Catherine
A. Roberts
Associate
Professor
Department
of Mathematics and Statistics
Northern
Arizona University
Flagstaff,
AZ 86011-5717
Randy
Gimblett
Associate
Professor
School
of Renewable Natural Resources
The
University of Arizona
Tucson,
Arizona, USA 85721
A computer program called the Grand Canyon River Trip Simulator (GCRTSim) has been developed by teams at the University of Arizona and Northern Arizona University for use by managers at the Grand Canyon National Park. GCRTSim consists of a database and a simulator, as well as extensive analysis tools. The database will eventually contain approximately 500 trip diaries collected in 1998 and 1999 that report all stops for activities and camping along the 226 mile Colorado River corridor within the purview of the National Park Service. The simulator provides users with the opportunity to set up prospective launch schedules for rafting trips and to run seasons off these artificially launch calendars. Both the trip diary database and the results of the simulations can be analyzed using extensive graphing tools. The analysis can provide insight into the impacts of rafting traffic on the treasured resources along the Colorado River corridor.
Key Words Colorado River, Simulation, Computer, Grand
Canyon National Park, Rafting, Management, Launch Schedule, River, Model
The 1989 Colorado River Management Plan
(CRMP) governs the recreational rafting
traffic on the Colorado River within the Grand Canyon National Park
(GRCA). This document sets limits on
use and is the guiding document for park managers in charge of supervising and
governing both commercial and noncommercial use of the river for rafting
purposes. To help supplement the
ability of managers to understand the complex human-environment interactions in
this setting, a team of faculty and students from the University of Arizona's
School of Renewable Natural Resources and from Northern Arizona University's
Department of Mathematics and Statistics have worked since April 1998 on the
Grand Canyon River Trip Simulator Project (GCRTSim).
The goal of GCRTSim is two fold -- to improve
understanding of the current conditions and to predict the possible outcomes of
changes to the current set of regulations guiding river rafting traffic. First, we collected a sufficient number of
trip diaries from rafting parties and we used this data, for example, to inform
the park service about the frequency of use of various camping and attraction
sites. The data from these trip
reports, coupled with extensive expert interviews, informed the development of
an artificial-intelligence and statistical based computer simulation that
models rafting traffic along the Colorado River. The simulator can approximate the behavior of rafting trips under
a wide range of natural or imposed conditions.
GCRTSim can thus consider an imaginary launch schedule or a proposed set
of new regulations and execute several season's worth of river trips. The resultant data can subsequently be
analyzed to provide insight into the potential consequences of the imaginary
launch schedule or proposed set of new regulations. The intent is to provide the park managers with more information
about the existing conditions on the Colorado River, as well as enable them to
gain insight into the potential consequences of any new management actions
under consideration.
Designing a computer simulation model to examine
the complex interactions between humans and the natural environment represents
a novel approach for managers in the National Park system. While it is a natural next step in the
management of natural resources to take advantage of the potential offered by
sophisticated computer models, to date little has been done in this arena. One author, Randy Gimblett, describes some
recent work developing a related intelligent-agent based program to study the
interactions between jeep tours, bicyclists and hikers in a recreational
setting in Sedona AZ in (Gimblett et al 1996).
In this application, the ambitious use of a large data set, statistical
analysis, artificial-intelligence techniques such as fuzzy logic, etc. have
been used in combination. The GCRTSim
computer simulation is a new approach for providing natural resource managers
with the ability to set up alternative management scenarios and witness the
potential outcomes of those changes on the system.
The first step was to collect data -- not only
to understand the popularity of various camping and attraction sites along the
Colorado River corridor, but also to understand the reasoning and logic
employed by trip leaders when executing their trips. We needed to have as detailed a picture of the use patterns on the
river, as well as an understanding of how various trip leaders make decisions
about where to stop, when to stop, and how long to remain at a given
location.
In 1998 and 1999, hundreds of trip leaders were
asked to complete trip itineraries (for sample pages, see Fig. 1 and Fig.
2). These trip reports listed the time
in and time out for every reasonable location -- we identified 250 sites
between the launching spot at Lees Ferry and Diamond Creek (the location where
GRCA stops monitoring people and activity on the Colorado River). Approximately 500 trip diaries were
collected, representing about a 50% return rate for the commercial trips and a
30% return rate for the private trips.
