Sunlight and Temperatures: Finland versus Europe, part II

In the previous post the amount of sunlight in Finland was compared against some cities in Europe.

The sunlight itself is not enough for the plant to thrive. Combination of temperatures which stimulate photosynthetic ability and activity is what the tree makes grow. Also has to be kept in mind that the amount of sunlight shown in the previous post represents exactly that: amount of sunlight but not the light which is absorbed by the plant! The continuation tries to address that issue.


From the same site as earlier the average high temperatures are extracted being shown in the graph below:


The light blue thick line is Helsinki data. The high average temperatures are used because they represent the day temperatures, not the night ones when the trees metabolism slows down.

That together with previously documented graph of sunshine…

Sunny hours

… served as the basis for the next step.

The rate of photosynthesis

In order to asses the ability of the tree to grow it is necessary to estimate the trees photosynthesis rate which depends on the temperature.

The photosynthetic rate is extracted from the documented table. The simplified curve (triangular shape) was created for temperate coniferous trees with initial/boundary points as below:

Temperature Photosynthesis rate
-3 0
25 1
35 0

Multiplying photosynthetic rate (as a function of temperature) with the available sunlight amount makes the next graph:


The bell curve of Helsinki is very strong in summer, especially July with sudden drop in August and very low values for September.

It is also visible that too high temperatures are not favorable for the tree to grow. I consider the drops (very strong for Athens, less for other cities) as a clear sign of the summer dormancy. Does that itself defines it is another story but this is nearer the reality than the sunlight or temperature alone can show.

Annual growth

Comparing the curves form the latest graph is not simple. The simplest way is to create an integral on them to estimate the surface area which would represent the annual “growth ability” (the latest is purely my term :D).

Those values normalized around the Helsinki value (which now equals to 1) makes the data for the next graph showing the relative growth ability (there must be a better name but right now my brain is stuck with this!). Now the comparison is much simpler and it gives also more value than just “better” or “worse”.


Growth period extension

On all graphs above I included the line/bar with title “Helsinki (extended), Finland“. On line graphs it is the dashed light blue line which is mostly overlapping with the basic Helsinki curve.

The “extended” values are the same as basic Helsinki set of data except that the average high temperatures for March and April are increased by 5 degrees C. The idea was to compare the difference in other curves/comparisons if the spring would be more favorable and what I kept in mind was the greenhouse ability to keep the temperatures even just by 5 degrees above the normal ones (in average) over those 2 months.

The latest graph shows that Helsinki jumps to be in par with Berlin and right after the rest all way more south European cities. The rest of north and west was left behind.

Update: Growth period extension 2

After Janis comment I added the next step. “Extending” growth season even more for September and October by also 5 degrees C. The values are marked by “Helsinki (extended2), Finland”.

The results show that Helsinki jumped over Berlin, though not really coming much closer to Istanbul which is very much understandable.

Conclusion of mine

This is plain theory! Yes, yes and absolutely yes.

Do you need this calculation to know that warmer spring helps in growth?! No, of course not but in order to play with concrete values, to be able to compare them one to another some data manipulation is needed. Before this “research” I would not consider stating that growing a bonsai in Finland might be easier than in UK/Central Europe after figuring out how to avoid the winter dangers of course.

But now I can. It is just my statement but as such it suffices to me 🙂

Understanding the potential could lead to other implications on the way how to grow bonsai here in the north. Some are already mentioned in Janis blog and for sure will come more when practical actions/procedures prove them.

Also to be kept in mind is the following:

  • the used values are average per month over longer period of years
  • the “temperate trees” is very generic and should be considered as such

The data and all calculation is available here.

Sunlight: Finland versus Europe

Idea of my “research” was to compare the conditions to grow bonsai between Finland and the rest of Europe.

Potential of solar energy in Finland, the name tells it all.

