1. Calculate an area of each patch in Field Calculator (shp)

2. Then Raster > Conversion > Rasterize (Vector to Raster)

3. Set the resolution of the output raster grid to 1000 × 1000 m

Here are some screenshots

@Anneleen, I suppose you want each cell to hold the sum of that fraction of forest polygon area that is overlaying some cell. So the problem is to sum up on a cell by cell basis, not to assign a single value to a cell.

You can realize that as a vector overlay problem.

The workflow might look somehow complicated, but you can semi-automatize it as a processing model. You benefit from as much detail information as possible.

Dear @ Detlev Neumann , I am interesting to make disaggregation of emissions over a city. Here some steps that I want to develop, but I would like to get more information of this kind of works:

(a) Intersect the regular grid with the urbanized areas GIS file

(b) Join the intersected landuse map with the cells file, in order to have the urbanized surface statistic per cell.

(c) Compute the weight of urban covering for every cell

(d) Assign to every cell the emissions by multiplying the total CO emission to the weight calculated in (c)

Best regards