Slide 1
I’d like to acknowledge my collaborators Siobhan and Petteri.
Siobhan is at CSIRO, which is the government funded institute in Australia that runs and develops our climate simulator ACCESS.
Petteri was at CSIRO when I began working with him, but he’s now moved to the Finnish Met Institute to become a leader of a research team there.
Siobhan and Petteri are the large-scale coupled modelling experts, and they’re guiding me through that aspect of this project.
Slide 2a
As I’m the only speaker in this minisymposium from outside the US, I thought I’d begin with some geography.
We’re in Stanford, of course, which is roughly located where the red dot is on the left.
I live and work in Adelaide in Australia, which is located roughly at the red dot at the bottom right.
For those of you that like to pick an accent, I originally come from just outside London, which is indicated by the dot in the centre.
Slide 2b
My research focuses on Antarctic sea ice, and particularly the marginal ice zone, which is the sea ice in contact with the open ocean.
Slide 2c
I was taken by the word `issues’ in the title of this conference.
The first issue I want to raise is that I have not been to the Antarctic marginal ice zone.
It’s a bit like trying to get to the moon, and those that get to decide who goes there don’t seem to value sending mathematicians.
The only mathematician I know who has gone there is Ken Golden from Utah, who I’m sure you know.
Slide 3
The marginal ice zone looks very different to the other parts of the ice cover and has very different properties.
These differences revolve around the difference in floe sizes.
By floe I mean a discrete chunk of floating sea ice.
In the interior part of the ice cover, the floes are kilometres in width, and they’re tightly packed. That means the motions are generally slow and the floes grind against each other.
In comparison, the marginal ice zone is a highly dynamic region. The floes there are on the order of tens to hundreds of metres in diameter, and they’re typically separated by open water or slush ice. That means winds and currents easily displace them.
The smaller floe sizes in the marginal ice zone are controlled by ocean surface waves, which propagate into the ice cover and cause breakage.
Slide 4
Several researchers have investigated floe size distributions.
They used aerial photography, which they applied some floe detecting image analysis.
The main finding was that a power law governs the floe size distribution, which is to say that it’s scale invariant.
I’ll note the work of Takenobu Toyota in particular, as he investigated the marginal ice zone. He found that the exponent of the power law is smaller in the marginal ice zone.
This is …
Slide 4
Sea ice models used for operational forecasting and climate research don’t differentiate between the marginal ice zone and the inner pack ice. In particular, they don’t contain information on the smaller floe sizes in the marginal ice zone.
It’s reasonable to ask why they need to.
Historically, the marginal ice zone has been an Antarctic rather than an Arctic phenomenon, because Antarctic sea ice is exposed to the Southern Ocean and the large storm waves created there, whereas Arctic sea ice is shielded by land.
What’s going on in the Arctic tends to dominate the development of sea ice models.
But now, with the onset of climate change, large areas of the Arctic are turning into marginal ice zones.
That’s creating new shipping routes and opportunities for offshore engineering activities, which require models.
It’s also speculated that the different dynamic and thermodynamic properties of the marginal ice zone means the sea ice is retreating more rapidly than we can predict with models designed for continuous pack ice.
That all means that this has become a very active area in the last 2 to 3 years. ONR has two large research initiatives on this topic, for example.
The problem is that no one has been able to quantify the importance of the marginal ice zone yet.
That’s my motivation, although I’m not going to be able to give you a number today.
Slide 5a
Hobart in Tasmania is the base for most of the sea ice scientists in Australia. When I first went there to speak to them, one of the field scientists asked me if I was a modeller or a theoretician.
I told him I was a mathematical modeller, and that I didn’t know which category that fit into.
After a while I worked out that to him I was a theoretician. However, what I’m trying to do in this project is to be a modeller.
Slide 5b
This chap also told me that it was well known that theoreticians and modellers always moan about each other.
Theoreticians tend to do very sophisticated things with idealised models, without much thought as to how they’ll be implemented in large-scale models, and modellers subsequently ignore them.
The work done on modelling the marginal ice zone is a perfect example of this.
Most of what I’ve done in this project has been to strip the theory back till it can be used in a large-scale sea ice model.
Slide 6
The model does require two essential components.
The first is a model of how sea ice breaks up in response to waves.
I’m using Dany Dumont’s work, as a basis for my breakup model.
It models wave-induced breakup as being due to flexural failure.
The cartoon schematic illustrates the model.
Wave motion causes the ice to flex. If the strain exceeds a specified limit, breakup occurs.
The breaking length is a knowledge gap at the moment.
Dany used half a wavelength, as that’s the theoretical distance between successive strain maxima.
