Tuesday, August 14, 2018

July global surface TempLS down 0.045 °C from June.

The TempLS mesh anomaly (1961-90 base) fell a little, from 0.680°C in June to 0.635°C in July. This is opposite to the 0.052°C rise in the NCEP/NCAR index, while the UAH satellite TLT index rose more (0.11°C).

The post is late again this month, and for the same odd reason. Australia submitted a CLIMAT form with about 1/3 the right number of stations, mostly SE coast. Kazakhstan, Peru were late too, but Australia is the big one. That data still isn't in. I've modified the map in the TempLS report to show the stations that reported last month (but not this) in a pale blue to show what is missing.

There were some noted heat waves, but relatively restricted in space and time. There was a big blob of heat covering Europe, N Africa and up to W Siberia. Mid Siberia was cold, as was Greenland and nearby sea, and Argentina. Arctic was cool, Antarctic warmer. N America was warm, especially W Coast and Quebec. SSTs continued rising overall.

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




Friday, August 3, 2018

July NCEP/NCAR global surface anomaly up by 0.052°C from June

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average rose from 0.209°C in June to 0.261°C in July, 2018. June was cold by recent standards, so that is a modest recovery. In the lower troposphere, UAH rose more, by 0.11°C.

Notably, there were heat waves in W and N Europe, extending in a band through Russia, and into N Sahara. Parts of W and E North America were also hot, but unevenly so. Cool areas in S America and Southern Africa, and Central Siberia. The Arctic was mixed, with some cold, and the Antarctic even more so.

BoM is on El Niño Watch, meaning about a 50% chance, they say, but nothing yet.

Arctic Ice seems to have thawed rapidly lately, but there may be recent artefacts. JAXA has been irregular.


Tuesday, July 17, 2018

GISS June global down 0.06°C from May.

The GISS land/ocean temperature anomaly fell 0.06°C last month. The June anomaly average was 0.77°C, down from May 0.83°C. The GISS report notes that it is the equal third warmest June in the record. The decline contrasts with the virtually unchanged TempLS; the NCEP/NCAR index declined a little more. Satellite indices both rose a little.

The overall pattern was similar to that in TempLS. Very warm in N Central Siberia and Antarctica. Warm in most of N America, and also in Europe and Middle East. Rather cold in S America and Arctic.

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

Wednesday, July 11, 2018

Extended portal to the BoM station data.

I maintain a page of portals to various climate datasets, which sometimes just has a link, and sometimes something more active, giving what I think is more convenient access. The Australian Bureau of Meteorology has a large amount of well organised data on its site. There is a lot that you can get to via the Climate Data Online page. There is also station metadata, which I had previously made an access frame on the page. This is now extended, to gather together as much station data as I can in one place. So that includes metadata, station climate statistics, and detailed records of monthly average maxima (TMax) and minima (Tmin), and corresponding daily data. BoM does not provide Tmax+Tmin averages.

There are various notions of station here. BoM actually has a huge set, but many have rainfall data only, and those are omitted here. There is a subset that have AWS, and post data in a different way, to which I provide a separate portal button. Then there is the ACORN set, which is a set of 110 well maintained and documented stations, for which the data has been carefully homogenised. It starts in 1910. BoM seems proud of this, and the resulting publicity has led some to think that is all they offer. There is much more.

I've tried to provide the minimum of short cuts so that the relevant further choices can be made in the BoM environment. For example, asking for daily data will give a single year, but then you can choose other years. You can also, via BoM, download datafiles for individual stations, daily for all years, or in other combinations.

The BoM pages are very good for looking up single data points. They are not so good if you want to analyse data from many stations. Fortunately, all the data is also on GHCN Daily, for which I have a portal on the same page. It takes a while to get on top of their system - firstly generating the station codes, and then deciphering the bulky text file format. But it's there.

For the new portal, the top of the table looks like this:



If you click on the red-ringed button, it shows this:



To get started, you need to choose a state. Then a list of stations, each with a radio button, will appear below. Then, from the lilac bar, you should choose a data type, eg daily Tmax. Then you can click on a station button. Your selection will appear in a new tab to which your browser takes you. From there you can makes further choices in the BoM system.

Your station choice will also appear beside the square button below the lilac (and above the stations). This button now has the same functionality as the station button below, so you don't have to scroll down to make new data choices. You can indeed make further data choices. These will make new tabs, to facilitate comparisons, but up to a max of the two most recent.



Tuesday, July 10, 2018

WUWT and heat records.

I'm on the outer again at WUWT (update - seems OK now). The issue is recent heat records, which WUWT wants to challenge because of alleged inadequacies in the stations. Not that the thermometers were inaccurate, but that the environment was not representative of climate. My contention was that this was only relevant to climate science if scientists were using them as representative of climate, and for most of the stations at issue, they weren't.

Since I did quite a bit of reading about it, I thought I would set down the issues here. The basic point is that there are a large number of thermometers around the world, trying to measure the environment for various purposes. Few now are primarily for climate science, and even fewer historically. But they contain a lot of information, and it is the task of climate scientists to select stations that do contain useful climate information. The main mechanism for doing this is the archiving that produces the GHCN V3 set. People at WUWT usually attribute this to NASA GISS, because they provide a handy interface, but it is GHCN who select the data. For current data they rely on the WMO CLIMAT process, whereby nations submit data from what they and WMO think are their best stations. It is this data that GISS and NOAA use in their indices. The UKMO use a similar selection with CRUTEM, for their HADCRUT index.

At WUWT, AW's repeated complaint was that I don't care about accuracy in data collection (and am a paid troll, etc). That is of course not true. I spend a lot of time, as readers here would know, trying to get temperature and its integration right. But the key thing about accuracy is, what do you need to know? The post linked above pointed to airports where the sensor was close to the runways. This could indeed be a problem for climate records, but it is appropriate for their purpose, which is indeed to estimate runway temperature. The key thing here is that those airport stations are not in GHCN, and are not used by climate scientists. They are right for one task, and not used for the other.

I first encountered this WUWT insistence that any measurement of air temperature had to comply with climate science requirements, even if it was never used for CS, in this post on supposed NIWA data adjustments in Wellington. A station was pictured and slammed for being on a rooftop next to air conditioners. In fact the sataion was on a NIWA building in Auckland, but more to the point, it was actually an air quality monitoring station, run by the Auckland municipality. But apparently the fact that it had no relation to climate, or even weather, did not matter. That was actually the first complaint that I was indifferent to the quality of meteorological data.

A repeated wish at WUWT was that these stations should somehow be disqualified from record considerations. I repeatedly tried to get some meaning attached to that. A station record is just a string of numbers, and there will be a maximum. Anyone who has access to the numbers can work it out. So you either have to suppress the numbers, or allow that people may declare that a record has been reached. And with airport data, for example, you probably can't suppress the numbers, even if you wanted. They are measured for safety etc, and a lot of people probably rely on finding them on line.

