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Zone summerizing - Aspect   Steffi Goldacker Feb 27, 2004
Re: Zone summerizing - Aspect   Dan Patterson Feb 27, 2004
Re: Zone summarizing - aspect   William Huber Feb 27, 2004
Re: Zone summarizing - aspect   Dan Patterson Mar 01, 2004
Re: Zone summarizing - aspect   Steffi Goldacker Mar 03, 2004
Re: Zone summarizing - aspect   William Huber Mar 03, 2004
Re: Zone summarizing - aspect   Dan Patterson Mar 03, 2004
Re: Zone summarizing - aspect   Steffi Goldacker Mar 10, 2004
Re: Zone summarizing - aspect   William Huber Mar 10, 2004
Re: Zone summarizing - aspect   Analisa Gunnell Apr 05, 2007
Re: Zone summarizing - aspect   William Huber Apr 05, 2007
Re: Zone summarizing - aspect   Eva Karau May 22, 2007
Re: Zone summarizing - aspect   William Huber May 23, 2007
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Subject Zone summerizing - Aspect 
Author Steffi Goldacker 
Date Feb 27, 2004 
Message Hallo ArcView3. unsers,
I have a problem with summerizing aspect within certain polygones. That is to say, I have a DEM-Grid, from which I have made an aspect grid. Now I want to calculate the "mean aspect" for my different polygones which I have in another grid. I have problems with aspects ranging in the north around 0 and 360° respectively, where a mean of e.g. 180° returns.

What can I do? Any suggestions.
Thanks a lot
Steffi 
   
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Subject Re: Zone summerizing - Aspect 
Author Dan Patterson 
Date Feb 27, 2004 
Message mean aspect can't be determined using simple averages, as you note the average of 10 and 350 degrees equals 180. To overcome this multiply the aspects by two then divide by the number of entries ie 20 + 700 = 720/2=360 which conceptually makes sense. Look for stats texts (specifically geology) that contain references to "spherical statistics" or "directional statistics". a book by Davies and N.M.R. Rock (I am not kidding, a geology stats text) come to mind but I don't have the references here. 
  Geomatics, Carleton University, Ottawa, Canada 
   
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Subject Re: Zone summarizing - aspect 
Author William Huber 
Date Feb 27, 2004 
Message We could use some "summerizing" of our aspect here: it's the dead of winter in PA ;-).

Multiplying the aspect grid values by a constant factor cannot possibly help. The problem is that aspect is not well-defined (aspects are defined only up to multiples of 360). Consider, for instance, the case where some aspects are 359 and others are 1. No matter how you slice it, the average will come out wrong. Dan, your approach works only when averaging two values at a time and it gives wrong answers in most cases anyway (because you have doubled all the angles, of course).

The correct solution depends on how you will use the averages, so I cannot recommend one in particular. But one method that will give reasonable answers is to convert each aspect into a (2D) vector, average them, and convert back to an aspect. This is easy: create cosine and sine grids, average them by zone, then recombine the results in the Field Calculator using an appropriately coded version of the arctangent (of which many examples abound in this forum: just search).

Other approaches are variants of this one. In many cases, you will also need the slope grid along with the aspect grid. From these you would create 3D vectors (the surface's unit normal field), average these, project them back into the coordinate plane, and compute an arctangent. It's the same as the first approach except you are computing a weighted average with the weights given by the cosine of the slope. This might be the appropriate mean value to use for insolation analyses, for instance, or for grid generalization. 
  --Bill Huber
Quantitative Decisions (http://www.quantdec.com )
More GIS Q&A at http://gis.stackexchange.com/q/3083/664 
   
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Subject Re: Zone summarizing - aspect 
Author Dan Patterson 
Date Mar 01, 2004 
Message I found the references Bill and as you suggest

angles measures clockwise from north

for each orientation calculate

Xi = cos (angle)
Yi = sin (angle)

sum resultant angles

Xr= sumof (Xi)
Yr= sumof (Yi)

mean direction= tan^(-1)(Yr/Xr)
References
J.C. Davis. Statistics and Data Analysis in Geology (Library of Congress number QE 48.8 D38) pp 315-351
N.M.R. Rock Numerical Geology (QE 48.8 R63) pp 226-245)

These references also provide some other statistical measures 
  Geomatics, Carleton University, Ottawa, Canada 
   
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Subject Re: Zone summarizing - aspect 
Author Steffi Goldacker 
Date Mar 03, 2004 
Message Dear Bill and Dan and,
thanks for your replys and sorry for my English, but "summerizing" cold old Germany would be nice too.
Anyway, as I am a beginner in Spatial Analyst projects I am a bit helpless how to create cosine and sine grids out of my "aspects of dem", as the grid is a floating point grid and I cannot open a table. 
   