The trip diaries represent trips of all lengths and propulsion types
(motorized, non-motorized). Although completing
the trip diaries was optional, we recognize that the data collected is,
nonetheless, far more comprehensive then anything previously available and we
feel comfortable that our database is statistically representative and
reasonable.
During 1998, extensive interviews were conducted
with over fifteen river guides. These
guides collectively represented years and years of experience running the
Colorado River either non-commercially (privately) or as guides for commercial
outfitters. They had experience at
various river flow regimes and with all types of watercraft (oars, paddle
boats, dories, motor boats). The intent
of the interviews was to learn as much as possible about the logic employed by
a river guide when taking a trip down the Colorado River. Questions were open-ended and
extensive. For example, to understand
how a guide might choose a campsite we asked questions such as, "When do
you start thinking about camping for the evening?", "What campsites do you like and why;
which ones do you try to avoid and why?",
"List every factor that goes into the selection process of choosing
a campsite and explain why each factor is important.". The result was a complex matrix of
possibilities for campsite selection based on every imaginable scenario or
situation that might be faced by a river guide. The scenarios could either be the result of human interactions
and decisions, or they could be the result of responding to the natural
environment. For example, a trip might
avoid a campsite because a conversation earlier in the day revealed that
another trip was planning to select that site (result of a human interaction
and decision) or, alternatively, a trip might avoid a campsite because when
they arrive a recent rainfall has rendered the campable area too small for
their group size (result of responding to the natural environment).
The simulation engine of the program represents
a hybrid program that uses both statistical data from the trip diary database
along with artificial intelligence algorithms developed from the expert
interview process. As development of
the simulation engine proceeded, additional analysis of the database or
additional querying of expert guides has been utilized as needed. The simulation engine is constructed as an
object-oriented system that uses elements of fuzzy logic in the decision
structure. Fuzzy logic is an artificial
intelligence construct that permits a decision to be made by weighing several
factors or variables in an appropriate manner.
Fuzzy logic theory provides a robust and full range of decisions making
tools that is suitable for capturing much of the nuance inherent in making
complex decisions in the natural environment of the Colorado River. For example, when a trip is choosing a
campsite, the current conditions of the river and the individual trip play a
role, as does the historical popularity of a campsite under consideration. Fuzzy logic takes into account all these
factors and weighs them appropriately so that each trip's campsite decision
represents a reasonable outcome for that given, particular set of
circumstances.
The simulation engine reads in a launch schedule
(that could represent the current launch schedule or a prospective calendar
created by the user) then creates and launches the trips from Lees Ferry. These simulated trips execute their days on
the river by choosing attraction sites for hikes or other activities, by
stopping for lunch, and by selecting an appropriate campsite each night. Certain trips must be at given locations on
certain times (e.g. some trips exchange passengers at Phantom Ranch) and the
trips are managed by the simulator to meet these fixed points as
scheduled. Moreover, a sophisticated
planning algorithm helps each simulated trip plan out an optimal schedule that
will, for example, include stops at the key attraction sites and ensure that
campsite selections are appropriate. A record is kept for each simulated trip
-- where and when it encounters other trips, where it chooses to engage in an
activity or to stop to camp, how long it stays, etc.
After running a simulation, the created database
can be queried to investigate the outcome of that particular launch
schedule. For example, one could query
the top ten attraction sites and compare this with the data from the real 1998
and/or 1999 trip diaries to observe any changes. There are a number of standard and non-standard queries possible
to help the user of GCRTSim judge whether the outcome of a simulation
represents an improvement or not over the current conditions in GRCA.
GCRTSim has the ability to run simulations
representing new prospective launch calendars.
It is also possible for the user to manipulate other conditions along
the river corridor. For example, the
user could restrict camping or activities at any number of sites. In this instance, a user could compare data
from, for example, the 1998 trip diaries as well as from simulations run off of
the 1998 launch schedule both with or without the added camping/activity
restrictions. A judgement could then be
made about the possible consequences of such a management action on the
dynamics of the river rafting traffic in the Colorado River corridor.
