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AcademicMapCalc: Educational Materials for Instruction
Berry, Joseph K.
Kensinger, Jerry
Abstract Desktop mapping has gained popularity in many disciplinesacross campus. The additional dimensionof “where” has provided new approaches to data analysis and decision formulation. However, instruction in grid-basedprocessing has been limited. Untilrecently, GIS software supporting surface modeling, geo-statistics and spatialanalysis has been too expensive and too complex for all but advancedcourses. The MapCalc educationalpackage is a set of inexpensive, Windows-based materials for learning mapanalysis concepts, considerations and procedures. The educational materials are suitable for self-learning andintroductory through advanced courses. The MapCalc Learner CD (US$21.95 plus shipping) consists oftutorial versions of Surfer (for surface modeling) and MapCalc (for spatialstatistics/analysis), a basic set of exercises and databases, the PrecisionFarming Primer and the Map Analysis online texts, and numerousapplication scenarios. The MapCalcAcademic CDs (US$495 plus shipping) contains all of the student materialsplus a multi-seat license for a single computer lab, an extensive set ofPowerPoint presentations for lectures, additional sets of exercises and exam questions/answers. This paper describes and demonstrates thematerials for both self-instruction and classroom teaching. Note: thispresentation contains several real-time demonstrations that are encapsulated inseveral of the figures. A more completedescription of these and other grid-based processing examples are online at www.innovativegis.com/basis. The reader is encouraged to review theexamples then download a free evaluation copy of the MapCalc program from www.redhensystems.com for hands-onexperience and springboard to the Learner or Academic versions for more indepth understanding of map analysis. Introduction Courses in Geographic Information Systems (GIS) technologyare proliferating on campus. What usedto be the domain of geography departments has diffused into applicationdisciplines ranging from forestry to business, engineering, law enforcement, publichealth and a multitude of other departments. A major factor fueling the expansion is inexpensive and user-friendlydesktop mapping software. These vector-based systems are ideal for learning thefundamentals of mapping and spatial database management. The educational experience with desktopmapping provides an excellent entry into GIS and hands-on experience inapplying the basic concepts. Anincreasing number of resources tailored to specific application areas areavailable. The datasets and structuredexercises provide meaningful learning experiences for a wide range of students. Basic thematic mapping and geo-query, however, only addressa portion of GIS capabilities. Yet itis apparent that grid-based map analysis hasn’t received the same attention inmost academic programs. This conditionoften is attributed to less familiar analysis techniques that are outside thestudent’s manual mapping experiences and thought to involve advanced statisticsand “map-ematical” modeling techniques. The result of this rationale is that exposure to grid-based analysisrarely occurs in most introductory courses. This paper describes some of the instructionalconsiderations surrounding grid-based map analysis. In addition it describes the inexpensive MapCalc Learner softwareand supporting materials for student and instructor alike. TheGrid-Analysis Frame Vector-based systems identify three basic map features thatcomprise all maps—points, lines and polygons. These features are suitable forcharacterizing discrete spatial objects, such as light poles, streets andproperty boundaries. However,continuous gradients, such as an elevation surface or a proximity map arepoorly represented as contour lines that generalize detailed data into a set ofintervals used for display. The introduction of a grid-analysis frame provides aframework for storage and processing of a fourth basic map feature—a surface. The grid-based construct enables display andprocessing of geographic space as a continuum. Its base spatial unit is a cell defined by the column and rowcoordinates of an imaginary grid superimposed over an area. The base spatialunit is a grid cell and is used to identify… · Points—single cell,
The top left portion of figure 1 shows an elevation surfacedisplayed as a traditional contour map, a superimposed analysis frame and a 2-Dgrid map. The highlighted portion ofthe table depicts the elevation value (1,635 feet) stored at one of the gridlocations. The remainder of the tableshows the values stored on other map layers at the same location. As the cursor is moved, the “drill-down” ofvalues for different locations are instantly updated. The plots in the lower portion of the figure show two typesof 3-D displays. Connecting the gridlines at the center of each grid space forms a lattice structure. The lengths of the lines are a function ofthe difference between the values stored at adjacent grid spaces. The result is a “wireframe” that forms thepeaks and valleys of the spatial distribution of the data. The color zones identify contour intervalsthat are draped on the frame. The larger plot in the lower-right portion of the figureshows a grid structure surface of the same data. The boundary lines for each grid space aredrawn to a relative height as function of the stored value. The result is a “stepped surface” thatdepicts the actual data defining the terrain and available for mapanalysis. MapAnalysis Procedures An important characteristic of grid-based data is that a maparea is subdivided into a uniform set of parcels (grid cells) that is used tocharacterize all map layers. The analysisframe provides the geographic consistency needed for investigating spatialrelationships within and among grid layers. However the consistency is obtained at a loss in positional accuracyunless the grid is very fine and approaches the X,Y reference grid used in avector-based system. The tradeoff between positional accuracy and analysisutility is key in determining appropriate applications for vector andgrid-based systems. In general, vectorsystems are best suited for computer mapping and geo-query of discrete mapfeatures but have limited map analysis capabilities. Grid systems, on the other hand, are ill suited for mapping andquery but contain a robust set of analytical operations. For example, consider calculation of terrain slope. In a vector-based system the relativedistance between contour lines graphically portrays steepness—closer the linesthe steeper slopes. But the ability tocalculate a slope map is practically impossible using this data structure.
