hydraulic-head observations are shown in figure 2.

Of the 501 hydraulic-head observations, 408 were

assigned to model layer 1 only, 73 were assigned to

model layers 1 and 2, and one observation was assigned to layer 2 only. Nineteen observations were

assigned to model layers 1, 2, and 3. Observations

simulated using more than one model layer represent
METHODS OF EVALUATION 7

deep, open-hole wells. For these observations, the

proportional contribution of each layer was calculated using the product of well length and initial

estimates for layer transmissivity. Simulated water

levels for these observations were calculated by

summing the products of the proportional contribution and the hydraulic head for each layer, as discussed by Hill and others (2000, p. 34–36).

The DVRFS ground-water flow is threedimensional, but the paucity of hydrologic data at

depth makes it difficult to determine vertical gradients. The most significant hydrologic data on the

deeper parts of the system probably are the flow rate

and location of warm-water springs.

The three-layer DVRFS model was calibrated

using the inverse ground-water flow model MODFLOWP (Hill, 1992), and the ideas for application of

optimal parameter estimation described by Hill

(1998). MODFLOWP has been replaced by MODFLOW-2000 (Harbaugh and others, 2000; Hill and

others, 2000), and as part of this report the threelayer DVRFS model of D’Agnese and others (1997,

1999) was converted to MODFLOW-2000.

METHODS OF EVALUATION

In the present report, the hydraulic-head observation locations used to calibrate the DVRFS model

was evaluated in the context of advective transport

predicted with the model. This analysis uses the

calibrated model to evaluate potential observations,

as suggested by Hill (1998, guideline 11). This section describes the predictions of interest, defines the

statistics used in the evaluation, and presents the well

groupings used in the analysis.

Predictions of Interest

In the DVRFS, the predictions of interest involve

potential transport of contaminants from beneath

Yucca Mountain and 14 Underground Test Area

(UGTA) sites on the Nevada Test Site (fig. 2). The

14 UGTA sites, listed in alphabetical order, are

Bourbon, Bullion, Clearwater, Corduroy, Coulommiers, Cumarin, Darwin, Diluted Waters, Gum Drop,

Houston, Pile Driver, Purse, Strait, and Tybo. Accurate simulation of this transport is plagued by a number of problems, including the fractured nature of the

subsurface material and the regional scope of the

model. In a regional model, it is impossible to represent accurately small features that can be important

to transport. A useful approach is to consider only

some of the transport processes involved. Here, only

advective transport, which is the transport that would

occur if the solute did not spread and encountered no

reactions with the surrounding rocks, is considered. It

is simply the transport that is produced, on average,

by bulk flow in the subsurface system. It can be

thought of as the first building block of transport,

upon which other complexities are added. Calculation of advective transport over large distances and

times is consistent with the scale of a regional model

because it is influenced by the regional conditions

more than other aspects of transport.

Advective transport is simulated using the Advective-Transport Observation (ADV) Package of

MODFLOW-2000 (Anderman and Hill, 1997). The

ADV Package uses particle-tracking methods nearly

identical to those of Pollock (1989) to determine

advective-travel paths; they differ in that the ADV

Package uses an interpolated layer thickness to calculate velocities at cell boundaries, as described by

Anderman and Hill (1997, p. 14, 60–61). To compute

the particle trajectory, particle displacement is decomposed into displacements in the three spatial

dimensions of the DVRFS model: north-south, eastwest, and vertical. This analysis of the directional

components of transport allows the importance of

observations to be evaluated based on the information they provide for each direction of transport.

In the present report, advective transport is simulated using the steady-state, three-layer DVRFS

model of D’Agnese and others (1997, 1999) and the

predictions are simulated using the pumpage and

recharge distributions of that model. The methodology does not require this to be so; different long-term

recharge and pumpage could be applied for the transport calculations. The present version of the ADV

Package, however, would not be able to represent a

transient flow field.

In this report, the advective travel paths are

evaluated; simulated travel times are not reported.

Simulated travel times are highly dependent on the

effective porosity of the aquifer materials. Widely

varying porosity values are attributed to the DVRFS

rocks and sediments (val

cited by Bedinger and others (1989)). Thus, simuues of 0.0001 to 0.37 are

lated travel times are likely to be considerably less

reliable than the simulated paths. Because of the wide

variation in porosity values, in combination with the

variations in hydraulic conductivities and hydraulic

gradients, it is likely that the time to travel a specified

distance will differ for the different paths.
8 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

INDEX MAP

NEVADA

CALIFORNIA

North 

Death Valley 

Subregion Central

Death Valley 

Subregion

South

Death Valley

Subregion

Nevada

DeathValley

Las Vegas

Diluted Waters

Cumarin

Bourbon

Gumdrop

Strait

Pile Driver

Corduroy

Coulommiers

Clearwater

Houston

Bullion

Tybo

Purse

Darwin

Yucca

Mountain

Observation wells open to Layer 1

Observation wells open to Layers 1 and 2 or

Layer 2 only

Observation wells open to Layers 1, 2, and 3

Underground Testing Area 

Yucca Mountain

California

0 10 20 30 40 50

KILOMETERS

Nevada

Test

Site

 Figure 2: Map showing locations of hydraulic-head observations used to calibrate the three-layer model of the 

Death Valley regional ground-water flow system (after D’Agnese and others, 1997, fig. 29, p. 6) 

The distance of advective travel considered can affect 

the results of the analysis. In this report, the distance 

is chosen to be long enough to allow the regional 

effects represented by the model to dominate the 

simulated transport, and short enough that the transport path is likely to be reasonably accurate. A transport distance of 10,500 m, or about seven grid 

dimension lengths, is considered here (the methodology presented for evaluating observation importance 

is, of course, applicable to any travel distance). Initial 

calculations indicated that considerable variation in

the measures of observation importance could occur 

along the travelpath, and that a good overall measure 

of observation importance to predictions could be 

obtained by averaging results over several points 

along the flow path. Prediction sensitivities and uncertainties are, therefore, calculated approximately 

every 1,500 m along the 10,500 m travel distance. 

Twelve of the 14 particle paths originating from 14 

UGTA sites result in predicted advective particle 
METHODS OF EVALUATION 9

displacements in 3 directions at 7 points. The other 

two particles, originating from UGTA sites in Yucca 

Flat (fig. 1), do not travel the entire 10,500 m, but 

rather discharge to a well in Yucca Flat. One particle 

path results in predicted advective particle displacements in 3 directions at 6 points, the other at 3 points. 

At the Yucca Mountain site, eight particles are 

tracked, so that results in predicted particle displacements from 8 cell origins in 3 directions at 7 points 

are considered in the analysis. Considering all the 

UGTA site particles and all the Yucca Mountain 

particles, there are a total of 447 advective transport 

predictions. 

As discussed in the following section, the measure of prediction uncertainty that is used in this report 

is the prediction standard deviation. Understanding 

what this means when the predictions are spatial 

components of advective transport can be difficult. 

To aid understanding, figure 3 shows an areal view 

of a simulated path from one of the sites, along with 

the seven points at which standard deviations are 

computed. For four of the points, lines that represent 

the standard deviations are shown in the east-west 

and north-south directions, the two directions visible 

in this areal view. Standard deviations for vertical

movement also are calculated, but are not shown in 

figure 3. 

