Map Making Fundamentals

Introduction: 

Understanding cartographic fundamentals in mapping is an essential skill set to maintain in the field of geography. To begin, it is important to note that there is a minimum of at least five mapping elements which should be incorporated into all generated maps, including:

1. North Arrow
2. Scale Bar
3. Locator Map
4. Watermark (map illustrator)
5. Data Sources

      (and a Title, of course)

Other elements to consider in cartographic design could include:

• A Legend
• Data Frame
• Company or Client Logo
• Labels and Annotations
• Disclaimers
• the Date
• etc. 

This lab is designed to ensure that each of these key components within maps and all other proper mapping techniques are being included and utilized by students for the remainder of this course, as well as for other projects extending well beyond the duration of the course. 

Methods & Results:

Part One: Creating A Map Series of Sandbox Terrain Survey-

In order to put these cartographic fundamentals to practice, students were asked to utilize their sandbox survey imagery from the previous two labs and generate a series of five maps using an interpolation method of their choosing. The first map produced would be a hillshade map view of the sandbox survey terrain, and the final four maps required would be oblique maps of the terrain viewed from four different angles. 

For the purposes of this lab, the interpolation method of choice utilized for the map series was the Kriging Interpolation Method. The four oblique map's angles were arranged so that when organized together, the series would allow for each sandbox corner to take a turn at the forefront of the map. North arrows are used to help the map reader visualize the sandbox's orientation within each of the maps represented. The final series of maps for the Sandbox Terrain Survey is presented below:

                 Map Series 1: Sandbox Terrain Survey, Kriging Interpolation Method

Metadata: The tools utilized in collecting data points for survey model included a meter stick, tacks, and a string used for girding. Data points collected from far sandbox across the street from Phillips Hall between 3:00 and 4:30 pm on Monday, January 30th .

Part Two: Hadlyville Cemetery, Mapping with Attributes-

The section section of the lab required students to construct another series of maps concerning the features of a number of graves located in the Hadlyville Cemetery in Eau Claire County, Wisconsin. Students were to generate a total of four maps, including three nominal maps, one denoting the year of death on each grave, another the last names associated with the graves, and the last involving a color coated scheme indicating if the graves are still standing or not. The last map required a numeric ranking again based on the years of deaths written upon each grave. The resulting maps are posted below:

Map 2: Nominal Year of Death Map

The first of this map series reveals the dates associated with each of the graves within the Hadleyville Cemetery. The years range from as early as 1859 to as recent as the year 2006. Many graves which appear within the same year occur in a row, but overall there is no progressive number series to indicate any order to the burials lied out.

Map 3: Nominal Last Names Map

The next map in the series reveals the last names that are associated with each of the graves. It is common to find alike names buried near to one another across the cemetery. It is safe to assume that these common last name clusters belonged to individual families or married couples. Some of the more commonly occurring names include "Beardsley" at the eastern-most section of the map, "Folley" to the north, and "Higley" and "Hadley" to the northwest.

Map 4: Nominal Color Coded Conditions Map

This map is another example of a nominal map, though it has been color coded to indicate whether or not each grave is still standing. In this instance, it is appropriate to include a legend within the map in addition to the original five elements of maps. The legend is useful in helping the reader to decipher why each of the graves are color coated as such. The blue dots symbolize the graves still standing while the red dots indicate graves which have fallen. The "Null" yellow dots most likely account for graves which are already laid out parallel to the ground, or are graves which perhaps no longer have a stone to mark them at all. Overall, it seems most of the graves in Hadleyville Cemetery are standing in good condition. 

Map 5: Numeric Proportional Ranking Map based on Years of Deaths

The last map in the series was a proportional interval map relating  the dated ages of the graves found within the cemetery by a ranking system. Each of the three point sizes represent a time span of approximately 50 years. The smallest dots account for the oldest set of graves; their 'year of death' dates range between 1859 throughout the remainder of the century. The middle sized dots pick up the dates again beginning in 1900, and maintaining through the beginning half of the twentieth century into 1950. The largest dots represent the newest of the graves found in the cemetery. Its 'year of death' listings range beginning in 1951 until 2006. 

