Map Analysis

Topic 11: Characterizing Micro-Terrain Features

© 2001
Map Analysis: Procedures and Applications in GIS Modeling

Identifying Micro-Terrain Features   describes techniques to identify convex and concave features 
Characterizing Local Terrain Conditions
  discusses the use of "roving windows" to distinguish localized variations
Assessing Terrain Slope and Roughness
  discusses techniques for determining terrain inclination and coarseness 
Characterizing Surface Flows
  describes the use of optimal path density analysis for mapping surface flows
Modeling Erosion and Sediment Loading
  illustrates a GIS model for assessing erosion potential and sediment loading


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Identifying Micro-Terrain Features     (return to top of Topic)

The past several columns investigated surface modeling and analysis.  The data surfaces derived in these instances weren't the familiar terrain surfaces you walk the dog, bike and hike on.  None-the-less they form surfaces that contain all of the recognizable gullies, hummocks, peaks and depressions we see on most hillsides.  The "wrinkled-carpet" look in the real world is directly transferable to the cognitive realm of the data world.       

However, at least for the moment, let's return to terra firma to investigate how micro-terrain features can be characterized.  As you look at a landscape you easily see the changes in terrain with some areas bumped up (termed convex) and others pushed down (termed concave).  But how can a computer "see" the same thing?  Since its world is digital, how can the lay of the landscape be transferred into a set of drab numbers? 

Figure 31-1. Identifying Convex and Concave features by deviation from the trend of the terrain. 

One of the most frequently used procedures involves comparing the trend of the surface to the actual elevation values.  Figure 31-1 shows a terrain profile extending across a small gully.  The dotted line identifies a smoothed curve fitted to the data, similar to a draftsman's alignment of a French curve.  It "splits-the-difference" in the succession of elevation values—half above and half below.  Locations above the trend line identify convex features while locations below identify the concave ones.  The further above or below determines how pronounced the feature is. 

In a GIS, simple smoothing of the actual elevation values derives the trend of the surface.  The left side of fig. 31-2 shows the actual and smoothed surfaces for a project area.  The flat portion at the extreme left is an area of open water.  The terrain rises sharply from 500 feet to 2500 feet at the top of the hill.  Note the small "saddle" (elevation dips down then up) between the two hilltops.  Also note the small depression in the relatively flat area in the foreground (SW) portion. 

In generating the smoothed surface, elevation values were averaged for a 4-by-4 window moved throughout the area.  Note the subtle differences between the surfaces—the tendency to pull-down the hilltops and push-up the gullies.   

While you see (imagine?) these differences in the surfaces, the computer quantifies them by subtracting.  The difference surface on the right contains values from -84 (prominent concave feature) to +94 (prominent convex feature).  The big bump on the difference surface corresponds to the smaller hilltop on elevation surface.  It's actual elevation is 2016 while the smoothed elevation is 1922 resulting in 2016 - 1922 = +94 difference.  In micro-terrain terms, this area is likely drier that its surroundings as water flows away from it.   

The other arrows on the surface indicate other interesting locations.  The "pockmark" in the foreground is a small depression (764 - 796 = -32 difference) that is likely wetter as water flows into it.  The "deep cut" at the opposite end of the difference surface (539 - 623 = -84) suggests a prominent concavity.  However representing the water body as fixed elevation isn't a true account of terra firma configuration and misrepresents the true micro-terrain pattern. 

Figure 31-2.  Example of a micro-terrain deviation surface. 

In fact the entire concave feature in the upper left portion of 2-D representation of the difference surface is suspect due to its treatment of the water body as a constant elevation value.  While a fixed value for water on a topographic map works in traditional mapping contexts it's insufficient in most analytical applications.  Advanced GIS systems treat open water as "null" elevations (unknown) and "mirror" terrain conditions along these artificial edges to better represent the configuration of solid ground.  

The 2-D map of differences identifies areas that are concave (dark red), convex (light blue) and transition (white portion having only -20 to +20 feet difference between actual and smoothed elevation values).  If it were a map of a farmer's field, the groupings would likely match a lot of the farmer's recollection of crop production—more water in the concave areas, less in the convex areas.   

