Lab 4: Surface Interpolation

 

In this lab you will use various spatial interpolation methods to create DEMs with different spatial resolutions. Please copy lab data to your working directory in c:\Users before you start. Lab data are in Lab4 folder at I:\Students\Instructors\Geoffrey_Duh\GEOG4593\. Answer and submit all questions listed at the end of the lab.

 

This lab involves the "resampling" of a DEM to different spatial resolutions using various spatial interpolation methods in ArcGIS. Type the answers to all questions at the end of each task, attach your maps (see Questions #2 and #3 below), and submit them to the instructor.

 

Instructions

 

This exercise guides you through the process of resampling a DEM to a coarser and a finer resolution. You will also convert a DEM to a gridded point feature class, then, use Inverse Distance Weighted (IDW), spline, and Kriging to interpolate the point data to form DEMs. The purpose of these exercises is to let you learn the methods to generate DEMs at various resolutions and understand the limitation of these methods.

  1. Add the dem grid in your lab folder to ArcMap. Check if the grid has a 30 meter cell size and a UTM projection. You need to fill in the column and row numbers in the blank table of Question 1.
  2. Enable Spatial Analyst extension from the Customize->Extensions... menu. Open ArcToolBox panel by clicking on the red toolbox icon. Open the Resample tool in Data Management Tools toolbox / Raster Processing toolset. Specify dem as the input raster, dem300 as the output raster (make sure you save it to your workspace!), and 300 as the output cell size. Check that the resampling technique is "NEAREST." Click OK to continue.
  3. Now you have created a 300 meter DEM by resampling. Check if the grid has a 300 meter cell size.
  4. Use the same Resample tool to resample dem300 to 30 meter DEMs using the following settings to create two output DEMs:

Input raster

Output raster

Output cell size

Resampling method

Dem300

Dem30n

30

NEAREST

Dem300

Dem30c

30

CUBIC
  1. We now try another approach to resample the 300 meter DEM to finer resolutions. First we need to convert the DEM grid into elevation points. Open the "Sample" tool in Spatial Analyst Tools toolbox / Extraction toolset. Specify dem300 as the input raster and as the input location raster, pnt300_table.dbf as the output, and NEAREST as the resample technique. Click OK to continue.
  2. When done, pnt300.dbf is added to ArcMap automatically. Take a look at the content of the table.
  3. From the ArcMap TOC, right-click on pnt300_table.dbf and select Display XY Data.... Make sure x is in the X field, y in the Y field, and dem300 in the Z field. Set the coordinate system the same as that of the dem300 layer (i.e., NAD_1927_UTM_Zone_11N). Click OK to execute the Display XY Data tool.
  4. A new point event layer is created and displayed in ArcMap. You need to export the point event data to a shapefile to make them permanent. Right click on the pnt300 events layer in ArcMap, select Data / Export Data, and save the output as pnt300.shp. You can change the layer symbology of pnt300.shp to display the elevation values (stored in the dem300 field) using graduated symbols.
  5. Now we will use spatial interpolation techniques to generate DEMs from the point data set we just created. The first method we use is Inverse Distance Weighted (IDW). The tool can be found at ArcToolbox/Spatial Analyst Tools/Interpolation. Double-click to open IDW. Specify pnt300 as the input points and dem300 as the z value field. Accept 2 as the power value. Change search radius type to fixed, the search distance to 300, the output cell size to 30, and the output raster to dem30idw (make sure you save it to your workspace!)
  6. The DEM automatically added to ArcMap uses a symbology that is difficult to show the subtle variations in the DEM. Change the symbology of the DEM layer from "classified" to "stretched". With this display option, the DEM is displayed as a grayscale map that shows the detail of the terrain.
  7. Now we use the Spline tool to do the spatial interpolation. Open the Spline tool in ArcToolbox. Specify pnt300 as the input points and dem300 as the z value field. Change spline type to Tension, output cell size to 30, and output raster to dem30spl. Accept other default values. Click OK to generate the DEM.
  8. Now we use the Kriging tool to do the spatial interpolation. Open the Kriging tool. Set pnt300 as the input points and dem300 as the z value field. Use Ordinary Kriging with Spherical model. Change search radius type to fixed, the search distance to 300, the output cell size to 30, and the output raster to dem30krg. Click OK to generate the DEM.
  9. After generating all these terrain surfaces, we face the question of which one is the best 30 meter DEM that we created based on a 300 meter DEM (or the point data set). We can do this either visually or quantitatively.
  10. Use the hillshade tool to create hillshade of dem, dem30n, dem30c, dem30idw, dem30spl, and dem30krg. Inspect and visually compare the outputs.
  11. There are many ways to assess the accuracy of interpolated data. Since we have the original 30 meter DEM, we can compare each interpolated DEM with the original DEM. We will use Raster Calculator to do the comparison.
  12. Start Raster Calculator. Click the "Environments..." button to open the Environment Settings dialog window. Click "Process Extent" to expand it. Use the extent drop-down list to select your IDW 30 meter layer (i.e., dem30idw) as the analysis extent. Click OK to activate the setting.
  13. On Raster Calculator, use the layers selection list to calculate the difference between dem30n and dem. That is, select dem30n from the layers selection list, then click minus ("-"), and select dem to complete the formula. Name the output as diffnear and save it to your workspace. Click OK to execute.
  14. Repeat steps 16 to create diffcubic, diffidw, diffspl, and diffkrg. Open the Properties windows of these layers and select the Source tab to view their statistics. Use the information to fill the min, max, mean columns in the Question #4 table.
  15. Use the raster calculator to calculate the square (e.g., diffnear * diffnear) of the difference surfaces. Open the Properties window of these squared difference surfaces and select the Source tab to view the statistics of these layers. Use excel or Windows' calculator to calculate the square root of the mean values of the squared layers to derive the RMSE (root mean square error). Use these values to fill the RMSE column in the Question #4 table.

 

Questions

  1. Using the information displayed in ArcMap to complete the table below.

Grid

# of Columns

# of Rows

Dem

 

 

Dem300

 

 

Dem30n

 

 

Dem30c

 

 

 

  1. Create and submit maps of dem, dem300, dem30n, dem30c, pnt300.shp, dem30idw, dem30spl, and dem30krg. You can put multiple maps in one page. Each map should be clearly labeled with a title and a sentence describing how it was created.

 

  1. Create and submit the hillshade maps of dem, dem30n, dem30c, dem30idw, dem30spl, and dem30krg. You can put multiple maps in one page. Each map should be clearly labeled. Which interpolated 30 meter DEM is the best based on your visual inspection on the maps you created in Questions 2 and 3? Why?

 

  1. Using the information displayed in ArcMap to complete the table below.

Grid

min

max

mean

RMSE

diffnear

 

 

 

 

diffcubic

 

 

 

 

diffidw

 

 

 

 

diffspl

 

 

 

 

diffkrg

 

 

 

 

 

  1. Based on the table above, which interpolated 30 meter DEM is the best? Please explain how you draw the conclusion.