I have spent a lot of time reading about the different types & theories, and have found many contradictions. I also happen to have a unique perspective, The majority of ponds were created by people that have not put much research into published pond and bio-filter design guidelines, so the ponds end up at being a random guess at what the pond needs to be healthy. There are some key factors that kept showing up.
High turn over rate; Pumps with actual flow rates that cycle the pond at least 1 or 2 times per hour.
High aeration; Waterfalls, fountains, aeration towers etc.
Regular water changes; At least 10% to 20%per week.
Running Current; Moving water so the fish have something to swim in.
After you get past the guessing stage and want to be a real pond enthusiast and employ an adequate filtration system, there are a number of factors to understand. Furthermore the efficiency of your filtration system will effect how much you spend on your pond, and how much electricity, water, and time you use. I hunted around and think I found some answers from the serious fish farming world in the book Aquaculture Engineering. With this information, filtration systems can be evaluated better, or you may be able to design your own system.
Trickle style media is not as efficient as submerged media. That's a shocker, there is currently a lot of hype about trickle filters being higher efficiency than submerged media. Possibly what the trickle filters are mostly doing is aerating the water more than a standard submerged media filter system. I believe a highly aerated submerged bio media is the best overall choice.
Does the bio-media (with bio film on it) need to be in dark, in the light, or does it not matter?
The filters need to be in the dark, or at least shielded from the light, because the light reduces the nitrification process.
Temperature range for best bio film growth
Bacterial activity occurs between 5 degrees C and 35 C, with the most activity at 30 c. With temperatures above 35 c, the bacteria may start to die off.
Best pH for nitrification
The best pH range for nitrification is between 8 and 9, which is high for a typical pond. Nitrification rate decreases when the pH falls below 7.
Oxygen concentration for optimum bio film development needs to be at or above 4mg per liter.
So adding an aerator just ahead of the bio reactor is a good idea.
Start up time using plastic media.
In ideal conditions, it takes between 20 and 40 days to mature a bio-filter.
Plastic media has been proven to show good results at hosting bio film. Thin new bio film has the highest nitrification rate, higher than older thick bio film. The reason the older film doesn't work as good, is because it is tougher for the oxygen and nutrients to get deep into the layers of the old bio film. Moving bed / fluidized bed reactors knock off the old bio film and allow new film to develop making them best.
Bio filter Media Calculations
K1 media has 259 sq ft of area per cubic foot of media, and has proven in aquaculture applications to be able to process 2 ounces of 40% protein food, per day, per 1 gallon of K1 media in a moving bed filter. Other filter manufacturers rate it at a lower efficiency, of about 0.61 ounces of food, per day, per gallon of K1 media. To get the K1 to “boil” properly, you can only fill it 40% full.
Example Using 55 gallon Barrel
A 24" fish that typically weighs around 134 ounces.
If you feed it 1% of it's body weight per day, then you are feeding 1.34 ounces of food per day, per fish.
1.34 / 0.61 per gallon of K1 = 2.19 gallons of K1 needed per 24" fish.
You can fill a 55 barrel 40% of the way with K1, so that is 22 gallons of K1
22 gallons of K1 / 2.19 gallons per koi = 10 of 24" koi per 55 gallon barrel filter
Other plastic media materials can be calculated similarly. You need to spend the time to calculate the square feet of media surface area that will fit in a cubic foot. As K1 is 259 sq ft per cubic foot of media.