Discussion of "How Climate Model Complexity Influences Sea Ice Stability"

[OSweetMrMath]

In the "2015 melting season" thread, ChrisReynolds linked to the article "How Climate Model Complexity Influences Sea Ice Stability" (Wagner and Eisenman 2015).

There has been some subsequent discussion on that thread about the article, but it has drifted off topic for that thread so I'm starting a new thread to continue the discussion. I will summarize the discussion so far. (I am quoting previous discussion but omitting images. I am also editing quotes for succinctness.)

The discussion had started with a post from ChrisReynolds about possible cyclic behavior in August extent melt.

(Image omitted.)

Dots put on that manually, to show the similarity with other recent years and what seems to be an emerging cyclic behaviour. It will be interesting to see if we have large losses next year in August. If there is a cycle, and not just random behaviour, this 'predicts' large August losses in 2016.

(I am omitting some other discussions of statistical significance, El Niño, and the general August cycle hypothesis.) Killian eventually responded with

That looks an awful lot like the wobbles approaching a phase change in a non-linear and/or chaotic system.

Then ChrisReynolds posted saying that modeling work by Eisenman provided the strongest argument in favor of bifurcations (or that the system exhibits phase changes), but a new paper this year shows that the bifurcations in those models are artifacts of the models.

The strongest evidence for a possible impending bifurcation has been within the extensive work of Ian Eisenman into simple models of the sea ice. This year Eisenman has published work showing that those modelled bifurcations are artefacts of the simple model, and by implication that the GCMs are correct in not showing bifurcation behaviour in the transition to a seasonally sea ice free state.

After some further brief discussion from greatdying2, jdallen, and sofouuk, ChrisReynolds linked to Wagner and Eisenman 2015.

(Quotes from greatdying2, jdallen, and sofouuk omitted.)

Have any of you read Wagner & Eisenman 2015 "How Climate Model Complexity Influences Sea Ice Stability" in its entirety?

That paper conclusively shows that the GCMs are right and the simple models are wrong in showing a rapid crash to a seasonally sea ice free state.

Jai Mitchell questioned the conclusions of the paper

from the paper's abstract.

If the associated parameters are set to values that correspond to the current climate, the ice retreat is reversible and there is no instability when the climate is warmed.

you think that this is conclusive???

and then

it seems quite plausible that the new complex GCM that the author (and chris) believes are more accurate, that bifurcation is an artifact and that a rapid collapse will not occur seems to rely on parameters that severely overstate the impacts of meridional water vapor and heat transfer and the impacts of this and seasonal insolation variability on the arctic.

Any GCM that states that we can "reverse" the loss of sea ice at current (and future!) warming states is severely flawed.

sofouuk points out that Jai is misinterpreting the conclusions of the paper.

the paper just says that meridonal heat transport means there won't be a sudden change to an ice free state - as temperatures gradually increase, the ice will gradually retreat. in theory if we reduced climate forcing the ice would grow back; that's not happening any time soon, of course

Adam Ash asserts that reality may be too complicated for any model to capture correctly.

In particular I do not think that it is at all 'safe' to say '...bifurcation is an artefact and that a rapid collapse will not occur..' when in fact the complexity of your model is such that the potential end result of the sum of all the driving elements diverges exponentially from any cursory target by the power of the number of variables.

jai agrees with Adam and reasserts the claims about the paper's conclusions.

Thanks, that was exactly what I was saying, but also in the knowledge that we have locked in 2.3 Degrees of globally averaged warming (above pre-industrial) at 400 PPMv CO2 and 1750 PPBv CH4 (in the absence of anthropogenic aerosols associated with fossil fuel consumption).

I am also absolutely certain that any model that projects a return of arctic sea ice to 1980 levels at current temperatures, in absence of global or regional climate modification, and ESPECIALLY in a scenario of continued future warming is not representative of reality.  That is what this paper implies.

Good luck with that shift in the MDO. . .

Finally, ktonine points out that jai is still misinterpreting the paper.

Some really, really, need to read what the authors wrote and attempt to understand it.

There was evidence from simple models that a 'tipping point' (instability, irreversibility) was possible.  This paper shows that the simple model was *too* simple and that the instability was an artefact of the model.  Hence, one cannot claim evidence for instability or irreversibility by citing the simple model.

This was Chris' original point: sufficiently sophisticated models show stability vis a vis known forcings.  *STABILITY* means no tipping point.  It means the ice will act in predictable ways given specific forcings.  Reversibility means that if the forcings reduce, the ice will return.  With tipping points it's very difficult to reverse - in some cases impossible - once the tipping point has been reached.

[OSweetMrMath]

I feel like a useful starting point for any further discussion is a summary of the background, methods, and conclusions of the paper. Perhaps this summary will clarify where some people have been talking past each other.

The starting point is that climate models with differing levels of complexity make sharply different predictions about the future behavior of Arctic sea ice. Two relatively simple models are energy balance models (EBMs) and seasonally varying single-column models (SCMs). Both models start with an assumption of a global ocean, possibly with an ice cover. (In other words, with no land masses.)

