Guest Post by Willis Eschenbach
A number of people have said Hey, in your previous post, the missing forcing is going into the ocean, so it’s still “in the pipeline”. I had considered that, but it didn’t make sense. I’ve taken a closer look, and it still doesn’t make sense.
According to the IPCC calculations in that post, about 0.7 W/m2 was missing. Let us assume that it is going into the ocean. Here’s my numbers, please check them. The spreadsheet doing the calculations is here.
Specific Heat Seawater 3.85 Joules/gram/C
Ocean Volume 1.3E+18 m3
Ocean Area 3.6E+14 m2
Global Surface 5.1E+14 m2
Average Ocean Depth 3700 m
Ocean Density 1.025 tonnes/m3
Year To Seconds 3.2E+07 seconds/yr
"Missing" Incoming Radiation 0.7 W m-2 over earth's surface
Equiv. Incoming Radiation To Ocean 1.0 W m-2
Annual Energy 3.1E+07 Joules/yr
Warming Ability 8.2E+06 grams C-1 / yr
1 m2 Column Weight 3793 tonnes
Column Weight 3.8E+09 grams
Warming since 1850 0.11 C (from spreadsheet)
Current Warming Rate 0.22 C/century
Time To Warm 1° at current rate 465 years/C
The reason that it didn’t make sense to me is that if that is the case, if the imbalance over the last 150 has warmed the ocean a tenth of a degree, and heat in the pipeline (assuming the 0.7 W/m2 imbalance continues) is going to give us a degree of warming in just under five hundred years … I just couldn’t believe that people were seriously thinking that was an issue.
So I suppose that’s possible, that the IPCC is right, and that half of the incoming energy is going into the ocean, warming it at the rate of one measly degree every half a millennium … But if that is so, does that mean that for practical purposes (neglecting the one degree by the year 2565, which is meaningless in human terms) we cut all of the IPCC warming forecasts (excuse me, scenarios) in half? Doesn’t that make the effective climate sensitivity in the real world, for our Grandchildren, by the year 2050, half of the number promulgated by the IPCC? Because the heat in the pipeline from the 0.7 W m-2 imbalance (0.22 C/century) will give us a whopping nine hundredths of a degree of ocean warming by 2050, unmeasurably small.
What am I missing here?
[UPDATE] Bob Tisdale graciously provided a link downthread to the oceanic heat content numbers. His graph shows the global heat content increasing by 7.8 MJoules per year per square meter.
If my numbers are correct (please check), this corresponds to a heat uptake (global average) of 0.17 W/m2. That would warm the ocean by a degree in 1900 years, so I think we can neglect that … and surely that’s enough time to do the mixing.
The missing heat is on the order of 0.7 W/m2. The evidence doesn’t show anywhere near that amount of heat going into the ocean. Including the ocean warming as explaining part of the missing heat, that still leaves on the order of a half a watt per square metre missing in the IPCC-based estimate … the ongoing mathematical mystery continues. All assistance solicited.
My own feeling is that the climate sensitivity is not fixed, but is a function of T, the temperature. It decreases with increasing T. This can be seen clearly in the tropics.
In the morning the ocean is cool, and the skies are clear. As a result, the surface warms rapidly. Climate sensitivity (degrees of temperature change for a given change in forcing) is high.
By about 10:30 or so, the ocean surface has warmed significantly. As a result of the rising temperature, cumulus clouds form. Despite increasing solar forcing, the surface does not warm as fast. Climate sensitivity is lower.
In the afternoon, thunderstorms form. These bring cool air and cool rain from aloft, and move warm air from the surface aloft. They cool the surface, bringing climate sensitivity near to zero.
Finally, thunderstorms have a unique ability. They can drive the surface temperature underneath them below the starting temperature. In this case, we have local areas of negative climate sensitivity – the forcing can be increasing while the surface is cooling.
As you can see, in the real-world context the idea that the temperature is some mythical constant “climate sensitivity” times the forcing change simply doesn’t hold water. Sensitivity goes down as temperature goes up in the tropics, the area where the majority of solar energy enters our climate system.