Exercise 1 Part 2

Introduction:

In part two of exercise one, we revisited our previous terrain model to correct any problems, and create a continuous surface using our data points.  It was determined a re-survey was required to attain more accurate results.  Our group decided to increase the detail of our model by using smaller units of measurement.  The previous 6 inch cells were changed to 8 cm allowing for better interpretation of our data. The methods of this report move from data collection to interpretation of the data.

Above is the sand table model we created. The top left feature seen is a volcano and a stream to the east. A large ridge extends across the western portion of the box.  The chunk of snow seen on the left was difficult to model accurately because of its hard edges and how the interpolation techniques work. (NOTE: this picture was not taken from the origin of our data)

 

Methods:

Similar to part one we recreated a Cartesian coordinate system using grid cells with unique X and Y values. Each cell measured 8 X 8 centimeters providing a sample size of 364 elevation (Z) points. 

The process of measuring the cells, each one measuring 8 square centimeters.

 

After the data is collected in the field, it needs to be manipulated so that X, Y, and Z values are the same units of measurement.  If the X and Y values are not also recorded in centimeter measurements on the spreadsheet, you will have unintentional vertical exaggeration once imported into ArcScene.  When the values were entered into excel the origin was also accidentally changed.  This was fixed by flipping the X values for each row.

By multiply the X and Y values by 8 any vertical exaggeration will be removed since all values are the same units (centimeters).  Below is a revised spreadsheet that is ready to be imported into the ArcMap software for further analysis.

                                                           

Now that all of the data is in the proper format, it can be imported into ArcMap.  This is a simple process of adding the table into the software and displaying the XY data. Once this is done, it will be displayed similar to the image below

The bulk of this project involves using various interpolation methods in analyzing the data in a continuous surface raster.  Five interpolation techniques were used in this process: Inverse Distance Weighted (IDW), Natural Neighbor, Kriging, Spline, and TIN. Following each explanation of the method an image is provided.

Inverse Distance Weighted interpolation calculates values between data points by weighting them according to their distance from the known points. Data points provided decrease in influence as they move further from a particular data point. Below is an image provide by ArcMap describing this method.

The yellow point in this image is created using an algorithm averaging the points surrounding them according to their distance. The greater the distance from this point, the less influence it has on new values. The image below shows how this technique estimates new values to provide a continuous elevation profile of our data.

Using IDW interpolation various features are distinguishable; however, the data points are still visible.

              

The next technique used to calculate a continuous surface is called Natural Neighbor.  Natural Neighbor interpolation uses adjacent data points to construct new values similar to IDW. Below is the data portrayed using this interpolation method.

Similiar to IDW interpolation, all of the features using Natural Neighbors are distinguishable. The image also appears much more smooth, showing a continuous elevation surface. Our river, shown in green, doesn't quite connect; however, as in the real world, river bottom surfaces also fluctuate.

Some of the interpolation tools are very difficult to explain. They use complex algorithms to estimate values not provided. Below is ESRI's explanation of Kriging interpolation.

Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. Unlike other interpolation methods in the Interpolation toolset, to use the Kriging tool effectively involves an interactive investigation of the spatial behavior of the phenomenon represented by the z-values before you select the best estimation method for generating the output surface. (ESRI)

The image below is our data having undergone kriging interpolation. Note the depression found at the top of our volcano in the south east is not present. This was taken into consideration for choosing the best method to represent our data.

Kriging provided a relatively continuous surface; although, it did not represent our model as well as IDW or Natural Neighbor.

 

Spline interpolation created the most accurate representation of our model. The elevation data appears to be very smooth compared to the other methods. The river found in the western portion of our model as well as the volcano is defined quite nicely.  Having additional data points would create an even more accurate depiction of our model’s surface.

The Spline tool uses an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points. (ESRI)

Spline interpolation provided both the most aesthetic as well as accurate depiction of our sand table model.

                                                         

A TIN (Triangular Irregular Networks) surface is created by connecting three data points to one another so that they do not overlap. Since the data points are evenly dispersed across the model, each triangle has the same area. This method provided the least aesthetic depiction of our continuous surface model.

                                                           

After using the different interpolation tools, the surface models are ready to be imported into ArcScene to be spatially examined in three dimensions. Each raster image is added to the program and selected to float on a custom surface. This creates a three dimensional model of our sandtable.
Below is the finalized product produced using the various interpolation methods of our data. (NOTE: None of the three dimensional images were given any vertical exaggeration.)

Inverse Distance Weighted interpolation created a surface model that made our features distinguishable; however, they were not as continuous as the other methods.

The Natural Neighbor interpolation provided a very accurate three dimensional surface model. It was very similar in appearance as the Spline model.

Kriging interpolation provided the least accurate results of our data. The stream and the volcano depression are hardly noticable.

Spline interpolation turned out very similar to Natural Neighbor. It provided the most continuous as well as the most accurate model of our sand table. All terrain features are clearly distinguishable.

Discussion:

As stated above, Spline interpolation created the most visually appealing and accurate portrayal of the data provided. The various landform features stand out from the rest and can be easily identified. Provided additional sample points, the digital models would be even more accurate.  If given more time on this project, smaller cells could result in more detailed images throughout the model.

Having the data arranged within a spreadsheet using matching units, also allows for the project to be reexamined in further detail if necessary.  If a certain feature needs to be examined further, one can simply go back to their constructed model, measure the X and Y coordinates, and add more points around the feature.

The final product. Spline interpolation rendered in three dimensions with 30% transparency and a hillshade elevation model underneath.

Conclusion:

This activity provided a great example stressing the importance of critical thinking. Each group devised their own plan to construct a digit surface model.  Having finished the project, we are now able to present our findings and learn from each other’s methods.

Although we used small models to portray features of earth’s surface, this technique still applies when examining a larger area.  Technique’s such as this can be used in field research with the minimum amount of technology.  Various aspects of this research will likely be encountered in my future as a geospatial analyst.