Another thing to say about records is that, if rejected, the previous record stands. And it may have no better provenance than the one rejected. WUWT folk are rather attached to old records. Personally, I don't think high/low records are a good measure at all, since they are very vulnerable to error. Averages are much better. I think the US emphasis on daily records is regrettable.

The first two posts in the WUWT series were somewhat different, being regional hot records . So I'll deal with them separately.

Motherwell

The WUWT post is here, with a follow-up here. The story, reported by many news outlets, was briefly this. There was a hot day on June 28 in Britain, and Motherwell, near Glasgow, posted a temperature of 91.8°F, which seemed to be a record for Scotland. A few days later the UKMO, in a blog post, said that they had investigated this as a possible record, but rules it out because there was a parked vehicle with engine running (later revealed as an ice-cream truck) close by.

As might be feared, this led in comments to accusations of dishonesty and incompetence at the UKMO, even though they had initiated and reported the investigation. But one might well ask, how could it happen that that could happen at a UKMO station?

Well, the answer is that it isn't a UKMO station. As the MO blog explained, the MO runs: "a network comprised of approximately 259 automatic weather stations managed by Met Office and a further 160 manual climate stations maintained in collaboration with partner organisations and volunteer observers" Motherwell is a manual station. It belongs to a partner organisation or volunteers (the MO helps maintain it). They have a scheme for this here. You can see there that the site has a rating of one star (out of five), and under site details, in response to the item "Reason for running the site" says, Education. (Not, I think, climate science).

So Motherwell is right down the bottom of the 400+ British stations. Needless to say, it is not in GHCN or CRUTEM, and is unlikely to ever be used by a climate scientist, at least for country-sized regional estimates.

So to disqualify? As I said above, you can only do this by suppressing the data, since people can work out for themselves if it beats the record. But the data has a purpose. It tells the people of Motherwell the temperature in their town, and it seems wrong to refuse to tell them because of its inadequacy for the purposes of climate science, which it will never be required to fulfil.

The WUWT answer to this is, but it was allowed to be seen as a setter of a record for Scotland. I don't actually think the world pays a lot of attention to that statistic, but anyway, I think the MO has the right solution. Post the data as usual (it's that or scrub the site), and if a record is claimed, vet the claim. They did that, rejected it, and that was reported and respected.

Ouarglu, Algeria

The WUWT post is here. On 5 July, this airport site posted a temperature of 124°F, said to be a record for Africa. There have been higher readings, but apparently considered unreliable. The WUWT heading was "Washington Post promotes another potentially bogus “all time high” temperature record"

But "potentially bogus" is what they would call a weasel word. In fact, all that is known is that the site is an airport (not highly trafficked). There is speculation on where the sensor is located, and no evidence that any particular aircraft might have caused a perturbation. The speculated location is below (red ring).



It is actually 92m from the nearest airport tarmac, and 132 m from the nearest black rectangle, which are spaces where an aircraft might actually be parked. It seems to me that that is quite a long way (It is nearly 400 m to the actual runway), and if one was to be picky, the building at about 25m and the road at 38 m would be bigger problems. But these are not airport-specific problems.

A point this time is that Ouarglu is indeed a GHCN monthly station. For the reasons I have described, it does seem relatively well fitted for the role (assuming that the supposed location is correct).

Los Angeles

The final post (to now) was on high temperatures around Los Angeles on 6 and 7 July. Several places were said to have either reached their maximum ever, or the maximum ever for that day. The WUWT heading was "The all time record high temperatures for Los Angeles are the result of a faulty weather stations and should be disqualified"

But it is very odd to suggest that a station should be disqualified from expressing its own record high. That is just the maximum of those figures, so if you disqualify the record high, you must surely disqualify the station. But why only those that record a record high?

Anyway, the complaints came down to the following (click to enlarge):

USCLA Power and LightVan Nuys AirportBurbank Airport


There were also sites at UCLA and Santa Ana Fire Station, which were on rooftops. Now the first thing about these is that are frequently quoted local temperature sites, but apart from USC, none of them get into GHCN V3 currently (Burbank has data to 1966). So again, they aren't used for climate indices like GISS, NOSS or HADCRUT. But the fact that, whatever their faults, they are known to locals means that the record high, for that site, is meaningful to LA Times readership. And it is apparent from some of the WUWT comments that the suggestion that it was in fact very hot accords with their experience.

Again, the airport sites are clearly measuring what they want to measure - temperature on the runway. And climate scientists don't use them for that reason. UCLA seems to be there because it is next to an observatory. I don't know why the Fire Station needs a themometer on the roof, but I expect there is a reason.

As a general observation, I think it is a rather futile endeavour to try to suppress record highs on a generally hot day because of site objections. Once one has gone, another will step up. And while one record might conceivably be caused by, say, a chance encounter with a plane exhaust or aircon, it would be a remarkable coincidence for this to happen to tens of stations on the same day. Occam would agree that it was a very hot day, not a day when all the planes aligned.

Conclusion

People take the temperature of the air for various reasons, and there is no reason to think the measurement is inaccurate. The WUWT objection is that it is sometimes unrepresentative of local climate. The key question then is whether someone is actually trying to use it to represent local climate. They don't bother to answer that. The first place to look is whether it is included in GHCN. In most cases here, it isn't. Where it is, the stations seem quite reasonable.





June global surface TempLS up 0.015 °C from May.

The TempLS mesh anomaly (1961-90 base) rose a little, from 0.679°C in May to 0.694°C in June. This is opposite to the 0.078°C fall in the NCEP/NCAR index, while the UAH satellite TLT index rose by a similar amount (0.03°C).

I've been holding off posting this month because, although it didn't take long to reach an adequate number of stations, there are some sparse areas. Australia in particular has only a few stations reporting, and Canada seems light too. Kazakhstan, Peru and Colombia are late, but that is not unusual. It is a puzzle, because Australia seems to have sent in a complete CLIMAT form, as shown at Ogimet. But, as said, I think there are enough stations, and it seems there may not be more for a while.

It was very warm in central Siberia and Antarctica, and quite warm in Europe US and most of Africa. Cold in much of S America, and Quebec/Greenland (and ocean).

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




Tuesday, July 3, 2018

June NCEP/NCAR global surface anomaly down by 0.078°C from May

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average fell from 0.287°C in May to 0.209°C in June, 2018. That follows a similar fall last month, and makes June now the coldest month since July 2015. In the lower troposphere, UAH rose 0.03°C.

It was warm in most of N America, but cold in Quebec and Greenland. Moderate to cool just about everywhere else, including the poles. Active map here.

