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## The Arctic Has Barfed

I was scanning my blog stats the other day – partly to see if people were reading my new post on the Blue Mountains bushfires, partly because I just like graphs – when I noticed that an article I wrote nearly two years ago was suddenly getting more views than ever before:

The article in question highlights the scientific inaccuracies of the 2004 film The Day After Tomorrow, in which global warming leads to a new ice age. Now that I’ve taken more courses in thermodynamics I could definitely expand on the original post if I had the time and inclination to watch the film again…

I did a bit more digging in my stats and discovered that most viewers are reaching this article through Google searches such as “is the day after tomorrow true”, “is the day after tomorrow likely to happen”, and “movie review of a day after tomorrow if it is possible or impossible.” The answers are no, no, and impossible, respectively.

But why the sudden surge in interest? I think it is probably related to the record cold temperatures across much of the United States, an event which media outlets have dubbed the “polar vortex”. I prefer “Arctic barf”.

Part of the extremely cold air mass which covers the Arctic has essentially detached and spilled southward over North America. In other words, the Arctic has barfed on the USA. Less sexy terminology than “polar vortex”, perhaps, but I would argue it is more enlightening.

Greg Laden also has a good explanation:

The Polar Vortex, a huge system of swirling air that normally contains the polar cold air has shifted so it is not sitting right on the pole as it usually does. We are not seeing an expansion of cold, an ice age, or an anti-global warming phenomenon. We are seeing the usual cold polar air taking an excursion.

Note that other regions such as Alaska and much of Europe are currently experiencing unusually warm winter weather. On balance, the planet isn’t any colder than normal. The cold patches are just moving around in an unusual way.

Having grown up in the Canadian Prairies, where we experience daily lows below -30°C for at least a few days each year (and for nearly a month straight so far this winter), I can’t say I have a lot of sympathy. Or maybe I’m just bitter because I never got a day off school due to the cold? But seriously, nothing has to shut down if you plug in the cars at night and bundle up like an astronaut. We’ve been doing it for years.

## A Simple Stochastic Climate Model: Climate Sensitivity

Last time I derived the following ODE for temperature T at time t:



where S and τ are constants, and F(t) is the net radiative forcing at time t. Eventually I will discuss each of these terms in detail; this post will focus on S.

At equilibrium, when dT/dt = 0, the ODE necessitates T(t) = S F(t). A physical interpretation for S becomes apparent: it measures the equilibrium change in temperature per unit forcing, also known as climate sensitivity.

A great deal of research has been conducted with the aim of quantifying climate sensitivity, through paleoclimate analyses, modelling experiments, and instrumental data. Overall, these assessments show that climate sensitivity is on the order of 3 K per doubling of CO2 (divide by 5.35 ln 2 W/m2 to convert to warming per unit forcing).

The IPCC AR4 report (note that AR5 was not yet published at the time of my calculations) compared many different probability distribution functions (PDFs) of climate sensitivity, shown below. They follow the same general shape of a shifted distribution with a long tail to the right, and average 5-95% confidence intervals of around 1.5 to 7 K per doubling of CO2.

Box 10.2, Figure 1 of the IPCC AR4 WG1: Probability distribution functions of climate sensitivity (a), 5-95% confidence intervals (b).

These PDFs generally consist of discrete data points that are not publicly available. Consequently, sampling from any existing PDF would be difficult. Instead, I chose to create my own PDF of climate sensitivity, modelled as a log-normal distribution (e raised to the power of a normal distribution) with the same shape and bounds as the existing datasets.

The challenge was to find values for μ and σ, the mean and standard deviation of the corresponding normal distribution, such that for any z sampled from the log-normal distribution,





Since erf, the error function, cannot be evaluated analytically, this two-parameter problem must be solved numerically. I built a simple particle swarm optimizer to find the solution, which consistently yielded results of μ = 1.1757, σ = 0.4683.

The upper tail of a log-normal distribution is unbounded, so I truncated the distribution at 10 K, consistent with existing PDFs (see figure above). At the beginning of each simulation, climate sensitivity in my model is sampled from this distribution and held fixed for the entire run. A histogram of 106 sampled points, shown below, has the desired characteristics.

