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.
CONSTANTS
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
INPUTS
"Missing" Incoming Radiation 0.7 W m-2 over earth's surface
OUTPUTS
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.
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You’re obviously not caring about our great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great grandchildren.
You heartless cad.
If there really is a missing 0.7 W/m2, then your calculation possibly explains why the Earth has stable climate for long periods, with the oceans acting like a giant storage heater!
COMMENT: I think you mean to say “heat sink” rather than storage heater, its certainly not warming much. – mike.
The oceans are not well mixed!
Pleas stop publishing your methods and data so that ordinary people can follow the arguments. It gives real climate scientists a bad name and brings the field into disrepute.
You are not a real climate scientist, so butt out of our private discussions. You know nothing, and we know where you live.
There are very few people that incite jealousy in me. You are one, Willis.
Keep the back of the envelope (LoL) numbers coming.
You have lots of fans – sadly mostly ageing males but ,no doubt, many eligible females.
( I have to be careful not to offend but in different circumstances I’d be a ‘groupie’.)
Most of the changes leading to an imbalance did not start until about 1900, and much of that fraction has operated only since about 1970, so thermal inertia is mainly responding to decadal rather than centennial imbalances. Given the estimated heat storage capacity of the ocean, combined with the negative forcing from aerosols, the IPCC estimates are consistent with observed temperature changes since 1910 in concert with standard estimates of climate sensitivity. For more data on ocean heat storage, see Levitus et al at Ocean Heat Content
Hansen and IPCC assume that the rise in the ocean heat content is all due to ‘a planetary radiation imbalance’ accumulation. However, there is a far more important factor: ‘equator-poles’ ocean current system’s efficiency.
More efficient system will transfer heat from the tropics to polar regions, thus retaining more of the initially absorbed solar energy = increase in ocean heat content (current GW, MWP).
The less efficient ‘equator-poles’ ocean current system releases the excess of the absorbed solar energy in the equatorial regions = cooling (less warming) of mid- and high latitudes (LIA).
You could think of the North Atlantic Precursor is a ‘regulator of the efficiency’ of the Atlantic Drift Current.
Since noone else is saying it; Its a Travesty.
Caveat – I’m no scientist (climate or otherwise), do not have a degree in any displine and can therefore be ignored.
BUT – my school science (admittedly from over 40 years ago) was that energy moves from hotter areas to colder areas. If this is still true in our brave new world of climamakeitupology then any area of the world’s oceans that are warmer than the air temperature will not be absorbing and retaining heat, it would be releasing at least some of it to the air. Hence, should you be using the entire area of the ocean in your calcs. Even if the sun’s energy in your calcs is all going into heating the ocean, isn’t it then releasing at least some of that enregy to warm the air and thus becoming cooler?
For example, whilst in the Australian Navy I was at Macquarie Island in 1985 and the water temperature was warmer than the air temp. Therefore, the water should have been releasing energy to the air.
So, what proportion of the world’s oceans are storing more heat than they are releasing and how does that affect your calculations?
“If there really is a missing 0.7 W/m2, then your calculation possibly explains why the Earth has stable climate for long periods, with the oceans acting like a giant storage heater!
COMMENT: I think you mean to say “heat sink” rather than storage heater, its certainly not warming much. – mike.”
Well I have always considered that the climate is just the output energy from the sun and the heat from inside the earth radiative energy input into a massive store in the form of the oceans, our climate being the interactive meeting layer between these things.
There are plenty of variables in all of the above.
I think what you were missing first is that climate sensitivity is an equilibrium sensitivity – the temperature that will be reached when everything has warmed up and in/out equilibrium is re-established.
Now you’re going to the other extreme of saying that we’ll have to wait until everything has uniformly warmed. But it isn’t like that.
Heating a body with a steady flux has a well-known theoretical solution – erfc’s, but looks like an exponential approach. Of course the ocean is much more complex. But what it says is that while you’re heating the top layers at first, most heat goes downward (easily at this stage) rather than needing to be reradiated as IR. The surface water warms quite rapidly.