A Colorado dryland wheat farmer knows that some of the best yields are in the lowlands while the uplands tend to "burn-out."  A farmer in Louisiana, on the other hand, likely see things reversed with good yields on the uplands while the lowlands often "flood-out."  In either case, it might make sense to change the seeding rate, hybrid type, and/or fertilization levels within areas of differing micro-terrain conditions.   

The idea of variable rate response to spatial conditions has been around for thousands of years as indigenous peoples adjusted the spacing of holes they poked in the ground to drop in a seed and a piece of fish.  While the mechanical and green revolutions enable farmers to cultivate much larger areas they do so in part by applying broad generalizations of micro-terrain and other spatial variables over large areas.  The ability to continuously adjust management actions to unique spatial conditions on expansive tracks of land foretells the next revolution. 

Investigate the effects of micro-terrain conditions goes well beyond the farm.  For example, the Universal Soil Loss Equation uses "average" conditions, such as stream channel length and slope, dominant soil types and existing land use classes, to predict water runoff and sediment transport from entire watersheds.  These non-spatial models are routinely used to determine the feasibility of spatial activities, such as logging, mining, road building and housing development.  While the procedures might be applicable to typical conditions, they less accurately track unusual conditions clumped throughout an area and provide no spatial guidance within the boundaries of the modeled area.   

GIS-based micro-terrain analysis can help us be more like a "modern ancient farmer"— responding to site-specific conditions over large expanses of the landscape.  Calculation of a difference surface simply scratches the surface of micro-terrain analysis.  In the next few columns we'll look other procedures that let us think like a raindrop while mapping the micro-terrain.  

 

Characterizing Localized Terrain Conditions     (return to top of Topic)

Last month's column described a technique for characterizing micro-terrain features involving the difference between the actual elevation values and those on a smoothed elevation surface (trend).  Positive values on the difference map indicate areas that "bump-up" while negative values indicate areas that "dip-down" from the general trend in the data.

Figure 31-3.  Localized deviation uses a spatial filter to compare a location to its surroundings. 

A related technique to identify the bumps and dips of the terrain involves moving a "roving window" (termed a spatial filter) throughout an elevation surface.  The profile of a gully can have micro-features that dip below its surroundings (termed concave) as shown on the right side of figure 31-3.   

The localized deviation within a roving window is calculated by subtracting the average of the surrounding elevations from the center location's elevation.  As depicted in the example calculations for the concave feature, the average elevation of the surroundings is 106, that computes to a -6.00 deviation when subtracted from the center's value of 100.  The negative sign denotes a concavity while the magnitude of 6 indicates it's fairly significant dip (a 6/100= .06).  The protrusion above its surroundings (termed a convex feature) shown on the right of the figure has a localized deviation of +4.25 indicating a somewhat pronounced bump (4.25/114= .04).   

Figure 31-4.  Applying Deviation and Coefficient of Variation filters to an elevation surface. 

The result of moving a deviation filter throughout an elevation surface is shown in the top right inset in figure 31-4.  Its effect is nearly identical to the trend analysis described last month-- comparison of each location's actual elevation to the typical elevation (trend) in its vicinity.  Interpretation of a Deviation Surface is the same as that for the difference surface discussed last month—protrusions (large positive values) locate drier convex areas; depressions (large negative values) locate wetter concave areas. 

The implication of the "Localized Deviation" approach goes far beyond simply an alternative procedure for calculating terrain irregularities.  The use of "roving windows" provides a host of new metrics and map surfaces for assessing micro-terrain characteristics.  For example, consider the Coefficient of Variation (Coffvar) Surface shown in the bottom-right portion of figure 31-4.  In this instance, the standard deviation of the window is compared to its average elevation—small "coffvar" values indicate areas with minimal differences in elevation; large values indicate areas with lots of different elevations.  The large ridge in the coffvar surface in the figure occurs along the shoreline of a lake.  Note that the ridge is largest for the steeply-rising terrain with big changes in elevation.  The other bumps of surface variability noted in the figure indicate areas of less terrain variation. 

While a statistical summary of elevation values is useful as a general indicator of surface variation or "roughness," it doesn't consider the pattern of the differences.  A checkerboard pattern of alternating higher and lower values (very rough) cannot be distinguished from one in which all of the higher values are in one portion of the window and lower values in another.   

Figure 31-5.  Calculation of slope considers the arrangement and magnitude of elevation differences within a roving window. 