Histogram of 106 points sampled from the log-normal distribution used for climate sensitivity in the model.

Note that in order to be used in the ODE, the sampled points must then be converted to units of Km2/W (warming per unit forcing) by dividing by 5.35 ln 2 W/m2, the forcing from doubled CO2.

## Bits and Pieces

Now that the academic summer is over, I have left Australia and returned home to Canada. It is great to be with my friends and family again, but I really miss the ocean and the giant monster bats. Not to mention the lab: after four months as a proper scientist, it’s very hard to be an undergrad again.

While I continue to settle in, move to a new apartment, and recover from jet lag (which is way worse in this direction!), here are a few pieces of reading to tide you over:

Scott Johnson from Ars Technica wrote a fabulous piece about climate modelling, and the process by which scientists build and test new components. The article is accurate and compelling, and features interviews with two of my former supervisors (Steve Easterbrook and Andrew Weaver) and lots of other great communicators (Gavin Schmidt and Richard Alley, to name a few).

I have just started reading A Short History of Nearly Everything by Bill Bryson. So far, it is one of the best pieces of science writing I have ever read. As well as being funny and easy to understand, it makes me excited about areas of science I haven’t studied since high school.

Finally, my third and final paper from last summer in Victoria was published in the August edition of Journal of Climate. The full text (subscription required) is available here. It is a companion paper to our recent Climate of the Past study, and compares the projections of EMICs (Earth System Models of Intermediate Complexity) when forced with different RCP scenarios. In a nutshell, we found that even after anthropogenic emissions fall to zero, it takes a very long time for CO2 concentrations to recover, even longer for global temperatures to start falling, and longer still for sea level rise (caused by thermal expansion alone, i.e. neglecting the melting of ice sheets) to stabilize, let alone reverse.

## A Simple Stochastic Climate Model: Deriving the Backbone

Last time I introduced the concept of a simple climate model which uses stochastic techniques to simulate uncertainty in our knowledge of the climate system. Here I will derive the backbone of this model, an ODE describing the response of global temperature to net radiative forcing. This derivation is based on unpublished work by Nathan Urban – many thanks!

In reality, the climate system should be modelled not as a single ODE, but as a coupled system of hundreds of PDEs in four dimensions. Such a task is about as arduous as numerical science can get, but dozens of research groups around the world have built GCMs (General Circulation Models, or Global Climate Models, depending on who you talk to) which come quite close to this ideal.

Each GCM has taken hundreds of person-years to develop, and I only had eight weeks. So for the purposes of this project, I treat the Earth as a spatially uniform body with a single temperature. This is clearly a huge simplification but I decided it was necessary.

Let’s start by defining T1(t) to be the absolute temperature of this spatially uniform Earth at time t, and let its heat capacity be C. Therefore,

$C \: T_1(t) = E$

where E is the change in energy required to warm the Earth from 0 K to temperature T1. Taking the time derivative of both sides,

$C \: \frac{dT_1}{dt} = \frac{dE}{dt}$

Now, divide through by A, the surface area of the Earth:

$c \: \frac{dT_1}{dt} = \frac{1}{A} \frac{dE}{dt}$

where c = C/A is the heat capacity per unit area. Note that the right side of the equation, a change in energy per unit time per unit area, has units of W/m2. We can express this as the difference of incoming and outgoing radiative fluxes, I(t) and O(t) respectively:

$c \: \frac{dT_1}{dt} = I(t)- O(t)$

By the Stefan-Boltzmann Law,

$c \: \frac{dT_1}{dt} = I(t) - \epsilon \sigma T_1(t)^4$

where ϵ is the emissivity of the Earth and σ is the Stefan-Boltzmann constant.

