Creation of a Computer Modeling Course for Undergraduate
Earth Science Students
Kirsten M. Menking
Department of Geology and Geography, Vassar College, Poughkeepsie, NY
12604, [email protected]
ABSTRACT
Entire fields within the Earth sciences now exist in which
computer modeling has become the primary work of the
discipline. Undergraduate geology/Earth science
programs have been slow to adapt to this change, and
computer science offerings frequently do not meet
geology students' needs. To address these problems, a
course in Computer Modeling in the Earth Sciences has
been developed at Vassar College. The course uses the
STELLA (Structural Thinking Experimental Learning
Laboratory with Animation) iconographical box
modeling software to teach the fundamentals of
dynamical systems modeling and then builds on the
knowledge students have gained with STELLA to teach
introductory programming. Modeling topics include
U-Pb concordia/discordia dating techniques, the impact
of climate change on a chain of lakes in eastern
California, heat flow in permafrost, and flow of ice in
glaciers by plastic deformation. The course has been
received enthusiastically by students, who reported not
only that they enjoyed learning the process of modeling,
but also that they had a newfound appreciation for the
role of mathematics in geology. Fully documented and
debugged STELLA and Fortran models along with
reading lists, answer keys, and course notes are available
to anyone interested in teaching a course such as this.
INTRODUCTION
In recent years computer modeling has gained
importance in geological and environmental research as
a means to generate and test hypotheses and to allow
simulation of processes in places inaccessible to humans
(e.g., outer core fluid dynamics, see Olsen and others,
1999), too slow to permit observation (e.g.,
erosionally-induced uplift of topography, see Small and
Anderson, 1995), or too large to facilitate construction of
physical models (e.g., faulting on the San Andreas, see
Ward and Goes, 1993). Fields within the Earth Sciences
now exist in which computer modeling has become the
core work of the discipline. Examples include
simulations of past climates, seismic hazards, and
hydrogeology.
The increasing importance of computer modeling
has led to an apparent disconnection between the
direction in which geological research is moving and the
curriculum in many undergraduate programs.
Examination of course offerings at several highly
selective undergraduate institutions reveals that none
offer a course in computer modeling in geology. Thus, as
students begin their graduate research careers, they may
enter the world of modeling with little or no preparation.
While undergraduate Earth science students should,
in theory, be able to take courses in computer science to
address their future computational needs, in practice,
finding suitable courses can be difficult. For example,
with the exception of one independent study course, the
Vassar College Computer Science department does not
464
offer courses in individual programming languages.
Instead, they teach courses such as Software
Development Methodology, Computer Organization,
Algorithmics, and Artificial Intelligence. While these
courses are appropriate for students majoring in
computer science, they do not serve geology students'
needs. It is for these reasons that I decided to create a
course that would address the mechanics of computer
modeling within the context of geologic and
environmental problems. Students would learn how to
glean relevant information from the primary literature,
how to break down complex geological and
environmental problems into their component parts and
relationships, how to represent those parts symbolically,
and how to relate them to one another mathematically.
In creating a course in Computer Modeling in the
Earth Sciences, my goal was also to motivate students to
enhance their mathematical abilities. While I have found
geology students to be quite capable in mathematics,
many express anxiety over perceived inadequacies and
are reticent to enroll in math courses that would prove
useful to them in their future careers. Furthermore, while
many students are readily able to manipulate and solve
equations, they don't know where to begin when asked
to solve real problems. In creating the Computer
Modeling in the Earth Sciences course, I hoped to
develop students' abilities in solving real world
problems and to build their confidence such that they
might be inspired to acquire further training in
mathematics.
I have taught the course three times now, and the
sections that follow describe the pedagogical tools that I
have used, the course structure, student responses,
problems I have encountered, and availability of course
materials. In addition, the broader impacts of the course
on the undergraduate curriculum and on students'
post-graduation careers are considered.