Conclusion:

Each of the maps provided within the two map series showcased above maintain all five elements of mapping essentials within them, including a north arrow, scale bar, locator map, watermark, and list of data sources. When useful, additional mapping elements can be added to the map, such as the legends featured within the last two maps in the second series. Overall, this lab was a useful exercise in the review of mapping element essentials and cartographic fundamentals. 

Sources:

Hadleyville Cemetery Geodatabase (provided by professor)
ESRI Software

Sandbox Survey (part 2): Visualizing and Refining the Terrain Survey

Introduction: 

In the previous lab, students were assigned to groups of three and asked to construct and survey an elevation model featuring a ridge, hill, depression, valley, and plain using the terrain in an approximate square meter sandbox. Each group was supplied with tape, string, thumb tacks and some meter sticks in order to construct a grid system pattern and survey the terrain. Groups used various tactics of sampling in order to collect elevation data points from their terrain. The data points collected were then normalized by entering the coordinate points into an Excel document as individual x-, y-, and z-value attributes.

Data normalization is the process of organizing data into a table, with each column representing one attribute of the data presented. In this case, normalizing the data meant that for the table produced in Excel, each x-value needed to be entered into one continuous column labeled 'X-Values,' all y-values entered into a continuous column marked 'Y-Values,' and so on so forth so that each row was comprised of four columns (the OID, x-, y-, and z-values). When looked at as a whole, each row within the excel file would make up one coordinate point (this group had 400 coordinate points, therefore 400 rows of data points).

When done correctly, the X,Y (and Z) coordinates of an Excel file may be uploaded as data points into ArcMap as a grid system. From here, students would be able utilize tools in ArcMap to manipulate the data points and illustrate various 2D files of 3D projections of the terrain, which could then be transported into ArcScene to ultimately generate the 3D digital models of the terrain created in the sandbox during the previous lab.

Methods:

Once the data has been normalized in Excel, the file containing these points is ready to be uploaded into the geodatabase stationed in ArcMap using the 'add XY data' tool option. After the table has been imported, it can be converted into a point feature class, which will reveal the grid-like pattern students previously constructed in their sandboxes onto the map. These points can be symbolized to represent individual values from each data point collected, but the image does not provide a good visual as to the varying gradations between each data point value.

To obtain the 3D visual, one can use the tools under the 3D Analysis option in ArcToolbox, where a variety of interpolation methods can be selected from to provide the 2D output of the image desired. This image is stored in the geodatabase in raster format, and can be uploaded into ArcScene to be viewed in 3D with an option to rotate it to view various angles. For the purposes of this lab, all 3D models utilized were oriented so that they would be viewed in the same direction as the sandbox landscape was while being constructed in the field.

Once the models had been generated, the symbology and orientation set, these 3D images could then be exported in 3D format as a .png file to be returned to ArcMap as raster features for mapping and scaling. Since the files re-added to ArcMap were raster features, scale could not be automatically inputted into the maps as is traditionally done. Instead, scale was reflected using the 'drawing' toolbar in ArcMap to illustrate the general size of the actual sandbox being mapped (1 x 1 meter).

Students were to explore 3D analysis using the following five interpolation methods:

1. IDW (Inverse Distance Weighted)-

The IDW interpolation method uses the assumption of Tobler's First Law of Geography (things that are nearer are more similar to one another than things at a further distance away) to fill in the gaps between the sampled data points. The points collected in the field are weighted with the greatest amount of influence and diminished directly with distance from there. The resulting 3D model, then, resembles a somewhat "lumpy" image, the collected weighted points at the peak of the lump as seen in figure one below. This method tends to only be useful if the data being modeled has minimal variations in the range between the points collected, but is normally not the "go-to" method in 3D modeling.

2. Natural Neighbors-

Also known as "area-stealing" interpolation, the natural neighbors interpolation method uses the same weighted distribution technique as in the previous method, but generally tends to do a better job of smoothing out its transitions between the weighted data points, generating a less "lumpy" as can be seen in figure two.

3. Kriging-

The kriging interpolation model is constructed using the weighted average of all nearby collected data points to fill in the unsampled points within the grid using a specific formula. This method is ideal in many instances since it prioritizes smooth transitions between sampled data points, while still providing the best unbiased prediction of the values inbetween. An example of the sandbox terrain using the Kriging interpolation model is pictured in figure three below. 