To consider the effect of a change in temperature, suppose that T1(t) = T0 + T(t), where T0 is an initial equilibrium temperature and T(t) is a temperature anomaly. Substituting into the equation,

$c \: \frac{d(T_0 + T(t))}{dt} = I(t) - \epsilon \sigma (T_0 + T(t))^4$

Noting that T0 is a constant, and also factoring the right side,

$c \: \frac{dT}{dt} = I(t) - \epsilon \sigma T_0^4 (1 + \tfrac{T(t)}{T_0})^4$

Since the absolute temperature of the Earth is around 280 K, and we are interested in perturbations of around 5 K, we can assume that T(t)/T0 ≪ 1. So we can linearize (1 + T(t)/T0)4 using a Taylor expansion about T(t) = 0:

$c \: \frac{dT}{dt} = I(t) - \epsilon \sigma T_0^4 (1 + 4 \tfrac{T(t)}{T_0} + O[(\tfrac{T(t)}{T_0})^2])$

$\approx I(t) - \epsilon \sigma T_0^4 (1 + 4 \tfrac{T(t)}{T_0})$

$= I(t) - \epsilon \sigma T_0^4 - 4 \epsilon \sigma T_0^3 T(t)$

Next, let O0 = ϵσT04 be the initial outgoing flux. So,

$c \: \frac{dT}{dt} = I(t) - O_0 - 4 \epsilon \sigma T_0^3 T(t)$

Let F(t) = I(t) – O0 be the radiative forcing at time t. Making this substitution as well as dividing by c, we have

$\frac{dT}{dt} = \frac{F(t) - 4 \epsilon \sigma T_0^3 T(t)}{c}$

Dividing each term by 4ϵσT03 and rearranging the numerator,

$\frac{dT}{dt} = - \frac{T(t) - \tfrac{1}{4 \epsilon \sigma T_0^3} F(t)}{\tfrac{c}{4 \epsilon \sigma T_0^3}}$

Finally, let S = 1/(4ϵσT03) and τ = cS. Our final equation is

$\frac{dT}{dt} = - \frac{T(t) - S F(t)}{\tau}$

While S depends on the initial temperature T0, all of the model runs for this project begin in the preindustrial period when global temperature is approximately constant. Therefore, we can treat S as a parameter independent of initial conditions. As I will show in the next post, the uncertainty in S based on climate system dynamics far overwhelms any error we might introduce by disregarding T0.

## A Simple Stochastic Climate Model: Introduction

This winter I took a course in computational physics, which has probably been my favourite undergraduate course to date. Essentially it was an advanced numerical methods course, but from a very practical point of view. We got a lot of practice using numerical techniques to solve realistic problems, rather than just analysing error estimates and proving conditions of convergence. As a math student I found this refreshing, and incredibly useful for my research career.

We all had to complete a term project of our choice, and I decided to build a small climate model. I was particularly interested in the stochastic techniques taught in the course, and given that modern GCMs and EMICs are almost entirely deterministic, it was possible that I could contribute something original to the field.

The basic premise of my model is this: All anthropogenic forcings are deterministic, and chosen by the user. Everything else is determined stochastically: parameters such as climate sensitivity are sampled from probability distributions, whereas natural forcings are randomly generated but follow the same general pattern that exists in observations. The idea is to run this model with the same anthropogenic input hundreds of times and build up a probability distribution of future temperature trajectories. The spread in possible scenarios is entirely due to uncertainty in the natural processes involved.

This approach mimics the real world, because the only part of the climate system we have full control over is our own actions. Other influences on climate are out of our control, sometimes poorly understood, and often unpredictable. It is just begging to be modelled as a stochastic system. (Not that it is actually stochastic, of course; in fact, I understand that nothing is truly stochastic, even random number generators – unless you can find a counterexample using quantum mechanics? But that’s a discussion for another time.)

A word of caution: I built this model in about eight weeks. As such, it is highly simplified and leaves out a lot of processes. You should never ever use it for real climate projections. This project is purely an exercise in numerical methods, and an exploration of the possible role of stochastic techniques in climate modelling.

Over the coming weeks, I will write a series of posts that explains each component of my simple stochastic climate model in detail. I will show the results from some sample simulations, and discuss how one might apply these stochastic techniques to existing GCMs. I also plan to make the code available to anyone who’s interested – it’s written in Matlab, although I might translate it to a free language like Python, partly because I need an excuse to finally learn Python.

