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# Ocean heat uptake

Previously we have gone through the concepts of radiative forcing and climate feedbacks. In order to understand how fast the earth’s temperature responds to a radiative forcing, we need to understand the role of ocean heat capacity and how heat is transported away from the upper ocean and into the deep ocean.

The ocean is the largest thermal reservoir on earth on the timescales we are interested in and the effective heat capacity of the ocean will determine how fast the earth responds to a radiative forcing. The effective heat capacity is the amount of energy required to change the temperature of the thermal reservoir by 1 degree. The amount is dependent on the density of the reservoir, the specific heat capacity (the energy required to change 1 kg of the substance by 1 degree) and the volume of the reservoir (given by the area and the depth). As an example: The energy required to heat up 2.5m of the ocean with 1 degree is the same amount required to heat up the entire atmosphere by 1 degree. This is due both to the large density of water compared to air and the four times larger specific heat capacity.

It is important to note that the effective heat capacity does not change the temperature the earth will have when it has equilibrated to the new radiative forcing. It only changes the time it takes to reach this new equilibrium. In other words, the effective heat capacity only influences the transient climate response (the temperature change seen before the climate system has equilibrated to the new radiative forcing) , not the equilibrium temperature response (the temperature change when the climate system has equilibrated to the new radiative forcing).
The transient response is determined by the timedependent nature of the radiative forcing, the effective heat capacity of various thermal reservoirs in the climate system, and the different feedback mechanisms, which dampen or amplify the temperature response while the equilibrium response is only dependent on the radiative forcing and feedback.

An important aspect of the effective heat capacity is that it varies over time, as the heating penetrates more deeply into the ocean the effective heat capacity will increase (because the depth of the ocean that is experiencing a change in temperature increases). How fast and how much the effective heat capacity increases is depending on the efficiency of the downward heat loss into the deep oceans.

Figure: Example showing how the size of the effective heat capacity influences the speed of the warming. The radiative forcing and feedbacks are the same in both curves. If the effective heat capacity is small the temperature change will happen quickly.