Statistics for Evaluating Observation 

Locations 

In this section the statistics used standard deviations, which are used to measure prediction uncertainty, is presented. Next, it is shownhow the 

calculation of prediction standard deviations can be 

altered to reflect the omission of one or more of the 

observation locations, and how this can be used to 

calculate an “increased uncertainty statistic.” Increased uncertainty statistics can be used to indicate 

observation location importance. Finally, use of these 

statistics is discussed. 

Prediction Standard Deviation—Measure of Prediction 

Uncertainty 

The importance of observations to model predictions was evaluated by using the linear statistical 

inference equation for calculating standard deviations 

on predictions (Draper and Smith, 1981; Hill, 1998): 

[ ] ( ) 2/1 1 2 )( ll l

T

Z

T

z Z XXXXss −

′ = ω (1) 

K2

K3

5000 m

σNS

σEW

Pahute Mesa 

UGTA Site

Figure 3: Areal view of a particle path simulated from

an UGTA site using the ADV Package. Seven locations are shown along the path; at four of these, bars 

are shown. The bar length reflects the size of a standard deviation: vertical bars are σNS, the standard 

deviation for movement in the north-south direction; 

horizontal bars are σEW, the standard deviation for 

movement in the east-west direction. The σEW reflect 

the uncertainty with which advective transport in the 

east-west direction is calculated; the σNS reflect the 

uncertainty with which advective transport in the 

north-south direction is calculated. K2 and K3 identify 

the hydraulic conductivity, as listed in table 1.

 

where 

l z′ is the  th predicted value, here advective 

transport in one of the three grid directions; 

 identifies one prediction; 

l z s ′ is the standard deviation of z′l; 

2

s is the calculated error variance; 

X Z is the 447 by 23 matrix of sensitivities of the 

predictions with respect to the model parameters, with elements equal to j ∂ ′ / ∂bzl ; 

X is the matrix of sensitivities of the simulated 

equivalents of the observations (y′i) with respect to the 23 model parameters, with elements equal to ji ∂ ′ / ∂by ; 
10 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

T indicates the transpose of the matrix;

( )−1XX Tω is a symmetric, 23- by 23-square linear

approximation of the parameter variancecovariance matrix;

bj is the jth parameter; and

ω is the matrix of weights on observations used

in the calibration, and is diagonal in this

application.

The parameter covariance matrix ( )−1

XX Tω

and the sensitivity matrix X are discussed in Sun

(1994, p. 72) and Hill (1998, p. 24–26; 77). Standard deviations describing the precision of the waterlevel measurements were used to calculate the

weights in ω , as described by D’Agnese and others

(1997, 1999). Those standard deviations ranged from

10 to 250 m; the largest values occur in areas of steep

hydraulic gradients. In the report presented here, all

23 parameters defined by D’Agnese and others

(1997, 1999) are included. The hydraulic-head and

spring-flow calibration data supported estimation of

9 of the 23 defined parameters in the DVRFS model.

The remaining 14 parameters were not estimated for

a variety of reasons, including the fact that the simulated equivalents of the calibration data were insensitive to these parameters. However, the predicted

advective transport paths are not necessarily insensitive to these parameters. The prediction uncertainty

calculated in this report reflects the uncertainty and

sensitivity to all 23 defined model parameters, which

means that calculated values of prediction uncertainty better represent the actual parameter uncertainty. Independent information on the 14 nonestimated parameter values was included in the

calculation of prediction uncertainty through the use

of prior information (Sun, 1994, p. 35, 141, 145; Hill,

1998, p. 25–26). Weights on the prior values reflect

the uncertainty in the independent information about

flow system properties represented by these parameters. The parameter values, the estimated 95 percent

confidence interval for the native (untransformed)

parameter value, and the associated standard deviations are presented in table 1.

Increased uncertainty statistic

A modified version of equation 1 that is used in

this report to evaluate the effect of the omission of an

observation location on the prediction uncertainty is

defined as follows:

[ ] ( ) 2/1 1

)()()(

2

)( )(  

T

Zii

T

iZiz XXXXss −

′ = ω (2)

where

iz )( s 

′ is the standard deviation of the  th simulated value, z′, calculated without the ith observation location;

( ) 1

)()()(

−

ii

T

i ω XX is a symmetric, square 23- by 23-

parameter variance-covariance matrix

calculated with information for the ith observation omitted;

X(i) is the matrix of sensitivities of the simulated

equivalents of the observations (y′i) with

respect to the 23 model parameters, with the

sensitivities for the ith observation omitted;

and

ωi)( is the diagonal matrix of weights on observations used in the calibration, with the value

for the ith observation omitted.

In the computer program developed for this report, equation (2) is calculated by setting the weight

of the ith observation to zero. Equation 2 is written

for the case in which one observation location is

omitted. The extension to omitting more than one

observation location is straightforward. To omit one

or multiple observations, in the computer program

the one or multiple associated weights are set to zero.

In equation 2, the value of s2 is the same as in equation 1 because the calculated variance of the regression from the calibrated model is thought to best

estimate the error variance it approximates.

To produce a convenient measure of observation

importance that can be easily evaluated, the percent

increase in uncertainty is used, and is calculated as:

[( iz )( s 

′ /  z s ′ ) – 1.0] × 100 (3)

This is referred to as an increased uncertainty statistic, or percent increased uncertainty.

Dimensionless scaled sensitivity

While equation (3) measures the importance of

observation locations to predictions, it does not indicate whether the importance is dominated by the

sensitivities in X and X(i), or X Z . Analysis of the

results produced by equations 2 and 3 is aided by

knowledge of which set of sensitivities dominates a

given situation. Also, the well groupings described

below are designed, in part, based on sensitivities.
METHODS OF EVALUATION 11

Without scaling, the sensitivities for one parameter

can not be compared to those of another parameter.

To allow such comparisons, the statistic used was the

dimensionless scaled sensitivity, ssij (Hill, 1998,

p. 14), calculated as

21 ' j ii

j

i

ij b

b

y

ss ω 















∂

∂ =

(4)

where

i identifies one of the observations;

j identifies one of the parameters;

bj is the jth estimated parameter;

j

i

b

y

∂

∂ '

is as described for equation 1, and is

evaluated at the final parameter values

of D’Agnese and others (1997); and

ω ii is the weight for the ith observation.

Using the statistics

To test the importance of individual or multiple

observations to advective transport predicted by the

DVRFS model, the following procedure is used.

First, all 501 hydraulic-head observation locations

are included, and the standard deviation of the eastwest, north-south, and vertical particle position at

seven locations along the first 10,500 m of each

particle path is computed using equation 1. (For two

UGTA sites fewer than seven locations and paths

shorter than 10,500 m are considered, as described in

the section “Predictions of Interest.”) Next, selected

elements of the weight matrix (ω ) are set to zero,

and the standard deviations are recalculated as in

equation 2. Finally, the effect of the omitted observation(s) on the prediction uncertainty is quantified

using equation 3. Larger percent increases in uncertainty indicate observations or groups of observations

that are more important to the prediction.