I am very excited to finally share this project with you all! Check back soon for the next installment.

## Climate change and the jet stream

Here in the northern mid-latitudes (much of Canada and the US, Europe, and the northern half of Asia) our weather is governed by the jet stream. This high-altitude wind current, flowing rapidly from west to east, separates cold Arctic air (to the north) from warmer temperate air (to the south). So on a given day, if you’re north of the jet stream, the weather will probably be cold; if you’re to the south, it will probably be warm; and if the jet stream is passing over you, you’re likely to get rain or snow.

The jet stream isn’t straight, though; it’s rather wavy in the north-south direction, with peaks and troughs. So it’s entirely possible for Calgary to experience a cold spell (sitting in a trough of the jet stream) while Winnipeg, almost directly to the east, has a heat wave (sitting in a peak). The farther north and south these peaks and troughs extend, the more extreme these temperature anomalies tend to be.

Sometimes a large peak or trough will hang around for weeks on end, held in place by certain air pressure patterns. This phenomenon is known as “blocking”, and is often associated with extreme weather. For example, the 2010 heat wave in Russia coincided with a large, stationary, long-lived peak in the polar jet stream. Wildfires, heat stroke, and crop failure ensued. Not a pretty picture.

As climate change adds more energy to the atmosphere, it would be naive to expect all the wind currents to stay exactly the same. Predicting the changes is a complicated business, but a recent study by Jennifer Francis and Stephen Vavrus made headway on the polar jet stream. Using North American and North Atlantic atmospheric reanalyses (models forced with observations rather than a spin-up) from 1979-2010, they found that Arctic amplification – the faster rate at which the Arctic warms, compared to the rest of the world – makes the jet stream slower and wavier. As a result, blocking events become more likely.

Arctic amplification occurs because of the ice-albedo effect: there is more snow and ice available in the Arctic to melt and decrease the albedo of the region. (Faster-than-average warming is not seen in much of Antarctica, because a great deal of thermal inertia is provided to the continent in the form of strong circumpolar wind and ocean currents.) This amplification is particularly strong in autumn and winter.

Now, remembering that atmospheric pressure is directly related to temperature, and pressure decreases with height, warming a region will increase the height at which pressure falls to 500 hPa. (That is, it will raise the 500 hPa “ceiling”.) Below that, the 1000 hPa ceiling doesn’t rise very much, because surface pressure doesn’t usually go much above 1000 hPa anyway. So in total, the vertical portion of the atmosphere that falls between 1000 and 500 hPa becomes thicker as a result of warming.

Since the Arctic is warming faster than the midlatitudes to the south, the temperature difference between these two regions is smaller. Therefore, the difference in 1000-500 hPa thickness is also smaller. Running through a lot of complicated physics equations, this has two main effects:

1. Winds in the east-west direction (including the jet stream) travel more slowly.
2. Peaks of the jet stream are pulled farther north, making the current wavier.

Also, both of these effects reinforce each other: slow jet streams tend to be wavier, and wavy jet streams tend to travel more slowly. The correlation between relative 1000-500 hPa thickness and these two effects is not statistically significant in spring, but it is in the other three seasons. Also, melting sea ice and declining snow cover on land are well correlated to relative 1000-500 hPa thickness, which makes sense because these changes are the drivers of Arctic amplification.

Consequently, there is now data to back up the hypothesis that climate change is causing more extreme fall and winter weather in the mid-latitudes, and in both directions: unusual cold as well as unusual heat. Saying that global warming can cause regional cold spells is not a nefarious move by climate scientists in an attempt to make every possible outcome support their theory, as some paranoid pundits have claimed. Rather, it is another step in our understanding of a complex, non-linear system with high regional variability.

Many recent events, such as record snowfalls in the US during the winters of 2009-10 and 2010-11, are consistent with this mechanism – it’s easy to see that they were caused by blocking in the jet stream when Arctic amplification was particularly high. They may or may not have happened anyway, if climate change wasn’t in the picture. However, if this hypothesis endures, we can expect more extreme weather from all sides – hotter, colder, wetter, drier – as climate change continues. Don’t throw away your snow shovels just yet.