There are several roving window operations that track the spatial arrangement of the elevation values as well as aggregate statistics.  A frequently used one is terrain slope that calculates the "slant" of a surface.  In mathematical terms, slope equals the difference in elevation (termed the "rise") divided by the horizontal distance (termed the "run").   

As shown in figure 31-5, there are eight surrounding elevation values in a 3x3 roving window.  An individual slope from the center cell can be calculated for each one.  For example, the percent slope to the north (top of the window) is ((2332 - 2262) / 328) * 100 = 21.3%.  The numerator computes the rise while the denominator of 328 feet is the distance between the centers of the two cells.  The calculations for the northeast slope is ((2420 - 2262) / 464) * 100 = 34.1%, where the run is increased to account for the diagonal distance (328 * 1.414 = 464).   

The eight slope values can be used to identify the Maximum, the Minimum and the Average slope as reported in the figure.  Note that the large difference between the maximum and minimum slope (53 - 7 = 46) suggests that the overall slope is fairly variable.  Also note that the sign of the slope value indicates the direction of surface flow—positive slopes indicate flows into the center cell while negative ones indicate flows out.  While the flow into the center cell depends on the uphill conditions (we'll worry about that in a subsequent column), the flow away from the cell will take the steepest downhill slope (southwest flow in the example… you do the math). 

In practice, the Average slope can be misleading.  It is supposed to indicate the overall slope within the window but fails to account for the spatial arrangement of the slope values.  An alternative technique "fits a plane" to the nine individual elevation values.  The procedure determines the best fitting plane by minimizing the deviations from the plane to the elevation values.  In the example, the Fitted slope is 65%… more than the maximum individual slope.   

At first this might seem a bit fishy—overall slope more than the maximum slope—but believe me, determination of fitted slope is a different kettle of fish than simply scrutinizing the individual slopes.  Next time we'll look a bit deeper into this fitted slope thing and its applications in micro-terrain analysis. 
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Author's Notes: An Excel worksheet investigating Maximum, Minimum, and Average slope calculations is available online at the "Column Supplements" page at http://www.innovativegis.com/basis.

 

Assessing Terrain Slope and Roughness     (return to top of Topic)

The past few columns discussed several techniques for generating maps that identify the bumps (convex features), the dips (concave features) and the tilt (slope) of a terrain surface.  Although the procedures have a wealth of practical applications, the hidden agenda of the discussions was to get you to think of geographic space in a less traditional way—as an organized set of numbers (numerical data), instead of points, lines and areas represented by various colors and patterns (graphic map features).   

A terrain surface is organized as a rectangular "analysis grid" with each cell containing an elevation value.  Grid-based processing involves retrieving values from one or more of these "input data layers" and performing a mathematical or statistical operation on the subset of data to produce a new set numbers.  While computer mapping or spatial database management often operates with the numbers defining a map, these types of processing simply repackage the existing information.  A spatial query to "identify all the locations above 8000' elevation in El Dorado County" is a good example of a repackaging interrogation.    

Map analysis operations, on the other hand, create entirely new spatial information.  For example, a map of terrain slope can be derived from an elevation surface, then used to expand the geo-query to "identify all the locations above 8000' elevation in El Dorado County (existing data) that exceed 30% slope (derived data)."  While the discussion in this series of columns focuses on applications in terrain analysis, the subliminal message is much broader—map analysis procedures derive new spatial information from existing information.   

Now back to business.  Last month's column described several approaches for calculating terrain slope from an elevation surface.  Each of the approaches used a "3x3 roving window" to retrieve a subset of data, yet applied a different analysis function (maximum, minimum, average or "fitted" summary of the data).   

Figure 31-6. 2-D, 3-D and draped displays of terrain slope. 

Figure 31-6 shows the slope map derived by "fitting a plane" to the nine elevation values surrounding each map location.  The inset in the upper left corner of the figure shows a 2-D display of the slope map.  Note that steeper locations primarily occur in the upper central portion of the area, while gentle slopes are concentrated along the left side. 

The inset on the right shows the elevation data as a wire-frame plot with the slope map draped over the surface.  Note the alignment of the slope classes with the surface configuration—flat slopes where it looks flat; steep slopes where it looks steep.  So far, so good. 