In energy balance models, the assumption is that solar radiation depends on latitude, but not time of year, so there are no seasons. (You can justify this as an average across the entire year.) Heat is absorbed by the ocean or the surface of the sea ice, and then diffuses away from the equator toward the poles. At equilibrium the total outgoing longwave radiation is equal to the total incoming top-of-atmosphere net solar radiation.

Because the incoming solar radiation depends on latitude, the equilibrium temperature (and therefore the presence or absence of surface ice) also depends on latitude. Because the albedo depends on the presence or absence of ice, the net solar radiation depends on the presence or absence of ice. In other words, the net solar radiation at any latitude is a function of both the angle of the sun in the sky and whether there is open ocean or sea ice at that latitude.

The outgoing longwave radiation depends on the temperature of the ocean or ice surface, and also whether or not there is ice at the surface.

Because the ocean temperature changes as the latitude increases, there is also a heat diffusion represented by a meridional heat transport as heat flows from the hotter lower latitudes to the colder upper latitudes.

This is essentially the entire model. The heat transport is assumed to flow due north. There are no ocean currents and no seasonal variation, so at equilibrium there is a single fixed latitude, below which the entire world is open ocean and above which the entire world is a frozen ice cap.

For reasonable choices of the model parameters in the underlying equations, we get reasonable ocean temperatures and a reasonably sized polar ice cap.

Next, introduce an additional climate forcing term into the model, representing the additional retained energy due to increased atmospheric carbon dioxide. They find that as the forcing increases, the heat energy, and therefore the temperature, initially increases approximately linearly with the forcing. If x is the sine of the latitude at which the ice appears, then x also increases approximately linearly with the forcing, until the latitude reaches 79°. Then suddenly the ice collapses and the global temperature jumps up. This point of ice collapse and temperature increase is the bifurcation that Killian was referring to.

If you are in a world where some forcing has occurred but you are below the bifurcation point, then if the forcing is reduced, the ice level automatically increases and the temperature decreases linearly as the forcing is reduced. However, after the bifurcation point, so there is no remaining polar ice cap, the forcing can be substantially reduced while the global temperature stays above freezing and there is no polar ice cap. If the forcing is reduced sufficiently that the temperature at the pole drops below freezing, a large polar ice cap spontaneously appears.

The critical thing here is that the amount of forcing at which an existing ice cap suddenly collapses is much higher than the amount of forcing at which an ice-free planet gains an ice cap. The forcing increases and the ice thickness at the pole reduces to about 0.75 m while the ice cap extends to a latitude of 79°. Then all of the remaining ice melts and the temperature at the pole jumps to around 0.5 °C. (All of these numbers are eyeballed from Figure 5 in the paper.)

If the forcing starts decreasing at that point, the temperature at the pole slowly decreases to 0, then suddenly the polar ice cap freezes over to a depth of 1.6 m at the pole and down to a latitude of about 72°. Once the ice cap melts, the forcing must be reduced by around 0.8 W/m^2 in order for the ice cap to refreeze. This difference in the behavior of the ice depending on whether or not the ice cap already exists is a bifurcation (or hysteresis or phase change).

If the forcing is negative, then a similar bifurcation occurs as the temperature gets colder. The latitude of the ice slowly decreases, then suddenly jumps to 0 and we have a snowball Earth. The forcing then must substantially increase before the ice starts melting, at which point a wide band of ocean near the equator suddenly reappears.

[OSweetMrMath]

I am wordy. This will be several posts.

In the previous post, I described the annual-mean energy balance model, and how it leads to the existence of a bifurcation point. In this post, I will describe the seasonally varying single-column model.

The initial setup for the single-column model is similar to the energy balance model. Assume that the entire planet is an ocean, and subject to a net solar radiation (which depends on latitude and albedo) and outgoing longwave radiation (which depends on temperature and therefore latitude). We also assume that there are no ocean currents, so temperature and ice thickness depend only on latitude.

In contrast to the energy balance model, the single-column model assumes there is no heat diffusion, so solar radiation which arrives at a particular point on the globe stays there until it is released as outgoing longwave radiation. On the other hand, single-column models include the seasonal variability of the incoming solar radiation and a thermodynamic model for ice melting and freezing. This means that the energy balance model can only really claim to describe average ice levels, but single-column models can track the increase and decrease of ice over the course of a year, finding both the minimum and maximum extent of the ice.

When a forcing is introduced, the conclusions are similar to those of the energy balance model. As the forcing increases, the maximum and minimum ice extent decreases until first the pole becomes seasonally ice free and then the seasonal ice collapses, and the pole becomes ice free year round. (A bifurcation occurs.) In a slightly more complex single-column model, there may also be a bifurcation as the sea ice minimum approaches 0, as the minimum sea ice suddenly collapses after previously linearly decreasing.

Once the pole is ice free year round (or is ice free at the minimum in the more complex model), a substantial reduction in the forcing must occur before ice reappears. For the model used in the paper, the forcing must reduce by 7 W/m^2 in order for ice to reappear.

