Think. Quantitatively.

Every year I tell my students something like: ‘When you finish any calculation in physical chemistry, have a look at the number you have ended up with and see if it is a reasonable number. Is it about the size you would expect? If it isn’t, go back and find the mistake. If you are in an exam and pressed for time, write: ‘I know this number is the wrong size, but I can’t find where I went wrong.’ Or, just change the order of magnitude to the order of magnitude it ought to be, and hope I don’t read your working carefully.’

Every year, I get more cautionary tales to tell my students when I tell them this- assignments I have received with chemical bonds blithely reported as longer than the distance from here to Alpha Centauri, molecules heavier than the Sun, energies for chemical reactions greater than the annual output of all the power plants in Europe.

The chapter ‘The Spur of the Moment’ of Kim Stanley Robinson's book 'Green Mars' is about a project to build a sea in Hellas Planitia in the southern hemisphere of Mars, a sea that is quoted as being ‘1000 by 300 km’. It order to give the project verisimilitude, numbers for amounts of water are quoted throughout the chapter.


p.400:

It was a running river, in an obviously riverine valley, placid in some places, agitated in others, with gravel fords, sandbars, braided sections, crumbling lemniscate islands, there a big deep lazy oxbow, frequent rapids, and far upstream, a couple of small falls. Under the tallest waterfall they could see the pink foam turn almost white, and patches of white were then carried downstream, to catch on boulders and snags sticking out from the bank.

‘Dao River,’ Diana said. ‘Also called the Ruby River by the people who live there.’

‘How many are there?’

‘A few thousand. … Upstream there are family homesteads and the like. And of course then the aquifer station at the head of the canyon, where a few hundred of them work.’

‘It’s one of the biggest aquifers?’

‘Yes. About three million cubic metres of water. So we’re pumping it out at a flow rate- well, you see it there. About a hundred thousand cubic metres a year.’

10⁵ m³ per year = 274 m³ per day = 3 litres per second

To put this number in perspective:
“Older firehoses with 2.5 inch diameter equipped with a 1.5 inch nozzle can typically deliver 20-40 litres of water per second” (Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World, Benny Lautrup)

I suppose the description of the river *could* apply to something that one could easily step over, but I do not think this was the author’s intention.


p.416

One day at the office, news came in from the Hellespontus. They had discovered a new aquifer, very deep compared to the others, very far away from the basin, and very big. Diana speculated that earlier glacial ages had run west off the Hellespontus range, and come to rest out there, underground- some twelve million cubic meters, more than any other aquifer, raising the amount of located water from 80 % to 120% of the amount needed to fill the basin to the -1-kilometer contour.


Let’s see, the Hellas Planitia basin is quoted as being 1000 by 300 km. That’s an area of 10⁶ m × 3 × 10⁵ m, or 300 billion square metres.

Twelve million cubic metres would cover 300 billion square metres to a depth of

1.2 × 10⁷ m³ / 3 × 10¹¹ m²

= 4 × 10^-5 m.

40 microns.

So if this raises the amount of located water from 80 % to 120 %, at a first approximation the Hellas Sea will be 0.12 mm deep.

I confess myself unimpressed by this feat of areological engineering.

I expect KSR made the common undergraduate mistake of assuming
1000 cubic metres = 1 cubic kilometre. I wonder if the numbers have been corrected in later printings?

Green Mars, p.346

My favourite bit so far has been the chapter 'The Scientist as Hero'. Unfortunately, from time to time poor Sax is set up as a bit of reductionist straw man. Take this exchange, from the beginning of the chapter 'Social Engineering', where Saxifrage Russell is talking to a hippy-dippy psychologist type:


There is a drive towards complexification that is directly opposed to the physical law of entropy. Why should that be?

I don’t know.

Why do you dislike it so when you can’t say why?

I don’t know.

This mystery of life is a holy thing. It is our freedom. We have shot out of physical reality, we exist in a kind of godlike freedom, and the mystery is integral to it.

No. We are still physical reality. Atoms in their rounds. Determined on most scales, random on some others.

Ah well. We disagree. But either way, the scientist’s job is to explore everything. No matter the difficulties! To stay open, to accept ambiguity…



I've written some new lines for Sax. I reckon it should go like this:

There is a drive towards complexification that is directly opposed to the physical law of entropy. Why should that be?