The 3-D view of slope in the lower left, however, looks a bit strange.  The big bumps on this surface identify steep areas with large slope values.  The ups-and-downs (undulations) are particularly interesting.  If the area was perfectly flat, the slope value would be zero everywhere and the 3-D view would be flat as well.  But what do you think the 3-D view would look like if the surface formed a steeply sloping plane? 

Are you sure?  The slope values at each location would be the same, say 65% slope, therefore the 3-D view would be a flat plane "floating" at a height of 65.  That suggests a useful principle—as a slope map progresses from a constant plane (single value everywhere) to more ups-and-downs (bunches of different values), an increase in terrain roughness is indicated.   

Figure 31-7. Assessing terrain roughness through the 2nd derivative of an elevation surface. 

Figure 31-7 outlines this concept by diagramming the profiles of three different terrain cross-sections.  An elevation surface's 2nd derivative (slope of a slope map) quantifies the amount of ups-and-downs of the terrain.  For the straight line on the left, the "rate of change in elevation per unit distance" is constant with the same difference in elevation everywhere along the line—slope = 65% everywhere.  The resultant slope map would have the value 65 stored at each grid cell, therefore the "rate of change in slope" is zero everywhere along the line (no change in slope)—slope2 = 0% everywhere.   

A slope2 value of zero is interpreted as a perfectly smooth condition, which in this case happens to be steep.  The other profiles on the right have varying slopes along the line, therefore the "rate of change in slope" will produce increasing larger slope2 values as the differences in slope become increasingly larger. 

So who cares?  Water drops for one, as steep smooth areas are ideal for downhill racing, while "steep 'n rough terrain" encourages more infiltration, with "gentle yet rough terrain" the most.  

Figure 31-8.  2-D, 3-D and draped displays of terrain roughness. 

Figure 31-8 shows a roughness map based on the 2nd derivative for the same terrain as depicted in Figure 31-6.  Note the relationships between the two figures.  The areas with the most "ups-and-downs" on the slope map in figure 31-6 correspond to the areas of highest values on the roughness map in figure 31-8.  Now focus your attention on the large steep area in the upper central portion of the map.  Note the roughness differences for the same area as indicated in figure 31-8—the favorite raindrop racing areas are the smooth portions of the steep terrain.   

Whew!  That's a lot of map-ematical explanation for a couple of pretty simple concepts—steepness and roughness.  Next month we'll continue the trek on steep part of the map analysis learning curve by considering "confluence patterns" in micro terrain analysis.

 

Characterizing Surface Flows     (return to top of Topic)

Last month's discussions focused on terrain steepness and roughness.  While the concepts are simple and straightforward, the mechanics of computing them are a bit more challenging.  As you hike in the mountains your legs sense the steepness and your mind is constantly assessing terrain roughness.  A smooth, steeply-sloped area would have you clinging to things, while a rough steeply-sloped area would look more like stair steps. 

Figure 31-9.  Map of surface flow confluence. 

Water has a similar vantage point of the slopes it encounters, except given its head, water will take the steepest downhill path (sort of like an out-of-control skier).  Figure 31-91 shows a 3-D grid map of an elevation surface and the resulting flow confluence.  It is based on the assumption that water will follow a path that chooses the steepest downhill step at each point (grid cell "step") along the terrain surface.   

In effect, a drop of water is placed at each location and allowed to pick its path down the terrain surface.  Each grid cell that is traversed gets the value of one added to it.   As the paths from other locations are considered the areas sharing common paths get increasing larger values (one + one + one, etc.).  

The inset on the right shows the path taken by a couple of drops into a slight depression.  The inset on the left shows the considerable inflow for the depression as a high peak in the 3-D display.  The high value indicates that a lot of uphill locations are connected to this feature.  However, note that the pathways to the depression are concentrated along the southern edge of the area.   

Now turn your attention to figure 31-10.  Ridges on the confluence density surface (lower left) identify areas of high surface flow.  Note how these areas (darker) align with the creases in the terrain as shown on the draped elevation surface on the right inset.  The water collection in the "saddle" between the two hills is obvious, as are the two westerly facing confluences on the side of the hills.  The 2-D map in the upper left provides a more familiar view of where not to unroll your sleeping bag if flash floods are a concern. 

Figure 31-10.  2-D, 3-D and draped displays of surface flow confluence. 

