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Filling in the gaps: 3D mapping Arizona's Basin and Range aquifer in the Prescott Active Management Area

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Filling in the gaps: 3D mapping Arizona's Basin and Range aquifer in the Prescott Active Management Area

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FILLING IN THE GAPS:
3D MAPPING ARIZONA’S BASIN AND RANGE AQUIFER IN THE PRESCOTT ACTIVE
MANAGEMENT AREA
by
Amanda Cuesta

A Thesis Presented to the
FACULTY OF THE USC DORNSIFE COLLEGE OF LETTERS, ARTS, AND SCIENCES
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY

August 2020

Copyright 2020 Amanda Cuesta
ii

To my mom and friends- thank you for all your support.

iii

Acknowledgements
I’d like to thank the Arizona Department of Water Resources for all the data used to complete
this project and helping form the initial concept. I am also grateful to Dr. Marx for serving as my
advisor and making sure I stayed on track. Thank you to Dr. Swift and Dr. Duan for your
contributions as my committee members. Lastly, I’d like to thank my friends and family for
keeping me going when I wasn’t sure I could.
iv

Table of Contents
Dedication .................................................................................................................................. ii
Acknowledgements ................................................................................................................... iii
List of Tables ..............................................................................................................................v
List of Figures ........................................................................................................................... vi
List of Abbreviations................................................................................................................ vii
Abstract .................................................................................................................................. viii
Chapter 1 Introduction ................................................................................................................1
1.1. Managing Arizona’s Water ............................................................................................. 2
1.2. Motivation ...................................................................................................................... 3
Chapter 2 Related Works ............................................................................................................7
2.1. Arizona Hydrogeology ................................................................................................... 7
2.2. The value of 3D modeling .............................................................................................. 9
2.3. Modeling aquifers in 3D ............................................................................................... 10
2.3.1. Interpolation methods .......................................................................................... 11
Chapter 3 Data and Methods ..................................................................................................... 14
3.1. Scope............................................................................................................................ 14
3.2. Data .............................................................................................................................. 14
3.3. Design .......................................................................................................................... 16
3.3.1. Well selection ...................................................................................................... 16
3.3.2. Interpolation ........................................................................................................ 17
3.3.3. Analyses and demonstrations ............................................................................... 20
Chapter 4 Results ...................................................................................................................... 22
4.1. Model ........................................................................................................................... 22
4.2. Validation ..................................................................................................................... 24
4.3. Accuracy without the model ......................................................................................... 25
Chapter 5 Conclusions .............................................................................................................. 27
References ................................................................................................................................ 30
Appendices ............................................................................................................................... 34
Appendix A Data ............................................................................................................... 34
Appendix B Model Validation Results ............................................................................... 35
Appendix C Traditional Method Accuracy ......................................................................... 36

v

List of Tables
Table 1 Material Permeability ................................................................................................... 18
Table 2 Semivariogram Model Selection ................................................................................... 19
Table 3 Parameter Comparison.................................................................................................. 20

vi

List of Figures
Figure 1 Groundwater Use vs. AZ Population .............................................................................3
Figure 2 AZ Well Density ...........................................................................................................5
Figure 3 Basin and Range Aquifer ...............................................................................................8
Figure 4 Model Outputs ............................................................................................................ 23
Figure 5 Model Validation Wells .............................................................................................. 24
Figure 6 Traditional Method Accuracy Assessment Wells ......................................................... 25

vii

List of Abbreviations
3D Three dimensions or three-dimensional
ADWR Arizona Department of Water Resources
AMA Active Management Area
ANFIS Adaptive Neuro-fuzzy Inference System
AZGS Arizona Geological Survey
DEM Digital elevation model
EBK Empirical Bayesian Kriging
EBK3D Empirical Bayesian Kriging 3D
GMA Groundwater Management Act
GWSI Groundwater Site Inventory (Database)
IDW Inverse Distance Weighting
INA Irrigation Non-expansion Area
LAU Lower Alluvial Unit
MAU Middle Alluvial Unit
NAD27 North American Datum 1927
NAD83 North American Datum 1983
NAVD88 North American Vertical Datum 1988
TIN Triangulated Irregular Network
UAU Upper Alluvial Unit
USGS United States Geological Survey

viii

Abstract
Despite Arizona relying on Arizona groundwater to meet a significant portion of its water needs,
the locations of Arizona’s groundwater aquifers are not fully mapped, and methods to interpolate
the locations of aquifers from test boreholes remain inaccurate. In response, this study
implements a workflow leveraging three-dimensional (3D) interpolation to fill in that knowledge
gap within a study site: the Prescott Active Management Area surrounding Prescott, Arizona.
Using borehole log data and digital elevation models, the 3D extent of permeable layers are
mapped, serving as proxies for aquifers and aquitards, respectively. This project makes use of
Empirical Bayesian Kriging 3D (EBK3D) to interpolate permeability data in three dimensions.
When tested on four random boreholes, this model correctly predicted an aquifer 80% of the time
in comparison to 42% using traditional 2D interpolation. The model’s improved accuracy
provides an approach to improve drillers’, policymakers’, and scientists’ understanding of the
hydrologic activity in the area. Such an improvement may lead to better-informed storage
models, changes in water management, and greater cost efficiency when drilling new wells.

