In Part Seven – GCM I through Part Ten – GCM IV we looked at GCM simulations of ice ages.
These were mostly attempts at “glacial inception”, that is, starting an ice age. But we also saw a simulation of the last 120 kyrs which attempted to model a complete ice age cycle including the last termination. As we saw, there were lots of limitations..
One condition for glacial inception, “perennial snow cover at high latitudes”, could be produced with a high-resolution coupled atmosphere-ocean GCM (AOGCM), but that model did suffer from the problem of having a cold bias at high latitudes.
The (reasonably accurate) simulation of a whole cycle including inception and termination came by virtue of having the internal feedbacks (ice sheet size & height and CO2 concentration) prescribed.
Just to be clear to new readers, these comments shouldn’t indicate that I’ve uncovered some secret that climate scientists are trying to hide, these points are all out in the open and usually highlighted by the authors of the papers.
In Part Nine – GCM III, one commenter highlighted a 2013 paper by Ayako Abe-Ouchi and co-workers, where the journal in question, Nature, had quite a marketing pitch on the paper. I made brief comment on it in a later article in response to another question, including that I had emailed the lead author asking a question about the modeling work (how was a 120 kyr cycle actually simulated?).
Most recently, in Eighteen – “Probably Nonlinearity” of Unknown Origin, another commented highlighted it, which rekindled my enthusiasm, and I went back and read the paper again. It turns out that my understanding of the paper had been wrong. It wasn’t really a GCM paper at all. It was an ice sheet paper.
There is a whole field of papers on ice sheet models deserving attention.
Let’s review GCMs first of all to help us understand where ice sheet models fit in the hierarchy of climate simulations.
GCMs consist of a number of different modules coupled together. The first GCMs were mostly “atmospheric GCMs” = AGCMs, and either they had a “swamp ocean” = a mixed layer of fixed depth, or had prescribed ocean boundary conditions set from an ocean model or from an ocean reconstruction.
Less commonly, unless you worked just with oceans, there were ocean GCMs with prescribed atmospheric boundary conditions (prescribed heat and momentum flux from the atmosphere).
Then coupled atmosphere-ocean GCMs came along = AOGCMs. It was a while before these two parts matched up to the point where there was no “flux drift”, that is, no disappearing heat flux from one part of the model.
Why so difficult to get these two models working together? One important reason comes down to the time-scales involved, which result from the difference in heat capacity and momentum of the two parts of the climate system. The heat capacity and momentum of the ocean is much much higher than that of the atmosphere.
And when we add ice sheets models – ISMs – we have yet another time scale to consider.
- the atmosphere changes in days, weeks and months
- the ocean changes in years, decades and centuries
- the ice sheets changes in centuries, millennia and tens of millenia
This creates a problem for climate scientists who want to apply the fundamental equations of heat, mass & momentum conservation along with parameterizations for “stuff not well understood” and “stuff quite-well-understood but whose parameters are sub-grid”. To run a high resolution AOGCM for a 1,000 years simulation might consume 1 year of supercomputer time and the ice sheet has barely moved during that period.
Ice Sheet Models
Scientists who study ice sheets have a whole bunch of different questions. They want to understand how the ice sheets developed.
What makes them grow, shrink, move, slide, melt.. What parameters are important? What parameters are well understood? What research questions are most deserving of attention? And:
Does our understanding of ice sheet dynamics allow us to model the last glacial cycle?
To answer that question we need a model for ice sheet dynamics, and to that we need to apply some boundary conditions from some other “less interesting” models, like GCMs. As a result, there are a few approaches to setting the boundary conditions so we can do our interesting work of modeling ice sheets.
Before we look at that, let’s look at the dynamics of ice sheets themselves.
Ice Sheet Dynamics
First, in the theme of the last paper, Eighteen – “Probably Nonlinearity” of Unknown Origin, here is Marshall & Clark 2002:
The origin of the dominant 100-kyr ice-volume cycle in the absence of substantive radiation forcing remains one of the most vexing questions in climate dynamics
We can add that to the 34 papers reviewed in that previous article. This paper by Marshall & Clark is definitely a good quick read for people who want to understand ice sheets a little more.
Ice doesn’t conduct a lot of heat – it is a very good insulator. So the important things with ice sheets happen at the top and the bottom.
At the top, ice melts, and the water refreezes, runs off or evaporates. In combination, the loss is called ablation. Then we have precipitation that adds to the ice sheet. So the net effect determines what happens at the top of the ice sheet.
