The TempLS mesh anomaly (1961-90 base) was 0.442deg;C in February, down from 0.642°C in January. December and January were down about 0.2°C from earlier months, so that is getting quite cool. Last time it was this cool was Feb 2014, at 0.389°C. There was a smaller 0.08°C drop in the NCEP/NCAR reanalysis base index.

The prominent feature was a cold band in N America extending from Alaska to Texas. N Russia was also very cold. There was a warmer band to the south, from Centralk Asia into China. The Arctic was also relatively warm.

Here is the temperature map, using the LOESS-based map of anomalies.

As always, the 3D globe map gives better detail.

## Friday, March 5, 2021

## Saturday, February 13, 2021

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## GISS January global up by 0.06°C from December.

The GISS V4 land/ocean temperature anomaly was 0.86°C in January 2021, up from 1.10°C in December. TempLS however reported little change. Jim Hansen notes that it was much cooler than last year, being only the sixth warmest January in the record.

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

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

## Saturday, February 6, 2021

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## January global surface TempLS same as December (cool).

The TempLS mesh anomaly (1961-90 base) was 0.62deg;C in January, also 0.62°C in December. That followed a large drop from 0.877°C in November. There was a small 0.0008°C rise in the NCEP/NCAR reanalysis base index.

The prominent feature was a cold band through Siberia, extending into central Asia. The corresponding parts of N America were very warm. Eastern Europe was warm, extending into N Africa. Antarctica was cold.

Here is the temperature map, using the LOESS-based map of anomalies.

As always, the 3D globe map gives better detail.

The prominent feature was a cold band through Siberia, extending into central Asia. The corresponding parts of N America were very warm. Eastern Europe was warm, extending into N Africa. Antarctica was cold.

Here is the temperature map, using the LOESS-based map of anomalies.

As always, the 3D globe map gives better detail.

## Friday, January 15, 2021

###
## GISS reports 2020 as warmest year (virtual tie with 2016).

GISS reports 2020 as warmest year (virtual tie with 2016).

The GISS V4 land/ocean temperature anomaly was 0.81°C in December 2020, down from 1.13°C in November. That made the 2020 average 1.02°C, to 2 decimals the same as 2016. NOAA, like TempLS, had 2020 very slightly behind (by 0.02°C, vs TempLS 0.005°C).

None of these differences are significant. I calculated that if just one week had been 0.26°C warmer in 2020, TempLS would have rated 2020 warmest. In mid-December, the daily average fell by about 0.4°C and stayed low. If that had been delayed by a week, that would have made the difference.

Jim Hansen's report, with many more details, is here.

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

The GISS V4 land/ocean temperature anomaly was 0.81°C in December 2020, down from 1.13°C in November. That made the 2020 average 1.02°C, to 2 decimals the same as 2016. NOAA, like TempLS, had 2020 very slightly behind (by 0.02°C, vs TempLS 0.005°C).

None of these differences are significant. I calculated that if just one week had been 0.26°C warmer in 2020, TempLS would have rated 2020 warmest. In mid-December, the daily average fell by about 0.4°C and stayed low. If that had been delayed by a week, that would have made the difference.

Jim Hansen's report, with many more details, is here.

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

## Wednesday, January 6, 2021

###
## TempLS global surface 2020 just cooler than 2016 (virtual tie).

TempLS December 2020 results are in, and that makes a complete average for 2020. I had calculated that a December average anomaly (1961-90) of over 0.681°C would be enough to make 2020 the hottest year, which seemed quite likely, given the November average was 0.891°C and the lowest month of 2020 to date was 0.704°C. However, December was very cool, at 0.628°C, a drop of 0.263°C. That meant that 2020 averaged 0.852°C, whereas 2016 was 0.857°C. Here is a table of those TempLS anomaly averages:

The TempLS result is based on 8603 land stations of GHCN V4 which have reported to date, along with ERSST. More (about 800) land stations will post results during January, and this will alter the result a little. An increase of 0.054°C needed to put 2020 ahead is possible, but not very likely. TempLS usually matches GISS NASA fairly well, but given the closeness, whether GISS 2020 comes out ahead is not predictable from this.