SOFTWARE
Building on the work of DeWet (1994), Moore and Derry
(1995), Levy and Mayer (1999), and Bice (2001), I chose
the STELLA (Structural Thinking Experimental Learning
Laboratory with Animation) icon-based dynamical
systems modeling software developed by High
Performance Systems, Inc. (now Isee Systems) for this
course. STELLA is a finite difference modeling tool
designed to facilitate understanding of complex systems
composed of multiple interacting components. It has
been used to research such widely ranging topics as
hydrological processes (Lee, 1993), impact of
eutrophication on dinoflagellate populations (Costanza
and Gottlieb, 1998), crude oil exploration and depletion
(Ruth and Cleveland, 1993), and the inorganic carbon
cycle in a near-shore coastal area (Norro and
Frankignoulle, 1996).
STELLA, although applicable to complex basic
research, is also easy to use and therefore accessible to
students. The software allows visual representation of
reservoirs and fluxes as boxes connected by flow arrows
Journal of Geoscience Education, v. 54, n. 4, September, 2006, p. 464-470
Figure 1. STELLA model graphic of a course exercise designed to explore the impact of climate change on the
Owens River chain of lakes in eastern California. (a) Runoff from the Sierra Nevada mountains fills the box
representing Owens Lake, whose volume is then used to determine the lake surface area. This surface area is
multiplied by an evaporation rate to determine the volume of water removed from the lake ("evap from
Owens" outflow arrow). If the amount of water remaining in the lake after the evaporation step exceeds the
maximum volume the lake can hold, excess water is transferred to the next lake in the chain ("overflow to
China" arrow). Additional converters (circles) hold volume/depth relationships, and maximum area (O max a)
and depth (O max d) boundary conditions. (b) Location map of the Owens chain of lakes. c) Chart showing
cyclic (sine curve) changes in runoff from Sierra Nevada and subsequent effect on Owens River chain of lakes.
(figure 1). Dependencies of variables are represented
with linking arrows, and circles, called converters, hold
values of constants and equations. A few clicks of the
mouse allow the user to set initial conditions, model time
step, mathematical relationships between variables, and
simulation length. An internal graphing program allows
the modeler to watch the progress of up to five different
variables at a time.
While students can construct their models entirely
within the iconographic interface, they can also view the
equations the computer must solve by going to the
equation level of the software (figure 2). This equation
level serves as a convenient bridge to programming, and
as students grow in competence and confidence in their
STELLA modeling, I introduce them to Fortran, one of
the most widely used programming languages in the
Earth Sciences today. The process of coding requires
students to learn how the computer handles real versus
integer numbers, how the computer keeps track of
variable values from timestep to timestep by means of
dimensioned arrays, how "do loops" are constructed, and
how logical statements work. To facilitate the Fortran
programming I use Compaq's Visual Fortran software,
which includes a helpful color-coding system for
different program components, and which also has a
compiler that makes debugging of program errors
straightforward.
COURSE FORMAT
The Computer Modeling in the Earth Sciences course is a
senior seminar-level course taken primarily by juniors
and seniors. The format of the course has been as follows:
each week, a different pair of students was responsible
for presenting readings taken from the geological
literature that formed the basis for that week's modeling
Menking - Creation of a Computer Modeling Course for Undergraduate Earth Science Students
465
Figure 2. Equation level in STELLA for the model shown in figure 1. Only equations for the Owens Lake
reservoir are shown. First line shows the basic differential equation the computer solves to update the Owens
Lake volume reservoir each timestep. Second line shows initial condition for Owens Lake reservoir. For
OUTFLOWS, the amount of water evaporating from Owens Lake in each time step is determined by
multiplying lake surface area by 1.34 m/yr vertical evaporation rate. Overflow to China lake occurs if lake
volume continues to exceed the maximum volume of the lake at its spill threshold after the evaporation step.
Owens Lake’s depth and area are determined based on the volume in the reservoir. If the volume in the
reservoir is less than or equal to zero, depth and area are set to zero. If the volume in the reservoir is at the
maximum spill threshold, depth and area are set to their maximum values.
project. Students then carried out an exercise designed to
assist them in creating their models. In developing each
exercise, I tried to minimize "cookbooking," and instead
aimed to have the students generate their models largely
independently, with my role being to facilitate their
conceptualization of each problem and to offer hints
when they got stuck. In each succeeding week, I gave the
students fewer clues as to how to construct their models,
such that by the end of the semester, they were on their
own.