Increased prediction uncertainty statistics are calculated in this report for the advective-transport paths

of particles originating from beneath Yucca Mountain and the 14 UGTA sites. Beneath Yucca Mountain two particles, one at the water table and one just

below the water table, were introduced at each of the

eight finite-difference cells underlying any part of the

footprint of the proposed repository. The vertical

offset feature of the ADV package controls initial

vertical particle position. Particles were placed below

the water table a distance equal to 0.01 times the

layer thickness of 500 m, or 5 m. For the 14 UGTA

sites, a similar procedure was pursued. Particles

were introduced at and below the water table at the

center of the finite-difference cell in which the site is

located. These particles were tracked for 10,500 m

and again sensitivities and standard deviations were

calculated for seven positions along the path.

Two sets of particles are used because the ADV

package moves particles down from the water table

only if there is recharge. Dispersion processes may

promote downward migration and some of the tests

at some of the UGTA sites were below the water

table. Including the particle below the water table

provides some accounting for these circumstances.

The results from at or below the water table are selected for subsequent use, depending on which indicates the largest increase in uncertainty. The paths

starting at or slightly below the water table have very

similar trajectories in the east-west and north-south

directions, but for paths that migrate through cells

with no recharge, the travel can differ significantly in

the vertical direction. In this case, a path that starts

even slightly below the water table will migrate

deeper. A path starting at the water table will remain

at the water table.

This procedure resulted in evaluation of advective transport paths from a total of 15 origins (14

UGTA sites and Yucca Mountain). Three coordinate

directions of motion parallel to the grid directions;

that is, movement in the east-west, north-south, and

vertical directions represent the advective transport

path simulated from each site. Prediction standard

deviations are calculated in each of the three coordinate directions at each of the seven travel distances.

A separate prediction standard deviation is computed

for each direction because the particle tracking procedure is implemented by calculating particle displacements in each of the three directions. This large

amount of information is summarized in different

ways for different purposes, as described below.

Grouping of Observations

To provide a convenient way of presenting results and determining geographic areas of importance

in the monitoring network, the 501 hydraulic-head

observations were grouped by depth and location. All

wells within a group are open to the same model

layer(s) and classified as either shallow (open to

model layer 1 only), intermediate (open to model

layers 1 and 2, or only 2), or deep (open to model

layers 1, 2, and 3). All group are also located geographically near one another and within the same
12 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

Death Valley subregion (fig. 2). Categorizing the

observations solely by depth and location, however,

did not address the possibility that observations located near one another might not contribute to prediction uncertainty in the same manner, as is likely to

occur when hydraulic properties change abruptly, as

in the DVRFS system. To obtain groups of wells that

are likely to be similar in this way, the dimensionless

scaled sensitivities of equation 4 were used. Observations with significantly different dimensionless

scaled sensitivities were placed in separate groups.

This process resulted in 49 groups: 39 shallow

(group names begin with SH), 7 intermediate (group

names begin with INT), and 3 deep (group names

begin with DEP). The group to which each observation belongs is shown on figure 4. The number of

observations within any of these groups varied

greatly, ranging from 1 to as many as 31 (table 2).

Initially, the four groups that had the largest effect

also had the largest number of observations (77, 35,

76, and 35). These groups were subdivided into

smaller groups and their importance substantially

decreased. Thus, no group was allowed to consist of

enough observations to influence the apparent importance of the group by sheer number alone.

RESULTS OF EVALUATION

Results of omitting individual and groups of observations are used to evaluate the importance of the

observations to advective transport uncertainty at the

UGTA and Yucca Mountain sites. Highly important

observations and groups are of interest, because these

are locations where the analysis presented here indicates that continued hydraulic-head monitoring is

important. Less important observations and groups

are also of interest, because their locations are areas

where some wells might be removed from the monitoring network.

The effect on advective transport uncertainty of

omitting individual head observations is presented

first. As much as possible, the groups to which the

observations belong (defined in the previous section)

are indicated, in order to clarify the observation locations involved. The effect on advective transport

uncertainty of omitting groups of observations from

certain geographic areas is presented next. The analysis of results for both individual and groups of observations is focused on addressing the following four

questions:

(1) Is an observation (or group) important to any

prediction?

(2) How does observation (or group) importance

vary with transport direction?

(3) What is the breadth of the observation (or

group) importance?

(4) How does observation (or group) importance

vary on a site-specific basis?

Together, the answers to these questions help

identify observations and groups that are most and

least important to advective transport uncertainty at

the considered sites. The last question requires a

large number of graphs; the summarized results that

answer the first three questions are expected to be

more useful.

Finally, the consequences of omitting a set of

100 observation locations rated individually as being

of low importance is presented.

Omission of Individual Observations

Is an observation important to any of the predictions?

As a measure of whether an observation is

important to any advective transport prediction, an

average percent increase in prediction standard deviation is calculated when each of the 501 head observations is individually omitted. This average percent

increase is calculated using the following procedure.

First, the percent increase in prediction uncertainty

(equation 3) is calculated for each coordinate direction at each distance along the particle paths propagated from beneath each of the 15 origins (14 UGTA

sites and Yucca Mountain). Next, to obtain a single

summary measure of the effect of removing an individual observation location on prediction uncertainty

at each site, the percent increases are averaged for the

seven travel distances and three coordinate directions

for each site. The largest average percent increase

from the 15 origins is plotted in figure 5. Because of

the averaging method used, the values shown do not

indicate whether the observation is important to

advective transport for all or only one direction, or all

or only one origin, but the graph clearly shows which

observations are important to advective transport in

at least one direction for at least one origin.

The results shown in figure 5 indicate that the

shallow observations 17, 55, 107, and 145, located

in Oriental Wash, Emigrant Valley, Oasis Valley,

and Beatty, respectively, are most important. The

importance of observations 17 and 107 results in

part because they have very large dimensionless

large scaled sensitivity to parameter K3 (low hydraulic conductivity). These K3 and K4 hydraulic large
 

RESULTS OF EVALUATION 13

Shallow Observation Groups

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

Model column number

Model row number

SHL1 SH2a

SH2b SH2c

SHL3 SH4a

SH4b SHL5

SHL6 SHL7

SHL8 SHL9

SH145 SH10a

SH10b SH10c

SH11 SH12

SH13 SH107

SH14a SH14b

SH15 SH16

SH17 SH18

SH19 SH20

SH21 SH22

SH23 SH24

SH25 SH26

SH27 SH28

SH29 SH30

SH31

17

55

145

107

Las Vegas

Nevada

Test Site

Intermediate and Deep Observation Groups

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

Model column number

Model row number

INT1

INT2

INT3

INT4

INT5

INT6

INT7

DEP1

DEP2

DEP3

Las Vegas

Nevada

Test Site

(A)

(B)

Figure 4. Maps of (A) shallow and (B) intermediate and deep observation locations and location 

groups. The letters in the group names indicate that the observations are: SH, open to model layer 

1; INT, open to model layers 1 and 2, or layer 2 only; and DEP, open to layers 1, 2, and 3. All rows

and columns are 1,500 meters wide.
14 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

Table 2: Observation location group name and number of observation

locations in each group

Group Number of

observations Location (fig. 4)

