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buffer distance

DaveStockdale

Is there an easy way to determine for an irregularly shaped polygon, what the buffer distance would need to be to create a buffered polygon of a specified size? For example I have a polygon of 500 acres, and I need to create a polygon of 10% greater area, i.e. 550 acres. Is there a way to calculate what the buffer size would need to be in such a case?

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NeilAyres

Probably because the area of the buffered circle in ArcMap is not really a circle, but an "NGon", something that looks pretty much like a circle, but is in fact a bunch of vertices going around the edge. All those tiny little arcs along the edge, add up to your difference.

KimOllivier

The approximation calculating the buffer distance using the perimeter looks fine to me.

You don't actually have to create a featureclass if you use geometry objects that have been added to Arcpy recently. Just copy the featureclass into a polygon geometry and then use arcpy functions to buffer it. All in memory, extremely fast and easy so it should be quite ok to iterate.

DaveStockdale

That may be, but I think the abstraction (circle) would work for me in this situation, since this is for a programmatic EIS and they are wanting to know the effects of different weed treatments over a large area, not a specific project site. The 10% per year was the approximate minimum rate of spread of the weeds as estimated by the resource specialists. The rate could be as much as 24%, and I would model that as well.

DaveStockdale

I tried using your Excel idea and compared it with manually doing 5 buffers in ArcMap, using your formula for the buffer distance. Doing it in Excel got quite different buffer distances than doing it in ArcMap, but the end result was extremely close, 99+ percent. So I'm rather puzzled as to why that should be.

Year	Len	Area	Buffer Distance	Acres	ArcMap/Excel	Len (ArcMap)	Area (ArcMap)	Buffer Distance(ArcMap)	Acres(ArcMap)
0	582477.514	47218070.03	8.1064	11668	1.000000	582477.514	47218070.03	8.1064	11668
1	629695.584	51939877.03	8.2484	12834	0.998870	569034.055	51881183.41	9.1174	12820
2	681635.461	57133864.73	8.3819	14118	0.998816	570108.553	57066214.23	10.0097	14101
3	738769.326	62847251.21	8.5070	15530	0.998997	572501.946	62784212.6	10.9666	15514
4	801616.577	69131976.33	8.6241	17083	0.999418	577001.417	69091740.99	11.9743	17073
5	870748.553	76045173.96	---	18791	0.999744	581227.094	76025680.41	---	18786

RobertBorchert

The issue with multiplying 1.1 times the number of years would be huge. multiply 1.1 times 5 years and that would be an increase of 5.5 times the size. Or rather 550% larger

In excel we can calculate the new area and parameter and get it pretty close. I just tried it and the 5th year was very very close to doing the whole thing five times.

3 columns.

Row 1 Len(A1) Area(B1) Buffer(C1) The first values for Len and Area come from you polygons. the first buffer is

=((B2*1.1) -B2)/A2 this will fill in C2

A2 and B2 came from the polygosn

for cell A3 =A2 * (1 + (C2/100)) then drag it down

for cell B3 =B2*1.1 drag it down

for cell C3 drag C2 down

I did this with my example. By creating 5 buffers in ArcMAP the final increase was 3.939114292 by running this trough Excel I came up with 3.939114202

So I would think if you export your polygons with ObjectID, shape length and shape area you can calculate the 5 and 10 year buffer sizes rather quickly. then you can bring the table back in and with a join populate the 5 and 10 year buffers.

However, I would say in Access we could build a calculation that would add up the new area and length and in a single iteration calculate the final buffer for 5 and 10 year.

DanPatterson_Retired

ok... I am a bit confused... wouldn't the invasive species spreading out by a distance from an edge by whatever means? Was you 10% based upon dissimilar distance measures? It would be interesting to look at some real location since there may indeed be directionality in the data. There have been some discussions long ago on directional buffers to try and replicate that effect (ie for wind-related processes). Just a thought, since I am curious why it is area that you are focusing on, if the real process might be one of an advancing front (whether linear, or non-linear over time)

You can experiment with the math, start with a circle (for instance), radius 10, calculate area, increment the area by 0.5 for several time steps, calculating area and determining the difference from the previous time step. The change in radius ( or radii for other geometric shapes) while produce a predictable change in area and difference. If you have enough time steps, you can determine the radii for complex shapes if the centroid remains fairly fixed but the front advances (ie the spokes of an ever increasing wheel)

DaveStockdale

Thanks. That seems to work for one iteration. What I need to do is show the increase of invasive weeds that are spreading at the rate of 10% a year, 5 and 10 years out. So I would have to run it 5 and 10 times, using the area and length from each iteration as the input for the next. Even putting the calculations into a script, that still leaves a lot of intermediate datasets to get rid of.

What I did was to abstract the weed polygon into a circle, calculating the radius from the shape_area using the formula area = pi x radius squared. Then calculate the area of the 5 and 10 year circles using the formula = * 1 +( ) and calculate the radius of the new area circle. The buffer distance is then radius-new minus radius-original.

I did try your formula on my circles modifying it to (( * 1.1[Number of years])- )/ but that resulted in a larger circle than I got from my original method.

The Increase Polygon Area tool in the Production Mapping toolset will give you a polygon with a slightly larger area than specified, but it involves a lot of trial and error, and doesn’t work well on large, irregular polygons.

Dave Stockdale

GIS Program Manager

Forest Service

Sawtooth National Forest, Supervisor's Office

p: 208-737-3278

f: 208-737-3236

drstockdale@fs.fed.us<mailto:drstockdale@fs.fed.us>

2647 Kimberly Road East

Twin Falls, ID 83301

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If you create a field to buffer by that is a Double type. Here is the formula you use in field calculator.

(( [SHAPE_Area] * 1.1)- [SHAPE_Area])/ [SHAPE_Length]

Just change the 1.1 value to what ever percentage change you want times 100

RobertBorchert

Here is a simple formula.

A1 = current area retrieved from Shape_Area

L1 = current shape_Length

D = buffer distance (what we are trying to find)

% = how much you want to change. Shown as a number i.e. 10% = 1.10 etc

A1 * % = A1 + (L1 x D)

when moved around

((A1 x %) - A1)) = D

I tried it out on a lake before submitting. The area times 10% came out to 13791.312701 and the calculated result was 3.074344911282261549753763646194 for distance. The final area was 13820.829974. It is very close end polygon was 10.29 percent larger.

You can even create a new double field and calculate the new buffer distance for your entire polygon set all at one time and then use toolbox to buffer everything at once. For reference. Here is the polygon I buffered.

DaveStockdale

Thanks gentlemen, I will try these.

DanPatterson_Retired

you could try

http://www.arcgis.com/home/item.html?id=10b2645c4fcd4daf97100720d417424c

RichardFairhurst

There is no simple formula unless you are dealing with a circle or only the simplest of polygon shapes. One post I found ([R-sig-Geo] How to buffer a polygon by area) suggests it can be done in several buffer iterations if you allow for some level of tolerance for some imprecision in the percentage.

Another approximate method that may work is based on a ratio of the area to the perimeter length and is shown in Creating polygons as % of original area using ArcGIS Desktop? - Geographic Information Systems Stack Exchange

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