The Warmer The Icier

Guest Post by Willis Eschenbach

A WUWT commenter emailed me with a curious claim. I have described various emergent phenomena that regulate the surface temperature. These operate on time scales ranging from minutes to hours (e.g. dust devils, thunderstorms) to multi-decadal (e.g. Atlantic Multidecadal Oscillation, Pacific Decadal Oscillation). He suggested that there is also a much slower thermostatic mechanism at play over thousands of years and longer.  Here’s how I understand it.

He said that when it gets warmer, the atmosphere is more moist, so there is more snow on Antarctica. This translates into more ice on the ice cap, which puts increased pressure on the ice below. Now, the ice gain at the surface and the ice loss in the calving of the Antarctic glaciers is in some kind of long-term very slow-moving steady state. Pressure at the top squeezes out the ice on all sides. So increasing the ice mass over time would lead to more calving, which in turn would cool the surrounding ocean. He said this slow process shown below functioned as a long-term factor promoting thermal stability.

Warming –> increased Antarctic snowfall –> thicker ice cap –> increased iceberg calving –> cooling

He suggested I should look into the rate at which the ice has historically accumulated at the Vostok ice core location in Antarctica. He thought that the ice accumulation rate was a function of temperature. His idea was that Vostok shows that increased temperatures lead to increased antarctic snowfall, which in turn increases the rate at which the ice accumulates on Antarctica. So I took a look.

The ice core from Vostok is a technological marvel. They drilled 3.3 kilometers (two miles) straight down into the ice, and extracted a core of undisturbed ice. Then they analyzed it one metre by one metre, along the entire length of the core. The variations in temperature calculated from the core are well-known, they show the history of the last four ice ages:

Figure 1. Temperature record from the Vostok ice core. The zero point on the temperature scale is modern-day temperature. Temperature is calculated from the variations in the 18O oxygen isotope as recorded in the ice core. Present-day values are at the left of the graph. DATA SOURCE: NOAA Paleoclimate

Here, you can see the ice ages, interrupted by short periods of warming … well, short by geological scales at any rate. The most recent warm period, on the left, has lasted about 10,000 year (10 kya). (As an aside, for me the mystery is not what it was that slowly and gradually pushed us into each ice age with lots of fits and starts. The thing that perplexes me is what it was that abruptly yanked us out of each ice age in one extremely fast period of great warming. But I digress …)

Although I had seen that before, I’d never looked at the ice accumulation rates. Figure 2 shows the annual rate of accumulation of ice at Vostok.

Figure 2. Ice accumulation rate record from the Vostok ice core. Since the measurements are taken every metre along the ice core, the accumulation rate is calculated as the reciprocal of the age differences from one measurement to the next. Present-day values are at the left of the graph.

Urg. That was not too appealing. Clearly, what we are seeing is the progressive compression of the ice layers as we drill deeper and deeper into the ice cap. Millions of tonnes of ice on top have progressively flattened the deeper layers. Makes it hard to see any relationship. I considered various ways to model the compression of the layers and remove it … and discarded them all.

What I did notice, though, was that as we see at the left hand end of the graphic above, new snow is fairly bulky. But it gets compressed quite rapidly at first. After that initial rapid compression of the snow into ice, however, the compression is somewhat linear from that time onwards. So I decided to omit that first part of the data, which is about five thousand years. I then plotted up the remaining ice accumulation data, and I included the temperature data on the same graph so I could compare them.

Figure 3. Ice accumulation rate record (blue) and temperature record (red) from the Vostok ice core. Both records start a 5000 years before present. Recent values are at the left of the graph.

Dang … surprisingly, his claim was looking much, much better. So I took a first cut at modeling the ice accumulation rate from the temperature data. I’ve included the depth as a second explanatory variable. Here is the result of the estimation of the ice accumulation rate as a function of depth and temperature:

Figure 4. Ice accumulation rate record (blue), temperature record (red), and estimated ice accumulation rate based on temperature and age (black) from the Vostok ice core. All records start at 5000 years before present. Recent values are at the left of the graph.

Now we’re getting somewhere, but there is still a problem. Because the layers are progressively flattened with depth, the response of the ice accumulation rate to temperature is also progressively flattened with depth. To allow for this, I included the product of the two variables (depth and temperature) in the analysis, giving the following result:

Figure 5. Ice accumulation rate record (blue), temperature record (red), and estimated ice accumulation rate based on temperature, age, and age*temperature (black) from the Vostok ice core. All records start at 5000 years before present. Recent values are at the left of the graph.

Well, there you have it. Ice accumulation in Antarctica is assuredly a function of temperature. What’s not to like? His hypothesis is obviously correct. Done and dusted, right?

Well … in a word, no. I didn’t like it at all.

The problem that I had with the good fit is an odd one … the fit is too darn good. Nothing in nature fits that well, down to the tiny wiggles in the blue and black lines at the right of the graphic. Correlations that good make my nose twitch, they set off my bad number detector..