2 pictures from the above title, giving reliable data:


Finish cities






Excerpt from above title:

The amount of solar energy is about the same in Finland as in Central Europe, but most of the radiation (1170 kWh/m² per year) is generated in the southern part of Finland during May to August. (VTT, 43, 2015) In Finland, there is more diffuse radiation than direct radiation. Diffuse radiation is more effecting, because in southern Finland half of the radiation is diffuse radiation. Diffuse radiation means that the sunlight has been scattered by molecules and particles at the atmosphere, but has still made it down to the surface of the earth. Solar irradiation is lower in northern Europe than in central or southern Europe. The average daily irradiation in Finland is about 900 kWh/m².

The same can be seen on the map of European solar irradiation. More data per country is also available.

Finland (south) is sunnier than Sweden/Norway, part of Be-Ne-Lux, UK and Ireland!

Average sunshine in Europe shows Helsinki compared to other cities, 1780 hours versus:

  • 1546 in Brussels/Belgium,
  • 1504 in Cologne/Germany
  • 1364 in Birmingham/UK

More accurate date per month to see when is the most light and how it compared with other months/cities can be done via solar calculator.

Not to loose the link to this interesting material:

The long days of a temperate-Arctic growing season provide an integrated fluence of photosynthetically active radiation (PAR, λ = 400–700 nm) similar to mid-latitudes (Jagels and Day 2004). Compared with mid-latitudes, however, the Arctic light regime provides irradiances below the photosynthetic saturation point of many tree species for a greater amount of time (higher proportion of “useful” radiation). In addition, irradiance in the Arctic lies for a greater proportion of time within the more linear portion of the photosynthetic light response curve, where photosynthetic efficiency (mol CO2 fixed per mol incident quanta) is maximized.


Graph of the sun light per city during the year shows the relation between the cities (Thanks Jani!):

Sunny hours

It is easilly visible that south of Finland is not at all having low level of sun light. All UK cities (from the available statistics) are below. It does show slightly narrower bell curve than some other cities but all of them are way more south.

My 5 cents
  • The lack of sun is not an excuse for not growing bonsai or to complain of slow/insufficient growth.
  • The slightly longer autumn is actually even better for plants to prepare for overwintering.
  • I have not noticed summer dormancy in my trees. They grow all the time during the summer. Maybe the speed slows down but to me not noticeably.

What does create difficulties over here is the severe winter. Nevertheless, with correct tools/structures that can be overcome. Any garden suffices, balconies are slightly bigger problem but not at all impossible!

So, only I can say is, take your tools and take the challenge 😀

Next: Relating monthly temperatures with the sun light.

Soil and fungus

Below is the set of documents I have found while investigating here and there relation between:

Temperature (in North European cold climate) ⇒ Fertilizer and soil type

Why that came to my mind was an interview with Walter Pall where he talks about fertilizers and bacterias being efficient only above 12 degrees C (at 05:40). The summers here are very mild and way too many nights drop below 12C. Having pots soil temperature drop so much would mean or:

  • using artificial fertilizer only (where nourishment is already available to the plant to be absorbed)
  • find another way to improve decomposition on lower temperatures

So here is what I found. Half of it I didn’t understand 😀 but it does gave me the direction on what to try. This will serve more as a memo for myself when I forget about all these facts…in case I am interested again to find them. And it was fun looking for these things 🙂


I started by asking myself a question:

Q: What is the relation between soil temperature and tree growth/survival?

The document getting my attention was:

Seasonal Changes in Soil Temperature and in the Frost Hardiness of Scots pine Roots under Subarctic Conditions: Comparison with Soil Temperature and Snow-Cover under Different Simulated Winter Conditions

I consider “mineral soil” in below sentences being bonsai soil.

During most of the sampling time, the frost hardiness of the roots in the humus layer was greater than in the mineral soil. There was a clear relationship between the soil temperature and the frost hardiness of roots. The temperature in the humus layer was after late August continuously lower than in the mineral soil. The results obtained in this study indicate that cold acclimation of the roots is much slower than that of the shoots. The needles survived temperatures of -20 °C even though they had not experienced air temperatures of below 5 °C. Roots attained a similar frost hardiness level only after experiencing temperatures of 0 °C or below for a period lasting many weeks.
This suggests that during winter with exceptionally fast decrease in soil temperature the roots of Scots pine may be damaged.

