Why is cumulative CO2 Airborne Fraction nearly constant?.

Airborne Fraction of CO2 is the ratio of the amount observed in the atmosphere to the amount emitted. I have been writing (here and here) about how it seems to be extraordinarily stable. In saying this I define and plot it in a different way to the usual, in which it appears more variable, leading to speculation about trend. I'll say more about this different way below. But I think I have worked out the explanation for the stability, and it isn't obvious.

People tend to think first of Henry's Law, which suggests a fixed partition of a solute (including gas) between two phases. This is a material property, and refers to equilibrium, which does not apply to CO2 in air/sea. It applies even less to the land sink, which is quite important.

In this note, I will show that the constancy, perversely, depends on the dynamics, and is a result of the near exponential increase in CO2 emissions. This effect is mostly independent of the actual mechanism for the sinks. It is really a consequence of linearity with exponential increase.

Since this post is something of a math proof, here is a TOC:

• Cumulative plotting
• Exponential emissions
• Steady observed airborne fraction
• Linearity and superposition.
• Airborne fraction invariance
• Airborne fraction if emissions growth is not exponential

GWPF Temperature Adjustments inquiry - no news.

Two months ago, I wrote about the inquiry announced by the Global Warming Policy Foundation. You know, the one fanfared in the Telegraph. "Top Scientists Start To Examine Fiddled Global Warming Figures"

The news then was that after receiving submissions on June 30, they decided that they wouldn't write a report re the terms of reference, but maybe some papers. They had however said that they would publish the submissions. So I thought I should look in every two months or so to see what has happened.

But this time, no news. Just the report of September 29, confirming intended inaction. I'll check again next year.

Using NOMADS data - movies

I've cracked the system for efficiently using NOMADS data. I'm using an R package rNOMADS. It's a system where you can quiz and selectively download a large set of gridded data. It gives me access to many new resources for high frequency data, including reanalysis.

Anyway, as a first experiment, I downloaded GFS 0.5° surface relative humidity data ("gfs_0p50","rh2m"). This data is prepared for the forecast system, and held for about 12 days. So here we have a movie of the data from 11th to 23rd November, at 6 hour intervals. This is all experimental; the movie is ogg, so should show on Firefox and Chrome, but probably not on IE or Safari. Update - I've made an alternative mp4 version, which works in Safari at least. It has the usual controls - you may need to pass the mouse pointer below the picture to make them show. Blue is high humidity, red dry. A color key will appear at some stage.

NOAA October 0.98°C!

The NOAA report is out, and shows the global anomaly rose from 0.90°C in September to 0.98°C in October. The report says that it was the hottest measured October, but in fact it was the highest anomaly of any month in the record by quite a long way, ahead of 0.9°C in just the previous month.

As expected, the rise was less than for GISS. The reason is coverage of Antarctica. Antarctica had been very cold, and switched to warm in October. GISS, which weights by total area, is very sensitive to this, and so lagged in Sept, followed by a big jump. My TempLS grid does the same. But NOAA only counts the grid cells with information, which are few in Antarctica. Consequently, it rose to a record anomaly in September, with a relatively smaller rise in October. Still, that means it upped the record by 0.08°C.

TempLS grid behaved in much the same way as NOAA, as it usually does. It rose by 0.06. The regional pattern of warmth described in the NOAA report is much as described in the TempLS report.

Update. I'll comment further on some questions in the TempLS October post. First, as Olof noted, Barzil and Greenland, not then in, had a considerable warming effect. So the rise in TempLS mesh, at 0.24°C, ended up exactly the same as GISS. And TempLS grid at 0.06 was very close to the 0.08°C rise for NOAA. This is the usual correspondence, relating to the respective methods.

There was also the question of SST. TempLS, in its attribution analysis, showed a small contribution from SST. But HADSST3 had actually declined. This made me more cautious about TempLS-based prediction. But the NOAA report showed NOAA ocean at 0.85°C, a rise of 0.04, very similar to the TempLS attribution. And that figure was also a record for any month, improving on the previous month's record.