The cool December was foreshadowed in the NCEP/NCAR reanalysis tracking, which also showed a drop of 0.263°C. The first part of the month was warm, but after about ten days there was a drop of about 0.4°C, and no recovery.

The main very cool region was over Kazakhstan and parts of Russia nearby, with an extension over Mongolia and into China. The ENSO region of the Pacific coast, and also SE, was cool (La Nina). Elsewhere it was mostly (relatively) warm, especially around the Arctic, extending into Canada and Scandinavia. Most of Europe was warm, and also the Sahara.

Here is the temperature map, using the LOESS-based map of anomalies.

Nov 2020 | 0.891 | Ave 2016 | 0.857 |

Dec 2020 | 0.628 | Ave 2020 | 0.852 |

Diff | 0.263 | Diff | 0.005 |

The TempLS result is based on 8603 land stations of GHCN V4 which have reported to date, along with ERSST. More (about 800) land stations will post results during January, and this will alter the result a little. An increase of 0.054°C needed to put 2020 ahead is possible, but not very likely. TempLS usually matches GISS NASA fairly well, but given the closeness, whether GISS 2020 comes out ahead is not predictable from this.

The cool December was foreshadowed in the NCEP/NCAR reanalysis tracking, which also showed a drop of 0.263°C. The first part of the month was warm, but after about ten days there was a drop of about 0.4°C, and no recovery.

The main very cool region was over Kazakhstan and parts of Russia nearby, with an extension over Mongolia and into China. The ENSO region of the Pacific coast, and also SE, was cool (La Nina). Elsewhere it was mostly (relatively) warm, especially around the Arctic, extending into Canada and Scandinavia. Most of Europe was warm, and also the Sahara.

Here is the temperature map, using the LOESS-based map of anomalies.

## Sunday, December 27, 2020

###
## How averaging absolute temperatures goes wrong - use anomalies

There has been a series of posts at WUWT by Andy May on SST averaging, initially comparing HADSST with ERSST. They are here, here, here, here, and here. Naturally I have been involved in the discussions; so has John Kennedy. There has also been Twitter discussion.My initial comment was here:

The trend was toward HADSST and a claim that SST had been rather substantially declining this century (based on that flaky averaging of absolute temperatures). It was noted that ERSST does not show the same thing. The reason is that HADSST has missing data, while ERSST interpolates. The problem is mainly due to that interaction of missing cells with the inhomogeneity of T.

Here is one of Andy's graphs:

In these circumstances I usually repeat the calculation that was done replacing the time varying data with some fixed average for each location to show that you get the same claimed pattern. It seems to me obvious that if unchanging data can produce that trend, then the trend is not due to any climate change (there is none) but to the range of locations included in each average, which is the only thing that varies. However at WUWT one meets an avalanche of irrelevancies - maybe the base period had some special property, or maybe it isn't well enough known, the data is manipulated etc etc. I think this is silly, because they key fact is that some set of unchanging temperatures did produce that pattern. So you certainly can't claim that it must have been due to climate change. I set out that in a comment here, with this graph:

Here A is Andy's average, An is the anomaly average, and Ae is the average made from the fixed base (1961-90) values. Although no individual location in Ae is changing, it descends even faster than A.

So I tried another tack. Using base values is the simplest way to see it, but one can just do a partition of the original arithmetic, and along the way find a useful way of showing the components of the average that Andy is calculating. I set out a first rendition of that here. I'll expand on that here, with a more systematic notation and some tables. For simplicity, I will omit area weighting of cells, as Andy did for the early posts.

I haven't given values for the sums S, but you can work them out from the A and N. The point is that they are additive, and this can be used to form Andy's A2-A1 as a weighted sum of the other averages. From additive S:

S1=S1a+S1b and S2=S2a+S2c

or

A1*(Na+Nb)=A1a*Na+A1b*Nb, or

A1*N=A1a*Na+A1b*Nb+A1*Nc

and similarly

A2*N=A2a*Na+A2c*Nc+A2*Nb

Differencing

(A2-A1)*N=(A2a-A1a)*Na-(A1b-A2)*Nb+(A2c-A1)*Nc

or, dividing by N

A2-A1=(A2a-A1a)*Wa-(A1b-A2)*Wb+(A2c-A1)*Wc

That expresses A2-A1 as the weighted sum of three terms relating to Ra, Rb and Rc respectively. Looking at these individually

A2-A1 = 0.210 + 0.431 -1.455 = -0.813

So the first term representing actual changes is overwhelmed by the other two, which are biases caused by the changing cell population. This turns a small increase into a large decrease.

