Cartographic Fundamentals: Essentials in Map Creation.

Background
In order to ensure data collected in the future is properly presented, it is critical to understand the fundamentals of presenting data through a map. In a followup to the sandbox survey, effective map design became the focus of this exercise. Using one of the interpolation methods of the last exercise, an effective map needed to be generated properly conveying the interpolation method of the sandbox plot. In addition, several maps would be generated of the Hadleyville Cemetery located in Eau Claire County, Wisconsin. Every map generated, in addition to being cartography pleasing and including the relevant data, would contain the five primary components needed in order to interpret a map: a north arrow, scale bar, locator map, watermark, and data source. A north arrow simply denotes the direction of true north based on a maps orientation. A scale bar provides the necessary scale needed to properly picture and analysis the data. A locator map is a sub-map created that shows the location of the study or survey in relation to the larger surrounding area. A watermark denotes the creator of the map. The data source is simply when and where the data was taken from or recorded.
Part 1 Results
Due to the nature of this exercise, stating the process of the map construction would be redundant. Thus, the focus of the results will be on the completed map data. Part 1 focuses on the map generated from the spline interpolation method created from the original 212 points gathered from the sandbox plot on January 31, 2017. As a review, spline interpolation generates a model which creates a surface that passes through the recorded points while bending as little as possible between the points.

Figure 1: An elevation map of the sandbox plot (center) taken on the University of Wisconsin, Eau Claire Campus. Included is a collection of 3 dimensional views of the sandbox plot from the western corner (top right), southern corner (top-middle right), eastern corner (bottom-middle right), and northern corner (bottom right). Also included is a reference map (left) depicting the location of the sandbox plot on the University of Wisconsin, Eau Claire campus.

The maximum elevation of any given location in the spline interpolation terrain map is 5.11683 cm, the minimum elevation is -8.22476 cm, and the average elevation is -2.19799 cm. In addition, the topography of this survey area can be defined by several primary regions (Figure 1). The entire right side of the survey area, is dominated by a deep trench which runs the height of the survey area. This particular feature reaches the lowest possible elevation of the survey area, an elevation of approximately -8.7 cm, and rarely rises above -7 cm in the confines of the trench. Outside the trench, the elevation rises to approximately -2 cm. The very center of the survey area, from top to bottom, is characterized by a rather featureless plain. This plain averages out to an elevation of -2 cm. In the bottom left corner of the survey, a about 50 cm in length and a maximum of 5.1 cm in height stretches up the y axis of the survey. The far top left corner of the survey contains a pronounced, circular hill with an elevation of approximately 5 cm. The rest of the top left corner is distinguished by a circular depression ringed by a ridge. The depression falls to an elevation of approximately -5 cm and the cirular ridge around it reaches an elevation of approximately 3 cm.
Part 2 Results
The Hadleyville Cemetery of Eau Claire County is a fairly simple feature. The cemetery exits south of W441 Country Road HH, with the area to the south and the west of the cemetery being used as farmland, the area to the east being primarily forest, and the area north of the road being primarily open fields. However, the primary focus of this cemetery is the graves which are contained within it (Figure 2).

Figure 2: A series of maps for the Hadleyville Cemetery graves in Eau Claire County, Wisconsin: a map labeling each grave’s year of death with a corresponding reference map (top left), a map labeling the last name on each grave with a corresponding reference map (bottom left), a map showing the condition of each grave as defined by whether it is standing or not with a corresponding reference map (top right), and a map depicting the year of death on each grave as a ranked symbol with a corresponding reference map (bottom right).

The newest graves in the cemetery seemed to be focused to the northern and eastern portions of the cemetery. In addition, the graves of the south east  portion of the cemetery do not yet mark years of death. The oldest graves are largely confined to the western portion of the cemetery and to a small cluster in the wooded area to the far south eastern portion of the cemetery. In addition, graves are mostly grouped by family name. The north eastern portion of the cemetery contains the Sessions, Schultz and Peterson families. The north central portion of the cemetery is dominated by Foley graves. The western portion contains the Hastings, Cleasby, Hadley, Knight, Higley and Johnson family graves. The central area of the cemetery contains the Petersen, Huchinson, and Corwin families. The north central portion contains the Olson and Hanson families, while the far southern area contains the Robins, Chase, and a portion of the Cleasby family graves. When accessing the whether the graves are standing or not, several observations can be made. The majority of the graves appear to be standing. However, much of the data listing the state of the graves was listed as "null" and thus had to be mapped as an unknown data. This relates back to issues found within the metadata itself. The metadata for the gravestones, when accessed in ArcCatalog, is largely undocumented. There is little listing when the data was collected, who it was collected by, and what it was collected for. Thus, steps that can be taken to correct the data are limited. This undermines the integrity of the data at large.  From what can be seen, however, very few graves are non-standing. These few grave tend to be the oldest in the cemetery, with several in the center and far south eastern portions of Hadleyville.
Sources
Hupy, J. (2017). Cartographic Fundamentals: Essentials in map creation, description, and interpretation. Eau Claire, Wisconsin

Sandbox Survey Part 2: Visualizing and Refining your Terrain Survey.