There isn’t a drive towards complexification. There’s a drive towards differentiation, a drive which is basically the same as the physical law of entropy. You have just selected your data to focus on the end of the bell curve where complex things are happening, ignoring the fact that the curve is getting bigger and broader all the time.

Well, you’re entitled to your opinion. But I think your view saps all the mystery out of the universe. This mystery of life is a holy thing. It is our freedom. We have shot out of physical reality, we exist in a kind of godlike freedom, and the mystery is integral to it.

Why are you so eager to call everything you don’t understand ‘a mystery’?

Its not that I’m eager, it’s just that I feel there’s more to life than can be explained by physical science.

Why don’t you stop feeling, and try thinking, instead? What if the mystery is just an artifact of your imperfect understanding? What if the mystery, and the ‘godlike freedom’ just exist in your head? And what exactly do you mean by ‘shot out of physical reality’? You should define your terms.

Ah, my friend, don’t be mean! We disagree. But either way, the scientist’s job is to explore everything…

Green Mars, pp.135, 177, 251-253

One problem with schemes for the terraforming of Mars is the need for a source of an inert gas to give an atmosphere of similar composition to Earth. A higher partial pressure of oxygen than we have here would ‘vigorously accelerate combustion’, tend to intoxicate us, and make technological civilisation impossible, while a much lower total atmospheric pressure would not be able to support Earth-like weather. The partial pressure of oxygen required to support combustion declines with declining total pressure, so even this lower total atmospheric pressure option might be dangerously combustible if it had enough oxygen present to support life. So, where is this inert gas to come from?

Getting nitrogen from Titan won’t stand up to any sort of cost-benefit analysis.

There are unlikely to be enough noble gases trapped deep underground from radioactive decay to amount to a hill of beans.

Thus, it has been suggested that molecular nitrogen could be obtained by ‘burning nitrates’, which seem to be present (or may be present) in considerable amounts in the Martian crust.

However, simply heating nitrates will not be very effective as a way to ‘dilute’ oxygen. For instance:

2Na(NO₃)₂ + heat → 2NaNO₂ + O₂

2NaNO₂ + more heat → Na₂O + NO + NO₂

2Ca(NO₃)₂ + heat → 2CaO + O₂ + 4NO₂

Thus ‘burning’ nitrates generates lots of toxic gas, and some extra oxygen.

Of course, with more energy input:

2NO₂ + much more heat → N₂ + 2O₂

So we have got some nitrogen eventually, but at a cost of 2.5 oxygen molecules per nitrogen molecule.

If we don’t want to add lots of extra oxygen to the atmosphere, we will have to add a reducing agent instead, and do something more like ‘burning’ . On Earth, if we had lots of extra nitrogen dioxide we wanted to get rid of, we would do something like:

NO₂ + 2H₂ → N₂ + 2H₂O

Or

NO₂ + C → N₂ + CO₂

Or more realistically, something like

4NO₂ + C₃H₈ → 3CO₂ + 4H₂O + 2N₂

The problem is that there is not a lot of carbon or hydrogen on Mars that is not already incorporated in carbon dioxide or water. I haven’t googled to find out how much hydrogen has been located/postulated on Mars, but a crude atom balance suggests that if we want to burn nitrates with enough hydrogen to generate one nitrogen atmosphere, we need to burn at least two whole hydrogen atmospheres. I don’t think this is available, it would surely have outgassed long ago. I have found references to methane clathrates on Mars, which may be there in similar amounts to the nitrates (perhaps) and would allow the reaction

2NO₂ + CH₄ → CO₂ + 2H₂O + N₂

The problem here is that it would be a very significant bit of geo-engineering to mine the methane and get it to the nitrates, or vice versa, and we are adding to the carbon dioxide load that we need to get rid of later.

So what other reducing agents are available? I suggest that much more cost-effective than bringing nitrogen from Titan would be to bring down some Iron-Nickel asteroids and rust them in nitrogen dioxide. The mass that would be transported would be much larger, but the distance would be much shorter, and there would be no need to do any complicated collection and packaging and transport, just provide the right nudge of energy to send the asteroid on a collision course with Mars.

