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Module 4
Table of contents
  1. Clean Up Your Workspace Selection
  2. Method 1
    1. Zonal Statistics as Table
  3. Method 2
    1. Raster to Polygon Conversion and Intersection
    2. Calculate the Green Vegetation Area and Dissolve by CT
    3. Data Normalization
  4. Inspect and Compare the Outputs
    1. Ordinary Least Squares Regression

Spatial Analysis

A key aspect of GIS is overlaying multiple data layers to generate new information. There are typically multiple solutions to a given problem in GIS. Here, we are going to look at two methods for combining a raster layer and a vector layer:

1) Zonal Statistics: This method is faster, but can be applied in a more limited number of circumstances.

2) Raster to Polygon Conversion: This method involves converting between data types and requires more steps, but it is more flexible.

Clean Up Your Workspace Selection

From here on out, we are only goin to be working with the VanCMA_CT_2016 so you can remove the Van_DA_2016 layer.

Method 1

Zonal Statistics as Table

We are going to overlay the vector data on the raster data to measure the mean NDVI value for each census tract using the Zonal Statistics as Table tool. Then we will Join the resulting output table to add the NDVI values by CT to the layer. A join is a way to add tables to a layer based on a specific column. You can reference the video below for guidance.

1 Find the Zonal Statistics as Table tool in the Geoprocessing pane, choose VanCMA_CT_2016 as the feature zone data, and Van_Greenest_ProjectRaster as the Input value raster.

  • Set CTUID as the Zone Field
  • Select All statistics types

2 Right click on VanCMA_CT_2016 and choose Joins and Relates > Add Join.

  • Set CTUID as the Input Join Field
  • Choose the Zonal Statistics table as your input. (the name should look something like ZonalST_VanCMA_1)
  • Make sure CTUID is selected as the Join Table Field as well

3 Inspect the Join

  • Open the attribute table and note the new columns at the end

Method 2

Raster to Polygon Conversion and Intersection

We are going to convert the classified raster layer to a vector layer. Then we can overlay the resulting vector layer with the VanCMA_CT_2016 layer using an intersect which will let us calculate the total green vegetation area per CT in the next step. You can reference the video below for guidance.

1 Find the Raster to Polygon tool in the geoprocessing pane.

  • Set the Classified NDVI image as the Input raster
  • Choose Value as the Field

2 Find the Intersect tool in the geoprocessing pane. It will combine the feature classes where they overlap and exclude all other areas. We’ll talk a lot more about this tool.

  • Set Van_DA_2016 and the output from the raster to polygon conversion as the inputs. Then click run.
  • Change the symbology and open the attribute table to confirm the results look like what we’d expect.

Calculate the Green Vegetation Area and Dissolve by CT

Now we are going to calculate the total green vegetation area by CT, and toss out a bunch of the unnecessary data. You can reference the video below for guidance.

1 Add a new field to the VanCMA_CT_2016_Intersect layer called “Green_Veg_Area” so we

  • Name the field Green_Veg_Area
  • Make sure the data type is Double.

2 Choose Select by Attribute and set your query to: Where gridcode is equal to 3.

3 Right click on Green Veg Area and choose Calculate Field. This allows us to define a function and apply it to the table.

  • Set the expression to: Green_Veg_Area = Shape_Area
    • Note you only need to complete the right side of the equation
    • This will simply copy the shape area for the green vegetation areas, we will work with a more complex expression on the next page.

4 We want to assign all other rows a 0. We can quickly invert our selection with the Switch button.

  • Calculate the field again, but with Green_Veg_Area = 0
    • We have selected gridcode 1 & 2 (Not vegetation) so they all get zeros.

Data Normalization

One last thing step! We need to account for a confounding factor. The CTs are different sizes. To better compare the CTs (which are vastly different sizes), lets Normalize our results by the total area of each CT! Normalizing, sometimes also referred to as standardizing, is the process of dividing one variable by another variable to account for their relationship. It can help us identify patterns that might be masked by a confounding variable.

1 Add a new field called “PCT_Green_Space”.

  • Make sure you set the data type to Double

2 Calculate the field using the following equation:

  • PCT_Green_Space = SUM_Green_Veg_Area/Shape_Area
    • Note you only need to complete the right side of the equation

3 Right click on PCT_Green_Space and select “Statistics”

  • This will bring up some descriptive statistics for this field.

Inspect and Compare the Outputs

Lets see how the two methods compare?

1 Open the Attribute Table of VanCMA_CT_NDVI_Veg. Double click on Mean_NDVI to sort by that column in ascending/descending order. Take note of the CTUIDs for of the CTs with the highest values. Now look at SUM_Green_Veg_Area and PCT_Green_Space. Do they all match up, or are there some differences?

2 Create a new Scatter plot. Set the X-axis to Mean_NDVI and the Y-axis to SUM_Green_Veg_Area. Look at the R2 score and think about the relationship between these variables. Now change the Y-axis to PCT_Green_Space and not how the relationship changes.

3 Change X-axis to Mean_NDVI the Y-axis to Housing. Make sure to Exclude the zeros using the same procedure as earlier then look at the resulting relationship. Is the Mean_NDVI a good predictor of housing cost? Create a second scatter plot with Housing on the Y-axis but set the X-axis to PCT_Green_Space. Does it gives a better result? Make sure to filter the second chart

4 In addition to filtering by a selection, you can also filter a scatterplot by Extent. This will limit the points on the chart to only the polygons visible in the map window. Then try filtering by extent and panning/zooming around your the Metro Vancouver area and take note of how the charts and R2 values update as you move around.

hi

Ordinary Least Squares Regression

Like the name suggests, simple linear regression is … simple. It can only account for the influence of one independent variable at a time. Reality is rarely this straightforward and typically there are numerous factors influencing a dependent variable. A more general version of linear regression is known as Ordinary Least Squares regression. This model allows us to account for multiple dependent variables. For instance, a three factor OLS model (three dependent variables) would look something like this:

\[Y=aX_1 + bX_2 + cX_3 + d\]
  • X1, X2, and X3 are all dependent variables and a, b, and c are their respective coefficients (slopes) while d is the intercept.
  • Imagine a simple example that might be used in the real word: trying and estimate the total damage in dollars (Y) from a storm:
    • X1 = maximum wind speed
    • X2 = total rainfall
    • X3 = population of area effected.
  • This model won’t give a perfect estimate, but by accounting for two aspects of the storm it will do a much better job describing the storm than just wind speed or rainfall alone. Further, by accounting for population it will give us some idea of number of people impacted. A storm in an uninhabited area wont cause much damage regardless of its strength, but in a large metro area it will cause significant damage.

Think about how this model might be applied to improve our analysis?