Later there is more IR loss, as radiative balance is approached. The rate of penetration of heat to the greater ocen depth reduces. The rate of warming tapers off, approaching equilibriun rather like a tapering exponential.
So there are multiple time scales. You get most of the warming in a few decades, but the long time scale is even longer than your 465 years.
To add to my earlier comment, one can’t average temperature changes over the entire ocean, because the upper 300-700 meters tend toward equilibrium on decadal scales and the entire ocean over centennial scales. We live on the surface, and so our observed temperatures (including the documented rises in SST) reflect what is happening in the upper layers. If we induced no further perturbations from now on, a 0.7 to 0.9 W/m^2 imbalance would ultimately even out as a very tiny temperature change over the next 500 years if no feedbacks were generated. With feedbacks, the change is larger, and with long term feedbacks, greater still. However, the SST and global temperature changes over coming decades would be substantial, and of course, if CO2 continues to rise, outstripping aerosol cooling, the rise will be greater.
I’ve done similar calculations for myself, but don’t think they prove the IPCC is wrong. Here are a couple of factors to consider that you make have missed.
1) The current forcing hasn’t been applied for all 160 years since 1850. A rough estimate is that the average forcing has been a little less than half of the current forcing.
2) Temperature change lags forcing, but the amount depends on whether climate sensitivity is 2 or 4.5 (assuming it is anywhere within this range). There are estimates that, if the current forcing remained unchanged, temperature would rise another 0.5 degC. Therefore one could add 0.5 degC to the observed rise of 0.7 degC before doing calculations.
3) When you calculate how much energy it takes to warm the whole ocean 1 degC and compare it to the “excess energy retained” by GHG forcing, you quickly realize that it takes roughly a millennium to warm the whole ocean. Unfortunately, the whole ocean doesn’t mix quickly, it also takes about a millennium for deepwater sinking near the poles to the bottom of the ocean to return to the surface. Ocean temperature differences caused summer and winter only penetrate about 100 meters below the surface during six month long seasons. So you aren’t dealing with a system at equilibrium. In this type of non-equilibrium situation, we have to rely on climate models to predict how rapidly heat is transfered from the surface to deeper regions of the ocean. (Lindzen has said that climate models use unreasonable parameters for diffusion of heat into the deeper ocean.) With the Argo buoys, we may finally have data accurate enough to tell if climate models are correct.
Does this mean that its worse than we thought?
Well the warmists certainly have a major problem because there is in fact nothing in the pipeline. The upper ocean, which is supposed to absorb 80% of any radiative balance, has failed to gain ANY heat energy over the last 8 years! In fact there is a slight decline in upper ocean heat content.
http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/
Funny how this never gets discussed in the media! It absolutely kills the warmist Alarmist theories!
Willis,
I will say here and now that I have enjoyed, and profited from you frequent posts. You are missing nothing.
I have this to say though; do you not think that the answer lies in the positive? Or could it be a negative persuasion?
The answer, surely, is that we do not know enough of this science.
Oops! That should say radiative IMbalance!
With (according to WP) the energy capture from photosynthesis being more than 100 terawatts, is the “missing” energy instead being used by the biosphere in response to the increased CO2/warming? I would guess that it is in the right order of magnitude.
There’s no evidence it’s going into the oceans, Willis. The rise in the NODC Ocean Heat Content data appears to be caused by natural variables. OHC in the North Atlantic is the product of Atlantic Meridional Overturning Circulation (AMOC), ENSO, and Sea Level Pressure:
http://bobtisdale.blogspot.com/2009/10/north-atlantic-ocean-heat-content-0-700.html
The big shift in the North Pacific OHC appears to have been caused by a change in Sea Level Pressure:
http://bobtisdale.blogspot.com/2009/12/north-pacific-ocean-heat-content-shift.html
And the other ocean basins are dominated by ENSO:
http://bobtisdale.blogspot.com/2009/09/enso-dominates-nodc-ocean-heat-content.html
To calculate the thermal mass of the ocean you apparently calculated assuming an average ocean depth of 3700 meters, but when looked at over a period of a few years, the effective depth of the ocean is somewhere in the range of 40 to 100 meters.