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Subject Re: Zone summarizing - aspect 
Author William Huber 
Date Mar 03, 2004 
Message Steffi,

Use the Map Calculator. The expressions look like

([Aspect] * (0.01745329)).Cos

and

([Aspect] * (0.01745329)).Sin

The constant in there converts degrees to radians (SA's developers couldn't come up with a consistent way to measure angles and did not even provide a simple mechanism for conversion...) 
  --Bill Huber
Quantitative Decisions (http://www.quantdec.com )
More GIS Q&A at http://gis.stackexchange.com/q/3083/664 
   
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Subject Re: Zone summarizing - aspect 
Author Dan Patterson 
Date Mar 03, 2004 
Message don't forget Bill's Grid Statistics
http://arcscripts.esri.com/details.asp?dbid=948300728
to get the sum of each grid 
  Geomatics, Carleton University, Ottawa, Canada 
   
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Subject Re: Zone summarizing - aspect 
Author Steffi Goldacker 
Date Mar 10, 2004 
Message I have done so. Created cosine and sine grids, have my grid summarized by zone with each grid (sine and cosine)and calculated the "atan" as shown in the statistics and divided by o.o1745329 to get angles in degrees for each summarized zone in my grid theme. As I have many different zones, so I have many different aspects summarized. The Angels which are the result of the calculation: tan^(-1)(Yr/Xr)don`t tell me the true angels in a 360° circle for each summerized zone but the angel to be added to 0° or 180° or subtracted from 360° or 180° respectivly. How can I solve this problem to get the real mean aspect (0 - 360°)of each summerized zone in a grid theme? 
   
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Subject Re: Zone summarizing - aspect 
Author William Huber 
Date Mar 10, 2004 
Message Any function depending only on the ratio y/x cannot distinguish the direction determined by (x,y). Thus, all systems where serious numerical work is done implement the Fortran ATAN2 function, which takes two arguments, y and x, and returns the direction. Spatial Analyst provides this (although ArcView itself does not!); the syntax is

[x].ATan2([y])

See the help page for 'ATan2' for details. 
  --Bill Huber
Quantitative Decisions (http://www.quantdec.com )
More GIS Q&A at http://gis.stackexchange.com/q/3083/664 
   
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Subject Re: Zone summarizing - aspect 
Author Analisa Gunnell 
Date Apr 05, 2007 
Message So, you're saying that we need to use the ATan2 function instead of the ATan? I've tried this, but still my results are between 179 through -179 (after I convert back from radian to degrees).

frustrated non-mathematician 
   
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Subject Re: Zone summarizing - aspect 
Author William Huber 
Date Apr 05, 2007 
Message Analisa,

I am puzzled: the range from -179 to 179 practically covers a full circle. What is wrong with that? 
  --Bill Huber
Quantitative Decisions (http://www.quantdec.com )
More GIS Q&A at http://gis.stackexchange.com/q/3083/664 
   
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Subject Re: Zone summarizing - aspect 
Author Eva Karau 
Date May 22, 2007 
Message Hi,

This is a follow-up question to William Huber’s post from 4/5/07. Analisa mentioned that after the atan2 transformation, her grid values ranged from 179 through -179, and though this covers the full circle, I’d like to know how these values translate back to the 0 to 360 range of traditional aspect values. I am using ArcGrid to do the same thing as previous posters – summarizing aspect by zones, and I got as far as the atan2 statement that produced the grid from 179 through -179. Maybe I’m missing some obvious step in converting these values back to aspect ranging 0 – 360?

Thanks much in advance,

K
 
   
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Subject Re: Zone summarizing - aspect 
Author William Huber 
Date May 23, 2007 
Message Eva,

It works just like longitude: compute modulo 360 degrees. Thus, for example, -111 degrees is the same as -111 + 360 = 249 degrees.

I'm sure you could have discovered this yourself by inspecting the results of the calculation. 
  --Bill Huber
Quantitative Decisions (http://www.quantdec.com )
More GIS Q&A at http://gis.stackexchange.com/q/3083/664