This post is a “gedunkan” to illustrate something that happens in simple systems. It’s prompted by a discussion in comments in the discussion about the conversion of Ocean Heat Content to equivanlent Temperature Change. This is not intended as explaining the complexities of what happens in the ocean, but merely to show a feature that makes it difficult to unambigously interpret what is happening in the depths of a body based on data about the total heat content in the lower and mid layers of a body heated from above.
The Gedanken
In this Gedanken or “toy” problem, we will example a very deep solid body that is heated from above. This body could be made from solid block of any very good heat conductor (e.g copper, aluminum, gold) which we insulate at the sides. We will assume the sides are perfectly insulated. The very bottom of the block will be dunked in an stirred ice water bath keeping it the bottom surface of the aluminum at T=0C. At time t=0 we assume the temperature of the aluminum is T=0. The conceptual diagram is show below:
In our mind we will partition the upper layer illustrated and call it “atmosphere”. (For the purpose of the gedanken, ignore the fact that the earth’s atmosphere is not aluminum. We can discuss in what ways this problem is similar or different from “the earth’s climate system” in comments.) The next layer down is the “top ocean”, the next down is the “top 2000 meters” and the lowest bit is “the lower ocean”. We will not explore what it means for the bottom of the ‘ocean’ to be kept at 0C.
Now we start the actual gedaken: at the top of the aluminum block we place an element that can either heat or cool the top of the block. This element provides a controlled heat flux of Q= 0.1 cosine (πt) where t is time. That is illustrated with the red arrows. Note that the heat flux is positive for 0<t< 1/2 then it goes negative. This is shown below:
HeatAtTop
Below, I’ve illustrated how temperature varies with depth at three different times, two at times < 1/2; the third a bit afterwards.
The earliest time illustrated is shown in blue, as nearly everyone expects, the heating at the top causes the temperature at the top of the block to rise. Because the bar is conductive, heat propagates downwards. The red trace shows the progression in temperature over time. Because heat flux at the surface remains positive in the time frame from the blue trace to the red one, the temperature at the surface continues to rise, ahd heat continues to propagate downward.
Finally, the green trace represents a time just after 1/2, when heat flux at the top surface turns negative. What happens during this time is a bit complicated. At the very top surface, heat is sucked out at the top. So this tends to cool the top of the block. At the same time recall that at t=1/2, the temperature at the top of the block is higher than the temperature lower down. So, at that point, conduction acts to suck heat away from the top and down to the bottom. So, the “top” layer loses heat both because the heat flux at the top turned negative and by conduction to lower layers.
When creating the green trace, I chose a point in time when the top three points had lost sufficient heat such that the maximum temperature is now between the third and fourth triangles on the left hand side of green trace. For those who think ‘this doesn’t happen’: Yes it does. Go into a desert before sunset. The top of the sand will be hot, dig a bit: the sand lower down will be cooler. Go later: the top will have cooled, but if you dig a bit, the sand lower down will be warmer than the top. This happens.
Returning to the figure: At the point in time represented by the green trace, conduction will act to transfer heat from points closer to the maximum point toward those further away. So: to to the right of the 4th point from the left, conduction will cause heat to flow deeper into the block while for points to the left of the peak it will cause heat to flow upward toward the surface. We could show more and more traces. But for now, I won’t. Instead, I’ll discuss the relevance to the discussion of interpreting what it might mean
- A top layer cools
- A mid layer warms
- The lower layer warms (possibly even faster.)
Note that in my conceptual figure of the block, I divided the region into “atmosphere”, “top ocean”, “mid ocean”. Suppose we were to mentally place the division bewteen atmosphere between between the three green triangles on the left and the forth to the left:
In that case, it’s fairly easy for someone integrating by eye to determine that the mean temperature (or heat content) of the top layer would cool slightly, while those of all lower lower layers warm during the time period from the “red” trace to the “green” trace. It happens that if I continue this exercise, depending on the choice of where I place the “mid” and “lower” layer partitions, I can get all sorts of behaviors.
I can have the
(top layer cool, mid layer warms , lower layer warms less quickly than midlayer)
(top layer cools, mid layer warms slowly, lower layer warms more quickly than midlayer)
(top layer cools, mid layer cools, lower layer warms)
and so on. And I’ve only just started the oscillating heat application, and (because EXCEL bogs down) I haven’t didn’t make by block deep. Let’s suppose I continue to apply oscillating heat. Look at the temperature variation with depth at time 2 which is the first full cycle of heat appliation:
Given this illustration of what happens in a very very simple physical system, I think you might want to contemplate what one might conclude if the only thing one knows about a “haitus” in surface heating is the “ocean” to heats when the atmosphere displays a “hiatus” from previous heating. I would suggest that unless someone fills in more blanks, it’s difficult to conclude much at all. Because if the heat is applied from the top and stalls, this is precisely what happens with no need of introducing any fancy theory about “enhanced mixing” at lower layers, or “the top didn’t really stall”, or “heat is hiding” or whatever. It’s just what happens in a simple system.