[jdallen]

I am wordy. This will be several posts.

That is fine, sir.  Thank you for summarizing and starting this thread.

[OSweetMrMath]

So now we have two models, both of which show a bifurcation effect. The models are unrealistically simple, but they still are assumed to reveal truths about the behavior of the sea ice.

The conclusion of the models can be stated that as atmospheric forcings increase, the (equilibrium) sea ice extent will linearly decrease until the moment that it suddenly collapses. Once this collapse occurs, even if we could reduce the atmospheric forcings, small reductions would not bring the sea ice back.

One possible implication is that if the Arctic ever becomes ice free in summer due to weather, it is guaranteed to continue to be ice free during the summer. Subsequent weather variability will never be sufficient to make the ice reappear.

More generally, this justifies predictions that while sea ice extent has been decreasing more or less linearly for the last 30 or so years, the Arctic could potentially melt out and become ice free during the summer at any time. Predicting when this might occur is essentially impossible, but it is plausible that it could occur next year.

But these are very simple models. We also have comprehensive global climate models (GCMs), which model actual Earth ice extent as they take into consideration the many features of the Earth's climate and geography that the energy balance models and single-column models ignore.

The global climate models do not show bifurcation effects. The conclusion from the global climate models is that ice extent will decrease linearly as the atmospheric forcings increase, and if the atmospheric forcings decrease, the extent will increase linearly, even if we get to a state where the Arctic is ice free year round. There are no observed bifurcations.

So here is the question: is the bifurcation observed in energy balance models and single-column models real? The first possibility is that the models are capturing something real about the behavior of the ice, and the global climate models, with their focus on the global climate, are not correctly modeling the Arctic sea ice. The sea ice could potentially collapse at any time, and if it is wiped out by a summer storm, it is never coming back.

The second possibility is that the simple models are too simple. In reducing the problem to one which is small enough to be easily simulated (and even to have analytic solutions, in some cases), the models no longer reflect the actual behavior of sea ice in the real world. Regardless of whether the global climate models are "correct", there is no model support for the idea that the sea ice could collapse, and even if it does collapse due to weather, there is no mode support for the idea that the sea ice cannot (temporarily) recover.

This paper addresses that question. The authors built a model which combines an energy balance model and a single-column model. This model can in fact be reduced to either of the simpler models by setting the appropriate parameters to zero. At the same time, this model is in no way a global climate model. The authors find that with the new model, the bifurcation does not occur. Instead, as the forcing increases, the sea ice linearly decreases to zero. If the sea ice is at zero and the forcing is decreased, the sea ice linearly increases. There is no hysteresis.

Furthermore, through an analysis of the model behaviors, they can provide arguments for why the simple models have model errors which cause the bifurcation effects.

Conclusion: there is no mathematical or scientific support for the idea that sea ice has bifurcations. The evidence is that the current sea ice loss is due to the increased atmospheric forcings of carbon dioxide and other effects. As the forcings increase, the sea ice will continue to melt. But it is not expected to suddenly collapse, and if we ever end up with an ice free Arctic due to weather effects (rather than purely because of the forcing), there is no reason why it cannot recover when the weather changes.

To be clear, the conclusion is absolutely not that at current carbon dioxide levels, the sea ice extent can return to the level it was at in the 70s. The conclusion is that even if carbon dioxide levels increase to the point that all Arctic sea ice melts, if the carbon dioxide level can be reduced to that of the 70s, the Arctic sea ice extent will return to the level it was in the 70s.

[sofouuk]

nothing to add of any significance, tho it might have been safer to end with 'sea ice levels will EVENTUALLY (shouting intended) return to 70s levels', before anyone starts complaining that there are long time lags

[Jim Hunt]

A third possibility is that current comprehensive global climate models are too simple. For a wordy discussion on the deficiencies of such models when it comes to sea ice see also:

The Distributed Arctic Sea Ice Model

By way of one example, I recently discussed "waves-in-ice" with a climate modeller from the Hadley Centre. It seems their models don't incorporate such things.

I realise that Chris Reynolds is of the opinion that he has "gone emeritus", but nonetheless Prof. Peter Wadhams still seems to be of the opinion that:

In the end, it will just melt away quite suddenly.

Wagner & Eisenman state that:

an idealized representation of sea ice and climate with seasonal and latitudinal variations in a global domain. The surface is an aquaplanet with an ocean mixed layer that includes sea ice when conditions are sufficiently cold. We consider only zonally-uniform climates.]The model used in this study [is] an idealized representation of sea ice and climate with seasonal and latitudinal variations in a global domain. The surface is an aquaplanet with an ocean mixed layer that includes sea ice when conditions are sufficiently cold. We consider only zonally-uniform climates.

The real world is much more complex than that!

[greatdying2]

So the argument goes like this?

Certain simple models show A. Certain other, more complex models do not show A. Assume that these complex models better reflect reality than these simple models. Therefore A cannot happen.

One need not read the details of the models, in their entirety or otherwise, to see that this is, in general, a fallacious argument. In fact, it might be useful for those who've delved deeply into such details to take a step back and realize: they're just models!