1

Chapter 1 Introduction
Arizona is a rapidly growing desert state. This means increased demands on our total water
supply, even though the state is in an ongoing drought. In order to meet these growing needs,
Arizona heavily relies on groundwater. It is little wonder, then, that groundwater is thoroughly
monitored within the state. In fact, in 1980, the Arizona Department of Water Resources
(ADWR) designated five areas as needing extra legislation and monitoring efforts. These areas,
known as active management areas (AMAs), have depth-to-water measurements taken more
often than other parts of the state and are subject to stricter regulations.
Despite the extra attention given to these areas, knowledge of the aquifers that supply
their water is somewhat lacking. The United States Geological Survey (USGS) released a water
atlas in 1995, summarizing the aquifers that can be found throughout the United States (Robson
and Banta 1995a; Robson and Banta 1995b). Arizona was shown to have two principal aquifers,
the Basin and Range aquifer and the Colorado Plateau aquifer. These maps are useful for
showing where the groundwater is in planar space, but what about its vertical extent? Current
data tend to cover specific study areas if it is in 3D. Still, most data regarding aquifer locations
are either in 2D in the form of cross sections or simply left as tabular descriptive data.
This study aims to fill in both the knowledge and model gaps by using interpolation to
create a 3D model of the Basin and Range aquifer. The present study only focuses on the
Prescott AMA, but it will likely be extended to the other AMAs in the future. As lithologic data
can be assumed to be stable, barring significant tectonic activity, all available borehole data is
eligible for inclusion, regardless of observation date.
2

1.1. Managing Arizona’s Water
As discussed previously, Arizona is a desert state that relies on groundwater to meet a
large portion of its water needs. To combat the overuse that was occurring throughout the state,
Arizona legislation adopted strict codes for managing the state’s water resources with special
emphasis placed on preserving its groundwater. This effort was brought to the forefront of public
awareness when the state government signed the Groundwater Management Act (GMA) into
effect in 1980 (Jacobs and Holway 2004; ADWR n.d.b)
The GMA accomplished several critical goals, the effects of which are still affecting
daily life in Arizona. First, it established the Arizona Department of Water Resources, the
agency responsible for monitoring and preserving the state’s water. Second, it outlined a plan to
allocate groundwater so that safe yield, or net-zero aquifer withdrawal, may in time be achieved.
The act also involved securing funding for the Central Arizona Project, a canal that carries water
from the Colorado River for use in Maricopa, Pima, and Pinal counties to decrease their reliance
on groundwater. Finally, it established four active management areas and two Irrigation Non-
expansion Areas (INAs). A fifth AMA was later distinguished from a portion of the Tucson
AMA and a third INA were established in 1982. These areas are subject to tighter regulations
than the rest of the state, each with a specific goal. For the Phoenix, Tucson, and Prescott AMAs,
this goal is reducing groundwater withdrawal to the safe yield amount. The Santa Cruz AMA’s
goal is to maintain safe yield to prevent water table drawdown and protect riparian habitats. Pinal
AMA’s goal is to safely continue agriculture without jeopardizing future water supplies (ADWR
2010a; ADWR 2010b; ADWR n.d.c; Jacobs and Holway 2004). The effectiveness of the GMA
is illustrated in Figure 1.
3

1.2. Motivation
Every year, the state of Arizona relies on groundwater to meet the demands of its
growing population, accounting for 43% of the state’s total water supply from 2001 to 2005
(ADWR 2010b). Since the inception of the Arizona Department of Water Resources (ADWR),
the population has grown from about 3 million people to 7 million. This averages to a 3%
growth in population per year (ADWR 2010b). Surprisingly, this growth is not translating to
increasing use of the state's groundwater supply. In fact, recent reports indicate that the state is
using the least groundwater it has since the 1950s. This is due to strict regulations and shifting
dependence to other sources, such as the Colorado River (ADWR n.d.). Even though these
statistics are promising, Arizona must carefully track how much groundwater is being used, who
is using it, and where it is being drawn from.
In an effort to better track and regulate groundwater use, the Arizona Department of
Water Resources has designated five "active management areas" since its inception. These are
Figure 1: This diagram illustrates the impact of the GMA and concurrent creation of the Arizona
Department of Water Resources. Note that after ADWR is established, total water use
continuously decreases.
4

areas where groundwater withdrawal most severely exceeds its safe yield, or the amount of
groundwater that can be considered renewable. The active management areas, where 82% of the
population lives and where most withdrawal occurs, are targeted for additional regulatory
measures. These include, but are not limited to, restricting the amount of groundwater that can be
withdrawn legally, preventing the expansion of irrigated areas, and strict permitting requirements
for new withdrawals (ADWR 2016).
All of these regulations serve one primary purpose— to protect Arizona’s aquifers. One
of Arizona’s two primary aquifers, the Basin and Range aquifer underlies approximately 200,000
square miles of land, extending through seven states (Robson and Banta 1995a). Of particular
interest to this study is the stretch underneath southern Arizona that lies under all five active
management areas. As mentioned previously, these are the areas with the greatest overuse of
groundwater. For them to all be withdrawing from the same aquifer makes it critical that
scientists understand where exactly the aquifer is in three dimensions. This allows accurate
volume calculations and, by extension, more accurate monitoring of aquifer conditions.
Additionally, the Basin and Range aquifer was chosen for representation over the Colorado
Plateau aquifer because the water-bearing units can generally be identified with more confidence
and the geologic structures within the basins, where the aquifer is located, are relatively
straightforward (Robson and Banta 1995 a; Robson and Banta 1995b).
Modeling the entire Basin and Range aquifer is outside the scope of this project. Instead,
it is modeled within a single AMA with the intention to expand its coverage in the future. The
study is conducted within AMA boundaries in order to inform both scientists and decision
makers of subsurface details within the state’s most hydrologically delicate areas. The AMAs
5

are population hot spots, the focus of most groundwater scientists’ models, and the areas that see
the most groundwater-related issues.
Of the five AMAs, Prescott is the focus of this study. The primary reason for this
decision is that it has the highest density of wells covering its entire area, as shown in Figure 2.
More wells in an area equate to more borehole data to inform the model and, by extension, a
more accurate model. The Prescott AMA’s areal extent is reasonable to complete in the
timeframe of this study but large enough to hold significance. Finally, and perhaps most
importantly, such a model does not exist yet for the area. All the information on the aquifer is
currently stored as descriptions, tables, or cross sections (Anderson, Freethey, and Tucci 1992;
Gootee, et al. 2017). The move to 3D representation is long overdue.
This model benefits several
groups. The Field Services Section at
ADWR has expressed interest in such
a model to help better explain what
their field measurements represent.
They hope to be able to input well
construction data and see how the well
relates to permeable layers. For
example, is it screened within multiple
distinct layers, creating a composite
water level? Or does the water level
represent a single hydrologic unit?
Figure 2: A density map of well locations overlain by
outlines of the AMAs with the Prescott AMA in orange.
Darker greens indicate greater well density.
6

