This is a complex subject and, in ways, a circular one: warmer climate air melts surface glacial ice; warm air warms surface ocean water; warm surface water melts bottom layer glacial ice; melting bottom ice speeds melting of interior ice layers; surface ocean water cools; cooler surface temperatures cool the deep ocean; a cooler ocean affects weather patterns; variously changing weather patterns warms the air and we go round again. As of 2011, scientists of British Antarctic Survey (BAS) said that the relationship between air and sea temperatures and melting ice is not fully understood:
scientists do not fully understand the relationship between air and sea temperature, and the melting of ice. (BAS 2011)
However, new research published November 2012 by BAS and JPL explains some of the interconnection of effects between warming oceans, melting ice (both sea ice and glacial) and climate change. Briefly, according to BAS in 2012, while sea-ice cover is changing because of melting glacial ice on an ocean-wide scale, some areas are losing and some other areas are gaining sea ice. The Antarctic wind patterns that have been affected by warmer air temperatures drive sea ice in new patterns from long established ones. Since 1992, NASA’s Jet Propulsion Laboratory (JPL) has used US Defense Meteorological satellites to map "individual daily ice motion measurements" (BAS 2011).
The connection between global warming and ice melting and its effect on climate is explained in part by BAS. Briefly, sea ice and glacial ice (in ice shelves, which are glacial ice rather than seasonally affected frozen sea water) reflect solar heat and provide insulation for ocean temperatures (much in the same way Russian snow insulates Russian wheat crops). As shelf and sea ice melt, less heat is reflected and more absorbed in oceans adding to warming air and oceans and leading to more rapid ice melting. The alterations in air temperature affects winds, which in turn affect sea ice dispersion, ice melting, water temperature and climate change.