SHL1 4 South Death Valley Subregion

SH2a 26 Pahrump Valley

SH2b 26 Pahrump Valley

SH2c 25 Pahrump Valley

SHL3 5 Greenwater Range/Valley

SH4a 18 Ash Meadows

SH4b 17 Ash Meadows

SHL5 8 Specter Range

SHL6 16 Indian Springs

SHL7 2 East Central Death Valley subregion

SHL8 2 Furnace Creek

SHL9 12 Beatty

SH145 1 Beatty, Observation 145

SH10a 26 Amargosa Valley

SH10b 25 Amargosa Valley

SH10c 25 Amargosa Valley

SH11 18 Yucca Mountain

SH12 14 Frenchman Flat

SH13 6 Oasis Valley

SH107 1 Oasis Valley, Observation 107

SH14a 18 Yucca Flat

SH14b 17 Yucca Flat

SH15 5 Emigrant Valley, includes observation location 55

SH16 6 Coyote Hole Playa

SH17 16 Sarcobatus Flat

SH18 22 Pahute Mesa

SH19 6 Stonewall Flat

SH20 3 Kawich Range/Gold Flat

SH21 6 Stewart Valley

SH22 12 Pahrump Valley East

SH23 1 Mercury Valley

SH24 3 Amargosa Valley South

SH25 1 Shoshone Mountain

SH26 1 Emigrant Valley East

SH27 1 Grapevine Canyon

SH28 2 Oriental Wash, includes observation location 17

SH29 1 Kawich Valley

SH30 1 Spring Mountain

SH31 4 Pahrump Valley South

INT1 5 Ash Meadows

INT2 22 Pahute Mesa

INT3 3 Buckboard Mesa

INT4 31 Yucca Flat

INT5 9 Yucca Mountain

INT6 2 Beatty

INT7 4 South Central NTS

DEP1 16 Pahute Mesa

DEP2 2 Yucca Flat

DEP3 4 Yucca Mountain
RESULTS OF EVALUATION 15

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501 

Observation number

Percent increased uncertainty

SHL1 SH2a

SH2b SH2c

SHL3 SH4a

SH4b SHL5

SHL6 SHL7

SHL8 SHL9

SH145 SH10a

SH10b SH10c

SH11 SH12

SH13 SH107

SH14a SH14b

SH15 SH16

SH17 SH18

SH19 SH20

SH21 SH22

SH23 SH24

SH25 SH26

SH27 SH28

SH29 SH30

SH31 INT1

INT2 INT3

INT4 INT5

INT6 INT7

DEP1 DEP2

DEP3

55

100

103

257

428

437

17

107

145

Figure 5: Is the observation location important to any of the predictions? Large values identify important observation

locations. For each observation location, the value from the one origin with the largest percent increase is shown.

Symbols associated with the observation groups are used. No symbol is plotted if all values for the observation location are less than 0.01. The high rating indicated for observation 17 is questionable, as discussed in the text.

scaled sensitivities to parameter K4 (very low hydraulic conductivity); observation 55 has a very

dimensionless scaled sensitivity to conductivity parameters are associated with hydrogeologic units

located in the vicinity of the advective-transport

paths. Observation 145 has a parameter RCH0, which

is the primary recharge parameter associated with the

recharge distribution at Yucca Flat.

The individual omission of many of the observations between 251 and 301, which are all shallow and

located mainly in Ash Meadows and Amargosa Valley, increases prediction uncertainty slightly more

than most other observations (fig. 5). Omission of

observations 100 or 103 located in the eastern portion

of the Central Death Valley subregion, and intermediate-depth observations 428 or 437 of Buckboard

Mesa also resulted in prediction standard deviation

increases that exceeded 1 percent.

Further analysis of observation 17 suggests that

this observation ranks as important to the advective

transport uncertainty largely because there is groundwater pumping in the well that this observation represents, which is commonly called the Roosevelt well.

This water well was assigned an average pumping
16 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

rate of 137 cubic meters per day (m3/d) in the

three-layer DVRFS model. The pumped water is

thought to be derived from local conductive material,

but low hydraulic-conductivity rocks dominate the

500-m thick cell so that the overall hydraulic conductivity is associated with parameter K4. The effect of

the pumping causes simulated head at this location to

be highly sensitive to the very low hydraulic conductivity of the model cell (parameter K4). Because of

this high sensitivity and because the advective transport paths are also sensitive to parameter K4, the

analysis used here indicates that observation 17 is

important to the predicted transport. When the pumping in the model cell containing observation 17 is

removed from the simulation, the percent increase in

prediction uncertainty that would be plotted in figure

5 is only about 0.6 percent. Thus, under the condition

of no pumping in this cell, observation 17 would no

longer be one of the most important observations to

predicted advective transport. In this report, it was

concluded that the situation at observation location

17 means that its high rating was caused by model

approximations that would not translate into hydraulic head at this location being as important as indicated by the numerical rating. Thus, it is not listed as

one of the most important observation locations in

the Summary and Conclusions section of this report.

The importance of considering local conditions

in evaluating the results of the analysis presented

here is made obvious by the situation for observation

17. Concerning pumpage, it should be noted that the

DVRFS model contains 208 pumping wells, 172 of

which are located in cells that are also represented by

head observations. No other observation determined

to be most important was located in a cell with a

pumping well, and no other conditions were detected

to suggest that these locations were not as important

as indicated.

Individual omission of the large majority of observations increased prediction uncertainty by less

than 1 percent (fig. 5). Generally, for areas with a

high density of observations, such as the Ash Meadows and Amargosa Valley areas (groups SH4a-b,

SH10a-c, and SH24, fig. 5, table 2), omission of

individual observations results in a range of increases

in prediction uncertainty. This result suggests that

omitting some of the observations in these locations

from the monitoring network would not significantly

diminish the future use of the data set, and would still

result in a good geographic coverage of observations

in the monitoring network.

The 19 observation locations that reflect hydraulic heads deeper in the system (groups DEP1, DEP2,

and DEP3 in fig. 5) were shown to be not very

important given the criteria considered in this report.

Their locations are associated with shallow observation locations that also generally are rated as low

importance. The value of deep observations to testing

conceptual models, however, is stressed. As a result,

none of these observations are omitted in the scenario

discussed below.

How does observation importance vary with

advective transport direction?

Figure 6 addresses how observation importance

varies with advective transport direction. This figure

shows the average percent increase in prediction

uncertainty, by transport direction, which results

when each of the 501 head observations is individually omitted. The average percent increase plotted is

obtained by first computing the percent increase in

prediction uncertainty for each coordinate direction

at the seven distances along the paths propagated

from beneath each of the 15 origins. Then, for each

origin and direction, the percent increases at the

seven distances are averaged. The percent increase

plotted in figure 6 for each direction is the largest of

the 15 average percent increases.

Figure 6 shows that omission of some observations results in different effects on prediction uncertainty in the east-west, north-south, and vertical

transport directions. Consider observation 107, which

is one observation location identified in figure 5 as

most important to predicted advective transport.

Removal of this observation results in much smaller

prediction uncertainty increases in the vertical direction than in the east-west or north-south directions.

Omission of some of the observations in the range

401 through 451, which are mostly intermediatedepth observations (table 2) results in a smaller increase in prediction uncertainty in the north-south

direction than in the east-west or vertical directions

(fig. 6). This result helps explain why some intermediate-depth wells are more important to vertical flow.

It is not clear why the difference in importance in the

north- south and east-west directions occur, and this

issue is not pursued here.

What is the breadth of each observation’s importance?

