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# Experiments in carbon cycle with Sage

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1.
edited February 2011

I just emailed Staffan about these experiments, but it's better to have the conversation here.

He wrote:

what did you have in mind ?

I wrote:

For starters, I think it would be really fun to see the increases in CO2 from here:

ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt

plotted in various ways, for example:

1. the increase each month,
2. the increase each 2 months, divided by 2,
3. the increase each 6 months, divided by 6
4. the increase each 12 months, divided by 12
5. the increase each 24 months, divided by 24

OR, do the same thing using "seasonally corrected" data, which they also provide.

On the blog people have been suggesting more sophisticated filtering methods, which would also be interesting, but these are nice and simple.

It looks like there's data for each month starting with May 1964. Before that, some of the data is missing (e.g. February-April 1964), but they give "interpolated" data, and that should be okay.

He wrote:

I am also thinking that should put some "Tutorials ...in Sage" using Azimuth themes but keeping the programming part very simple - documenting the process. Or is that too low level?

Nothing is too low level! I might even learn Sage if the level is low enough, and that would make me very happy.

Comment Source:I just emailed Staffan about these experiments, but it's better to have the conversation here. He wrote: > what did you have in mind ? I wrote: > For starters, I think it would be really fun to see the increases in CO<sub>2</sub> from here: > [ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt](ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt) > plotted in various ways, for example: > 1. the increase each month, > 2. the increase each 2 months, divided by 2, > 3. the increase each 6 months, divided by 6 > 4. the increase each 12 months, divided by 12 > 5. the increase each 24 months, divided by 24 > OR, do the same thing using "seasonally corrected" data, which they also provide. > On the blog people have been suggesting more sophisticated filtering methods, which would also be interesting, but these are nice and simple. > It looks like there's data for each month starting with May 1964. Before that, some of the data is missing (e.g. February-April 1964), but they give "interpolated" data, and that should be okay. He wrote: > I am also thinking that should put some "Tutorials ...in Sage" using Azimuth themes but keeping the programming part very simple - documenting the process. Or is that too low level? Nothing is too low level! I might even learn Sage if the level is low enough, and that would make me very happy.
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2.
edited February 2011

It would also be nice to see some of these CO2 increases on the same graph as the "Nino-3 SST index", or maybe "Nino-3.4" or "Nino-5". These are sea surface temperatures in various patches of the Pacific Ocean:

Monthly data for these regions is available here.

Which region is both close to Hawaii and upwind from Hawaii? I guess Hawaii is that brown dot around 20° N. I guess Nino-3 is the best, since the winds blow from the east.

Comment Source:It would also be nice to see some of these CO<sub>2</sub> increases on the same graph as the "Nino-3 SST index", or maybe "Nino-3.4" or "Nino-5". These are sea surface temperatures in various patches of the Pacific Ocean: <img width="500" src="http://ggweather.com/enso/nino_regions.gif" alt = ""/> Monthly data for these regions is available <a href="http://www.cpc.ncep.noaa.gov/data/indices/sstoi.indices" rel="nofollow">here</a>. Which region is both close to Hawaii and upwind from Hawaii? I guess Hawaii is that brown dot around 20&deg; N. I guess Nino-3 is the best, since the winds blow from the east. <img src = "http://earthsci.org/processes/weather/wea1/normaloceancirc.gif" alt = ""/>
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3.

If you want to look at ENSO correlations, you might consider the Multivariate ENSO Index (MEI), a weighted average of simpler ENSO indicators.

I'm not sure whether it matters what region of the ocean is upwind from Mauna Loa. I suspect the main effect of ENSO on atmospheric CO2 will be through its climatic effects on terrestrial vegetation, not its direct effects on the ocean carbon cycle.

Comment Source:If you want to look at ENSO correlations, you might consider the <a href="http://www.esrl.noaa.gov/psd/people/klaus.wolter/MEI/mei.html">Multivariate ENSO Index</a> (MEI), a weighted average of simpler ENSO indicators. I'm not sure whether it matters what region of the ocean is upwind from Mauna Loa. I suspect the main effect of ENSO on atmospheric CO2 will be through its climatic effects on terrestrial vegetation, not its direct effects on the ocean carbon cycle.
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4.
edited February 2011

Cool. I just got decked by a bacteria last wednesday and had over 39 C for some days but I just started my antibiotics cure today so I'll wait until I've got no more fever and a clear head :-)

Comment Source:Cool. I just got decked by a bacteria last wednesday and had over 39 C for some days but I just started my antibiotics cure today so I'll wait until I've got no more fever and a clear head :-)
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5.