The top portion of figure 2 shows 2-D and 3-D views of a slopemap derived using the analysis frame. The larger 3-D display on the right shows the slope map draped over theelevation surface. Note that the steepareas (green) and flat areas (red) align with the appropriate surfaceinclinations providing visual conformation of the calculated slope values. As diagramed in the figure, the processinginvolves moving a 3x3 window over the entire elevation surface and calculatingthe slope of a plane that best fits the nine elevation values in the rovingwindow. The bottom portion of the figure shows a derived surface flowmap. Note that the areas withhigher flow values (green) align with the small ravines visible on the terrainsurface. The process simulates a dropof rain falling at each grid cell, tracing its steepest downhill path whileaccumulating the number of paths that cross each cell. Higher numbers on the flow map indicatelocations of water confluence. ProblemSolving The result of an individual map analysis operation is theassignment of a computed value (slope and flow in the previous example)for every grid cell of a new map layer. Sequencing operations develop analysis procedures, such as erosionpotential, as depicted in Figure 3. Figure 3. Acommand macro contains logically sequenced map analysis operations that solve aproblem. The two red arrows in the figure link the MapCalc commandswith the 3-D displays of the slope and flow maps. Calibrating and combining the two maps construct a simple erosionpotential model. Common sense suggeststhat areas with steep slopes and heavy flows tend to have higher erosion thanflat areas with minimal flows. The sequence of commands listed in the macro accomplishesthree things—1) derives the slope and flow maps (using the SLOPE and DRAINoperations), 2) calibrates these layers for gentle-moderate-steep andlight-moderate-heavy classes (RENUMBER), and 3) combines the two maps into asingle erosion potential map (COMPUTE). The procedure used a simple mathematical trick where the slope classesare assigned the values 1, 2 and 3 while the flow classes are assigned 10, 20,and 30. Adding the two maps generates atwo-digit code with the first number (tens digit) indicating the slope classand the second number (ones digit) indicating the flow class—e.g., 11 isn’t aneleven but a “one-one” depicting a location with a gentle slope (1) and a lightflow (1). The map in the lower-right corner shows all of thecombinations of slope and flow classes that occur in the project area. The color-coded arrows identify thecombinations as to whether erosion (orange) or deposition (blue) is likely tooccur. While this simple erosion modelis far from complete it has general merit and aptly illustrates theconstruction of a command macro used to evaluate a GIS model.
Figure 4 diagrams an extension to the simple model thatgenerates an effective proximity map to open water based on the interveningerosion potential. The RENUMBERoperation is used to calibrate the map in figure 3 into a “friction” mapcharacterizing the relative difficulty of erosion—1= high …10= minimal erosionpotential. The SPREAD operation (dialogbox in lower-left) is used to calculate effective distance from the streams andlakes on the water map. This process islike successive buffers in a vector-based system but the buffers reach fartherin areas of high erosion potential—a “variable-width” buffer that is responsiveto intervening conditions. Consider the sketch in the top portion of the figure. A simple buffer of 250 feet on either sideof the stream would allow soil-disturbing activities near the top of the steepinclination that would likely result in considerable sediment raining down onthe stream. On the other side of thestream, activities would be prohibited although the terrain is perfectly flatand erosion potential minimal. Avariable-width buffer, however, reaches much farther on the right side and muchless on the left—not 250 feet regardless of conditions.