## Climate Change and Atlantic Circulation

Today my very first scientific publication is appearing in Geophysical Research Letters. During my summer at UVic, I helped out with a model intercomparison project regarding the effect of climate change on Atlantic circulation, and was listed as a coauthor on the resulting paper. I suppose I am a proper scientist now, rather than just a scientist larva.

The Atlantic meridional overturning circulation (AMOC for short) is an integral part of the global ocean conveyor belt. In the North Atlantic, a massive amount of water near the surface, cooling down on its way to the poles, becomes dense enough to sink. From there it goes on a thousand-year journey around the world – inching its way along the bottom of the ocean, looping around Antarctica – before finally warming up enough to rise back to the surface. A whole multitude of currents depend on the AMOC, most famously the Gulf Stream, which keeps Europe pleasantly warm.

Some have hypothesized that climate change might shut down the AMOC: the extra heat and freshwater (from melting ice) coming into the North Atlantic could conceivably lower the density of surface water enough to stop it sinking. This happened as the world was coming out of the last ice age, in an event known as the Younger Dryas: a huge ice sheet over North America suddenly gave way, drained into the North Atlantic, and shut down the AMOC. Europe, cut off from the Gulf Stream and at the mercy of the ice-albedo feedback, experienced another thousand years of glacial conditions.

A shutdown today would not lead to another ice age, but it could cause some serious regional cooling over Europe, among other impacts that we don’t fully understand. Today, though, there’s a lot less ice to start with. Could the AMOC still shut down? If not, how much will it weaken due to climate change? So far, scientists have answered these two questions with “probably not” and “something like 25%” respectively. In this study, we analysed 30 climate models (25 complex CMIP5 models, and 5 smaller, less complex EMICs) and came up with basically the same answer. It’s important to note that none of the models include dynamic ice sheets (computational glacial dynamics is a headache and a half), which might affect our results.

Models ran the four standard RCP experiments from 2006-2100. Not every model completed every RCP, and some extended their simulations to 2300 or 3000. In total, there were over 30 000 model years of data. We measured the “strength” of the AMOC using the standard unit Sv (Sverdrups), where each Sv is 1 million cubic metres of water per second.

Only two models simulated an AMOC collapse, and only at the tail end of the most extreme scenario (RCP8.5, which quite frankly gives me a stomachache). Bern3D, an EMIC from Switzerland, showed a MOC strength of essentially zero by the year 3000; CNRM-CM5, a GCM from France, stabilized near zero by 2300. In general, the models showed only a moderate weakening of the AMOC by 2100, with best estimates ranging from a 22% drop for RCP2.6 to a 40% drop for RCP8.5 (with respect to preindustrial conditions).

Are these somewhat-reassuring results trustworthy? Or is the Atlantic circulation in today’s climate models intrinsically too stable? Our model intercomparison also addressed that question, using a neat little scalar metric known as Fov: the net amount of freshwater travelling from the AMOC to the South Atlantic.

The current thinking in physical oceanography is that the AMOC is more or less binary – it’s either “on” or “off”. When AMOC strength is below a certain level (let’s call it A), its only stable state is “off”, and the strength will converge to zero as the currents shut down. When AMOC strength is above some other level (let’s call it B), its only stable state is “on”, and if you were to artificially shut it off, it would bounce right back up to its original level. However, when AMOC strength is between A and B, both conditions can be stable, so whether it’s on or off depends on where it started. This phenomenon is known as hysteresis, and is found in many systems in nature.

This figure was not part of the paper. I made it just now in MS Paint.

Here’s the key part: when AMOC strength is less than A or greater than B, Fov is positive and the system is monostable. When AMOC strength is between A and B, Fov is negative and the system is bistable. The physical justification for Fov is its association with the salt advection feedback, the sign of which is opposite Fov: positive Fov means the salt advection feedback is negative (i.e. stabilizing the current state, so monostable); a negative Fov means the salt advection feedback is positive (i.e. reinforcing changes in either direction, so bistable).

