Melting of floating sea ice affects global temperature, but not the sea level, while melting of land-based ice affects both. We know that the total volume of the Arctic and Antarctic ice caps is 30-40 million km3. Of this total volume, the land ice is about 25-35 million km3 (2.5-3 million km3 in Greenland, 20-30 million km3 in Antartica and 1-2 million km3 elsewhere).
Most studies agree that the loss of ice mass is only around 1% per decade, while the drop in the area that the ice covers is about 10% per decade (13% in the Arctic). The area of the Arctic sea is 14 million km2, the area the ice covers is maximum in February and minimum in September. As of today, this coverage has been the lowest in September 2012, when it was 4.6 million km2. All studies agree that the rate of melting is increasing. This rate is the fastest on the Arctic waters, which are warming the fastest on the planet and according to most projections. If the present rate of global warming continues, the Arctic will be ice-free by 2040.
Assuming that the total volume of ice on the planet is about 30 million km3 and the weight of each km3 is 0.92 billion tons, melting all this ice would require about 2.16 x 105 Mtoe (million ton oil equivalent) of heat, coming mostly from the oceans. The removal of this heat would cool the oceans, but the size of this cooling effect is neglibible compared to the yearly heat input into the oceans from global warming, which in the top one-kilometer layer today totals 1.5 x 108 Mtoe/yr (0.41 W/m2). Considering that this total results in a temperature rise of only about 0.012 °C/yr, and that this quantity of heat is nearly 1,000 times more than the cooling effect of the melting ice caps (2.16 x 105 Mtoe), the cooling effect is insignificant.
While the cooling effect of the melting ice is negligible, the heating effect of removing the ice cover from the surface of the oceans is significant, because the Arctic ocean alone covers 1% of the Earth's surface. The melting of sea ice results in substantial heating because ice acts like a mirror, reflecting solar energy back into space, while the uncovered ocean and land surfaces absorb it. This occurs because as more and more of the ice cover disappears from the surface of the Arctic ocean (6.5 x 106 km2), that surface is changing from highly reflective into a heat-absorbing land and water surface (Figure 1). This is called the "ice-albedo feedback" effect.
In addition to the albedo effect, melting the permafrost also heats the planet because it releases large amounts of greenhouse gases tha further contribute to global warming. Heating caused by the albedo and permafrost effects is much greater than the cooling caused by melting ice. Therefore, the overall process of ice melting actually heats the planet.
How fast are ocean levels rising?
Even if emissions stopped today, a substantial sea level rise is inevitable. The sea level is rising in a "double-delayed" process. It is twice delayed because the heat first has to accumulate in the ocean before its temperature starts rising, and this accumulation starts only after the concentration of atmospheric greenhouse gases increases. Consequently, the ocean level rises very slowly. In addition, the water produced by melting is distributed over an immense area (3.62 x 108 km2, 72% of the planet's surface). Therefore, during the past 20 years, it has increased only by about 0.1 m (~ 0.3 ft).
So today, the yearly rise in the level of the oceans is only about 5 mm. Similarly negligible is the level rise due to thermal expansion. Figure 2 shows that the drastic rise in CO2 concentration resulted only in a slight increase in ocean temperature, which in turn caused only an insignificant rise in the ocean level. On the other hand, process control tells us that after the time delay passes, the melting process will accelerate and once the "tipping point" is reached, it can become irreversible. This can occur when the melting due to rising ocean temperature is further accelerated by the shrinking of the area of reflective ice, which is replaced by vegetation that not only absorbs heat, but also releases the greenhouse gas, methane.
This double-delayed process also has a large inertia, and once the rate of melting reaches the tipping point, it can become next to impossible to stop. This means that should all the 25 million km3 of land ice on our planet melt, the 362 million km2 surface of the oceans will rise by some 69 meters (226 feet). It is projected that the melting will first occur on Greenland because the temperature in Antartica is changing much slower, if at all—which I do not understand—but even if just the 2.5 million km3 ice on Greenland melts, the ocean levels will rise by some 7 meters (23 feet).
Heat engine drives climate and weather
Along with centrifugal, Coriolis and gravitational forces, the movements of air and water are influenced by the "heat engine." The Coriolis effect is caused by the Earth’s rotation, because a point near the Equator, where the Earth is wider, rotates faster than a point near the poles. You can visualize this by assuming that you are standing near the equator and are throwing a ball (a projectile in Figure 3) in a straight line to your friend standing further to the north. Since you are moving faster than your friend, the ball will land east of your friend. The same occurs to the wind and the ocean currents, which are moved by the wind. Therefore, these currents bend to the right in the northern hemisphere (clockwise) and counterclockwise in the southern.
The heat engine consists of two gigantic heat conveyors: the winds themselves, and the ocean currents caused by the winds. The temperature difference between the tropics and the polar regions drives both. The ocean currents have more influence on the climate, because the mass of the oceans is more than a thousand times greater than that of the atmosphere, while the effect of the atmosphere is faster. The gravitational, centrifugal and Coriolis forces are constant, but the force contributed by the heat engine is changed by global warming.