Some will wonder: Could I make this problem more complicated and still show the main result? Sure. But I can’t simultaneously make it simple and sufficiently complicated to match the dynamics of the ‘earth ocean’. If I add complications, that can cause people to think the behaviors has somethign to do with the complications when, in fact, the behavior is a sort of leading order very simple behavior. So, for discussion, I think this is best. The purpose is merely to let people see this and reflect. If you have complications that interest you, I might be able to explore some of the simpler ones. (Though, I have to admit, I did this in EXCEL which is behaving like a lard-ass cranky program. )
Still, discussion is welcome.
I don’t have a good mental model of how the ocean temperatures work. So thanks for the thoughts.
Some questions. Am I correct the models do not account for the heat storing capacity of the oceans? Also, I understand the oceans have a heat capacity 49 times that of the atmosphere from a post at Real Climate. What does it mean to reach equilibrium between the oceans and the atmosphere?
Let’s say there were some magic forcing that would cause the atmosphere to tend towards 1 degree “C” hotter than it is today. Does the ocean then need to be 1 degree “C” warmer to be at equilibrium with the atmosphere?
If the heat exchange between the ocean and atmosphere is efficient, then the ocean would suck heat out of the atmosphere quickly, and the greater the out of balance between atmosphere and ocean, the faster the exchange would operate. The faster the exchange operates, the better the ocean buffer is of storing extra heat. And the longer an imbalance between extra captured energy by earth would take to show up as actual increases in temperature.
In other words, the more heat is stored in the oceans, even with the models being entirely correct, the longer it will take to have an actual effect on climate.
Lucia,
This is a nice demonstration.
It might be interesting also to plot the time-dependent T at 3 or so fixed depths together with the surface flux (thus giving an idea of the relative phase of T(z) and F).
Lucia,
A good thought experiment. The real ocean is not uniform in ‘conductivity’, there is net heating at the surface (not alternating heating/cooling that averages zero), and there is net upwelling, so fluctuation due to variation in heating rate would be along a declining ‘equilibrium temperature profile’. But ‘waves’ of temperature would be expected to propagate downward.
Re: Ed Barbar (Comment #119740)
If the fluxes and circulation are correct, then the heat storage in the oceans should be (approximately) correct.
Working under the usual assumptions (i.e. the climate system is in some of steady state over a few-decade timescale), it would mean, among other things, that there would be no net heat exchange between the atmosphere and oceans (and space). The ocean gains and loses exactly enough heat to keep it as it is.
Generally speaking the ocean is warmer at the top than the bottom, and warmer at the equator than the poles. If the new equilibrium were such that the atmosphere were about 1°C warmer than the old equilibrium, then I suppose the ocean top would also have to be warmer to match, but I don’t think the temperature profile in the entire ocean would have to warm by a uniform 1°C.
Well, the oceans are part of the climate too! So, I suppose the right thing to say is that it would probably take longer to notice some fixed change in the global mean surface temperature. (Hence the inverse relationship between ocean vertical mixing and “transient climate sensitivity.”)
Re: SteveF (Comment #119742)
If you think of this as heating “anomaly,” then it’s fine. 😉
Lucia, I don’t know whether you’ve mulled over the issues in “borehole” temperature inversion, which is related to this problem.
Essentially, it’s the inverse problem: it attempts to reconstruct temperature history by measuring temperatures at different depths in drillholes (mostly old mineral exploration drillholes) but also glacier drillholes.
The matrices are near (very-near) singular and hence the inversion isn’t worth very much IMO. The decomposition of the matrix gives components that look like Chladni components and thus there are some stereotyped reconstructions.
Oliver,
“If you think of this as heating “anomaly,†then it’s fine.”
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Not sure I understand what you mean. Over most of the ocean surface area there is indeed a net flux downward (on the order of 10 watts/M^2 in the tropics, less at higher latitudes, negative in a few areas of deep convection).
Re: SteveF (Comment #119745):
Lucia’s is a 1-d model. It doesn’t matter that “most” of the ocean surface area experiences downward heat flux, so long as the net flux is zero when integrated over the entire surface.. The periodic flux condition represents a time-dependent “anomaly” of integrated flux.
How quickly does a pie bake in a vacuum oven?
And why doesn’t it matter?
Steve McIntyre (Comment #119744),
I suspect the complications are far worse for the ocean than for a borehole inversion. At least with the borehole you can be sure the material is not moving too much. Turbulence from eddy down-mixing would seem to be impossible to accurately describe, and horizontal movement (tends of thousands of times greater than vertical mixing rates) means vertical mixing far away from the location of the profile measurement (over a wide range of times past) influences the profile. In the ocean, an inversion looks impossibly difficult.
The bottom of the ocean is renewed with fresh, cold brine, annually and the surface of the ocean loses a layer of water through evaporation and pole-ward motion.
What you need to model is a stack of discs, where a cold disc is placed at the bottom of the stack and one is removed from the pile at the illuminated surface.
We have heat added to the surface and cold added to the bottom.
Note also we have 365 high heat/low heat cycles a top a single warm/cool annual cycle.
Oliver
Thanks, I would have done more, but EXCEL seems to balk. Several versions ago it handled more cells before getting finicky. Now I think I have to do this in R. I also want to do a version where the heat is added in in the third layer, and the top “radiates”. But…well.. EXCEL!
Lucia, this is a very nice but somewhat limited model has already been stated.