The following reaction is certainly thermodynamically favourable, though I don’t have an idea of what its activation energy might be:

6NO₂ + 8Fe → 3N₂ + 4Fe₂O₃

While this uses considerably more mass of reductant to produce the same amount of nitrogen than methane would, instead of having to be painstakingly mined and collected like the methane, the asteroids could be crashed down into the nitrate deposits in one foul swoop. The reaction does not produce any extra carbon dioxide that will need to be scrubbed out later.

Some Knols

I thought I should put a link to Marco Parigi's knol on reading Richard Dawkins 'The God Delusion', and my knol on reading Stuart Kauffman's 'The Origins of Order: Self-Organisation and Selection in Evolution', as a prod to get myself to finish the latter!

Dark Matter?

Every time I read back over my list of publications, I am struck by how most of the good ones seem to have sunk without a trace. Most of the ones where I thought I had discovered something interesting and novel about the universe, or had hit upon an interesting and novel way of looking at something we already knew about, have very few citations, or none at all. Perhaps I should do a series of posts on my top five papers with no non-author citations? Hmm, I have been neglecting this blog lately, and a theme like that might help.

Anyway, a few years ago a colleague gave me a weighty chapter he had written, entitled A Quantum Approach to Dark Matter, which I was slack (It is 63 pages long) and never got around to reading (It *is* 63 pages long). Remembering it today, I thought I would first check to see what other people thought of it- I am a mere chemist, and can only identify very dubious theoretical physics as dubious at a glance. I found my colleague had four published articles in the area over the past half-decade, and none of them had been cited at all. This is a tragedy. It is dreadful to spend years wrestling with an idea, to hone and shape it into a form you think is fit to present to the world, expound it with all the energy and clarity at your command, shepherd it into print, and then see it be ignored completely. Hence, I thought I would put a link to the chapter here. And I really will read it myself, I promise. And put an ignorant chemist's critique here on the web, at the very least, so Google can find it.

Some time ago I was asking the question: ‘How good are these climate models? What sort of predictive value have they shown in modelling future climate? After all, we’ve been doing them for a few decades now.’

A nice person on realclimate.org (there are some, not all of them treat people who disagree with them as the demonised other) directed me to a classic paper by Hansen et al.

"If you want an indication of how well these models do you can go get (J. Geo Res. 93 (1988) 9341) the Hansen GCM paper that people talk about, and compare their results with observed patterns of warming and other things."

Here is the plot from that paper showing the response of overall global temperature (which the authors argue convincingly is a much better parameter than any subset of the data, e.g., whether it snowed at my house or not in a given year) for three different scenarios- A being continued exponential growth, B being a more subdued form of business as usual, and C if drastic cuts are implemented starting a few years ago.

I went and got the Hadcrut3 data set and plotted it on top of this one, as near as I was able, and got this.

There are other data sets out there. I shall plot some of the others and put them up for you.

The Hansen et al. model predicts the greatest degree of warming at high latitudes, fitting observations, but the model also reproduces another feature of observed weather, that those latitudes have the highest natural variability from one year to another.

Update 2012:
Here is another three years of data. I do realise I haven't plotted any of the other data sets. Bad me. The red points are the average of 13 monthly data points averaged on each month, while the blue points are the actual Hadcrut3 monthly global averages you can download yourself.

In which I place myself beyond the pale of civilised discourse

Firstly, an observation on scientific models, coagulated in the enthralling world of emulsion polymerisation:

Whenever you are trying to model some complex phenomenon, the fit of the model to the data can be improved by adding more adjustable parameters. A complex phenomenon will usually be dependent on a large number of factors, but the fact that the model fits the data better when you incorporate an additional factor may or may not mean that new factor is important: it might just mean that the additional parameter(s) you have incorporated are improving your fit. This is another thing the David Sangster told me: ‘With enough adjustable parameters, you can fit a camel.’

So there is a tension between the complete model, which contains all the factors that ought to be physically important – but might be meaningless because of all the guesstimated parameters you have put in to quantify these factors- and the simple model, which ignores things that might be physically important, but also avoids adjustable parameters. If you go too far in one direction, you get a model that can fit any possible data; too far the other, you get the well-known ‘assume a spherical horse’ punchline.

