Beyond
Mapping II
|
Spatial
Reasoning book |
What’s in a Model? — outlines
the different types of models and describes their characteristics
The GIS Modeling Babble-Ground — describes
a Classification Guide for GIS Modeling
Layers to Tapestry — describes
a technique for determining the set of nth best
paths between two points
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What’s in a Model?
(GeoWorld, )
Each
year I conduct a lot of courses and workshops on GIS. As you might imagine they frequently move
beyond the fundamental concepts to futuristic musings. One topic consistently captures the
imagination of participants and dominates informal discussion (you know, the
elevated B.S. in the sunken lounge)— what are the types and characteristics
GIS models? The accompanying outline
is the current state of a "sourdough" handout used to provoke this
impassioned discussion... what do you think?
Do
you know of any model types or characteristics missing from the outline? Are any in the outline misrepresented?
The
following are other terms often used to describe models: physical, atomistic, holistic,
constrained, fragmented, dispersed, data, analytical, diffusion, scale,
optimizing, simulation, analytical, process, synthetic, systems, flow,
statistical, mathematical, hierarchical, binary... Can you explain what is
meant by these terms? Are any
relevant? Where might they fit into the
outline?
Do
you see any utility in developing a comprehensive classification scheme for GIS
modeling?... or is this just another esoteric and academic (gee, that might be
redundant) exercise? Who would benefit from
such an outline?
_______________________
TYPES
AND CHARACTERISTICS OF GIS MODELS
I. MODELING: Material
and Symbolic — Positional, Thematic and Temporal
A
model is a “representation of reality” in either 1) Material form (tangible
representation) or 2) Symbolic
form (abstract representation).
GIS
Modeling involves symbolic representation of Positional
properties (WHERE), as well as Thematic (WHAT) and Temporal
(WHEN) attributes describing characteristics and conditions of space and time.
II. GENERAL TYPES OF MODELS: Structural and Relational
1) STRUCTURAL: focuses on the composition and construction
of things; Object and Action
·
OBJECT MODEL
— Static Entity-based which forms a visual representation of an item;
e.g., an architect's blueprint of a building.
Characteristics include scaled, 2 or 3-dimensional, symbolic
representation.
·
ACTION MODEL
— Dynamic Movement-based which tracks the space/time relationships of
items; e.g., a model train along its track.
Characteristics include time-slices, change detection, transition
statistics, and animation.
2) RELATIONAL: focuses on the interdependence and
relationships among factors; Functional and Conceptual
·
FUNCTIONAL
— Input/Output-based which tracks relationships among variables; e.g.,
storm runoff prediction. Characteristics
include cause/effect linkages, hard science, and sensitivity analysis.
·
CONCEPTUAL
— Perception-based which incorporates both fact interpretation and value
weights; e.g., suitability for outdoor recreation. Characteristics include heuristics (expert
rules), soft science, scenarios.
III. TYPES OF GIS MODELS:
Cartographic and Spatial
1) CARTOGRAPHIC MODEL
— automation of manual techniques which traditionally use drafting aids and
transparent overlays; e.g., a map identifying locations of productive soils and
gentle slopes using binary logic expressed as a geo-query.
2) SPATIAL MODEL — expression of mathematical
relationships among mapped variables; e.g., a map of surface heating based on
ambient temperature and solar irradiance using multi-value logic expressed as
variables, parameters and relationships.
IV. GIS MODEL CHARACTERISTICS:
Scale, Extent, Purpose, Approach, Technique, Association and Aggregation
1) SCALE: Micro and
Macro
·
MICRO — contains high-resolution
of space, time and/or variable considerations governing system response; e.g.,
a 1:1,000 map of a farm with the crop specified for each individual field
revised each year.
·
MACRO — contains
low-resolution of space, time and/or variable considerations governing system
response; e.g., a 1:1,000,000 map of land use with a single category for
agriculture revised every ten years.
2) EXTENT: Complete
and Partial
·
COMPLETE
— includes entire set of space, time and/or variable considerations governing system
response; e.g., a map of an entire watershed or river basin.