Some kind of conclusion/answer I extracted from this is:

A: Trees should get milder frosts before the full winter hits for several weeks before full winter hardiness for roots is obtained

Nothing new.

Tony Tickle mentions it, also in Nigel Saunders video is similar information. I am sure more of the same can be found on internet.

In case I ever wonder what is relation between temperature and soil depth in these areas here it is: Annual variation of soil temperature at different depths

Next question:

Q: Is there/What is the difference between Forest/Organic and Agricultural/Mineral soil?

I consider “agricultural/arable soil” here being bonsai soil, in need of constant fertilizing.

Properties of humus of natural forest soil and arable soil

The content of organic carbon in agriculturally used soil was 68.8% lower, as compared with the average content of total organic carbon in the layers from 0 to 30 cm of the forest soil. Arable soil also demonstrated a definitely lower content of nitrogen than the forest soil. In forests soils a constant supply of fresh organic matter (quantitatively higher than in arable soils) significantly modifies properties of humic acids. In arable soils oxidization processes are more intensive than
in forest soils.


Organic matter, Humus, Humate, Humic Acid, Fulvic Acid and Humin: Their importance in soil fertility and plant health
A fertile soil should contain from 2-8% organic matter, most soils contain less than 2%. Humus is the major soil organic matter component, making up 65% to 75% of the total. The availability of trace minerals is a requirement for the formation of humic substance. Some of the main functions of humins within the soil are to improve the soil’s water holding capacity, to improve soil structure, to maintain soil stability, to function as an cation exchange system, and to generally improve soil fertility.

Because of the relatively small size of fulvic acid (FA) molecules they can readily enter plant roots, stems, and leaves. As they enter these plant parts they carry trace minerals from plant surfaces into plant tissues. Fulvic acids (FAs) are key ingredients of high quality foliar fertilizers. Foliar spray applications containing fulvic acid (FA) mineral chelates, at specific plant growth stages, can be used as a primary production technique for maximizing the plants productive capacity.

Many of the organic compounds released by fungi aid in forming humus and soil crumbs. When Humic acids (HAs) and fulvic acids (FAs) are applied to plant leaves the chlorophyll content of those leaves increases. As the chlorophyll concentration increases there is a correlated increase in the uptake of oxygen. Chlorophyll development within plant leaves is more pronounced when fulvic adds (FAs) are present in the foliar fertilizer.

Well, this gave me lots of data with which I can hardly do anything 😀 Nothing new again. No breakthrough though none of it I expected either.

Fungi does appear as the agent for soil conditioning.

Coming back to the original questions version:

Q: What is relation between decomposition and soil temperature?

Comparison of temperature effects on soil respiration and bacterial and fungal growth rates

Soil bacterial and fungal growth rates in cold climates usually have optimum temperatures below 30 °C, with activity values decreasing at higher temperatures.

Fungi as a group are more adapted to low soil moisture conditions than bacteria and would therefore be more important in dry soil.
Persson et al.[18] found a difference in temperature dependence of respiration in a forest and an agricultural soil, in that a lower minimum temperature for respiration (tmin) was found in the former soil. One proposed explanation is that fungi are more important in the forest soil and are more active at low temperatures than bacteria [18–21].
One was an agricultural soil with a dry weight of 88% of the wet weight, a pH of 7.8 and an organic matter content of 5%. The other was a humus soil (the A01/A02 horizon) from a forest with mainly spruce, with a dry weight of 29% of the wet weight, a pH of 4.1 and an organic matter content of 82%. A temperature of 45 °C was not included in the fungal activity measurements, since it was assumed to be too high a temperature for fungal activity. The respiration rate increased with increasing temperature over the whole temperature range in the agricultural soil (Fig. 1(a)) and up to 40 °C in the humus soil.

The calculated apparent minimum temperature for bacterial growth (tmin) was −8.4 °C for the bacterial community from the agricultural soil and −12.1 °C for that from the humus soil.
The calculated apparent minimum temperature for fungal activity (tmin) was estimated to be −12.3 and −17.5 °C for the fungal community from the agricultural and humus soil, respectively.

