Almost all consumer lamps are now labelled with watts consumption and
lumens output. For humans, lumens per watt is a good measure of the efficiency
of a lamp in meeting human ability to see, because it is based on the relative
sensitivity of our eyes (the red curve at right).
Plants respond very differently to light than humans do. The green curve shows the relative effectiveness of light in producing plant growth. The black curve shows a common definition of plant growth effectiveness used by the lighting industry - as you can see, it matches the needs of plants only a little better than lumens do.
Plants respond to wavelengths other than the green curve for non-growth functions such as flowering initiation, just as humans respond to wavelengths other than the red curve for non-visual needs, such as the production of Vitamin D. However, fresh-water aquarists mostly aim for plant growth.
What we aquatic plant growers need is a true plant-growth lumen (PGL). Here is how to calculate one.
First, obtain the spectrum of the lamp output (you'll have to get it from lighting engineers at the manufacturer; you won't find it on the package or in stores), and its lumen rating. If the spectrum is supplied in energy units such as watts (most are), you must convert it to a photon scale by multiplying each intensity by its wavelength.
Then, using the table below, multiply each spectral value of the lamp by the matching spectral factor for plants. For example, multiply the lamp intensity at 450 nm by 0.213 The result will be the spectrum of the lamp as a plant sees it. Add up all the numbers and call the result P (for Plant).
Next, multiply the lamp spectrum by the matching spectral factors for lumens. The result will be the spectrum of the lamp as a human sees it. Again, add up all the numbers, call it L (for Lumens).
Finally, multiply the lamp lumens by P and divide by L to get the PGL.
Here is an example: a 60 W incandescent lamp, whose output is shown in the black curve of graph 2 at right. The lamp output is 855 lm. Following the above procedure, the red curve is the way a human sees the light, the green, the way a plant sees it. The ratio of P to L is 1.26, so it produces 855 x 1.26 = 1077 PGL.
If the spectral data is not in 10 nm bands, or covers less range than 350-750 nm, this method will still work as long as the data is uniformly spaced over its range. Simply use the nearest values in the table below, the same ones for both P and L. Since the method only calculates a ratio between human and plant lumens, the units of lamp spectral intensity don't matter, as long as they are in photons, not energy.
The result of such analyses is clear: very few 'plant growth' or 'aquarium' lamps outperform cheap standard-spectrum fluorescent tubes or compact fluorescent lamps for growing aquarium plants.
Graph 3 at right shows why. Three lamps are shown, with their output in relative photons per second in 10 nm bands. The black curve is a standard warm-white tube, the others two different plant-growth lamps. The extended spectrum of most plant-growth lamps is obtained at the expense of total output. And, the tiny production volume of the specialist lamps compared to standard warm-white makes them much more expensive.
'White' Light-Emitting Diode (LED) lamps designed to replace incandescents are mostly based (2015) on a 460 nm blue LED combined with a yellow phosphor; a typical spectrum is shown as graph 4. Phosphors are still being developed for this role, and blue LEDs are under active development to improve efficiency at high power; also some manufacturers combine more than one LED type or add filter layers to improve the colour-rendering index. Expect rapid changes until the technology settles down.
The new COB-LED arrays change everything for specialist applications. Chips are available with native light spectra from near-UV to far-IR and are so small that many can be combined in one fixture to produce just about any desired spectrum. The longer the native wavelength, the higher the efficiency at high powers. Graph 5 is the spectrum of a 64x3W unit combining six different LEDs to optimize greenhouse seedling growth. There are units optimized for field-crop growth, flowering, fruit set, aquarium coral appearance, and just about any other spectrum one could wish. It all results in plant growth efficiencies far higher than any single-unit has ever produced. When this technology trickles down to lamp replacements, expect double today's 80 lm/W efficiencies. And, even better plant growth.
human, plant and 'quantum' sensitivity
Now that you have a Plant Growth Lumen, how do you use it to grow aquarium plants?
A commonly quoted measure of aquarium lighting in North America is 'watts per gallon': tube-fluorescent watts per US gallon for 10 hours per day. 1 watt per gallon is considered low light, 2 medium, 3 high. Although easy to criticise on the surface, it has proven to be an acceptably reliable measure in practise. So, how can it be converted to units that can be understood by the majority of the world that has access neither to US gallons nor to US lamps?
The efficiency of fluorescent lamps varies with length, as shown above. Most aquarium lamps here are 24", so 1253 lm for 20 W, 63 lm/W is a reasonable efficiency to use as a baseline for conversion. For a warm-white lamp, this is equivalent to 36 PGL/W. Since there are 3.785 liters in a US gallon, 1 'watt per gallon' converts to about 100 PGL-hr/l. For example, a 10 watt compact fluorescent lamp (420 PGL) operated for 12 hours per day over a 50 litre tank gives 420*12/50 = 100 PGL-hr/l, low light.
Now, you are ready to choose your plants based on their light requirements. Here is a listing of the best aquarium plants with their light requirements. Of course, plants respond to factors other than light - pH, fertilisers, trace elements, temperature, just to name a few. But, this note should help you get their light requirements in order.
other notes on physics
All light intensities on this page are in photons per second (Einsteins), not watts, as the activity of chlorophyll depends on the number of photons absorbed, not their energy.
Graph 1: The red curve is the CIE definition of the lumen (1924). The green is the average for 26 species of herbaceous plants from Inada, Plant Cell Physiol. 17(2):355-365 (1976). McCree has published similar results in Agric. Meteorol. 9:191-216 (1972), as have Sager et al. Trans. ASAE 31(6):1882-1889 (1988). Black shows the most common definition of Photosynthetically Active Radiation (PAR) approximated by "quantum light meters". PAR is also known as PPF, Photosynthetic Photon Flux. All are normalised for equal areas under the curves.
Graph 2: The black curve was calculated from the Planck radiation equation for 2856 K (CIE Standard Illuminant A). The lumens output for a typical 60 W lamp is from the US FTC Facts for Consumers. Note that economy 60 Wbulbs, such as those sold by Rona, produce only 520 lumens.
The filament temperatures of the 15T10 (2470 K) and halogen (3000 K) lamps were calculated from their published lumens output and the Stefan-Boltzmann equation. The outputs of warm white lamps are averages from a survey by Joseph Sellinger. All other data was obtained from manufacturers' web sites, and refers to specific lamps. Brands are shown only when they perform significantly better than standard fluorescent lamps. Most manufacturers list only "initial lumens", so the above tables are based on them. (Fluorescent lamps typically produce only 87% of their initial lumens averaged over their lifetime.)
The table of spectral factors below shows the values of graph 1.
Spectral Factors nm lumen plant 350 .000 .041 360 .000 .047 370 .000 .056 380 .000 .071 390 .000 .098 400 .000 .134 410 .001 .165 420 .004 .198 430 .011 .222 440 .023 .232 450 .038 .212 460 .060 .198 470 .091 .201 480 .139 .212 490 .210 .224 500 .326 .237 510 .504 .241 520 .706 .242 530 .859 .248 540 .951 .263 550 .993 .289 560 .993 .313 570 .950 .340 580 .868 .369 590 .756 .397 600 .630 .420 610 .503 .443 620 .380 .461 630 .266 .476 640 .175 .493 650 .108 .509 660 .061 .523 670 .032 .535 680 .017 .525 690 .008 .421 700 .004 .273 710 .002 .122 720 .001 .081 730 .000 .062 740 .000 .046 750 .000 .032