Thanks, Raul. You're engaging with the formulation of my model itself, rather than TABULA's technical execution of it. But that is still worth doing, definitely so, and I have it on my to-do list for an extended discussion of model building in TABULA. Your analysis of carbon concentration gives me a flying start here. Thank you.
Just to comment on it a bit, before turning back to the nuts'n'bolts of TABULA: I'm aware that my atmosphere model is highly simplified. Perhaps oversimplified – but I'd be happy if I could establish the model as at least being a start in the direction of accurately costing the carbon in the atmosphere. The intended audience is applied math classes in the 14-18 age-group, with the objective of imparting a syllabus of mathematical modelling. To draw an analogy: if I were explaining how computers work (as I used to do to 1st year university students on an IT course) I'd get them to build, or at least examine, a simple "computer" consisting of a circuit board with a cheap CPU, 8K of memory and highly simplified data I/O circuitry. Then go on to describe (briefly!) what is needed when building a Windows PC or an Apple Mac. The very limitations of the model bring home to the student the nature of what it lacks, besides making it easy to comprehend. I'd adopt the same approach for a mathematical model of the atmosphere. You have to ask: fit to do what? Predict the weather? No. Estimate the weight of CO2 in the atmosphere as part of a CDR feasibility study? Yes – at least, to get a conversation going about it. What I propose to do for the wiki pages that document the builtin samples 0-9 is to have a list of where the model could be improved. Part of this will be a list of challengeable assumptions. Two are of particular importance: 1. The model of SAMPLE9 assumes the atmosphere is homogeneous, so that CO2 is evenly distributed. This is far from being the case. Using ppm CO2 measured at sea level will significantly overestimate the weight of CO2 in the atmosphere. ESRL explicitly states: "The Mauna Loa data are being obtained at an altitude of 3400 m in the northern subtropics, and may not be the same as the globally averaged CO2 concentration at the surface." https://www.esrl.noaa.gov/gmd/ccgg/trends/index.html …BTW It's the Mauna Loa data that I'm using in item {2}. But this is a matter of choice, which is just what the model should permit. 2. People loosely talk of "carbon" as in "carbon reduction". The model deals only with CO2. But there is other "carbon" in the atmosphere in the form of far stronger greenhouse gases: CFCs and methane to name just 2. It's fortunate that the model can skirt that area of complexity, because the Mauna Loa data stream 1960-2019 as published is only for CO2. Though for all I know they are measuring other gases too nowadays. And the plant being operated by the firm Carbon Engineering confines itself to CO2 also. One area I'd like to extend the model is to compare its estimate of the weight of CO2 with that published by James Lovelock in "Gaia". He pooh-poohs the very idea of carbon capture, asserting (without giving details) that the amount of CO2 needing to be captured would make a conical mound of dry-ice 1/3 of a mile high (though I'm going from memory here). Well that's not difficult to estimate using TABULA – or at least build models for estimating, which isn't quite the same thing. The only iffy bit is: what gradient should we adopt for the side of the mound? Well, the class could have fun with this, printing old photos of slag-heaps from Google Images and measuring angles with a protractor. Yet more assumptions to make: does a heap of slag behave like a heap of dry ice? Or more to the point, considering the purpose of the exercise: are there any obvious reasons why it doesn't? This is the very stuff of mathematical modelling. Getting back on-topic: one issue your discussion has alerted me to is this: a snapshot of the displayed t-table has its limitations as a tool for getting a feel for what the model *does*. TABULA does display the formula for each computed line: but only if you click on the line. I'm going to reintroduce a graphical display of the t-table, and I'm playing with a gl2 prototype. There is scope for coloring the arrows, or decorating them with little symbols: ⨁ ⨂ etc… to represent the computation actually taking place. Most physics formulas are simple sums and products, so the idea may have some mileage in it. Ian Clark On Fri, 7 Jun 2019 at 23:30, Raul Miller <[email protected]> wrote: > I was trying to find a profile of how CO2 is distributed with > altitude, and I didn't find that. > > I did find > https://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth%27s_atmosphere > which indicates that CO2 levels have been relatively low for millenia, > but if you go back far enough, they have been much, much higher than > what we're seeing now. > > But it did have a link to a page with an estimate of carbon in the > atmosphere of 720 gigatons: > https://en.wikipedia.org/wiki/Atmospheric_carbon_cycle > > CO2 has a molecular weight of 44g/mol and O2 has a molecular weight of > 32g/mol, and C has a molecular weight of 12g/mol. If "carbon" here was > C rather than CO2, that would mean that the change in mass of CO2 > since 