N in a Jaubert System are removed by the denitrification bacteria which will develop in the lower part of the deep sand bed and the plenum. P is removed via a few methods - if it is dissolved it's level in the water can be lowered by ejecting phosphate as an aerosol through air bubbling (see further below) and if kalkwasser is added it causes rapid precipitation of dissolved phosphate which in turn deposits itself on the substrate where algae can absorb it and also bacteria (see further below)
"Jaubert Method/NNR
This method is actually a modified version of the Berlin Method and was conceived by Jean Jaubert in the late 1980s though some limited study began even before then. Much research and application has been conducted on this method by Sam Gamble and Bob Goemans (the later of the two who coined the phrase "Natural Nitrate Reduction" (NNR). Basically, this method utilizes a plenum in which an open space of water is located under a deep layer of sand at the bottom of the tank. This open space remains primarily anoxic which allows high levels of bacteria that are hypoxic (lives in a low oxygen environment) to thrive. This low oxygen area conflicts with the high oxygen area of the main water column above the sand bed which results in an extremely slow movement of water through the sand bed itself. This slow water movement keeps the lower areas of the sand bed anoxic and nutrients cycling instead of accumulating at the tank bottom (nutrient sink), therefore the beneficial hypoxic bacteria thrive. Studies have shown that a depth of 4 inches to be ideal when utilizing a plenum. A shallower sand bed would be far less efficient. Any depth exceeding 4 inches would impact the system negatively, changing the sand beds redox which would result in nitrogen storage (not good). So, the bottom line is: when going with a plenum, ensure that you have a 4-inch sand bed depth."
Taken from
http://www.reeftime.com/reef-articles/basics-of-reefkeeping/planning-your-system/41.htm/41.htm just as a reference. More studies are available.
Re phosohates and airstone:
"In a Jaubert system one may employ aeration, algae harvest, protein skimming, and or kalkwasser dosing to manage the phosphate level. The spontaneous precipitation of calcium phosphate in marine aquariums that are maintained at natural seawater pH helps to lower the dissolved phosphate level, given adequate supply of calcium. However, this process is easily overwhelmed with high inputs of phosphate from the makeup water or from the food added for a large population of fish. In addition, dissolved organically bound phosphate can persist in the water, and particulate organic phosphate accumulates in the substrate. As I mentioned, protein skimming helps to remove dissolved phosphate. The bubbling action of airstones can also lower the dissolved phosphate level in the water by ejecting phosphate as an aerosol (see Spotte). Dosing the aquarium with kalkwasser (calcium hydroxide solution) causes rapid precipitation of dissolved phosphate due to the supply of calcium ions and the increase in pH caused by the hydroxide ions. The precipitated phosphate is insoluble at natural seawater pH, so while it accumulates in the aquarium in the bottom substrate, it is generally not available to the water column. Algae growing on the substrate may be able to obtain the phosphate by secreting special enzymes that digest it. Algae may also employ the activities of symbiotic bacteria that secrete enzymes to liberate phosphate bound to the gravel or tied up in organic detritus. Harvesting and removing algae such as Caulerpa spp. from the aquarium is a way to export phosphate. Particulate phosphate (organic and inorganic) can also be exported via protein skimming, and siphoning to remove it during water changes."
Taken from
http://www.advancedaquarist.com/2002/9/aafeature