·
PARTIAL — includes
subsets of space, time and/or variable considerations governing system
response; e.g., a standard topographic sheet with its "artificial
boundary" capturing limited portions of several adjoining watersheds.
3)
PURPOSE: Descriptive and Prescriptive
·
DESCRIPTIVE
— characterization of the direct interactions of system components to gain
insight into system processes (understand); e.g., a wildlife population
dynamics map generated by simulation of life/death processes.
·
PRESCRIPTIVE
— characterization of direct and indirect factors which are related to system
response used in determining appropriate management action (decide); e.g., a
campground suitability map based on
interpretation landscape features.
4) APPROACH: Empirical and Theoretical
·
EMPIRICAL
— based on reduction (analysis) of field collected measurements; e.g., a
map of soil loss for each watershed in a region generated by spatially
evaluating the Universal Soil Loss Equation.
·
THEORETICAL
— based on the linkage (synthesis) of proven or postulated relationships
among variables; e.g., a map of spotted owl habitat based on accepted theories
on owl preferences.
5) TECHNIQUE: Deterministic and Stochastic
·
DETERMINISTIC
— direct evaluation of a defined relationship (results in a single repeatable
solution); e.g., a wildlife population map based on one model execution using a
single "best" estimate to characterize each variable.
·
STOCHASTIC
— simulation of a probabilistic relationship (results in a range of possible
solutions); e.g., a wildlife population map based on the average of a series of
model executions using probability functions to characterize each variable.
6) ASSOCIATION: Lumped and Linked
·
LUMPED — the state/condition
of each individual location is independent of other map locations
(point-by-point).
·
LINKED — the
state/condition of an individual location is dependent on other map
locations (vicinity, neighborhood or region).
7) AGGREGATION: Cohort and Disaggregated
·
COHORT — executed for
groups of objects having similar characteristics; e.g., a timber growth
map for each management parcel based on a look-up table of growth for each
specific set of landscape conditions.
·
DISAGGREGATED
— executed for each individual object; e.g., a map of predicted biomass
based on spatially evaluating a regression equation in which each input map
identifies an independent variable, each location a case, and each value a
measurement (usually raster-based grid cells).
8) TEMPORAL: Static and Dynamic
·
STATIC — treats time
as constant and model variables do not vary over time; e.g., a map of
timber value based on forest inventory and relative access to existing roads.
·
DYNAMIC — treats time
as variable and model variables change as a function of time; e.g., a
map of the spread of pollution from a point source.
_________________________
Author's
Note: next month we will translate the outline into
a generalized “Classification Guide for GIS Models”... sound like fun, or more
pedagogical pomposity?
The GIS Modeling
Babble-Ground
(GeoWorld, )
As
you might recall from dozing off face down on last month's Beyond Mapping
column there is a myriad of dimensions to GIS modeling. Hopefully you wrestled with the brief
descriptions, dismissed some and added others.
Modeling is as personal as the underwear you buy or the politics you
support. GIS modeling perspectives are
the result of the data you keep and the things you do. A county clerk, city engineer, forester, and
market forecaster work with radically differing data for multitude of divergent
purposes. In the applied arena, what
constitutes GIS modeling to one is rarely the same as it is to another— hence
the "babble-ground" lines are drawn in the sand of confusion.
However,
if you strip away the details of specific applications, common threads appear
among the GIS models themselves and the modeling processes undertaken. Last month's article attempted to capture
some of the more important threads. The
factors discussed have been stripped of their verbiage and summarized into the
Classification Guide shown in the figure below.
Figure 15-4. A completed Classification Guide evaluating an animated set of maps predicting wildfire growth for hourly time steps.
One
of the most frustrating aspects of any classification scheme is being forced to
assign something to just one of two choices (binary logic). It’s like those dumb questions on the SAT
exam— not everything is black and white.
In fact, those who see good arguments for grey are more likely the
creative individuals. In the
Classification Guide the descriptors for each factor identify opposing
extremes. The ten dots separating the extremes
provide a range of possible responses— you simply place an "X" at the
appropriate spot along the continuum.
The dichotomies have been arranged so a clustering of marks toward the
left indicate models that are easier to comprehend without a PhD in Complex
Studies.