Policymakers can use the data collected by the Field Services section in combination with
information about the area’s permeability to decide whether to implement new use restrictions or
where to focus recharge efforts. Groundwater modelers have also expressed interest for the sake
of better informing their models.
The groups that will most benefit from this model, though, are well owners and drillers. It
can help them make more informed decisions regarding where to place a new well and how deep
to drill it in order to successfully and sustainably withdraw water. It will also help avoid wasting
time and resources associated with drilling beyond a water-bearing unit and having to backfill
the hole or drilling a completely dry well.
Given the above information, a 3D model of Arizona’s aquifers could benefit nearly
everyone in the state either directly or indirectly. The remainder of this manuscript follows the
process of creating the model, beginning with related works followed by the methodology to be
used in creating the model. It concludes with a presentation of the results and a discussion of the
findings.

7

Chapter 2 Related Works
This chapter presents a review of the literature related to creating this 3D model of the Basin and
Range Aquifer. The review begins with an overview of hydrogeology within Arizona, including
characteristics of major aquifers. That is followed by a discussion of the value of 3D modeling in
the spatial sciences. The chapter concludes with a look at what has been done in the past
regarding aquifer modeling with a focus on the methods used.
2.1. Arizona Hydrogeology
With Arizona’s groundwater being so strictly regulated, it is valuable to understand the
conditions under which these aquifers formed and how to identify them in drill logs. The
majority of this information is provided by the United States and Arizona Geological Surveys
(USGS and AZGS, respectively).
In 1995, the USGS released a Groundwater Atlas of the United States. This document,
which provides identifying and contextual information for all major aquifers in the United States,
identifies two main aquifers within Arizona. These are the Colorado Plateau aquifer in the
northeast and Basin and Range aquifer in the south and west (Miller 2000). Both of these
primary aquifers are comprised of multiple sub-aquifers and are often referred to as plurals (i.e.,
Basin and Range aquifers).
The Colorado Plateau aquifer consists of four sub-aquifers: Coconino-De Chelly, Dakota-
Glen Canyon, Mesaverde, and Uinta-Animas. The hydrogeologic layers in this aquifer are
mostly consolidated sedimentary rocks, including sandstone, conglomerates, and shales.
Limestone, coal, and gypsum are also fairly common layers. The relationships between these
layers has been described as “complicated” (Robson and Banta 1995b). As Robson and Banta
8

(1995b) indicate, the layers’ properties are so inconsistent that individual layers have been shown
to be aquifers in one area while acting as aquitards, or flow-inhibiting layers, in another. The
large number of hydrogeologic units and their inconsistencies create too much uncertainty for
inclusion in this project. Instead, the Basin and Range aquifer is the focus.
The Basin and Range aquifer, the extent of which is shown in Figure 3, is much more
straight-forward, hydrogeologically speaking. Depending on the classification scheme used,
there are only two to four hydrogeologic units (Gootee et al. 2017). The discrepancy regarding
the number of hydrogeologic units stems from differing opinions on whether to designate certain
sections as a new unit or the continuation of a series of deposits. These units are, for the most
part, consistent throughout the
aquifer’s extent. The tectonic
disturbances that created the
aquifer’s namesake basins and
ranges occurred prior to the
deposition of the alluvial units.
That is to say that there were no
major deformations in the area
after deposition of the aquifer
units began (Anderson,
Freethey, and Tucci 1992;
Robson and Banta 1995a).
Using Gootee et al.’s
classification scheme, which is
Figure 3: The extent of the Basin and Range Aquifer. The
aquifer is highlighted in yellow. Modified from Robson, S G,
and E R Banta 1995.
9

also the one used by ADWR, there are three hydrogeologic units: the upper, middle, and lower
alluvial units. Anderson, Freethey, and Tucci (1992) group Gootee’s upper and middle alluvial
units into a single unit, but their lower units are in agreement. The shallow upper alluvial unit
(UAU) is characterized by fine sediment with coarser deposits near mountains. The middle
alluvial unit (MAU) is well-cemented conglomerates and mudstones. Sand and siltstone grading
into mudstone are characteristic of the lower alluvial unit (LAU). Evaporite deposits are also
common in this unit near basin centers.
2.2. The value of 3D modeling
Three-dimensional modeling is utilized in a wide variety of disciplines, both those that
are commonly associated with the spatial sciences such as geology and those that are not, like
surgery. This wide range of uses speaks to the value of 3D modeling. With 3D modeling being
used in such a wide variety of disciplines, it is important to examine what exactly makes it more
beneficial than other forms of data storage and manipulation.
The primary advantage of 3D modeling is that it allows the data to be explored as it
would be in person. We experience the world in three dimensions, so it is more intuitive to have
information displayed in three dimensions than in two dimensions. Such a display makes it easier
for experts to spot errors and anomalies than it would be when looking at 2D displays or tabular
data (Akpan and Shanker 2017). It also makes conveying information to non-experts easier
because it is an intuitive format that accurately conveys the world as it is experienced.
A meta-analysis by Apkan and Shanker (2017) found that most researchers from a variety
of fields conclude that displaying information in three dimensions is “more potent and leads to
better analysis”. Aldiss et al. (2012) reached a similar conclusion, citing 3D models’ ability to
incorporate geologic features exactly as observed, by extension allowing them to understand
10

