# light wattage vs tank depth (or: musings of a lunatic)



## Tyrone Genade (Jan 1, 2005)

Hello,

Before I continue I would like to quote a very wise man:



> It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
> 
> Richard P. Feynman


I am, if you might not have guessed, an experimentalist.

This is a table comparing input wattage (i.e. how many watts of light you have over your tank) to the PAR at a particular depth.










Here is the math: PAR @ depth = [(1.1 x 0.8 x reflector-efficiency) x total-watts] x e[sup](2.33 x depth-in-m)[/sup]. Several assumptions were made.

I decided on a conversion factor of 1.0 for tube wattage to PAR based on the data at http://www.aquabotanic.com/lightcompare.htm. This value has an error of +/- 0.2. I have assumed 75% reflector efficiency and that about 80% of this light actually enters the tank. This reflector efficiency was arbitrarily chosen based on Cor's calculations which debunk the 95% efficiency claims and that 50% efficiency is probably too low when you have a good reflector. If you have no reflector and the tube is about 15 cm above the tank which is 30 to 45 cm wide you need to multiply the input wattage by between 3 and 4... Which means you need about 180 W/m2 over a 3 foot tank to grow most plants well. This translates to 50 W.

The attenuation coefficient* was derived from four sources: Paddy Water Environ (2010) 8:267-275 for data on a reservoir in Taiwan; Wetlands Ecol Manage (2007) 15:509-519 for the shallows of Lake Victoria; Hydrobiologia *522: *301-310, 2004 for a reservoir in Venezuela; and the data of Tom Barr at http://www.barrreport.com/showthrea...ice-low-PAr-values-who-knew?p=32330#post32330. My value (2.24 +/- 0.77) is an average of these values. I decided on lake values in tropical climates to compensate for the angle of the sun at temperate latitudes (which result in not only lower input PAR but also a bias for certain facets of the spectrum---think red sunset/sunrise when the sun is low) and because a large lake better represents our small fishtanks with regular water changes when it comes to the accumulation of organic compounds which absorb light as it travels through the water. I chose to vary depth in increments of 5 cm as this was good enough. I didn't go much beyond 400 PAR starting input as we then begin to talk about ridiculous wattages over the tank and 400 PAR is already considered to be high.

Here is the data graphically represented:










How did I arrive at low and high PAR values for various plants? There is a table at http://amania.110mb.com/Chapters/Tech/light-par.html which gives PAR values for various plants. The highest minimum value is 63 for Myriophyllum and the lowest minimum is 11 for Microsorium. Most of the "easy" plants are in the 20-30 PAR range. Very little hard data is available in this regard. http://202.39.251.199/encyclopaedia/plantShow gives lux values which do not correlate with the data on the Russian site.

This is a very simplistic model and I am not looking to make things complicated. The more complications the more assumptions the greater the chance of stuffing up. We have data that there is a drop in light intensity with depth and we have data that we need about 30-40 PAR at the bottom of the tank to grow plants. How much power do we need over the tank? Plants are pretty adaptable, all we need is a good guess.

So how reliable is my theory (i.e. guess)? At http://www.barrreport.com/showthrea...Aqua-Forest-and-nice-low-PAr-values-who-knew? we have Tom Barr reporting a drop in uE/m2/s from 150 to 30-40 uE/m2/s (this is the ONLY hard data I could find for aquariums for comparison). He insists that he measured at several points in the fishtank and this is the range of the values he obtained. Various other objections were raised in the thread and debunked. I guessed the tank he showed to be between 50 and 45 cm deep. My values in this depth range is 40-50 uE so my attenuation coefficient is too low for this tank. For the other data, my coefficient is too high (I calculate 1.24 with the data). What is required is more data from freshwater aquariums which is the *purpose of this thread*. I need people with PAR meters or lumenometers to use them, measure the PAR or Lumen values at various depths in their tanks and post the data here so a better estimate of aquarium light attenuation can be calculated.