Let's
tackle an easy example and force our responses to the extremes. Consider Michelangelo's sculpture of Venus
deMilo... sure its a model (abstraction), or she sure has us all fooled by
sitting so still. Within the limits of
the Classification Guide, she's
·
Material
(one big piece of marble; no abstract symbols here)
·
Structural
(the model characterizes her construction; don't know about her relationships)
·
Object (visual
rendering of just her; no movable parts)
Now
she's not a GIS Model, but if she were she would be
·
Cartographic
(manual techniques; no wimpy mathematics)
·
Micro (about a 1:1
scale; unless she's a scaled version of Goliath's mom)
·
Partial (missing arms
and legs; or maybe they were nicked in a Bekins move)
·
Descriptive
(wow, and how; doesn't tell you what to do... she's just a rock)
·
Empirical
(direct measurement; or Mickey-A had an active imagination)
·
Deterministic
(direct single solution; hips and shoulders have no chance of being attached
elsewhere)
·
Linked (the hip bone
is connected to the thigh bone...; can't talk about her chin without noticing
her eyes)
·
Disaggregated
(one-of-a-kind; though millions strive for a favorable comparison)
·
Static (hasn't
changed for centuries; the whole effect is dynamite, but not dynamic)
Now
let's try a tougher one— an animated set of maps predicting wildfire growth for
hourly time steps. The accompanying
figure indicates "refined" response positioning along each of the
scales, whereas the following discussion identifies the extremes. The first part is easy, with the fire model
tending toward
·
Abstract
(or you had better get a hose)
·
Relational
(fire ignition is dependent on several mappable factors including terrain,
vegetation type/condition, and weather)
·
Functional
(mostly uses fire science research tracking the relationships among variables)
Now
for the more perplexing part involving GIS model type and characteristics.
·
Spatial (lot of math
behind this one)
·
Micro (at each
instant the model is only considering the fire front and its immediate
surroundings)
·
Partial (until the
fire is extinguished)
·
Descriptive
(unabated fire propagation without fire management actions)
·
Empirical
(based on field calibrated equations)
·
Deterministic
(based on a defined set of input parameters)
·
Linked (adjacent
parcels are the next to burn)
·
Disaggregated
(independently considers each burning location and its propagation options)
·
Dynamic (both diurnal
and on-going fire behavior conditions change model variables)
Whew! Now try your hand at "classifying"
the following representations of reality and/or your own favorite GIS models...
·
Mount Rushmore's faces of the presidents
·
A landscape architect's cardboard model
of a National Park
·
An elk habitat map
·
A set of seasonal maps of elk habitat
·
An elk population dynamics model
responding to landscape conditions and predator/prey interactions
·
A GIS implementation of the Universal
Soil Loss Equation for a watershed
·
A GIS implementation of the Horton
·
A crop yield prediction map
·
Maps of wildfire risk generated each
morning
·
A dynamic wildfire growth model
responding to temperature fluctuations, complex wind vectors and fire abatement
actions
_______________________
Author's
Note: A
classic reference for modeling is Mathematical Modeling with Computers, by
Jacoby and Kowalik, Prentice-Hall, 1980.
Ample "poetic license" was used in extending the basic
modeling framework to the unique conditions and approaches used in GIS
modeling.
(GeoWorld, )
Most
of us will agree that there are three essential elements to GIS— data,
operations and applications. To use the
technology you need a bunch of digital maps, an analytic "engine" to
process the maps, and interesting problems to solve. However, not all of us have the same view of
the relative importance of the three elements.
Some have a data-centric perspective, as they
prepare individual data layers and/or assemble the comprehensive databases GIS
needs. Others are operations-centric
and are locked in on refining and expanding the GIS toolbox of processing and
display capabilities. A third group is applications-centric
and sees the portentous details of data and operations as merely impediments to
problem solving. Such is the fractious
fraternity of GIS.
In
the early years, the data and operations orientations dominated the developing
field. As GIS matures, the focus is
shifted to applications. As a result,
attention is increasingly directed toward the assumptions and linkages embedded
in our GIS models— the map analysis solutions to pressing problems. In essence, we are weaving our data layers
into complex, logical tapestries of map interrelationships. A crucial component to this evolution is an
effective mechanism to communicate model logic, as well as processing
flow.