Introduction
This lab served as a follow up to the previous field exercise, in which a group of students constructed a sample terrain in a roughly one square meter sand box. Afterwards, each group of students was tasked with sampling and surveying the terrain using a variety of sampling techniques. In the previous lab, a hybrid systematic-stratified sampling technique was used to gather 212 points from across the plot and record their respective x, y, and z data in cm. In the original plot, the x and y "0" values were arbitrarily set to one corner, while the z "0" value was set to the height of the grid overlayed on the terrain, with the point recorded above the grid having a positive z-value (height), and the points below the grid having a negative z-value. In this lab, the data would be normalized in order to be interpolated using a variety of interpolation techniques. Data normalization refers to organizing any collected data logically based on fields organized into a graph or table. However, a list of 212 data-points showing their x, y, and z coordinates holds little value, as it is difficult to visualize the original terrain using just the raw organized data. The interpolation procedure would generate a number of digital 3D models  of the original terrain, allowing for simple and effective visualization of the data.
Methods
First, the data was normalized into a series of x, y, and z fields in an Excel document. The data was set a numeric, with the number of decimal values being set for each field in order to prevent computing error for when the data would be imported into ArcGIS. Afterwards, the data was added to a ArcMap viewer by using the 'add XY data' command found under the 'File' menu. Each field of the data was matched to the corresponding x, y, and z values required by the function, and the data was added to the map. In order for the data to be used in a functional form, the X,Y data was exported as its own shapefile, which was added to the map document. The data-points were then color coded to visualize their z values in relation to one another (Figure 1).

In this form, the data could be properly utilized for interpolation methods. Five would be the primary focus of this lab: IDW, Natural Neighbors, Kriging, Spline, and TIN interpolation.
IDW interpolation uses an inverse distance weighting to generate values for points and location not originally sampled. In other words, it uses the surrounding points to generate an average based on how far away the surrounding points are. Due to the nature of this method, ridges and valleys are lost if they were not part of the original survey. However, this survey works well if the original sample was sufficiently dense and recorded most of the ridge and valley features. This method however does maintain the integrity of each point originally recorded. This means that the generated 3D model will show a bump-like pattern across the model, where each bump shows where one of the original survey points was record. This is both helpful and non-helpful. While it preserves the original data, it creates an unnatural looking pattern across the generated model of the terrain.
Natural Neighbors is an interpolation method which calculates a points's z value based on the weighted value of the surrounding points. By weighting each of the surrounding points, this creates a terrain model that is far smoother than a simpler nearest neighbor interpolation, which using the surrounding values without providing appropriate weight to each value.
Kriging is an interpolation technique that makes a mathematical assumption that there is a spatial correlation between sample points that can be reflected in the distance and direction between points. This method generates a model with a degree of predictional accuracy at the cost of adding directional and distance bias in the model. In the end, the model may end up smoother than the original terrain.
Spline interpolation is a method that forces the model to generate a surface with passes through the recorded points while bending as little as possible between the points. This model effectively measures gently varying features like slope and elevation very well, at the cost of losing the natural curvature of the original terrain.
TIN interpolation, or triangular irregular networks, generates a model of the surface by using a series of triangles which make up the surface between all sampled point. This, like IDW, preserves the original values of the sampled points. Unlike IDW, it does not have the problem of generating a bump covered surface. Instead, terrain features are largely maintained at the cost of generating a simple looking model without the natural curves and bends of the original terrain.
Regardless of which method used, they all largely involved similar steps. Each model was generated using the corresponding 3D analysis tool found in ArcMap and by inputting the original data-point feature class into the function. Each resulting interpolation model could be visually in 3D using ArcScene and by adjusting the settings to correctly show vertical exaggeration in each of the models. From here, each model was oriented with the original x,y orientation of the original survey. Each interpolation model was then exported as both a JPEG and a VRML file. Each JPEG file of each interpolation method was arranged with a photograph of the original sandbox terrain (Figures 2-6). The orientation was set the way it was to both make comparisons to the collected data-points and original terrain simpler and more effective. The original terrain, along with minimum and maximum z-values for both the terrain and generated models, provided the scale for each interpolation. Scale and orientation are critical for these exports, as without them the 3D generated models lose meaning and value to real-world context. Without scale and orientation, they cannot be connected back to the real world phenomenon used to generate the model.
Results
 Of the interpolation methods used, the Spline interpolation method seems to have generated the most accurate representation of the original terrain. In the IDW model, the characteristic bumps can be see typically generated by the method (Figure 2).