The various spatial analysis techniques for characterizing terrain surfaces introduced in this series provide a wealth of different perspectives on surface configuration.  Deviation from Trend, Difference Maps and Deviation Surfaces are used to identify areas that "bump-up" (convex) or "dip-down" (concave).  A Coefficient of Variation Surface looks at the overall disparity in elevation values occurring within a small area.  A Slope Map shares a similar algorithm (roving window) but the summary of is different and reports the "tilt" of the surface.  An Aspect Map extends the analysis to include the direction of the tilt as well as the magnitude.  The Slope of a Slope Map (2nd derivative) summarizes the frequency of the changes along an incline and reports the roughness throughout an elevation surface.  Finally, a Confluence Map takes an extended view and characterizes the number of uphill locations connected to each location.   

 The coincidence of these varied perspectives can provide valuable input to decision-making.  Areas that are smooth, steep and coincide with high confluence are strong candidates for gully-washers that gouge the landscape.  On the other hand, areas that are rough, gently-sloped and with minimal confluence are relatively stable.  Concave features in these areas tend to trap water and recharge soil moisture and the water table.  Convex features under erosive conditions tend to become more prominent as the confluence of water flows around it. 

Similar interpretations can be made for hikers, who like raindrops react to surface configuration in interesting ways.  While steep, smooth surfaces are avoided by all but the rock-climber, too gentle surfaces tend too provide boring hikes.  Prominent convex features can make interesting areas for viewing—from the top for hearty and from the bottom for the aesthetically bent.  Areas of water confluence don't mix with hiking trail unless a considerable number of water-bars are placed in the trail.   

These "rules-of-thumb" make sense in a lot of situations, however, there are numerous exceptions that can undercut them.  Two concerns in particular are important— conditions and resolution.  First, conditions along the surface can alter the effect of terrain characteristics.  For example, soil properties and the vegetation at a location greatly effects surface runoff and sediment transport.  The nature of accumulated distance along the surface is also a determinant.  If the uphill slopes are long steep, the water flow has accumulated force and considerable erosion potential.  A hiker that has been hiking up a steep slope for a long time might collapse before reaching the summit.  If that steep slope is southerly oriented and without shade trees, then exhaustion is reached even sooner. 

In addition, the resolution of the elevation grid can effect the calculations.  In the case of water drops the gridding resolution and accurate "Z" values must be high to capture the subtle twists and bends that direct water flow.  A hiker on the other hand, is less sensitive to subtle changes in elevation.  The rub is that collection of the appropriate elevation is prohibitively expensive in most practical applications.  The result is that existing elevation data, such as the USGS Digital Terrain Models (DTM), are used in most cases by default.  Since the GIS procedures are independent of the gridding resolution, inappropriate maps can be generated and used in decision-making.   

The recognition of the importance of spatial analysis and surface modeling is imperative, both for today and into the future.  Its effective use requires informed and wary users.  However, as with all technological things, what appears to be a data barrier today, becomes routine in the future.  For example, RTK (Real Time Kinematic) GPS can build elevation maps to centimeter accuracy— it's just that there are a lot of centimeters out there to measure.  

The more important limitation is intellectual.  For decades, manual measurement, photo interpretation and process modeling approaches have served as input for decision-making involving terrain conditions.  Instead of using GIS to simply automate the existing procedures our science needs to consider the new micro-terrain analysis tools and innovative approaches they present.
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Author's Notes: The figures presented in this series on "Characterizing Micro-Terrain Features" plus several other illustrative ones are available online as a set of annotated PowerPoint slides at the "Column Supplements" page at http://www.innovativegis.com/basis.

 

Modeling Erosion and Sediment Loading     (return to top of Topic)

Last month's discussions suggested that combining derived maps often is necessary for a complete expression of an application.  A simple erosion potential model, for example, can be developed by characterizing the coincidence of a Slope Map and a Flow Map (see the previous two columns in this series).  The flowchart in the figure 31-11 identifies the processing steps that form the model— generate slope and flow maps, establish relative classes for both, then combine.

Figure 31-11.  A simple erosion potential model combines  

While a flowchart of the processing might appear unfamiliar, the underlying assumptions are quite straightforward.  The slope map characterizes the relative "energy" of water flow at a location and the confluence map identifies the "volume" of flow.  It's common sense that as energy and volume increase, so does erosion potential.   