GCRTSim allows for numerous types of graphs and
charts from a database (real or simulated) to help give the user insight into
Colorado River rafting dynamics. To
help illustrate some of the uses for GCRTSim, it is important to note that the
trip report database itself represents a wealth of valuable information. To date,
only the 1998 trip reports are available for analysis. Not only is it useful to examine the
"real data" from the trip reports, but comparisons are also possible
between this "real data" and various simulation runs. Simulations were run using a launch calendar
judged as a typical schedule under the 1989 CRMP. Simulations were run at both 100% use levels and then again at
50% use level. Comparisons were made
between the simulations and are presented here.
For example, simple "top ten" lists of
campsites or attraction sites are possible.
In Fig. 3, a list of the most popular attraction sites from the 1998
trip reports are shown. The next two
figures show the same data from two simulation runs. In Fig. 4, a simulation run using a launch schedule that
represents a typical schedule at 100% use levels is used. In Fig. 5, the simulation run used a launch
schedule representing approximately 50% use levels -- about half of the
launches were removed from the standard launch calendar. This involved some judgements, but for the
most part, the 50% use launch schedule represents an even cut of all trip
types, considering such features as propulsion type, commercial/private and
trip length. Comparing Fig. 3 and Fig.
4 helps us understand the ability of the simulation to replicate the current
conditions along the river. To date,
the simulated trips are choosing the same top ten attraction sites, but at a
lower frequency than that reported in the real data. Consequently, efforts are underway to refine the model to better reflect the current conditions
on the river. Comparing Fig. 4 and Fig.
5 provides some insight into how reducing the number of launches might affect
the selection of attraction sites.
Again, the historical popularity of these sites keep them as key
attraction sites regardless of the use level, although the amount of use that
these sites experience does change.
An important distinction between the "real
data" and the "simulated data" can be viewed by examining Fig. 6
and Fig. 7. In each case, the graph
shows the distribution of all trips along the river corridor on a particular
day -- July 15, 1998. The horizontal
axis shows the river mile, the vertical axis shows the number of trips that
reported being at each location on that particular day. In Fig. 6, the data shows only the "real
data" from the trip reports collected from July 15, 1998. Clearly, several trips were on the river
that day but we did not collect the data.
In Fig. 7, the distribution of a complete launch schedule simulation is
given for July 15, 1998. While it does
not match up perfectly with the trip diary data, it still gives a sense for the
distribution of parties along the river corridor. The higher peaks represent more trips having been at those
locations on that same day. A closer
analysis of these peaks can lead to insights about contacts between parties and
congestion at certain key attraction sites.
Another helpful analytical tool is represented
in Fig. 8, Fig. 9 and Fig. 10. Here,
the horizontal axis represents the day of the trip while the vertical axis
represents the river mile. The focus
here is only on trips of length 15 days.
All of the records for 15-day trips were averaged together to create one
line that represents the average or the "typical" 15 day trip. The slope of this line gives a sense of the
velocity of the trips as they travel down the Colorado River corridor. Comparisons between these graphs give us a
sense of the accuracy of our simulator.
For example, the slope of the line in Fig. 8 matches very closely with
the slope of the line in Fig. 9. After
day 10 (so, on the final third of the trip), however, the real data average
trip speed and average trip location is slower than the simulated data. This indicates that the simulation might
have some error that becomes obvious after running the trips more than ten
days, and helps identify an area for further attention in our refining efforts.
The next three figures show the same output but
take the average of all the trips, not just the ones of 15 day duration. The average of all the trips from the 1998
trip report database gives the line in Fig. 11. This must be interpreted carefully. On the one hand, this line captures the average location of each
trip on a daily basis. On the other
hand, it also represents trips of many different lengths. The decrease after day 6 is not due to trips
backtracking along the river (this is impossible). What is shows is that there are trips of length 6 or 7 days that
travel the entire river corridor (all 250 miles) in six or seven days and then
they are removed from the data set. On
day 7, you are only viewing trips that are of length greater than or equal to
seven days. A simulation on a full 100%
use level launch calendar is graphed in Fig. 12 and a 50% use level is shown in
Fig. 13. These are useful to use
because it provides an indication that the simulation is capturing the real
data flow of rafting trips in some sort of "average" sense. The similarities in the graphs in these
figures support a certain robustness in the simulator's ability to capture the
basic flow of rafting traffic on the Colorado River.