structures in a way that they were unable to using other methods of examining their data. An
analysis by Brzobohata et al. (2012) found that 3D modeling had fewer errors when compared to
traditional methods used in bone reconstructions. Though that study is concerned with medical
modeling instead of geographic modeling, it would not be a stretch to assume that the same
would be true in a geographic context.
Finally, 3D models allow phenomena to be visualized that cannot be readily observed in
person. Whether it be because the object of observation is under hundreds of feet of rocks, such
as an aquifer, or the object is too delicate to be handled, such as in medical observations
(Brzobohata et al. 2012) and archaeology (D'Amelio, Maggio, and Villa 2015), 3D modeling
gives form to the otherwise unseeable.
2.3. Modeling aquifers in 3D
There have been numerous studies completed modeling groundwater aquifers in three
dimensions. Each study uses a somewhat unique approach, but most share some broad
similarities. The current study drew on the similarities to create a basic plan of action. The
differences between studies were carefully considered while deciding the specific methods to be
used, such as software and interpolation method. In making these decisions, methods that exactly
honor the data were preferred, as were methods that could accomodate data with spatial trends.
The first major similarity between all reviewed studies is the inclusion of borehole
lithologic logs. Most of this data comes from drilling water wells, but some researchers have also
used oil exploration boreholes and wells (Gootee, et al. 2017; Jerbi, et al. 2018; Neinkamp 2016;
Nury, et al. 2010). Additional data that has been used less consistently includes digital elevation
models (DEMs), cross sections, water levels for unconfined aquifers, as well as seismic and
resistivity data.
11

The process of generating 3D aquifer data is generally agreed upon between the studies
mentioned previously. The first, and most tedious, step is gathering borehole information and
interpreting the logs. Drillers often use inconsistent wording on their logs, creating the need for
human interpretation before correlation is possible. Once the logs are reinterpreted, the bounding
surface between units can be plotted and interpolated in 3D.
The program and method used to complete this interpolation seem to vary widely based
on researcher preference and suitability for the study area. After thorough comparisons of
methods, Neinkamp (2016) found that for study areas with trends in elevation, Empirical
Bayesian Kriging (EBK) in ArcGIS is most suitable to use for interpolation. The Conde study
(2014) found Inverse Distance Weighting to be acceptable, also in ArcGIS. Other researchers
used more specialized software to complete the interpolation, such as Rockware (Jerbi, et al.
2018) or GOCAD (Nury et al. 2010). In my experience, most people that would use this model
have ArcGIS available and are at least somewhat familiar with the program. Creating the model
in ArcGIS ensures that interested parties will be able to view and manipulate the model. In
contrast, a more specialized program may not allow the same due to proprietary file types.
Because there is an elevation trend to the study area, EBK is the interpolation method used.
2.3.1. Interpolation methods
The remainder of this chapter examines interpolation methods used in similar studies.
The largest portion discusses the various forms of kriging, followed by a discussion of other
methods that have been used.
2.3.1.1. Kriging
Kriging is an exact interpolation method in which the data is honored as it was observed.
This means that after interpolation, the output values at measured points match the input values
12

at those points. It assumes that points near each other in space have values more similar to each
other than to points that are farther away, a phenomenon known as spatial autocorrelation
(Columbia University Mailman School of Public Health, n.d.). These two defining characteristics
are ideal for this project as geologic data is always autocorrelated, and the data must be truthfully
represented in the model for it to be an improvement over other representations.
In order to define the relationship between data points, kriging relies on semivariograms.
Semivariograms are plots that display the distance between points on the x-axis and the squared
difference of the points’ values along the y-axis (Esri n.d). A model is then fit to this plot, similar
to a line of best fit in regression analysis. The model is what allows predictions to be made in
unmeasured locations since it is essentially an equation representing how the data changes
between measured points.
There are several types of kriging methods available, each with unique benefits and
assumptions. The two main categories are ordinary kriging, which assumes that the relationship
between data points only depends on distance, and universal kriging, which assumes the
direction of separation also matters (Dunlap and Spinozola 1984). A third, more recently
developed type of kriging is Empirical Bayesian Kriging (EBK). This method can accommodate
data for which a single model does not fit the entire study area. It automates the semivariogram
modeling process by modeling subsets of the data and adjusting the model each time until the
best fit for the full study area is achieved. EBK can also accommodate data that is not normally
distributed, an advantage over most other kriging styles. Additionally, an estimate of errors may
be created, which adds credibility to the interpolated surface (Esri n.d.).
13

2.3.1.2. Other methods
Though the various forms of kriging seem to be the preferred way to interpret
hydrogeologic data, other methods are available. The most simplistic of these other methods is
inverse distance weighting (IDW). Like kriging, IDW is an exact interpolation method. Rather
than using semivariograms and models to determine the relationship between data points, IDW
assumes a linear relationship based only on the distance between the points (Ohmer, et al. 2017).
This method is less computationally demanding and requires fewer user-set parameters but is
often less accurate than more sophisticated methods when dealing with geologic or hydrologic
data.
A less commonly used interpolation method, specifically regarding hydrologic data, is
adaptive neuro-fuzzy inference system (ANFIS). This method works on the assumption that
there is not a clear or well-defined boundary to the data. ANFIS iteratively creates prediction
rules for the fuzzy data and has been shown to generate outputs fairly similar to those from
ordinary kriging. For a more detailed explanation, the reader is referred to Kurtulus et al. 2011.
Though these other interpolation methods are useful, they are not the most appropriate for the
data in this study due to trends in the data and its relatively well-defined boundaries.
14

Chapter 3 Data and Methods
This chapter outlines the project’s design, as well as the data needed to complete the involved
tasks.
3.1 . Scope
This study covers the Prescott AMA with an approximately one square mile planar
resolution model of the Basin and Range aquifer. Vertical data was aggregated into fifty-foot
intervals during digitization prior to display and interpolation. These intervals were assigned one
of three possible values: 100 if the interval is dominantly permeable, 0 if dominantly
impermeable, or 50 if the log was not detailed enough to determine permeability. The data used
to create the model and their related complications are discussed further in the next section.
3.2. Data
The primary data used to create this model was the well borehole logs that are completed
by the drillers as wells are constructed. These contain lithologic information about the layers that
are drilled through and are made publicly available as part of wells’ registration documents
through ADWR. All borehole data had to be joined to ADWR’s Groundwater Site Inventory
(GWSI) database, which contains GPS-verified location information for each well as well as all
measured water levels. The GPS latitudes and longitudes are given in NAD27 degrees-minutes-
seconds accurate to 0.5 seconds
Though every well has a borehole log and accurate location information, inconsistencies
within the well borehole data complicated the interpolation stage of creating the model. A
majority of wells only have driller logs instead of the more favorable geologist or lithologic logs.
15