The various combinations of slope and flow span from high erosion potential to deposition conditions.  On the map in the lower right, the category "33 Heavy Flow; Steep" (dark blue) identifies areas that are steep and have a lot of uphill locations contributing water.  Loosened dirtballs under these circumstances are easily washed downhill.  However, category "12 Light Flow; Moderate" (light green) identifies locations with minimal erosion potential.  In fact, deposition (the opposite of erosion) can occur in areas of gentle slope, such as category "11 Light Flow; Gentle" (dark red).   

Before we challenge the scientific merit of the simplified model, note the basic elements of the GIS modeling approach— flowchart and command macro.  The flowchart is used to summarize the model's logic and processing steps.  Each box represents a map and each line represents an analysis operation.  For example, the first step depicts the calculation of a SlopeMap from a base map of Elevation.  The actual command for this step, "Slope Elevation for SlopeMap," forms the first sentence in the command macro (see author's note).   

The remaining sentences in the macro and the corresponding boxes/lines in the flowchart complete the model.  The macro enables entering, editing, executing, storing and retrieving the individual operations that form the application.  The flowchart provides an effective means for communicating the processing steps.  Most "GIS-challenged users" are baffled by the detailed code in a command macro but readily relate to flowchart logic.  In developing GIS applications, the user is the expert in the logic (domain expertise) while the developer is the expert in the code (GIS expertise).  The explicit linkage between the macro and the flowchart provides a common foothold for communication between the two perspectives of a GIS application. 

It provides a starting place for model refinement as well.  Suppose the user wants to extend the simple erosion model to address sediment loading potential to open water.  The added logic is captured by the additional boxes/lines shown in figure 31-12.  Note that the upper left box (Erosion_classes) picks up where the flowchart in figure 31-11 left off. 

Figure 31-12.  Extended erosion model considering sediment loading potential considering intervening terrain conditions.     

A traditional approach would generate a simple buffer of a couple of hundred feet around the stream and restrict all dirt disturbing actives to outside the buffered area.  But are all buffer-feet the same?  Is a simple geographic reach on either side sufficient to hold back sediment?  Do physical laws apply or merely civil ones that placate planners?   

Common sense suggests that the intervening conditions play a role.  In areas that are steep and have high water volume, the setback ought to be a lot as erosion potential is high.  Areas with minimal erosion potential require less of a setback.  In the schematic in figure 31-12, a dirt disturbing activity on the steep hillside, though 200 feet away, would likely rain dirtballs into the stream.  A similar activity on the other side of the stream, however, could proceed almost adjacent to the stream. 

The first step in extending the erosion potential model to sediment loading involves "calibrating" the intervening conditions for dirtball impedance.  The friction map identified in the flowchart ranges from 1 (very low friction for the 33 Heavy Flow: Steep condition) to 10 (very high friction for 11 Light Flow; Gentle).  A loose dirtball in an area with a high friction factor isn't going anywhere, while one in an area of very low friction almost has legs of its own.   

The second processing step calculates the effective distance from open water based on the relative friction.  The command, "SPREAD Water TO 50 THRU Friction OVER Elevation Uphill Across For Water_Prox," is entered simply by completing a dialog box.  The result is a variable-width buffer that reaches farther in areas of high erosion potential and less into areas of low potential.  The lighter red tones identify locations that are effectively close to water from the perspective of a dirtball on the move.  The darker green tones indicate areas effectively far away. 

But notice the small dark green area in the lower left corner of the map of sediment loading potential.  How can it be effectively far away though right near a stream?  Actually it is a small depression that traps dirtballs and can't contribute sediment to the stream— effectively infinitely far away. 

Several other real-world extensions are candidates to improve model.  Shouldn't one consider the type of soils?  The surface roughness?  Or the time of year?  The possibilities are numerous.  In part, that's the trouble with GIS— it provides new tools for spatial analysis that aren't part of our traditional procedures and paradigms.   Much of our science was developed before we had these spatially-explicit operations and is founded on simplifying assumptions of spatial independence and averaging over micro conditions.  But now the "chicken or egg" parable is moot.  Spatial analysis is here and our science needs updating to reflect the new tools and purge simplifying assumptions about geographic relationships.
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Author's Note: The MapCalcTM program by Red Hen Systems, Inc., was used for processing and display of the examples presented in this series.  An online tutorial extending the discussions is available at www.redhensystems.com.  

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