The final two figures illustrate the ability of
GCRTSim to compare the output from a simulation with the pre-established
Management Objectives. These objectives
were established in the 1989 CRMP and are the guidelines that the National Park
Services employs in order to see if a given launch scenario results in the
types of conditions on the river that are considered acceptable. For example, one management objective
regards the number of river contacts per day.
The objective is that there should be an 80% probability that a trip
will make contact with seven or fewer parties, with up to 90 minutes in sight
of less than 125 other people. In Fig.
14, a simulation run based on 100% use showed that this particular management
objective resulted in an average probability of 54.53% that the party contacts
will remain within the management standards.
In Fig. 15, a simulation run based on 50% use showed that this same
management objective resulted in an average probability of 91.09% that the
party contacts will remain with in the management standards. It is results like these that will enable
the users of GCRTSim to judge the potential of alternative management scenarios
under consideration.
To summarize, GCRTSim is both a repository for
an extensive database of trip reports completed during 1998 and 1999 and an integrated statistical and
artificial intelligence-based computer simulation that models complex, dynamic
human-environment interactions in the river corridor of the Grand Canyon
National Park. It will be used by
managers at GRCA to help understand the potential impact of various alternative
management scenarios for rafting trips on the Colorado River.
In
many ways, this represents a preliminary report since the 1999 trip diary data
is not yet available and since additional improvements and refinements for the
simulation engine are planned for much of the year 2000. The real test will be subsequent to this,
when the model is used extensively to examine the potential outcomes of various
alternative launch schedules. The
insight that can be provided by GCRTSim is expected to be a valuable
contribution to a complex situation, that of managing rafting traffic on the
Colorado River in an optimal way for both recreators and for the natural
resource itself.
The
authors would like to acknowledge the team members involved in this project:
Dr. Terry Daniel, Dr. Michael I. Ratliff, Micheal Meitner, Susan Cherry, Doug
Stallman, Rian Bogle, Rob Allred, Joanna Bieri, Gary O'Brien, Dana Kilbourne
and Ed Weidemann. This project would
not be possible without funding from the Grand Canyon National Park, the
University of Arizona and Northern Arizona University. The authors also wish to thank the countless
people who have contributed to our understanding of the complex nature of
running rafting trips down the Colorado River. This includes Linda Jalbert,
Laurie Domler and others from GRCA, the Grand Canyon River Outfitters Association,
the Grand Canyon Private Boaters Association, the Grand Canyon River Guides and
several social science researchers involved with the GRCA.
List of Figures
Figure 1 - first page of the River Trip Report
form
Figure 2 - sample page from the River Trip Report
form
Figure 3 - top ten activity sites, 1998 trip
report database
Figure 4 - top ten activity sites, 100% use
simulation
Figure 5 - top ten activity sties, 50% use
simulation
Figure 6 - distribution of trips over a day,
1998 trip report database
Figure 7 - distribution of trips over a day,
100% use-level simulation
Figure 8 - average trip profile for 15 day trip,
1998 trip report database
Figure 9 - average trip profile for 15 day trip,
100% use-level simulation
Figure 10 - average trip profile for 15 day
trip, 50% use-level simulation
Figure 11 - average trip profile for all trips,
1998 trip report database
Figure 12 - average trip profile for all trips,
100% use-level simulation
Figure 13 - average trip profile for all trips,
50% use-level simulation
Figure 14 - management objective for river
contacts/day - 100% use-level simulation
Figure 15 - management objective for river
contacts/day - 50% use-level simulation
Colorado River Management Plan, 1989, National
Park Service, Department of the Interior.
Gimblett, H. R., B. Durnota & R.M. Itami.
Spatially-Explicit Autonomous Agents for Modelling Recreation Use in Complex
Wilderness Landscapes. Complex International Journal. Vol. 3 1996.
Mathematicians Offer Answers
to Everyday Conundrums: Shooting the Virtual Rapids SCIENCE Vol 283, 12
Feb 1999, pg. 925. (Barry Cipra)
Update of River Research at
Grand Canyon Colorado River SOUNDINGS August 1998,
pgs. 1-3 (Linda Jalbert).