Drillers do not have universal standards for descriptions or sampling intervals, and many do not
have geologic training. Because there are no standard requirements, many logs do not contain
sufficient information to discern hydrogeologic units and may not accurately reflect the
permeability of an interval.
Even amongst the wells that do have adequate logs, the descriptions, and by extension
coding, of units varies. Additionally, due to the drillers’ lack of geologic training, there is no
guarantee that the descriptions are accurate. For example, an interval may be described as
“granite”, implying no permeability, when in reality, it should have been described as “fractured
granite,” which is instead highly permeable. Errors such as these may obscure the true extent of
permeable units, causing inaccurate representations and correlations. Unfortunately, there is little
that can be done to correct these issues or verify the descriptions’ accuracies, since many drillers
discard the borehole materials after the log is complete. Logs that seem inconsistent with their
surrounding area may be flagged as potentially erroneous but must still be included in the model.
To selectively exclude these wells because they seem inconsistent would introduce bias in the
model and would not be true to the data available.
Other data that is used to improve model accuracy include a digital elevation model
(DEM) produced by and freely available through the USGS. The logs need to be plotted relative
to the surface elevation at the wells’ locations for proper correlation. The DEM, which has
approximately 30-meter planar resolution and 3-meter vertical resolution, is used to define
surface elevation. All data needs are summarized in Appendix A.
16

3.3 Design
3.3.1. Well selection
The first step in this process is deciding which wells to include in the model. There is no
readily available database of well permeability status, and the time necessary to manually input
that data for every single well in the study area would be far greater than that available for this
study. For this reason, the wells are sampled from rather than including all available data.
To begin, the well logs must first be geocoded. Thanks to the GWSI database, this step
was almost entirely automated. The database contains latitude and longitude coordinates for all
wells that have been visited by ADWR field staff, as well as identifying information such as the
wells registration identification numbers. Because registration documents, and by extension the
borehole logs they contain, are stored by registration number, these files were easily joined to a
shapefile of GWSI points to complete the geocoding. In this process, only matches were kept
when joining the registration data so that only wells with completed logs were included. Finally,
to speed processing time, the wells were clipped within a ten-mile buffer of the study area. The
buffer helps minimize edge effects.
Once the data is reduced to only include the study area, the wells may be sampled. They
were sampled to be approximately one mile apart by overlaying a one-mile fishnet grid on the
study area and selecting the most central feature in each cell using the Central Feature tool. This
method assures as even a distribution of data as possible. Due to artifacts from old data entry
methods, some grid cells returned multiple central features with the same geographic
coordinates. In this case, the first log of the group was selected for inclusion to prevent the
introduction of biases.
17

3.3.2. Interpolation
Once the wells are selected for inclusion, they can be digitized. As mentioned in section
3.1, the fifty-foot intervals were assigned one of three values based on the dominant permeability
status. Driller descriptions typically include a number of keywords that can be used to determine
permeability, with the first material listed typically being the most dominant. To clarify, an
interval listed as clay and sand would be determined to be mostly clay with some sand and thus
designated impermeable. If the interval were instead described as sand and clay, it would be
deemed permeable since sand is interpreted as the dominant material. A full list of keywords
encountered while digitizing logs is included in Table 1, as well as whether they are permeable
or not.
The spaces between well locations can then be interpolated. In this case, Empirical
Bayesian Kriging (EBK) is used (Neinkamp 2016). The three-dimensional version of EBK,
available through ArcGIS Pro, is used to avoid the time-consuming process of interpolating
individual layers. Instead, the tool is run on all the data at once to produce a singular output. This
output illustrates the predicted permeability throughout a series of stacked “sheets” that can be
scrolled through to view different depths in the model.
There are six semivariogram models that can be used in the interpolation. In order to
select the best fitting one, interpolation using each model was run on a subset of the data
consisting of 151 data points. All parameters besides the semivariogram model were kept at their
default values for this test. When all models were tested, the Whittle semivariogram model was
found to produce the most realistic and true-to-data results. The cross-validation results were
used to reach this decision, but it should be noted that this validation method is intended for
continuous data. As such, the results should be viewed as a way of comparing outputs instead of
18

a scientifically meaningful validation of the output itself. The results of the semivariogram
comparison are included in Table 2.
Table 1: Material permeability. A table listing all keywords used to determine permeability.
Drillers' logs contain these keywords in various combinations with many different descriptors to
create unique logs for a well.
Permeable materials
Sands Conglomerate Cinders "Lost circulation"
Gravel Breccia Verde Formation Coconino sandstone
"Fractured" anything Malapai Kaibab Limestone Alluvium
Cavernous or honeycomb
limestone
"Soft" anything Toroweap formation Redwall Limestone
Martin Formation Tuff Schnebly Hill Formation Dolomite

Impermeable materials
Clay Limestone Hickey Formation Metamorphics
Silt Volcanics or basalt Supai Group Shale
Bedrock Caliche

19

Table 2: Semivariogram model selection. Cross-validation results comparing the various
available semivariogram models on a subset of the data.
Semivariogram
model
Average
CRPS
Inside
90%
Inside
95%
RMSE
RMSE
Standardized
Average
Standard
Error
Goal:
Small as
possible
= 90 = 95
Small
as
possible
= 1
Small as
possible
Power 20.75 87.42 90.72 37.24 0.99 37.56
Linear 20.98 88.08 91.39 37.64 0.99 38.24
Thin plate
spline
21.51 88.75 92.05 38.75 0.98 40.16
Exponential 20.72 88.74 90.07 37.4 1 37.52
Whittle 20.73 88.74 90.07 37.38 1 37.41
K-bessel 20.73 88.08 90.07 37.36 1.01 37.42

