Producing raster that shows decay of weighted points

Question

I have a points layer representing the locations of urban green spaces, each containing an associated cooling intensity value and decay coefficient in the attribute table. I want to show the decay of cooling intensity in all direction for each green space point based on its assigned decay coefficient as a raster layer. Similar to how a heat map of points would look, I would want to see the cooling intensity gradually fade away from the points and blending together with the cooling intensity of nearby points.

I am using the following cooling intensity decay equation to show how the cooling intensity of a green space point will decrease with distance travelled away:

y = a + B * ln(x)

where:

y = cooling intensity at given distance (starting from 0 meters and increasing away)
x = distance away from the green space (starting from 0 meters and increasing away)
B = cooling intensity decay coefficient
a = intercept

And so what I want to do is take my points layer, each with its own assigned cooling intensity value and B coefficient in the attribute table, and then apply my decay equation to each point, and produce a raster layer that shows the cooling intensity decay for all green space points.

I have looked into kernel density and interpolation tools, but I have not found any tools that will allow me to apply an equation to a points layer to create the raster layer I am looking for. I would ideally like to show interaction between the cooling intensities of green spaces close together in distance, where cooling intensities between nearby green spaces will be greater depending on the cooling intensities of those nearby green spaces. Is this possible in QGIS?

Answer 1

Any GIS should be able to do this. Simply compute Euclidean distance (ED) to your parks and use raster calculator:

Con("ED" > 0,a+B*Ln("ED"),a)

which says, use a if distance is greater than zero, otherwise use formula. You might need additional expression to convert negatives to 0.

You cannot accumulate park effects, it might very well result in higher cooling (>a) outside parks than inside.