topic Power parameter and IDW in ArcGIS Spatial Analyst Questions

Power parameter and IDW

BillGaertner — Tue, 04 Mar 2014 03:31:18 GMT

I am working on an analysis that involves polygons and points with values and I am using IDW to predict the values of pixels in between. I need the values of the points to have a 50% impact on the values of the surrounding pixels when they are 3 miles away from the source data and a 0% impact when they are 5 miles away. I am wondering if anyone knows of a formula I could use to determine what power value would get me the results I am looking for. I'm basing this slightly off of a graph that is on one of the help pages for the IDW tool, a copy of which is attached. I'm hoping that there is a formula that would generate those different curves.

Is this possible or does anyone have any ideas?

Thanks

Re: Power parameter and IDW

curtvprice — Sat, 11 Dec 2021 20:48:05 GMT

There are two issues here: the weight and the maximum search distance. The search distance is a parameter to the IDW tool.

As for the weights, here's how it's done using the simple IDW formula of inverse-distance-squared weight and setting it to 0.5:

0.5 = 1 / x²
x² = 2
x = 2^0.5

Here's a check in the Python window to make sure I got that right:

>>> 100 * ( 1 / ((2 ** 0.5) ** 2))
49.999999999999986

Remember these weights are *relative*: if two points are equal distance they both get 50% each weight, if only one point is in distance, it gets 100% weight.

Re: Power parameter and IDW

BillGaertner — Sat, 11 Dec 2021 20:48:08 GMT

There are two issues here: the weight and the maximum search distance. The search distance is a parameter to the IDW tool.

As for the weights, here's how it's done using the simple IDW formula of inverse-distance-squared weight and setting it to 0.5:
0.5 = 1 / x²
x² = 2
x = 2^0.5
Here's a check in the Python window to make sure I got that right:
>>> 100 * ( 1 / ((2 ** 0.5) ** 2))
49.999999999999986
Remember these weights are *relative*: if two points are equal distance they both get 50% each weight, if only one point is in distance, it gets 100% weight.

Curtis, thanks for the response.

When I have used search distance, it always seems to result in a less smooth raster. I was hoping to use the power parameter in a similar way and specify a distance at which the source values have a 0% weight on the value of the pixels. It might be easier if I forget about the 50% weight at a certain distance and just focus on the 0% weight at a certain distance. How could you use a formula, like the one you posted, to specify that a source value has a 0% weight on a pixel once it gets 5 miles away?