Once the students completed their models, I gave
them a series of experiments to perform to develop an
understanding of system dynamics. As with model
construction, students were initially given more
assistance and then were gradually expected to develop
their own experiments to foster their abilities to create
and test hypotheses. An independent modeling project
toward the end of the semester allowed each student to
explore individual interests and culminated in a
substantial paper and presentation to the class. Grades
were based on the weekly modeling assignments,
weekly presentations, and the various components of the
independent modeling project.
The class met one day a week in a four-hour block. I
decided to teach the course in this format based largely
on my own experience with modeling. I have found that I
need a long block of uninterrupted time to create a
model, either in STELLA or in Fortran. If I am forced to
take my attention away from the model for a period of
days, I need between a half hour and a day (depending
466
on the complexity of the model) to refresh my memory of
where I was in the process. Colleagues who model have
expressed similar needs for long, uninterrupted time
blocks, and student evaluations of the course indicate
that the format was highly effective.
Modeling concepts covered in the course included
open vs. closed systems; behavior of systems, including
steady state, oscillation, linear growth and decay, and
exponential growth and decay; positive and negative
feedback loops; response and residence times; initial and
boundary conditions; if-then-else logical statements;
different integration methods, such as Euler and
Runge-Kutta; how to choose a time step; how to
determine the appropriate level of model complexity;
and the limitations of models. Modeling topics included
the global phosphorus cycle, U-Pb concordia/discordia
dating techniques, heat flow in permafrost, Earth's
energy balance and temperature, James Lovelock's
Daisyworld, the impact of climate change on a chain of
lakes in eastern California, and scarp diffusion.
Students were enthusiastic about their independent
projects, and used them to explore both geological
processes and phenomena from other disciplines in
which they were double-majoring. Their projects
included biological controls on purple loosestrife, an
invasive plant; eutrophication of Lake George in upstate
NY; flow of water in the Hudson and Yangtze Rivers;
isostatic uplift and glacial rebound; the Wage-Fund
Doctrine economic model; a model of traffic flow
incorporating a stop light; flow of groundwater via
Journal of Geoscience Education, v. 54, n. 4, September, 2006, p. 464-470
Darcy's Law; predator-prey relationships; and the flow
of ice in glaciers by plastic deformation (since developed
into a modeling exercise). Because many of these topics
were beyond my abilities to assist them in the limited
time available, students were evaluated not on the
success or failure of their models to replicate observed
behavior but on the quality of the project, presentation,
and final paper. For those whose models did not yet
work by the end of the semester, I was particularly
interested in their abilities to critically analyze their work
and to explain what they thought might need to be
changed in order to get their models to replicate
observed behavior.
I taught an initial version of the Computer Modeling
in the Earth Sciences course to ten students in the spring
of 2001, using only the STELLA software. In June of that
year, I received National Science Foundation funding
that allowed me to incorporate Fortran programming
and formal evaluation of the course the next two times it
was taught, in spring 2003 (six students) and spring 2005
(four students). The apparent decline in enrollment for
the course each time it was offered was related not to the
course itself but to fluctuations in the number of students
opting to major in geology over that time interval.
Typical enrollments for Vassar geology senior seminar
courses are around 5 +/- 2 students, and the class of 2001
was unusually large, having 12 total members, eight of
whom decided to take the modeling course.
STUDENT RESPONSES TO THE COURSE
For the most part, I was amazed by my students'
enthusiasm for the class. In all three offerings, they
thoroughly enjoyed working with STELLA, particularly
when it came time for them to do their independent
projects. Some students expressed frustration with
modeling throughout the course, but their frustration
generally gave way to "high-fives" and shouts of "we are
so cool!" when they successfully debugged their models
and got them to work. I had anticipated that students
would need a lot of encouragement in developing their
modeling skills, and I found myself in the role of
coach/cheer leader as much as in the role of teacher. At
the same time, the students really took ownership of the
course, and I often found them working on their weekly
modeling projects and presentations late on Friday
evenings, a testament to how seriously they took the
class and to how much they enjoyed it.