The temperature dependence of fungal and bacterial growth differed in that the former group was less inhibited by low temperatures and the latter less inhibited by higher temperatures

The advantage of fungi at low temperatures is in accordance with the finding that fungi dominated in high-altitude soils during winter and spring, when the soil was covered with snow, whereas bacteria appeared to dominate during summer under snow-free conditions [20,21,26].

The advantage of fungi at low temperatures may also explain the high amounts of fungal biomass found in forest soils during cold periods.

Graph shows that below 12C in Humus soil fungis are more active

Aaha! 12 degrees C again mentioned for bacterias. But now the new player appearing even clearer: fungi.

A: Fungi is better decomposing agent than bacterias in colder climates! In lower temperatures, fungi operates better in humus/organic soil than agricultural soil.

Organic soil + fungi looks to be a new direction.

A simpler document about bacteria vs. fungi: Fungi vs. bacteria

Q: What kind of fungi, what are main characteristics and roles?


Overall, the relationship between plants and mycorrhizal fungi depend mainly on the availability of nitrogen, phosphorus, carbon, and water (1). Since areas within the environment vary in nutrient and water availability, this can have a major effect on whether or not a mycorrhizal relationship can form between a plant and the fungus.

If an environment’s soil does not contain much nitrogen and phosphorus, it is likely that a mycorrhizal relationship will occur and a plant is more likely to allocate its carbon to the roots (4). This is because the plant needs nitrogen and phosphorus in order to prosper. This can also be true in areas where water is not easily accessible. As noted earlier, mycorrhizae expand the surface area of roots and therefore aid in the uptake of water. If an environment is lacking in moisture available to plants, it is likely that a mycorrhizal symbiosis will occur to aid in the uptake of water. Also, the environment where mycorrhizae will be found change depending on the type of mycorrhizae.

Mycorrhizal Fungi in Hydroponics – Questions and Answers

Should I feed mycorrhizae carbs? (e.g. molasses?)

Molasses and other carbs are good for feeding bacteria and other types of fungi. But you don’t need to feed the mycorrhizae. The plant feeds them! You are better off adding products which contain humic acids (organic growers can use high quality organic inputs such as North Atlantic sea kelp) to promote more root exudates (food for the mycorrhizae).

Q: How to attract/activate more fungi in the soil?

Interactions between needles of Pinus resinosa and ectomycorrhizal fungi

In comparison with mineral soil, forest litter contains large concentrations of leachable organic compounds with potentially strong effects on mycorrhizal fungi.

The pine needles increased density of all species of mycorrhizal fungi used in experiments. We used a needle concentration of 0.5% in the first experiment, resulting in a total watersoluble phenolic concentration of approx. 126 µg tannic acid equivalents g−” solution. The concentration we used seems to be relevant, as it lies between the concentrations provided by fresh litter and humus.

The experiments of this study were performed in the absence of saprotrophic fungi and bacteria. Bending & Read (1996, 1997) have shown that, whereas many ectomycorrhizal fungi have difficulty in hydrolysing polyphenolic molecules, some saprotrophic fungi have none. Thus, the presence of saprotrophs in the forest floor might have a strong influence on the interaction between mycorrhizal fungi and litter. 

Succession of fungi and fauna during decomposition of needles in a small area of Scots pine litter

When the fine root system of pine developed through accumulated old needles (F1 layer), mycorrhizal fungi penetrated the needles and seemed to impede any further bacterial development.

Faunal activity led to the presence of holes in all pine needles in the F1 layer, thus allowing the dominant fungi to enter the pine material.

Colonization of decomposing Sphagnum moss litter by mycorrhizal roots in two types of peatland ecosystems

Some mycorrhizal fungi were shown also to possess the capability to degrade more complicated and resistant molecules present in plant cuticle or secondary cell walls, and this occurred owing to the secretion of e.g. esterases, polygalacturonases, xylanases, cellulases, thyrosinases, peroxidases, poly- and monophenol oxidases, laccases, and even ligninases. Thus, the saprotrophic role of ectomycorrhizal fungi in ecosystems is also recently considered.