The BoM still says that ENSO is neutral, but with chance of El Niño in the (SH) spring.

Arctic sea ice is a bit confused for now. Jaxa has been off the air for nearly two weeks, said to be computer issues, but NSIDC is also odd. Much discussion at Neven's of satellite troubles.
Update: No sooner said than JAXA has come back on. Nothing much to report; 2018 is not far behind, but quite a few recent years are ahead. NSIDC reported a big day melt, which might have been a catch-up.


Monday, July 2, 2018

Hansen's 1988 prediction scenarios - numbers and details.

There has been a great deal of blog posting on the thirtieth anniversary of James Hansen's famous Senate testimony on global warming, and the accompanying 1988 prediction paper. I reviewed a lot of this in my previous post and I have since been in a lot of blog arguments. I suppose this has run its course for the moment, but there may be another round in 2020, since Hansen's prediction actually went to 2019.

Anyway, for the record, I would like to set down some clarification of what the scenarios for the predictions actually were, and what to make of them. Some trouble has been caused by Hansen's descriptions, which were not always clear. This is exacerbated by readers who interpret in terms of modern much discussed knowledge of tonnage emissions of CO2. This is an outgrowth of the UNFCC in early 1990's getting governments to agree to collect data on that. Although there were estimates made before 1988, they were without benefit of this data collection, and Hansen did not use them at all. I don't know if he was aware of them, but he in any case preferred the much more reliable CO2 concentration figures.

Sources

I discussed the sources and their origins in a 2016 post here. For this, let me start with a list of sources:
  • Hansen's 1988 prediction paper and a 1989 paper with more details, particularly concerning CFCs
  • Some discussions from 10 years ago: Real Climate and Steve McIntyre (later here). SM's post on scenario data here. See also Skeptical Science
  • A 2006 paper by Hansen, which reviews the predictions
  • From that 2007 RC post, a link to data files - scenarios and predicted temperature. The scenarios are from the above 1989 paper. I'll call this data Scen_1
  • A RealClimate page on comparisons of past projections and outcomes
  • A directory of a slightly different data set from Steve McIntyre here, described here. I'll call that Scen_2. The post has an associated set of graphs. It seems that SM calculated these from Hansen's description.
  • A recent Real Climate post with graphs of scenarios and outcomes, and also forcings.
  • I have collected numerical ascii data in a zipfile online here. H88_scenarios.csv etc are Scen_1; hansenscenario_A.dat etc are Scen_2, and scen_ABC_temp.data.txt is the actual projection.

Hansen's descriptive language

The actual arithmetic of the scenarios is clear, as I shall show below. It is confirmed by the numbers, which we have. But it is true that he speaks of things differently to what we would now. Steve McIntyre noted one aspect when Hansen speaks of emissions increasing by 1.5%:

"One idiosyncrasy that you have to watch in Hansen's descriptions is that he typically talks about growth rates forthe increment , rather than growth rates expressed in terms of the quantity. Thus a 1.5% growth rate in the CO2 increment yields a much lower growth rate than a 1.5% growth rate (as an unwary reader might interpret)."

Hansen is consistent though. His conventions are
  • Emissions of CO2 are always spoken of in terms of % increase. Presumably this is because he uses tonnages for CFCs, where production data is better than air measurements, and % works for both. Perhaps he anticipated having CO2 tonnages some time in the future.
  • So emissions, except for CFCs, are actually quantified as annual increments in ppm. He does not make this link very explicitly, but there is nothing else it could be, and talk of a % increase in emissions translates directly into a % increase in annual ppm increment in the numbers.
  • As SM said, you have to note that is is % of increment, not % of ppm. The latter would in any case make no sense. In Appendix B, the description is in terms of increments
  • Another usage is forcings. This gets confusing, because he reports it as ΔT, where we would think of it in W m-2. He gives in Appendix B for CO2 as the increment from x0=315 ppm of a log polynomial function the current ppm value. This is not far from proportional to the difference in ppm from 315. Other gases are also given by such formulae.
  • An exception to the use of concentrations is the case of CFCs. Here he does cite emissions in tons, relying on manufacturing data. Presumably that is more reliable than air measurement.
Note that each scenario also includes an aerosol calculation, which is where volcanoes come in.

Arguments

Update. Eli notes in comments that he went through a lot of this in 2006, here, and continued here. I'll show his forcing graph below.  

I'll just briefly summarise some of the misconceptions I battle in blogs:
  • Ignoring scenarios
    Many people want to say that Hansen made a prediction, and ignore scenarios altogether. So naturally they go for the highest, scenario A, and say that he failed. An example Noted by SkS was Pat Michaels, testifying to Congress in 1998, in which he showed only Scenario A. Michaels, of course, was brought on again to review Hansen after 30 years, in WSJ. This misuse of scen A was later taken up by Michael Crichton in "State of Fear", in which he said that measured temperature rise was only a third of Hansen's prediction. That was of course based, though he doesn't say so, on scenario A, which wasn't the one being followed.

    In arguing with someone rejecting scenarios at WUWT, I was told that an aircraft designer who used scenarios would be in big trouble. I said no. An aircraft designer will not give an absolute prediction of performance of the plane. He might say that with a load of 500 kg, the performance will be X, and with 1000 kg, it will be Y. Those are scenarios. If you want to test his performance specs, you have to match the load. It is no use saying - well, he thought 500 kg was the most likely load, or any such. You test the performance against the load that is actually there. And you test Hansen against the scenario that actually happened, not some construct of what you think ought to have happened.
  • Misrepresenting scenarios
    This is a more subtle one, that I am trying to counter in this post.People want to declare that scenario A was followed (or exceeded) because tonnage emissions increased by more than the 1.5% mentioned in Hansen. There are variants. These are harder to counter because Hansen made mainly qualitative statements in his text, with the details in Appendix B, and not so clear even there.

    But there isn't any room for doubt. We have the actual numbers he used (see sources). They make his description explicit. And they are defined in terms of gas concentrations only (except for CFCs). Issues about how tonnage emissions grew, or the role of China, or change in airborne fraction, are irrelevant. He worked on gas concentration scenarios, and as I shall show, the match with scenario B was almost exact (Scen A is close too).

Scenario arithmetic for CO2

. As mentioned, Hansen defined scenario A as emissions rising by 1.5% per year, compounded. The others differed by a slightly slower rate to year 2000. Scenario B reverted to constant increases after 2010, while scenario C had zero increases in CO2 ppm thereafter. See the graphs below. With all the special changes in Scenario B, it still didn't get far from Scenario A over the 30 years.