I was impressed with my students' ability to pick up
Fortran in the 2003 and 2005 semesters. They wrote their
first program after only three weeks of class, and
required much less help in debugging their codes than
anticipated. Students were able to use the equations from
their STELLA models in their Fortran codes and then
focus on the looping structure, declaration and
dimensioning of variables, and input and output
commands that Fortran requires.
In the 2003 and 2005 offerings of the course, I
administered formal questionnaires at the beginning and
end of the semester to gauge my students' levels of
preparedness for the course, attitudes towards
mathematics, and feelings about how the course
impacted their knowledge and abilities. These
questionnaires and summaries of students' narrative
responses can be obtained from the authors.
In the end of class questionnaire, students reported
that they felt the course was highly effective in teaching
the basics of system dynamics and how systems could be
modeled, that they found the iconographic structure of
STELLA very useful in learning modeling, and that the
STELLA modeling prepared them well for the work in
Fortran. Responses to the question 'how would you
describe the impact of this course on your general
understanding of system dynamics and of how systems
can be modeled?' included:
''Before I took this course I had no idea how people
knew what they knew about systems with large scales
and long timescales. Now I see how useful a
computer model can be to understanding this. I also
learned that the models can be simple but still give a
lot of information. This class has been so useful in
making geologic problems realistic."
"This class had a tremendous impact on my general
understanding of modeling and system dynamics. It
has helped me to realize how valuable modeling can
be in geology and how to go about modeling a
problem."
"I have learned much particularly in regards to
troubleshooting and assessing the limitations of
models, running experiments with models and both
simplifying and adding complexity to modeled
systems."
"Highly effective, I now understand what modeling a
system consists of and can think about such relations
mathematically much better than I could six months
ago."
Like Moore and Derry (1995), I found that my
students developed feelings of competence and
empowerment from their new skills and that they
enjoyed the creative aspects of modeling. Due to time
and budgetary constraints, high school science classes
often present science as a catalog of facts to be learned,
rather than as a creative process. As a consequence,
undergraduate students often do not understand how to
construct hypotheses from observational data or how to
test those hypotheses (PKAL, 2000). By its very nature,
computer modeling fosters experimentation, and
students in my course came to see that geology is a
dynamic science to which they can contribute, not just a
body of knowledge to be memorized.
MATHEMATICAL SKILLS AND ATTITUDES
I administered an initial quiz/questionnaire, in which
students were asked to solve a number of problems and
were also asked what level of math they had attained to
that point and their comfort level with math. The
questionnaire component can be obtained from the
authors. Of the ten students taking the course in the 2003
and 2005 semesters, three were double-majoring in
physics or math and had taken courses in linear algebra,
ordinary differential equations, and multivariable
calculus; two more had advanced beyond calculus to
linear algebra; three had taken 1-2 semesters of college
calculus; and two had not taken math beyond high
school calculus. Two out of ten students found math
difficult, frustrating, and not particularly relevant.
Another five expressed neutral attitudes, stating that
they sometimes enjoyed math, but often found it difficult
and frustrating. Not surprisingly, the three physics and
math double majors said they loved math.
Menking - Creation of a Computer Modeling Course for Undergraduate Earth Science Students
467
Figure 3. Improvement in quiz scores over the semester as a function of mathematical preparation and
attitudes towards math. Students with weaker math backgrounds and with more negative attitudes towards
math showed the greatest improvement in their quiz scores over the semester (% change = percentage of
correct answers on end of semester quiz minus percentage of correct answers on beginning of semester quiz).
The basic quiz that I administered, covering
algebraic operations, trigonometry, exponentials, unit
conversions, story problems, and asking students to link
mathematical concepts to geological phenomena (such
as exponential decay and radioactive decay of isotopes or
oscillatory behavior and diurnal cycles) revealed, not
surprisingly, more difficulty among those students who
had weaker preparation and those who found math
difficult than among those who enjoyed math and had
taken courses beyond calculus.
