I'll bet if you had checked your PO4 levels using Merck test kit you'd have been very surprised at how high your phos actually was. Most home test kits, and those at your lfs, are just for general readings. In fact most Phos tests cannot read to the lowest point necessary, basically if they show ANY PO4 you've already got an out of control phosphate level. They work great for tracking a tank over time and giving a reference point but are not laboratory grade tests. Brands like Salifert, Tunze, and Merck are not generally done for free as each test would usually cost $2 or more, that's per Trite, Amm, Trate, Pos, CA, Alk.. To use these tests it could easily cost $20 per batch.
So let me compare an algae bloom to a fire and to your yard.
If a fire is started from simple ignition source it will burn. If there is not enough combustibles nearby the fire will quickly burn out.
So your ignition point is the new brighter lighting. In a normal system the few excess nutrients (combustibles in the fire) would be quickly used and the algae (fire) would run it's course using up the available nutrients to create algaes.
If you add an accelerant to the fire, think petrol, the fire rages out of control.
What do we always complain about as hobbyists? When our algae runs out of control. What makes algae grow quickly? Excessive nutrients. Like the fire you can have a small algae problem but without the nutrients (petrol) it will quickly use itself up and go away. Remove the petrol source and the fire comes back under control. You can still have the ignition source (lighting) without a fire once all the combustibles (nutrients) are used up.
And your yard.
Does a yard grow a lush beautiful green without any attention at all? No. Will a yard continue to produce results with only sun and water? No. Once the grass begins to grow it uses up the nutrients from the ground. When we mow people tend to rake and throw the clippings away (think refugium), this in turn physically removes the nutrients and minerals from the ground that were once blades of grass. Over much time the mineral and nutrient composition of the yard are thus compromised to the point that we must add FERTILIZERS back into the soil to keep the yard looking nice. Without the fertilizers the yard starves to death. What you say? Algae and grass live on photosynthesis alone? Wrong. Algae and grasses use photosynthesis to process the nutrients it absorbs into the simple sugars it uses to grow and reproduce. Once you remove the fertilizer one point along the chain is broken and will prevent your yard from looking well until you add the fertilizers back. So now you ask what are fertilizers? Fertilizers consist of PO4, ammonia, and Nitrates. We spend a lot of our time as hobbyists battling all 3 of those products. Have you ever watered your plants using old water from a freshwater tank? Wow it makes plants and grasses grow like gang busters (think to yourself as adding petrol to a fire, what happens there?). Now that we positively know that Phos and nitrAtes cause photosynthetic organisms to grow out of hand it is much easier to see where the algae problems come from.
On one quick note if the problem of the original poster was a brown slimy algae on the glass you have excess silica in your water. Same as before, if you clean your source water the diatomaceous algae spores will quickly use up the available "food" until it dies off. Same theory we are applying to all algae.
There is a chain here that if you remove a piece of it, algae will not produce. Lighting and nutrients work hand in hand. If you can remove the excess nutrients then you can run high wattage lighting without fear of an algae problem. That is fact. It is as much a fact that you can have a continuous spark, or ignition source, without having a fire so long as there is no combustible. Remove the food and the algae dies. Same with the lighting, if the lighting was previously underpowered you could have tons of excess nutrients because the algae has reached a saturation point, a point where it can only process so much nutrients so quickly due to the limiting factor of the lighting. So add higher powered lighting to a tank full of TrAtes and PO4 and just like that the algae will play catch up since ALL it's needs are being met.
This is the same theory applied to how many fish can we add to our tanks. If our biological filtration has "X" amount of bacteria on it's surface and has pleasantly been processing wastes for a period of time that was sufficient and we decide to add another fish, it will take time for the bacteria to play catch up. So we add another load to the system and the bacteria bloom within our filters. During this time we are adding more wastes onto the display tank because the filter cannot process the waste, what we call a mini cycle. Once the bacteria levels colonize the substrate and level off with the new bio-load the problem goes away and in theory if parameters are met, Trite, Am, and Trate will quickly fall in line. However if the bio-load is to high the bacteria will never catch up and the wastes will accumulate in the display.
Everything we do is a balancing act.
So what can we do?
Here is a list to check yourself against.
1.) Use high quality RO/DI water for every water change or top off. Any water that goes into your reef or "algae free" tank should always be that pure. By limiting your source water you can then target the tank itself for potential problems.
2.) Use a more efficient skimmer.
3.) Clean your filtration more often. If you have a canister filter clean it bi-weekly if possible.
4.) Do more frequent and larger water changes.
5.) May need to cut down on the feedings.
If it is truly bad you may need some of this to conquer the problem. These items are stop-gaps. Not everybody needs them all or even all the time. When the problem goes away and husbandry skills improve these items may not need to be used ever again.
6.) An ozone generator to bind proteins to scavenger O3 molecules that can easily be scrubbed from the water by a good skimmer.
7.) A UV sterilizer to kill free floating algal spores, thereby reducing their abilities to spread.
8.) A phosphate reactor using ferric oxides to strip the water of PO4.
9.) Add a refugium to grow and harvest algae away from the main display tank.
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So yeah that's why I never blame the light, I blame the current state of the tank.
Some may say that the lighting spectrum plays a role, it does. If you have old 10K bulbs they may be producing 8K or less. This dips into the realm where algae thrive better than higher organisms. But again if there is no food to process, no amount of photosynthesis will allow the algae to grow. Lower spectrum lighting in a proper set up will cause corals to grow so fast as to strip the water clean of nutrients and therefore the coral will grow faster than algae can reproduce, thereby preventing it's growth. Slip up as a hobbyist and miss one important part and limit the growth of the coral and BAM the table will turn for the worst and the algae will over take the stunted coral, in reality the coral no longer synthesizes the nutrients and the algaes will. I've seen several frag grow out tanks of 125g or larger using a method of 8K lighting for amazing growth, the frags are then removed to a tank with 14K-20K lighting to create the intense colors.
So again a clean tank is a manageable tank.
The more you know, the easier it is.
And as always, do more water changes.