Funnily, I feel like being back in my undergrad physics lectures where we discussed the “optimal depth” of a wine cellar 🙂 being affected by a short day-night and a longer seasonal temperature oscillation.
Concerning the ocean we have to remember that water is a fluid, and heat transfer in fluids also happens by convection which is normally faster than conduction (diffusion).
Warmer water is less dense than cooler (ignoring the fact that it’s densest at 4C) and it will move up under the influence of gravity. Without having something quantitative at hand I could only speculate what would happen in the next-to-simplest model.
SteveF
The problems would be far worse for the ocean. At least the borehole taken in suitable locations might be approximately 1 d. That is: heat flux is predominantly in the vertical direction. In the ocean, we know that some sort of imaginary “borehole” in the ocean would not work.
Still, I would think the inverse problem is difficult. It’s one thing if you know the temperature really is sinusoidal and you just want to get the phase. In that case, even some measurement noise added to the core might not be too big a deal. But if the temperature at the surface varied in some complicated way, diffusion will smear out features. If you super impose noise, it could be very very difficult to solve the inverse problems. These things are typically difficult to solve anyway.
I just wanted to say Thanks for all you do here Lucia and all of the active participants. You really push deeply into the details of many issues that are glossed over by the majority. I know this is just a simple demonstration and one that anyone who has done soil temperature profile work would be quick to confirm but it is something that many have a hard time grasping until it is graphically displayed.
I have never looked at a temperature log from an off shore drilling rig but I imagine somebody could find what the sea floor temperature is 50 meters down and you could have a general heat flux from the bottom if one was interested. (excluding vents and volcanic activity)
Doc Martyn–
Yes. The real ocean is more complicated. You are describing 2 or 3 d effects, and other effects that this model cannot do. The purpose is merely to show that even in this simple case, it’s not easy to interpret the type of info Real Climate showed. You need a lot more detailed information.
Oliver,
” It doesn’t matter that “most†of the ocean surface area experiences downward heat flux, so long as the net flux is zero when integrated over the entire surface.”
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Sure, but any real-world measurement of temperature profile would not be one dimensional. All I was trying to point out is that almost nowhere would the change in profile over time approximate the one-dimensional thought experiment… it would always have a non-linear profile on which “anomalies” would be superimposed.
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As Carrick pointed out, the exact mechanisms and relative importance of those mechanisms is not clearly known… where they clearly known, coupled GCM’s would not overestimate ocean heat uptake by ~50%.
Lucia,
” These things are typically difficult to solve anyway.”
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Perhaps the understatement of the week. 🙂 (Nearly singular matrices and all that.)
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When I was very young, I naively tried to solve a 20 variable/20 unknowns set of equations (real visible spectrum data, nearly singular). Surprise does not adequately describe what I felt when the “solution” exploded into nonsense… disbelief is closer.
SteveF writes “Over most of the ocean surface area there is indeed a net flux downward (on the order of 10 watts/M^2 in the tropics, less at higher latitudes, negative in a few areas of deep convection).”
Where did you get this result from? Levitus has it as an average of about 0.4W over the last 60 odd years. You did say net right?
TTTM,
We are talking about different things. The shape of the thermocline (close to exponential decay shape from a little below the mixed layer) is the result of continuous (global) upwelling.. except in regions of deep convection at high northern and southern latitudes, where there is strong net downwelling of very cold water. This is of course the ‘thermohaline circulation’; cold water descends at high latitude, spreads over the ocean at great depth, and slowly rises and warms, with an average circulation time in the range of 1,000 years. Which is to say, there is almost everywhere net upwelling of cold water. Heat from the surface mixes down via eddy diffusion at a rate which depends on a number of factors, but the net upwelling combined with eddy driven down-mixing is what defines the shape of thermocline. In any case, cold upwelling water starts at ~2C and warms (very gradually) to the surface temperature along its journey to the surface. The heat needed to warm the water is provided from above, so most everywhere there is a net downward flux of heat from the surface (but not in regions of deep convection, where there is a strong net downward flow of very cold water). The average rate of upwelling outside the regions of deep convection is ~ 4 meters per year, so each square meter of ocean surface in the warmest tropics would have to supply (on average) a downward flux of ~(27C – 2C) * (4,000,000) = 10^8 calories per year/M^2, or 4.18 * 10^8 joules per year/M^2. A year has 3.16 * 10^7 seconds, so the net flux downward is: 4.18 * 10^8/3.16 * 10^ = 13.2 watts/M^2. In cooler regions, the flux would be less. (This is a rough approximation, not an exact calculation.)
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The Levitus number is calculated based on a change from the first measured “average” shape of the thermocline over time. IOW, ocean surface warming means a little more heat is down-mixed, so the temperature vs depth function along the thermocline changes with surface warming, all else being equal. Of course, the great leap of faith is that the rate of thermohaline circulation is not also changing significantly. If the thermohaline circulation were to decrease by 5%, then that would cause more heat accumulation along the thermocline, even at constant surface temperature, and vice versa, faster thermohaline circulation would tend to reduce apparent heat accumulation. So like all things climate, it is complicated.