I’m planning to test the sensitivity of the model to this parameter.
Slide 7
All we need to know then is the distribution of wave energy in the marginal ice zone.
We can take incident wave forcing from the open ocean from a wave model – I’m using Wavewatch 3.
But, sea ice attenuates the incident wave energy with distance as it travels through the marginal ice zone.
If it didn’t the waves would propagate all the way through the ice cover, breaking it all, and thus turning the entire region of sea ice into a marginal ice zone.
The attenuation is not a simple process though. For example, it’s a low pass filter, which means that it attenuates short period, high frequency waves most rapidly. Long period waves can propagate for hundreds of kilometres before they’re fully attenuated.
Wave scattering theory is standard for modelling the attenuation process. It attributes attenuation as being due to wave reflections produced when waves interact with individual ice floes.
However, viscous theories have also become popular. These model the ice cover as being a viscous continuum on the ocean surface.
It’s likely that these theories are valid in different regimes, which are determined by the properties of the ice cover and the incident waves.
Whilst there’s some debate still going on, I’m using measurements of attenuation, which were made by my collaborator Alison Kohout in the Antarctic marginal ice zone in 2012.
The dataset shows a clear functional relationship between the attenuation rate, alpha, and the wave period. I’ve parameterised that relationship with a simple fit.
This method may be a gross average, but at least it’s real.
Slide 8
I’m implementing the wave attenuation and wave-induced breakup into the CICE sea ice model.
This is the Los Alamos sea ice model, and it’s one of the most popular sea ice model components in operational and research models.
CICE works on a gridded ocean surface, where if we’re talking about climate research the cells are often 1 degree, which is approximately 30kms in length in the marginal ice zone.
I’m using version 4.1. In that version the only place that floe size appears is in the model of lateral melt. At the moment the floe size is set to 300m, as a tuning parameter.
However, the lateral melt affects the ice fraction, which is otherwise known as the surface concentration. This affects the way sea ice is transported around the ocean surface, which affects everything else in the model.
I’ve crudely summarised the CICE algorithm in the bottom block on this slide, and indicated where my code fits into it.
I’ve placed it at the beginning of each timestep so that the floe sizes in the marginal ice zone can influence the subsequent thermodynamics, and hence the dynamics.
Slide 9
In this first version of my model the floe sizes represents the average for each cell.
At each timestep, I pick up an incident wave forcing from the Wavewatch 3 model in cells at some constant latitude outside the ice cover, but as close as possible to cells containing sea ice. That latitude changes in time as the sea ice expands and contracts.
I take average spectral parameters from Wavewatch: these are the significant wave height, the peak period and the mean direction. But I map these to an idealised wave spectrum, which I propagate through the ice cover and attenuate.
I’ve also implemented a simple floe-bonding scheme, which doubles the floe sizes over a time step if the temperatures are low enough till they reach a 300m maximum. This is important, because if I didn’t do this the floes that are broken near the coast in summer remain there during winter.
Slide 10
I’m now going to show you some preliminary results using a standalone version of the CICE model.
They’re from 6 months into a year long run.
The ice fraction is on the left, the significant wave height is in the middle, and the floe sizes are on the right.
They’re essentially to show that the model is working and giving sensible results.
For reasons I won’t attempt to explain, the wave and ice data I used are inconsistent: the wave data is from 1979 and the sea ice data is from around 10 years ago.
So we can’t read too much into the results. But, the results aren’t complete rubbish, as I’ve synchronised the days and times during the year.
Note that in certain regions, particularly on the east here, the waves have to travel hundreds of kilometres to reach the sea ice. I’m only considering attenuation due to sea ice.
Slide 11
The results on this slide show the differences to the ice fraction and ice thickness caused by the smaller floe sizes.
They’re the results of the run with the smaller sizes minus the results from a baseline run with the floes set to 300m throughout the ice cover.
The ice fraction shows the greatest differences at the ice edge, i.e. the marginal ice zone, which is to be expected. The trend is generally for the smaller floes to produce a lower fraction, which, again, is to be expected, although there’s also a region of higher concentration, which is likely due to some impact on the ice transport.
The thickness shows the greatest changes deep into the ice cover, which is likely a memory from where the ice edge was during the summer.
Remember, these are difference over only 6 months, and are likely to increase for runs of several years or decades.
Slide 12
I’m now driving towards that goal of quantifying the impact of small floes in the marginal ice zone on the Antarctic sea ice.
I’m also planning to implement the new floe sizes into the latest version of CICE, which has an updated transport model, which explicitly depends on floe size.
Finally, there’s the question of validation, which I’ll only say will be challenging.