Distance operations in MapCalc involve calculation of aseries of concentric rings about a starting location (point feature) or set oflocations (line or polygon feature). These rings are analogous to the ripples generated by tossing a rockinto a pound—splash, one away, two away, etc. Every grid cell in the map area is assigned its “ripple number” withlarger values indicating greater distances. When viewed as a 3-D plot, simple proximity forms a bowl-like accumulationsurface about the feature (top-right plot in figure 5) with the startinglocations of the water map forming the “valley” and increasing proximityforming the “mountains.” Effective proximity considers the intervening conditions asthe wave propagates. The result is awarped-bowl-shaped accumulation surface with varying slopes that correspond tochanges in conditions. Steeper areasindicate locations that are effectively farther away than simple straight-linedistance suggests. Simple distance is defined as “the shortest, straightline between two points.” Simpleproximity relaxes the limitation of just two points to “…among sets oflocations,” such as all water cells to all other grid cells. Effective proximity further relaxesthe assumption of straight-lines allowing distance measurement to simulatemovement considering the effects of relative and absolute barriers. The ability to characterize realisticconnectivity among map features and relax the oversimplifying assumptions ofEuclidean geometry greatly extends simple buffer analysis in desktop mappingsystems—“as-the-crow-flies.”. But if straight-line connectivity is not assumed, thequestion arises what is the “shortest, not necessarily straight routeconnecting two points?” This involvesoptimal path analysis that tracks the steepest downhill path over an proximitysurface. In effect, this processretraces the route the wave front took from the starting location(s) around andthrough the intervening barriers to any other location on the surface. Like walking through a parking lot with alot of mud puddles you could choose to go around some and slowly trek throughothers. In effect accumulationsurface analysis evaluates all possible routes and assigns the shortest—thevalue indicates the distance away and the optimal path indicates the route. The concept of connectivity can be expanded to include visualconnectivity by considering straight-rays in three-dimensional space. If the ridge occurs between two points onecannot be seen from the other. If theray is not interrupted, the two points are visually connected. Grid-based visibility analysis, however,does not use vector calculations in three-dimensional space. It uses the distance “ripples” to identifythe distance from a viewer location and calculates the difference in elevationto derive a “rise to run” ratio (tangent) between two points. If the ratio is larger than any of theratios of the previous rings along the cell is marked as seen and that ratiobecomes the one to beat as the wave front continues. In effect, the algorithm goes “splash” at a viewer cell and thewave front propagates carrying the tangent to be beat that is evaluated at eachlocation as it is crossed. The result is a map that identifies a viewer location’s viewshed—alllocations that can be seen. If multipleviewer locations are considered a visual exposure surface is derived—mapvalues indicate the number of times seen. If the viewer cells have differential weights a weighted visualexposure surface is generated. Ifthe weights are both positive (beautiful things) and negative (ugly things) a net-weightedvisual exposure surface is generated. For example, a recreation planner might generate such a map to use inlocating a hiking trail that has the best views of beautiful features whileavoiding visual connections to ugly things. MapCalcEducational Software and Materials The discussion in the previous section illustrates just afew of the map analysis capabilities contained in MapCalc.
The twenty-six analytical operations are grouped into fiveclasses—reclassify, overlay, distance, neighborsand statistics—as listed in figure 6. The previous discussions involved the analytical operations of SLOPE(neighborhood), RENUMBER (reclassify), COMPUTE (overlay), DRAIN, SPREAD, andRADIATE (distance). A cross-referenceto comparable operations in other grid-based systems is included in thedocumentation. For example, the translationto GRID commands (a module of ARCINFO GIS system by ESRI) is SLOPE= slope, DRAIN=flowaccumulation, RENUMBER= reclassify, SPREAD= costdistance, andRADIATE=visibility. Command entry in MapCalc is made through pop-up dialog boxessimilar to the one shown in the lower-right portion of figure 4. Each command forms a complete andgrammatically correct English sentence that is added to the command macro logas it is executed. These macros can beedited, modified, and interleaved with descriptive notes then saved forre-execution. The use of an intuitivecommand language is ideally suited for teaching as complex programminglanguages often confuse and intimidate students with minimal computerexpertise. Contextual help is availablefor all commands.