The basic arithmetic for Scenario A is that, if a1, a2, a3 are successive annual averages of CO2 ppm, then
(a3-a2)/(a2-a1) = 1.015
or the linear recurrence relation a3 = a2 +1.015*(a2 - a1)

There is an explicit solution of this for scen_2, which is the set Steve Mc calculated:

CO2 ppm = 235 + 117.1552*1.015^n where n is the number of years after 1988. That generates the dataset.

The formula for the actual Hansen set is slightly different. Oddly, the increment ratio is now not 1.015, but 1.0151131. This obviously makes little difference in practice; I think it arises from setting the monthly increment to 0.125% and compounding monthly. However
1.00125^12 = 1.015104 which is close but not exact. Perhaps there was some rounding.
Anyway, with that factor, the revised formula for Scen_1 is

Scen A: CO2 ppm = 243.8100 + 106.1837*1.0151131^n

Scenario B is much more fiddly from 1988-2000, though a straight line thereafter. Hansen describes it thus
"In scenario B the growth of the annual increment of CO2 is reduced from 1.5% yr-1 today to 1% yr-1 in 1990, 0.5% yr-1 in 2000, and 0 in 2010; thus after 2010 the annual increment CO2 is constant, 1.9 ppmvyr-1".

It isn't much use me trying to write an explicit formula for that. All I can report is that Scen_1 does implement that. I also have to say that this definition is too fiddly; the difference between A and B after all that fussy stuff is only 0.44 ppm at year 2000.

Scenario C is then CO2 ppm = 349.81 + 1.5*n for n=0:12; then constant at 367.81.

Conclusion

Hansen's descriptions of the scenarios are not always clear. But we have the numbers used, and then it is seen to be consistent, with the scenarios defined entirely in terms of gas concentrations.

Graphs

In the latest RealClimate, Gavin showed plots of the graphs and data for trace gases. Note how the data for CO2 sits right on scenario B. This is the Scen_1 data (click to enlarge):





For comparison, Steve McIntyre showed graphs for his Scen_2, with data to 2008 only. There is no visual difference from scenario plots of Scen_1.



Gavin also gave this plot of forcing, which demonstrates that when put together, the outcome is between scenarios B and C. This was also Steve McIntyre's conclusion back in 2008.




And here is another forcings graph, this time from Eli's posts in 2006 linked above (click to enlarge):

Saturday, June 23, 2018

Hansen's 1988 predictions - 30 year anniversary.

It is thirty years ago since James Hansen's famous Senate testimony on global warming. This has been marked by posts in Real Climate and WUWT (also here), and also ATTP, Stoat, Tamino. As you might expect, I have been arguing at WUWT.

The more substantive discussion is on the accompanying 1988 prediction paper. This was a remarkable achievement, which used runs of an early GISS GCM to forecast temperatures for the next thirty years. These forecasts are now often checked against observations. I wrote about them here, here and here. Each post had an active plotter which allowed you to superimpose various observation data on Hansen's original model results. It's annual data, to match Hansen's prediction. Since sientists can't know how much carbon society will choose to burn, Hansen analysed three scenarios (A, B and C) which covered the range between no restraint and successful limiting. Arguments then ensue as to which scenario actually happened. At least, that is what people should argue about, although they have a tendency to drift off into "Hansen said..." or even orse "we were told...".

Anyway, I'll leave discussion of that for the moment, and show the interactive plotter. The diagram in the background is Hansen's original plot, which is of anomalies relative to base years 1951-80, and uses GISS Ts as the observed data set (this had recently been published (Hansen and Lebedeff)). I have used that base where possible, else I match the dataset to GISS Ts over 1981-2010 (satellite data). Data is annual to end 2017. Sources are linked here.



To operate, just choose datasets to plot using the radio buttons, and Clear All if you want to start again. You can't erase curves without restart.

In interpreting these, I think weight should be given to GISS Ts, since it is what Hansen had available and used. Later indices incorporating SST rise more slowly. And I have reluctantly included troposphere data, which is definitely not what Hansen was predicting. Properly interpreted, I think the predictions are excellent. But that comes back to deciding which scenario is appropriate. I discussed this extensively here. We have detailed versions of the sequences of gas concentrations that quantified the scenarios, and while CO2 followed scenario B, others were much lower. CH4 and CFCs were below scenario C, so overall a result between B and C is to be expected. And that is what is mostly observed, though GISS Ts is higher.

Update. I have a zipfile online here which has numerical data for both scenario gases and temperature prediction; details here. I used it to calculate trends, in °C/Century, for the 30 years 1988-2017: (Further update - I fixed an error in scenario rates - now trend for B is larger)

Scenario AScenario BScenario C
3.022.841.23
GISS TsGISS LOTempLS mesh
2.211.831.86
HADCRUTCowtan&WayNOAA LO
1.791.981.78
BEST LO
2.00


In that analysis of scenarios, I showed some old plots. Gavin Schmidt, at Real Climate, has shown some updated values, and I'll show his plots. I mentioned that there are two sets of scenario data. One is IMO the original, as I discuss there, but Gavin uses a slightly different set, which I think was digitised from graphs. Anyway, here is the RC plot:



For the CFC plots; scenario C assumed that the Montreal agreements on curbing them, still being negotiated, would be approved and would work. A and B were more sceptical, but C was right. For methane, the concentration not only rose rather slowly, but was revised downward even before 1988.

Overall, in placing the outcome between scenarios B and C, Gavin gives this plot of combined forcings:



What the showing of combined temperature records shows is that Hansen's 1988 prediction is about as good as it could be, because it sits within the scatter of modern records. The difference between GISS Ts and GISS land/ocean is comparable to the difference between GISSlo and scenario B.

As a check on my active plot above, here is RealClimate's rendition of the case for GISS land/ocean with the same scenarios:





Tuesday, June 19, 2018

GISS May global down 0.03°C from April.

The GISS land/ocean temperature anomaly fell 0.03°C last month. The May anomaly average was 0.82°C, down slightly from April 0.85°C. The GISS report notes that it is the fourth warmest May in the record. The decline is very like the 0.038°C fall, of TempLS Mesh, although the NCEP/NCAR index declined rather more.

The overall pattern was similar to that in TempLS. Warm in most of N America, and equally warm in Europe, especially around the Baltic. Warm in East Asia, especially Siberia. Antarctica mostly warm. Still a pattern of warm patches along about 40°S.

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

Sunday, June 10, 2018

May global surface TempLS down 0.038 °C from April.

The TempLS mesh anomaly (1961-90 base) fell a little, from 0.716°C in April to 0.678°C in May. This is less than the 0.09°C fall in the NCEP/NCAR index, while the satellite TLT indices fell by a similar amount (UAH 0.03°C).

It was very warm in much of N America, except NE Canada (cold), and very warm in Europe. Cold in E Siberia, but warm in East Asia generally. Again a pattern of warm blobs around 40-50 °S, though less marked than in recent months. Quite warm in Antarctica (relatively).