Lucia, a practical bit of evidence. As an offshore fishing enthusiast (swordfishing off the continental shelf of the NE), we always send temperature probes down to 500 M looking for the thermocline where baitfish tend to accumulate. In 30 years I have never witnessed a surfaced temp that was lower than at depth. Doesn’t matter whether it was noontime, 3 am or time of year. For what it is worth.
SteveF writes a long description of where he’s coming from including the following statement “The heat needed to warm the water is provided from above, so most everywhere there is a net downward flux of heat from the surface ”
Thats not my understanding of the general process which I thought was that upwellings happened much more regionally and not “generally all over the ocean”. La Nina is a good example of one. Your description doesn’t sound energy neutral to me.
I’m not saying you’re wrong of course because I’ve never had reason to doubt my previous understanding. Do you have a reference at all?
By serendipity, I was just looking for an R script I’d used to do this very thing in order to reproduce the “tautochrones” illustrated in the first graph of Willis Eschenbach’s post here: http://wattsupwiththat.com/2012/06/18/time-lags-in-the-climate-system/ and finally put my finger on it shortly before I read this post.
It’s takes a few minutes to run, and it’s a few hundred lines. But I can send it if you want it.
Lucia
Thanks for showing the lags.
David Stockwell finds that ocean thermal inertia caused a Pi/2 (90 deg) or 2.75 year lag in ocean temperature from the driving 11 year solar cycle. See: On the Dynamics of Global Temperature
Re: TimTheToolMan (Sep 26 19:40),
There are areas where upwelling reaches the surface, but mostly it doesn’t. Mass ocean circulation is wind and tide driven, not directly temperature/density driven. (See Wunsch here )
DeWitt writes “There are areas where upwelling reaches the surface, but mostly it doesn’t.”
Thats how I understand it to be too.
And then “Mass ocean circulation is wind and tide driven”
I would have said…that applies to surface currents and then deep currents are driven by thermohaline circulation (ie sinks at the poles and then migrates towards the equator) as well as Coriolis effects but now I’ll read your reference to find out what they say 🙂
Re: TimTheToolMan (Comment #119766)
It’s a closed circulation, so a high-latitude “sink” by itself is not necessarily enough to sustain the overturning circulation. The source DeWitt gave will probably give some good insight as to why this is.
TTTM,
” Do you have a reference at all?”
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See for example: http://oceanworld.tamu.edu/resources/ocng_textbook/chapter08/chapter08_05.htm which describes Walter Munk’s early work and some later measurements of eddy driven diffusion rates. Note that there is a thermocline almost everywhere, and that pretty much requires continuous upwelling. Upwelling is by no means perfectly uniform, but it does take place over much of the ocean.
DeWitt writes “Mass ocean circulation is wind and tide driven”
OK, now I’ve read that article I see they greatly stress the “wind driven” aspect of the currents. Fair enough and obviously all deep currents have to “obey” in the sense they must support circulation towards where the winds were blowing the water from.
But saying currents like the gulf stream is wind driven is a stretch. By wind driven I assume he meant the wind gets the water moving rather than directs it along the coast and that is provided by geography.
I guess the take home from that article is that the wind provides the initial energy for the moving water. After that many factors affect where it goes.
So now back to SteveF’s description…are you (SteveF) suggesting that in general the thermocline is constantly tending to sink (ie warm the waters below by diffusion) whereas the THC is constantly pushing it up (and the surface water generally migrating toward the poles to support that) ?
I’m trying to understand your suggestion here…
Re: TimTheToolMan (Comment #119769)
If the Gulf Stream isn’t wind-driven, then what else could it be?
SteveF quotes “This was a remarkable observation because we expect downward mixing would continuously deepen the thermocline. But it doesn’t. Therefore, a steady-state thermocline requires that the downward mixing of heat by turbulence must be balanced by an upward transport of heat by a mean vertical current W.”
I should have seen you’d posted and read your reference before I asked…. Thans SteveF.
Oliver writes “If the Gulf Stream isn’t wind-driven, then what else could it be?”
Well the wiki says this “The trade winds blow westward in the tropics,[11] and the westerlies blow eastward at mid-latitudes.[12] This wind pattern applies a stress to the subtropical ocean surface with negative curl across the north Atlantic Ocean.[13] The resulting Sverdrup transport is equatorward.[14] Because of conservation of potential vorticity caused by the northward-moving winds on the subtropical ridge’s western periphery and the increased relative vorticity of northward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the western boundary current known as the Labrador current.[15] ”
So afaics is wind driven but geography directed.
Well thanks all. I’ve learned a few useful things today 🙂
TTTM,
“are you (SteveF) suggesting that in general the thermocline is constantly tending to sink (ie warm the waters below by diffusion) whereas the THC is constantly pushing it up (and the surface water generally migrating toward the poles to support that) ?”
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It was Walter Munk, not me, but yes, that is exactly what I was trying to explain. The circulation/upwelling depends mostly on shear from tidal currents and wind to drive mixing; otherwise, the whole ocean would be pretty uniformly cold below the depth where significant light penetrates, and there would be not enough density difference with latitude for much circulation to take place.
SteveF “It was Walter Munk, not me, but yes, that is exactly what I was trying to explain.”