The chemical composition of needle and leaf litter from Scots pine, Norway spruce and white birch in Scandinavian forests

Concerning organic chemical components, the spruce needle litter had significantly higher concentrations of lignin and mannan than all the other litters and lower levels of ethanol-soluble substances, cellulose and galactan than the pine needle litter. Further, it had lower concentrations of water solubles, rhamnan and xylan than the birch litter.

A: Pine needles/Sphagnum moss to be incorporated into the soil.

Sphagnum moss is also favored by Colin Lewis. No bark, no leafs, no coconut fibers. Just sphagnum moss. Those and pine needles can be found in any sqaure meter of Finish forest! 🙂 Back to the basics. The best solution usually IS in front of your nose 😀

Some more documents on different aspects on what fungi needs in the soil to operate:

Root Fungus Stores a Surprising Amount of the Carbon Sequestered in Soil: Unlike bacterias who needs more nitrogen fungi needs more carbon to grow and function.

FertilizerInorganic fertilizers exclude carbon-containing materials except ureas.

This would mean that by using inorganic fertilizers fungi has nothing to eat. So, if fungi is to be encouraged inorganic fertilizer is not a correct choice or at least not sufficient.

Plant Structure & Function: What plant parts contain celulose/lignin which is important for saprotrophic fungi to digest.

Q: What is relation of saprotrophic and mycorrhizal fungi, do I need both?

Mycorrhizal and saprotrophic fungal guilds compete for the same organic substrates but affect decomposition differently

Through competitive interactions, mycorrhizal fungi can thus indirectly regulate litter decomposition rates by restraining activities of more efficient litter saprotrophs.

What I understood is that:

A: Saprotrophic produce nourishment by decomposing organic material to be absorbed by mycorrhizal and plant.

Both needed.


Cold climate of Northern Europe

⇒ Low temperature

⇒ Fungi

⇒ Organic soil components (as addition/conditioner to mineral soil)

Pine needles & Sphagnum moss


I am very happy with the investigation. Did it ring the new bells, found extremely new information, not logical or not expected? No! These are already used by others. What I did not know nor found directly related is colder climate vs. soil components through “activating” fungi as the main decomposer.

Some care must be taken considering acidity of soil when these are added. Needles in different stage of decomposition might be a good idea. I got PH testing paper strips so I can get some idea how it works before I put the first victim into it.

Is pine needles/sphagnum moss necessary? I am positive Kaizen Bonsai’s detailed information is really truth that it is better to add just humus via specific soil additions than play with degradable organic compounds. I don’t think anyway pine needles/sphagnum moss combination should be the only source of nourishment to be used. I plan to use Tibolar RS with which I have some results already but about that will produce another post sometimes.

But I think for experienced grower it is easy to estimate the moment and amount of special fertilizer/soil conditioner/humus for trees to make thrive. For a beginner like me I somehow believe it is not that simple and that plain mineral soil will too easily leave the plant with zero nourishment if not enough given. Also, most of my trees are not fully established ⇒ more organic material in soil could help…perhaps…maybe 🙂

Indoor Bonsai Light Calculator – Derivation


The following page is dedicated to deriving the equation summing the light energy a tree receives from the sun. The results of this equation and its calculations is shown in another page and without explanation from there this part is not going to be clear.

If you notice anything incorrect, derived wrong, typo, assumption wrong or anything not really correct in your opinion please do comment the page and point me to the mistake which I need to correct. It is not intended to provide wrong info/calculation but rather involve into finding new data/info to help simplify light demand calculations.


For the beginning it is important to “set the stage”, conditions under which the derivation is performed:

  • The tree is an indoor type = tropical specie = sun shines12h/day
  • It “will be” a fully sunny day with no clouds 🙂
  • There is no object throwing a shadow on any part of the tree = the tree stands “alone” in the field, no forest grouping or similar
  • The tree foliage is approximated by a half ball
  • The diameter of the tree foliage ball equals the trees height
The approximation by the ball is chosen in order to simplify mathematics in here 🙂 I am sure similar derivation and results can be produced by another type, perhaps even better approximation and maybe easier than this one.