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



Data from Canada delayed this report by a couple of days. Following my recent post on the timing of data arrival, I kept a note of how the TempLS estimates changed day by day as May data came in. The TempLS report is now first posted when the SST results are available, but I wait until all large countries are in before writing a post about it. Here is the table (Melbourne time):
DateNumber stations (incl SST)Temperature
June 0545160.676
June 0648290.723
June 0752940.709
June 0853720.708
June 0953810.709
June 1054740.678

Canada (late) did have a cooling effect.

Read More

Sunday, June 3, 2018

May NCEP/NCAR global surface anomaly down by 0.09°C from April

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average fell from 0.377°C in April to 0.287°C in May, 2018. This cancels out the last two months of increase, and matches the February average.

It was for once warm in both in North America (except far N) and Europe especially Scandia. Russia was cold in the W, warm in the East. Nothing special at either pole. Probably the main contributor to the drop was a chill in the N Atlantic region, including Greenland. Active map here.

I had thought that the gradual warming might be associated with the decline of La Niña. But the changes are small, so shouldn't be over-interpreted. The BoM still says that ENSO is neutral, and likely to stay so for a few months.


Thursday, May 31, 2018

To see the month's GHCN coverage, patience is needed.

I often see on contrarian sites graphs, usually from NOAA, which are supposed to show how sparse is GHCN-M's coverage of land sites, as used by the major US temperature indices. The NOAA monthly reports usually show interpolated plots, but if you go to some legacy sites, you can get a plot like this:





It is a 5x5° grid, but it does look as if there are a lot of empty cells, particularly in Africa. But if you look at the fine print, it says that the map was made April 13. That is still fairly early in the month, but NOAA doesn't update. There is a lot of data still to come. Station coverage isn't ideal, but it isn't that bad.

I took issue with a similar graph from SPPI back in 2010. That was quite a high visibility usage (GISS this time). Fortunately GISS was providing updates, so I could show how using an early plot exaggerated the effect.

The issue of spread out arrival of data affects my posting of monthly TempLS results. I calculate a new monthly average temperature each night, for the current month. I post as soon as I can be reasonably confident, which generally means when the big countries have reported (China, Canada etc). I did comment around January that the temperatures were drifting by up to about 0.04°C after posting. I think that was a run of bad luck, but I have been a little more conservative, with stabler results. Anyway, I thought I should be more scientific about it, so I have been logging the arrival date of station data in GHCN-M.

So I'll show here an animation of the arrival of March 2018 data. The dates are when the station data first appears on the posted GHCN-M file. Click the bottom buttons to step through.


The colors go from red when new to a faded blue. The date is shown lower left.

The behaviour of the US is odd, and I'll look into it. About 500 stations post numbers in the last week of February. I presume these are interim numbers, but my logging didn't record changing values. Then another group of stations report mid April.

Otherwise much as expected. The big countries did mainly report by the 8th. A few medium ones, like South Africa, Mongolia, Iran and Sudan, were quite a lot later. But there is substantial improvement in overall coverage in the six weeks or so after April 1. Some of it is extra stations that arrive after a country's initial submission.

There certainly are parts of the world where more coverage would be useful, but it doesn't help to exaggerate the matter by showing incomplete sets. The good news from the TempLS experience is that, even with an early set, the average does not usually change much as the remaining data arrives. This supports the analysis here, for example, which suggests that far fewer stations, if reasonably distributed, can give a good estimate of the global integral.

Tuesday, May 29, 2018

Updating the blog index.

I wrote late last year about improving the blog topic index, which is top on the page list, to right. I've now tinkered a bit more. The main aim was to automate updates. This should now work, so the index should always be up to date.

The other, minor improvement was to add a topic called "Complete listing" This does indeed give a listing of all posts, with links, back to the beginning of the blog in 2009. It includes pages, too (at the bottom), so there are currently 751 in the list, organised by date.


Friday, May 25, 2018

New interactive updated temperature plotting.

As part of the Moyhu latest data page, I have maintained a daily updated interactive plotter. I explained briefly the idea of it here. There is a related and more elaborate annual plotter kept as a page here, although I haven't kept that updated.

I think interactive plotting is a powerful Javascript capability. You can move the curves around as you wish - expanding or contracting the scales. You can choose which of a large set of data offerings to show. You can smooth and form regression lines.

But the old version, shown with that old post, looks a bit raw. I found I was using it more for display graphs, so I have cleaned up the presentation, using PrintScreen on my PC, and pasting the result into Paint. I have also simplified the controls. I had been using draggable popup windows, which are elegant, but not so straightforward, and don't make it easy to expand facilities. So I have reverted to an old-fashioned control panel, in which I can now include options such as writing your own headings and y-axis label. There is now also the option of changing the anomaly base, and you can choose any smoothing interval. Here is how it looks, in a working version:


You can choose data by clicking checkboxes on the left. Dragging in the main plot area translates the plots; dragging the pointer under the x-axis changes the time scale, and dragging vertically left of the y-axis changes the y-scale. At bottom left (below the checkboxes), there is a legend, only partly visible. This reflects the colors and choice of data, and you can drag it anywhere. The idea is that you can place it on the plot when you want to capture the screen for later presentation.

The control panel has main rows for choosing the regression, smoothing and anomaly base. When you want to make a choice, first tick the relevant checkbox, and then enter data in the textboxes. Then yo make it work, click the top right run button. The change you make will apply either to all the curves, or just to one nominated on the top row, depending on the radio buttons top left. The nominated curve is by default the last one chosen, but you can vary this with the arrow buttons just left of the run button. However, the anomaly base can only be altered for all, and the color selection only for one.

Choosing regression over a period displays the line, and also the trend, in the legend box, in °C/century units. You can only have one trend line per dataset, but possibly with different periods. If you want to make a trend go away, just enter a date outside the data range (0 will do). You could also deselect and reselect the data.

Smoothing is just moving average, and you enter the period in months. Enter 1 for no smoothing (also the default).

There are two rows where you can enter your own text for the title and y-axis label. Click run to make it take effect. The title can include any HTML, eg bold, text-size etc. You can use heading tags, but that takes up room.

Color lets you choose from the colored squares. A choice takes effect immediately, for the nominated data only.

Generally keep the checkboxes in the control panel unchecked unless you are making a change.

For anomaly base, you can also enter an out of range year to get no anomaly modification at all. The plots are shown each with the suppliers base. I don't really recommend this, and it tends to get confused if you have already varied base choices.