I added the first set of plots for the interpolated column and the trend (seasonally corrected) with default aspect ratio for list_plot(i think sage uses and set to 1 , which makes a circle look like a circle

John I wonder if you intended time series, w simple_moving_average(k)

Return the moving average time series over the last k time units. Assumes the input time series was constant with its starting value for negative time. The t-th step of the output is the sum of the previous k - 1 steps of self and the k-th step divided by k. Thus k values are averaged at each point.

Or is that too complex for people reading Azimuth?

Comment Source:I added the first set of plots for the interpolated column and the trend (seasonally corrected) with default aspect ratio for list_plot(i think sage uses and set to 1 , which makes a circle look like a circle John I wonder if you intended time series, w simple_moving_average(k) Return the moving average time series over the last k time units. Assumes the input time series was constant with its starting value for negative time. The t-th step of the output is the sum of the previous k - 1 steps of self and the k-th step divided by k. Thus k values are averaged at each point. Or is that too complex for people reading Azimuth?
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6.

See the new last plot which is with moving average 6 months over the interpolated whole co2 series

Comment Source:See the new last plot which is with moving average 6 months over the interpolated whole co2 series
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7.

I have done a bit of update in SAGE ,concerning fft, Hurst exponent for the co2 series, but i still need to add it here in Azimuth

Comment Source:I have done a bit of update in SAGE ,concerning fft, Hurst exponent for the co2 series, but i still need to add it here in Azimuth
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8.
edited February 2011

Cool stuff, Staffan!

John I wonder if you intended time series, w simple_moving_average(k)

I'm not quite sure what you mean by that question. But:

So far all your graphs show the amount of CO2 (perhaps seasonally corrected, etcetera). I would really like to see the increase in CO2, time-averaged in various ways, such as:

• the increase each month,

• the increase each 2 months, divided by 2,

• the increase each 6 months, divided by 6

• the increase each 12 months, divided by 12

• the increase each 24 months, divided by 24

So: take the amount one month, minus the amount the previous month, and then do moving averages as follows:

Return the moving average time series over the last k time units. Assumes the input time series was constant with its starting value for negative time. The t-th step of the output is the sum of the previous k - 1 steps of self and the k-th step divided by k. Thus k values are averaged at each point.

This sounds good and not "too complex for people reading Azimuth".

Comment Source:Cool stuff, Staffan! <img src = "http://math.ucr.edu/home/baez/emoticons/thumbsup.gif" alt = ""/> > John I wonder if you intended time series, w simple_moving_average(k) I'm not quite sure what you mean by that question. But: So far all your graphs show the _amount_ of CO<sub>2</sub> (perhaps seasonally corrected, etcetera). I would really like to see the _increase_ in CO<sub>2</sub>, time-averaged in various ways, such as: * the increase each month, * the increase each 2 months, divided by 2, * the increase each 6 months, divided by 6 * the increase each 12 months, divided by 12 * the increase each 24 months, divided by 24 So: take the amount one month, minus the amount the previous month, and _then_ do moving averages as follows: > Return the moving average time series over the last k time units. Assumes the input time series was constant with its starting value for negative time. The t-th step of the output is the sum of the previous k - 1 steps of self and the k-th step divided by k. Thus k values are averaged at each point. This sounds good and not "too complex for people reading Azimuth".
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9.

ok i will do that. Maybe I was getting carried away by learning about Time series in Sage :-) I also added some text on the significance of the Hurst exponent and how it shows that it is not a random walk plus one plot of the fft . But I will focus on increases now .

Comment Source:ok i will do that. Maybe I was getting carried away by learning about Time series in Sage :-) I also added some text on the significance of the Hurst exponent and how it shows that it is not a random walk plus one plot of the fft . But I will focus on increases now .
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10.

