Interpolating a Surface

For this assignment, we will interpolate the same data that we used for the choropleth map to create an isarithmic (contour) map. In Illustrator, we will make a two-map layout that includes both the choropleth and isarithmic maps. The purpose is to compare the two different mapping methods.


Open ArcMap and import a shapefile. If it is a standard ESRI file that is write-protected (as is in this case), choose Data (right-mouse click), then choose Export to export as a new file. The file will have an automatic name and destination folder, which is fine to use in this project in all the steps.

1) Add calculated field

Navigate to ArcToolbox (red toolbox icon near top of screen) and expand /Data Management Tools / Fields / Add Field

Why? Up to now, we've been normalizing the data in the symbology tab. We can't do this with interpolation and therefore must make a new column for this normalized data. Name this field an appropriate name for the data you are normalizing (i.e.Popover85) for population over 85. You will also want to set “field type” as FLOAT. Click OK.

Next, expand ArcToolbox / Data Management Tools / Fields/Calculate Field

This is how we create the normalized data. Choose your new field from above, and set it its parameters.

Example using above situation:

                  Popover85 = ([POP85])/[POP2010]) * 100

We are setting our new field (Popover85) to be a percentage of the total population in 2010. Click OK. You can right-mouse click on the new layer that was just created (under “Layers heading on left side of screen) and choose “Open Attribute Table.” Then scroll all the way to the right and you should see your new field that was just added and normalized.

2) Features-to-Point

Expand ArcToolBox /Data Management Tools /Features /FEATURE TO POINT. Be sure to check INSIDE.

This will create a centroid for each polygon with the polygon's attributes. These points become the known pixels in the "sparse matrix" and form the basis of the interpolation. Other values will be calculated around these points.

3) Create a surface using IDW interpolation (or Kriging)

Next, we will be creating a surface using IDW with a fixed radius.

Under ArcToolbox/expand Spatial Analyst dropdown arrow/ Interpolation/IDW

Click the Input points dropdown arrow and click the point dataset you want to use. Click the Z value field parameter dropdown arrow and click the field you want to use. Use a grid size value of .005. This will take less than 10 minutes and create an image less than 10,000 x 10,000 pixels which is appropriate for this project.

At the bottom of this window, click the Environments button / Processing Extent / choose Same as layer states (or you'll get clipping)

Specify a name for the output, or leave the default to create a temporary dataset in your working directory.

4) Extract by Mask

Under Geoprocessing (at top of page) / ArcToolbox / Spatial Analyst Tools / Extraction / Extract by Mask

Choose the IDW or Kriging surface and the states map and right-mouse click.

Go to Symbology and color the map.

5) Contours

Under Geoprocessing / ArcToolbox / 3D Analyst / Raster Surface / Contour

Choose an appropriate contour interval for your data by examining your classified data legend. Generally the highest value produced from the interpolation (i.e. 12,000 for Popover85) divided by 3 is a good place to start.

Go to Symbology and color the map (use "stretched" for the classification). “Stretched” creates color ramps with no distinct values between different shades and works well in contour maps.


6) Create a legend with 10 boxes between low and high. Shade and label appropriately.

Classify with equal interval (if appropriate) and create 10 classes. Use colors that are similar to your choropleth map. You may want to do this step in Illustrator after the map is exported as an .ai file.

7) Export to .ai

Export four files: US48, Alaska, Hawaii, and the 10-class legend. Use the Albers Equal Area projections that we have used in previous projects.

8) Note on Esri panels

Esri uses a strange system for background raster images, like the interpolated surface. They essentially make panels that extend across the whole page and then mask them with the outline of the area. This causes problems with placing features next to each other in Illustrator.

The solution is to create a tight box around each of the map elements before exporting as an Illustrator file. This limits the size of the panels.

Even with this, you will need to trace Alaska and Hawaii in Illustrator so that the white areas around each state don't overlap the US48 map.

9) Final map:

Make a two-map layout that compares the corresponding choropleth map to this interpolated version. Include a paragraph that explains the process that was used to create both maps. Save as png and pdf.

The paragraph should explain the difference between the two mapping methods. Mention the distribution only to emphasize how each mapping method emphasizes or de-emphasizes particular aspects of the distribution. The choropleth and isarithmic map must use similar color schemes. Examine these links for some background on these mapping methods:

Example interpolated surface


Example Layout

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