The course appears to have had a large impact on the
students with weaker math backgrounds. A quiz
administered at the end of the semester revealed a
substantial improvement in their mathematical abilities
(figure 3), which was matched by a change in attitude
toward math. In response to the question 'Did the course
have any impact on your understanding of the
usefulness of math in geology?' students said:
"Yes, this is one of the only courses which has done
so."
"Yes, it had a huge impact. This class showed me that
calculus is very important in the study of geology.
Because of this class I'm planning on taking calculus."
"DEFINITELY!! I am going to try and improve my
math skills and fix any holes and deficiencies I have."
"I already had faith in the importance/usefulness of
math in geology and this course has helped confirm
these feelings."
468
"Yea - now I wish I'd taken more math. I may take
some next year but haven't had any since freshman
year. For the practical applications such as this you
have to be able to truly understand it, not just do it."
These comments reveal that students no longer
regarded math as a subject beyond their abilities, but
rather as a body of knowledge and method for solving
problems that they were entitled to learn. Indeed, three
of the five students who had taken only high school or
college calculus, when asked this question, replied that
the course had profoundly influenced them and that they
planned to enroll in more math in the near future. Two of
these students did in fact do so.
STUDENT DIFFICULTIES
While the Computer Modeling in the Earth Sciences
course has proven to be highly effective in meeting its
goals, I also encountered a number of difficulties. First,
some students had difficulty analyzing their model
results critically and finding mistakes in their models.
These students often tried to explain their results by
invoking relationships between variables that were not
explicitly incorporated into their models or by
attributing their results to factors that they did not
include in their models. For example, a student might
call upon changes in temperature during the late
Pleistocene to explain the faulty behavior of a model
designed to assess the impact of changes in runoff on
lake levels, despite the fact that the model did not
incorporate any kind of temperature dependence.
Typically the student miscast an equation somewhere or
neglected to specify a boundary condition that led the
Journal of Geoscience Education, v. 54, n. 4, September, 2006, p. 464-470
model to behave incorrectly. Some students had great
difficulty understanding that results were not
automatically valid and correct, and therefore used
convoluted reasoning to try to explain their results.
While most students eventually learned to critically
analyze their results and to trust their intuitions when
confronted with results that didn't make sense, there
occasionally were one or two who didn't by the time the
semester ended.
Another problem is that the majority of students had
difficulty with casting equations such that the order of
operations was carried out correctly. They often
misplaced parentheses and seemed quite stymied by
how to represent long, complicated equations in the
parenthetical form required by the computer. Due to the
nature of the course, with students developing their own
models and codes, it took a lot of time to debug
problems, and I found myself spending 20 minutes at a
time with an individual student trying to find the one
misplaced parenthesis before being able to move on to
the next student. This meant that students were often
waiting for help, a situation that could be rectified by use
of a teaching assistant.
BROADER IMPACTS OF THE COURSE
Figure
4.
Use
of
numerical
modeling
by
Earth/Environmental Science graduate students.
Students have used models in their own thesis and
dissertation research (Research) or in courses such as
Hydrogeology (Coursework). Fully half of students
have had to evaluate model outputs reported in the
geologic literature (Evaluation). A minority reported
no involvement with modeling (Not used).
The Computer Modeling in the Earth Sciences course has
impacted other areas of the curriculum in the Geology
and Environmental Studies programs at Vassar College.
STELLA models are now part of the introductory
environmental geology course, a senior seminar in
Paleoclimatology, and the Essentials of Environmental
Science, taught in the Environmental Studies program.
In addition, students who took the modeling course have
been able to conduct senior thesis research incorporating
numerical modeling. In 2000-2001, two students used the
U.S. Department of Agriculture Soil and Water
Assessment Tool (SWAT) rainfall/runoff model (Arnold
et al., 1996) to assess the impact of global climate change
on the water supply for Portland, Oregon. Another
student used the SWAT model in 2003-2004 to simulate
flow of the Casperkill stream that runs through the
Vassar College campus. Part of this student's work
involved writing Fortran programs to compute total
daily rainfall and to select daily maximum and minimum
air temperatures from 20-minute measurements of these
variables made at our campus meteorological station.