Figure 7 and table 3 summarize the effects of

omitting an observation on the examined UGTA sites

and Yucca Mountain. This figure shows that for 31

observation locations, omitting the observation loca-
RESULTS OF EVALUATION 17

East-west advective transport distance

0.01

0.1

1

10

100

1,000

Percent

1 51 101 151 201 251 301 351 401 451 501

increased uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1,000

Percent

1 51 101 151 201 251 301 351 401 451 501

increased uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1,000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased uncertainty

107

107

107

Figure 6: Is the observation location important to any of the predictions in each of the coordinate directions? Large

values identify important observation locations. For each observation location, the value from the one origin with

the largest percent increase is shown. Symbols associated with the observation groups are used. No symbol is plotted

if all values for the observation location are less than 0.01. (See figure 5 for explanation of symbols.) 
18 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

Table 3: Observation locations where the maximum uncertainty in any coordinate direction increases by one percent

or more with omission of the observation location.

Number

of sites Observation locations

15 17, 107, and 145

12 55

11 257

10 100 and 103

8 113, 275, and 276

7 258, 269, 270, 271, and 279

6 262 and 428

4 83

2 32, 437, and 495

1 14, 24, 37, 111, 273, 402, 414, 431, and 496

tion individually increases prediction uncertainty

by one percent or more for at least one of the 15

origins.Omitting observation locations 17, 55, 100,

103, 107, 145, and 257individually increases uncertainty by more than one percent at 10 origins or

more. As discussed above, the results for observation

location 17 are strongly dependent on the pumping

condition at the well this observation represents and

the hydraulic conductivity of the finite difference

cell. Observation locations 55, 100, 103, 107, and

145 were identified in figure 5 as being important to

at least one of the predictions.

In addition to showing that the omission of certain observations has a large consequence at one or

more origins, figure 7 also points out observation

locations that are not important at the one-percent

level to advective transport at any of the 15 origins.

The wells associated with these observation locations

are likely candidates for reduced monitoring.

How does observation importance vary on a

site-specific basis?

Appendix A presents the results on a sitespecific basis. These figures show the effect for each

of the 15 origins of individually omitting each of the

501 observation locations in the three coordinate

directions. The results show that the origins can be

roughly grouped by geographic area, in terms of the

effects of omitting observation locations on prediction uncertainty. These effects are similar among

UGTA sites Bullion, Clearwater, Darwin, Houston,

Purse, and TYBO, all of which are located on Pahute

Mesa or Rainier Mesa (fig. 2). The effects of omitting individual observation locations are also similar

among UGTA sites Bourbon, Corduroy, Coulommiers, Cumarin, Diluted Waters, Pile Driver, and

Strait, all of which are located on Yucca Flat or

Frenchman Flat (fig. 2).

Omission of observation locations 17, 55, 107,

and 145, which are identified as most important in

figure 5, generally causes the largest increases in

prediction uncertainty at sites on both Yucca Flat and

Pahute Mesa. However, there are a number of interesting differences in the results for the two geographic areas. For sites on Yucca Flat, there are

several observation locations in the range 151

through 250 that, when omitted, cause an increase in

calculated prediction uncertainty of greater than 0.1

percent in the east-west and north-south directions.

Conversely, for the sites on Pahute Mesa, there are

far fewer observation locations in this range that, if

omitted, would cause more than 0.1 percent increase

in prediction uncertainty. Many of the observations

in the range 151 through 250 are in groups SH5,

SH6, SH10a, SH10b, and SH10c, which are in the

Specter Range, Indian Springs, Ash Meadows, and

Amargosa Valley (table 2, fig. 1). Observations in

these locations probably are more important to transport from beneath Yucca Flat than in Pahute Mesa

because these observation locations overlie a large

region of hydraulic conductivity zone K5 (mostly

lower carbonate aquifer; value in table 1) in the

model. Predicted advective transport paths from

Yucca Flat are generally much more sensitive to

to parameter K5 than are predicted paths from

Pahute Mesa.

The effect of omitting observation locations on

calculated prediction uncertainty in the vertical direction is also significantly different at sites in the two

geographic areas. At the Pahute Mesa sites, omitting

observation locations typically has a similar effect on

prediction uncertainty in all three coordinate directions. At the Yucca Flat sites, omitting observation

locations typically has a greater effect on prediction

uncertainty in the east-west and north-south directions than in the vertical direction. This result is most

likely because east-west and north-south transport

at the Yucca Flat sites tend to be sensitive to both

hydraulic conductivity and recharge parameters,

whereas vertical transport is mostly sensitive to rerecharge parameter RCH0. Thus, hydraulic-head

observation locations with large dimensionless scaled

sensitivities to the hydraulic-conductivity parameters
RESULTS OF EVALUATION 19

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1 51 101 151 201 251 301 351 401 451 501

Observation number

Number of origins

Figure 7: How pervasively is the observation location important? Large values identify observation locations that are important to advective transport originating from many of the sites.

0.01

0.1

1

10

100

1,000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation group

Maximum percent increase

east-west transport

north-south transport

vertical transport

Figure 8: Largest percent increase in the uncertainty of advective transport in the east-west, north-south, or vertical

directions, at any of the 15 sites (14 UGTA sites and Yucca Mountain). Large values indicate that the observation

group is important to simulation of transport from the water table beneath one or more of the 15 origins.
20 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

will tend to be more important to transport in the

east-west and north-south directions than in the vertical direction.

Omission of Observation Groups

Omission of observation groups is aimed at providing information about which geographic areas of

the DVRFS are most and least important to the advective transport predictions. Analysis of individual

observations identified specific observations that, if

omitted, cause large increases in prediction uncertainty. Less important individual observations, when

omitted as a group, may have different results. This

analysis is especially important when, as in this report and in many studies of ground-water systems,

observations are clustered geographically.

The following discussion is presented using essentially the same four questions considered for individual observation locations.

Is a group important to any of the predictions

and how does group importance vary with 

transport direction?

Whether omission of an observation group significantly increases prediction uncertainty at any of

the UGTA sites or Yucca Mountain can be assessed

using figure 8. For each of the 49 groups, the maximum increase in uncertainty is shown for each transport direction at any of the seven distances for any of

the 15 origins that results when the group is omitted.

By this assessment, observation groups SH4a,

SHL6, SH145, SH107, SH15, and SH28 are identified as the most important, because omitting each of

these groups caused a maximum increase of greater

than 10 percent in at least one direction for one or

more origins (fig. 8). These groups of observations

are located in, respectively, Ash Meadows, Indian

Springs, Beatty, Oasis Valley, Emigrant Valley, and

Oriental Wash (table 2). The results for group SH28

are dominated by the results for observation 17, and

thus for reasons discussed above, the conclusion that

group SH28 is important must be viewed in light of

the influence of pumping on the results for observation 17.

Groups SHL8, SH23, SH25, SH26, SH29, SH30,

and INT6 are those that if omitted would have the

smallest effect on prediction uncertainty (fig. 8).

These groups of observations are located in, respectively, Furnace Creek, Mercury Valley, the Shoshone

Mountains, Emigrant Valley, Kawich Valley, the

Spring Mountains, and Beatty (table 2). The results

for these groups suggest that removal of some individual observations in these areas would have minimal effect on the calculated advective transport

uncertainty. The result for Furnace Creek is suspect

because it probably results from the constant-head

boundary imposed along Death Valley in the threelayer model. Alternate representations of that boundary are likely to significantly increase the evaluated

importance of those observation locations.