More details to remember coming out of this approximation are:
  • Leaves cover all spaces of the half ball, there are no holes through which the sun goes through not reaching chlorophyll.
  • No leaf is shadowing another one below it. If it would the numbers wouldn’t change much but mathematics would get just too complex.
  • The leaf surface is tangential to the surface of the ball, perpendicular to the ball radius vector.
  • The set of leaves can be considered one bigger leaf whose surface vector is the sum of vectors of all leaves in the group.
  • Considering the sun is moving east-west, the north-south axis of the ball is irrelevant for the calculation. The effective length of the balls surface will equal to H, not 2r*pi/2 (half of balls circumference) and the surface vector in north-south directions are irrelevant.
  • The angle of sun movement, 0 to pi,  equals to 12h of the day length.
  • The suns movement is uniform across the sky and its effect in the first 6h (0, pi/2) will be the same as the last 6h (pi/2, pi).
  • The height of the tree is irrelevant What is relevant is the width/height of the trees green foliage, the half ball in this case, and as such its width (H) and height (H/2) are of the most importance. When comparing it to a realistic one those dimensions should be compared/related.


The next diagram should serve as the graphics to the equations derived below:



Total light energy

The total light energy, luminous energy [lum*second], the tree receives is:

Q_{total} = Q_{sun} + Q_{shade}

In other words it is:

  • direct light, light received from the sun shone directly onto the foliage +
  • diffuse light, light received in shade condition when the tree shades itself from the sun.

Example, when the sun shines in the morning from the east, the west side of the tree is in shadow but under diffuse light of the day.


Direct light

The light received directly from the sun depends on:

  • the light strength, Ev illuminance, [lx].
  • surface (S) the light is thrown upon, [m2].
  • surface vector towards the light vector.
  • period of time [seconds] (due to seconds being too small unit for our purposes time will be handled in hours).

Q_{sun} = E_{v} * S * sin\gamma * \Delta t

S, surface of the section of the ball being under direct light is derived from the balls width (north-south) and its depth/height:

S = H * dx

x – east-west depth of the surface, is derived from the foliage ball integration angle (alpha):

dx = \frac{H}{2} * d\alpha

Surface then becomes:

S = \frac{H^{2}}{2} * d\alpha

Time period the sun shines can also be represented as another integration angle, the sun movement angle (beta):

\frac{\Delta t}{\Delta \beta} = \frac{12}{\pi}

12 here represents 12h of sunshine.

dt = \frac{12}{\pi}d\beta

Angle between sun and surface of the balls section can also be represented via the ball angle and the sun movement angle:

\gamma\ = \frac{\pi}{2} - \alpha + \beta

The full formula for direct light becomes:

Q_{sun} = E_{v}\frac{H^{2}}{\pi}12 \int \int cos(\alpha-\beta)d\alpha d\beta

The 12h time while the sun shines can be divided into 2*6h where each 6h section is described by the same formula. The result of integration over 6h of sunshine (beta = [0,pi/2]) can be therefore multiplied by 2 to receive the same amount for the whole day.

The 6h sunny part of the day is then integrated over 2 angles:

\beta = [0,\frac{\pi}{2}], \alpha = [0,\beta+\frac{\pi}{2}]

The starting angle of the tree foliage ball under the sun starts from 0 (for the first 6h of the day it is always under the sun) and it ends on sun position + 90 degrees (pi/2) as the half of the ball is always under the sun, and always a different part of it.

The integration goes on:

\int_{0}^{\frac{\pi}{2}} \int_{0}^{\beta+\frac{\pi}{2}} cos(\alpha-\beta)d\alpha d\beta =

\int_{0}^{\frac{\pi}{2}} [-sin(\beta-\beta+\frac{\pi}{2}) + sin\beta] = \int_{0}^{\frac{\pi}{2}}(1+sin\beta)d\beta =

= [\beta + cos\beta], \beta=[0,\frac{\pi}{2}] =

= \frac{\pi}{2} + 1

The final result ends to be:

Q_{sun}=\frac{12}{\pi}*(\frac{\pi}{2} + 1)*E_{v}*H^{2} =


defining the amount of light the surface of the approximate tree foliage of height H receives during the 12h of day without any obstruction on the horizon nor shade applied by any object near the tree (see the conditions listed above).