I had started with the raw data and no preconceptions. Now I knew what I was looking at and looking for, so I went off to research what might explain it. To do that, I looked at the various methods for dating an ice core. Turns out there are four of them—count the annual rings, align to known events, radioactive dating, and use a “flow model”. Problem is that the first three methods only get us back about 80,000 years into the past. Beyond that, it’s all flow models. Which is OK, and they are likely fairly accurate. The problem lies elsewhere, in the input variables to the various flow models. Here’s the list of what goes into the models:

• Temperature
• Ice thickness
• Flow patterns
• Gross accumulation rates
• Ice rheology, the study of how much ice deforms and moves in response to pressure.

I’m sure you can see the problem. In my calculations, the net accumulation rate shown in blue above is a function of the age change per metre of ice core. Makes perfect sense, that’s how you calculate it. If it takes a hundred years to add a metre of ice, the accumulation rate is equal to 1 metre / 100 years = 10 mm/year.

The problem is that in their model, the age change per metre in turn is very much a function of the temperature. And that means that we expect the net accumulation rate to be a function of the temperature. It is inherent in the calculation—accumulation is a function of age, and age is a function of temperature, so accumulation is a function of temperature.

As a result, the graphs that I have shown above have very little inherent meaning. It’s like showing that one equals one. The commenter was correct that he found a correlation … it just didn’t prove anything.

This also means we cannot use the correlation above to support the commenter’s theory that increased temperature leads to increased accumulation rates.

However, all is not lost. This analysis does point out one important thing—the best judgement of the scientists studying the question is that indeed, ice accumulation rates in Antarctica are strongly positively correlated with temperature. They say that counterintuitively, a warmer world indeed means more Antarctic ice.

So … IF the scientists are indeed right, then this analysis also allows for a couple more deductions. One is that near the surface, which is to say near the present, the depth and depth*temperature terms of the estimate are small. This means that the recent annual addition of snowfall to the icecap is about 20 mm (of ice equivalent) per year.  The change in that accumulation rate per degree of warming is about 1.25 mm/year This implies that for each additional °C of warming, the accumulation rate goes up/down by about 6%.

The graph also shows that during the end of the most recent ice age, the annual accumulation rate was only about half of the current rate.

All of which would suggest that the change is large enough to support the idea of a slow restorative force opposing any change in temperature. Since at the start of an ice age the annual addition to the icecap drops rapidly to as low as 50-60% of its previous value, surely that much of a decrease in ice accumulation must result in a correspondingly reduced amount of iceberg calving at the ocean.

How much energy is involved in the change? Well, to first melt and then evaporate a cubic metre of ice takes about 90 watt-years of energy. The change in accumulation rate between ice age and interglacial is about 10 mm/year, which is about a metre per century difference.

This means that the change in energy between ice age and interglacial due to the variation in ice buildup is about 0.9 watts per square metre constant change over the surface of Antarctica. This is a fairly small effect.

However, in contemplating this situation, I realized that one oddity of this method of moving latent heat around in the form of ice is that the ice is added over two dimensions, over the surface area of Antarctica. But at the other end of the process, the ice is squeezed out in one dimension, along the coastline. Given the relative area (11.1E+6 km^2) and the coastline length (18.0E+3 km) of Antarctica, this is a concentration of about six hundred to one. This means the 0.9 W/m2 across the continent becomes about 0.9 * 618 ≈ 550 watts of heating or cooling per metre of coastline. This variation in iceberg calving rate represents a strong local change immediately adjacent to the coastline.

Next, let’s consider what this variation in ice calving rate along the Antarctic coastline does. The key underlying concept to keep in mind is that vast amounts of heat are being exported constantly from the tropics to the poles, where the heat is radiated into space. The transportation is done by both the ocean and the atmosphere, both of which move heat polewards 24/7.

As a result, the rate at which the planet can lose energy is constrained by the speed of the oceanic and atmospheric circulation. The general rule is, anything that speeds up oceanic circulation will cool the planet down, and vice versa.

The circulation around Antarctica is shown below.

Figure 6. Circulation patterns around Antarctica (right side of drawing).

Setting the details aside, the takeaway message from this graphic is that when the Antarctic coastline gets more ice input from the glaciers, the speed of the circulation increases because more cold water is sinking downwards around the continent.

And on the other hand, when there is less ice around the Antarctic coast the circulation will slow down. There will be less cold water to drive the downwelling leg of the thermal circulation.

So the entire feedback loop looks like this:

Warmer southern ocean –> wetter atmosphere –> more snow on Antarctic interior –> more glacier calving around Antarctic perimeter –> increased oceanic circulation –> increased global cooling.

Anyhow, that’s what I found out today. Of course, your conclusions from the same facts may be totally different …

Regards to everyone,

w.

My Usual Request: If you disagree with me or anyone, please quote the exact words you disagree with. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.

My Other Request: If you think that e.g. I’m using the wrong method on the wrong dataset, please educate me and others by demonstrating the proper use of the right method on the right dataset. Simply claiming I’m wrong doesn’t advance the discussion.

EDIT: Willis accidentally left figure 6 out of the body of the text, but made it the featured image for the post from the set of images he uploaded. I’ve corrected that problem – Anthony