Hey Joe, some corrections to the numbers in your post. These corrections are minor:
- The specific heat of water is almost 6X that of air at the same temperature. SH of water is 4.186 joule/gram. SH of air is 0.718 joule/gram.
- The density of water is 816X the density of air. Water density is 1.0 gram/cc. Air density is 0.001225 gram/cc.
- Not sure how you did your calculation, but the thermal energy required to heat 1 gram of water 1 degree C is 3281X the energy required to heat 1 gram of air...fairly close to your number.
- The calculations are done using the mass of the air & water, not the volume
- The above numbers apply to water at 4 degrees C and air at STP (standard temperature and pressure which is 0 degrees C and 0.998 atmosphere)
You say that ice is more reflective that water, which isn't quite true. But there's a wrinkle. A couple basics:
- Water and ice have almost the same emissivity, 0.98 vs 0.97. Emissivity is the efficiency with which a material absorbs or radiates thermal energy.
- Water and ice have almost the same index of refraction, 1.34 vs 1.31. So if the angle of incoming thermal radiation is low,the energy will be reflected equally.
- Ice has about half the specific heat of water, so it will not take on as much thermal energy as water. But a 2:1 ratio isn't very significant.
The wrinkle - you are correct that the polar regions do not absorb thermal energy as much as equatorial regions, but it's not because of the basic properties of the materials (water vs ice). the primary reason is the low angle of incident solar radiation that arrives at the poles. Most of the energy is reflected back into the atmosphere. If the poles were all water, the same would happen as now when they are mostly ice.