Most observational estimates (largely ocean reanalyses) have Fov as slightly negative. If models’ AMOCs really were too stable, their Fov‘s should be positive. In our intercomparison, we found both positives and negatives – the models were kind of all over the place with respect to Fov. So maybe some models are overly stable, but certainly not all of them, or even the majority.

As part of this project, I got to write a new section of code for the UVic model, which calculated Fov each timestep and included the annual mean in the model output. Software development on a large, established project with many contributors can be tricky, and the process involved a great deal of head-scratching, but it was a lot of fun. Programming is so satisfying.

Beyond that, my main contribution to the project was creating the figures and calculating the multi-model statistics, which got a bit unwieldy as the model count approached 30, but we made it work. I am now extremely well-versed in IDL graphics keywords, which I’m sure will come in handy again. Unfortunately I don’t think I can reproduce any figures here, as the paper’s not open-access.

I was pretty paranoid while coding and doing calculations, though – I kept worrying that I would make a mistake, never catch it, and have it dredged out by contrarians a decade later (“Kate-gate”, they would call it). As a climate scientist, I suppose that comes with the job these days. But I can live with it, because this stuff is just so darned interesting.

## Permafrost Projections

During my summer at UVic, two PhD students at the lab (Andrew MacDougall and Chris Avis) as well as my supervisor (Andrew Weaver) wrote a paper modelling the permafrost carbon feedback, which was recently published in Nature Geoscience. I read a draft version of this paper several months ago, and am very excited to finally share it here.

Studying the permafrost carbon feedback is at once exciting (because it has been left out of climate models for so long) and terrifying (because it has the potential to be a real game-changer). There is about twice as much carbon frozen into permafrost than there is floating around in the entire atmosphere. As high CO2 levels cause the world to warm, some of the permafrost will thaw and release this carbon as more CO2 – causing more warming, and so on. Previous climate model simulations involving permafrost have measured the CO2 released during thaw, but haven’t actually applied it to the atmosphere and allowed it to change the climate. This UVic study is the first to close that feedback loop (in climate model speak we call this “fully coupled”).

The permafrost part of the land component was already in place – it was developed for Chris’s PhD thesis, and implemented in a previous paper. It involves converting the existing single-layer soil model to a multi-layer model where some layers can be frozen year-round. Also, instead of the four RCP scenarios, the authors used DEPs (Diagnosed Emission Pathways): exactly the same as RCPs, except that CO2 emissions, rather than concentrations, are given to the model as input. This was necessary so that extra emissions from permafrost thaw would be taken into account by concentration values calculated at the time.

As a result, permafrost added an extra 44, 104, 185, and 279 ppm of CO2 to the atmosphere for DEP 2.6, 4.5, 6.0, and 8.5 respectively. However, the extra warming by 2100 was about the same for each DEP, with central estimates around 0.25 °C. Interestingly, the logarithmic effect of CO2 on climate (adding 10 ppm to the atmosphere causes more warming when the background concentration is 300 ppm than when it is 400 ppm) managed to cancel out the increasing amounts of permafrost thaw. By 2300, the central estimates of extra warming were more variable, and ranged from 0.13 to 1.69 °C when full uncertainty ranges were taken into account. Altering climate sensitivity (by means of an artificial feedback), in particular, had a large effect.

As a result of the thawing permafrost, the land switched from a carbon sink (net CO2 absorber) to a carbon source (net CO2 emitter) decades earlier than it would have otherwise – before 2100 for every DEP. The ocean kept absorbing carbon, but in some scenarios the carbon source of the land outweighed the carbon sink of the ocean. That is, even without human emissions, the land was emitting more CO2 than the ocean could soak up. Concentrations kept climbing indefinitely, even if human emissions suddenly dropped to zero. This is the part of the paper that made me want to hide under my desk.