Diffuse light

If the sun doesn’t shine directly on a leaf of the tree, the leaf being in shadow of the tree itself, it still receives the diffuse light from the sky.
The typical direct sun light strength is 100.000 lx. To simplify the calculation for the foliage part in shadow it is assumed that the direct sun strength is 80.000 and that every dot of the tree foliage ball receives the diffuse light all the time, 20.000 lx. For the leaves under the sun the light amount would sum up coming to 100.000 lx (80k+20k) while the leaves not under the direct sun at that very moment would receive light at levels of 20.000 lx.

The simplified calculation of the light energy the tree foliage ball receives during the 12h day is:


Q_{0} = E_{0}\frac{4r^{2}\pi}{2}12 = E_{0}\frac{4H^{2}\pi}{8}12 =6\pi*E_{0}*H^{2}=

defining the light energy the whole tree foliage ball receives from diffuse light during the 12h day with the sky not being obstructed by any object near by the tree.

Special cases

Light from imaginary-all-around-fully-shining sun

The sun light energy the tree foliage would receive in imaginary situation if the sun would be all around the tree, not moving but shining on every dot on the tree perpendicular to the leaf surfaces and shining all 12h constantly with the brightest strength (100.000 lux) would be:

Q_{max} = \frac{4r^{2}\pi}{2} *E_{v}*12 = 6\pi*E_{v}*H^{2}

This is derived for theoretical comparison what value it would be IF such condition would apply. This formula has no practical value in nature.
As mentioned, all leaves surfaces are perpendicular to the “sun” light vector making the cosine of that angle (90 degree) become 1 and therefore irrelevant in the calculation.

Light received by the upper half of the tree foliage ball

The next lines in a similar fashion derive formula showing amount of light the upper half part of tree foliage receives during the 12h sunny day:
Q_{s} = E_{v}*H*\frac{\sqrt{3}}{2}\frac{H}{2}\frac{12}{\pi}*\int \int cos(\alpha-\beta)d\alpha d\beta
which should be integrated in 2 ranges:
\alpha = [\frac{\pi}{6},\beta+\frac{\pi}{2}], \beta=[0,\frac{\pi}{3}]
making the light energy be:
Q_{1} = \frac{3\sqrt{3}}{\pi} * E_{v} * H^{2} * \frac{\pi}{3}
\alpha = [\frac{\pi}{6},\frac{5\pi}{6}], \beta=[\frac{\pi}{3},\frac{\pi}{2}]
making the light energy for that period:
Q_{2} = \frac{3\sqrt{3}}{\pi} * E_{v} * H^{2} * \frac{\sqrt{3}}{2}
After summing those 2 periods and multiplication by 2 due to the period repetition (2 times 6h of the same conditions) the end result looks like:

Q_{s} = 2 * \frac{3\sqrt{3}}{\pi} * E_{v} * H^{2} * (\frac{\pi}{3}+\frac{\sqrt{3}}{2})

Q_{s} = 6.33 * E_{v} * H^{2}

If you followed so far hopefully you have something to comment 🙂Huh, this is the end 😛

Back to all posts about indoor shelf

Indoor Bonsai Light Calculator

Basis for the graphics from:

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.


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,

[lumen * h]
Luminous energy,
[lumen * h]
Fictive constant illuminance
Cloudy day
100000 = Ev
Trees upper
half only


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.

I focused on the LED spot lights as they showed to be able to provide enough light energy and possibility to focus that light to the right parts of the tree. The lumen amounts though are valid for any type of light sources. Only the very lowest row of the table 2 is LED spot light dependent.

It is considered that if the table shows X LED spot lights that means that the light power is distributed over the tree uniformly. In practice it is very difficult to succeed in that. Some light will overlap and produce the peak on that spot, some light will not hit the tree foliage which is therefore lost. All of that would mean that careful consideration has to be done when distributing the light to be applied to the tree.



power [lumen]
Nr of LED spot lights

Table 2.


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.


  • 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.

The tree likes it. It grew with even 2 spot lights last year but continues much better under 5.
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