This also means that when you are modelling a complex phenomenon, you will tend to base your model on the processes that are best known, where you don’t have to pick numbers out of the air for your adjustable parameters, and you will ignore if you possibly can the role played by processes that are less understood, which would force you to bring in rubbery parameters.

Now to place myself beyond the pale. Some time ago I made the assertion:

‘Anthropogenic global warming is a fact, but we shouldn’t do anything about it.’

The second part of this statement is a considered opinion, based on facts and reasoned deductions from them. The first part of this statement, I have realised over the last few months, is based on an irrational mood.

That is: in the laboratory, and considering the atmospheres of the planets in toto, there is a perfectly splendid mechanism by which increasing the concentration of atmospheric carbon dioxide should increase temperatures. It is a really good mechanism, based on rock-solid physics. But is there any evidence that this mechanism is responsible for observed temperature change globally? Evidence, in the scientific sense, is where a model has predictive value: it does not just fit the data we have, but tells us what future data is going to look like. I did not examine this question before I made the statement above. Instead, I relied on the irrational mood that it seemed like wishful thinking that there was some sort of feedback mechanism providentially cancelling out this Greenhouse warming effect.

Let us consider these two famous graphs:

What do they tell us? They show us a correlation between carbon dioxide concentration and average global temperature. They also tells us, very clearly, that there are factors other than carbon dioxide which contribute to the world’s temperature.

We could also draw graphs that show some sort of a correlation between sunspot activity and global temperature, and earthshine and global temperature, and the number of pirates and global temperature. The last of these three graphs would be a joke circulated by the Church of the Flying Spaghetti Monster. The other two are graphs where it is easy to construct a testable mechanism for how the correlation might work. These mechanisms are not as solid or as well understood as the Greenhouse mechanism. They rely on more rubbery adjustable parameters. If we ignore them, do we have a spherical horse? If we include them, do we have a camel?

What is signal, and what is noise, in the Hadcrut3 temperature curve?

An idea that was in fashion when I was an undergraduate was the Gaia hypothesis of James Lovelock. You don’t hear much about it nowadays. You might remember that it was all about negative feedbacks keeping the global ecosystem in balance, life keeping things tickety-boo for life. I bring it up here as a hand-waving justification for a recent shift in my irrational mood: given that there is a grain of truth in Lovelock’s ideas, it now seems to me reasonably likely that there would be a negative feedback mechanism tending to minimise the effects of any carbon dioxide we add to the air.

I must now revise my assertion:

‘Anthropogenic global warming is a conjecture with limited predictive value, and we shouldn’t do anything about it.’

And I have to apologise for some of the slighting references to global warming denialists I have made previously.

And unfortunately I have nerfed one of the major motivations for establishing this blog, which was to use any perceived authority associated with my real name to push the line that we shouldn’t take any action to stop anthropogenic global warming. By denying AGW to be a fact, I have placed myself outside the pale of civilised discourse and disqualified myself from making any statements on the issue that will be taken seriously.

Son cosas de la vida…

14% more First Year students agree balancing redox equations is fun!

In a striking improvement over last year's already high student enthusiasm for balancing redox equations, the proportion of students agreeing that balancing redox equations is fun has risen to 83%!

A little note about chain transfer to butyl methacrylate

For good or evil, this paper, which I began writing in 1999 at the request of Professor Bob Gilbert, is finally published. It is a tremendous pleasure to finally be a co-author with David Sangster, the eminence d'or of Australian polymer science. He is the source of the quote which informs my every waking action:

'Just because the model fits the data, it doesn't mean the model is true.'

I have today (10/11/09) found a splendid biography of David Sangster on the website of the University of Sydney.

Royal Society Discussion Paper, Ocean acidification due to increasing atmospheric carbon dioxide. Part Two.

The RSC discussion paper explains the division of ocean waters between an upper zone, where calcium carbonate formation is possible, and a colder lower zone, where it is not possible. The fact that mass transport between these zones is very slow is stressed. The paper does not actually give a pH profile of the ocean, but here is one:

(The little dark dots are the data from today; the big circles are attempts to figure out the situation at various times in the past, which is what the paper I sourced this from is about.)