While preserving the original minimum and maximum z-values, this has generated a model which is hindered by a distracting phenomenon which was not present in the original terrain. The Natural Neighbors interpolation method generated perhaps the second closest digital representation of the original terrain. Most of the original terrain features are preserved, along with the corresponding x and y values (Figure 3).

However, the model appears more jagged than the original terrain did. The Kriging model, in contrast, looks far too smooth when compared to the original terrain . Do to the Kriging technique focusing on distance and directional relation between points, many of the important surface features have been lost. The ridge and valley of the original terrain have been largely flattened and smoothed out. Even the maximum and minimum z-values have been greatly reduced in regards to the original terrain (Figure 4).

Of all the interpolation methods, spline seems to have generated the most representative digital terrain. Its strikes a balance between the smoothness of the Kriging method while maintaining the jagged ridge and valley best represented by the Natural Neighbors methods (Figure 5).

In doing so, the maximum z-values, and perhaps all recorded z-values, have been distorted. The maximum z-value is greater than the original, while the minimum z-value is lower than the original. Terrain shape has been maintained by sacrificing the integrity of the original recorded values. TIN perhaps best represents the original points survey. All of the original survey points maintain their original x, y, and z values. However, this model is lest looking the roughest because of this. All non-recorded data is represented by triangles which bridge the gap between data-points (Figure 6).

This leaves the model looking primitive in comparison to other interpolation methods, which used some for of mathematics to determine z-values for points not originally recorded. In the end, all of these methods combine to create an accurate representation of the terrain originally surveyed, and provide the stepping off point for the digital mapping of the survey data. If this survey were to be performed again, more points would be collected from the bottom half of the survey area, and less from the top half. The number of data-points for and surrounding the ridge were perhaps too few, and there were too many points recorded from the plain of the original terrain, creating too large of a focus on a featureless area.
Conclusion
This survey provides what would be an effective staring off point for any large scale survey. Using this small scale terrain survey, both a viable survey technique can be constructed for a larger area and a interpolation method may be chosen to correctly display what the large scale survey intends to focus on. The only real difference this survey has from a large scale one is the size of the survey and the relative ease this survey was conducted, in contrast with a full-scale one. This sandbox terrain survey was conducted with minimal effort using simple tools and relatively few people (3) in a short span of time (2 hours). In contrast, a full scale county survey may take days or weeks pf hard work, with often a grid based survey being impossible due to both time constraints and a sometimes inability to reach the desired sample-point location by convenient means of travel. Interpolation methods, in addition, can be used for other forms of data. Water tables, soil types, and precipitation are just a few of the forms of data that can be measured and represented by survey and interpolation methods.
Sources
ArcGIS Help, In ArcGIS Resources. Retrieved 2/14/2017, from http://resources.arcgis.com/en/help/

Hupy, J. (2017). Sandbox Survey part 2: Visualizing and refining your terrain survey.. Eau Claire, Wisconsin.

Field Activity: Creation of a Digital Elevation Surface

Introduction and Background
In this introductory lab to the processes of field methods, groups of students were tasked with developing a model terrain in sandboxes located on the University of Wisconsin, Eau Claire campus grounds. The size of the sandboxes were slightly greater than on square meter, and the constructed terrain was required to have a minimum of the listed terrain features: ridge, hill, depression, valley, plain. Afterwards, the group was tasked with sampling the terrain, using any on of a variety of sampling techniques.
Sampling, from a spatial perspective, means gathering a number of coordinate points (x,y,z) in order to generate a terrain map of a larger area (rgs.org). Rather than continuously mapping an entire area, sampling is used to provide a general picture by using the collected data points to generate a terrain estimate for the desired area. This is done because it is often not practical in terms of time, energy, manpower, and monetary expense to continuously map an entire area without complex and expensive equipment.
There are three types of sampling methods generally used in data collection: random, systematic, and stratified. Random refers to using a simple computer program to randomly select any number of data points for a given survey to sample. Due to the nature of this selection process, this is by far the least biased of the listed methods, as any one of the available sampling points may be selected. In systematic sampling, points are selected based on an even or regular spatial distribution. For example, every five meters over a given transect distance. This method is both more straightforward than random sampling and provides a good overall coverage of a study area, at the disadvantage of being more biased, sometimes over or under representation. Stratified sampling is a bit more complicated. It involves dividing a known area into smaller groups or subsets which are sampled separately. This is done to prevent particular areas from being missed. This technique is frequently used in surveying habitats in an area. This sampling method shares the benefits of random or systematic sampling, which it can be used with, and it can be used to make comparisons between the subsets. However, this requires the subsets to be accurately defined. However, in all of these sampling methods, a grid is usually overlayed on the sampling area to simplify the collection process, as data-points are usually taken from where the x and y planes intersect.
Methods
First, the terrain was constructed in the sandbox located near Phillips Hall of the UW Eau Claire Campus (Figure 1).