The main thing to note is that the numbers are all much smaller. That is both because the range of anomalies is much smaller than absolute temperatures, but also, they are more homogeneous, and so more likely to cancel in a sum. The corresponding terms in the weighted sum making up A2-A1 are

A2-A1 = 0.210 + 0.012 + 0.029 = 0.251

The first term is exactly the same as without anomalies. Because it is the difference of T at the same cemo, subtracting the same base from each makes no change to the difference. And it is the term we want.

The second and third spurious terms are still spurious, but very much smaller. And this would be true for any reasonably choice of anomaly base.

However, you can do better with infilling. Naive anomalies, as used un HADCRUT 4 say, effectively assign to missing cells the average anomaly of the remainder. It is much better to infill with an estimate from local information. This was in effect the Cowtan and Way improvement to HADCRUT. The uses of infilling are described here (with links).

*"Just another in an endless series of why you should never average absolute temperatures. They are too inhomogeneous, and you are at the mercy of however your sample worked out. Just don’t do it. Take anomalies first. They are much more homogeneous, and all the stuff about masks and missing grids won’t matter. That is what every sensible scientist does.*

*..."*

The trend was toward HADSST and a claim that SST had been rather substantially declining this century (based on that flaky averaging of absolute temperatures). It was noted that ERSST does not show the same thing. The reason is that HADSST has missing data, while ERSST interpolates. The problem is mainly due to that interaction of missing cells with the inhomogeneity of T.

Here is one of Andy's graphs:

In these circumstances I usually repeat the calculation that was done replacing the time varying data with some fixed average for each location to show that you get the same claimed pattern. It seems to me obvious that if unchanging data can produce that trend, then the trend is not due to any climate change (there is none) but to the range of locations included in each average, which is the only thing that varies. However at WUWT one meets an avalanche of irrelevancies - maybe the base period had some special property, or maybe it isn't well enough known, the data is manipulated etc etc. I think this is silly, because they key fact is that some set of unchanging temperatures did produce that pattern. So you certainly can't claim that it must have been due to climate change. I set out that in a comment here, with this graph:

Here A is Andy's average, An is the anomaly average, and Ae is the average made from the fixed base (1961-90) values. Although no individual location in Ae is changing, it descends even faster than A.

So I tried another tack. Using base values is the simplest way to see it, but one can just do a partition of the original arithmetic, and along the way find a useful way of showing the components of the average that Andy is calculating. I set out a first rendition of that here. I'll expand on that here, with a more systematic notation and some tables. For simplicity, I will omit area weighting of cells, as Andy did for the early posts.

#### Breakdown of the anomaly difference between 2001 and 2018

Consider three subsets of the cell/month entries (cemos):- Ra is the set with data in both 2001 and 2018 (Na cemos)
- Rb is the set with data in 2001 but not in 2018 (Nb cemos)
- Rc is the set with data in 2018 but not in 2001 (Nc cemos)

Set data | N | Weights | 2001 | 2018 |

2001 or 2018 | N=18229 | S1, A1=S1/(Na+Nb)=19.029 | S2,A2=S2/(Na+Nc)=18.216 | |

Ra 2001 and 2018 | Na=15026 | Wa=Na/N=0.824 | S1a, A1a=S1a/Na=19.61 | S2a, A2a=S2a/Na=19.863 |

Rb 2001 but not 2018 | Nb=1023 | Wb=Nb/N=0.056 | S1b, A1b=S1b/Nb=10.52 | S2b=0 |

Rc 2018 but not 2001 | Nc=2010 | Wc=Nc/N=0.120 | S1c=0 | S2b, A2b=S2b/Nb=6.865 |

I haven't given values for the sums S, but you can work them out from the A and N. The point is that they are additive, and this can be used to form Andy's A2-A1 as a weighted sum of the other averages. From additive S:

