Field Activity 2, Visualizing and Refining terrain.

Introduction

The objective of this excercise was to take the data that we had collected in our terrain survey, and represent the terrain in a model.  This was done by importing the data into ArcGIS.  To make a continuous three dimensional model out of the XYZ coordinates that we had, a method of interpolation had to be used.  In this lab we experimented with the following methods of interpolation:
 

§  IDW
§  Natural Neighbors
§  Kriging
§  Spline
§  TIN

After a model was made it was apparent that it would be necessary to resample a few areas in the terrain to get a better representative model.  Our group collected more survey points from the areas that we felt were somewhat misrepresented in the model and then we updated our XYZ coordinates and again performed the interpolation methods.

In this lab we will be determining how much information it takes for interpolations to render an accurate depiction of the surveyed terrain.  What we should away from this activity will be how to make accurate models, and how to update surveys.  This activity is very practical and accurate if we ever need to take a survey of some kind of terrain, and then need to model it.

Figure1.  Terrain to be modeled in this activity

Methods
After the XYZ coordinates from our survey were recorded in an Excel spreadsheet, the data was imported into ArcGIS and saved as a feature class in a geodatabase that had been created and titled to store features from this activity.

After this was done, the  interpolation methods were performed.  When this was done, the rasters (and TIN) were viewed in ArcScene.  To preface this, it is important to have a rudimentary understanding of what interpolation is.  Interpolation is a way to use coordinates or data points to produce a continuous raster.  Interpolation can be utilized when there is an assumption that the data that is closer to your collected points will be similar in value, and that they can be used to help estimate what values the raster cells should have.  ArcHelp has a good example of how interpolation can be used to make an elevation raster.  A picture of this is shown below.




Figure 2.  Screenshot of ArcHelp example of Interpolation being utilized to produce a raster for elevation surfaces.

The first method of interpolation used was IDW.  IDW stands for the Inverse Distance Weighted technique.  This technique uses the distance from the raster cell to the supplied coordinate to determine how much influence the coordinate value will have.  The method assumes that the coordinates have less influence as distance increases, which can be somewhat problematic when trying to successfully graph ridges.



Figure 3.  3D model of terrain produced using IDW.  Important aspect to note is the bumpy quality of the image, explained by the methods assumtion that distance away from a coordinate point will decrease the influence the coordinate has on the raster cell value.
 

The next method of interpolation used was Kriging.  In some respects Kriging is similar to the IDW technique in that it uses inverse distance weighting as part of its prediction for the values to fill the raster cells.  It is unique however, in that it also takes into account the overall spatial arrangements of the supplied coordinate and can use this to improve the quality of its predicition.  When comparing Kriging to IDW, you can see that the Kriging method does a better job at recognizing the features in the terrain.

Figure 4.  3D model of terrain produced using Kriging.  Important aspect to notice is the relative smoothness of the features when compared to the IDW technique.
 

The next method of interpolation used was the Nearest Neighbor technique.  The Nearest Neighbor Technique is arguably one of the most simple and straightforward methods.  It doesn't make too many assumptions about the data, and will only approximate raster cell values based on the values of the nearest coordinate points.  For this reason, it can avoid some problems made by assumptions of other methods, but it works best for extremely detailed data because it will not predict trends or patterns.

Figure 5.  3D model of the terrain using Nearest Neighbor.  Important aspect to notice is the relatie roughness around some of the features due to the fact that nearest neighbor does not predict patterns. 

The next method of interpolation used was Spline.  The Spline technique estimates values using a mathmatical function that results in a smooth surface that passes through the coordinate points.  This technique would work best for models of terrain that are relatively smooth.

Figure 6.  3D model of the terrain using Spline.  Important aspect to notice is the relative smoothness of the features in this renering compared to some of the other methods.

The next method of interpolation used was creating a TIN.  A TIN is a triangular intergrated network.  It is different from the other methods because this does not produce a method.  The technique uses the coordinates to produce triangulated vertices which can then be used to produce a model.  While this technique can produce a useful model, it is limited by the fact that it lacks a certain level of realism.

Figure 7.  3D model of the terrain created by making a TIN.  Important aspect to notice is that it is composed of triangles, and it is not a raster like the other renditions.

Our group decided that we thought Spline best represented our actual terrain, but that the model could be improved in a few areas.  We saw that that specifically the ridges and depression of the model looked slightly different from the terrain that we had produced.  For this reason we decided that we could improve our model by taking additional elevation measurements from these areas and then use the updated coordinates to produce a 3D model.

