Just some rando...
13.4kJ/day UVB:
[(13.4kJ/m^2) × (1000J/1kJ) × (1m^2/10,000cm^2) × (1,000,000μJ/1J)]
÷
[(6hrs) × (60min/hr) × (60s/min)]
=
62μW/cm^2 @ 6hrs/day
Their measurements were
weighted toward 300nm, although idk if they followed Caldwell's weighted action curve exactly, or just created a normal distribution curve centered at 300nm.
Humans use a weighted scale when determining the risk of sun exposure called the ultraviolet index. This weighting that's applied to the emitted UVB puts more value in certain individual wavelengths within the UVB range (280nm - 320nm) than others. It's actually very drastic, so much so that if you were to compare a 297nm WV to a 319nm WV (only 22nm seperate the 2 WV's, they are very close) using the Ultaviolet Index method, the 297nm would be multipled by a 100% weighting factor, while the 319nm would be multiplied by a ~1% weighting factor (refer to erythemal action curve).
Every WV has a corresponding erythemal weight that will be applied or multiplied. All these individual results are added up and then the total is divided by 25mW/m2 to arrive at a UVI. So UVI is a 2 part or 3 part calculation. First you'd multiply the actual intensity of the WV being emitted (mW/m2) by the weighting factor or by the corresponding erythmal %, then you'd add up all the results of those multiplications, and finally you'd divide the total sum by 25mW/m2 to arrive at a calculated UVI.
For the sake of argument let's say you only had (1) 297nm LED, and (1) 319nm LED, both emitting 10mW/m2 of UVB radiation.
10mW/m2 @ 297nm × (100%)
=
10mW/m2 of weighted UVB
10mW/m2 @ 319nm × (1%)
=
0.1mW/m2 of weighted UVB
10mW/m2 of erythmally weighted UVB from 297nm
+
0.1mW/m2 of erythemally weighted UVB from 319nm
=
10.1mW/m2 total of erythemally weighted UVB
(10.1mW/m2) ÷ (25mW/m2)
=
0.414;
0.4 UVI
^^All that is just to show how drastic the change in effect is with only a small change in WV. At 297nm all of the emission is effective, while at 319nm only 1% is effective. This realization that certain wavelengths effect us more or less within a given range, is also the same realization noticed with plants, certain WVs have much greater effect on other WV's even if they are all within the "UVB" range.
The study was weigting the UVB emitted from the fs-40 lamps around 300nm just like we weight UV around 297nm when calculating a UVI. This means that the ~62μW/cm2 @ 6hrs/day, or the 13.4kJ/m2·day, is
not the whole story and not the target intensity of "generic" UVB one should strive to achieve for similar results. 62μW/cm2 was weighted around 300nm so the actual total amount of UVB was probably much greater.
Here's Caldwell's weighting curve (blue curve, "1") used in the study to calculate the % of effectiveness per WV for plants, ie action (within the UVB range at least).
This is a fs-40 lamp SPD...
It looks like it peaks around ~312nm. They'd have multiplied each WV's intensity on the fs-40 by the corresponding effective % from Caldwell's action curve. Or they'd have multiplied each WV's intensity on the fs-40 by a corresponding effective % from a normal distribution curve they made up but influenced by Caldwell's action spectrum and centered around 300nm. I'm just not comprehending what exactly they mean by...
"weighted with a generalized plant action
spectrum (UV-B,,, Caldwell, 1971), normalized at 300nm."
In conclusion, we don't have a clue except by trial and error lol. Generally the THC does go up as shown here and other places, but as far as determining what WV's and what intensities via this study is going to be difficult. If you are using 300nm LED, then I'd assume you could closely mimic the weighted intensities documented and realize similar results, though the intensities stated are not total UVB but rather weighted UVB and the fs-40 extends considerably more into lower WV UVB than a typical reptile bulb, so I'd imagine you'd want even more than stated in the study if using an arcadia ect.
Here's an overlay of the fs-40 (faded green) and an Acadia 12% (black)...
**
On a side note, I was trying to estimate UVI previously without digitizing the SPD, I've since found a free graph digitizer which could be implemented to back calculate a UVI from a total UVB measuremt in μW/cm2. It also means that you could calculate a UVI with a PPFD measuremt and the relative SPD of a source (if the PPFD meter picked up UVB radiation).
Graph digitizer...
if I play nice ..
pubs.rsc.org