Figure 8 also provides information on transport

direction, and shows that the patterns evident in the

results for individual observation locations are repeated.

What is the breadth of each group’s importance?

Figure 9 presents a greater level of detail by

showing the number of origins for which the average

uncertainty in a particular direction increases by a

specified percentage. The observation groups were

assigned to one of four categories of importance

(high, moderately high, moderate, and low) on the

basis of the mean uncertainty increases that resulted

from their omission (table 4). The most important

groups were those that when omitted produced mean

increases greater than or equal to 10 percent at any

UGTA site or Yucca Mountain. Groups of moderately high importance produced mean increases in

prediction uncertainty greater than or equal to 5

percent but less than 10 percent. Moderately important groups produced mean increases greater than or

equal to one percent but less than 5 percent. The

least important groups produced mean increases in

prediction uncertainty less than 1 percent at any of

the origins.

The number of origins for which the mean uncertainty increases more than 10 percent with omission of the data group is shown in figure 9a and table

4. The results indicate that removal of groups SH4a,

SH145, SH107, SH15, or SH28 has the largest effect

on the transport uncertainty. Group SH145 consists

of only observation location 145, yet still has the

greatest effect on uncertainty in the east-west and

vertical transport directions. Omission of SH4a resulted in standard deviation increases greater than 10

percent for six origins in the east-west direction and

seven origins in the north-south direction. Omission

of group SH107 resulted in uncertainty increases

greater than 10 percent for four origins in the eastwest direction.
RESULTS OF EVALUATION 21

0

5

10

15

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation group

Number of origins

east-west transport

north-south transport

vertical transport

(a)

0

5

10

15

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation group

Number of origins

(b)

0

5

10

15

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation group

Number of origins

(c)

Figure 9: Number of origins (of the 14 UGTA sites and Yucca Mountain) for which the mean uncertainty increases

(a) more than or equal to 10 percent with the omission of the observation group, (b) more than or equal to 5 percent but

less than 10 percent with the omission of the observation group, and (c) more than or equal to 1 percent but less than

5 percent with the omission of the observation group.
22 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

Table 4: Importance of observation groups categorized by the percent increase in

uncertainty with omission of the observation group

[All ranges exclude the lowest percentage and include the largest percentage. For example,

1 to 5 percent indicates greater than 1 percent and less than or equal to 5 percent]

Low

(< 1 percent )

Moderate

(1 to 5 percent)

Moderately high

(5 to 10 percent)

High

(>10 percent)

SHL1 SH2c SHL5 SH4a

SH2a SHL3 SHL6 SH107

SH2b SH4b SH145

SHL8 SHL7 SH15

SHL9 SH10a SH28

SH10c SH10b

SH12 SH11

SH20 SH13

SH21 SH14a

SH22 SH14b

SH23 SH16

SH25 SH17

SH26 SH18

SH27 SH19

SH29 SH24

SH30 INT1

SH31 INT2

INT5 INT3

INT6 INT4

INT7 DEP1

DEP2

DEP3

Omission of SH28 caused an increase greater

than 10 percent for one origin in the vertical direction

and five origins in the east-west direction. Omitting

SH15 caused a mean uncertainty increase of greater

than 10 percent for one origin in the east-west direction. This analysis suggests that only groups containing shallow observations are of greatest importance

to the predicted transport paths. However, these results do not imply that the deeper observation locations are unimportant. Although removing them does

not greatly increase prediction uncertainty as calculated in this report, they provide valuable information

about the deep geologic and hydrologic conditions in

the DVRFS, and thus are considered to be more

important than strictly indicated by the analyses

presented here.

The most important observation groups are not

geographically closest to the UGTA sites and Yucca

Mountain. Highly important groups SH4a, SH145,

SH107, and SH28 are all located off the Nevada Test

Site (table 2). SH4a is located in Ash Meadows south

of the NTS, and groups SH145 in Beatty and SH107

in Oasis Valley are west of the NTS. SH28 includes

two observation locations in Oriental Wash, one of

which is observation location 17, which suffers difficulties discussed earlier in this report. This group is

omitted from conclusions drawn from this work.

SH15 contains observation 55, located in the northeast corner of the Nevada Test Site, but the other

observations in this group are located in Emigrant

Valley, northeast of the NTS. As discussed in the

context of removing individual observations, dimensionless scaled sensitivities partially explain the large

effects that removal of some groups have on advective transport uncertainty. The observation in group

SH107 is highly sensitive to K4 and observations
RESULTS OF EVALUATION 23

from SH15 are highly sensitive to K3. These parameters represent the hydraulic conductivities of hydrogeologic units present in the vicinity of Yucca

Mountain and several of the UGTA sites.

Four of the five most important observation

groups were dominated by one individual observation. SH145 and SH107 consisted of only one

observation each, 145 and 107, respectively. SH15

was dominated by the increase in uncertainty of

observation 55, and SH28 includes observation 17,

as previously discussed. However, SH4a, located in

Ash Meadows, had no individual observations ranked

of high importance, but collectively the observations

were highly important. Other groups also located in

Ash Meadows, including intermediate depth observations, consistently ranked as more important than

other groups. These results imply that Ash Meadows

is an important area of the flow system, when all

observations in the area are considered.

Figures 9a and 9b together show that there are

two observation groups of only moderately high

importance: SHL5 and SHL6. Omission of these

groups produces mean increases equal to or greater

than 5 percent and less than 10 percent for at least

one UGTA site or Yucca Mountain, but produces no

mean increases of greater than or equal to 10 percent

for any origin. The two groups are located some

distance from the advective transport prediction

locations. SHL5 is in the Specter Range, south of the

NTS, whereas SHL6 is at Indian Springs (table 2)

east of the NTS.

There are 20 groups whose omission produces

mean increases equal to or greater than 1 and less

than 5 percent for at least one UGTA site or Yucca

Mountain, but no mean increases of greater than or

equal to 5 percent at any origin (figs. 9a, b, c). These

groups of moderate importance are listed in table 4.

Finally, there are 22 groups that produce mean increases of less than 1 percent at any origin. These

are the groups of least importance, and are listed in

table 4.

How does observation group importance vary on

a site-specific basis?

Omission of different observation groups affects

transport uncertainty at specific sites as shown in

Appendix B. The maximum, minimum, and mean

percent increases in prediction uncertainty are plotted

for each transport direction. Most mean increases fall

between 0.1 and 10 percent. These graphs show more

information than could be shown in figure 6 because

of the large number of individual observations.

The 14 UGTA sites and Yucca Mountain are

all sensitive to groups in Pahrump Valley (SH2a, b,

c), Ash Meadows (SH4a, b), Beatty (SHL9 and

SH145), and Amargosa Valley (S10a, b, c). Specific

sites, however, show far more sensitivity to specific

groups. Mean uncertainty at Clearwater increased 11

percent in the east-west direction with omission of

group SH15. Bourbon, Corduroy, Coulommiers, and

Pile driver all show east-west mean uncertainty increases of greater than 10 percent for omission of

groups in Oasis Valley (SH107) and Oriental Valley

(SH28) (see previous comments about observation

location 17, which is in group SH28).