After the terrain was constructed, a 20 by 20 x,y grid was overlayed on top of the terrain using colored line, with both the x and y point 0 being set to one corner of the box (Figure 2). The points would be sampled from the intersection of the x and y lines on the grid, and the height of the line would act as the z coordinate, with terrain higher than the line being recorded as positive and below being recorded as negative.

In our sampling method, it was decided we would start on point 1,1 and sample every other column in the y row 1 (3,1;5,1;7,1;etc) until the end of the sample area was reached. From here, we would skip row 2 and move on to row 5, once again starting on point 1,5 and sampling every other point in that row (1,3;3,3;5,3;etc). This sampling method was used until a major feature was reached in the plot (valley, ridge, etc), and which point every x,y coordinate was collected (Figure 3). This is because elevation (z -coordinate) varied greatly at these locations, so it was deemed necessary to gather as much data around these features to prevent the under representation of the slope of these features later on. In addition, once row 11 of the y coordinate plane was reached, it was deemed necessary to sample every data-point in the row. This was because the majority of the constructed features, included the valley, depression, plain, and parts of the valley. In addition, to prevent valuable data from being lost with these features so closely packed together, the even y rows were no longer skipped during the sampling process. With this, sampling included all points from row 11 to row 18. Overall, we used a hybrid systematic-stratified sampling method with a 20x20 grid set up over the terrain and a distance of roughly 6 cm between any two adjacent points on the y or x planes. Total, the x, y, and z coordinates were collected in cm's from 212 points sampled over the entire plot. It was designed in this way to increase the focus on crucial terrain features while minimizing the focus on minor features.

Discussion and Results
As mentioned before, a total of 212 survey points were collected. The maximum values for the x, y, and z coordinate values (in cm's) were 114, 108, and 5, respectively, the minimum x, y, and z values (in cm's) were 5, 7, and -8, the mean values (in cm's) were 59.9, 71.2, and -2.7, and the standard deviations were 32.91, 29.16, and 2.29. Of these, the z values hold the most significance as they contain the terrain values of the sampling, while the x and y values determine how these points relate to one another. From the mean value, we can determine that most of the terrain fell below zero cm's for the z coordinate. As mentioned before, the sampling method became more precise as it moved into crucial terrain features, particularly at the top half of the plot, where sampling increased in preciseness in order to accommodate the increased density of features. While the hybrid systematic-stratified sampling method provided a balance between efficiency and precision, this left a greater focus on certain areas, leaving out those ares considered unimportant. In order to accommodate for this in the future, random sampling should be conducted on the skipped points in the future in order to decrease biased data-collection in the future.
Conclusion
In the end, this field activity provided the grounds for future sampling on a greater scale. While this particular sampling was taken from a relatively small total surface area (roughly one square meter), it still fulfilled  the basic principles of spatial sampling techniques. By overlaying the sample area with a grid and constructing a hybrid sampling strategy, a model can be generated of the sample area for later use. This model will provide both an accurate estimate of the terrain and will be generated using terrain sampling data that was taken from a collection of points out of the total sample area. This exercise provides the basis for further surveying of physical features on a macro scale (county, etc) which also function viably in terms of time, manpower, and cost. Similar sample methods could be used to survey the Chippewa Valley, with just the x, y, and z recorded values being greater in scale to accommodate. While the survey performed in the sandbox did an adequate job of sampling the area provided, it illustrated several points to take into consideration for a large scale survey. In a large scale survey, multiple survey techniques may be needed in order to create a balance of sample accuracy, minimal bias, and proper efficiency. In addition, more complex tools than line and rulers will be needed by groups of individuals in order to record survey data.
Sources

Google Earth View. Retrieved 2/7/2017, from https://www.google.com/maps/place/44%C2%B047'48.2%22N+91%C2%B029'54.3%22W/@44.796723,-91.5006167,560m/data=!3m2!1e3!4b1!4m5!3m4!1s0x0:0x0!8m2!3d44.796723!4d-91.498428

Hupy, J. (2017). Field Activity # 4: Creation of a Digital Elevation Surface using critical thinking skills and improvised survey techniques. Eau Claire, Wisconsin.

Sampling techniques. In RGS.org. Retrieved 2/7/2017, from http://www.rgs.org/OurWork/Schools/Fieldwork+and+local+learning/Fieldwork+techniques/Sampling+techniques.htm