During our orignial survey (see original survey) we had made a grid, and then taken an elevation measurment in the center of each grid cell.  To update the survey, we made the same grid, and then took measurents on the four corners of each grid cell (only in the areas that we had determined needed better representation).  The areas that we had determined needed better representation were the hill, ridges, and depression.  Important conditions to note during our survey revision is the fact that there had been a snowfall, which had the potential slightly alter the elevation of our terrain in certain areas.  We tried to minimize the effects of this by lightly brushing away the recent snow, and by trying to take elevation measurements where the snow was dense and not fluffy.

When we went to add elevation measurements to the coordinates we already had, we ran into a few problems.  This was due to how we set up our coordinate system when entering the data from our original survey.  Instead of putting the centimenter measurements for the X and Y coordinates, every five centimeters was essentially counted as one unit. when updating the coordinates, we had to look at what grid cell it corisponded to, and then determine if we should add or subtract .25 from the X and Y values based on which direction from the center of the grid cell the new measuremnt was taken at.  The main problem we had with this, was that it was difficult to conceptualize and tedious to enter the data, but we eventually were able to successfully update the coordinates, so that we would have better representation for the areas that we were concerned about.

Figure 8.  Original survey points shown on the left, updated survey points shown on the right.

When the Spline interpolation technique was performed using the updated coordinates, the results were not what we had hoped for.  The Spline interpolation from our original data had been relatively smooth, and seemed to match our terrain relatively closely.  The Spline interpolation using the updated coordinates seemed to actually be worse when compared to several of the other techniques, including IDW which had been our least accurate model so far.

Figure 8.  3D model made using updated survey coordinates and the Spline interpolation technique.  Important aspect to notice is that it almost looks like an IDW model, and the resulting model looks less like the terrain than the non updated spline model.

Discussion
One of the most important questions to answer is how the model made using the updated coordinates turned out the way it did, and what errors would have had to occur to get us a 3D model that looks so different from the terrain.  Initially there was a question of whether the XY coordinates were correct because we were having troubles conceptualizing how to correctly enter it.  however looking at the updated XYZ coordinates in ArcMap, the points were in the correct XY location.

Figure 9.  Coordinates were entered with the correct XY coordinates.

The error therefor must have come from the Z coordinate, or the elevation measurements.  ArcScene was useful in looking at how the XYZ coordinates related to the Spline interpolation model.  The following pictures show either the original or updated spline models and how they compare with the original and updated XYZ coordinates.


Figure 10.  Original Spline model shown with original XYZ coordinates



Figure 11. Updated Spline model shown with original XYZ coordinates

Figure 12.  Updated Spline model shown with updated XYZ coordinates

Figure 13.  Original Spline model shown with updated coordinates

Figure 14.  Magnification of the disparity seen between the original spline model and the updated XYZ coordinates.

The way that spline works is by using a mathematical function to create a smooth surface that runs through all of the coordinate points.  In order for the spline model to pass through the coordinate points, it needed to create the sloping abrupt peaks that we see in the updated model.  These peaks are not seen in our terrain, but they are represented in the coordinates.  This suggests that the error came from some part of our methodology when collecting the elevation measurements in our second survey.

Most likely, when we tried to minimize the effect of the snowfall, we overcorrected and brushed away snow that was part of the original terrain we had made.  This would explain why we have coordinates that exist below where they would be expected.  Essentially, we changed the terrain in a significant way, so that when we took new elevation measurements to add to our existing data, the model lost accuracy because it was basically mapping coordinates from two different terrains.  This is of course, discouraging news given the amount of time that our group spent on updating the survey, but it does encourage us to be more aware in the future to avoid similar problems. 

There were probably several factors that kept us from realizing that our data was inconsistent.  We we started collecting around 5:00pm, and it was getting colder and darker as we were out there.  We wanted to finish as quickly as possible, and because of this we weren't stopping to ask ourselves whether the elevation data we were collecting made sense when we compared it to the original survey points.  Additionally, when we were entering the coordinates into an excel spreadsheet, we were so concerned with making sure our X and Y coordinates were correct we didn't take time to really look at the elevation data. 

Conclusion
If we were to do this project again we probably would have done it differently.  When addressing the issue of the snowfall and how it affected the terrain, it might have been better to either leave it be, or to take an entire new survey to account for it.  Each of these solutions would have had its own issues.  If we left the new snowfall, we might see a similar disparity between the original and updated coordinates.  If we were to start an entire new survey, it would have taken us much longer to complete.  In the end, our revisionary survey did not work out, and the most accurate model we have was obtained using the Spline interpolation method with the data collected from the original survey.


Figure 15.  Spline was chosen as the best interpolation technique to represent our data.

The original objective of the excerisise was ultimately completed.  We have a 3D model of the terrain that fits well with what the actual terrain looks like.  We also have a better knowledge of the various interpolation techniques that can be done in ArcMap.  If we were to do the project over again, I think that we would have been more careful to make sure that the elevation points that we were taking when we were adding coordinates to our survey made sense when compared to the coordinates that we already had.