I hadn’t read it at that point, I was trying to reason out what you’d meant. Thanks for the lesson, though. It puts the claims of the changing thermocline due to AGW better into perspective for me.
These inter-temporal effects coupled with the fact that the delta-Ts necessary to account for the actual heat transfer to the oceans are very small probably make this a really tricky measurement problem, aside from all the modeling issues.
CPV – I would imagine this is why the Argo data is so noisy. I am surprised that is shows variations of up to 5% of the heat content “anomaly” over 3-month periods. But, maybe the annual cycle and ENSO etc. really do cause it to vary by around this magnitude (I forget if the anomaly is seasonally adjusted).
Thank you Lucia. I was trying to make these points at CA yesterday but without the graphics people didn’t believe me. I think a key point is that the “complications” of the real ocean (upwelling, cold water recharge, turbulence, stratification) are too roughly known to make any kind of parsing of a “pause” or change in heat uptake. Thus “it is going into the ocean” is like “the dog ate my homework”–hard to disprove but not very plausible.
Likewise, if the ocean can take up more heat after 2000 and cause a pause, maybe it decided NOT to take up so much heat from 1979 to 1998 and CREATED a warming period. So you need to careful who you call your friends. We can more formally call this a post hoc fallacy which needs to be proven, not just waved around.
Re: ARGO and other measurements. The ocean measurements are not at fixed locations but from floating and drifting instruments. Even though there are a lot of them, they are still sparse in a real sense. This is particularly true for periods before 2003. It is very dubious that fluctuations on monthly timescales are real. Accuracy is also not as good as people might wish (notice how diplomatically I put that…).
Bob
I believe you. There are reasons why the solid does not act like the liquid. For example: When the top surface of a liquid cools, it gets more dense. An instability will occur and cold water will tend to sink. Nevertheless, there are features in the problem modeled that are analogous to what’s in water– the limitation being that this sort of over simplication can only show that trying to interpret whether heat “went into the depths” based on merely examining the trends in two lower layers can be misleading. There are many things that could be consistent with the problem.
Unfortunately, to do something like this with a liquid requires discussing 2 and 3 d effects or having “conductivity” change when there is a temperature inversion. (So, for example, we might deem that when temperature gradient tips, the entire top layer suddenly “mixes”. In such a case we really would have to start including both the diurnal cycle and a longer term cycle to gain understanding. It’s not at all clear that we can do that and still have a “simple” toy problem.
The only goal of this exercise is to show that, it is a bit difficult to simply deem that the fact that the temperature continues to rise in lower depths while it remains flat on the surface has an unambiguous interpretation (or that it means some sort of enhanced mixing and so on.) This is not to say it’s not worth observing that temperature below continue to rise. It is worth observing that and it does mean something. But precisely which range of ‘explanations’ for the pause this knocks out of contention is not clear.
Craig
The big difficulty I have with this is that if it’s warming whether over the long term, short term or what-have-you, of course some heat will go into the ocean. And of course, because the ocean is a big heat sink relative to air, a greater number of Joules will go into the ocean that into the atmosphere. But also, because the ocean is deep and the heat is deposited at the top of the ocean and also over land (and into dirt itself!), and lots of complicated things happen at the very top of the ocean (evaporation, heat transfer with the air, ) interpreting what is happening by looking at the trend in the bottom layer, trend in the mid layer and trend in the air is not easy.
So… yes. Heat may be going into the ocean. That’s what you would expect if the relative temperature or air/ocean is such that heat tends to move from air to ocean even in a system where mixing doesn’t change anything about hat happens in the ocean dynamics. Or, it could happen if mixing changes. But if the only thing we look at is the trends over two ocean layers relative to the atmosphere, the pattern we are seeing could equally well be forcing did decline, so air temperature dropped… and the ‘appearance’ of ocean warming is just the fact that ‘thermal diffusivity’ (due to convection or conduction) is positive.
We could do all sorts of tweaks on this problem: But thermal diffusivity alone can move heat from a location that is “warmer” to one that is “colder”.
Craig Loehle,
The post-hoc explanations are troubling only because they are carefully selected to not reduce the expectation of rapid future warming. If it were handled in a straighforward way, eg. “The temperature has not been rising as fast as we expected, and we don’t really know why.” That would be a lot better, especially if a list of possible causes followed… including the most obvious/likely cause… the models may overstate climate sensitivity. I find it ridiculous that climate scientists don’t address the obvious issue; I think they risk reducing the field to irrelevance.
Craig Loehle (Comment #119778): This has bothered me for some time. If someone allows that current heat could go into the ocean and someday come back to bite us, who is to say that this very thing didn’t happen at the end of the 1880’s and then came back in the 1980’s?
Trenberth is really going to have to go with the Gaia concept and some kind of sentience in the oceans to have this “now and only in the future” kind of physics going on.
Lucia,
I was trained as an electrochemist, so I know something about solving the diffusion equation. Although I’ve probably forgotten most of it. In electrochemistry, it’s concentration and electrode current density instead of temperature and heat flux. For a diffusion controlled process, if you ramp up the concentration at the electrode surface by changing the electrode potential and then hold at some level, the electrode current decays as t^-0.5. You would have to invoke convection to increase mass transfer, such as a rotating disk electrode, to have the concentration at the interface be constant while the current remained constant too. And that applies only if the change in concentration in the bulk can be neglected.