Generally, the increases in prediction uncertainty

that result from omission of observation groups are

similar among the UGTA sites located on Pahute

Mesa and Rainier Mesa (Bullion, Clearwater, Darwin, Houston, Purse, and Tybo), and are similar

among the UGTA sites located on or near Yucca Flat

and Frenchman Flat (Bourbon, Corduroy, Coulommiers, Cumarin, Diluted Waters, Pile Driver, and

Strait), as shown in Appendix B. The similarity of

results by geographic area is consistent with the

results of omitting individual observations, discussed

above and shown in Appendix A. The graphs in

Appendix B show that at five of the six Pahute Mesa

and Rainier Mesa sites, omission of only one group

(SH145) results in a maximum prediction uncertainty

increase of greater than or equal to 10 percent in the

east-west direction. For the Pahute Mesa sites, there

are no groups that when omitted cause increases of

greater than 10 percent in the north-south direction.

In contrast, at six of the Yucca Flat sites, there are

two or more groups that, when omitted, cause a

maximum uncertainty increase of greater than 10

percent in the east-west direction. At most Yucca Flat

sites, there is one group that when omitted causes an

increase of greater than 10 percent in the north-south

direction.

Figure 9, Appendix B, and table 4 indicate that

no observation groups containing intermediate or deep

wells are of moderately high importance. Omission

of INT4, located in Frenchman Flat, was of moderate

importance and consistently resulted in larger increases in prediction uncertainty for the UGTA sites

located near Yucca Flat and Frenchman Flat (Bourbon, Corduroy, Coulommiers, Cumarin, Diluted

Waters, and Strait). The remaining observation

groups with wells open to model layers two and three

are of only and moderate (INT1, INT2, INT3, and

DEP1) or low importance (INT5, INT6, INT7, DEP2,

and DEP3) on the basis of the ranking suggested
24 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70

Model row number

Las

Vegas

Nevada

Test

Site

Model column number

Figure 10: The 100 least significant shallow and intermediate hydraulic-head observation 

locations that were removed to evaluate the importance of observations at these locations.

 

above. Observation wells finished to greater depths 

are far fewer than their shallow counterparts, however, so hydraulic-head measurements from these 

wells are still considered to be important. 

One possible use of the observation groups is 

to help devise a more efficient ground-water monitoring network. Various scenarios can easily be calculated using the methods described in this report. 

Omission of a Set of 100 Low-Importance Individual 

Observation Locations 

This section presents an example of how the 

methods presented in this report can be used to 

evaluate the importance of a set of observation 

locations distributed throughout the region. The 100 

observation locations omitted were selected based on 

the results shown in figure 5; of the shallow and 

intermediate observations, the 100 with the smallest 

percent increase in uncertainty were omitted. The 

result was that, on average, the prediction uncertainty 

was increased by 0.59 percent; the values in the three 

coordinate directions calculated as for figures 6 and 8

are 0.68 in the east-west direction, 0.52 in the northsouth direction, and 0.74 in the vertical direction. 

These results suggest that the water levels in the 

wells associated with these observations could prudently be measured less frequently. The locations of 

the 100 observation locations are shown in figure 10. 
SUMMARY AND CONCLUSIONS 25 

SUMMARY AND CONCLUSIONS 

The ranking of observation location importance 

in the Death Valley regional ground-water flow 

model was accomplished by removing individual 

observation locations and assessing the resulting 

effects on particle transport position uncertainty 

calculated using linear theory. Geographic location of 

the observations and dimensionless scaled sensitivities were used to sort the observations into groups, 

which were used for presentation purposes and to 

evaluate areas of observation location importance. 

The statistic used to evaluate the effect of omitting 

observations is the percent increase in prediction 

uncertainty, as measured using prediction standard 

deviation, that results when an observation location 

or group is omitted.

As a first step, individual hydraulic-head observation locations that are most important to advective 

transport predictions were identified. This was accomplished in part by individually omitting each of 

the 501 observations. The results of this analysis 

showed no definitive trend in significance related to 

location or depth of the individual observations. The 

removal of individual observation locations 55, 107, 

and 145 caused the greatest prediction uncertainty

increases, with mean percent increases for the three 

coordinate directions ranging from 5.3 to 49.0 for 

these single wells. These observation locations are 

clearly the most important based on the analysis. A 

fourth observation location, 17, was rated as important based on the calculations, but further consideration suggested that its importance was closely related 

to model simplifications. It is not, therefore, suggested as being an important location for future 

monitoring.

As a second step, groups of hydraulic-head observation locations that are most important to advective transport predictions were identified. Results for 

the 49 groups considered indicate that four groups 

located off the Nevada Test Site have the greatest 

impact on prediction uncertainty. The group which 

contains observation location 17 was also rated as 

important, but because of the concerns mentioned in 

the previous paragraph, this group is not included in 

the list of important groups. 

The validity of the conclusions drawn from the 

evaluation of observations depends on how well the 

model represents the salient features of the flow 

system. This representation was evaluated by 

D’Agnese and others (1997, p. 95–113) by considering model fit to observed hydraulic heads and spring 

flows and the plausibility of estimated parameter 

values and simulated flows. This analysis “suggests 

that the model is a reasonable representation of the 

physical system, but evidence of important model 

error exists.” (D’Agnese and others, 1997, p. 117). 

This statement suggests that the evaluation of the 

importance of observation locations to predictions 

made with the present DVRFS model is likely to be 

useful, but results need to be viewed with caution. 

The assessment of the importance of the observations is only in the context of advective transport 

predictions from Yucca Mountain and 14 UGTA 

sites. The evaluation presented here uses the pumpage and recharge distribution described in D’Agnese 

and others, 1997) for both the calibration conditions 

and the prediction conditions, and can be used to 

identify observation locations important to predictions of interest given that flow field. While calibration conditions cannot be changed once a model is 

calibrated, the prediction conditions can be changed 

to reflect anticipated future conditions. Significant 

changes in the prediction flow field conditions produced, for example, by additional pumpage or significantly different recharge could change the 

importance of observation locations. Evaluation of 

such alternatives would require a repetition of the 

analysis presented here. In designing such alternatives, it is useful to note that, in general, the flowpaths of interest probably are less sensitive to short 

term variations in the flow field than long-term 

changes. To the extent that this is true, reevaluation 

using a steady-state simulation could provide substantial information about which observation locations were important given different prediction flow 

fields. Transient simulations would be more involved, but would, of course, be more useful still, 

and absolutely necessary in some circumstances. 

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ground-water flow parameter-estimation model 

MODFLOWP: U.S. Geological Survey Open-File 

Report 97-14, 67 p. 

Bedinger, M.S., Langer, W.H., and Reed, J.E., 1989, 

Hydraulic properties of rocks in the Basin and Range 

Province, in Bedinger, M.S., and others (eds.), Studies of geology and hydrology in the Basin and Range 

Province, southwestern United States, for isolation of 
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high-level radioactive waste—Basis of characterization and evaluation: U.S. Geological Survey Professional Paper 1370-A, p. A16–A18. 

D’Agnese, F.A., Faunt, C.C, Turner, A.K., and Hill, M.C., 

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Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, 

M.G., 2000, MODFLOW-2000, The U.S. Geological 

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modularization concepts and the ground-water flow 

process: U.S. Geological Survey Open-File Report

00-92, 121 p.

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estimating parameters of a transient, threedimensional ground-water flow model using nonlinear regression: U.S. Geological Survey Open-File 

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E.R., 2000, MODFLOW 2000, the U.S. Geological 

Survey modular ground-water model, User’s guide to 

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processes: U.S. Geological Survey Open-File Report 

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controlled experiment in ground-water flow model 

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James, B.R., and Gorelick, S.M., 1994, When enough is 

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no. 12, p. 3499–3513. 