The "third option" that Jim Hunt points out is a virtual certainty. It would be hubris to claim that one knows, based on any models whatsoever, what can and cannot happen in the real arctic.

(Sorry if this post comes off as grumpy. I'm just a bit tired of people asserting that because they have read this or that paper, that they are certain of the truth. This is just not how science works. No expert (scientist) would be so confident, especially regarding models.)

[Adam Ash]

So now we have two models, both of which show a bifurcation effect. The models are unrealistically simple, but they still are assumed to reveal truths about the behavior of the sea ice.

Thanks OSweetMrMath!  I suspect you enjoyed putting those notes together - I certainly enjoyed and appreciated reading them.

I had been looking at wave forms used to create square waves for power supplies, and that rang a bell when i saw the mix of cyclic inputs and the possibility of boolean outputs from climate models with varying degrees of complexity.  I thought it was worth pointing out that some of the most benign sets of inputs can (intentionally or unintentionally) produce boolean outputs under some conditions.

I then added my observation (which I still stand by) that increasingly disaggregated models always run risks of severe unanticipated excursions when boundary conditions are approached, simply because of the inherent instability of numerous cyclic functions adjusting their harmonics. 

Its is gratifying that the current more complex GCMs do not find tipping points, but as we know, these models are a poor far second best to the complexity of the real world.  Thus at best all that can be said from this work is that the models do not detect instability IN THE MODELS under the given conditions.

While that reassurance may be helpful, it does not give me a strong reason to preclude some instability (tipping points, even) from the list of possible real-world outcomes which could arise from our current rather rash global climate experiment. 

[sofouuk]

So the argument goes like this?

Certain simple models show A. Certain other, more complex models do not show A. Assume that these complex models better reflect reality than these simple models. Therefore A cannot happen.

no, the argument goes like this: there is no evidence from any sea ice model that sea ice area will suddenly crash and refuse to reappear. anyone is welcome to try to model the effect of increased wave action, or anything else, on the ice pack, and if realistic parameter settings lead to a sudden crash when a tipping point is reached, that would be a very interesting finding. but no one has done that and (this is a key point for amateur observers to consider) most of the experts are skeptical that it will happen, so, based on the available evidence as it stands, we proceed on the assumption that it probably won't happen, unless or until the available evidence is updated. that's how science works

[sofouuk]

note that this argument is essentially about feedback effects - sudden crashers believe that positive feedback effects will dominate the endgame, slow transitioners believe the negative will. EBMs show a sudden crash due to positive albedo feedback, the increased wave effects argument is that more open water - more waves - greater fragmentation - faster melting - more open water, etc, while the simplest negative feedback is that as the ice edge retreats northwards it gets harder to melt what's left of the ice bcz the melting season gets shorter the further north you go (Chris' slow transition is a more sophisticated version of the same basic idea). there are plenty of other potential feedback effects to consider, and such effects are notoriously difficult to predict accurately, which seems to be the main complaint of other commentators here: therefore we should hesitate to draw any definite conclusions. maybe so, but the people who have the best (necessarily intuitive) grasp of the relative strengths of all the competing feedbacks are the scientists who try to model this, and it is noteworthy that very few of them are sticking their necks out to say a sudden crash is imminent - wadhams can't be taken seriously after this year's prediction

[crandles]

Adam Ash asserts that reality may be too complicated for any model to capture correctly.

In particular I do not think that it is at all 'safe' to say '...bifurcation is an artefact and that a rapid collapse will not occur..' when in fact the complexity of your model is such that the potential end result of the sum of all the driving elements diverges exponentially from any cursory target by the power of the number of variables.

If this was believed to be the case about climate in general, the climate modelling groups just wouldn't get the funding they do.

Climate is considered to be a boundary condition problem not a chaotic initial condition problem. Perhaps there could be chaotic interactions if we throw in a few more forcings or effects that are currently not modelled. However the evidence so far is that this doesn't happen - concentrate on the major forcings and the models tend to give you a not unreasonable idea of what will happen even though the models are far from perfect.

Models are better at some things than others. GCMs are not particularly good at indicating exact level of ice. This doesn't mean the way the modelled ice responds to forcings isn't reasonably realistic.

If you don't like what the models say, then it is possible to invoke some extra necessary complexity so that the result 'diverges exponentially' or chaotically or into a bifurcation or ... Possible yes, but is it likely? Doesn't seem likely to me given all the evidence that weather is chaotic but climate is not. Important matters that are likely to have large effects get modelled first. Yes, modellers may have missed out something important. May but not likely, and without evidence for it, invoking such possibilities seems like it might amount to grasping at any straws.

Perhaps we shouldn't rule out idea of ice having some chaotic or bifurcation behaviour within a climate system that has so far entirely looked like a boundary condition problem not a chaotic initial condition problem. However I don't think we should attach anything more than a low probability to this.

[Adam Ash]

Thanks Crandles.  I was going to say 'Fair comment', but its more than that, your's is informed comment while mine is mostly WAGs based on very imperfect understanding of the depth of your art.

