by Helena Mitasova, Geographic Modeling Systems Laboratory, Department
of Geography,
and Lubos Mitas, National Center for Supercomputing Applications,
University of Illinois at Urbana-Champaign, USA
This unit is part of the NCGIA
Core Curriculum in Geographic Information Science. These materials
may be copied for study, research, and education purposes, but please credit
the author and the NCGIA Core Curriculum in GIScience. All commercial
rights reserved. Copyright 1998 by Helena Mitasova and Lubos Mitas.
Your comments on these materials are welcome. A link to an
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Advanced Organizer
Topics covered in this unit
definition of process modeling and simulations
types of processes relevant to GIS
approaches to process modeling and simulations
calibration, error propagation and sensitivity analysis
integration of process models and GIS
application examples
Intended learning outcomes
after learning the material covered in this unit, students should be able
to
characterize types of processes and simulations relevant to GIS
identify methods and their suitability for various processes
explain the integration of GIS and models at different levels
discuss GIS relevant issues with a modeling specialist
write simple process modeling tools using map algebra
Definition of process modeling and simulation: theoretical concepts
and computational methods that describe, represent and simulate the functioning
of real-world processes;
computer simulations are becoming a 'third way' of performing research,
expanding thus traditional experimental and theoretical approaches:
simulation can be regarded as a numerical experiment, but it often requires
advancements in theory
simulations can provide information which is impossible or too expensive
to measure, as well as insights which are not amenable or too complicated
for analytical theory methods
models are simplified abstractions of reality representing or describing
its most important/driving elements and their interactions
simulations can be regarded as model runs for certain initial conditions
(real or designed)
Purpose of modeling and simulations:
analysis and understanding of observed phenomena
testing of hypotheses and theories
prediction of spatio-temporal systems behavior under various conditions
and scenarios (both existing and simulated, often performed to support
decision making)
new discoveries of functioning of geospatial phenomena enabled by unique
capabilities of computer experiments
Role of GIS :
storing and managing input data and results
pre-processing of input data (editing, transformation, interpolation, derivation
of parameters, etc.)
interactions between hydrosphere, atmosphere, lithosphere and biosphere
socio-economic/anthropogenic processes
transportation
urban, population
production (manufacturing, farming (see unit 181)
distribution and services (see unit 174)
interactions between socio-economic processes
interaction of natural and anthropogenic phenomena (e.g., environmental
models, food production, forestry, mining)
based on the type of spatial distribution, process models describe
the behavior of phenomena represented by:
homogeneous or spatially averaged units, e.g. subwatersheds, counties,
polygons (sometimes referred to as lumped models) with processes
described by ordinary differential equations
fields/multivariate functions discretized as rasters, grid cells or
meshes (distributed models) with processes described by partial
differential equations or cellular automata (see unit
054)
networks (systems of nodes and links, see unit 064)
points representing individuals and agents
combinations of fields, networks and points
based on the nature of spatial interactions, (see unit 021 and unit
123) models involve :
no spatial interaction, only location dependent behavior
short-range, close neighborhood interaction
long-range/expanding interaction
based on the type of underlying physical or social process, models
simulate
fluxes (over a surface, through network, in 3D space),
including: diffusion, dispersion, advection,
convection, reaction, radiation and heat transfer
proliferation and decay (chemical processes, radioactive decay)
population dynamics (birth/death, competition, predator/prey, epidemics)
intelligent agents (systems of independent entities which interact between
themselves and with environment with a certain degree of decision making
capabilities)
based on the spatial extent of modeled phenomena models are
local
regional
global
multiscale or nested models (Steyaert 1993 in
Goodchild et al. 1993), with
high resolution models used to calibrate the large scale, low resolution
models,
output of large scale models used as an input for small scale models
3. Approaches to modeling and simulations
real processes are complex and often include non-linear behavior, stochastic
components and feedback loops over spatial and temporal scales, therefore
models can represent the processes only at a certain level of simplification
empirical models are based on statistical analysis of observed data,
and they are usually applicable only to the same conditions under which
the observations were made (for example the Universal Soil Loss Equation
for modeling annual soil loss based on terrain, soil, rainfall and land
cover factors, Renard et al. 1991)
process based models are based on understanding of physical, chemical,
geological, and biological processes and their mathematical description
(for example, hydrologic and erosion models SIMWE: Mitas and Mitasova 1998,
CASC2D: Saghafian 1996 in Goodchild et al 1996)
models of complex systems often use combination of empirical and process
based approaches
3.1 Deterministic models
model processes which are often described by differential equations, with
a unique input leading to unique output for well-defined linear models
and with multiple outputs possible for non-linear models;
equations can be solved by different numerical methods (after discretization:
modification to run on a grid or a mesh, and parametrization: seting parameters
to account for subgrid processes):
finite difference
principle (Press et al 1992)
example (Saghafian 1996 in Goodchild et al 1996: CASC2d)
finite element
principle, meshes (Burnett 1987)
example (Vieux 1996 in Goodchild et al 1996: r.water.fea)
path simulation
principle: based on random walker representation, note: not to be confused
with stochastic simulations
example: Figure 1 - path simulation solution
of sediment flow continuity equation and resulting spatial distribution
of erosion (red) and deposition (blue) (SIMWE model, animation,
Mitas and Mitasova 1998).