Once the semivariogram was selected, the interpolation could be run on the full dataset. It
was run a total of five times, changing various parameters each time in order to get the most
accurate results. Again, the output of cross-validation was used to compare the outputs but
should not be considered a validation of the output. The parameter settings found to produce the
most realistic results used the Whittle semivariogram, overlap factor of 3, 200 simulations, and
first-order trend removal. Though it would be interesting to examine if other-order trend
removals would be more appropriate for the data, the only options presented in this
interpolation’s parameters are first-order or no trend removal. Table 3 outlines the comparison of
runs with custom parameters.

20

Table 3: Parameter comparison. A comparison of the cross-validation results on the full dataset
using the Whittle semivariogram and various custom parameters.

Average
CRPS
Inside
90%
Inside
95%
RMSE
RMS
Standardized
Average
Standard
Error Notes
Goal:
Small as
possible
= 90 = 95
Small as
possible
= 1
Small as
possible
Default
parameters
14.61 85.8 91.05 28.75 0.97 28.93
Custom1 14.41 85.28 91.18 28.5 0.97 28.55
Overlap factor 3. 100
simulations.
Custom2 14.39 85.25 91.13 28.5 0.97 28.51
Overlap factor 3. 200
simulations.
Custom3 12 85 90.54 29.35 1.3 26.39
Overlap factor 3. 200
simulations. Empirical
transformation.
Custom4 14.32 85.25 91.19 28.32 0.97 28.51
Overlap factor 3. 200
simulations. No
transformation. First-
order trend removal.

3.3.3. Analyses and demonstrations
Upon completion of model construction, the model must be checked for accuracy and
validity. The model is manually cross-validated for an analysis of accuracy. To do this, a number
of wells are examined that were not included in the model’s creation. As with the interpolated
wells, they are divided into 50-foot intervals that are deemed primarily permeable or not. Those
same intervals are plotted in the model to determine predicted permeability. Matches between the
model and log are counted as correct, mismatches are counted as errors. For the purposes of this
study, a probability of 50% or higher is considered permeable, and thus a positive location of the
aquifer, but future users may set the cut off to better suit their needs. For example, a driller may
want to avoid drilling an area with under 70% certainty and so would only be concerned with
locations above that threshold.
21

The final step in this process is to demonstrate ways in which the model can be used.
After all, having this visualization is great, but it is ultimately unnecessary if it does not make
answering questions easier than current data forms. To illustrate the improvement this model
offers over traditional ways of working with the data, four wells throughout the study area were
selected. These wells included information on where water was encountered during drilling or if
the well was completely dry. Each 50-foot interval past the last water encounter is considered an
error, since the driller is assumed to have expected water at the greater depths. Additionally,
wells that were dry at the time of drilling are counted as incorrect at all intervals, as the driller
expected to encounter water at some point in the well.
22

Chapter 4 Results
This chapter discusses the results of creating and validating the model. It also includes a
measurement of accuracy for traditional methods for drilling decision-making.
4.1. Model
Interpolating the well information yields a model consisting of layers illustrating
permeability likelihood. Each layer represents one foot of depth. They can be scrolled through
individually using the slider bar, or a range of values can be viewed at once by setting the top
and bottom values on the slider bar.
In this model, darker blues represent greater certainty that the interval is permeable. By
extension, these are also the intervals where the aquifer is most likely to be present. In Figures 4a
through d below, only areas with 50 percent likelihood or greater are symbolized. The layers are
shown in 500-foot aggregates in order to illustrate general trends with decreasing elevation, but
any range of values can be represented.
At higher elevations, the aquifer is most likely to be in the southern portion of the study
area. With increasing depth, the likelihood switches to be more probable in the northern portion
of the study area.
23

Figure 4a: 500-foot aggregate of the
model. The interval shown is from the
highest elevation, 2386 feet above datum,
to 1886 feet.
4b: The next 500 feet in the model.
Elevations represented are 1886 feet to
1386 feet.
4c: Elevations represented are 1386 feet
to 886 feet.
4d: Elevations are 886 feet to 386 feet.
24

4.2. Validation
Validating the model yielded imperfect results. Four wells’ drillers’ logs were compared
to the model output in order to determine whether the model accurately predicts permeability or
not throughout the study area. These wells are shown in Figure 5. The four wells, randomly
selected to represent their respective quadrants of the study area, consisted of a total of 35
intervals. Of those intervals, 14 did not have model-predicted permeability consistent with the
permeability predicted based on the drillers’ logs. This is a 60 percent accuracy.
The northeastern well, ID 203937, presented some issues during validation. Based on the
driller’s log, this well was drilled through different materials than its neighbors. Because of this,
its permeability does not match its neighbors’ and was predicted incorrectly for the majority of
its intervals. Had this well not been included in the validation, the accuracy would have been 80
percent, or 20 of 25 intervals. Future work will have to examine if the model does a poor job
representing that region of the study area or
if that well happens to be a fluke. The
results of validation for each interval are
included in Appendix B.

