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The earth's oceans account for about 71% of its surface area and 97% of its water.
This is aptly described by NASA oceanographer Josh Willis as the earth's Heat Bucket.
After combining all the data, Willis found that between mid-1993 and mid-2003, the heat content of the upper 750 meters of Earth’s global ocean increased at an average rate of 0.86 watts (plus or minus 0.12 watts) per square meter. Just 0.86 watts per square meter may not sound like much until you consider that we are talking about an area of about 337 trillion square meters (the 93 percent of the world ocean that Willis studied).
James Hansen ran five climate simulations covering the years 1880 to 2003 to estimate change in Earth’s energy budget.
Taking the average of the five model runs, the team found that over the last decade, heat content in the top 750 meters of the ocean increased by 6.0 plus or minus 0.6 watt-years per square meter.
The model described in Gerald North's book, A Simple Climate Model starts with a linear deterministic model of a single slab of the ocean (a 1-box model).
In this code the model will be go down to a depth of 80m.
The NOAA's Office of Climate Observation (OCO) concisely describes some of the physical aspects of oceans and climate:
Water vapor, evaporated from the ocean surface, provides latent heat energy to the atmosphere during the precipitation process. In units of 1,000 km3 per year, evaporation E over the oceans (436) exceeds precipitation P (399), leaving a net of 37 units of moisture transported onto land as water vapor. On average, this flow must be balanced by a return flow over and beneath the ground through river and stream flows, and subsurface ground water flow. The average precipitation rate over the oceans exceeds that over land by 72% (allowing for the differences in areas), and precipitation exceeds evapotranspiration over land by this same amount (37) (Dai and Trenberth 2002). This flow into the oceans occurs mainly in river mouths and is a substantial factor in the salinity of the oceans, thus affecting ocean density and currents. A simple calculation of the volume of the oceans of about 1330x106 km3 and the through-flow fluxes of E and P implies an average residence time of water in the ocean of over 3,000 years.
Changes in phase of water, from ice to liquid to water vapor, affect the storage of heat. However, even ignoring these complexities, many facets of the climate can be deduced simply by considering the heat capacity of the different components of the climate system. The total heat capacity depends on the mass of the substance involved as well as its capacity for holding heat, as measured by the specific heat of sea-water...
The atmosphere does not have much capability to store heat. The heat capacity of the global atmosphere corresponds to that of only a 3.2 m layer of the ocean. However, the depth of ocean actively involved in climate is much greater than that. The specific heat of dry land is roughly a factor of 4.5 less than that of seawater (for moist land the factor is probably closer to 2). Moreover, heat penetration into land is limited by the low thermal conductivity (the degree to which a substance transmits heat), of the land surface; as a result only the top two meters or so of the land typically play an active role in heat storage and release (e.g., as the depth for most of the variations over annual time scales). Accordingly, land plays a much smaller role than the ocean in the storage of heat and in providing a memory for the climate system. Major ice sheets, like those over Antarctica and Greenland, have a large mass but, like land, the penetration of heat occurs primarily through conduction (molecular transfer of energy due to a temperature gradient), so that the mass experiencing temperature changes from year to year is small. Hence, ice sheets and glaciers do not play a strong role in heat capacity, while sea ice is important where it forms.