4.  Spline-

Like the previous kriging method, spline interpolation uses a mathematical formula that ultimately aims to reduce the overall curvature of the surface within the area sampled. As illustrated in figure four, this again results in a much smoother surface in the transition between collected data points.

5. TIN (Triangular Irregular Networks)-

The last interpolation method, TIN interpolation, creates a series of edges connecting various collected data points to form a network of triangles and reveal a general outline of the sampled surface. In areas where the surface varies more drastically, TIN is able to provide a higher resolution than it does in areas with little variance in values. A drawback to this technique, however, is its limited popularity as a result of its costs to build and process. 

Results:

The first interpolation method used, the IDW interpolation, illustrated a "lumpy" 3D image shown in Figure One, as promised in its description under the methods section. The 400 data points which were collected during the original surveying can somewhat be seen at the peaks and troughs created by the weighted points. This method, though it may be beneficial in some instances to be able to see that original data beneath the created surface, is not the most visually appealing, nor accurate in predicting the unsampled data between the sampled data points, and is therefore not a commonly selected option in 3D mapping.

Figure 1: IDW Interpolation Model

The natural neighbors interpolation method illustrated in Figure Two generates a much more likely option between the first two methods. The weighted distribution at collected data points is still visible, but the transition between data points illustrates a much smoother surface than the first option had provided.

Figure 2: Natural Neighbors Interpolation

Figure Three reveals the kriging interpolation method in use. Here, again, the surface is generally smooth. This option is supposed to be the least biased in generating values for its unsampled points. Perhaps this is why this option seems to reveal the least amount of color variance from the surface beginning its lowest points, to the depths of the area. 

Figure 3: Kriging Interpolation

The fourth figure utilizes the Spline interpolation method. As stated in its description, this interpolation type provides the smoothest outcome of all five methods. It limits the curvature of the surface, but still somehow manages to create the most uniform surface. Some errors can be seen in the image produced, however, in both hill areas on the surveyed display. The etched blending in the side of the hills may indicate error in measurements performed while in the field. In a follow up survey, these measurements could be taken with more care for accuracy and a smaller rounding value than the quarter inch that this group had decided upon. 

Figure 4: Spline Interpolation

The last interpolation method, TIN, is the most distinct of the five method options. The method utilizes edges and resolution to illustrate the surface model. The triangular network pattern that results from these edges connecting the data points can be clearly seen in Figure Five below, and is especially evident in the caldera-looking feature at the lower left corner of the sampled area. 

Figure 5: TIN Interpolation

Conclusion:

Interpolation can be used for a multitude of purposes. Some of these include mapping of rainfall, watertables, chemical concentrations, noise frequencies, and soil-type distribution. There are also many more options of interpolation methods to choose from in addition to the five options previewed for lab this week. Some other types include PointInterp, Trend, and Density. 

The last few weeks of lab allowed students to familiarize themselves with the practice of field sampling, data normalization, and 3D modeling with Interpolation. 

Sources:

http://www.spatialanalysisonline.com/HTML/index.html?kriging_interpolation.htm

http://pro.arcgis.com/en/pro-app/help/analysis/geostatistical-analyst/how-inverse-distance-weighted-interpolation-works.htm

http://resources.arcgis.com/en/help/main/10.1/index.html#//005v00000027000000

Sandbox Survey (part 1): Creating a Digital Elevation Surface Model

Introduction:

Sampling is an effective time and resource saving tool that is often utilized in the process of data collection. Many times, a study interest may realistically be too large to undertake a thorough and detailed collection of all the existing data that is beneficial to the study. In these instances, sampling allows the data collector focus on a small-scale representation of their study interest in order to make generalizations about the larger picture as a whole. For geographers, this is an ever-familiar skill set that has been frequently exercised-- identifying key themes and patterns at local scales, and analyzing them in relation to other themes and patterns found elsewhere, in an overall attempt to make better sense of our world. 

