actually in aquaponics you don't really change the water, you top it off. The nitrates are taken care of by the plants/produce. Since the nitrates are kept in check the little top off's are all that's necessary to replenish nutrients. The system acts similar to nature. The river analogy is off, there's no such thing as a river that starts and ends nowhere. Rivers are part of the hydrogen cycle.
http://www.globalchange.umich.edu/g...ectures/kling/water_nitro/water_cycle_web.jpg
rainfall/snow start it, it then runs into a lake or ocean. The nitrates do not evaporate and simply adding more freshwater WILL NOT make them go away. Something else has to deal with them or the fish will die. The cycle itself does nothing for it. Also consider natural ponds that receive nothing more than the occasional rainfall with not other water being removed except through evaporation which again doesn't help nitrates.
Those simply advocating w/c must never have experienced bad local tap water. There are some on here who have to deal with 80ppm nitrates from the tap! what good is a w/c then? You must use something else to deal with them, you can't rely on the new water to take care of the problem for you. This is where anerobic filters, algae scrubbers, plant filtration, and aquaponics come in.
The OP says he has an aquaponics system with tropicals and he uses the UGF along with a HOB that has a plant in it for the goldfish. My guess is he needs more plants, then he won't have to worry about w/c, just top offs. Though in my experience standard plants chew little nitrates per plant. Fruit/vegetable bearing ones tend to do more as the produce takes up quite a bit of resources.
In the end much to the chagrin of many on here there is no 1 way to "properly" take care of fish. There are problems and there are ways to deal with them but no one solid "everyone must do this" way. Yes that includes the almighty water change.