On daily and seasonal timescales, the heat storage by the climate system plays a large role in mitigating the influence of the changes in the radiative flux at the top of the atmosphere. Those variations in heat storage for the ocean, atmosphere and ground can be estimated by:
$$\mathrm{rate}\phantom{\rule{1em}{0ex}}\mathrm{of}\phantom{\rule{1em}{0ex}}\mathrm{change}\phantom{\rule{1em}{0ex}}\mathrm{in}\phantom{\rule{1em}{0ex}}\mathrm{heat}\phantom{\rule{1em}{0ex}}\mathrm{storage}=\underset{V}{\int}\rho {c}_{m}\frac{\partial T}{\partial t}dV\phantom{\rule{0ex}{0ex}}$$  (2.27) 
where $\rho $ , c_{m} and T are the density, specific heat capacity and temperature of the media (i.e. atmosphere, sea or ground) included in the volume V. This term can be approximated by:
$$\mathrm{rate}\phantom{\rule{1em}{0ex}}\mathrm{of}\phantom{\rule{1em}{0ex}}\mathrm{change}\phantom{\rule{1em}{0ex}}\mathrm{in}\phantom{\rule{1em}{0ex}}\mathrm{heat}\phantom{\rule{1em}{0ex}}\mathrm{storage}\simeq {m}_{m}{c}_{m}\frac{\partial {T}_{m}}{\partial t}={C}_{m}\frac{\partial {T}_{m}}{\partial t}\phantom{\rule{0ex}{0ex}}$$  (2.28) 
where m_{m}, c_{p, m} and T_{m} are the characteristic mass, specific heat capacity and temperature of the media that is storing heat and C_{m} is the effective heat capacity of the media (measured in Jm^{2}K^{1}). The value of m_{m} is strongly dependent on the volume that displays significant changes in heat content on the timescale of interest.
On the seasonal timescale, the heat content of the whole atmosphere changes. If we use a value for c_{p} of 1000 JK^{1}kg^{1} and a mass of 10^{4}kg.m^{2} (assuming hydrostatic equilibrium, this corresponds roughly to a pressure of 10^{5} Pa), we get an estimate of C_{m} for the atmosphere of:
$${C}_{m\mathrm{,\; atmosphere}}=1000\cdot 1{0}^{4}=1{0}^{7}{J\phantom{\rule{0.27778em}{0ex}}K}^{1}{\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}$$  (2.29) 
Only the top 50 to 100 metres of the sea display a significant seasonal cycle in temperature. Using a specific heat capacity of water of 4000 JK^{1}kg^{1}, and a mass of 7.5 10^{4}kg.m^{2},(i.e. 75 m times 1000 kg.m^{3}), we have.
$${C}_{m\mathrm{,\; ocean}}=4000\cdot 7.{5}^{}1{0}^{4}=3{.}^{}1{0}^{8}{J\phantom{\rule{0.27778em}{0ex}}K}^{1}{\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}$$  (2.30) 
The ground has a specific heat capacity similar to that of the ocean but only a few metres are affected by the seasonal cycle. As a consequence, the effective heat capacity of the ground is much lower than that of the ocean on this time scale.
This rough comparison clearly shows that the effective thermal capacity of the sea is an order of magnitude larger than that of the atmosphere and the ground on a seasonal timescale. As a consequence, the sea stores much more energy during summer than the other media, energy that is released during winter. This moderates the amplitude of the seasonal cycle over the sea, by comparison with the land. A strong difference in the amplitude of the seasonal cycle is also seen in land areas that are directly influenced by the sea (at midlatitudes, because of the westerly winds, this means land masses to the east of the oceans, such as Europe) compared to land masses far away from sea (Fig. 2.16). A similar analysis on a daily timescale shows that, heat storage by land, sea and atmosphere are all important.

For decadal to centennial variations, such as the warming observed since the mid 19^{th} century, thermal heat storage in the first hundred metres depth of the ocean (and at greater depths in regions of deep water formation) also moderates the transient temperature changes (see Chapter 6). On much longer time scales, such as the glacialinterglacial cycles, we have to take into account the full depth of the ocean ($\sim $4000m). For deglaciation, which is faster than the glacial inception (see Chapter 5), we can estimate the order of magnitude of the mean ocean temperature at a 2°C change in 5000 years. This corresponds to a mean heat flux at the ocean surface of 0.03Wm^{2} (= 4000 m . kg.m^{3} . 4000JK^{1}kg^{1} . 3°C / [5000 . 365 . 24 . 3600 s]). This demonstrates that the change in oceanic heat storage plays a negligible role but the inertia of the ice sheets has to be taken into account on these time scales.