In addition, there are over fifty “tools” for displayingmaps, investigating data, charting, windowing, importing/exporting, andmanaging files (see figure 7). Allinteraction with the software is through graphical user interfaces and standardWindows icons including buttons, scroll lists, hot-fields, etc. The interface is designed so mostinteraction is completed through mouse-clicks with minimal keyboard entry. Data exchange includes most grid formats andpopular desktop mapping files. The MapCalc educational system comes in three forms—a freedownload of the program, the MapCalc Learner package for students and theMapCalc Academic for instructors. TheLearner CD contains the MapCalc and Surfer tutorial systems, exercises/databases,application demos and two online texts—Map Analysis, acompilation of Dr. Berry’s “Beyond Mapping” column in GEOWorld and PrecisionFarming Primer, a compilation of his “Inside the GIS Toolbox” column inagInnovator. There is a crosslisting of tutorial exercises keyed to these books and Dr. Berry’s other books BeyondMapping and Spatial Reasoning (Wiley & Sonspublishers).
The MapCalc software by Red Hen Systems (www.redhensystems.com) has extensivecapabilities in spatial analysis and statistics. The Surfer software by Golden Software (www.goldensoftware.com) providesextended capabilities in surface modeling and 3-D graphics. The MapCalc tutorial version is constrainedto a 100x100 grid configuration (10,00 grid cells) and some of Surfer’s outputfeatures are constrained in the tutorial version. Both software systems have data exchange tools and accept datafor creating your own databases. The MapCalc Learner package is designed forstudent and self-learning and licensed for educational use on a single computer. It is distributed on a single CD forUS$21.95 plus shipping and handling. The MapCalc Academic package is designed for instructors andcontains all of the Learner materials plus lecture PowerPoint’s, additionalexercises, one-day workshop and full introductory course materials supportingclassroom instruction. The materialswere developed by Dr. Berry (www.innovativegis.com/basis)who has over 30 years of GIS teaching experience and has presented hundreds ofworkshops and numerous college courses on map analysis. The Academic package includes multiple-seatlicense for educational use in a single computer lab and are distributed on twoCDs for US$495.00 plus shipping and handling. Conclusion The discussion in the “Problem Solving” section of thispaper illustrates a small set of the analytical operations in grid-based mapanalysis. The live demonstrations andonline annotated applications provide a wealth of experience in GIS modelingand spatial reasoning. The sequencingof analytical operations to form application macros enables users to truly“think with maps” within a problem-solving context. In many respects GIS modeling is as different as it issimilar to desktop mapping. While amajority of the extended capabilities are conceptually intuitive and have beenknown for decades, their practical application has been shrouded in complex andexpensive software that has kept map analysis out of most classrooms. The MapCalc educational materials enable students andinstructors an opportunity to get hands-on experience in applying this powerfulyet often overlooked side of GIS technology. For less than the cost of a textbook, a student can havestate-of-the-art map analysis software on his or her own computer. For less than most single seat licenses, aninstructor can populate an entire computer lab, as well as getting a jump-starton integrating grid-based analysis within their courses through the extensiveteaching support materials. Biography Joe Berry is the Presidentof Berry & Associates // Spatial Information Systems, consultants andsoftware developers in GIS Technology. Also he serves as Special Projects Manager with Red Hen Systems and theKeck Scholar in Geography at the University of Denver. Contacts: Berry & Associates, 2000 South College Avenue, Suite300, Fort Collins, Colorado 80525; phone: (970) 215-0825; E-mail: jberry@innovativegis.com; Website:www.innovativegis.com/basis. Jerry Kessinger is a SeniorSoftware Engineer with Red Hen Systems, a
systems development companyspecializing in multimedia mapping and data
processing for site-specificagriculture. Contacts: Red Hen Systems,2310
E. Prospect Road, SuiteA
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