models describe processes at various levels of temporal variation
steady state, withno temporal variations, often used for
diagnostic applications
time series of steady state events, computed by running a steady
state model with time series of input parameters, this approach is commonly
used for estimation of long term average spatial distributions of modeled
phenomena
dynamic, describing the spatio-temporal variations during a modeled
event, used for prognostic applications and forcasting
3.2 Stochastic models
model spatio-temporal behavior of phenomena with random components
unique input leads to different output for each model run, due to the random
component of the modeled process, single simulation gives only one possible
result
multiple runs are used to estimate probability distributions
conditional simulations combine stochastic modeling and geostatistics to
improve characterization of geospatial phenomena
behavior of dynamic stochastic systems can be described by different types
of stochastic processes, such as Poisson and renewal, discrete-time and
continuous-time Markov process, matrices of transition probabilities, Brownian
processes and diffusion (Nelson 1995, Molchanov and Woyczynski 1997)
3.3 Rule based models
model processes governed by local rules using cellular automata:
non-linear dynamic mathematical systems based on discrete time and space
(Wolfram 1984)
principles
cellular automaton evolves in discrete time-steps by updating its state
according to a transition rule which is applied universally and synchronously
to each cell at each time step.
value of each cell is determined based on a geometric configuration of
neighbor cells which is specified as a part of the transition rule.
complex global behavior may emerge from application of simple local rules,
thus useful for simulating systems that are not fully understood but for
which their local processes are well known.
examples
urban growth simulation models: diffusion-limited aggregation (Batty and
Longley 1994), innovation diffusion model (Clarke 1996, Park and Wagner
1997)
spatially explicit ecological models
forest fire simulation (Clarke et al 1994)
3.4 Multi-agent simulation of complex systems
model movement and development of groups of many interacting agents
agent is any actor in a system, that can generate events that affect itself
and other agents, a typical agent is modeled as a set of rules, responses
to stimuli
individual-based models represent movement/development of individual
entities over space and time based on local rules
hierarchical models can be built by nesting multiple collections of agents
with their schedule of activity
example:
SWARM - multiagent simulation of complex systems (Minar et al 1996, Booth
1997)
4. Models and reality
calibration
the role of parameters and their limits are evaluated by parameter scans
(Clarke 1996 in Goodchild et al 1997 CDROM, Mitas et al. 1997)
Figure 2 - parameter scan for sediment
flow and erosion/deposition for detachment capacity coefficient changing
from 0.001-10,
animation
model results are compared with experiments and parameters are set to values
which ensure the best reproduction of the experimental data
sensitivity analysis, error propagation and uncertainty is performed
to estimate impact of errors in input data on the model results (2.10:
u096)
causes of inconsistency between models and reality (Steyaert 1993
in Goodchild et al 1993)
only limited number of interacting processes can be treated
process may not be well understood or is treated inadequately
resolution and/or scale may be inadequate
numerical solution can be too sensitive to initial conditions
model can be incorrectly applied to conditions when its assumptions are
not valid
errors in input data
5. GIS implementation
simple modeling is supported by most commercial GIS, especially within
the raster subsystems (ARCGRID, ArcView Spatial Analyst, Intergraph ERMA,
IDRISI, GRASS, ERDAS)
full integration of complex models may require
extensions of standard GIS functions such as support for temporal and 3D/4D
data and meshes for finite element methods
opening of data formats and incorporation of customization and application
development tools stimulate coupling of commercial GIS and modeling
use of object oriented technology facilitates more efficient GIS implementation
and merges the different levels of coupling.