This scenario wasn’t too hard to reach, either – if climate sensitivity was greater than 3°C warming per doubling of CO2 (about a 50% chance, as 3°C is the median estimate by scientists today), and people followed DEP 8.5 to at least 2013 before stopping all emissions (a very intense scenario, but I wouldn’t underestimate our ability to dig up fossil fuels and burn them really fast), permafrost thaw ensured that CO2 concentrations kept rising on their own in a self-sustaining loop. The scenarios didn’t run past 2300, but I’m sure that if you left it long enough the ocean would eventually win and CO2 would start to fall. The ocean always wins in the end, but things can be pretty nasty until then.

As if that weren’t enough, the paper goes on to list a whole bunch of reasons why their values are likely underestimates. For example, they assumed that all emissions from permafrost were  CO2, rather than the much stronger CH4 which is easily produced in oxygen-depleted soil; the UVic model is also known to underestimate Arctic amplification of climate change (how much faster the Arctic warms than the rest of the planet). Most of the uncertainties – and there are many – are in the direction we don’t want, suggesting that the problem will be worse than what we see in the model.

This paper went in my mental “oh shit” folder, because it made me realize that we are starting to lose control over the climate system. No matter what path we follow – even if we manage slightly negative emissions, i.e. artificially removing CO2 from the atmosphere – this model suggests we’ve got an extra 0.25°C in the pipeline due to permafrost. It doesn’t sound like much, but add that to the 0.8°C we’ve already seen, and take technological inertia into account (it’s simply not feasible to stop all emissions overnight), and we’re coming perilously close to the big nonlinearity (i.e. tipping point) that many argue is between 1.5 and 2°C. Take political inertia into account (most governments are nowhere near even creating a plan to reduce emissions), and we’ve long passed it.

Just because we’re probably going to miss the the first tipping point, though, doesn’t mean we should throw up our hands and give up. 2°C is bad, but 5°C is awful, and 10°C is unthinkable. The situation can always get worse if we let it, and how irresponsible would it be if we did?

## Modelling Geoengineering, Part II

Near the end of my summer at the UVic Climate Lab, all the scientists seemed to go on vacation at the same time and us summer students were left to our own devices. I was instructed to teach Jeremy, Andrew Weaver’s other summer student, how to use the UVic climate model – he had been working with weather station data for most of the summer, but was interested in Earth system modelling too.

Jeremy caught on quickly to the basics of configuration and I/O, and after only a day or two, we wanted to do something more exciting than the standard test simulations. Remembering an old post I wrote, I dug up this paper (open access) by Damon Matthews and Ken Caldeira, which modelled geoengineering by reducing incoming solar radiation uniformly across the globe. We decided to replicate their method on the newest version of the UVic ESCM, using the four RCP scenarios in place of the old A2 scenario. We only took CO2 forcing into account, though: other greenhouse gases would have been easy enough to add in, but sulphate aerosols are spatially heterogeneous and would complicate the algorithm substantially.

Since we were interested in the carbon cycle response to geoengineering, we wanted to prescribe CO2 emissions, rather than concentrations. However, the RCP scenarios prescribe concentrations, so we had to run the model with each concentration trajectory and find the equivalent emissions timeseries. Since the UVic model includes a reasonably complete carbon cycle, it can “diagnose” emissions by calculating the change in atmospheric carbon, subtracting contributions from land and ocean CO2 fluxes, and assigning the residual to anthropogenic sources.

After a few failed attempts to represent geoengineering without editing the model code (e.g., altering the volcanic forcing input file), we realized it was unavoidable. Model development is always a bit of a headache, but it makes you feel like a superhero when everything falls into place. The job was fairly small – just a few lines that culminated in equation 1 from the original paper – but it still took several hours to puzzle through the necessary variable names and header files! Essentially, every timestep the model calculates the forcing from CO2 and reduces incoming solar radiation to offset that, taking changing planetary albedo into account. When we were confident that the code was working correctly, we ran all four RCPs from 2006-2300 with geoengineering turned on. The results were interesting (see below for further discussion) but we had one burning question: what would happen if geoengineering were suddenly turned off?