Update. I've shown below the latest recent plot, from here. It shows the global indices set to a common anomaly period of 1981-2010. You can see how TempLS and GISS are currently moving in tandem, as are TempLS grid and NOAA.

GISS October 1.04°C, record month anomaly.

GISS is out, a bit late. But it is at or above expectations. At 1.04°C, up by 0.24°C from September 0.8°C. That is well clear of the previous highest, 0.97°C in Jan 2007, which was itself something of an outlier.

Update. Needless to say, 2015 is pulling away in the progress to hottest year. Sou has the story here, with her updated chart. Looks like 2015 will be at least 0.1°C hotter than any previous year. It will be hard to gin up uncertainty about that.

The rise is almost the same as TempLS mesh, 0.235°C. Here is a plot of the last 20 years, monthly, with annual average overlaid:


Graphs are below the jump.

Airborne fraction CO2 and the Bern model

We've been discussing IPCC projections and RCPs in relation to the airborne fraction (AF) of CO2. The AF is the fraction of CO2 emitted that remains in the air, relative to the amount emitted. In an earlier post I showed that if you plotted cumulative emissions against total CO2, it was very linear, implying a close to constant AF. You get different constants depending on whether you look at just FF emissions, or total, including land use.

At first constant AF might seem to be a consequence of Henry's Law. But that gives a fixed phase partitioning at equilibrium, which we don't have (not to mention acid/base chemistry). It might seem surprising that the time varying sink uptake could give that result.

So I tried with the dynamics of the Bern model. This is what the IPCC would probably use if they were to express an opinion on the future of AF (which they don't). The Bern model yields an impulse response function for a pulse of CO2 injected into the atmosphere. In this version, it makes that out of the sum of decaying exponentials of periods ∞, 171, 18 and2.57 years. If you filter total emissions with this function (reversed), that gives the modelled growth of the amount of CO2 in the air at any time. A caveat; fitting observed AF was no doubt one of the considerations in designing the Bern model.

So I did that. I'll show the results below. Plotting accumulated CO2 against cumulative emissions, the result is still remarkably linear. And the slope, at 0.436, is remarkably close to what I found with observed CO2 (0.439). OK the caveat applies, but the constancy is the real result.

Google Map for GHCN V4

I have a series of Google Maps tools, which you can read about on the Gallery page. The latest (till now) is here, on adjustments. In this post, I have made one in similar style for GHCN V4 Beta.

The tool shows a Google map with the usual facilities, but with markers for the stations in GHCN V4. You can click on a marker to bring up some details. The main utility is that you can choose different marker colors for different subsets. An important color is "Invis". It earlier stood for invisible, though it is now implemented by removing the marker from the map (you can get it back).

At the right you can see an orange-background table of the color options, and a cyan table of selection criteria. The selections come with a more/less sign that you can toggle, and a textbox where you can write a criterion number. Tick the left checkbox to make it live. The color table has radio buttons to make the color happen, and on the other side a count of how many of that color there are.

Nothing happens until you then click on a color radio button. When you do, the markers are sorted according to the live (checked) selection options, and those that qualify change to that color. This is "and" logic; all criteria have to be satisfied. You'll find it useful to sometimes switch to negative logic - make Invisible the options you don't want. If no checkboxes are ticked, everything will change.

I've included Lat and Lon so that you can look at a restricted area. I was thinking of performance there - the map can get sluggish if too many markers are visible. In fact, I haven't had performance problems, but that may be because my computer has upgraded.

At the bottom a selection box allows you to make color itself an option. You can subset from the classes you have discriminated.

Some examples of things you might want to do:

• Set endyr>2014 to pink the stations currently reporting. Or set endyr<2015 and then Invis to remove those that are not
• Begin by making everything Invis (just click it).
• Set duration >100 to pink (or cyan etc) long duration stations.
• Set startyr>1850 and Invis to leave only the very early stations

The pop-up tags give dates, name and the GHCN Inventory number. The first two letters of that are an abbreviation for the country (details here).