In particular is it something that could in principle be measured in our lifetime, or are we stuck with calculating it based on our best understanding of how heat
flows between the ocean and the atmosphere?
Regarding heat
flow between the ocean and atmosphere, keep in mind that hte average surface temperature of the global oceans is about 17C, which is warmer than the near - surface atmosphere (on average).
Not exact matches
Understanding how carbon
flows between land, air
and water is key to predicting how much greenhouse gas emissions the earth,
atmosphere and ocean can tolerate over a given time period to keep global warming
and climate change at thresholds considered tolerable.
Increased warming of the cool skin layer (via increased greenhouse gases) lowers its temperature gradient (that is the temperature difference
between the top
and bottom of the layer),
and this reduces the rate at which heat
flows out of the
ocean to the
atmosphere.
As you say, the net
flow of energy is always
between a warmer
ocean surface
and a colder
atmosphere.
Did warming of the earth ever start, or was it just a variation in the
flow of energy
between ocean and atmosphere?
Yes they ad up: the natural
flows in
and out are huge
and only rough estimates, but the difference
between the natural inflows
and outflows (for
oceans and vegetation
and all other processes together) is well known, as that is the difference
between increase in the
atmosphere and the human emissions.
There is of nevertheless a time lag
between the increase or decrease in energy
flow from the
oceans and the ability of the
atmosphere to restore the equilibrium.
ENSO is a product of changing turbulent
flow rates
between the
ocean and the
atmosphere.
This is the weather,
and is largely responsible for heat
flow between atmosphere and ocean.
Accumulating GW gases in the
atmosphere alter the thermal gradient
between ocean and space, so energy
flows less readily from
ocean to
atmosphere to space,
and just like wearing a jacket on a cold day does not force more energy into your body, but rather allows the body to retain more energy.
Carbon
flows between the
atmosphere, land,
and ocean in a cycle that encompasses nearly all life
and sets the thermostat for Earth's climate.
With steady pCO2 in the
atmosphere, the pressure difference
between ocean pCO2
and pCO2 of the
atmosphere changes
and thus the
flows from one to the other.
Even if not all sinks are known to any accuracy, neither the partitioning
between vegetation
and oceans (one of them even may be a net source), we know with reasonable accuracy that all natural
flows together form a net sink of average 3 GtC / yr (ad that is the difference
between emissions
and accumulation in mass in the
atmosphere).