Friday, March 16, 2018

GISS February global temperature unchanged from January.

GISS cooled, February anomaly average was 0.78°C, same as January (GISS report here). That differs from TempLS mesh, which rose by 0.06°C, as did the NCEP/NCAR index.

The overall pattern was similar to that in TempLS. Warm in the Arctic (very) and Siberia, Eastern USA, and also a band from Nigeria through to W India, bit warmest around the E Mediterranean. There was a band of cold in Canada below the Arctic extending into the US upper mid-west, and in Europe. Both show an interesting pattern of mostly warm patches in the roaring Forties.

As usual here, I will compare the GISS and previous TempLS plots below the jump.

Tuesday, March 13, 2018

Buffers and ocean acidification.

This is an ongoing topic of blog discussion - recently here. I have written a few posts about it (eg here), and there is an interactive gadget for seawater buffering here. One of my themes is to reduce the emphasis on pH. The argument is that it is present in very small quantity; the buffering inhibits change, and so it is not a significant reagent. Because of its sparsity, it was until recently hard to measure. So both with measurement and conceptually, it is better to concentrate on the main reagents. These are CO₂, bicarb HCO₃⁻ and carbonate CO₃⁻². Carbonate is also involved in a solubility equilibrium with CaCO₃.

There is resistance to defocussing on H⁺, based on older notions that it is the basis of acidity. But for 95 years we have had the concept of Lewis acidity, in which a proton is just one of many entities that can accept an electron pair. CO₂ is another such Lewis acid. And to it makes possible the description of the overall reaction of CO₂ absorption

CO₃⁻² + CO₂ + H₂O ⇌ 2HCO₃⁻

as a Lewis acid/base reaction, in which carbonate donates an electron pair to CO₂. I propound that, but meet resistance from people who think Lewis acidity is an exotic modern concept.

I've realised now that that isn't necessary, because the notion of buffering isn't tied to any notion of acidity. So I can set up buffer equations just involving those three major reagents.

pH Buffer

A buffer is normally described as an equilibrium

A + H ⇌ HA

where HA is a weak acid, A the conjugate base and H a proton. I have dropped the charge markings. The system operates as a buffer as long as substantial concentrations of both A and HA are present. I'll denote concentrations as h, a and ha.

The maths of the buffer system comes from the equations

h*a/ha = K(M)
ha + h = cH(H)
ha + a = cA(A)
Eq (M) is the Law of Mass Action. Eq (H) is mass balance of H, and (A) of A. As the reactions of the equilibrium proceed, the numbers on the right are invariant within the reactions. The equilibrium will shift if one of them changes from outside effect.

The equations are a mixture of multiplicative and linear, and in the buffer calculator I used a Newton-Raphson method to solve the coupled systems. But for one buffer there is a simple way which illustrates the buffering principle. The iteration for given K, cH and CA goes: starting with h=0
1 solve (H) and (A) for a and ha
2 solve (M) for h and repeat (if really necessary)

Under buffer conditions K is small, and so is H, and so changing h will not make much relative change to ha and a, and so in turn will not affect the next iteration of h that emerges from solving (M). The process converges quickly and ensures h stays small. The buffer is perturbed by changing cH or cA, either by adding reagents or by perturbing other equilibria in which reagents are involved. Eq (M) ensures that h not only remains small, but is fixed by the slowly changing ratios of the major species.

Here is a worked example. A litre of 1M A, 1M HA, pKa=8 (so pH=8).
Add 0.1M HCl, sufficient to reduce pH of water to 1.
Then, ignoring volume change:
ha=1.1 (eq H, total H) and ha+a=2 (eq A) so a=0.9.
Then from (M), h=1e-8*1.1/0.9=1.222e-8
On iteration, the corrections to (H) and (A) would be negligible. The pH has gone from 8 to 7.91

Now there is no mention of any kind of acidity in this math. The only requirement is that there is a ternary equilibrium in which one component H is in much lower concentration than the others. H could be anything So I didn't need to talk about Lewis acids (it helps understanding but not the buffer math).

Bjerrum plot

The classic way of graphing buffer relations is with a Bjerrum plot. This takes advantage of the fact that you can divide a and ha by cA, and eq (M) is not changed. Eq H would be, but you can let it go if h is specified as the x-axis variable. Then M is solved to show a/cA and ba/cA (which add to 1) as functions of h, or usually, -log10(h). Actually, Bjerrum plots are really only interesting for coupled equilibria. Here is a Wiki example:

Generalised buffer - sea water

Sea water buffering is complicated, in normal description, by the interaction of two pH buffers (numbers from Zeebe)
HCO₃⁻+H⁺ ⇌ CO₂ + H₂OK1: pKa=5.94
CO₃⁻²+H⁺ ⇌ HCO₃⁻K2: pKa=9.13

The pKa for a H,A,HA buffer is the pH at which ha=a. K1, K2 are the equilibrium constants, as in Eq (M). So it is a complicated calculation. But the two can be combined, eliminating the sparse component H⁺, as before