At the bottom, when the ice sheet is very thin, heat can be conducted through from the atmosphere to the base and make it melt – if the atmosphere is warm enough. As the ice sheet gets thicker, very little heat is conducted through. However, there are two important sources of heat for surface heating which results in “basal sliding”. One source is geothermal energy. This is around 0.1 W/m² which is very small unless we are dealing with an insulating material (like ice) and lots of time (like ice sheets). The other source is the shear stress in the ice sheet which can create a lot of heat via the mechanics of deformation.
Once the ice sheet is able to start sliding, the dynamics create a completely different result compared to an ice sheet “cold-pinned” to the rock underneath.
Some comments from Marshall and Clark:
Ice sheet deglaciation involves an amount of energy larger than that provided directly from high-latitude radiation forcing associated with orbital variations. Internal glaciologic, isostatic, and climatic feedbacks are thus essential to explain the deglaciation.
..Moreover, our results suggest that thermal enabling of basal flow does not occur in response to surface warming, which may explain why the timing of the Termination II occurred earlier than predicted by orbital forcing [Gallup et al., 2002].
Results suggest that basal temperature evolution plays an important role in setting the stage for glacial termination. To confirm this hypothesis, model studies need improved basal process physics to incorporate the glaciological mechanisms associated with ice sheet instability (surging, streaming flow).
..Our simulations suggest that a substantial fraction (60% to 80%) of the ice sheet was frozen to the bed for the first 75 kyr of the glacial cycle, thus strongly limiting basal flow. Subsequent doubling of the area of warm-based ice in response to ice sheet thickening and expansion and to the reduction in downward advection of cold ice may have enabled broad increases in geologically- and hydrologically-mediated fast ice flow during the last deglaciation.
Increased dynamical activity of the ice sheet would lead to net thinning of the ice sheet interior and the transport of large amounts of ice into regions of intense ablation both south of the ice sheet and at the marine margins (via calving). This has the potential to provide a strong positive feedback on deglaciation.
The timescale of basal temperature evolution is of the same order as the 100-kyr glacial cycle, suggesting that the establishment of warm-based ice over a large enough area of the ice sheet bed may have influenced the timing of deglaciation. Our results thus reinforce the notion that at a mature point in their life cycle, 100-kyr ice sheets become independent of orbital forcing and affect their own demise through internal feedbacks.
In this article we will focus on a 2007 paper by Ayako Abe-Ouchi, T Segawa & Fuyuki Saito. This paper is essentially the same modeling approach used in Abe-Ouchi’s 2013 Nature paper.
The Ice Model
The ice sheet model has a time step of 2 years, with 1° grid from 30°N to the north pole, 1° longitude and 20 vertical levels.
Equations for the ice sheet include sliding velocity, ice sheet deformation, the heat transfer through the lithosphere, the bedrock elevation and the accumulation rate on the ice sheet.
Note, there is a reference that some of the model is based on work described in Sensitivity of Greenland ice sheet simulation to the numerical procedure employed for ice sheet dynamics, F Saito & A Abe-Ouchi, Ann. Glaciol., (2005) – but I don’t have access to this journal. (If anyone does, please email the paper to me at scienceofdoom – you know what goes here – gmail.com).
How did they calculate the accumulation on the ice sheet? There is an equation:
Ts is the surface temperature, dP is a measure of aridity and Aref is a reference value for accumulation. This is a highly parameterized method of calculating how much thicker or thinner the ice sheet is growing. The authors reference Marshall et al 2002 for this equation, and that paper is very instructive in how poorly understood ice sheet dynamics actually are.
Here is one part of the relevant section in Marshall et al 2002:
..For completeness here, note that we have also experimented with spatial precipitation patterns that are based on present-day distributions.
Under this treatment, local precipitation rates diminish exponentially with local atmospheric cooling, reflecting the increased aridity that can be expected under glacial conditions (Tarasov and Peltier, 1999).
Paleo-precipitation under this parameterization has the form:
P(λ,θ,t) = Pobs(λ,θ)(1+dp)ΔT(λ,θ,t) x exp[βp.max[hs(λ,θ,t)-ht,0]] (18)
The parameter dP in this equation represents the percentage of drying per 1C; Tarasov and Peltier (1999) choose a value of 3% per °C; dp = 0:03.
[Emphasis added, color added to highlight the relevant part of the equation]
So dp is a parameter that attempts to account for increasing aridity in colder glacial conditions, and in their 2002 paper Marshall et al describe it as 1 of 4 “free parameters” that are investigated to see what effect they have on ice sheet development around the LGM.
Abe-Ouchi and co-authors took a slightly different approach that certainly seems like an improvement over Marshall et al 2002:
So their value of aridity is just a linear function of ice sheet area – from zero to a fixed value, rather than a fixed value no matter the ice sheet size.
