I like to think of Air moreso in terms of Lightning + Wind possibilities. The way I see Lightning vs Fire is that Fireballs/Firestorms are much larger and used for killing many, many enemies. Whereas Chain-Lightning is far more powerful (higher attack) although can only hit connected units, and only a limited finite number, say 20 people, jumping from one to the other, maybe it cannot "criss-cross" and therefore rarely be able to wipe a whole unit in one go, however tending to fry the most powerful/leveled soldiers within the unit. Fire (wide area of effect, less damage), Lightning (more focused area, much higher damage) in addition Fire could have firewalls and fire-elementals, while Air could have hurricanes, arrow buffs/debuffs, flying unit buffs/debuffs, Sail-boat buff/debuffs, as well as Dust-Tornadoes and Water-Cyclones and Fire-Tornadoes (turn your(any) burning unit into a fire-tornado to attack the enemy).
Water can be primarily a Support/Terraform ability ... although I think it would be nice to flood parts of the battlefield by raising the groundwater, as well as filling the air/atmosphere with moisture by calling Rainclouds over the battlefield. The presence of lots of water on the battlefield (through terraform spells) can weaken fire-spells (as such a "defensive" mechanism vs fire) as well as allow further water/ice abilities, and cross-over spells like Water-Cyclone.
Either the amount of "water saturation" you can achieve, its Mana Cost, or both, should heavily depend on terrain type.
Water-based terraforming should be most effective in Coast/Jungle, near as effective in grassland/floodplains, and to be ineffective/less effective in the desert (although cold places should allow for ice spells automatically (without presence of water), just not the pure "water" spells)
By flooding parts of the battlefield you can create obstacles for the enemy, slowing them down, and you can also use the "body magic" sphere of Water to buff and heal your units. Most Ice spells would either freeze units for x turns (as well as dealing initial damage) or simple damage spells like flying ice-cycles, as well as defensive measures like "Ice Wall" which can block enemy units as well as cause initial damage to any enemy units nearby the wall when it was first created.
Also a "Blizzard" spell to slow enemy units over a wide area and give very small amount of damage over time (a wider and less powerful version of Firestorm, also Firestorm doesn't slow down units)
Earth spells could actually terraform the terrain, Raise hills from nothing, bring down other hills, causing Earthquakes (any area of effect you want "click and drag" all units in the area are unable to move for x turns and recieve small amount of damage, area of effect alters mana cost), as extreme as Raising a Volcanoe. Other, defensive measures could include walls of earth, and an experimental and possibly overpowered spell called "submerge" which you would select as many of your soldiers as possible, to either attempt to dodge enemy spells or the side-effects of your own Volcanoe spell, and for a certain amount of time (your choosing?) your units are "safe" underground, although they still recieve any over-time effects as normal, and no spells can be cast upon them (unless its mystical spells I suppose). The one drawback to this spell is that eventually you have to surface (possibly a mana-drain situation) and you would not want to be out-flanked once that occurs. I think primary use of submerge would be to dodge an opponents Volcanoe, FireStorm, Blizzard, or Hurricane spells.
earlier I meantioned Water spells to Saturate the playing field via either Rainclouds or Groundwater. Well, I think an Earth-spell should be able to eliminate ground-water saturation, and an Air-spell should be able to eliminate Raincloud saturation.