Another student created a STELLA model for her senior
thesis on the impacts of deforestation in Nepal.
To assess the extent to which students were engaging
in modeling after graduating from Vassar, I
administered an alumni survey in the spring of 2005. I
was able to get in touch with 32 of the 53 students who
graduated between 1998 and 2004, and designed two
surveys, one for those students who had taken my
modeling course and one for those who hadn't.
Questions for both groups included whether they were
still involved in the Earth Sciences, either in graduate
school or in a job, whether they were involved in any
numerical modeling work, and if so, what computer
languages they used. Those who hadn't taken my course
were asked to provide information on where they
acquired their modeling skills and whether having had
an introduction to modeling at Vassar would have been
helpful. The group that took the Vassar modeling course
was asked whether the course had prepared them for the
work they were now doing. While several students were
no longer involved in Earth Science/geology, nearly
three quarters were in graduate school in some aspect of
Earth or Environmental Science or were employed in
geologic consulting.
Of the fourteen students in Earth or Environmental
Science graduate programs, 43% were involved in
modeling as part of their own research, and fully half had
to evaluate modeling projects and results published in
the geological literature (figure 4). Seventy percent of
students engaged in modeling acquired their skills
entirely in graduate school, but only 30% of these
students had the benefit of being able to take a course in
modeling. The remaining 40% were either on their own
or had some assistance from a graduate advisor or fellow
students. About a third of the students now engaged in
modeling had taken the Vassar Computer Modeling in
Earth Sciences Course, but these students also reported
having to acquire additional knowledge on their own.
One student who is currently finishing a dissertation
in computational astrogeophysics, and who had no
experience with modeling prior to attending graduate
school, reported that she is modeling "24-7" and using
Fortran, C++, Matlab, and a host of other languages. She
stated that she "acquired [her] modeling skills during
grad school, through research hours and informal
channels. In other words, in the gutter," and stated that
having an introductory class in college, particularly in
Fortran, would have helped her enormously. Another
student who didn't have the Vassar course and is now
working on a Ph.D. in biogeochemistry stated "I never
got to take your modeling course, but I would have
added it to my course list if I knew what I now know,"
and yet another doing a Ph.D. in stable isotope ecology
responded "I feel like modeling has become the core of
Earth Science and I don't know what's going on most of
the time." This same student, when asked whether she
needs to incorporate others' modeling results into her
work said, "Yes, this happens frequently."
Another student who needs to rely on modeling
results reported by others spoke of the difficulty she has
in evaluating those results given that she never had a
modeling course: "I have enough knowledge to
Menking - Creation of a Computer Modeling Course for Undergraduate Earth Science Students
469
understand how models are used but I don't think I have
enough knowledge to really evaluate how
good/accurate a model is." Conversely, a student who
took the Vassar modeling course and is now in graduate
school in volcanology said that while he is not currently
modeling himself, "the conceptual understanding of how
models work and the practical knowledge of how they
are constructed have been invaluable skills that have
allowed [him] to intelligently evaluate and assess the
merits of modeling work conducted by [his] colleagues."
Another, who completed a master's in hydrological
modeling, reported that the Vassar course "helped [him]
understand the theoretical approach behind modeling
various systems." This student also spoke of the
importance of exposure to Fortran and Matlab.
It is quite clear that students understand the
importance of acquiring modeling skills, and that wider
training of geology/Earth science students in these skills
is necessary. Furthermore, the fact that so many students
are still left to acquire their modeling skills on their own
suggests that we as educators should be stepping in to fill
this need.
AVAILABLE COURSE MATERIALS
For anyone interested in teaching a course such as
Computer Modeling in the Earth Sciences, I have created
a website on which I have posted the syllabus for the
course, a reading list, documented STELLA and Fortran
models, copies of exercises and answer keys, and course
notes. I have also posted supplementary information that
explains the motivations behind each exercise,
background mathematics and concepts needed to
understand the exercise, and typical problems
encountered by students.
