topic Re: Calculate average values from observations within a distance weighted by the square of the inverse distance in ArcGIS Spatial Analyst Questions

Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 05:54:47 GMT

I have a shape file for U.S. county centroid, and another shape file for temperature point observations across the U.S.

I'd like to calculate the average temperature for each of the county centroid, from the temperature observations within a certain distance of the centroid, weighted by the square of the inverse distance. Could anyone let me know which tool(s) should I use to get this outcome? Thanks very much in advance.

Alec

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

NeilAyres — Fri, 03 Jun 2016 07:16:32 GMT

"weighted by the square of the inverse distance", distance to / from what?

Wouldn't just a simple IDW interpolation of the temperature points, then get the average for each county be good enough?

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

DanPatterson_Retired — Fri, 03 Jun 2016 08:02:47 GMT

besides the math issue trying to obtain county level information from country level data is a very poor mix of data source scale. Have you explored the possibility that data may be available at the county level, or at worse, the state level?

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Fri, 03 Jun 2016 09:59:24 GMT

You can do that with model builder,

Just add two fields in U.S. county centroid Feature class, the first field you will calculate a certain distance (weighted by the square of the inverse distance).the second field for average temperature values but you will let that field Null

then run buffer tool using the distance field.

select by location for all temperature point observations within each polygon

use summary statistics tool to get average

get this value and make field calculate in the second field that you created

you will use iteration selection, to do that for each polygon buffer.

thanks

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 12:28:46 GMT

Hi Neil, it is distance from a county centroid to any temperature point that is within a certain distance of the centroid, say 100 kilometres. I think IDW interpolation creates a raster layer. Then zonal statistics could get an average value for a county. But this is still different from what I intend to do. Thank you for your reply.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 12:31:18 GMT

Hi Dan, thank you for your reply. I am using temperature as an example. I also need to get many other variables. But there is no available county level data.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 12:38:02 GMT

Hi, Abdullah, your suggestion is very good. I am new to GIS so need to explore a bit how to use model builder to get this done.

But for the first distance field, what should be entered at first? I am not sure what a certain distance means. I will need all the temperature points within 100kms of a county centroid. Does it mean the first field needs to be 1/10000?

Thanks again for your reply.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Fri, 03 Jun 2016 13:01:15 GMT

Is the distance 100 km for all centroid county or it is varies ?

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 13:25:57 GMT

It is fixed at 100km radius for every county centroid.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Fri, 03 Jun 2016 13:46:28 GMT

very good you will not need to add two fields

you will create one field only in County centroid feature for ( average temperature)

and I will create the model , and I will attach

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Fri, 03 Jun 2016 14:18:34 GMT

That is very much appreciated.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Fri, 03 Jun 2016 15:38:47 GMT

The model is ready.

Just you should add field for average temperature to county centroid shape file before use the model.

you can download the model in attachment

and the picture below for model design

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Sat, 04 Jun 2016 08:16:33 GMT

Hi Abdullah, thank you so much for this. I will try this next Monday. Will let you know how it goes.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Sat, 04 Jun 2016 17:02:18 GMT

You will find two model

First for none weighted Just( mean temperature)

Second for weighted by the square of the inverse distance with the following equation:

Sqr (1 / Distance ) * temperature value

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Mon, 06 Jun 2016 10:29:03 GMT

I think the model is working. It has been a few hours and it is still running. I have over 4000 temperature points and over 3000 county centroids. This is probably why it takes so long.

And just to make sure, the second is weighted by the inverse of distance squared -- (1/distance*distance), not the inverse of square root of distance -- 1/sqrt(distance), right? I saw you had them both above.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Mon, 06 Jun 2016 20:30:23 GMT

The number of temperature points will not cause any problem, but 3000 county centroid is mean 3000 iterations in model.

and it will take long time.

the two equation above is same.

The first equation for VB in field calculator and it give the same result of the second manual equation .

If you want other one please write it in manual form . thanks

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

DanPatterson_Retired — Sat, 11 Dec 2021 17:39:34 GMT

I think the confusion is arising because the thread title says ... square of the inverse distance... whereas it appears he wants based upon inverse distance squared, perhaps the desired incarnation needs to be specified. For some variants... you can add your own

>>> import math
>>> distance = 4
>>> 1.0/(distance*distance)   # inverse distance squared
0.0625
>>> math.sqrt(1.0/distance)   # square root of the inverse distance
0.5
>>> math.pow((1.0/distance),2) # alternate
0.0625
>>>

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Tue, 07 Jun 2016 02:02:09 GMT

Okay, I think the weighting in Abdullah's model is not what I meant then. I wanted to use either row 03 or row 07 in Dan's response. Could you let me know how to edit the model? Thank you very much.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

AbdullahAnter — Tue, 07 Jun 2016 16:04:21 GMT

I updated the model as row 03 in Dan reply.

I think that what you want, isn't that?

you can download it in attachments.

Re: Calculate average values from observations within a distance weighted by the square of the inverse distance

ZHIZUO — Wed, 08 Jun 2016 00:27:05 GMT

Thank you so much! Yes, this is what I want.