Choosing the correct predicate for calculating mean patch area per grid cell in QGIS

Question

In QGIS, I have two vector layers - one vector layer is basically a grid, where each grid cell is of size 100x100m, while the other vector layer is Building Footprints data (a collection of polygons representing building outlines).

My requirement is to calculate the Mean Patch Area and Patch Count for every grid cell. I am trying to estimate these two metrics through the "Join Attributes By Location (Summary)" function -- but when I do so, I'm getting unexpected results.

These are the settings with which I executed the above function:

After execution, most of the grid cells are displaying the Mean Patch Area and Patch Count as expected - however, there are certain edge cases that are causing some issues. Consider this scenario, where a patch is overlapping with 2 grid cells:

My requirement is that the Grid Cell on the Top will only consider the portion of the patch that falls inside it, meaning that the Mean Patch Area will be very small when compared to the Mean Patch Area calculated for the Bottom Grid Cell. However, that doesn't seem to be the case; the Mean Patch Areas for the Top and the Bottom Grid cells are close (201 m.sq. and 245 m.sq.).

How, then, do I run this function such that such edge cases are also correctly estimated? I am trying with other predicates (overlap, contains etc.) as well - will update once I know more.

Answer 1

1. I have 2 layers: Buildings and Grid

2. I use "Split with Lines" algorithm and set the tool as below:

The output will be polygons split by the border lines of each grid cell.

3. We need to add the ID of the cell into each resulting part of the polygon after splitting it by using the "Intersection" algorithm.

Below is the resulting layer:

4. Let's open the attribute table of "Intersection" layer: (Now we know each part belongs to which grid number)

5. We can then calculate the area of each polygon part using the "Field calculator":

6. You should be able to calculate the statistics from the resulting table:

7. You can use the "Statistics by Categories" algorithm to calculate statistics based on the Area and the category being the ID of the Grid.

In short, as long as you can create the parts in each grid and assign the Grid ID they are in, you could also calculate the area, from there generate all sorts of statistics.

I would use QGIS Graphical Modeller if I had to redo this operation often.