Note that the vast majority of the volume of the ocean is cold, and relatively acidic. This deep ocean is where an enormous amount of carbon is stored. Transport of carbon dioxide out of or into this layer will not be controlled by thermodynamics (i. e., where carbon dioxide it would most dearly love to be), but by kinetics (i. e., how fast it can get there). Thus, it does not matter to this zone whether or not we are adding carbon dioxide to the atmosphere at a rate unparalleled in Earth’s history or not, because that will not control how fast it gets there. It has to run the gauntlet of the warm water- where it may or may not be converted into calcium carbonate- first.

Remember the figures in the last post on how the carbonic acid equilibria change with temperature. I am now going to make the assertion- which I should now go out and try to verify- that the deep ocean is more acidic *because* it is cold.

To qualify this as-yet-unverified assertion of mine, I should say that I have not yet found any data on the pressure dependence of the pKa values in solutions of reasonable ionic strength, which is also likely to be important.

I suggest that the temperature gradient of the ocean is probably what generates the pH profile, and because transport of carbon dioxide into or out of the ocean is slow compared to how much is already there, it is the temperature dependence of the carbonic acid equilibria which control the speciation observed. Note also that the boundary between the carbonate-forming zone and the non-carbonate forming zone, from our figures below showing what the equilibria do, is going to be dependent both on the pH of the upper layers and their temperature.

Now… if climate change means anything, it means the oceans warming up. Heating the ocean and reducing the pH will pull the carbonate/bicarbonate equilibrium in different directions. I don’t know which is likely to be more significant.

Because the historical record does not show carbon dioxide spouting out of the ocean immediately as temperature increases, but lagging about 1000 years, I am not at all worried about degassing of carbon dioxide starting some feedback loop of badness : until that cold lower ocean where most all of the carbonic acid species are sitting warms up, there is no reason for significant amounts of carbon dioxide to leave the ocean. That is, if degassing of the ocean *is* the reason for the increase in carbon dioxide lagging historical temperature changes. It might not be.

Royal Society Discussion Paper, Ocean acidification due to increasing atmospheric carbon dioxide. Part One.

My thoughts keep returning to the ‘de-alkalinisation of the oceans’. I started thinking about this the other day, first because I came across that article on coccolithophores in Science, and second because one of my students is writing a review article on the use of polymer additives to stop scale formation in desalination plants. The main scales formed in these plants are calcium sulfate at high temperatures, but at somewhat lower temperatures calcium carbonate or magnesium hydroxide.

The first thing you want to know about, if you want to stop scale forming, is what are the characteristics of the solution it is forming from. So early on in the draft appears this table:

(TDS is ‘total dissolved solids’.)

I went back and had another look at the Royal Society discussion paper that I referenced before. This is the paper referenced everywhere in the web where people are fretting about ocean de-alkalinisation. The range of pH values quoted in this table is greater than the range shown in the pretty map in the Royal Society report. In fact, the range of pH values in this table is greater than the size of the maximum change in surface water pH they predict for Figure 5.

So my first thought was, if changes in surface seawater alkalinity are likely to cause bad effects, we ought to be able to see these effects already in ‘canary in the coalmine’ water bodies- shallow, warm places like the Persian Gulf. The reefs there don’t seem to be in particularly good shape but there doesn’t seem to be any evidence that seawater alkalinisation is contributing to their woes. Anyway, this table got me thinking about the problem again.

In discussing the formation of calcium carbonate scale, my student had to talk about the dependence of the equilibrium constants K₁ and K₂ on temperature and the total ionic strength of the solution, and had referenced this paper by Millero et al., where the following figure appears:

The Millero et al. paper also summarises data from a lot of previous work and gets it all to fall on the same line- see this, for instance:

In case you don’t remember,

pK_a = –log₁₀(K_a),

and in this case, K₁ is the equilibrium constant for the reaction:

H₂CO₃ → HCO₃^– + H⁺

and K₂ is the equilibrium constant for this reaction:

HCO₃^– → CO₃^2– + H⁺

These figures are telling us that in seawater (where I^0.5 ~ 0.83), the equilibrium position of both these reactions is further over to the right hand side than if they were happening in common or garden distilled water. And they also tell us that the warmer the water, the further the equilibrium will be over to the right hand side as well.

I plotted up a graph showing how the speciation of pH should change in seawater using the values in this paper and got this figure:

The Royal Society Figure 2 is pretty much the same as mine. It shows carbonate kicking in at a slightly lower pH, but there are different K₂ values floating around in the literature and I'm not sure what value they used.