How is Ts calculated? That comes, in a way, from the atmospheric GCM, but probably not in a way that readers might expect. So let’s have a look at the GCM then come back to this calculation of Ts.
Atmospheric GCM Simulations
There were three groups of atmospheric GCM simulations, with parameters selected to try and tease out which factors have the most impact.
Group One: high resolution GCM – 1.1º latitude and longitude and 20 atmospheric vertical levels with fixed sea surface temperature. So there is no ocean model, the ocean temperature are prescribed. Within this group, four experiments:
- A control experiment – modern day values
- LGM (last glacial maximum) conditions for CO2 (note 1) and orbital parameters with
- no ice
- LGM ice extent but zero thickness
- LGM ice extent and LGM thickness
So the idea is to compare results with and without the actual ice sheet so see how much impact orbital and CO2 values have vs the effect of the ice sheet itself – and then for the ice sheet to see whether the albedo or the elevation has the most impact. Why the elevation? Well, if an ice sheet is 1km thick then the surface temperature will be something like 6ºC colder. (Exactly how much colder is an interesting question because we don’t know what the lapse rate actually was). There will also be an effect on atmospheric circulation – you’ve stuck a “mountain range” in the path of wind so this changes the circulation.
Each of the four simulations was run for 11 or 13 years and the last 10 years’ results used:
From Abe-Ouchi et al 2007
It’s clear from this simulation that the full result (left graphic) is mostly caused by the ice sheet (right graphic) rather than CO2, orbital parameters and the SSTs (middle graphic). And the next figure in the paper shows the breakdown between the albedo effect and the height of the ice sheet:
From Abe-Ouchi et al 2007
Figure 2 – same color legend as figure 1
Now a lapse rate of 5K/km was used. What happens if the lapse rate of 9K/km was used instead? There were no simulations done with different lapse rates.
..Other lapse rates could be used which vary depending on the altitude or location, while a lapse rate larger than 7 K/km or smaller than 4 K/km is inconsistent with the overall feature. This is consistent with the finding of Krinner and Genthon (1999), who suggest a lapse rate of 5.5 K/km, but is in contrast with other studies which have conventionally used lapse rates of 8 K/km or 6.5 K/km to drive the ice sheet models..
Group Two – medium resolution GCM 2.8º latitude and longitude and 11 atmospheric vertical levels, with a “slab ocean” – this means the ocean is treated as one temperature through the depth of some fixed layer, like 50m. So it is allowing the ocean to be there as a heat sink/source responding to climate, but no heat transfer through to a deeper ocean.
There were five simulations in this group, one control (modern day everything) and four with CO2 & orbital parameters at the LGM:
- no ice sheet
- LGM ice extent, but flat
- 12 kyrs ago ice extent, but flat
- 12 kyrs ago ice extent and height
So this group takes a slightly more detailed look at ice sheet impact. Not surprisingly the simulation results give intermediate values for the ice sheet extent at 12 kyrs ago.
Group Three – medium resolution GCM as in group two, and ice sheets either at present day or LGM, with nine simulations covering different orbital values, different CO2 values of present day, 280 or 200 ppm.
There was also some discussion of the impact of different climate models. I found this fascinating because the difference between CCSM and the other models appears to be as great as the difference in figure 2 (above) which identifies the albedo effect as more significant than the lapse rate effect:
From Abe-Ouchi et al 2007
And this naturally has me wondering about how much significance to put on the GCM simulation results shown in the paper. The authors also comment:
Based on these GCM results we conclude there remains considerable uncertainty over the actual size of the albedo effect.
Given there is also uncertainty over the lapse rate that actually occurred, it seems there is considerable uncertainty over everything.
Now let’s return to the ice sheet model, because so far we haven’t seen any output from the ice sheet model.
GCM Inputs into the Ice Sheet Model
The equation which calculates the change in accumulation on the ice sheet used a fairly arbitrary parameter dp, with (1+dp) raised to the power of Ts.
The ice sheet model has a 2 year time step. The GCM results don’t provide Ts across the surface grid every 2 years, they are snapshots for certain conditions. The ice sheet model uses this calculation for Ts:
Ts = Tref + ΔTice + ΔTco2 + ΔTinsol + ΔTnonlinear
Tref is the reference temperature which is present day climatology. The other ΔT (change in temperature) values are basically a linear interpolation from two values of the GCM simulations. Here is the ΔTCo2 value:
So think of it like this – we have found Ts at one value of CO2 higher and one value of CO2 lower from some snapshot GCM simulations. We plot a graph with Co2 on the x-axis and Ts on the y-axis with just two points on the graph from these two experiments and we draw a straight line between the two points.
To calculate Ts at say 50 kyrs ago we look up the CO2 value at 50 kyrs from ice core data, and read the value of TCO2 from the straight line on the graph.