Figure 5: The four wells used to validate the
model.
25

4.3. Accuracy without the model
To see if the interpolated model offered any improvement over the more traditional ways
of deciding where and how to deep to drill, a comparable analysis of error was conducted on four
similarly spaced wells. The locations of these wells are shown in Figure 6. These wells all had
notes on their drillers’ logs indicating the depth at which water was encountered or if the well
was dry at the time of drilling. From these, the drillers’ predictions of water location were noted
as either correct or incorrect. If the well was dry, the full length was deemed incorrect since the
driller assumed there would be water at some point in that drilling. Likewise, all depths drilled
past the last water encountered were also considered incorrect. This is based on the assumption
that the driller believed more water could be encountered by drilling deeper. Except in the case
of dry wells, all intervals above the first water are designated “correct” because the driller would
have assumed the need to drill deeper to reach water.
With these four wells, a total of 33
intervals were examined for accuracy.
Of those intervals, 19 were incorrect.
This equals an error of 57.6%, or a
42.4% accuracy. The results for each
interval can be seen in Appendix C.
A nearly all of the incorrect
intervals, specifically 17 of them, come
from a single well that was dry at the
time of drilling. This well, ID 229762, is
the northeastern one of the group. An Figure 6: The location of wells used to examine
standard drilling placement methods.
26

examination of this borehole log and its neighbors reveals a similar situation to the problematic
model validation site. That is to say that this well is also through different material than its
neighbors- the area changes rapidly between granite, basalt, ash, and other volcanic materials.

27

Chapter 5 Conclusions
This study created a 3D model of the aquifer located under Prescott, Arizona. Wells were
selected to be approximately one mile apart and cover the full study area. Drillers’ logs were
examined in 50-foot intervals to determine permeability based on the materials drilled through.
This information was then interpolated using Empirical Bayesian Kriging 3D in order to create
prediction surfaces indicating how likely locations are to be permeable and thus act as an aquifer.
Four wells were selected to evaluate accuracy for both the model and traditional methods of
drilling.
Results indicate that the model is significantly more accurate than traditional methods,
with the methods having 60 percent and 42.4 percent accuracies, respectively. Both assessments
of accuracy include a single well with completely or nearly completely inaccurate predictions. In
both instances, this well is the northeastern well of the group. This suggests that the geology of
this region in the study area is more complicated than previously believed and is therefore
difficult to predict aquifer locations from. The model performs poorly in such areas and should
not be used in its current state to predict aquifer locations in areas that are not relatively
homogenous. Still, when it comes to these two wells, the model performs better than traditional
methods. The model predicted 1 of 10 intervals correctly, or 10 percent accuracy, whereas
traditional methods predicted 0 of 17 correctly, 0 percent accuracy.
Though this model offers greater accuracy over standard decision-making methods for
drilling, there is still plenty of room for improvement. As indicated by the low accuracy in
heterogenous areas, the model cannot confidently be applied to areas with rapidly changing
geology. Future iterations of this project could digitize the wells exactly as described in their logs
instead of using 50-foot intervals. The output has one-foot vertical resolution anyway, and doing
28

so would allow finer scale vertical changes to be captured and could potentially improve
accuracy, especially in the northeastern region. Future versions may investigate other
interpolation methods, as well. Though EBK was deemed most appropriate of the methods
considered, the extent to which the user can control parameters in universal kriging could
potentially increase the model’s accuracy further. Whether another interpolation method is tested
or not, it is critical that the current model be further validated using methods such as leave-one-
out.
An additional use that I would like to illustrate in the future, which would be especially
interesting to researchers, is incorporating and updating water levels yearly to track changes
within the aquifer. Having these changes illustrated, rather than just listed in tables, could help
researchers quickly spot areas with sharp declines in water levels and address the causes before it
becomes a major water shortage. It could also help scientists notice when water levels are
nearing the bottom of the permeable layer, indicating the end of the aquifer’s utility. Adding this
extra layer of information would also help improve the model. Water levels that are inconsistent
with the model, such as being deeper than the permeable layer, would provoke deeper
exploration of the area’s geology and possibly revision of the model.
With the average well costing between 10 and 30 dollars per foot to drill (Merrill Drillng
& Water Systems 2020), any misjudgment in placement or necessary depth can quickly become
costly. In the case of the dry well discussed in the results chapter, the well was drilled to 808
feet- at an average cost of $20 per foot, that mistake cost over $16,000. Having a model such as
the one created in this project could help prevent these dramatic losses that can be disastrous for
the well-owner. One well driller based in Utah notes on their site that "in most cases, the depth
required to produce an adequate yield from the groundwater supply cannot be determined before
29

drilling begins" (Mike Zimmerman Well Service LLC 2015). Though few drillers are as open
about the topic, this sentiment seems to be shared by most drillers. In a state like Arizona, where
water is in short-supply and high-demand, this is not acceptable. The model developed for the
present study represents a step towards a more systematic and scientific approach to well
drilling— one that will result in higher confidence before drilling and less wasted resources for
all involved parties.

30

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34

Appendix A Data
Precision
Not ideal.
Drillers are
inconsistent
with
observation
intervals when
completing logs
High – strict
standards and
quality checks
in place
Med-high
Accuracy
Not ideal.
Drillers are
inconsistent
with
descriptions
when
completing
logs
Location
information to
0.5 seconds.
Water level to
0.1 foot
Approx. 30 m
horizontal, 3 m
vertical
Scale
Statewide.
Clip to study
area.
Statewide.
Clip to study
area.
Nationwide.
Clip to study
area.
Source
Conde et al.
2014, De
Donatis et al.
2005, Gootee
et al. 2017,
Neinkamp
2016, Nury et
al. 2010
Conde et al.
2014, De
Donatis et al.
2005, Gootee
et al. 2017,
Neinkamp
2016, Nury et
al. 2010
Conde et al.
2014, De
Donatis et al.
2005, Nury et
al. 2010
Quality
Good.
Format is
inconvenient,
but all wells
have complete
records that
can be
digitized.
Good. All
data is field
verified and
quality
assured.
Good
Attributes
Well Reg
ID, Drill
Code, USCS
Code, Layer
Top, Layer
Bottom
Latitude,
Longitude,
Well Reg
ID, Basin,
Depth to
Water
Elevation
Format
PDF
Oracle
Database
Raster
Content
Scanned copies of
the borehole logs.
Not geocoded,
joined to
corresponding
Groundwater Site
Inventory (GWSI)
point for location
All identifying
information on
field verified sites.
Geocoded by
NAD27
coordinates in
degrees, minutes,
and seconds
1/3 arc-second
resolution
elevation data
Dataset
Borehole
logs
ADWR
GWSI
Database
DEM
35