By this time, having completed several thousand years of model simulations, we realized that we were getting a bit carried away. But nobody else had models in the queue – again, they were all on vacation – so our simulations were running three times faster than normal. Using restart files (written every 100 years) as our starting point, we turned off geoengineering instantaneously for RCPs 6.0 and 8.5, after 100 years as well as 200 years.

## Results

Similarly to previous experiments, our representation of geoengineering still led to sizable regional climate changes. Although average global temperatures fell down to preindustrial levels, the poles remained warmer than preindustrial while the tropics were cooler:

Also, nearly everywhere on the globe became drier than in preindustrial times. Subtropical areas were particularly hard-hit. I suspect that some of the drying over the Amazon and the Congo is due to deforestation since preindustrial times, though:

Jeremy also made some plots of key one-dimensional variables for RCP8.5, showing the results of no geoengineering (i.e. the regular RCP – yellow), geoengineering for the entire simulation (red), and geoengineering turned off in 2106 (green) or 2206 (blue):

It only took about 20 years for average global temperature to fall back to preindustrial levels. Changes in solar radiation definitely work quickly. Unfortunately, changes in the other direction work quickly too: shutting off geoengineering overnight led to rates of warming up to 5 C / decade, as the climate system finally reacted to all the extra CO2. To put that in perspective, we’re currently warming around 0.2 C / decade, which far surpasses historical climate changes like the Ice Ages.

Sea level rise (due to thermal expansion only – the ice sheet component of the model isn’t yet fully implemented) is directly related to temperature, but changes extremely slowly. When geoengineering is turned off, the reversals in sea level trajectory look more like linear offsets from the regular RCP.

Sea ice area, in contrast, reacts quite quickly to changes in temperature. Note that this data gives annual averages, rather than annual minimums, so we can’t tell when the Arctic Ocean first becomes ice-free. Also, note that sea ice area is declining ever so slightly even with geoengineering – this is because the poles are still warming a little bit, while the tropics cool.

Things get really interesting when you look at the carbon cycle. Geoengineering actually reduced atmospheric CO2 concentrations compared to the regular RCP. This was expected, due to the dual nature of carbon cycle feedbacks. Geoengineering allows natural carbon sinks to enjoy all the benefits of high CO2 without the associated drawbacks of high temperatures, and these sinks become stronger as a result. From looking at the different sinks, we found that the sequestration was due almost entirely to the land, rather than the ocean:

In this graph, positive values mean that the land is a net carbon sink (absorbing CO2), while negative values mean it is a net carbon source (releasing CO2). Note the large negative spikes when geoengineering is turned off: the land, adjusting to the sudden warming, spits out much of the carbon that it had previously absorbed.

Within the land component, we found that the strengthening carbon sink was due almost entirely to soil carbon, rather than vegetation:

This graph shows total carbon content, rather than fluxes – think of it as the integral of the previous graph, but discounting vegetation carbon.

Finally, the lower atmospheric CO2 led to lower dissolved CO2 in the ocean, and alleviated ocean acidification very slightly. Again, this benefit quickly went away when geoengineering was turned off.

## Conclusions

Is geoengineering worth it? I don’t know. I can certainly imagine scenarios in which it’s the lesser of two evils, and find it plausible (even probable) that we will reach such a scenario within my lifetime. But it’s not something to undertake lightly. As I’ve said before, desperate governments are likely to use geoengineering whether or not it’s safe, so we should do as much research as possible ahead of time to find the safest form of implementation.

The modelling of geoengineering is in its infancy, and I have a few ideas for improvement. In particular, I think it would be interesting to use a complex atmospheric chemistry component to allow for spatial variation in the forcing reduction through sulphate aerosols: increase the aerosol optical depth over one source country, for example, and let it disperse over time. I’d also like to try modelling different kinds of geoengineering – sulphate aerosols as well as mirrors in space and iron fertilization of the ocean.

Jeremy and I didn’t research anything that others haven’t, so this project isn’t original enough for publication, but it was a fun way to stretch our brains. It was also a good topic for a post, and hopefully others will learn something from our experiments.

Above all, leave over-eager summer students alone at your own risk. They just might get into something like this.