CO₃⁻² + CO₂ + H₂O ⇌ 2HCO₃⁻

Now we still have an essentially ternary equilibrium, since the concentration of water does not change. And [CO₂] is still small. It is essentially a buffer equation, but buffering [CO₂]. The equations now are, with A=CO₃⁻², HA=HCO₃⁻ and H=CO₂:

h*a/ah² = K(M')
ha + a + h = cC(C)
ha + 2*a = cE(E)

The additive equations are different; I've renamed them as (C) (total carbon, or dissolved inorganic carbon cC=DIC) and (E) (cE = total charge, or total alkalinity TA). K can be derived from the component buffers above, K=K2/K1, so -Log10(K) = 9.13-5.94 = 3.19

Summarising for the moment:
  • I have replaced two coupled acid/base buffers with a single equilibrium with buffering properties, eliminating H⁺.
  • The components are the main carbonate reagents, which we can solve for directly.
  • The additive equations conserve the measurement parameters DIC and TA.
  • CO₂ replaces H⁺ as the sparse variable, and also the measure of (Lewis) acidity.

Bjerrum plot for generalised buffer

This uses the same idea of choosing a x-axis variable, and using the equation that results from eliminating it from the additive equations as the constraint, scaling wrt its rhs. The x-axis here uses the scarce species H=CO₂, and the eq (E) for total alkalinity is suitable for normalising, since cE=TA does not change as h varies. So the new plot variables are
  • x = -log10(h/cE)
  • y = 2*a/cE
  • y'=1-y=ha/cE
Here is the plot, using standard concentrations a=260, ha=1770 μM, K=K2/K1=6.46e-04, so TA=2290 μM

For the simple pH buffer, the curves would be tanh functions; here they are similar but not symmetric. More acid solutions are to the left; the green line represents equilibrium h for those conditions; adding CO₂ does not change the normalising TA and moves the green line to the left.

Perturbing an equilibrium by forcing concentration

Again a natural iteration can be used for the equations, based on the small component. However, in the real OA problem, we don't add a finite amount of reagent, but force an new change in the buffered quantity [CO₂] by air change. Then the buffering effect works in reverse; a small change forces big changes elsewhere.

Suppose we have a pond of seawater, with standard concentrations a=260, ha=1770, h=[CO₂]=10 μM. Suppose the pCO₂ in air rises by fraction f. We don't actually need to know what pCO₂ is, just use Henry's law to say [CO₂] will increase in the same ratio. We can't use eq (C), because change in cC is unknown, but eq (E) says Δha = -Δa. Letting x be the fractional change in a, and m=2*a/ha=0.294, so the fractional change in ha is -m*x so from (M') we have,
(1+f)*(1+x)/(1-m*x)² = 1 (ratio change)
or f+x*(1+f+2*m) = (m*x)² (ratio change)

We could solve this as quadratic, but it is instructive to iterate, solving
x<- -="" br="" f-="" f="" m="" starting="" with="" x="2"> With f=0.1 (10%) the iterates are -0.07175, -0.07166737, -0.07166755

The first term is good enough. The key result is that a 10% change in atmospheric CO2 makes a 7% change, at equilibrium, with [CO₃⁻²], even though its concentration remains very small. Note that there is no reference to pH in this calculation. pH can be recovered from eq (M).

Repeating that main result; if m=[CO₃⁻²]/[HCO₃⁻] and the fractional change in gas phase pCO₂ is f, then the fractional change x in [CO₃⁻²] is given to very good approximation by
x = f/(1+f+2*m)
Estimates of m vary, but are usually around 0.1. So the fractional reduction in [CO₃⁻²] is comparable to the fractional increase in pCO₂.

Of course that is an equilibrium calculation, and the mixing time of the whole ocean is very long, so it could only apply to surface layers. It also omits the key question of CaCO₃ dissolution, which could restore [CO₃⁻²]. That dissolution is seen as the penalty, and this quantifies it.

Summarising again the virtues of this approach:
  • It eliminates H⁺ and deals with the reagents directly
  • The natural measures are the Dissolved Inorganic Carbon (DIC) and Total Alkalinity, both easily lab-measured and with data available
  • It gives a useful approximation to the natural forcing condition, which is change in pCO₂ in the air
  • The concept is that [CO₂] is buffered rather than pH. That leads directly to the consequence that trying to force a change in [CO₂] passes directly to a change in carbonate instead.

Wednesday, March 7, 2018

February global surface TempLS up 0.05 °C from January.

The TempLS mesh global anomaly (1961-90 base) rose from 0.603°C in January to 0.655°C in February. This is almost the same as the 0.054°C rise in the NCEP/NCAR index, while the satellite TLT indices fell by a similar amount.

The main warmth was in the Arctic and Siberia, Eastern USA, and also a band from Nigeria through to W India, bit warmest around the E Mediterranean. There was a band of cold in Canada below the Arctic extending into the US upper mid-west, and in Europe.