Off Topic:
I read the released SPM….wow, just wow! They absolutely will not allow for the possibility that the foundation of the whole exercise (high climate sensitivity) is looking less likely in the face of slower warming. I am not really surprised, but it is still a little shocking to actually seen the deni@l of reality laid out in detail.
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Another disturbing issue: repeated references to specific policies to avoid this or that… as if there is any certainty in the IPCC projections…. it is really breathtaking arrogance in light of the extreme uncertainty in the projections.
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I did see two encouraging things: 1) no best estimate of climate sensitivity….. they really don’t have a clue, and are finally admitting that, and 2) the ‘semi-empirical’ estimates of extreme sea level rise (Rahmstorf et minions) is discounted in the SPM as very unlikely. The SPM suggest ~50 cm rise by 2100 even with substantial continued emissions; not a huge change from AR4 (My guess is ~20% lower, but that is a relatively modest difference). A lot of people already knew that the Rahmstorf projections were nutty, but it is still nice to see a clear refutation of such nonsense by other ‘real climate scientists’. I guess the IPCC poobahs have a limited tolerance for alarming projections that will for sure be proven wrong within a decade or two. They should have applied the same criterion to the rest of the SPM projections before putting finger to keyboard.
If increased CO2 likely causes more energy to be absorbed by the earth, but it’s incredibly difficult to say how exactly much more, what the transport of that energy will look like over various time scales, and what the effect on local and global climate metrics the transport of that energy will have, what are we left with as questions we can actually answer with enough confidence to make any type of political or economic recommendations?
Whatever the details on energy penetration into the ocean are, people seem to miss the basic point that it can’t significantly warm the Earth later. The following shows the argument:
The Big Myth of the Oceans Causing a Temperature Pause
The oceans of the Earth cover about 70% the surface of the Earth, and based on the entire area of the Earth, average about 3,000 m deep. This volume of water has slightly over 500 times the total mass of the atmosphere. In addition, the specific heat of water is about 4 times that of air. Thus the temperature increase of oceans to energy input would be only 1/2000 the temperature increase of the atmosphere for the same amount of energy input. The claim is being made that the oceans are somehow swallowing extra solar energy that previously had been heating the Earth surface and atmosphere, causing a global warming pause, and this excess energy will somehow be released later and heat the atmosphere to a dangerous level.
The claim is based on an increase of average temperature of the layer of seawater measured down to 2,000 m with Argo sensors. The temperature increase is blamed on excess energy of about 0.5 W/m2 over normal absorbed and retained solar radiation due to CO2 level increase and positive feedback effects. When the excess is absorbed by the ocean rather than directly heating the atmosphere and surface, it is claimed this delays the energy release to sometime in the future.
If we use the claim that excess absorbed energy by seawater is now 0.5 W/m2, the energy absorbed by the seawater would add about 8E21 J/year, or 8E22 J/decade to the oceans. This would cause the oceans to heat about 0.013C per decade (or 0.13C/century). However, there are several problems with this claim, since the energy was not seen going down from near surface measurements. For the present argument, I accept the claim, and consider what can happen.
In a full century of this level of energy collection by the oceans, the temperature would increase on average by 0.13C. The total energy increase would be about 8E23 J. This is a huge amount of energy. If it all released to the atmosphere and retained while being released, it would warm the atmosphere 260C. Boy is that scary. In fact, if the energy could all be released, it would be over a period of time, and some would heat the surface, and most would be radiated to space, but there could be a significant temperature increase. Or could there?
Anyone who understands thermodynamics knows that it is the temperature difference that controls heat-transfer not the energy content of a source. Thus the ocean temperature increase of 0.13C in the full century would, at most, cause a surface temperature rise of 0.13C. This is nearly two orders of magnitude less than the present models claim the average surface temperature would increase by 2100. In face there is no rational mechanism for the 0.13C to even transfer to the surface in a reasonable time scale. Deep ocean currents and their transport to eventual surface locations are known to take from hundreds to thousands of years. Only surface water can transfer heat to the atmosphere. The hypothesis that the oceans are swallowing the excess energy, to cause the lack of continued warming, and that this energy can be released later to cause large levels of heating, is falsified.
Leonard Weinstein: “If we use the claim that excess absorbed energy by seawater is now 0.5 W/m2”
I haven’t been following this aspect of the debate. What’s the source of that figure?
Joe,
The NOAA/NESDIS/NODC Ocean Climate Laboratory put out a graph updated from Levitus et. al. 2012 for heat content of the 0-2000m Global Ocean, with Heat Content shown for about 1958 through 2012. The smoothed curve turned up about 1990 to a slope that has stayed near constant through 2012, with a slope of about 8E22 J/decade. Working backward from this for the full 3,000 m depth, the input energy would be about 0.7 W/m2. However, I also looked at the near surface rise rate, and concluded this lower ocean level value was probably a bit high, and rounded down to an input estimate of 0.5 W/m2. Using the slightly larger value would not matter much (0.2C rather than 0.13C per century.)