Starting from way out in the cold, I'm just trying to discover my own version of meaning among all this.  Your guidance is much appreciated, tho not so highly regarded that I will let it go completely unchallenged!  Bear with me, and my ilk.  Thanks.  AA

[crandles]

there are plenty of other potential feedback effects to consider, and such effects are notoriously difficult to predict accurately, which seems to be the main complaint of other commentators here:

I agree with what you are saying.

I think it worth noting that if you want to push the idea that 'it is notoriously difficult to predict' such missing feedbacks, then you might expect at least some of the models to show a crash. Instead they all show a Gompertz shape:



Adding different things into models seems it can affect level of ice but the gompertz like shape seems to remain. Why not a single case showing accelerating decline towards zero ice? Why would adding more effects to be modelled (presumably expected to be less significant effects as you add more) be different than the differences in the array of models we have seen so far?

Consequently, I would much rather trust the gompertz shape that all the models produce than trusting just one or a few particular models.

How many different models and how many different versions have there been? At some point it becomes more sensible to think the gompertz shape coming out every time might actually mean something rather than continually praying to the god of the gaps. No doubt some people will prefer to continue to pray to their god of the gaps.

[seaicesailor]

A third possibility is that current comprehensive global climate models are too simple. For a wordy discussion on the deficiencies of such models when it comes to sea ice see also:

Wagner & Eisenman state that:

an idealized representation of sea ice and climate with seasonal and latitudinal variations in a global domain. The surface is an aquaplanet with an ocean mixed layer that includes sea ice when conditions are sufficiently cold. We consider only zonally-uniform climates.]The model used in this study [is] an idealized representation of sea ice and climate with seasonal and latitudinal variations in a global domain. The surface is an aquaplanet with an ocean mixed layer that includes sea ice when conditions are sufficiently cold. We consider only zonally-uniform climates.

The real world is much more complex than that!

I believe as others that a realistic model of MYI creation/retention/destruction is needed.

To illustrate an idea of irreversibility and tipping point (crossed in 2007), suppose that the greenhouse effect diminishes to pre-2000 levels. The Arctic starts recovery of its structure and extent, but very slowly, due to the difficulty of FYI to survive. Note that the albedo effect and other positive feedbacks ---such as waves and enhanced ice transport--- keep working against recovery even under lower greenhouse effect, so long as deformable and easy-to-melt FYI lets large extents of ocean open.

Only an extraordinary year of exceptional cloudy and cold weather could accelerate the recovery of the Arctic to its previous state. A "trigger year"  that would set the Arctic up to the original branch of this hysteresis, just as 2007 was a "trigger" year that set the Arctic down in the branch where it lies right now.

Said so, scientists need to use simple models to understand the effect of different mechanisms step by step. By looking at GCM runs you can extract a lot of data, some information, and maybe a bit of knowledge if you are lucky. Anyway, the GCM itself is heavily simplified, or better put, it includes many physical/chemical processes, some of them are heavily modelled by necessity (CPU time).

[greatdying2]

So the argument goes like this?

Certain simple models show A. Certain other, more complex models do not show A. Assume that these complex models better reflect reality than these simple models. Therefore A cannot happen.

no, the argument goes like this: there is no evidence from any sea ice model that sea ice area will suddenly crash and refuse to reappear. anyone is welcome to try to model the effect of increased wave action, or anything else, on the ice pack, and if realistic parameter settings lead to a sudden crash when a tipping point is reached, that would be a very interesting finding. but no one has done that and (this is a key point for amateur observers to consider) most of the experts are skeptical that it will happen, so, based on the available evidence as it stands, we proceed on the assumption that it probably won't happen, unless or until the available evidence is updated. that's how science works

Yes, this way of putting it is more reasonable (although I don't agree that just making a model with any particular behaviour would be dispositive).

"There is no available reliable evidence to suggest a bifurcation." Yes. But that's all.

Scientists would not then say, "we thus assume the available evidence is correct and so it cannot happen or probably will not happen." Before drawing conclusions, scientists would instead weigh the strength of the available evidence. Are the available models and other evidence sufficiently reliable to draw strong conclusions?

I don't think so. It seems to me that the basic attitudes of at least some leading climate scientists about what to expect in the cryosphere can be summarized as: "Don't rely heavily on models and expect the unexpected."

See for example this video at 2:31.

! No longer available

Or in this entire video, especially at 3:25 to 3:57, 5:12, 6:04.

! No longer available


Science is not about assumptions. It is about uncertainties.

[wili]

crandles wrote: "Important matters that are likely to have large effects get modelled first."

That's not always the case, of course. If even probably large, important effects are seen as hard to model or too full of uncertainties to be able to say much for certain about them, they tend to be left out of models. You can't model what you can't model.

Think of carbon feed backs that are certainly going to play a major roll going forward but have generally not been very fully incorporated into climate models until recently.

In other cases, such things may be included, but the uncertainties are large, and new understanding of the dynamics may alter the models significantly--think of clouds and aerosols in climate models.