Programmers
and system analysts routinely use diagramming techniques for communication of
data/processing flow. Structure and flow
charts, as well as data flow, entity relation, control flow, and state
transition diagrams, are but of few of the various approaches. Each technique invokes a subtly different
perspective in communicating structure and logic. For example, a Data Flow Diagram emphasizes
the processing steps used in converting one data set into another. The technique uses large circles to symbolize
operations, with the lines connecting those representing data sets (Figure 1). Its design draws one's attention to the
processing steps over the data states, thereby best serving an
operations-centric orientation.
Figure 1. Data Flow Diagram.
Processing-oriented
diagrams work well for non-spatial information processing. They relate data about entities through
indexed files. In these instances, the
specifications in a database query are paramount. Instances of geo-query, such as "where
are all the locations that have slopes over 13% AND unstable soils AND are
devoid of vegetation," use standard database management systems
technology. Standard diagramming
techniques, in such instances, is most appropriate.
However,
spatial analysis techniques go beyond the repackaging of existing data. For example, if you want establish
variable-width buffers around salmon spawning streams it's a different
story. You need to simultaneously
consider intervening slopes, ground cover, and soil stability as you
"measure" distance. If you
want to establish a map of visual exposure density to roads, you need to
consider maps of the road network, relative elevations at a minimum.
These,
and the myriad of other spatial analysis procedures, have strong data
dependency. They are not just setting a
few parameters for traditional, non-spatial processing techniques. Spatial analysis is an entirely new kettle of
fish. It is dependent upon the unique
geographic patterns of the data sets involved— definitely data-centric
conditions.
A
GIS
Modeling Flowchart, or "map model," takes such a
perspective. The top of Figure 2 uses a
flowchart to track the same data/processing steps as shown in the Data Flow
Diagram. Maps (i.e., data sets) are
depicted as boxes and operations (i.e., processing steps) are depicted as
arrows. This focus is obviously
data-centric as it draws your attention to the mapped variables, but also it is
arguably an applications-centric one as well.
Most users of GIS have prior experience with manual map analysis
techniques. They have struggled with
rulers, dot grids, and transparent overlays to laboriously draft new maps that
better address a question at hand. For
example, you may have circled areas where the elevation contour lines are close
together to create a map of steep slopes.
In doing so, attention is focused on the elevation data and the
resultant circles inscribed on the transparent overlay— the input and output
maps.
The
bottom portion of Figure 2 shows a “logic
modification” incorporating a preference to be near or within diverse
forested areas. A neighborhood operation
(scan) assigns the number of different vegetation types (COVERTYPE) within the
vicinity of each forested location (FORESTS).
Areas of high diversity are isolated (renumber), and a proximity map
from these areas (DF_PROX) is generated for the entire project area. Since several models might share this command
set, it is stored as a generalized procedure and is simply attached using the SubModel
or Procedure flowcharting "widget."
Figure 2. GIS Model Flowchart.
Figure
3 identifies a “processing modification”
to the model. In this example, a display
of the SUITABILITY map with roads vectors graphically overlaid (ROADS.BLN) is
used as a backdrop for the user to manually draw a potential set of SUITABLE
sites. Statistics on the sites
(STAT.TBL) are presented and the user can either accept them or redraw another
set of potential sites. When accepted,
the raster map is converted to vectors and stored. The example uses an extended set of "Connector,
File, Manual Operation, Conditional Branch and Non-Spatial Operation"
widgets.
Figure 3. Additional Flowchart Widgets.
So
what? All this seems to be "much
ado about nothing"... just a bunch of globs, lines and silly symbols. Actually, it may be GIS's ticket out of the
"black box" and into the light of creative applications. A simple flowchart of model logic is needed
by general users to understand and appropriately apply a model. A more complex flowchart extending to
processing flow is needed by the GIS specialist who wrestles with the actual
code. What we all need is a single
diagramming technique that can operate at both levels... a simple logical
expression which can be embellished with processing flow details.