Likewise for the other parameters. Here is ΔTinsol:
So the method is extremely basic. Of course the model needs something..
Now, given that we have inputs for accumulation on the ice sheet, the ice sheet model can run. Here are the results. The third graph (3) is the sea level from proxy results so is our best estimate of reality, with (4) providing model outputs for different parameters of d0 (“desertification” or aridity) and lapse rate, and (5) providing outputs for different parameters of albedo and lapse rate:
From Abe-Ouchi et al 2007
There are three main points of interest.
Firstly, small changes in the parameters cause huge changes in the final results. The idea of aridity over ice sheets as just linear function of ice sheet size is very questionable itself. The idea of a constant lapse rate is extremely questionable. Together, using values that appear realistic, we can model much less ice sheet growth (sea level drop) or many times greater ice sheet growth than actually occurred.
Secondly, notice that the time of maximum ice sheet (lowest sea level) for realistic results show sea level starting to rise around 12 kyrs, rather than the actual 18 kyrs. This might be due to the impact of orbital factors which were at quite a low level (i.e., high latitude summer insolation was at quite a low level) when the last ice age finished, but have quite an impact in the model. Of course, we have covered this “problem” in a few previous articles in this series. In the context of this model it might be that the impact of the southern hemisphere leading the globe out of the last ice age is completely missing.
Thirdly – while this might be clear to some people, but for many new to this kind of model it won’t be obvious – the inputs for the model are some limits of the actual history. The model doesn’t simulate the actual start and end of the last ice age “by itself”. We feed into the GCM model a few CO2 values. We feed into the GCM model a few ice sheet extent and heights that (as best as can be reconstructed) actually occurred. The GCM gives us some temperature values for these snapshot conditions.
In the case of this ice sheet model, every 2 years (each time step of the ice sheet model) we “look up” the actual value of ice sheet extent and atmospheric CO2 and we linearly interpolate the GCM output temperatures for the current year. And then we crudely parameterize these values into some accumulation rate on the ice sheet.
This is our first foray into ice sheet models. It should be clear that the results are interesting but we are at a very early stage in modeling ice sheets.
The problems are:
- the computational load required to run a GCM coupled with an ice sheet model over 120 kyrs is much too high, so it can’t be done
- the resulting tradeoff uses a few GCM snapshot values to feed linearly interpolated temperatures into a parameterized accumulation equation
- the effect of lapse rate on the results is extremely large and the actual value for lapse rate over ice sheets is very unlikely to be a constant and is also not known
- our understanding of ice sheet fundamental equations are still at an early stage, as readers can see by reviewing the first two papers below, especially the second one
Articles in this Series
Part One – An introduction
Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz
Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory
Part Four – Understanding Orbits, Seasons and Stuff – how the wobbles and movements of the earth’s orbit affect incoming solar radiation
Part Five – Obliquity & Precession Changes – and in a bit more detail
Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name
Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago
Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers
Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover
Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs
Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs
Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age
Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2
Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland
Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II
Fourteen – Concepts & HD Data – getting a conceptual feel for the impacts of obliquity and precession, and some ice age datasets in high resolution
Fifteen – Roe vs Huybers – reviewing In Defence of Milankovitch, by Gerard Roe
Sixteen – Roe vs Huybers II – remapping a deep ocean core dataset and updating the previous article
Seventeen – Proxies under Water I – explaining the isotopic proxies and what they actually measure
Eighteen – “Probably Nonlinearity” of Unknown Origin – what is believed and what is put forward as evidence for the theory that ice age terminations were caused by orbital changes
Basal temperature evolution of North American ice sheets and implications for the 100-kyr cycle, SJ Marshall & PU Clark, GRL (2002) – free paper
North American Ice Sheet reconstructions at the Last Glacial Maximum, SJ Marshall, TS James, GKC Clarke, Quaternary Science Reviews (2002) – free paper
Climatic Conditions for modelling the Northern Hemisphere ice sheets throughout the ice age cycle, A Abe-Ouchi, T Segawa, and F Saito, Climate of the Past (2007) – free paper
Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume, Ayako Abe-Ouchi, Fuyuki Saito, Kenji Kawamura, Maureen E. Raymo, Jun’ichi Okuno, Kunio Takahashi & Heinz Blatter, Nature (2013) – paywall paper
Note 1 – the value of CO2 used in these simulations was 200 ppm, while CO2 at the LGM was actually 180 ppm. Apparently this value of 200 ppm was used in a major inter-comparison project (the PMIP), but I don’t know the reason why. PMIP = Paleoclimate Modelling Intercomparison Project, Joussaume and Taylor, 1995.