I don't know enough about these models to speak to what would be such large-but-uncertain elements, but the global claim above needs at least some modification if it is meant to apply to all models.

[jai mitchell]

It seems to me that the cited paper's abstract should be added to the introduction of this thread:

ABSTRACT Record lows in Arctic sea ice extent have been making frequent headlines in recent years. The change in albedo when sea ice is replaced by open water introduces a nonlinearity that has sparked an ongoing debate about the stability of the Arctic sea ice cover and the possibility of Arctic “tipping points.” Previous studies identified instabilities for a shrinking ice cover in two types of idealized climate models: (i) annual-mean latitudinally varying diffusive energy balance models (EBMs) and (ii) seasonally varying single-column models (SCMs). The instabilities in these low-order models stand in contrast with results from comprehensive global climate models (GCMs), which typically do not simulate any such instability. To help bridge the gap between low-order models and GCMs, an idealized model is developed that includes both latitudinal and seasonal variations. The model reduces to a standard EBM or SCM as limiting cases in the parameter space, thus reconciling the two previous lines of research. It is found that the stability of the ice cover vastly increases with the inclusion of spatial communication via meridional heat transport or a seasonal cycle in solar forcing, being most stable when both are included. If the associated parameters are set to values that correspond to the current climate, the ice retreat is reversible and there is no instability when the climate is warmed. The two parameters have to be reduced by at least a factor of 3 for instability to occur. This implies that the sea ice cover may be substantially more stable than has been suggested in previous idealized modeling studies.

an offhand comment:  Model complexity doesn't affect sea ice stability! Not one bit!!!   

[epiphyte]

an offhand comment:  Model complexity doesn't affect sea ice stability! Not one bit!!!   

Oh I don't know - the convection from the increasing volumes of hot air generated by the ensuing debates might cause a fork in the jetstream, shifting the polar vortex southwards and channeling a series of typhoon remnants up over the pole in the middle of September, thereby dumping warm water on the last of the FYI and ironically causing it all to melt just before three feet of snow would otherwise have fallen on it and dramatically reduced the refreeze, and inadvertently acting to stabilize what would otherwise have been the perfect setup for a bonzo crash next year.

...Or something like that.
Or not

[ktonine]

So now we have two models, both of which show a bifurcation effect. The models are unrealistically simple, but they still are assumed to reveal truths about the behavior of the sea ice.

Thanks OSweetMrMath!  I suspect you enjoyed putting those notes together - I certainly enjoyed and appreciated reading them.

 ...Thus at best all that can be said from this work is that the models do not detect instability IN THE MODELS under the given conditions....

Agreed on the 1st point.  Thanks, OSweetMrMath, thorough and only as wordy as needed.

Adam, the takeaway is really that those models that *did* suggest a tipping point were *too* simple.  By adding just a couple of real-world variables - leaving them still lightyears away from the complexity of GCMs - the instabilities disappeared.

It's been almost a decade since Schröder, D., and W. M. Connolley (2007), Impact of instantaneous sea ice removal in a coupled general circulation model, Geophys. Res. Lett., 34, L14502, doi:10.1029/2007GL030253 and 4 years since Tietsche, S., D. Notz, J. H. Jungclaus, and J. Marotzke (2011), Recovery mechanisms of Arctic summer sea ice, Geophys. Res. Lett., 38, L02707, doi:10.1029/2010GL045698.  This paper doesn't tell us anything new about GCMs - except that now we know why the simplest of models were in disagreement with the GCMs (vis a vis tipping points for arctic sea ice). And that the analysis has been decided in favor of the GCMs.

[jai mitchell]

"Not perfect, but perhaps useful"

I recall Gavin Schmidt's discussion on modelling.

it seems to me that any work is good any effort towards a greater understanding is useful.  However, it should also be said that these models must correlate to real world observations to be effective.  There is incredible variability in these parameters, a residual but compounding interactive effect (the butterfly wings) could result in extreme model behavior and, if this interaction isn't well understood, may lead to model failure.

I have yet to see a coherent argument here that discusses how the model holds that, under current climate system forcings that the arctic sea ice is set to follow the model results and enact a  magical "recovery".

This is the results of their model outputs, unless, am I reading the paper incorrectly?  I don't think so!

[ktonine]

I have yet to see a coherent argument here that discusses how the model holds that, under current climate system forcings that the arctic sea ice is set to follow the model results and enact a  magical "recovery".

This is the results of their model outputs, unless, am I reading the paper incorrectly?  I don't think so!

Yes, you've been told several times you are reading it incorrectly.

You still are.

Go read again.

[OSweetMrMath]

Jai,

have yet to see a coherent argument here that discusses how the model holds that, under current climate system forcings that the arctic sea ice is set to follow the model results and enact a  magical "recovery".

This is the results of their model outputs, unless, am I reading the paper incorrectly?  I don't think so!

You are reading the paper incorrectly. The model does not hold that under current forcings, the arctic sea ice is set to recover.