Loaiciga, H.A., Charbeneau, R.J., Everett, L.G., Fogg, 

G.E., Hobbs, B.F., and Rouhani, S., 1992, Review of 

ground-water quality monitoring network design: 

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11–37. 

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Appendix A

Graphs showing the importance of individual

observation locations to advective transport

simulated from 14 UGTA sites.
28 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions

EXPLANATION OF SYMBOLS

(Figs. A1–A15)

SHL1

SH2a

SH2b

SH2c

SHL3

SH4a

SH4b

SHL5

SHL6

SHL7

SHL8

SHL9

SH145

SH10a

SH10b

SH10c

SH11

SH12

SH13

SH107

SH14a

SH14b

SH15

SH16

SH17

SH18

SH19

SH20

SH21

SH22

SH23

SH24

SH25

SH26

SH27

SH28

SH29

SH30

SH31

INT1

INT2

INT3

INT4

INT5

INT6

INT7

DEP1

DEP2

DEP3
Yucca Mountain

Figure A1. Percent increase in uncertainty for particle paths propagated from beneath Yucca Mountain.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
BULLION - Pahute Mesa

Figure A2. Percent increase in uncertainty for particle paths propagated from beneath BULLION.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1,000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
DARWIN - Pahute Mesa

Figure A3. Percent increase in uncertainty for particle paths propagated from beneath DARWIN.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
HOUSTON - Pahute Mesa

Figure A4. Percent increase in uncertainty for particle paths propagated from beneath HOUSTON.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
PURSE - Pahute Mesa

Figure A5. Percent increase in uncertainty for particle paths propagated from beneath PURSE.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
TYBO - Pahute Mesa

Figure A6. Percent increase in uncertainty for particle paths propagated from beneath TYBO.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
CLEARWATER - Rainier Mesa

Figure A7. Percent increase in uncertainty for particle paths propagated from beneath CLEARWATER.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
BOURBON - Yucca Flat

Figure A8. Percent increase in uncertainty for particle paths propagated from beneath BOURBON.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
CORDUROY - Yucca Flat

Figure A9. Percent increase in uncertainty for particle paths propagated from beneath CORDUROY.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
COULOMMIERS - Yucca Flat

Figure A10. Percent increase in uncertainty for particle paths propagated from beneath COULOMMIERS.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
CUMARIN - Yucca Flat

Figure A11. Percent increase in uncertainty for particle paths propagated from beneath CUMARIN.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
PILE DRIVER - Yucca Flat

Figure A12. Percent increase in uncertainty for particle paths propagated from beneath PILE DRIVER.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
STRAIT - Yucca Flat

Figure A13.. Percent increase in uncertainty for particle paths propagated from beneath STRAIT.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
DILUTED WATERS - Frenchman Flat

Figure A14. Percent increase in uncertainty for particle paths propagated from beneath DILUTED WATERS.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
GUM DROP - Shoshone Mountain

Figure A15. Percent increase in uncertainty for particle paths propagated from beneath GUM DROP.

Increased uncertainties equal the percent increase in simulated standard deviations for particle

position in the applicable direction that would be produced by removing an individual observation.

East-west advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

North-south advective transport distance

0.01

0.1

1

10

100

1 51 101 151 201 251 301 351 401 451 501

Percent increased

uncertainty

Vertical advective transport distance

0.01

0.1

1

10

100

1000

1 51 101 151 201 251 301 351 401 451 501

Observation number

Percent increased

uncertainty
44 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions
Appendix B

Graphs showing the importance of groups

of observation locations to advective transport

simulated from 14 UGTA sites
46 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions
Yucca Mountain

Figure B1. Percent increase in uncertainty for particle paths propagated from beneath Yucca

Mountain. The particle, originating at or below the water table, with the largest percent increase

is shown. Increased uncertainties equal the percent increase in simulated standard deviation for

travel distance in the applicable direction that would be produced by removing a group of

observations. Sensitivities are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
BULLION - Pahute Mesa

Figure B2. Percent increase in uncertainty for particle paths propagated from beneath BULLION.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
DARWIN - Pahute Mesa

Figure B3. Percent increase in uncertainty for particle paths propagated from beneath DARWIN.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
HOUSTON - Pahute Mesa

Figure B4. Percent increase in uncertainty for particle paths propagated from beneath HOUSTON.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
PURSE - Pahute Mesa

Figure B5. Percent increase in uncertainty for particle paths propagated from beneath PURSE.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
TYBO - Pahute Mesa

Figure B6. Percent increase in uncertainty for particle paths propagated from beneath TYBO.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
CLEARWATER - Rainier Mesa

Figure B7. Percent increase in uncertainty for particle paths propagated from beneath CLEARWATER.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
BOURBON - Yucca Flat

Figure B8. Percent increase in uncertainty for particle paths propagated from beneath BOURBON.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
CORDUROY - Yucca Flat

Figure B9. Percent increase in uncertainty for particle paths propagated from beneath CORDUROY.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
COULOMMIERS - Yucca Flat

Figure B10. Percent increase in uncertainty for particle paths propagated from beneath COULOMMIERS.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
CUMARIN - Yucca Flat

Figure B11. Percent increase in uncertainty for particle paths propagated from beneath CUMARIN.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
PILE DRIVER - Yucca Flat

Figure B12. Percent increase in uncertainty for particle paths propagated from beneath PILE DRIVER.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
STRAIT - Yucca Flat

Figure B13. Percent increase in uncertainty for particle paths propagated from beneath STRAIT.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel 

distance in the applicable direction that would be produced by removing a group of observations.

Sensitivities are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
DILUTED WATERS - Frenchman Flat

Figure B14. Percent increase in uncertainty for particle paths propagated from beneath DILUTED WATERS.

The particle, originating at or below the water table, with the largest percent increase is shown. Increased

uncertainties equal the percent increase in simulated standard deviation for travel distance in the applicable

direction that would be produced by removing a group of observations. Sensitivities are from a total particle

travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
GUM DROP - Shoshone Mountain

Figure B15. Percent increase in uncertainty for particle paths propagated from beneath GUM DROP.

The particle, originating at or below the water table, with the largest percent increase is shown.

Increased uncertainties equal the percent increase in simulated standard deviation for travel distance

in the applicable direction that would be produced by removing a group of observations. Sensitivities

are from a total particle travel distance of 10,500 meters.

East-west advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

North-south advective-transport distance

0.01

0.1

1

10

100

Percent increased

uncertainty

Vertical advective-transport distance

0.01

0.1

1

10

100

1000

SHL1SH2aSH2bSH2cSHL3SH4aSH4bSHL5SHL6SHL7SHL8SHL9SH145SH10aSH10bSH10cSH11SH12SH13SH107SH14aSH14bSH15SH16SH17SH18SH19SH20SH21SH22SH23SH24SH25SH26SH27SH28SH29SH30SH31INT1INT2INT3INT4INT5INT6INT7DEP1DEP2DEP3

Observation Group

Percent increased

uncertainty
62 Preliminary Evaluation of Importance of Existing Hydraulic-Head Observation Locations to Advective-Transport Predictions