Evidently someone has FORGOTTEN that WATER IS A THERMAL CONDUCTOR? !!!
A little PHYSIC FOR THOSE IN NEED..
Basic temperature of lower oceans, about 8 degrees C. (Below about 70 meters).
Basic temperature above the thermocline: About 15 degrees C. Direction of heat flow BY CONDUCTION = Surface to interior.
IF overall Atmosphere is at 15 degrees C (which it is) on the average there is a NEUTRAL flow into the oceans. Now, if there IS evidence of a 0.7 Watt/M^2 transfer into the oceans, axiomatically the ocean temp will go up. Then the REAL question becomes that of the RATE of conduction in the DOWNWARD direction versus UPWARD.
Since the “conduction” (assuming NO air movement) into the GASSES would be AUTOMATICALLY at a lower rate than through the LIQUID phase, the “extra energy” would diffuse into the lower ocean.
Making the concept that the large ocean would act as a “heat capacitor”, accounting for the ability to absorb many years of 0.7 watts/M^2 before the ocean would change its basic “internal energy” significantly.
As noted: the Argo bouys will provide valuable information in this realm.
Willis — The linked article is not directly related to you calculations, but is related in that it uses some rather basic calculations to do a ballpark sanity check on the sensitivity numbers.
It uses surface temperatures rather than the Argo data that is now available, and which I believe would be a more reliable test of the AGW hypothesis.
I’m surprised that I have not seen any discussion of this non-peer reviewed article.
Testing the AGW Hypothesis by George White.
http://www.palisad.com/co2/eb/eb.html
You are missing the lower inputs of the Sporer, Wolf, Maunder and Dalton Grand Minima over the last 1,000 years, as well as the RWP, MWP and other warm periods.
In order for the model to get a precise output, the input must be likewise precise and reasonably accurate.
What the models cannot seem to predict is the delta of input being one sign or the other, nor are they able to forecast change in delta. Over ages, those inputs have changed both delta and sign… both ways… and form glacial/interglacials.
Such things the models are oblivious to in both hindcast and forecast.
Bob Tisdale says: October 23, 2010 at 2:23 pm
————–
Bob
Thanks for the links, lot of useful info there.
From my point of view I found an interesting confirmation of my data.
Reduction in delay of NA OHC from about 10 to less then 5 years as confirmation in the efficiency of the North Atlantic currents heat transfer, resulting in the Arctic warming during 1990s.
Heat absorption by the oceans is a lot more complicated than the usual trite “the oceans have a massive heat capacity” line that warmists trot out. The land has a massive heat capacity too – all that rock goes a long way down.
First, take a look at some data. Sea temperature can vary 10 C from summer to winter near the coast. It’s less out in the middle of the oceans, but don’t confuse temperature with anomaly.
Sunlight shines through the top 100 m or so to warm a thick layer of water, but then rises by convection to the surface. The conduction and mixing with deeper layers is a much slower process. It’s also affected by such things as sea life like jellyfish who swim up and down from deeper waters to feed each day, stirring the layers up. But the effect most people pay the most attention to is the thermohaline circulation.
The heat capacity of the oceans is time-dependant. On short time-scales, for changes within a year, it is comparatively small. As one considers longer and longer times, its heat capacity increases, but the time taken to effect the heat transfers extends, so the heat can enter the reservoir only very slowly, and hence the power (energy/time) absorbed is small.
If one supposed (incorrectly) that water acted like rock and followed the 1D heat equation, then the penetration depth of a temperature change increases with the square root of time, so you get less and less heat capacity added each year as a change in surface temperature is sustained. Because of convection, stratification, and other effects, the relationship is probably something else entirely, and variable from place to place.
Anyway, the temperature of the oceans is now being measured by Argo, and it doesn’t appear to be accumulating there. Trenberth has commented on the missing heat being a problem for the models, although he managed to spin it as being “worse than we thought”.