The abstract states, "If the associated parameters are set to values that correspond to the current climate, the ice retreat is reversible and there is no instability when the climate is warmed." (Emphasis added)

You are reading this to say, "at current forcings, the ice retreat will reverse."

This is not what the abstract means, and is not supported by any further discussion in the paper. From the first paragraph of the paper, "Arctic sea ice is undergoing a striking, closely monitored, and highly publicized decline. A recurring theme in the debate surrounding this decline is the question of how stable the ice cover is, and specifically whether it can become unstable." (citations to other papers and references to figures in this paper are omitted from all quotes)

The question is not whether the extent (or other measure) is stable. (In other words, whether the extent will rise to the level of 1980 even in the face of current forcings.) The question is whether the decline is stable. In other words, can the decline transition to a sudden irrecoverable collapse?

From paragraphs 2 and 3, "This nonlinearity has long been expected to affect the stability of the climate system in the sense that it can potentially trigger abrupt transitions between ice-free and ice-covered regimes. ... The idea of an irreversible jump from one stable state to another gained momentum when studies using idealized latitudinally varying diffusive energy balance models (EBMs) of the annual-mean equilibrium state of the global climate encountered such bistability in realistic parameter regimes."

Later in the Introduction, "The discrepancy between the instabilities found in idealized models and the smooth ice retreat found in most comprehensive GCMs raises a conundrum: Is the disagreement between the two approaches the result of a fundamental misrepresentation of the underlying physics in GCMs, or is it rather the result of some aspect of the simplifications used in the idealized models? In more general terms, what physical processes dictate whether there are multiple sea ice states under a given forcing?"

In other words, are there two (or more) possible fixed equilibrium levels for the sea ice under the same forcing? Under a given forcing, the climate system will move toward an equilibrium. Is it possible that the equilibrium depends on the starting climate or the path taken by the climate to the equilibrium?

Section 3 of the paper describes the model results. From the first paragraph of section 3, "In this section we discuss the simulated climate in the parameter regime (D = D* and S₁ = S₁*), first with F = 0, then in the case where the climate is warmed by increasing F, and finally when F is ramped back down." Here D is the heat diffusion from the energy balance model and S₁ is the seasonal variability of solar radiation from the single-column model, both of which I've described in previous posts. F is the forcing.

The results for F=0 are given in the first paragraph of section 3a. "The associated surface temperature and ice thickness are roughly consistent with present-day climate observations in the Northern Hemisphere." The paragraph provides more numerical comparisons and refers to several graphs as well.

The results for increasing F are given in section 3b. The second paragraph of this section states, "the climate climate steadily warms and the seasonally varying sea ice cover steadily recedes until the pole is ice free throughout the year. The summer ice disappears at F = 2.5 W m^-2 and the winter ice at F = 11 W m^-2."

Once the winter ice disappears, the forcing is then decreased until the ice reappears again. The fundamental question is what level the forcing must be reduced to in order for the winter ice to reappear and what further level the forcing must be reduced to in order for the summer ice to reappear. In idealized models (the energy balance model or the single-column model, or similar models cited from other papers), the ice does not reappear until F is far below the level at which it disappeared. In comprehensive GCMs, when the forcing is decreased, the sea ice reappears at the same forcing level at which it disappeared.

The first paragraph of section 3c states that, "It is noteworthy that the sea ice declines smoothly, with no jumps occurring during the transition from perennial sea ice to seasonally ice-free conditions and then to perennially ice-free conditions. Rather, the summer and winter sea ice edges both respond fairly linearly to F." The third paragraph states, "After the climate has become perennially ice free, we slowly ramp F back down again. We find that the the ice recovers during cooling along the same trajectory as the ice retreat during warming, with no hysteresis. The linearity and reversibility of the response in the present model is consistent with results from most comprehensive GCMs, and it is in contrast with previous results from EBMs and SCMs." (Emphasis added)

The paper goes on to state that if S₁ is set to 0 rather than the physically realistic S₁*, the model reduces to an EBM. Likewise, if D is set to 0 rather than the physically realistic D*, the model reduces to an SCM. They then perform the same experiment, of increasing the forcing until the sea ice completely melts, and then decreasing the forcing until the sea ice reappears, in each of these cases.

From paragraphs 5-6 of section 4a, considering the EBM, "The system therefore does not support an ice cover with an equilibrium ice edge poleward of x_i = 0.98, or 79° latitude. We define two critical values of the forcing F: (i) F_w is the value at which the system first transitions to a perennially ice-free pole in a warming scenario, and (ii) F_c is the value at which the wintertime ice cover first reappears in a cooling scenario.… A saddle-node bifurcation occurs at each of these values in the parameter regime…. The width of the hysteresis loop is then defined as deltaF = F_w - F_c. Note that deltaF may be seen as a societally relevant measure of instability and associated irreversibility, since it indicates how much the radiative forcing would need to be reduced for the sea ice to return after crossing a tipping point during global warming, although it should be noted that this requires long time scales for the climate system to equilibrate."

The discussion of the SCM regime is more brief, but states in section 4b, "As in typical SCMs, we find bistability in the parameter regimes (D = 0, S₁ = S₁*), with deltaF = 7.0 W m^-2."