S1=S1a+S1b and S2=S2a+S2c

or

A1*(Na+Nb)=A1a*Na+A1b*Nb, or

A1*N=A1a*Na+A1b*Nb+A1*Nc

and similarly

A2*N=A2a*Na+A2c*Nc+A2*Nb

Differencing

(A2-A1)*N=(A2a-A1a)*Na-(A1b-A2)*Nb+(A2c-A1)*Nc

or, dividing by N

A2-A1=(A2a-A1a)*Wa-(A1b-A2)*Wb+(A2c-A1)*Wc

That expresses A2-A1 as the weighted sum of three terms relating to Ra, Rb and Rc respectively. Looking at these individually

- (A2a-A1a)=0.253 are the differences between the data points known for both years. They are the meaningful change measures, and give a positive result
- (A1b-A2)=-7.696. The 2001 readings in Rb have no counterpart in 2018, and so no information about increment. Instead they appear as the difference with the 2018 average A2. This isn't a climate change difference, but just reflects whether the points in R2 were from warm or cool places/seasons.
- (A2b-A1)=12.164. Likewise these Rc readings in 2018 have no balance in 2001, and just appear relative to overall A1.

A2-A1 = 0.210 + 0.431 -1.455 = -0.813

So the first term representing actual changes is overwhelmed by the other two, which are biases caused by the changing cell population. This turns a small increase into a large decrease.

#### So why do anomalies help

I'll form anomalies by subtracting from each cemo the 2001-2018 mean for that cemo (chosen to ensure all N cemo's have data there). The resulting table has the same form, but very different numbers:Set data | N | Weights | 2001 | 2018 |

2001 or 2018 | N=18229 | S1, A1=S1/(Na+Nb)=-.116 | S2,A2=S2/(Na+Nc)=0.136 | |

Ra 2001 and 2018 | Na=15026 | Wa=Na/N=0.824 | S1a, A1a=S1a/Na=-0.118 | S2a, A2a=S2a/Na=0.137 |

Rb 2001 but not 2018 | Nb=1023 | Wb=Nb/N=0.056 | S1b, A1b=S1b/Nb=-0.084 | S2b=0 |

Rc 2018 but not 2001 | Nc=2010 | Wc=Nc/N=0.120 | S1c=0 | S2b, A2b=S2b/Nb=0.130 |

The main thing to note is that the numbers are all much smaller. That is both because the range of anomalies is much smaller than absolute temperatures, but also, they are more homogeneous, and so more likely to cancel in a sum. The corresponding terms in the weighted sum making up A2-A1 are

A2-A1 = 0.210 + 0.012 + 0.029 = 0.251

The first term is exactly the same as without anomalies. Because it is the difference of T at the same cemo, subtracting the same base from each makes no change to the difference. And it is the term we want.

The second and third spurious terms are still spurious, but very much smaller. And this would be true for any reasonably choice of anomaly base.

#### So why not just restrict to Ra?

where both 2001 and 2018 have values? For a pairwise comparison, you can do this. But to draw a time series, that would restrict to cemos that have no missing values, which would be excessive. Anomalies avoid this with a small error.However, you can do better with infilling. Naive anomalies, as used un HADCRUT 4 say, effectively assign to missing cells the average anomaly of the remainder. It is much better to infill with an estimate from local information. This was in effect the Cowtan and Way improvement to HADCRUT. The uses of infilling are described here (with links).

## Tuesday, December 15, 2020

###
## GISS November global up by 0.25°C from October.

The GISS V4 land/ocean temperature anomaly was 1.13°C in November 2020, up from 0.88°C in October. That compares with a 0.188deg;C rise in the TempLS V4 mesh index. It was the warmest November in the record.

Jim Hansen's update, with many more details, is here. He thinks that it is clear that 2020 will pass 2016 as hottest year.

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

Jim Hansen's update, with many more details, is here. He thinks that it is clear that 2020 will pass 2016 as hottest year.

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

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