Radius around an origin - Raster

[YaserSadafi]

Hi,

I have a raster map with 1sqr kilometre cells with categorise different land covers (Total 9 categories). My goal is to find a specific area demand of land type around an origin which is a city and then find the radius around the city that covers this demand. I'm not sure how can I do this in ArcMap.

For example I have to figure out what radius satisfies the Forest land demand around my city.

Thanks,

Yaser

[curtvprice · Accepted solution]

There are many approaches to doing this. Here's an idea:

1. Run Euclidean DIstance with your city centroid (or perhaps polygon)

2. Run Slice to create integer distance ranges.

3. Do a selection on your land cover raster for forest land (raster layer selection , or use Set Null)

4. Run Zonal Geometry As Table to tabulate forest land by distance range.

5. Load the table into an excel spreadsheet (or equivalent) and doing a running sum of area.

6. At some point you'll hit your area cutoff. Interpolate the values between those on either side of your threshhold.

[YaserSadafi]

Hi Curtis,

Thanks for your reply. But the problem is I still don't know what is my distance. I mean I only know the demand area, each cell is a 1sqr kilometre, I have to select that number of cells around my specific origin according to area demand and then calculate the radius around the origin. Do you still recommend the same approach?

Regards,

[SepheFox]

In your example of forestland demand, is it 99 SQUARE kilometers you are looking for?

[YaserSadafi]

Hi Sephe,

No, the 99 is the example radius in km. That is an example of what my result is supposed to be. I mean a 27290 km^2 area of forestland around the city is the demand (is known, input of question) and I have to find the radius which satisfies the area. I have to do this for some other land-covers as well. 

Cheers

[DanPatterson_Retired]

If you problem were simple you would simply be solving for the area/radius of an annulus

where: R is the radius of the outer circle H  is the radius of the inner 'hole' π  is Pi, approximately 3.142

which simplifies a little to:

You cannot solve simply for the differences in the radii to produce your target area since your area of difference (ie the hole in the circle) is not circular about the origin.  For example if the area about the City centroid is 1000 km^2, then the radius of the circle to produce this can be solved by the above equations by setting H to 0 and rearranging the equations.

Lets assume that your target forest area is 750 km^2 ... implying 'hole' of is 250 km^2 is needed.

You would be tempted to use the above equations to set your area to 1000 km^2, determine its radius (R) then determine H to yield a hole area of 250 km^2 giving you your resultant target of 750 km^2.

It should become rapidly obvious that that solution only applies for an annulus.  So you have to solve the problem iteratively since your 'hole' isn't a whole but an area of any shape spread out within the circle.  So assuming that you have the centroid as the central location, then you have to 'buffer out' by values of R, via Euclidean distance, determine the area minus the 'chunks' in the buffer until you get your target area of 750 km^2.  I can guarantee you that the 'radius' you calculate will bear little resemblance to what is expected  from circle or annulus solutions.  In your visual, all you need to do is change the shape and location of the shoreline relative to the 'centroid' and you will get a different radius each time.

I have given a simple example of a circular hole in a circle ... aka an annulus.  I pose the question what would happen if it was a square within a circle centred about the centroid? or a triangle? or hexagon.  The simple geometric solutions will not suffice since you have an irregularly shaped water body which cuts out 'area' within the 'buffer' centered about your 'centroid.  Your solution is iterative given the geometry you have and your limitation of a circular shape centred about some location...which is the only way you can get a radius, since radii are relative to centers.

So Curtis has the solution, it can be coded but your input geometry is important.