There are two more buttons, on the right of the control panel. One is Trendback. This switches (toggles) to a style which was in the old version, and is described here, for example. It shows the trend from the time on the x-xis to present (last data) in °C/century. In that mode, it won't respond to the regression, smooth, or anomaly base properties. The other button is "Show data". This will make a new window with the numbers graphed on the screen. This can be quite handy for the trendback plots, for example. You can save the window to a file.

Here is how the plot might look if you drag the legend into place:









Thursday, May 17, 2018

GISS April global down 0.02°C from March.

The GISS land/ocean temperature anomaly  fell 0.02°C last month. The April anomaly average was 0.86°C, down slightly from March 0.88°C. The GISS report notes that it is still the third warmest April in the record. The fall is very similar to the 0.016°C fall, of TempLS Mesh, although the NCEP/NCAR index showed a slight rise.

The overall pattern was similar to that in TempLS. Cold in most of N America, and contrasting warmth in Europe. Warm in East Asia, especially arctic Siberia. Polar regions variable. Warm in S America and Australia, and for at least the third month, a curious pattern of warm patches along about 40°S.

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

Tuesday, May 15, 2018

Electronic circuit climate analogues - amplifiers and nonlinearity


This post is a follow-up to my previous post on feedback. The main message in that post was that, although talking of electronic analogues of climate feedback is popular in some quarters, it doesn't add anything mathematically. Feedback talk is just a roundabout way of thinking about linear equations.

Despite that, in this post I do want to talk more about electronic analogues. But it isn't much about feedback. It is about the other vital part of a feedback circuit - the amplifier, and what that could mean in a climate context. It is of some importance, since it is a basic part of the greenhouse effect.

The simplest feedback diagram (see Wiki) has three elements:



They are the amplifier, with gain AOL, a feedback link, with feedback fraction β, and an adder, shown here with a minus sign. The adder is actually a non-trivial element, because you have to add the feedback to the input without one overriding the other. In the electronic system, this generally means adding currents. Adding voltages is harder to think of directly. However, the block diagram seems to express gain of just one quantity, often thought of as temperature.

In the climate analogue, temperature is usually related to voltage, and flux to current. So there is the same issue, that fluxes naturally add, but temperature is the variable that people want to talk about. As mentioned last post, I often find myself arguing with electrical engineers who have trouble with the notion of an input current turning into an output voltage (it's called a transimpedance amplifier).

If you want to use electronic devices as an analogue of climate, I think a fuller picture of an amplifier is needed. People now tend to show circuits using op amps. These are elaborately manufactured devices, with much internal feedback to achieve high linearity. They are differential, so the operating point (see below) can be zero. I think it is much more instructive to look at the more primitive devices - valves, junction transistors, FETs etc. But importantly, we need a fuller model which considers both variables, voltage and current. The right framework here is the two port network.

I've reached an awkward stage in the text where I would like to talk simultaneously about the network framework, junction transistors, and valves. I'll have to do it sequentially, but to follow you may need to refer back and forth. A bit like a feedback loop, where each depends on the other. I'll go into some detail on transistors, because the role of the operating point, fluctuations and linearity, and setting the operating point are well documented, and a good illustration of the two port treatment. Then I'll talk about thermionic valves as a closer analogue of climate.

Two Port Network

Wiki gives this diagram:


As often, engineer descriptions greatly complicate some simple maths. Many devices can be cast as a TPN, but all it means is that you have four variables, and the device enforces two relations between them. If these are smooth and can be linearised, you can write the relation for small increments y as



Wiki, like most engineering sources, lists many ways you could choose the variables for left and right. For many devices, some coefficients are small, so you will want to be sure that A is not close to singular. I'll show how this works out for junction transistors.

This rather general formulation doesn't treat the input and output variables separately. You can have any combination you like (subject to invertible A). For linearity, the variables will generally denote small fluctuations; the importance of this will appear in the next section.

The external circuitry will contribute extra linear equations. For example, a load resistor R across the output will add an Ohm's Law, V₂ = I₂R. Other arrangements could provide a feedback equation. With one extra relation, there is then just one free variable. Fix one, say an input, and everything else is determined.

Junction transistors

I'm showing the use of a junction transistor as amplifier because it is a well documented example of:
  • a non-linear device which has a design point about which fluctuations are fairly linear
  • a degree of degeneracy, in that it is dominated by a strong association between I₁ and I₂, with less dependence on V₂ and little variation in V₁. IOW, it is like a current amplifier, with amplification factor β.
  • there is simple circuitry that can stably establish the operating point.
Here from Wiki, is a diagram of a design curve, which is a representation of the two-port relation. It takes advantage of the fact that there is a second relation which is basically between I₁ and V₁, with V₁ restricted to a narrow range (about 0.6V for silicon).



The top corner shows the transistor with variables labelled; the three pins are emitter E, base B and collector C. In TPN terms, I₁ is the base current IB; I₂ is the current from collector to emitter IC, and V₂ is the collector to emitter voltage VCE. The curves relate V₂ and I₂ for various levels of I₁. Because they level off, the dependence is mainly between IC and IB. The load line in heavy black shows the effect of connecting the collector via a load resistor. This constrains V₂ and I₂ to lie on that line, and so both vary fairly linearly with I₁.

The following diagrams have real numbers and come from my GE transistor manual, 1964 edition, for a 2N 1613 NPN transistor. The left is a version of the design curves diagrammed above, but with real numbers. It shows as wavy lines a signal of varying amplitude as it might be presented as base current (top right) and appear as a collector voltage (below). The load resistor line also lets you place it on the y axis, where you can see the effect of current amplification, by a factor of about 100. The principal purpose of these curves is to show how non-linearity is expressed as signal clipping.





I have included the circuit on the right, a bias circuit, to show how the design operating point is achieved. The top rail is the power supply, and since the base voltage is near fixed at about 0,6V, the resistor RB determines the base current curve. The load RL determines the load line, so where these intersect is the operating point.

So let's see how this works out in the two-port formulation. We have to solve for two variables; the choice is the hybrid or h- parameters:



Hybrid suggests the odd combination; input voltage V₁ and output current I₂ are solved in terms of input current I₁ and output voltage V₂. The reason is that the coefficients are small, except for h₂₁ (also β). There is some degeneracy; there isn't much dependence at all on V₂, and V₂ is then not going to vary much.So these belong on the sides they are placed. I₂ and I₁ could be switched; that is called inverse hybrid (g-). I've used the transistor here partly as a clear example of degeneracy (we'll see more).

Thermionic valve and climate analogue

From Wiki comes a diagram of a triode



The elements are a heated cathode k in a vacuum tube, which can emit electrons, and an anode a, at positive voltage, to which they will move, depending on voltage. This current can be modulated by varying the voltage applied to the control grid g, which sits fairly close to the cathode.