1960 would be about > > 80*44*7.2e11%12*410 > 5.15122e11 > > But running through your calculations with the change in mass > contributed by CO2 being 15.049 g/mol (44.01-28.96) gives a total mass > of CO2 change since 1960 of 2.162e11 and I have reason to believe that > that number is too high.. > > So if that 720 gigaton number is right, it probably represents a > weight of CO2 and not a weight of bare C. This gives weight of CO2 > change in atmosphere somewhere near > > 80*7.2e11%410 > 1.40488e11 > > Which better fits what I would expect after thinking about the base > numbers you presented. > > (Assuming the 720 number was correct - it's very easy to make mistakes > and people tend to be sloppy with labels -- assuming that everyone > knows what they were thinking.) > > Thanks, > > -- > Raul > > > On Fri, Jun 7, 2019 at 5:25 PM Raul Miller <[email protected]> wrote: > > > > Ok... working through the numbers. > > > > If 28.96 is the current molecular weight of air, then there is no > > increase from CO2 - instead, you would subtract from that weight to > > find the molecular weight of air in 1960. > > > > If currently, CO2 represents 410ppm of air, then I would expect that > > the total molecular weight of air has a g/mol contribution of > > 44*410%1e6 > > 0.01804 > > > > Note however that when I read up on the molecular weight of air, > > people make pains to mention that their numbers represent the dry > > weight of air, and sometimes talk about how this changes due to H2O. > > It would probably be worth understanding the details they provide as > > there's some subtle things going on here. > > > > Anyways, we don't just add the weight of the CO2 molecules - they are, > > roughly speaking, replacing other averaged molecules. So it's roughly > > the difference between the previous average weight and the CO2 average > > weight that's going to give us the increase in weight. > > > > So the change in atmospheric molecular weight would be less than the > > values currently listed on {4} and {5}. Still... your lines {4} and > > {5} look to be roughly within an order of magnitude or two for the > > change in average molecular atmosphere weight due to increased CO2 > > since 1960. > > > > But then we get to the mass of the atmosphere, and I think you've > > oversimplified: https://en.wikipedia.org/wiki/Atmosphere_of_Earth > > describes the structure of the atmosphere. Since CO2 is heavier than > > some other components (oxygen, nitrogen), it's not going to rise as > > much as the lighter gasses. Still, we could use the number on line > > {7} as an upper bound... > > > > I don't understand your lines {8} and {9} so I'll stop here. > > > > Thanks, > > > > -- > > Raul > > > > On Fri, Jun 7, 2019 at 12:18 PM Ian Clark <[email protected]> wrote: > > > > > > The addons math/tabula and its parent addons math/cal and math/uu have > been > > > largely rewritten and are now far stabler than they were. > > > > > > The main way to get to grips with TABULA is via studying the built-in > > > t-tables ("TABULA-tables") SAMPLE0--SAMPLE9… > > > > > > https://code.jsoftware.com/wiki/TABULA/samples > > > > > > The last one, SAMPLE9, is particularly noteworthy. See this page for > > > details… > > > > > > > https://code.jsoftware.com/wiki/TABULA/samples/cost_to_capture_atmospheric_CO2 > > > > > > Atmospheric CO2 concentration has been rising steadily since 1960, > when it > > > first began to be measured regularly at Mauna Loa, HI. At that time it > > > stood at <320 ppm (parts-per-million). Now it stands at >400 ppm, an > > > increase of over 80 ppm. > > > > > > This observed level of atmospheric carbon is gaining wider acceptance > as > > > having a damaging effect on the world's climate. Whether it does or > not, a > > > British Columbia-based firm called Carbon Engineering has built a > plant to > > > capture CO2 from the atmosphere, at a cost of <$100 per metric ton (100 > > > USD/t). They have attracted $68 million investments from Chevron, > > > Occidental and coal giant BHP. > > > > > > https://www.bbc.co.uk/news/science-environment-47638586 > > > > > > I don't want to take sides over this. Nor to invite the taking of > sides in > > > this thread. Rather it's my aim to develop tools to help the rest of us > > > explore the figures for ourselves, whatever side we're on. Relying on > > > specialists to do the calculations is simply to promote a new world > > > religion, with applied mathematicians as its priesthood. > > > > > > So I thought I'd take Carbon Engineering's current price and use > TABULA to > > > calculate what it would cost to restore atmospheric concentration to > 1960 > > > levels. > > > > > > The cost comes out rather high: around 57 times the projected USA > budget > > > deficit for FY2020, would you believe? > > > > > > This raises vital questions for me: > > > > > > ++ are the input figures reliable? I used Google to track them down, > but > > > have I copied them over correctly? > > > > > > ++ is TABULA doing it right? I'm terrified of orders-of-magnitude > errors, > > > which can so easily arise with a misplaced prefix 'k' (kilo-) or 'G' > > > (giga-). > > > > > > Would anyone fancy checking my calculations? > > > > > > Ian Clark > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