Joe,
The NOAA/NESDIS/NODC Ocean Climate Laboratory put out a graph updated from Levitus et. al. 2012 for Heat content of the 0-2000m Global Ocean Heat Content for about 1958 through 2012. The smoothed curve turned up about 1990 to a slope that has stayed near constant through 2012, with a slope of about 8E22 J/decade. Working backward from this, the input energy would be about 0.5 W/m2. Use of the 0 to 2,000 m depth is different from my 3,000 m calculation, but the difference is not important for the conclusion.
Thank you, Mr. Weinstein. Like most people, I suppose, I hadn’t done the math, but I was pretty sure it would bear out the reaction I had when I first heard the ocean-ocean-ate-my-heat argument: it was hard to believe those guys didn’t realize their argument’s other implications
Leonard Weinstein, how does this mesh with the observation that in a single year ocean related dynamics (i.e, ENSO) seem to be able to swing global temps rather dramatically (i.e., 1998).
thanks
On ocean circulation see the breakthrough in ocean flows:
Closure of the meridional overturning circulation through Southern Ocean upwelling, John Marshall and Kevin Speer Nature Geoscience DOI: 10.1038/NGEO1391
S Geiger,
There are large near surface temperature variations in the ocean, from different latitudes, and different depths. When you talk about increasing or decreasing total energy content of the deep ocean, you are considering a separate issue than when you talk about near surface movement of energy around, and getting temperature variation lasting from a few months to a few decades. The ocean is a huge heat sink and source, and changing of mixing or movement of large near surface currents (as in ENSO and Atlantic multidecadal variation) can absorb or release large amounts of near surface energy. However, when you talk of large long term average energy variation at large depths, this would only change the long term average surface temperature by the net increase in total energy calculated average temperature.The posts by Bob Tisdale, and his book would explain the near surface process much better than I can. The final point to make is that if the near surface absorbed more energy, it would on average, result in more surface heating, not a pause, and it is the near surface that does absorb almost all of the solar energy.
David L. Hagen,
…. and you could complicate that picture even further by throwing in the role of the Gyres and their impact on multi-annual and decadal variation.
http://www.ocean-sci-discuss.net/10/1619/2013/osd-10-1619-2013.pdf
Re: HR (Sep 29 10:34),
A decline since 2004 fits moderately closely with the peak of the AMO. A sine wave fit to the AMO index has a period of 66.6 years and peaks in 2011. That’s pretty close to 2004. Another indication is that the 365 day moving average of Arctic sea ice area has been nearly flat (and getting flatter) since 1/1/2007 when there was something of a regime change. From 2007-2011, the Arctic sea ice minimum area correlates well with the AMOC. 2004-2006 are clustered separately. I’ll be curious to see the AMOC numbers for 2012 and 2013. PIOMAS volume data should be available soon. I’m betting it will be discouraging to the doom and gloomers like Neven who were predicting an ice free Arctic ocean in the next two or three years
Small numbers, cherry picking, etc., but the negative trend in minimum Arctic sea ice area went away after adding 2013. In fact, the minimum area was within 1 standard deviation of the trend line for 1979-2006. Several other statistics like average sea ice concentration for September (CT area/NOAA extent) are also back on the long term trend lines.
Re: Leonard Weinstein (Comment #119812)
September 28th, 2013 at 1:18 pm
Leonard,
I am not convinced that your argument is valid. At the very least it is incomplete, I think.
It is certainly possible to engineer a physical system which transfers heat energy against a thermal gradient. In fact we use such systems (“heat pumps”) in many different applications – fridges, air-heat exchangers, air conditioning units, geothermal temperature control systems.
In order for your thermodynamic argument to be valid, you need to show that the ocean systems CANNOT duplicate the characteristics of a heat pump. However, a cursory look at the controls on ocean flows and temperatures would suggest the opposite, i.e. there are already a number of known mechanisms for heat transfer against the thermal gradient for both losses and gains. The main overturning circulations in both hemispheres transfer warmer water to cold depths because of salinity-controlled density gradients.
It seems more likely to me that the multidecadal ocean cycles are exactly energy dissipation-absorption cycles, but I cannot prove it.
Leonard,
Do take a look at the Marshall and Speers paper referenced by David Hagen above.
Re: Paul_K (Sep 29 22:03),
The density gradients mean less work has to be done to transfer heat, but the work needed to drive the heat pump comes from the wind driven surface currents creating a pressure gradient. See the link to an article by Wunsch in my comment above.
Leonard Weinstein (Comment #119812)
“In face there is no rational mechanism for the 0.13C to even transfer to the surface in a reasonable time scale.”
No-one said it would. The point is that this is a fluctuation on an existing flux, an overall circulation. We know most of the ocean is transporting heat downward – the surface is warm and the depths cold. But there are places where heat is advected up (or cold water goes down).
The argument of people like Balmaseda et al is that heat transported down reduces the temperature gradient, it doesn’t reverse it. That downflux had been part of the overall surface temperature balance. If reduced (by reduced stratification), the surface temperature warms. That doesn’t require that the transported heat returns to the surface.
Nick Stokes,
I have stated the increased temperature at depth could affect surface temperature. The issue is that the large thermal mass of a large depth of water results in a very small temperature increase for a large amount of energy input. Since the temperature difference, not the energy quantity drive heat transfer processes, the amount of excess heating would also be small, and limited by the temperature increase at depth. I would like to see any claimed process that could use an increase of temperature at deep locations of 0.13C result in the surface heating many times that amount.