I propose the triode here because it seems to me to be a closer analogue of GHGs in the atmosphere. EE's sometimes say that the circuit analogue of climate fails because they can't see a power supply. That is because they are used to fixed voltage supplies. But a current supply works too, and that can be seen with the triode. A current flows and the grid modulates it, appearing to vary the resistance. A FET is a more modern analogue, in the same way. And that is what happens in the atmosphere. There is a large solar flux, averaging about 240 W/m² passing through from surface to TOA, much of it as IR. GHGs modulate that flux.

A different two-port form is appropriate here. I₁ is negligible, so should not be on the right side. Inverse hyprid could be used, or admittance. It doesn't really matter which, since the outputs are likely to be related via a load resistor.

Climate amplifier

So thinking more about the amplifier in the climate analogue, first as a two port network. Appropriate variables would be V₁,I₁ as temperature and heat flux at TOA, and V₂, I₂ as temperature, upward heat flux at the surface. V₂ is regarded as an output, and so should be on the LHS, and I₁ as an input, on the right. One consideration is that I₂ is constrained as being the fairly constant solar flux at the surface, so it should be on the RHS. That puts V₁ on the left and pretty much leads to an impedance parameters formulation - a two variable form of Ohm's Law.

The one number we have here is the Planck parameter, which gives the sensitivity before feedback of V₂ to I₁ (or vice versa). People often think that this is determined by the Stefan-Boltzmann relation, and that does give a reasonably close number. But in fact it has to be worked out by modelling, as Soden and Held explain. Their number comes to about 3.2 Wm⁻²/K. This is a diagonal element in the two port impedance matrix, and is treated as the open loop gain of the amplifier. But the role of possible variation of the surface flux coefficient should alos be considered.

As my earlier post contended, mathematically at least, feedback is much less complicated than people think. The message of this post is that if you want to use circuit analogues of climate, a more interesting question is, how does the amplifier work?







Friday, May 11, 2018

TempLS monthly updates of global land and sea temperature

TempLS is a program I use to provide a monthly global land/ocean anomaly index, using unadjusted GHCNM V3 data for land, and ERSST V5 for SST. There is a summary article here. It is essentially a spatial integration, which reduces to an area-weighted average of the anomalies. My preferred method is to use an irregular triangular mesh to get the weights. It is then possible to separately sum with weights the stations of various regions. I have been doing this (as described here) for about three years as part of the monthly reporting. A typical plot for April is here

.

It shows the arithmetic contribution that each region makes to the published global average. It isn't itself a temperature of something; if you add all the continent colored bars shown, you get the land global amount, in red (that is new). And if you add land and SST you get the global, in black. Each bar is the weighted sum of locals divided by the global sum of weights. To get the regional average, the denominator would be the sum of weights for the region.

I plan now to more systematically post the land and SST averages, and also plots of regional averages. The SST will be particularly useful, because ERSST posts within a couple of days of the start of the month, so TempLS can produce a result much earlier than the alternatives. NOAA publishes a revision late in the month, but changes are usually small.

I have added TempLS_SST and TempLS_La to the sets normally displayed. You can find the numbers (anomaly base 1961-1990) under Land/SST in the maintained table of monthly data. There are trend plots in the Trend viewer. And they plots are available on the interactive plotter. Here is an example of recent data, compared with HADSST3 and NOAA SST:





I'll probably report the SST for each month in my first post for each month, along with the reanalysis average.

I'll show now the other possibilities in the monthly bar plot style. Showing the regional averages give sthis:



The regions are far more variable than the globals, which obscures the picture somewhat. Note the huge Arctic peaks. So I'll show also the progression of just the land, SST and globals. It is now practical to show more months. Here is the plot



It emphasises the variability of land relative to SST. This may be seen in better proportion by reverting to the first style, showing the contributions to the global average:



Again, red and blue (land and SST) add to the black total. It shows how monthly variations are dominated by the fluctuations on land. I'll find a way to include these extra graphs in the monthly reporting.



Thursday, May 10, 2018

April global surface TempLS down 0.016 °C from March.

The TempLS mesh anomaly (1961-90 base) fell a little, from 0.721°C in March to 0.705°C in April. This contrasts with a small 0.046°C rise in the NCEP/NCAR index, while the satellite TLT indices fell by a similar amount (UAH 0.04°C).

It was very cold in much of N America, except west, but very warm in Europe and E Siberia, and warm in East Asia generally. Also warm in Australia, Argentina, and once again a curious pattern of warm blobs around 40 °S. The Arctic and Antarctic were mixed.

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



Friday, May 4, 2018

Feedback, climate, algebra and circuitry.

I've been arguing again at WUWT ( (more here)). It is the fourth of a series by Lord Monckton, claiming to have found a grave error in climate science, so it is now game over. My summary after three posts is here.

The claim is, of course, nonsense, and based on bad interpretation of notions of feedback. But I want to deal here with the general use of feedback theory in climate, and the mystery that electrical engineers who comment on this stuff like to make of it. The maths of feedback is trivial; just simple linear equations. And it is best to keep it that way.

A point I often make in commentary is that climate science really doesn't make much use of feedback theory at all. Critics invoke it a lot more. I continually encounter people who think that feedback is the basis of GCMs. I have to explain that, no, they do not form any part of the structure of GCMs, and cannot. A GCM is a solver for partial differential equations. That means it creates for each step a huge array of linear equations relating variables from neighboring cells. That isn't always obvious in the explicit methods they tend to use, but there is still an underlying matrix of coefficients. And because each row just related a few neighboring values, the matrix is sparse. This is an essential feature, because of the number of cells. But global averages, such as would come from a feedback expression, are not sparse. They connect everything. So they cannot fit within the discretised pde framework.

Linear equations and feedback

Problems described as feedback are really just linear equations, or systems of a few linear equations; usually one less equations than unknowns, so on elimination, one variable is expressed as a multiple of another. I described here how a feedback circuit could be analysed simply by writing linear current balance (Kirchhoff rule) equations at a few nodes. In climate, the same is done by balancing global and time average heat fluxes, usually at TOA.

The paper of Roe 2009 is often cited as the most completely feedback oriented analysis. I'll show its presentation table here:

It gives the appearance that ΔR is both input and output, because it is a flux that is conserrved. But the more conventional feedback view is that ΔT is the output. If we take the multi-feedback version of (c)
ΔT = λ₀(ΔR + ΣciΔT )
which I can rewrite setting c₀=-1/λ₀ as just
ΔR + c₀ΔT + ΣciΔT = 0

This is just the equilibrium heat flux balance at TOA since each of the ciΔT is a temperature-responsive flux. I have given the c₀ΔT special status, because it is the Planck term, representing radiation guaranteed by the Stefan-Boltzmann law (c₀ = -4ΔT).