Because of the warmth in the Arctic, it is likely that indices will diverge according to the extent to which they represent it. TempLS grid, which is weaker there, showed a drop of about 0.04°C. As often, I would expect GISS to show a rise like TempLS mesh, while NOAA and HADCRUT may fall.

Here is the temperature map. As always, there is a more detailed active sphere map here.

Saturday, March 3, 2018

February NCEP/NCAR global anomaly up by 0.054°C from January

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average rose from 0.231°C in January to 0.285°C in February, 2018. The big dip in January continued in to the earlier part of February, then a considerable peak, and a modest dip and recovery at the end.

It was cold in the northern prairies and N Canada, but surprisingly, warm on average in E USA. Cold in Europe, extending through Morocco to Senegal. As much noted, very warm in the Arctic, and warm in a band from E Mediterranean to N India. Mixed in Antarctica, probably on average cool. Interactive map here.

I expect that Arctic-sensitive indices like GISS, Cowtan and Way, and TempLS mesh will show more warming than the others. Here is a temperature map looking down on the N Pole

Friday, February 16, 2018

GISS January global down 0.11°C from December.

GISS cooled, going from 0.89°C in December to 0.78°C in January (GISS report here). That is a smaller drop than TempLS mesh; I originally reported a 0.2°C fall, but later data changed that to a 0.16°C fall. GISS says that January 2018 was the fifth warmest in the record, and was cooler due to La Niña.
Update. I wrote this post based on the GISS report, as the data file was not posted for some time. It is now there, and I see that the December average has been adjusted up from 0.89&deg;C to 0.91&deg;C. That means the drop Dec-Jan is now 0.13&deg;C. This brings it close to the TempLS change of 0.16&deg;C. TempLS also incrased in December due to later data, so in both months GISS and TempLS now track well. 

The overall pattern was similar to that in TempLS. Cool in east N America and cold in far East Siberia. Very warm in west of Russia, and in the Arctic. A cool La Nina-ish plume, but warm in the Tasman sea and nearby land. The W US was warm, more so than TempLS showed. Also the W Russia hotspot extended well into central Europe.

As usual here, I will compare the GISS and previous TempLS plots below the jump.

Wednesday, February 7, 2018

January global surface tempLS down 0.2 °C from December.

TempLS mesh anomaly (1961-90 base) fell from 0.762°C in December to 0.565°C in January. This compares with the fall of 0.097°C in the NCEP/NCAR index, and a similar fall (0.16) in the RSS LT satellite index.
According to the reanalysis, the cause was a deep dip late in the month, which seems to be extending into February.

The main cool areas were central asia into Mongolia , and Eastern N America. Also Central Africa. Warm were NW Russia, extending into Europe, and N Canada/Alaska. Also a band right across temperate SH, but still very warm Tasman Sea and around.

Here is the temperature map:

Tuesday, February 6, 2018

Weirdness from Armstrong/Green and conservative media.

This was new to me when it popped up at WUWT. But apparently is has already been around for a week or so, at Fox News and The Australian. Economists Scott Armstrong and Kesten Green, who regard themselves (pompously) as authorities on forecasting, made a splash ten years ago when they made a challenge of a bet with Al Gore that their forecast of global temperature, based on no change, would be better over the next ten years than his. They even set up a website, to track his response, and presumably track the bet. And they got a good run in the conservative media at the time.

Gore never showed any interest - he just said that he doesn't bet. So it was empty noise. However, for some strange reason, there is now a volley of fantasy articles, attributing a bet to Gore (in which he had no say) and declaring him the loser. The terms of the bet are exceedingly arcane. Since they have to make up some warming forecast, they picked an "IPCC" forecast of 0.3°C warming for the decade.

The first thing to say is that the IPCC made no such forecast. They did, in the AR4 SPM that came out at abaout that time, say this:
For the next two decades, a warming of about 0.2°C per decade is projected for a range of SRES emission scenarios.
And it was for surface temperature, not the troposphere measure that Armstrong/Green decided on.

But that itself turns out oddly. They nominate UAH as a measure, which actually has a slightly higher trend over the period than surface measures. Here is the plot

And they are betting with zero trend (blue). The actual was more than double the "IPCC trend". They lose by a mile. But in the WUWT article, at least, they say the OLS trend for the period is 1.53°C/Century. But they prefer a measure they make up called Least Absolute Deviation (LAD).

Well, they would, wouldn't they, because they say that comes out to 1.14°C/Century, and on that basis they declare themselves the winner (since they have pinned Gore with the "IPCC" 3 C/century. Of course it is 2, not 3, so even on that basis they lose. But since they seem to have miscalculated the OLS trend by a factor of 3, I have no faith in their LAD calculation.

On the plot, I've marked a line with slope 1.14°C/century in green, and the Armstrong/Green zero forecast in blue. They all, as fitted lines should, pass through the mean of x and y. See if you think the "LAD" line (1.14) is a better fit. Or whether the no trend forecast is the winner.

Scott Armstrong is a professor of marketing. Kesten Green is a lecturer in Commerce. Neither seems to know much about what the IPCC actually says. And they seem pretty weak in statistics.