Changing temperature anomaly baselines

I wanted to check whether the choice of baseline can affect the calculation of  global temperature anomalies from station data. Each temperature index (GISS, Berkeley, CRU) uses different normalisation periods for calculating weather station temperature anomalies. I was surprised to discover that this choice makes no difference whatsoever to the results.

I used the new GHCN V4 which contains 27315 weather stations, and calculated the global average temperature anomaly relative to 5 different 30-year baseline periods using Spherical triangulation. Selecting different baselines restricts the analysis to those stations with sufficient data falling within those periods. Here are the results.

Global Land temperature anomalies calculated relative to 5 different baselines. The numbers in brackets are the number of stations contributing for each baseline period.

All the trends are very similar despite a factor of up to 8 difference in the number of stations used.  We can compare them all directly by offsetting each onto the same 1961-1990 baseline. To do this I simply scale each one by the offset difference between 1961-1990 (shown in ‘calc’ brackets).

All 5 baselines offset to the same 1961-1990 normalisation. The offsets are shown as Calc.

The results are surprisingly similar.  This means that the choice of baseline period is essentially arbitrary and does not affect the end result.

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January 2019 global average temperature remains unchanged – 0.73 C

Global averaged surface temperature for January 2019 was 0.73C using my spherical triangulation method merging GHCNV3 with HadSST3. This is unchanged since December 2018. The baseline used is always 1961-1990.

Monthly temperatures since 1998.

The Northern Hemisphere is shown here.

Temperature distribution Northern Hemisphere. Siberia is warmer than December while N.America is cooler.

and here is the Southern Hemisphere.

Souther Hemisphere shows high Australia temperatures while Antarctica is actually colder than normal.

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How does temperature depend on CO2?

Robert Rohde has produced a very nice animation of global temperatures as a function of CO2 levels in the atmosphere. Of course it is designed for public relations purposes in order to show increasing CO2 causes warming.  He even uses absolute temperatures which are not even directly measured. Here is my version of how temperature anomalies depend on CO2.

Fig 1. Land temperature (GHCN) and Global temperatures (HADCRUT4) plotted as a function of CO2 levels. GHCN-Daily agrees with Berkeley Earth Land temperatures. Normalised to 1961-1990 baseline.

After a rather uncertain temperature rise from pre-industrial (280ppm) temperatures, there is a long period with no net warming between CO2 levels of 300 to 340 ppm, corresponding to the  period ~1939 to ~1980. Warming afterwards continued as expected but then began tailing off towards a logarithmic dependency on CO2.

Many people will often glibly inform you that the CO2 greenhouse effect produces logarithmic radiative forcing, and state that this can easily derived from simple physics. However, few can really explain to you why it should be logarithmic, and it turns out that there is no simple proof as to why it should be. The often quoted formula for radiative forcing:

S = 5.35 \times \ln{\frac{C}{C0}}

can be traced back to a paper from 1998 in GRL (Myhre et al)

This formula is in reality a fit to some rather complex line by line radiative transfer calculations by hundreds of vibrational excitation states of CO2 molecules for absorption and re-emission of infrared radiation .  I have perviously described my own calculation of this radiative transfer and how you can fit a logarithmic dependency to it. The physical reason why increasing CO2 apparently produces a logarithmic forcing is that the central lines rapidly get saturated way up into the stratosphere, the strongest of which can then even cause cooling of the surface. Overall net warming is mostly due to strengthening of the weaker peripheral excitation  levels of the 15 micron band.

Fig 2: Calculated IR spectra for 300ppm and 600ppm using Planck spectra. Also shown are the curves for 289K and 220K which roughly corresponds to the Stratosphere. The central peak is cooling the planet because it lies high up in the stratosphere where temperatures are rising.

The net effect produces an apparent ‘logarithmic’ dependency, that I also calculated, and which is very similar to that of Myhre et al. Notice also how 3/4 of the “greenhouse” effect from  CO2  kicks in from zero to 400ppm.

Figure 1: Logarithmic dependence of radiative forcing on CO2 concentration up to 1000 ppm

The effect of increasing CO2 is to raise the effective emission height for 15micron IR radiation photons. The atmosphere thins out with height according to barometric pressure, and eventually the air is so thin that IR photons escape directly to space, thereby releasing energy from the atmosphere. Some IR frequencies can escape directly to space from the surface (the IR window). Others escape from cloud tops or high altitude water vapour and ozone.

The loss of energy from the top of the atmosphere drives convection and evaporation which is the primary heat loss from the surface. This process also drives the temperature lapse rate in the troposphere without which there could be no greenhouse effect. The overall energy balance between incoming solar insolation and the radiative losses to space determines the height of the tropopause and the earth’s  average temperature. A small sudden increase in CO2 will slightly reduce the outgoing radiative loss to space, thereby  creating an energy imbalance. This small energy imbalance is called “radiative forcing”. The surface will consequently warm slightly to compensate, thereby restoring the earth’s  energy balance.

This effect can be estimate from Stefan Boltzman’s law.

S = \sigma \epsilon T^4

DS = 4 \sigma \epsilon T^3 DT

If you assume T is constant (the answer increases by 1% for 1C if you don’t) then

DT = \frac{DS}{4 \sigma \epsilon T^3}

so with T = 288K and \epsilon \approx 0.6 and an effective insolation area of the earth of \pi \times R^2 this then  gives

DT \approx 1.6 \times \ln{\frac{C}{C0}} (^\circ C )

A steeper slope would be expected with net positive feedbacks

Figure 2 shows HadCRUT4.6 and my version of GHCNV3/HadSST3 plotted versus CO2 and compared to a logarithmic Temperature Dependence.

HadCRUT4.6 and 3D-GHCNV3/HadSST3 plotted versus CO2. The orange and purple curves show logarithmic temperature dependencies.

There is still a discrepancy in trends before CO2 reaches ~340ppm but thereafter temperatures follow a logarithmic increase with a scale factor of about 2.5. This implies a climate sensitivity (TCR) of about 1.7C .

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