I'm just dropping in and haven't been able to follow what's going on here, but if you take the one month change as standard, I'd look at either

$(1+Average Monthly Growth)^6 = 1+ \frac{6-Month Change}{Initial Amount}$

or

$exp(6 \times Average Monthly Growth) = 1+ \frac{6-Month Change}{Initial Amount}$

rather than average changes. Then look at the time series of that. Especially if you eventually wanted to relate this to some model.

Comment Source:I'm just dropping in and haven't been able to follow what's going on here, but if you take the one month change as standard, I'd look at either $(1+Average Monthly Growth)^6 = 1+ \frac{6-Month Change}{Initial Amount}$ or $exp(6 \times Average Monthly Growth) = 1+ \frac{6-Month Change}{Initial Amount}$ rather than average changes. Then look at the time series of that. Especially if you eventually wanted to relate this to some model.
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11.

Hi, Eric! It seems your scheme makes sense if we assume CO2 concentration grows roughly exponentially, while make makes sense if we assume it grows roughly linearly. In economics people tend to take exponential growth as a default and talk about percentage growth per year, but I'm not sure that makes sense here.

I'm also not sure it doesn't make sense here.

Comment Source:Hi, Eric! It seems your scheme makes sense if we assume CO<sub>2</sub> concentration grows roughly exponentially, while make makes sense if we assume it grows roughly linearly. In economics people tend to take exponential growth as a default and talk about percentage growth per year, but I'm not sure that makes sense here. I'm also not sure it _doesn't_ make sense here.
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12.
edited March 2011

Staffan wrote:

But I will focus on increases now.

Thanks. I would like to correlate them to the El Niño.

Nathan wrote:

If you want to look at ENSO correlations, you might consider the Multivariate ENSO Index (MEI), a weighted average of simpler ENSO indicators.

Thanks!

Renato Iturriaga noticed a paper about El Niño and the carbon cycle - I'll put a link to it on Experiments in carbon cycle with Sage.

The abstract:

The equatorial oceans are the dominant oceanic source of CO2 to the atmosphere, annually amounting to a net flux of 0.7–1.5 Pg (1015 g) of carbon, up to 72% of which emanates from the equatorial Pacific Ocean (Houghton et al., 1994; Tans et al., 1990; Takahashi et al., 1997). Limited observations indicate that the size of the equatorial Pacific source is significantly influenced by El Niño events (Feely et al., 1995; Wanninkhof et al., 1996; Murray et al., 1994; Feely et al., 1987; Inoue and Sugimura, 1992; Goyet and Peltzer, 1994; Archer et al., 1996), but the effect has not been well quantified. Here we report spring and autumn multiannual measurements of the partial pressure of CO2 in the surface ocean and atmosphere in the equatorial Pacific region. During the 1991–94 El Niño period, the derived net annual sea-to-air flux of CO2 was 0.3 Pg C from autumn 1991 to autumn 1992, 0.6 Pg C in 1993, and 0.7 Pg C in 1994. These annual fluxes are 30–80% of that of 1996, a non-El-Niño year. The total reduction of the regional sea-to-air CO2 flux during the 1991–94 El Niño period is estimated to account for up to one-third of the atmospheric anomaly (the difference between the annual and long-term-average increases in global atmospheric CO2 content) observed over the same period.

Emphasis mine.

Comment Source:Staffan wrote: > But I will focus on increases now. Thanks. I would like to correlate them to the El Ni&ntilde;o. Nathan wrote: > If you want to look at ENSO correlations, you might consider the Multivariate ENSO Index (MEI), a weighted average of simpler ENSO indicators. Thanks! Renato Iturriaga noticed [a paper about El Ni&ntilde;o and the carbon cycle](http://www.pmel.noaa.gov/pubs/outstand/feel1868/text.shtml) - I'll put a link to it on [[Experiments in carbon cycle with Sage]]. The abstract: > The equatorial oceans are the dominant oceanic source of CO2 to the atmosphere, annually amounting to a net flux of 0.7–1.5 Pg (10<sup>15</sup> g) of carbon, up to 72% of which emanates from the equatorial Pacific Ocean (Houghton et al., 1994; Tans et al., 1990; Takahashi et al., 1997). Limited observations indicate that the size of the equatorial Pacific source is significantly influenced by El Niño events (Feely et al., 1995; Wanninkhof et al., 1996; Murray et al., 1994; Feely et al., 1987; Inoue and Sugimura, 1992; Goyet and Peltzer, 1994; Archer et al., 1996), but the effect has not been well quantified. Here we report spring and autumn multiannual measurements of the partial pressure of CO2 in the surface ocean and atmosphere in the equatorial Pacific region. During the 1991–94 El Niño period, the derived net annual sea-to-air flux of CO2 was 0.3 Pg C from autumn 1991 to autumn 1992, 0.6 Pg C in 1993, and 0.7 Pg C in 1994. These annual fluxes are 30–80% of that of 1996, a non-El-Niño year. **The total reduction of the regional sea-to-air CO2 flux during the 1991–94 El Niño period is estimated to account for up to one-third of the atmospheric anomaly (the difference between the annual and long-term-average increases in global atmospheric CO2 content) observed over the same period**. Emphasis mine.
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13.
edited March 2011

