Basis for the graphics from: http://www.tumbex.com/tumblr/judazacubonsai/post/142870388296

One of the demands and difficult tasks for indoor bonsai growing is that tree needs enough light in order to develop. When having the tree inside the word “enough” usually refers to “provide as much as you can”. In the most if not all cases it is really true. It is very difficult, if even possible, to provide too much light and yet live in the same rooms together with the trees 😀


Nevertheless, I questioned myself often what is “enough” and how “good” light conditions my trees have inside.


Before jumping into conclusions and start just assuming 100k lx all around the tree would fulfill the requirements I tried to calculate how much light a tree receives from the sun during one day in nature. The calculation and derivation of the equations can be found here. As mentioned in that page if the reader notices a mistake in derivations/approximations/assumptions please do comment the page. Actually, comment the page in any case if you like 🙂 Any feedback is better than no feedback. It was not intended to over-engineer the subject, which perhaps I managed exactly doing that, but to think a little bit how some values are related around light in general.


I wanted to have an equation which shows me approximate light energy the tree receives during the day as a function of the tree height. With that approach it would be easy to estimate the quality of light conditions a specific tree grows in.

Results

The table 1 shows the derived equation dependent on tree height (H) and all other parameters already given under conditions mentioned under the link above. The table also contains the equations derived for 2 special cases. All explained in the link above.
The last column (fictive constant illuminance) contains lux values if the sun light would be constant the whole length of the day (12h) and perpendicular at each bit of the surface. The values help to compare an already existing indoor lighting or location for indoor bonsai growing by measuring it with a light-meter.

Light type	Luminous energy, f(E,H) [lumen * h]	Luminous energy, f(H) [lumen * h]	Luminous power [lumen]	Fictive constant illuminance [lx]
Direct	9.82∗Ev∗H2	785600*H2	65466*H2	41898
Diffuse	18.84∗E0∗H2	376800*H2	31400*H2	20096
Total	(9.82*Ev+18.84*E0)*H2	1162400*H2	96866*H2	61994
Cloudy day	18.84∗Ec∗H2	37680*H2	3140*H2	2009
All-around-sun	18.84∗Ev∗H2	1884000*H2	157000*H2	100000 = Ev
Trees upper half only	6.33∗Ev∗H2	633000*H2	52750*H2	33760

 

Table 1.

The table 2 is focused in estimating how many LED spot lights are enough to provide the same amount of luminous energy as received by the sun during the day under conditions mentioned in the link above, a perfect sunny day.

Conclusion

So, what’s the big deal in these equations/results?


Below are listed several of conclusions I see out of these numbers:

• 30% of light energy the tree receives on a sunny day comes from the diffuse light.

• The upper half of the trees foliage receives half of the light energy…sounds logical?! Keep in mind that the surface of the upper part of the tree under conditions mentioned in the above link is 4 times smaller than the lower part!
• 100k lx applied to the whole tree all around its foliage gives almost 2x the maximum light energy the tree gets in the nature from the sun. If the tree is being under lights for longer than 12h then the received light energy gets even higher. 

The values in the tables are maximum values of light energy the tree can receive in nature! The conditions listed in the link above consider the tree standing alone on the field with no object throwing a shadow and the sky is perfectly clear. More than this the tree can not receive in the nature!

If one starts replicating the values of luminous energy found in the table above consider that those values are going to apply daily in your bonsai shelf/set or wherever the tree is located. The tree in nature does have some days without the maximum luminous energy. The tree under artificial lights does not.

Some trees might be able to extract more out of more light they receive, speeding up their development, some perhaps not. I do not have enough competence to validate more on this issue but it should be logical that some species perhaps even suffer under the max light conditions, 12h a day, every single day.

The tables allow one to compare the light levels their trees receive under the present conditions and evaluate if that is enough and how “enough” that is. Providing light for a longer period of time might in some cases be enough and these equations could help in figuring out is it so.

Example

• Tree = 20cm, ficus microcarpa
• 5x LED spot lights (400lm) = 2000 lm
• lights are ON for 15h a day

• Luminous energy it receives is: 2000lm * 15h = 30k lumen hours
• or 2500 lumen during 12h of a day
• or 6 LED spot lights minimum

2500 is less than 3874 lumens from table 1 but 3874 is the maximum number a tree can receive in nature on a perfectly sunny day. The ficus is such to be able to survive with very low levels of light. That would perhaps give me a hint the tree is accustomed to being in a group or inside the darker forest, or under bigger trees shading it. If that all is true I consider 64% (100* 2500/3874 ), or 50% with some losses in light distribution, of max luminous energy to be received every day to be enough.