From the Conclusions section, "Previous studies using seasonally varying SCMs and spatially varying EBMs have found instabilities in the sea ice cover associated with the ice–albedo feedback. Studies using comprehensive GCMs, however, have typically not found such instabilities. Here we developed a model of climate and sea ice that includes both seasonal and spatial variations.… When we varied the parameters, we found that including representations of both seasonal and spatial variations causes the stability of the system to substantially increase; that is, any instability and associated bistability was removed.… This result may help to reconcile the discrepancy between low–order models and comprehensive GCMs in previous studies. Specifically, it suggests that the low–order models overestimate the likelihood of a sea ice "tipping point." … (T)he present model simulates sea ice loss that is not only reversible but also has a strikingly linear relationship with the climate forcing as well as with the global–mean temperature. This is in contrast with SCMs and EBMs, and it is consistent with GCMs."

Note that absolutely nowhere in the paper does it state that sea ice levels can rise to a level associated with a lower forcing, even at a higher forcing. In fact, it clearly states that equilibrium sea ice levels are linear with climate forcing. More forcing always results in less ice.

[jai mitchell]

MrO

Thank you for that excellent summary.  I very much appreciate the clarification. 

My daily observations of arctic sea ice behavior of the last 4 years indicates to me that the extreme seasonal variability is based largely on moisture and aerosol introduction at lower to mid troposphere levels,  In the spring.

This indicates a seasonal sensitivity to extremely variable inputs with a timing scale on the order of 1-2 months.  This was my observations of the 2012 fall.  the 2013-2014 "recovery" and the 2015 "return to normal" situations.  Please note that I am not considering extent or area which I feel are anachronistic parameters but rather PIOMAS volume estimates.

due to the extreme variability, then I look at the long-range hindcast to see if sea ice volume actually does track total global radiative forcing.  I find that it does not!  with a significantly accelerated rate of seasonal ice volume loss from 2003 to 2010 when a large increase in anthropogenic aerosols led to the cumulative forcing value to become quite linear, but volume lost increased exponentially!

compare net forcing



with ice volume loss acceleration under linear forcing (global) parameters



What gets me in the gut is that the seasonal inputs of aerosols are shown to be significantly large, with intense swings from positive to negative forcing from winter to spring.  These are regional effects and if they are, then their effects on a seasonal basis, in the arctic would be to severely reduce sea ice loss on the long term trend. 

http://www.reportingclimatescience.com/news-stories/article/aerosols-offset-up-to-22c-of-arctic-warming-says-study.html

The results demonstrate that aerosol-induced cooling has offset between 1.3oC and 2.2oC of greenhouse-gas-induced warming over the past century. The implication is that without aerosol cooling then the already large observed Arctic warming of 1.2oC would have been even bigger. This aerosol cooling offset seems to have been relatively more important in the Arctic than in the world as a whole, the researchers state.

[ktonine]

My daily observations of arctic sea ice behavior of the last 4 years indicates to me that the extreme seasonal variability is based largely on moisture and aerosol introduction at lower to mid troposphere levels,  In the spring.

The extremes of arctic seasonal variablility is what we'd expect given the extreme seasonal variation in solar irradiance.  It's to be expected when you have six-months of winter followed by six-months of summer.

I have to assume you mean large annual variations, but this would be very difficult to show without a complex GCM simulation.  Warmer air holds more moisture. It would be odd if the moisture content did not increase from winter to summer. Similarly, it's long been known that aerosol concentrations are high in late winter/spring and low in summer.  And again, this has much to do with the seasonal temperature increase; cool ice-phase clouds are less efficient at removing aerosols than are warmer clouds - especially when it becomes warm enough for precipitation.

So the simple fact that from winter to summer sees an increase in moisture and a decrease in aerosols is pretty much entirely predictable. Any trend in moisture or aerosols would be necessarily confounded with the a trend in temperature.  With the trend in moisture probably an effect of the trend in temperature and not vice-versa.   

Trends in aerosols will also be confounded by the trends in temperature, but can be analyzed a little easier by looking at the separate trends for atmospheric concentrations and surface concentrations.

[Killian]

I think simple applies here, and is what I was going to say before reading (most) of the thread:

1. If it gets cold enough, ice forms.

2. If it gets warm enough, ice melts.

3. There is no issue of whether or not 1 and 2 are true.

4. I was of the impression everyone understood we'd still have ice at the poles unless or until it gets *really* warm. (<-- I speaks science. ;-) )

5. *Really* warm here is almost certainly past the point of supporting anything like current civilizationm, so the point is only of scientific interest, relatively moot wrt policy.

FYI, 6. there was a paper a year or two ago re Antarctica that, as an aside within the paper, an instantaneous return to 260 (iirc) ppm was modeled. The poles began stabilizing "within decades."

Ergo, 7. no matter what you think of sea ice and bifurcations, the only thing that matters is returning to sub-300 ppm saves an awful lot of hurt in the future. --> Mitigation is key.