Sandbox Survey; Refining and Visualizing Terrain Survey

Introduction

            Visual information often leads to greater understanding then text information alone. Similarly, 3D information often conveys more then 2D information. When conveying information from one dimension to another (2D à 3D) requires a great deal more time to correctly and accurately display the information.

            As a follow up to the previous activity (Sandbox Survey), the task at hand for this exercise is to create a continuous surface of the sandbox terrain that was sampled. To sample the sandbox, a simple systematic sampling scheme was devised to fit the proportions of the sandbox, and get accurate representation of the features without oversampling or representing. The data was cataloged in a paper notebook (kept as a physical copy), and then transferred to an Excel table. This table was then normalized, to reduce the redundancy and improve the data integrity. Important measures were taken, in Excel, to make sure that the information in the spreadsheet is considered ‘numeric’. Unless the table is specified to be ‘numeric’ data, problems occur when the data table is imported into Esri powered Arcmap. The format of the Excel table is also important, and extra attention is needed in the planning stages to make sure the Y, X, and Z columns are in the right order. This is important because once the table is imported into Arcmap, interpolation techniques are applied to the data to create a smooth surface from the XY (Z) data, and if the table is not formulated correctly, huge inaccuracies can be found, and the product is often unrecognizable and the project must be started again.

Methods

            A major outcome of this project is to come to a better understanding of the various interpolation techniques that can be applied to XY data to produce a continuous surface to represent the area that was surveyed. Each technique utilizes its own mathematical algorithms to produce the surface.  Since each technique has a unique mathematical principle behind constructing it, slight differences in the outcome of the product are experienced, with each one presenting advantages and disadvantages. In order to gain a more in-depth understanding of what each method does, 5 different types (along with a 3D version) of spatial interpolation were performed on the data collected from the sandbox survey.

The first technique explored is the IDW, or inverse distance weighted interpolation. Specifically, this interpolation assumes that each measured point has an influence on other points surrounding, that diminishes with distance from the source point. In order to predict points surrounding the measured value points, IDW weights the points closed to the predicted point, and diminishes the point further away. This method produces a good result, if the assumption of the algorithm is true, that being, objects closer together are more similar then those farther apart. If this assumption is not met, like in our sandbox survey, spots can be noticed in the final product. (Fig. IDW). These anomalies, i.e. high spots, are variations in the elevation occurring around our measured points. Another problematic feature of IDW interpolation is the product does not feature any prediction of standard error, which can make justifying the method a challenge in a professional environment.

The next method that was used is the Natural Neighbors interpolation model. The algorithms for this model works on a multivariate approximation of a point, selecting the nearest point, and not consider the values of neighboring points at all. This model is relatively simple compared to IDW and other models. It has an advantage of being simple, and producing a quality, relatively accurate representation of the points.

The third method used for this project is the Kriging interpolation model, which uses a geostatistical method to estimate and predict points. Kriging interpolation uses the distance between points as a statistical reflection of a correlation between the measured points. Kriging produces a smooth surface from geostatistical methods, which gives it the added benefit of being able to produce a prediction surface, and have the capability to provide accuracy information. This type of interpolation model is best suited for data, which has a spatially correlated distance or directional bias. Although is provides a much more detailed surface, this model is a multistep process, and involves much more time constructing the model than ether model explored so far.

            The next interpolation model for this project is the Spline method. This model works to minimize the curvature of the surface by fitting a formula to a set of sample points, and bending the surface to ‘pass through’ the sample points. Spline is considered to be a deterministic model (along with IDW), by working with the measured points and basing the surface off the extent of similarity. This model works most effectively when it’s applied to gently varying surfaces like elevation or water table information. Spline interpolation does not however produce accuracy information, so if a highly technical report is needed for professional reasons, a more dynamic model might be better to apply. However, for the Sandbox survey project, this model produced the best surface interpolation of the methods we tried.  This is due to the fact that our group intentionally made a very minimal elevation changes (small relief), in order to produce a surface, which is not very drastic.

            The 5^th interpolation model that was produced is a Triangulated Irregular Network (TIN) model. TIN’s use triangle topography to connect nodes (X, Y, Z) and edges to create a continuous surface. TIN models represent elevation topography in a way, which illustrates a change by differing the size and angle of triangles. This particular model produces a surface that can effectively delineate change, and visualize elevation much different then other forms of surface interpolation. TIN models are fantastic at representing very rough surfaces, with many angles. An example of where TIN models are useful is representing a ridge of a mountain. Since the model uses triangles of various size and shape, a much more natural surface is produced. TIN modeling does have a disadvantage in representing surfaces that have gradual elevation change, or when objects are positioned close together. In the sandbox survey, both of these situations are represented, so a TIN surface would not be the best choice to represent our survey.

