[vox-tech] OT math question

[Dylan Beaudette]

On Wednesday 10 November 2004 08:52 am, Jeff Newmiller wrote:
> On Wed, 10 Nov 2004, Dylan Beaudette wrote:
> > I know this is quite off topic... however it deals with numbers generated
> > by a computer, so....
>
> *snicker*
>
> Well, given that part of my job is analyzing insolation data, I might
> as well weigh in on this, and it isn't any more off topic than many
> other threads we've tackled here.

Thanks!

> > So I have some solar insolation values- 1 value per day for an entire
> > year.
>
> 1) Insolation is often (almost always?) presented in units of kWh/m2/day
> ... since the standard "one sun" irradiance value is 1000 W/m2, these
> preferred units can be reinterpreted as sun-hours/day (hours per day that
> the sun could have shined at full power and obtained the same total
> insolation).

Good point. However, this is an initial look at some ways of characterizing 
solar insolation rather than using something like aspect alone...

> > the graph of solar insolation (y-axis) vs. day of year (x-axis) vary in
> > shape - sometime looking very similar to a Gaussian distribution. I would
> > like to characterize the relative fatness of these "Gaussian-like" graphs
> > with something like a coefficient of variation... however, to the best of
> > my knowledge things like the CV operate on frequency distributions, which
> > in this case would only be characterizing the variation within the
> > insolation values with respect to eachother.
>
> 2) Gaussians are just mathematical curves that happen to fit frequency
> data.  However, I think the interesting information in these plots would
> be lost by imagining these curves to be comparable to nice, ideal
> Gaussian distributions... for example, one characteristic of Gaussians is
> that they apply over an infinite input range... your input range repeats
> (every year), so in reality these humps are part of a repeating pattern.


Got it. After talking with one of my professors, it would seem that instead of 
trying to treat the curves as if they were a Gaussian, describing them with a 
Fourier series - which should capture all of the odd complexities that are 
visible in some areas (like site 106 in this graph: 
http://169.237.35.250/~dylan/solar/four_points4.png)

( thanks Pete for the ideas on how to describe Gaussian curves!)

So perhaps a better question- would octave or the like be the best way to 
calculate a Fourier series to approximate the data?

> > just for reference a sample image can be found here:
> > http://169.237.35.250/~dylan/solar/index.html#more
>
> 3) I would guess that the green and orange curves [1] represent locations
> in valleys. Noting how many days the insolation is less than some value
> could be useful. The threshold value would depend on the purpose to which
> the data are being applied... I would guess that less than half an hour
> per day of full sunlight would be pretty useless for most energy analysis
> purposes (such as building heating load or photovoltaic energy
> conversion).  For curves that don't reach the threshold, noting the
> minimum value could be useful.

these data are going to be used for soil genesis modeling, so i would imagine 
that there are some thresholds related to photosynthesis that would be of 
use... thanks!

> 4) The flatness at the top of some of the curves [2] is puzzling... almost
> like there is an overhang that creates more shadow in the summer, though I
> am having a hard time guessing how you would see that from an aerial view
> (tall trees with a significant height to their lowest branches, casting
> shadows nearby in the summer but further away in winter?).  A simple
> characterization of this feature would be what the maximum value is, but
> identifying the duration of flatness at the peak might be accomplished by
> determining how long the curve remained within some threshold of the
> maximum.

Although it is hard to tell from the maps next to the insolation graphs, this 
area has a lot of vertical relief over short horizontal distances... i.e. 
steep slopes. The algorithm that calculated solar radiation values takes into 
account surround terrain features, thus creating the oddly shaped insolation 
graphs at certain points.

> [1] http://169.237.35.250/~dylan/solar/cell1.png
>
> [2] http://169.237.35.250/~dylan/solar/four_points_map5.png
>
> > and if anyone is interested this is part of a dataset that was created
> > and is being visualized with the open source GIS package called GRASS.
> > (yeah for OSS!!)
>
> I've heard of it... but I tend to concentrate on one location at a time.

just in case Henry is reading, GRASS57 coupled with QGIS are 2 nice 
alternatives to the expensive proprietary GIS packages that he was trying to 
avoid.

> > thanks in advance, and sorry about the slightly off topic (and probably
> > bone headed) question...
>
> One way I wouldn't characterize this question as is bone-headed ...
> finding good modelling equations is tough... whether you use Linux or not.
> ;)
>
Thanks for the tip... Last night I was having doubts about my math skills. 
hehe


> PS: "Raditation"?

yes, i know, i can't spell


-- 
Dylan Beaudette
Soil Science Graduate Group
University of California at Davis