Nick Stokes (#119869) –
Let’s put some numbers to your words. In the “NoArgo 2000s” period, Balmaseda et al. figure 0.11 Wm-2 for the below-700m region, considered as an average over the global surface. Otto et al., for their (delta_F – delta_Q) calculation for the 2000s, use 1.95 Wm-2 for forcing, 0.65 Wm-2 for heat accumulation. I don’t see a small change in the thermal gradient helping to transport 0.11 Wm-2 downward, as having a material effect on the 1.3 Wm-2 used in the denominator of Otto et al’s ECS. It all seems rather, well, hand-wavy to me.
Nick Stokes,
“But there are places where heat is advected up (or cold water goes down).”
.
There are for sure places when cold water goes down, otherwise there would not be any thermohaline circulation. 🙂 But there is no absolute requirement that any heat be advected upward. Surface currents easily can close the mass balance…. so the flow of cold water could be 100% downward with no compensating upward flow of (slightly!) warmer water from below the surface. Which is not to say that there is not wind-shear driven overturning to considerable depth where the density difference between the surface and considerable depth is very small (like at high latitudes in the Southern Ocean). How much this contributes to overall heat uptake is seems uncertain…. lots of model based studies, not a lot of actual measurements.
Re: SteveF (Sep 30 08:19),
That doesn’t sound right. If you have mass moving downward, don’t you have to have mass moving upward somewhere else? You could move stuff around on the surface with no vertical movement, i.e. close the mass balance with surface currents. But that isn’t going to happen because the surface movement creates horizontal pressure gradients at depth, much like the latitudinal surface temperature gradient causes a latitudinal atmospheric pressure gradient that increases with altitude, eventually leading to jet streams.
DeWitt Payne (Comment #119876),
I should have been more clear: The circulation is mass balanced, of course. Yes, there has to be mass movement upward somewhere… and there is, with an average upwelling rate (outside downwelling regions at high latitudes) of about 4 meters per year. What I should have said is that there is no need for any local upwelling at high latitudes to “return heat to the surface” as Nick Stokes seemed to be suggesting.
Re: DeWitt Payne (Comment #119866) 

I’m not sure that’s exactly what Wunsch is saying, but definitely he is arguing that the work comes from wind and tide forcing (both at the surface and at depth).
By the way, for those interested there’s also a more detailed review paper:
Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech, 36, 281–314, doi:10.1146/annurev.fluid.36.050802.122121.
Re: Oliver (Sep 30 09:45),
I tend to oversimplify when I paraphrase.
That was published in 2004. As I remember, alarmists back then were still claiming that the thermohaline circulation would shut down if too much Arctic ice melted.
I want to repeat the point I have tried to make. If the deep ocean absorbs so much excess solar energy to cause a pause in global heating, this absorbed energy is in effect mostly lost to surface heating, and would not come back except as a very small effect over long time scale due to the small actual temperature increase. This still begs the issue of why any process would cause the deep ocean to all a sudden, in the new century, start absorbing much more solar energy than before. It can’t be more aerosols, that would also reduce solar intensity, not make it go deeper. If the pause is related to surface current changes (PDO, ENSO, AMO), like has been suggested, I agree that long period cycles of near surface heating and cooling can occur, but the issue I am referring to is DEEP OCEAN ABSORPTION.
Leonard
Thus far, I haven’t seen any graphs that show the deep ocean suddenly absorbing more energy– or at least not more at a rate that would require any explanation beyond ” it takes time for surface heat to get down there.” But RC seems to be telling us that soon all will be revealed. 🙂
Oliver,
See if you like this better:
Ocean circulation is part of a heat engine with sea water as the working fluid. The properties that make sea water a working fluid are heat capacity and proportionality of its density to pressure and salinity and inverse proportionality to temperature. But the engine isn’t driven by the changes in temperature and density from heat absorption and dissipation like an ammonia absorption refrigerator. It’s driven by wind and tides. Because it is driven by wind and tides, it can move energy with or against a temperature gradient, especially if the potential temperature gradient is near zero.
DeWitt,
I wasn’t really disagreeing with your description of how it works. I was just thinking maybe Carl Wunsch would say the ocean circulation isn’t like a heat engine at all, since as you note the circulation is mostly mechanically driven and just happens to participate in the hot-to-cold transport.
On the other hand, the coupled atmosphere-ocean system does seem to be a heat engine, so you’re also right to say the ocean circulation is a “part” of a heat engine.
DeWitt, Oliver,
If I understand correctly, Wunsch suggests that wind and tidal driven shear is mainly responsible for the mixing that produces the thermocline and the concurrent density differences between low and high latitudes. Once those differences in density exist, they do contribute significantly to thermohaline circulation
Re: SteveF (Sep 30 16:16),
The way I read Wunsch was that the density differences do not provide enough free energy to drive the circulation. I guess it depends on what you mean by contribute. Density difference plays a role, but it doesn’t dominate.
What are the numbers relating to deep sea oxidation of organic carbon falling from above? (It’s a concentrated energy source, which is why we like it).