5.1 Full integration - embeded coupling
model is developed and implemented within a GIS using the programing and
development tools of a given GIS (Application Programming Interface (API),
scripting tools, map algebra operations)
model is run as a GIS command,
inputs and outputs are in a GIS database and no data transfer is needed,
computation is efficient for adequately coded models, models written with
scripting tools may be slower,
portability is restricted because of dependence on a GIS within which the
model was developed and implemented,
examples
embeded coupling
r.hydro.CASC2d, r.water.fea in GRASS (Saghafian 1996, Vieux 1996 in Goodchild
et al 1996)
Darcyflow, Particletrack in ARCGRID (ESRI 1994)
map algebra implementation
water flow (example in GRASS r.mapcalc, Shapiro and Westervelt 1992)
dispersion: simple fire spread model (example in ARCGRID, ESRI 1994)
model development is supported by customization and application development
tools and extensions to map algebra (for example, Wesseling et al. 1996:
DYNAMITE for PCRaster, Park and Wagner 1997: Cellular-IDRISI, ESRI 1996:
Avenue)
5.2 Integration under a common interface - tight coupling
model is developed outside GIS and has its own data structures with exchange
of data between model and GIS hidden from user, although in some cases
the data files can be shared
GIS and model are linked through a common interface
interface often supports integration of GIS and several different models
for simulation of complex systems with interrelated processes
portability is restricted
examples: (see Web references)
SWAT, AGNPS, ANSWERS coupled with GRASS
SWAT, IDOR3D, BASIN-2 coupled with ArcView
5.3 Loose coupling
model is developed and run independently of GIS
input data are exported from GIS and results are imported to GIS for analysis
and visualization
portability - model can be used with different GIS
examples:
PAYSAGE-forest and habitat change (Hansen et al. 1996), coupled with Arcview/ArcInfo
SIMWE-erosion and deposition (Mitas and Mitasova 1998), coupled with GRASS,
but can run with any GIS which supports raster data
5.4 Modeling environments linked to GIS
aimed at modular, reusable model development
modeling environment is linked to GIS through interface or data import/export
examples:
SME: Spatial Modeling Environment (Maxwell and Constanza 1997)
SWARM: Multi-agent simulation of complex systems (Minar et al. 1996)
MMS-Modular Modeling System (Leavesley 1993 in Goodchild et al. 1993)
complex systems: integrated models of interacting processes
dynamic systems in 3D space
object oriented reusable model development environments
7. Summary
process modeling is aimed at improving our understanding and predicting
the impact of natural and socio-economic processes and their interactions
GIS provides supporting tools for modeling, especially spatial data management,
analysis and visualization
process models describe the behavior of phenomena represented by fields,
networks and individual agents with various types of spatial interactions
at local, regional or global scale
models can be rule based, deterministic, stochastic, multiagent
issues of calibration, error propagation and scale are important for realistic
simulations
GIS and models can be fully integrated or linked through data and interface
well developed applications are in hydrology, sediment and contaminants
transport, ecosystem modeling and urban growth
8. Review and study questions
find examples of proces models using phenomena represented by fields, networks
and points
name the type of processes and disciplines where deterministic models are
often used
give examples of models when GIS implementation as a script would be the
most effective
write a simple diffusion model using map algebra
9. Reference materials
9.1 Print References
Batty M and Longley P 1994 Fractal Cities. London, Academic Press.
Batty, M. and Xie, Y. 1994 Modelling inside GIS: Part 2. Selecting and
calibrating urban models using Arc/Info, International Journal of Geographical
Information Systems, vol. 8, no. 5, pp. 429-450
Urban growth modeling by cellular automata
Booth G 1997 Gecko: A continuous 2D World for ecological modeling. Artficial
Life Journal 3:3, 147-163.
Individual based simulation system for multiple species at multiple
trophic levels
Burnett D. S. 1987, Finite Element Analysis: From Concepts to Applications,
Addison-Wesley, Reading, MA.
Clarke K, Brass J, and Riggan P 1994 A cellular automaton model of wild
fire propagation and extinction. Photogrammetric Engineering and Remote
Sensing, 60, 1355-67.