The course materials can be accessed by going to
http://blackboard.vassar.edu, selecting the Login
button, and then using the word "geoguest" for both the
login name and the password. Once logged into
Blackboard, select the ADMIN-GEOL-GRANT link in
the "My courses" box to view the content on the site.
ACKNOWLEDGEMENTS
I gratefully acknowledge the support of the National
Science Foundation, which funded this work through the
Course Curriculum and Laboratory Improvement
Adaptation and Implementation track (Grant #0087996).
Any opinions, findings, and conclusions or
recommendations expressed in this material are those of
the author and do not necessarily reflect the views of the
National Science Foundation. I also thank Roger Y.
Anderson and Jeffrey R. Walker for their comments on
the manuscript, and Emily M. Geraghty and Robert C.
Thomas for their constructive reviews. Inspiration for
developing this course came from my graduate advisor,
Robert S. Anderson (University of Colorado, Boulder),
who teaches a similar course for graduate students, from
the late Rolfe Stanley, who taught a STELLA modeling
course at the University of Vermont for many years, and
from Andrew DeWet at Franklin and Marshall College,
who first introduced me to STELLA. I would also like to
thank Joel Dashnaw, Vassar College class of 2005, for his
hard work on the Blackboard site.
470
REFERENCES
Arnold, J.G., Williams, J.R., Srinivasan, R., and King,
K.W., 1996, SWAT: Soil and Water Assessment Tool.
USDA, Agricultural Research Service, Grassland,
Soil and Water Research Laboratory, 808 E.
Blackland Road, Temple, TX 76502.
Bice, D.M., 2001, Using STELLA models to explore the
dynamics of earth systems: experimenting with
Earth's climate system using a simple computer
model, Journal of Geoscience Education, v. 49, p.
170-181.
Costanza, R., and Gottlieb, S., 1998, Modelling ecological
and economic systems with STELLA: Part II,
Ecological Modelling, v. 112, p. 81-84.
DeWet, A.P., 1994, Integrating field observations with
physical and computer models in an introductory
environmental-geology
course,
Journal
of
Geological Education, v.42, p. 264-271.
Lee, J., 1993, A formal approach to hydrological model
conceptualization, Hydrological Sciences Journal, v.
38, p. 391-401.
Levy, J., and Mayer, L., 1999, Systems modeling of
nonequilibrium chemical reactions using STELLA,
Journal of Geoscience Education, v. 47, p. 413-419.
Moore, A., and Derry, L., 1995, Understanding natural
systems through simple dynamical systems
modeling, Journal of Geological Education, v. 43, p.
152-157.
Norro, A., and Frankignoulle, M., 1996, Biogeochemical
box modelling at small scale: Application to the
inorganic carbon cycle in the Bay of Calvi, Ecological
Modelling, v. 88, p. 101-112.
Olsen, P., Christensen, U., and Glatzmaier, G.A., 1999,
Numerical
modeling
of
the
geodynamo;
mechanisms of field generation and equilibration,
Journal of Geophysical Research B, Solid Earth and
Planets, v. 104, p. 10,383-10,404.
Project Kaleidoscope, What Works, <http://www.
pkal.org/whatwork.html>, May 2000.
Ruth, M., and Cleveland, C.J., 1993, Nonlinear dynamic
simulation of optimal depletion of crude-oil in the
lower 48 United-States, Computers Environment
and Urban Systems, v. 17, p. 425-435.
Small, E.E., and Anderson, R.S., 1995, Geomorphically
driven late Cenozoic rock uplift in the Sierra Nevada,
California, Science, v. 270, p. 277-280.
Ward, S.N., and Goes, S.D.B., 1993, How regularly do
Earthquakes recur? A synthetic seismicity model for
the San Andreas Fault, Geophysical Research
Letters, v. 20, p. 2131-2134.
Journal of Geoscience Education, v. 54, n. 4, September, 2006, p. 464-470