Section Five: Surface Creation

Back in Chapter Three, Section Three, we learned about four different continuous raster types, or surfaces, according to ArcGIS: slope, aspect, hillshade, shaded reliefs; and in Chapter Three, Section Four, we learned about two types of vector based continuous data: Contour Lines and TINs.  The goal of those sections was to introduce you to a couple of different kinds of raster and vector files, some of which you've worked with by this point in the lab portion of the class.  This section will introduce you to the surface creation tools used within ArcGIS which produce those layers, all of which start with a Digital Elevation Model or DEM (which you were also introduced to in Chapter Three, Section Three).

Figure 7.x: Chapter Three Concept Review
discrete_continuous_data
7.x.a: Continuous data surfaces are those for which there is no distinct boundaries for a single feature such as elevation, precipitation, or temperature, and each individual feature is dependent on an entire system, incapable of existing without the others.  7.x.b: Discrete data layers are ones where there are clear boundaries for the features which participate, and each independent feature could exist without the others.  Discrete data included features such as road networks, administrative boundaries, and some natural features, such as rivers. 
hillshadeshaded_relief
7.x.c: Hillshades surface layers, derived from DEMs, show a landscape if the sun were to shine down from a single point.  Areas which would be shaded from the sun based on the terrain and the sun angle are shaded in, while those which be illuminated in identical circumstances are colored in a brighter white.7.x.d: Shaded Relief layers are Hillshades with colors to add some visual distinction to the landscape instead of using a range of colors which span simply from black to white
slope-displayaspect-display
7.x.e: Slope is how steep the grade of the topographic surface is over a defined area.7.x.f: Aspect is the cardinal direction the slope faces.

All of the above surfaces are interpolated from a Digital Elevation Model (DEM), meaning the elevation value which was stored in the pixel was extracted and compared to the elevation values in the eight surrounding pixels using a focal operation.  The focal operation method (which we looked at briefly in Section 7.3.2: Raster Overlay Analysis) is a means of interpolating an acceptable value for one pixel based on the values in the surrounding pixel values.  Statistically, this method is good enough for solving for large areas and has been proven through testing and ground truthing (visiting an area to measure values and compare them to the solved values).

A slope surface layer is derived by using a modified slope equation between one pixel and the eight neighboring pixels.  Since focal operations solve for each individual pixel by examining the surrounding pixels, an entire DEM can be transformed into a slope surface layer fairly accurately.  Using this same method, the software can interpolate an aspect layer as well.  If the slope is known and the DEM is georeferenced (completed during the actual creation of the layer, long before it's in the hands of the end user), then the cardinal directions for the layer are known, meaning the software can declare when a slope is facing north, south, east, west, or somewhere in between. 

Figure 7.X: Solving for Slope with a Focal Operation
Solving Slopeslope_tool
Using the Focal Operation method, ArcGIS solves for the slope of the center pixel, e, by examining the rate of change for the three pixels above and three pixels below ([dz/dy]) and the three pixels to the left and the three to the right ([dz/dx]) as the input to the finding slope in degrees and converting from radians to degrees.  Considerations such as if the pixel contains a value or not (weight) and the size of each pixel (8 x cell size) are taken into account.  After finding the slope for pixel e, the focal window moves to the next pixel, pixel f, making it the center pixel and repeating the process using the next batch of the surrounding eight pixels.  This, like all background equations in ArcGIS, doesn't need to be memorized, since the software takes care of the solving for the technician.

The Contour line tool uses the extracted elevation values different from the way that the slope or elevation tools use them.  The Contour tool, which produces a vector layer instead of a raster layer, is basically a dot-to-dot tool (sound familiar?), connecting not vertices in numeric order, but instead connecting all of the values with are equal and at a given interval (for those of you who are into starting sentences with the word "technically", since the product is a polyline, there are indeed a series of vertices connected with straight lines, withe each vertex meeting it's proper definition with each one knowing it's place in the world and where in the order it comes.  The elevation values are used to create each polyline, after which said elevation value becomes a single attribute attached to the polyline in the attribute table).  For example, if a technician needed a contour layer with an interval of 100 feet for a DEM ranging from an elevation of 57 feet to 927 feet, the contour tool would first extract all of the known elevation values from a DEM for each pixel.  It would then find the lowest value for the entire data range (57 feet) and then find the next value divisible by 100 (100 feet).  It would create a single polyline feature which connected all the 100 foot values together across the landscape.  There may be one or there may be many polylines created, but each one is independent of the others (each one creates a single row in the attribute table) and none of them would intersect.  The tool would then find the next value divisible by 100 (200 feet) and complete the same task as the 100 foot interval.  The tool would continue for the 300 foot contour interval, the 400 foot interval, the 500, the 600, the 700, the 800, and lastly, the 900 foot contour interval.

Figure 7.X: The Contour Tool Up Close
elevation points
In this image, we see how the contour lines (seen as brown polylines) connect elevations of the same value (seen as black points), sometimes passing through the actual point (like on the 9,400 foot elevation line) and other times, passing through an imaginary point somewhere near a point with a very close value.  The contour lines cannot pass through an elevation point that doesn't match, but can pass near the point.

TINs are created in much the same way as the slope layers, with the output being a vector instead of a raster.  If the elevation values are known for a specific DEM, the elevation points extracted can be connected to the nearest neighbors.  TINs, by default, don't use every single point like the Raster to Point or Contour tools do.  They, instead, use a sample instead to create a flowing landscape, a setting which can be changed in the input of the tool.

Figure 7.X: The Output of the Raster to TIN Tool
TIN_Example
The Raster to TIN tool uses a DEM as the Input Raster and produces TIN as the output.  TIN layers are neither vector nor raster layers, but instead a different kind of spatial file all together.  In Chapter Three, we learned that there were three main kinds of data types, but the main kinds are not the only kinds.  In this image, drawn on top to the TIN layer, there are both a point and a polyline layer showing where the TIN tool places the nodes and edges (produced with the tools TIN Node and TIN Edge tools, respectively).