ESRI 1994, Cell-based Modeling with GRID, ESRI, Redlands, CA.
ESRI 1996, Avenue: Customization and application development for ArcView,
ESRI, Redlands, CA
Gardiner, C. W., 1985, Handbook of Stochastic Methods for Physics, Chemistry,
and the Natural Sciences, Springer, Berlin, 1985.
Goodchild, M.F, L. T. Steyaert, and B. O. Parks, eds., 1993, Geographic
Information Systems and Environmental Modeling,Oxford University Press,
New York.
proceedings from a conference in Boulder, CO, 1991 includes numerous
excellent examples of environmental models linked or integrated with GIS
Goodchild, M.F., L. T. Steyaert, and B. O. Parks, eds.,1996, GIS and Environmental
Modeling: Progress and Research Issues, GIS World, Inc., Ft. Collins, CO
proceedings from a conference in Breckenridge, CO, 1993 reflects
progress in integration of GIS and modeling
Goodchild M.F., L. T. Steyaert, and B. O. Parks, eds, 1997, GIS and Environmental
modeling (Santa Fe), NCGIA, CDROM
proceedings from a third conference held in Santa Fe 1996
Hansen A.J., Pattern R., DeGayner E., Marks B.L., 1996, Simulating forest
and habitat change in south-east Alaska with the landscape model PAYSAGE,
Transactions in GIS, 1(2), 119-136.
Maxwell T and Constanza R, 1997, An open geographic modelling environment,
Simulation Journal, 68(3), 175-185.
Minar N, Burkhart R, Langton C, Askenazi, M, 1996 The SWARM simulation
system: a toolkit for building multi-agent simulations. see
SWARM
Excellent description of multi-agent simulation principles using
the SWARM simulation system
Mitas L., Mitasova H. 1998 Distributed erosion modeling for effective erosion
prevention. Water Resources Research 34(3), 505-516.
example of process-based distributed model SIMWE with loose coupling
to GRASS
paper from a special issue devoted to visualization illustrates
use of visualization at different stages of modeling from data processing
through model development and application
Mitasova, H., L. Mitas, B.M. Brown, D.P. Gerdes, I. Kosinovsky, 1995, Modeling
spatially and temporally distributed phenomena: New methods and tools for
GRASS GIS. International Journal of GIS, 9 (4), special issue on integration
of Environmental modeling and GIS, p. 443-446.
Molchanov, S. A., W.A. Woyczynski, eds., 1997, Stochastic Models in Geosystems,
The IMA Volumes in Mathematics and its Applications.
Park S. and Wagner D. F. 1997 Incorporating cellular automata simulators
as analytical engines in GIS, Transactions in GIS, 2(3), 213-231.
Good description of cellular coupling automata with GIS in IDRISI
with useful spatial dynamic modeling examples
Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., 1992,
Numerical Recipes in C. The Art of Scientific Computing. Second Edition.
Cambridge University Press, p. 827-871
description of finite difference methods and algorithms, including
programs
Renard, K. G., Foster G. R., Weesies G. A. and Porter, J. P. 1991, Revised
Universal Soil Loss Equation. Journal of Soil and Water Conservation, 46(1),
p. 30-33.
description of an empirical erosion model commonly used with GIS
Shapiro, M., and Westervelt, J., 1992, R.MAPCALC, an algebra for GIS and
Image processing. U.S.Army Corps of Engineers, Construction Engineering
Research Laboratories, Champaign, Illinois, 422-425.
Srinivasan, R., and J. G. Arnold, 1994, Integration of a basin scale water
quality model with GIS, Water Resources Bulletin, 30(3), 453-462.
Wesseling C. G., Karssenberg D., Van Deursen W.P.A. and Burrough, P.A.,
1996, Integrating dynamic environmental models in GIS: the development
of a Dynamic Modelling language, Transactions in GIS, 1(1).
Westervelt J.D. and Hopkins L. B., 1998, Modeling Mobile Individuals in
Dynamic Landscapes, International Journal of Geographic Information Systems,
in press
White R and Engelen G 1994 Cellular dynamics and GIS: Modeling spatial
complexity. Geographical Systems, 1, 237-53.
Wolfram S, 1984 Universality and complexity in cellular automata. Physica,
10D, 1-35
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