            A final product that was created is a 3D surface representation.  For this, Arc scene was used. The surface was interpolated in 3D spatial analyst, using the Spline interpolation model, because it produced the best model for the sandbox survey data.  The 3D model was then exported into a .JPEG file. The surface image is presented in 3D, so two different perspectives were taken, the first from a 45-degree angle from the southwestern corner of the surface. The second representation was taken from a 45-degree angle from the opposite side, the northwest corner of the surface. These two orientations were chosen because each one shows the areas with the greatest relief, and the 45 degree angle accentuates the 3^rd dimension even though it is only being presented on a 2D planes (computer screen).

Results and Discussion

Figure 1

         This section will elaborate on the results of the 5 interpolation models that were produced for this project. In each model, the goal is to produce a smooth surface that displays visual evidence of the topographic features that were represented in the sandbox, those being a plateau, a ridge, a hill, a valley, and a depression. The first figure represented (fig. 1), is a product of the IDW interpolation model. This model is deterministic, which measures points from those surrounding. As mentioned before, the calculation of predictive points involves an unevenly distributed weight on the measured points. This uneven weighting to produce the surrounding points, the image displays a dotted surface, (fig.2), giving the illusion that there are tiny bumps of elevation throughout the surface. This is in fact a false representation of the real surface.

Figure 2

These consequent bumps can be diminished with further alteration of the input values, but for the time it would take to produce an output that still is represented with small bumps it is not a worthwhile investment. The IDW interpolation model is better suited for a highly texturized surface like a DEM of a rocky hillside.

           

Figure 3

The next technique for interpolation reviewed, is using the nearest neighbor model. Over all, the nearest neighbor technique produced a well-represented surface of the landscape that was surveyed. Figure 3 shows the image that is produced does have a few problem areas, which are notable. Most prominently, the ridge presents with a decrease in width along the entire axis.

Additionally, the eastern side of the ridge shows a bumpy surface, while the western side of the ridge shows a smooth surface transition. In truth, the surface was smooth across the entirety of the ridge. An explanation for the lumpy appearance of the eastern side of the ridge is found in the settings menu of the tool.

Figure 4

The nearest neighbor tool uses a “neighborhood” selection that defines the area that the tool will consider as a neighbor. A closer inspection, as represented by Fig (4), shows a consistent size of bump over the entire side of the eastern side of the ridge. This is a representation of the circle radius of the “neighborhood” selection. A similar effect can be seen in the western axis of the surface adjacent to the valley.

           

Figure 5

The Kriging technique resulted in the lowest quality product surface representation. Although this product was not a well fitting image of the sand box landscape, a probable cause is that this tool uses a model, which is quite complex, and offers many different selection menus’s to represent the   The depression in the northeast corner of the sandbox also looks much deeper, and the plateau as looks higher than in other images.
surface in more detail. Surface representation is a complicated and detail oriented subject. Much of the selections menus were out of the scope of this project, but the goal of introduction to the method was met in seeing the surface representation image. Fig (5). The kriging tool captured the general shapes of the features in the landscape. All of the features do show in the image, but each one is generalized to a great extent, showing a very washed out look.

The final deterministic interpolation method is using the spline model. This technique produced the smoothest, and most accurate details of the sandbox features of any. Figure 6 shows this model did a great job of representing the depression and the valley, which were approximately the same depth.

Figure 6

Another detail that was well presented in the spline model is the distinction in elevation between the ridge and the plateau. The plateau in the image is displayed as a elevation class lowers then the ridge, which is true of the actual landscape of the sandbox.

Figure 7

The final interpolation method that was used is a TIN. This technique produced a image that gave a much more 3D effect then the other interpolation methods examined today, the Arc scene produced 3D model excluding. The TIN model is very adapted to representing landscapes with large
amounts of relief. In areas of slight change, and in small spaces, the TIN model produced a slightly confusing and harsh image. I particular example of this is found in fig. (7), between the eastern side of the plateau and the western side of the ridge, is a darker area, which is challenging to interpret. Part of that effect is due to a hillshade tool, which helps define the features. But in this circumstance it presents with a challenge to interpret.

The final figures represent the 3D image produced in Arc scene. Fig (8) is presenting the surface produced from a perspective tilted to the southwestern, 45 degrees.

Figure 8

The next image, Fig (9) represents the surface from a 45-degree angle from the northeast corner. Both representations were chosen to show the construction of a real representation of the features. This model did a great job producing the image. Scale was set to a floating model so it could fit the data to a unique surface and not excessively over or under represent features in the sandbox landscape.

Figure 9

Conclusions

In conclusion, a greater knowledge of a survey format to conduct studies will greatly aid the proficiency and accuracy of the final product of the project. Comprehensive survey techniques facilitate the collection of quality data, which is crucial to any projects success. This relates to any kind of study where data is being collected from any time of environment. As often as can be allowed, the level of detail of the survey should be as large as necessary with out over collecting data points. These types of projects relates to many fields, including biology from sample distribution in lakes, or geology to study sedimentary formation, or hydrology looking into aquifers. There are many applications for survey and interpolation images. This type of project is a valuable study for future referencing.