Zooming in on the pH range important for discussing what is going on in the oceans:

Getting rid of the log scale, and looking at the carbonate/bicarbonate equilibrium only:

More to follow.

C'est la vie

A while ago the prolific Anonymous asked me:

What do you think about the de-alkalinisation of the oceans. Anything ruinously doom and gloom possible there? Is adaptation of water species quick enough by your reckoning?

I have recently been thinking about this a lot, due to work I am doing on calcium carbonate formation in desalination plants, and will offer a substantial critique of this particular bugbear soon.

But in the meantime, I came across this nifty figure in Science the other day and thought I would share it with you. If someone had asked me, 'how will marine organisms respond to changes in total carbonic acid species concentration?', I like to think I would have been prescient enough to draw a figure like this one. Find a niche and fill it: such is the way of living things!

Dialogo

Simplicio: Have you heard? The Powers wish to reduce the amount we teach, so that we will have more time for research, and thus will produce more and better research.

Sagredo: I think the second part of your syllogism does not follow from the first.

Simplicio: Why, how is that?

Sagredo: One of us cannot have more than twenty-four hours in a day. But if one has a single intelligent and dedicated postgraduate student, then one has forty-eight. If one has two, one has seventy-two, and so forth. It is the many hours that come from having many students that enable us to produce more and better research.

Simplicio: True, but I cannot see how having a few more hours for research can hurt us.

Sagredo: Where do you suppose postgraduate students come from?

Simplicio: Most of them are from places like Tartary and Hind, are they not?

Sagredo: Yes, many of them are. They are attracted from diverse foreign lands by the splendour of the learning in our land. But many other places of learning seek also to attract them, and day by day the scholars of their own lands grow wealthier and more astute, so that one day no more will come to us.

Simplicio: That would be a calamity! So where else do they come from?

Sagredo: We raise them here, by teaching undergraduates.

Simplicio: Aha! There is no problem, then. Under the new system we will surely continue to teach undergraduates.

Sagredo: Simplicio, do you suppose all undergraduates are suitable to become postgraduates?

Simplicio: I guess not. Some are damnably simple.

Sagredo: Yes, it is only the few who hunger and thirst for knowledge that are suitable to become postgraduates. If we give our undergraduates half as much as we did before, and other places of learning continue to offer a full cup of learning, where will undergraduates like that go?

Simplicio: You think they will not come here?

Sagredo: Many of them will not.

Simplicio: But surely there are many who would not leave our lovely place of learning for the City of Dreadful Night or other distant places?

Sagredo: Yes, we must pin our hopes on such as those. But consider: if we teach them half as much, what will we need to do when they commence as postgraduate students?

Simplicio: I am not sure. I recall there are forms to fill out?

Sagredo: Besides that. We must perforce teach them the other half, if they are to work as well as postgraduates in the City of Dreadful Night work. And when we have done that, what must we do?

Simplicio: I suppose we must fill in some more forms.

Sagredo: Yes, for by then the first year of their candidature will be over.

Simplicio: It would seem, then, that you think this change will diminish our chances of doing more and better research, rather than increase them?

Sagredo: Most certainly. Why would a student who would make a good postgraduate in Physics or Chemistry do an undergraduate degree at a place of learning that does not take that discipline seriously?

Simplicio: Then I suppose the Powers wish to reduce our teaching hours for some other reason?

Sagredo; That is what I had thought.

Simplicio: Perhaps it is that they must be reduced because of this thing that has come from Bologna?

Sagredo; Ah, but the places of learning that have already gone down that path teach many more hours than we do.

Simplicio: Hmm. Perhaps it is, Sagredo, that those studies they wish to cut are only those where the numbers of undergraduates have been falling, so that we may conserve our resources, as our wealth wanes?

Sagredo: That would be a sensible course of action- but you see, Simplicio, it is the studies where numbers of undergraduates are holding steady that the Powers wish to cut back.

Simplicio: Ah.I see. Perhaps- no, that makes no sense. (sighs)
I wish Salviati was here to explain what was going on.

Sagredo: So do I, Simplicio.

Simplicio: It is a pity the Powers never replaced him, when he took his renowned research group to Brescia...