Feedback reasoning and linear equations

Just resolving a linear equation is not a mathematical difficulty. So what is all the feedback talk about? Mainly, it is trying to see the equation as built up in parts. There is no math reason to do that, but people seem to want to do it. The process can be described thus:
  • Select (as in Roe above) a subset to refer to as the reference system. A logical set is the forcing and the necessary Planck response.
    ΔR + c₀ΔT + ΣcₖΔT = 0
    This is like a finite gain amplifier (c₀)
  • Express the other terms as feedbacks relative to c₀:
    ΔR + c₀ΔT *(1 - Σfₖ) = 0, fₖ = -cₖ/c₀
    The f's are then called the feedback coefficients. For stability (see next) they should sum to less than 1. Negative values make this more likely, and so are stabilising. As the coefficient of ΔT, diminishes, it increases the amount by which ΔT would have to change to keep balance. That is said to increase the gain, and creates a singular situation (of high gain) approaching zero.

Stability

If the singularity is passed (Σfₖ>1), and the coefficient of ΔT becomes positive, the system is unstable. The reason involves an extra bit of physics. Suppose total flux is out of balance. Then the region into which it flows will cool or heat. The coefficient here is, for a uniform material, called the heat capacity H, and is positive. For a complex region like the Earth surface, that is hard to quantify, but will still be positive. That is, heat added will make it warmer, not cooler. So the equation for temperature change following imbalance is
ΔR + cΔT = H*dΔT/dt
If c is positive, this has exponentially growing solutions, and so is unstable. For c negative, the solutions decay, and lead toward equilibrium.

It's often said that positive feedback is impossible, because it would mean instability. But in the above algebra, that is not true; the requirement is that Σfₖ>1. It is true if you choose a different reference system - just the forcing. That can only work in conjunction with a c₀ΔT where c is negative. Electrically, the reference system is then like an operational amplifier.

Summary so far

Systems often described using feedback terminology are really just linear equations (or systems). Feedback arguments do not yield anything beyond what elementary linear solving can do, including a stability criterion. But with linear algebra, you can identify the various steps of feedback reasoning if you want to.

Systems are not exactly linear

Roe points out that linear feedback is just the use of a first order Taylor Series expansion of a nonlinear relation. This is very direct seen as a linear system. If the forcing R is to be balanced by a flux F which is a function of T and variables u,v which depend on T, then to first order

dR = (∂F/∂T) dT + (∂F/∂u du/dT) dT + (∂F/∂v dv/dT) dT

each partial holding the other variables (from T,u,v) fixed. This gives the required linear relation with the bracketed terms becoming the c coefficients (but negative).

More advanced

There is a lot of approximation here. Not only linearity (usually OK) but also in the use of global averaging. But that doesn't mean linear analysis has to be discarded if you want to take account of these things. You can extend using an inexact Newton's method. Suppose we have the base system

R = F(u,v,T)

where again u and v are variables (like humidity) that depend on T. Suppose we have an initial state subscripted 0, and a perturbed state subscripted 1, of which R₁ is known. Then to first order

F(u₁,v₁,T₁) - R₁ = F(u₀,v₀,T₀) - R₁ + (∂F/∂T)₁ dT + (∂F/∂u du/dT)₁ dT + (∂F/∂v dv/dT)₁ dT = 0

This can be solved as before as a linear equation in dT. Then updating

T = T + dt, u = u + du/dT)₁ dT etc, we can solve again

F(u,v,T) - R₁ + (∂F/∂T)₁ dT + (∂F/∂u du/dT)₁ dT + (∂F/∂v dv/dT)₁ dT = 0

and iterating until F(u,v,T) - R₁. Note that I have not updated the partial derivatives, which are the feedback coefficients. That is what makes it an inexact Newton; convergence is a bit slower, but we probably don't have information to do that update.

So non-linearity is not a show-stopper; it just takes a little longer. This also allows you to work out a more complicated version of F, with, say, latitude variation. You can still use the simpler global feedback coefficients, so the extra trouble is only in the evaluation of F. The penalty will again be slower convergence, and it may even fail. But it gives a way to progress.



Thursday, May 3, 2018

April NCEP/NCAR global surface anomaly up by 0.046°C from March

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average rose from 0.331°C in March to 0.377°C in April, 2018, mainly due to a spike at the end of the month. It's the same rise and pattern as last month. The rises are not huge, but have been consistent since the low point in January, so that now April is the warmest month since May last year. This seems consistent with the fading of a marginal La Niña.

The big feature was cold in North America, except for the Pacific coast and Rockies. Much of Europe was warm, as was Australia. There was a lot of (relative) warmth in Antarctica, but the Arctic was patchy. Interactive map here.

The BoM says that ENSO is neutral, and likely to stay so for a few months.


Wednesday, April 18, 2018

GISS March global up 0.1°C from February.

GISS rose 0.1°C. March anomaly average was 0.89°C, up from February 0.79°C January (GISS report here). That is a greater rise than TempLS mesh, which rose by 0.04°C, as did the NCEP/NCAR index. But GISS did not rise the previous month, so the change over two months is about the same. Mar 2018 is about the same as Mar 2015, but below 2016 and 2017.

The overall pattern was similar to that in TempLS. A cold band across N Eurasia, and a warm band below across mid-latitudes. Warm in N Canada and Alaska, but cool around the Great Lakes. As with last month, 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.

Saturday, April 7, 2018

March global surface TempLS up 0.021 °C from February.

The TempLS mesh anomaly (1961-90 base) rose a little, from 0.683°C in February to 0.704°C in March. This is similar 0.046°C rise in the NCEP/NCAR index, while the satellite TLT indices rose by a similar amount (UAH 0.04°C).

There were two major bands of weather, one cold, one warm. The warm belt spread from N China to the Sahara, being very warm from Mongolia to Egypt. The cold band went from N Siberia to Britain, being very cold in NW Russia. Both poles were moderately warm. For the Arctic, this is a big reduction since last month, so indices like NOAA and HADCRUT might rise more than GISS. TempLS grid, which also undercounts poles, rose 0.07°C.

Another noticeable pattern, similar to last month, was a band of SST warmth extending right around the 35-45° S latitudes.

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



Tuesday, April 3, 2018


March NCEP/NCAR global surface anomaly up by 0.046°C from February

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average rose from 0.285°C in February to 0.331°C in March, 2018, mainly due to a spike at the end of the month.

Unusually, the Arctic was mostly cool. Cold in N Russia, extending through Europe to Spain. To the south of that cold, a warm band from China to the Sahara, which was probably responsible for the net warmth. US was patchy, but more cool than warm. Interactive map here.

On prospects, the BoM says that ENSO is neutral, with neutral prospects. Currently SOI looks Nina-ish, but BoM says that is due to cyclones and will pass.


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.