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This system has two radial filters and a media bed to keep the deep water culture raft very clean, An airlift pump keeps the water moving via an air compressor; no mechanical water pumps are required

Water levels in all the tanks are the same. By not raising the water from a sump tank only a small amount of energy is required to move the water laterally.

If this entire system were buried flush with the ground the thermal mass of the earth would help regulate the temperature very well during both summer and winter

Airlifts provides both water circulation and aeration. I believe airlift pumps can be more efficient than an external pump. (Ive never understood why submersibles are always less efficient, but the specs tend to indicate this).
Airlifts can be calculated.
This article Performance Study of an Airlift Pump with Bent Riser Tube presents an interesting conclusion is that bends in the riser pipe do not effect the performace of an airlift pump.
OPTIMIZATION OF A BACKYARD AQUAPONIC FOOD PRODUCTION SYSTEM
is a very good paper about aquaponics and it would be a very good source for information about airlift pumps but a critical table is missing. Id still recommend reading it for everything else it presents.

I found this calculator for airlift pumps. It is spot on against the real life experiments Ive conducted.

From my own experiments without math; I believe an airlift will provide enough water circulation. That is also what Keith Tatjana demonstrates in his paper in which he assumes a circulation rate of one fish tank volume twice per hour.
I think air blowers are more reliable than water pumps, and less expensive. Blowers do not provide the pressure like a compressor so this is a limiting factor when using a blower, but if at all possible use an air blower because air compressors like the Hydrofarm 70 and 110 lpm units tend to vibrate themselves to death.
I have not done any experimentation with how much ambient air temperature will affect the water temperature, but logically this would occur whether it be from an air stone or an airlift pump.
Other papers Ive found are

Performance Characteristics of Airlift Pumps withVortex Induced by Tangential Fluid Injection

Explore the Potential of Air-Lift Pumps and Multiphase
Explore the potential of air-lift pumps

A geyser pump, an improved airlift pump

The Geyser Pump improved the amount of water pumped from 40 gpm to 60 gpm in one experiment I conducted.
This Video shows the Geyser Pump I built. http://youtu.be/ztHBHULkHNQ