lascanopy - quadratic mean
Gordon Frazer
I have run the most recent version (160110) of lascanopy.exe and noticed that the quadratic average height is incorrect (see embedded graph). The quadratic average is the same as the generalized mean when p is equal to 2: QA = (sum(x^p)/n)^(1/p) (see embedded equations). It would appear as though Lascanopy is only computing: sum(X^2)/n.
Has anyone else noticed this? Martin mentioned that the user group has already vetted this metric and its computation, and that confirmation of a bug by the user group is the only way to have this metric revised.
Thank you for any feed back.
Gordon
Jan Rombouts
Hi Gordon,
Quadratic Mean Height was implemented by Martin on request of an Australian forest research organisation. It is indeed defined as sum(X^2)/n. It is not intended to be the quadratic mean as defined in mathematics.
This is a naming rather than a calculation issue. It is not a bug! Change the name if you must but do not change the formula.
Regards,
Jan
From: last...@googlegroups.com [mailto:last...@googlegroups.com]
On Behalf Of Gordon Frazer
Sent: Tuesday, 19 January 2016 2:39 PM
To: LAStools - efficient tools for LiDAR processing
Subject: [LAStools] lascanopy - quadratic mean
--
Download LAStools at
http://lastools.org
http://rapidlasso.com
Be social with LAStools at
http://facebook.com/LAStools
http://twitter.com/LAStools
http://linkedin.com/groups/LAStools-4408378
Manage your settings at
http://groups.google.com/group/lastools/subscribe
Gordon Frazer
Thank you for the quick explanation. I have not heard of this calculation before. It is simple enough to take the square root of -qav to compute the 'statistical' quadratic mean height. I hope that the rest of the forestry folks understand the difference. I suspect that -qav is useful because the square root tends to be a common transformation of Y and/or X in forestry-related regression models.
Best regards,
Gordon
Gordon Frazer
Just to avoid any future confusion it might be best if you revise your help file to say that -qav is the average square height rather than the quadratic average or mean. You can compute the statistically correct quadratic mean height by taking the square root of -qav. Also, I noticed in one of your forum threads that you refer to -qav as the quadratic average height, which it is clearly not since the units of measure are in meters or feet squared (m2 or ft2).
Thanks,
Gord
On Monday, January 18, 2016 at 8:21:10 PM UTC-8, Gordon Frazer wrote:
Martin Isenburg
David Herries
Susana in our team here sent through this update suggestion last January…
---------------
LASCANOPY README UPDATE SUGGESTION – 29/01/2015
Just a minor update that we have discovered in the interpretation of –qav metric, which I have been meaning to send through to you. The definition of a quadratic mean in maths is = SQRT (∑(h2)/n). However as implemented in LASCANOPY it is actually just the mean of the quadratic height, being = ∑ (h2)/n. This is fine, but worth noting that in comparison to software like FUSION etc the two metric’s are defined differently.
Current LASCANOPY README: “and a quadratic average '-qav' can be computed.”
Suggested Update: “and a mean of the quadratic height ‘-qav’ can be computed”
This would also apply for the -int_qav where it is actually a mean of the quadratic intensity.
We tracked the source of this down after chatting to Jan Rombouts and on chatting to him he noted he gave you the –qav formula as he found that “mean of the quadratic height” linearly correlated to tree volume as opposed to the quadratic average height which did not and therefore got you to add it as is. Therefore our suggestion is you leave this as is, but change the definition of it in the readme for future reference by others.
David Herries Interpine Group Ltd
Mobile: 021 43 5623 DDI: +64 7 350 3209 or Australia 0280113645 ext 721
Jan Rombouts
Hi David,
I very much favour your solution. By not renaming the –qav argument my painstakingly crafted production pipe lines will still work with the next version of Lascanopy :)
Jan