Power parameter and IDW

Question

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

idw_graph.png

Ke_Xu_0-1783435987976.jpeg

BillGaertner · Answer

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 = 20.5

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?

curtvprice · Answer

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 = 20.5

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.