Data which is sorely need is data on reflector efficiency and just how much of the light beamed down from the lights actually enters the aquarium. How much is lost between the source/reflector and the water? For this we need to know how much light there is just above the water's surface and just below it. From Cor's math one should be able to calculate the efficiency of your reflector, but this always going to be ball-park figure regardless as everyone's setup is going to be different (which is why I simply chose 75% reflector efficiency/light loss to start with---real measures may prove my guess very generous). What is also needed is data from tanks with tubes over them and tanks with spot-lights so see how the distribution of the light effects attenuation readings: is there a more even distribution with tubes, i.e. is the drop in PAR observed by Tom the product of the inverse square law or real water attenuation of the light? The reflectivity of water, diffusion with distance from the light source and reflector efficiency could probably be collapsed into a best guess general fudge factor. As I have mentioned, data is sorely lacking.

I am aware of http://www.advancedaquarist.com/2005/8/aafeature and my problem with it is "Figure 8 shows the light attenuation at depths equal to 2 ft of aquarium water, *assuming* the Kd values for the ocean water." In discussion I encounter one assumption upon another upon another... I am aware of the theory, and the data does not agree with it (i.e. the data says there is significant attenuation). Who is right, who is wrong? If you want to dispute the theory, bring data! I am happy to change the theory to suit the data, or dismiss it all together. But I am fed-up with the arm-chair experts who theorize ad infinitum without actually going out and taking measurements to test their assertions. In our musings on APSA one thing became glaringly obvious: there is a plethora of expert opinions based on extrapolated theory and a paucity of experimental observations. I'm hoping we can change that.

I expect that the data will show that the attenuation factor is closer to 1 than 2. Please supply at least 6 data points and indicate when last the water was changed as this will effect the light absorbing polyphenol concentrations. If you use activated carbon please say so. Some idea of how how many watts of light and the dimensions of your tank will also be useful when it comes to disproving my theory. (I entertain no illusion that I am correctly representing nature.)

I look forward to your input.

*In reality I mean a general fudge factor for how light intensity diminishes with water depth. I am aware there is more going on than light simply traveling along a straight line through water.


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## f1ea (Jul 7, 2009)

Nice start... to an interesting subject. Thanks for taking the time to bring forward your ideas...

I have a couple questions:

1) Which type of tube are you considering for your Watt values? T8, T5, CF, MH ?
2) Are the PAR values in your Total Watt vs. depth table measured/experimental; or did you obtain them from your formulas and assumptions??


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## Tyrone Genade (Jan 1, 2005)

Hello,

Sorry for the delayed reply. I was planning on a Cool Daylight T8 though it and the equivalent T5 and CF don't have much difference when it comes to PAR/W efficiency. This was also the most efficient T8 tube for which we could get data. MH are more efficiency.

Sadly, I see no one has bothered to supply some numbers to further the inquiry.


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## wet (Nov 24, 2008)

This is awesome work though, Tyrone. I do not have a PAR meter and cannot contribute, but I have wanted to build a calculator for this type of project for some time. I hope members with PAR meters read this thread.

For what it's worth, there are a group of guys on barrreport.com sharing Gerryd's PAR meter. Most prefer to limit light but there's at least a few guys who leave bulbs off and should be able to get you more data points on request.

Your graph:










The amania.110mb.com folks's table is interesting, and I am aware those folks have done great CO2 documents, but I find the idea of minimum thresholds of light by genus unlikely. I have a hard time believing that, say, Ludwigia repens requires ~25% more light than Rotala rotundifolia, for example, and think you could grow either under "low light" provided nutrients (including C) are good. Perhaps I just need to think of the data as "Epiphytic" "Rosette" "Stem" and so on.


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## JERP (Feb 4, 2003)

Well let me supplement your copious amount of data with a some anecdotal evidence 

I've had tall aquariums for 15 years or so now. My experience is that a taller tank does not need more lighting in a healthy tank. I've had beautiful sod lawns of lileopsis and microswords in a 24" high tank (~3" gravel bed in foreground).

Where I run into problems is when the tank isn't healthy. If the tank is even slightly cloudy, the low foreground plants and the more feeble stem plants dissolve almost instantly.

My point is that water clarity is a very important, and possibly the dominant factor, in measuring light penetration at depth and must be considered for any practical consideration and application of light wattage vs depth experiments.

good luck, this is good work you are doing.


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## joshvito (Apr 6, 2009)

here is an interesting post along the same line of thought
http://www.plantedtank.net/forums/lighting/105774-par-vs-distance-t5-t12-pc-2.html#post1093075


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