The process of sampling can be executed in a variety of ways. The three main types of sampling include random, systematic, and stratified. Somewhat self-explanatory, the process of random sampling involves the spontaneous selection of data, where all available data has an equal chance at being selected. This method is useful because it is the least bias of all three sampling techniques and can be applied to large sample populations. Systemic sampling is done according to a predetermined strategy or system. Data collected is done in even intervals along the study area. This strategy is useful since it allows for thorough coverage of the area in study. Lastly, the third type of sampling, stratified sampling, is used when the area in study is composed of smaller areas of a standard size. These smaller areas are each individually a smaller representation of the larger area, and should therefore be reflective of that. One example of this might be blocks within a given neighborhood. The neighborhood is the overarching study area, but each block may be miniature representations of what the neighborhood looks like as a whole.

For this lab, students were placed into groups of three and asked to construct an elevation surface of terrain using a sandbox approximately one square meter in size. The terrain needed to include a ridge, hill, depression, valley, and plain. Students were given tape, string, thumb tacks, and a few meter sticks in order to construct grid system and survey the terrain to be digitized in ArcMap during lab in the week to follow.

Methods

In beginning the project, the group determined that the best method to use for sampling the sandbox's terrain was the systemic line sampling method. This method uses the intersections on a standardized grid with uniform intervals as points for data collection across the sandbox terrain. The group felt that this was the best choice in order to have a good coverage of the sandbox terrain overall that would clearly outline the terrain features required to be used in its construction (a ridge, hill, depression, valley and plain).

Figure 1: Group Surveying and Recording Data

Of the two sandboxes located across Roosevelt Street from Phillips Hall, the group chose to begin constructing the terrain in the furthermost sandbox. Once each terrain feature had been constructed, the group focused on constructing the grid, pinning string to the sandbox's wooden frame at equal intervals measured by a meter stick. The intervals used were predetermined as a result of the sandbox frame size. The approximate square meter sandbox could be split into a 20x20 grid system with each square approximately 2x2 inches in size, allowing for a total of 400 data points to be collected, a sizable amount that could be conducted in reasonable time. One person in the group was responsible for recording the data while the other two alternated between rows in measuring the elevation level of the sand at the southwest corner of each grid line intersection.

Figure 2: Taking Measurements from Terrain Grid

In total, the operation took just over an hour and a half to complete. The string line was determined to be the surface (or sea level) of the terrain model, so most of the data collected was then negative in value. Due to the cold weather, the group decided first to transcribe these data points in a notebook to be transferred into an Excel file later on. After transferring it to the Excel file, a color scheme was added to the data plotted in the table so that the group could get a glimpse at what the terrain would look like once digitized in ArcMap. The group then also charted the data in a format that would be useful for transferring these points into ArcMap during the lab next week. Fragments of the resulting Excel data tables can be found below:

 

Chart 1: Excel Data and Normalization

Results/Discussion

Overall, the group managed to collect a total of 400 data points within the 20x20 grid.  The minimum value in our collection was -8 inches while the maximum value was a +4 inches. Since the string line was established as sea level, most of the data points fell below the line at negative values, the most commonly occurring value being -2 inches. Given the cold temperatures and tedious measurement requirements of the lab, this sampling method proved to be really useful and seemingly effective. 

Some issues did arise during the process of completing the lab. To begin, the freezing temperatures had managed to freeze much of the sand within the sandbox, and made digging the terrain for surveying difficult as it limited the areas which were soft enough to be molded. Secondly, as the group went on collecting data points, the string began to slack some in certain areas, It may have been more beneficial to double tack alternating string lines to improve its security. A third improvement could have been made in being more specific in collecting measurements. It seems the group did a lot of rounding to quarter inch markers in looking at the final data set. A better method would have been to conduct the measurements in centimeters to promote more accurate readings across the survey sample.

Conclusion:

Sampling is an effective tool to utilize in spatial settings as are commonly found in the field of Geography because it allows for larger scale analysis to be done on smaller scale levels, conserving both time and resources in the process. This activity relates well to the system used by the Public Land Survey System, which also maps out land plots into squares, but at a much larger scale. Overall, the survey system utilized was a decent system given the constraints of the weather, but of course, more data is always better. Perhaps creating more rows and columns within the grid system would have benefited the group, as it would have also resulted in the collection of more data points. Also, as noted previously, the group would have done better conducting the data point measurements in units of centimeters rather than in inches for better accuracy in numbers. 

Sources

http://www.rgs.org/OurWork/Schools/Fieldwork+and+local+learning/Fieldwork+techniques/Sampling+techniques.htm