Appendix B Model Validation Results
Registry ID Cadastral
Interval
Top
Interval
Bottom
Top
Elevation
Bottom
Elevation
Permeability
Model
Prediction
085371 B16002011ACD 0 50 1396 1346 N N
085371 B16002011ACD 50 100 1346 1296 N N
085371 B16002011ACD 100 150 1296 1246 N N
085371 B16002011ACD 150 200 1246 1196 N N
085371 B16002011ACD 200 250 1196 1146 N N
085371 B16002011ACD 250 300 1146 1096 N N
085371 B16002011ACD 300 350 1096 1046 Y N
085371 B16002011ACD 350 400 1046 996 Y Y
085708 B14002023DDC 0 50 1579 1529 Y Y
085708 B14002023DDC 50 100 1529 1479 Y Y
085708 B14002023DDC 100 150 1479 1429 Y Y
085708 B14002023DDC 150 200 1429 1379 Y Y
085708 B14002023DDC 200 250 1379 1329 Y Y
085708 B14002023DDC 250 300 1329 1279 Y Y
085708 B14002023DDC 300 350 1279 1229 N Y
085708 B14002023DDC 350 400 1229 1179 Y Y
085708 B14002023DDC 400 450 1179 1129 Y Y
200015 A13001012DCB 0 50 1430 1380 Y N
200015 A13001012DCB 50 100 1380 1330 N N
200015 A13001012DCB 100 150 1330 1280 N N
200015 A13001012DCB 150 200 1280 1230 N N
200015 A13001012DCB 200 250 1230 1180 N N
200015 A13001012DCB 250 300 1180 1130 N N
200015 A13001012DCB 300 350 1130 1080 Y N
200015 A13001012DCB 350 400 1080 1030 Y N
203937 A15001013BBA 0 50 1686 1636 N N
203937 A15001013BBA 50 100 1636 1586 Y N
203937 A15001013BBA 100 150 1586 1536 Y N
203937 A15001013BBA 150 200 1536 1486 Y N
203937 A15001013BBA 200 250 1486 1436 Y N
203937 A15001013BBA 250 300 1436 1386 Y N
203937 A15001013BBA 300 350 1386 1336 Y N
203937 A15001013BBA 350 400 1336 1286 Y N
203937 A15001013BBA 400 450 1286 1236 Y N
203937 A15001013BBA 450 500 1236 1186 Y N

36

Appendix C Traditional Method Accuracy
Registry ID Cadastral
Interval
Top
Interval
Bottom
Permeability Assumption
221467 A13001015DBD 0 50 Y C
221467 A13001015DBD 50 100 Y C
900258 B16002019DBC 0 50 N C
900258 B16002019DBC 50 100 N C
900258 B16002019DBC 100 150 N C
900258 B16002019DBC 150 200 N C
900258 B16002019DBC 200 250 N C
900258 B16002019DBC 250 300 Y C
900258 B16002019DBC 300 350 Y C
900258 B16002019DBC 350 400 Y C
900258 B16002019DBC 400 450 Y C
229762 A15001017CAB 0 50 N I
229762 A15001017CAB 50 100 N I
229762 A15001017CAB 100 150 N I
229762 A15001017CAB 150 200 N I
229762 A15001017CAB 200 250 N I
229762 A15001017CAB 250 300 N I
229762 A15001017CAB 300 350 N I
229762 A15001017CAB 350 400 N I
229762 A15001017CAB 400 450 N I
229762 A15001017CAB 450 500 N I
229762 A15001017CAB 500 550 N I
229762 A15001017CAB 550 600 N I
229762 A15001017CAB 600 650 N I
229762 A15001017CAB 650 700 N I
229762 A15001017CAB 700 750 N I
229762 A15001017CAB 750 800 N I
229762 A15001017CAB 800 850 N I
581540 B13002004CBB 0 50 Y C
581540 B13002004CBB 50 100 Y C
581540 B13002004CBB 100 150 N C
581540 B13002004CBB 150 200 N I
581540 B13002004CBB 200 250 N I

Abstract (if available)

Abstract Despite Arizona relying on Arizona groundwater to meet a significant portion of its water needs, the locations of Arizona’s groundwater aquifers are not fully mapped, and methods to interpolate the locations of aquifers from test boreholes remain inaccurate. In response, this study implements a workflow leveraging three-dimensional (3D) interpolation to fill in that knowledge gap within a study site: the Prescott Active Management Area surrounding Prescott, Arizona. Using borehole log data and digital elevation models, the 3D extent of permeable layers are mapped, serving as proxies for aquifers and aquitards, respectively. This project makes use of Empirical Bayesian Kriging 3D (EBK3D) to interpolate permeability data in three dimensions. When tested on four random boreholes, this model correctly predicted an aquifer 80% of the time in comparison to 42% using traditional 2D interpolation. The model’s improved accuracy provides an approach to improve drillers’, policymakers’, and scientists’ understanding of the hydrologic activity in the area. Such an improvement may lead to better-informed storage models, changes in water management, and greater cost efficiency when drilling new wells.

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Asset Metadata

Creator Cuesta, Amanda (author)

Core Title Filling in the gaps: 3D mapping Arizona's Basin and Range aquifer in the Prescott Active Management Area

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 06/16/2020

Defense Date 03/26/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3D mapping,aquifer mapping,Arizona,empirical Bayesian kriging,GIST,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Marx, Andrew (committee chair), Duan, Leilei (committee member), Swift, Jennifer (committee member)

Creator Email acuesta@tulane.edu,acuesta@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-318097

Unique identifier UC11663406

Identifier etd-CuestaAman-8592.pdf (filename),usctheses-c89-318097 (legacy record id)

Legacy Identifier etd-CuestaAman-8592.pdf

Dmrecord 318097

Document Type Thesis

Rights Cuesta, Amanda

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA