Bivariate display with ArcGis

It is not easy to visualize a bivariate map with ArcGis , i.e a map where the entities are categorized according to two variables located in two independent layers.

The colour assigned to each entity responds to a colour scale along two axes, X and Y:

Therefore each layer must be classified according to four classes. The entities which belong to the first class of each of the layers share the colour located at the bottom and left, those belonging to the strongest class of each layer will have the colour located at the top and on the right.

You do not have standard tools in ArcGis for this chore but a treatment model can resolve this absence. The treatment model that we propose is based on an original TWSAdmin idea published at

We have worked this model so that we can use it without prior editing, by supplementing it to take into account a classification of 4 × 4 and 6 × 6 classes and, finally, by translating and documenting it.

Here is the basic model:

The principle is simple: with the tool create a grid,  we create a two-dimensional grid of 4 × 4 cells (or 6 × 6) covering the considered area. The two rasters are reclassified according to the number of columns, then by the number of rows. One of the two values ​​is multiplied by 10 and the two reclassified rasters are added together. The raster is converted into polygons and combined with the two-dimensional mesh. Finally, we merge the polygons according to the value of the mesh.

Tool download

The file downloaded contains a toolbox with two models: one allowing a mesh of 4 × 4 cells and another a mesh of 6 × 6.

You have a toolbox for ArcGis 10, another for 10.1-10.2 and one for 10.3.

You also have two symbology files , one for the 4 × 4 grid and another for the 6 × 6 grid.

Finally you have two images representing the two grids to use as legend of the result obtained.

Example and how to use the tool

Let’s start with what you need to do before launching the tool:

1-Load the two raster layers you want to process.

For the example we will take the Slope layer and the ground Occupation layer that we used for Spatial Analyst articles and fuzzy logic ( Tutorial: create an aptitude map with ArcMap , with and without fuzzy criteria (1) ) .

Land Occupation


2-Locate the XY coordinates of the top left corner and bottom right corner of your rasters.

Add the Toolbox for your version of ArcGis:

4-Decide what type of classification you want for each of the rasters. You have the choice between three classification methods: classes of equal size, classes of equal areas and classes according to the natural thresholds. The choice of method is related to the type of data and the objectives of your work.

Here we will choose classes of equal size. So the classification will be similar to the one we made with fuzzy number tools, ie classifying the slope into 4 classes, whose limits can be associated with satisfaction values: null, modest, good, very good, and excellent.

5-Create a file geodatabase where intermediate operations will be performed. You can also use an existing geodatabase because only the result is retained after the model runs.

You can launch the tool. This setting window appears:

At the origin coordinate of the mesh you have to enter the XY coordinates of the top left corner marked in point 2.

At the Y axis coordinates, remove a few meters at the X coordinate of the mesh origin and add a few meters to the Y coordinate of the mesh origin.

In coordinates of the opposite corner, enter the coordinates listed in point 2.

Select the two rasters to process and the ranking method to apply.

Specify the file geodatabase to use for intermediate calculations.

Indicate the location and the output name of the resulting polygons layer. You can specify a different geodatabase from the one used for intermediate calculations.

Click OK.

Usually, the result layer should be displayed, but that will have to wait for future versions of ArcMap to be sure. So if it does not appear automatically, charge the result layer and import the legend provided with the toolbox (Bivariate_4_classes.lyr)

As for the tool, it’s over. However, the legend used by ArcMap is not very explicit. We will cheat a little to have a more meaningful presentation.

We will add a legend image and a legend text, but in the map window.

Add a copy of the image supplied with the tool (caption4classes.png). You will get a message saying the image is not georeferenced . Click OK.

Add the Georeferencing toolbar.

In the menu that appears, make sure that you are well positioned on the image you just loaded.

Open the Georeferencing menu and click Fit to display.

This brings the image into the map window.

You will use the image moving tools to reduce and move the image next to your result layer

With Scale you reduce the size of the image and with Shift you move it next to your result layer.

When you are satisfied, open the georeferencing menu and click Update Georeferencing .

Your image is now georeferenced and each time you load it into ArcMap , ArcScene , and so on , it will be placed here.

To complete the legend, you can create a layer of annotations and enter the texts you want. Since the annotation layer is geographical, the texts will always be placed in the same place.

On the result map, you can highlight any area that corresponds to a class in the legend by simply clicking the selection tool on one polygon of the class. This highlights all the polygons in the class:

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