As RobAmy and Lisak1 have pointed out, the key to oxygenating water is exposed surface area. Whether this is attained by actual size of the pond or through supplemental movement of water (turbulence) or a combination, the end result is the same.....Oxygen is added to the water column.
You have inquired as to numerical specs or formulae, Brokensword, for determining the results obtained through the use of different methods. These formulae do exist and I would be glad to supply links to them, but these are very complicated formulae used by engineers and would likely be of no practical use to the average person.
Instead I would like to discuss the nature of Oxygen and its relation to water.
As with any aspect of a pond, the subject of Oxygen should be looked at from many points of view. Everything in a pond is to some degree connected to everything else.
In air, Oxygen accounts for 20.9% of the total volume with most of the remainder being Nitrogen. This translates in 209 mg/L of Oxygen. The Oxygen bearing capacity of water is largely determined by temperature.
As can be seen in the above chart, the highest saturation level is attained at the freezing point of water...~14 mg/L Comparing this to the 209 mg/L present and available in the atmosphere, it can be quickly seen that water is not very efficient at absorbing Oxygen. Roughly 7% of available Oxygen at its highest capacity and only about 3% on a typical summer day.
Fortunately Nature has provided its aquatic creatures the ability to survive and flourish at these seemingly low levels.
The rate of absorption of Oxygen by water of the diffusion of Oxygen to water is primarily regulated by temperature and atmospheric pressure. At low temperatures and high atmospheric pressure more Oxygen will enter the water. Conversely, at high temperatures and low atmospheric pressures less Oxygen will enter the water. Ponds located at sea level will have a higher Oxygen carrying capacity than ponds at higher elevations.
Absorption/diffusion Of Oxygen is also influenced by the surface area of the body of water and by the current Oxygen saturation of same body of water.
The amount of water surface area available the more Oxygen will be absorbed/diffused. Much like a rain catchment system, the larger the surface area of the catchment basin the more rain water will be captured.
This available surface area can be augmented by creating turbulence. In Nature on large ponds and lakes this is accomplished by wind. In a Garden Pond, although wind may be a factor, turbulence is usually created by waterfalls, streams, aerators and even the fish. The water in the immediate vicinity of some of these may become super-saturated with Oxygen. This quickly spreads to the surrounding water column or is off-gassed.
Although absorption/diffusion is an important source of Oxygen, the majority of the Oxygen existing in a pond will naturally be created by the photosynthetic process of algae. For those Pondkeepers that abhor the presence of any algae growth, supplemental oxygenation through turbulence may a necessity.
One final thought. Water depth. This has been touched on in another thread on this Forum, but it is important to mention that Oxygen content in water decreases as depth increases. Outside of Wintertime, this is usually not an issue if the pond contains Koi and/or Goldfish; both of which are notorious in their ability to survive at extremely low Oxygen levels.