Experiments in carbon cycle with Sage

If my guess is wrong, please correct it! It's important that say where our data is coming from.

I also added a bunch of references at the end — they were on the blog, but it's good to have all this stuff in one place.

Comment Source:Staffan: I made a _guess_ about where you got your Mauna Loa CO<sub>2</sub> data and added this guess to [[Experiments in carbon cycle with Sage]] **If my guess is wrong, please correct it!** It's important that say where our data is coming from. I also added a bunch of references at the end &mdash; they were on the blog, but it's good to have all this stuff in one place.
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14.

You are ahead of me :-) Are you referring to that I didn't yet mention Mauna Loa as the source?

the only source i've used is that ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt

but I am going to add the correct graphs today and tomorrow.

Comment Source:You are ahead of me :-) Are you referring to that I didn't yet mention Mauna Loa as the source? the only source i've used is that ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt but I am going to add the correct graphs today and tomorrow.
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15.
edited November 2011

I updated the Sage part with plots on the annual increase plotted below the Keeling plot. I also found a good plot that shows correlation on ENSO with the carbon increase. I might add it if you want too?

Also I took away most of the code and just the kmain part and added a reference to the new published sage workksheet.

Comment Source:I updated the Sage part with plots on the annual increase plotted below the Keeling plot. I also found a good plot that shows correlation on ENSO with the carbon increase. I might add it if you want too? Also I took away most of the code and just the kmain part and added a reference to the new published sage workksheet.
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16.

just found where i've seen the enso correlation plot. its in lectures by Daniel Jacob and here it is slide 48 entitled "Emissions and global changes"

Comment Source:just found where i've seen the enso correlation plot. its in [lectures by Daniel Jacob and here it is](http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/lecture_eps133_chap6.ppt) slide 48 entitled "Emissions and global changes"
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17.
edited November 2011

Comment Source:snip wrong thread
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18.
edited November 2011

Hi! Thanks for pointing out those lectures. The correlation to ENSO looks rather weak. But I like the chart on page 50 showing how about 57% of CO2 emitted winds up in the atmosphere, on average, with huge annual variations!

As you probably remember, Renato Iturriaga was wondering about these thing on Azimuth (he did a blog entry on them), so I'll tell him about this file.

I also like the section on chemical reaction involving CO2, carbonate ions, bicarbonate ions and the like in the ocean. I find these a bit complicated and counterintuitive. This might be a good topic for a box model!

Comment Source:Hi! Thanks for pointing out those lectures. The correlation to ENSO looks rather weak. But I like the chart on page 50 showing how about 57% of CO<sub>2</sub> emitted winds up in the atmosphere, _on average_, with huge annual variations! As you probably remember, Renato Iturriaga was wondering about these thing on Azimuth (he did a [blog entry](http://johncarlosbaez.wordpress.com/2011/02/04/carbon-dioxide-puzzles/) on them), so I'll tell him about this file. I also like the section on chemical reaction involving CO<sub>2</sub>, carbonate ions, bicarbonate ions and the like in the ocean. I find these a bit complicated and counterintuitive. This might be a good topic for a box model!
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19.

I saw slide 50 also i might use it . Pls inform Renato if you want !

Yes I am using both his ch.6 slides but also ch3 ("simple models", so they might end up being boxed :-)

Comment Source:I saw slide 50 also i might use it . Pls inform Renato if you want ! Yes I am using both his ch.6 slides but also ch3 ("simple models", so they might end up being boxed :-)