# Choosing interpolation method for grid data?

I have a grid data of evenly spaced points that gives the number of people with a facebook account within a certain radius (approximately equal to the mid-distance between to points). From that I'd like to draw a smoothed map of my variable density of facebook users.

I read that available interpolation methods for that were :

• natural neighbours
• kriging, or IDW in the simpler way
• rectangular interpolation

1) Kriging seems to be a good idea in any case, still I wonder if rectangular interpolation could be more appropriate and far less complex since I have perfectly evenly spaced values ?

2) Are there any interpolation models that takes also as input the radius around each data point ? From what I understand all of the above methods use only X-Y coordinates and the value of the interest feature, not any radius around X-Y in which the value is the same.

From @Spacedman's comment, I see that I misunderstood my dataset. What I actually have is `z` values for a set of discs defined by a set of points `(X,Y)` and a unique radius `r*`. Which means, at that point I don't have a true grid to interpolate on.

An easy workaround is to assume that the density at each point (let's call them `f(X,Y)` by contrast with `z(X,Y,r*)`) is uniform in my disc, so that `f(X,Y) = a` in disc A. Since I know that `z(A) = a*pi*r^2`, I know that `a = z(A)/(pi*r^2)`. I know have values for a set of points, which are still consistent with the values of the disc they belong to.

What if the discs overlap ? I can't assume anymore that `f(X,Y) = a` around a whole disc since I may have different values for a same `(X,Y)`. Would taking the mean be outrageous ?

• Have a look at the point density tool if you are using ArcGIS desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/…, or heat mapping if you are using QGIS.qgistutorials.com/en/docs/creating_heatmaps.html
– GBG
Nov 8 '18 at 20:32
• Your data is number of people in a circle of area pi*r^2 where r is the circle radius, that gives you a density. You have that on a regular grid, so you can create a raster with that grid resolution. What you then want to do is - I guess - downscale (or is it upscale) to a higher resolution? By what factor? What is the resolution and size of your source sample grid? Nov 9 '18 at 8:19
• @Spacedman each point is separeted by 20km, which makes a really poor resolution in urban areas so I'd like to increase the resolution (let's say by a x10 factor in order to have a grid of point separated by 2km (1km radius). The thing is : I can ask for a grid of points positionned every 2km, but I can't ask for a radius for the value of less than 10km around each point. In this case, circle densities would overlap. I wonder if i can use that overlapping to increase precision or if it is just redundant information Nov 9 '18 at 12:53
• @GBG thanks, I'll have a look at that. Do you know which interpolation algorithm does the tool use ? I guess that it is IDW since I can give a radius in the parameters ? Nov 9 '18 at 13:01