The Earth’s historical global mean temperature record shows much variability, often changing by tenths of a degree from year-to-year. If this variability is somewhat cyclical, one could reason that the long term would approach a mean value of zero, indicating that as many positive temperature fluctuations occur as negative fluctuations. That describes the reality of noisy fluctuations — noise is a detectable signal but it does not necessarily impact the outcome of a trend.
A bias-free noise should not contribute to the long term trend in the global temperature time series either. The premise is that if we can remove this noise from the historical record, then we can make a more precise estimate of the underlying trend .
The candidates for noisy components are:
- The Southern Oscillation Index (SOI), which measures a large scale pressure differential
- Volcanic disturbances generating reflecting upper atmosphere aerosols
- Total Solar Insolation (TSI) differences from sun-spot activity
- Atlantic Meridional Oscillations (AMO) which are detrended fluctuations in the sea-surface temperature (SST)
These data sets are all easily available from sources such as NCAR and NOAA. The resolution of SOI is monthly data points stretching back to 1880.
The strongest contributing components of the set are (1) SOI and (2) volcanic disturbances.
The SOI is a red noise-like process which shows reversion to the mean properties. Since the SOI is a measure of the sea-level barometric pressure difference between Tahiti and Darwin, this is not expected to vary from zero when taken as a long term average. That makes it a potential candidate for variance reduction, as it will add no bias to the underlying trend estimation. The connection between SOI and global temperature is known to exist, showing a lag of around 7 months .
Volcanic disturbances are sporadic, appearing more like a shot-noise behavior. Only the largest of the disturbances add significant aerosols to the atmosphere, which will cause the atmosphere to cool temporarily. There are estimates for the amount of sulfates emitted and for the mean damped exponential residence time of the aerosols in the upper atmosphere .
The following figure shows how well the application of a scaled, lagged SOI and then a scaled, damped volcanic disturbance mapped to a growing trend matches that of the NASA’s GISS temperature record.
One can use a tool such as Eureqa to determine the proportional contributions to the fluctuations while at the same time fitting to the underlying trend.
The second order contributions come from (1) TSI sunspot variations and (2) AMO.
The TSI contribution is estimated to be around 0.05C for a 1 W/m^2 variation in solar variation, which essentially comes from the Plank response to an incoming thermal stimulus.
The Eureqa solution shown in Figure 3 recommended this value as well, which is an imperceptible perturbation to the SOI and volcanic signals.
The last contribution is due to the AMO index. This has some issues relating to the fact that the detrending and temperature fluctuations are “baked in” to the index since the AMO itself is derived from SST time series. However, Eureqa will find that the addition of the AMO signal to the mix will reduce the error of the model fit. The significant bumps and dips are further reduced as shown in the figure below.
The real objective of this exercise is to demonstrate how the noise artifact known as the “pause” or “hiatus” which has occurred in the last 15 years is simply that, an artifact of statistical fluctuations. By compensating the GISS temperature record with an unbiased estimator of the major noise terms, the true underlying trend is revealed and a flat noise spectrum is all that remains (see below).
The next obvious step is to estimate the log sensitivity of these de-fluctuated curves to the growing concentration of atmospheric CO2. The following chart shows log-sensitivity plots of TCR and ECS based on global mean surface temperature records. TCR uses global temperature from GISS while the estimation of ECS uses the land-only BEST temperature record (which eliminates the slow feedback caused by the ocean acting as a heat sink). Both these numbers match the mean estimates determined from paleo and modern instrumental evidence as well as first-principles physics models.
Look at the bottom ECS plot and note the log-regression best fit formula. The temperature anomaly goes down another 25C as the CO2 approaches 1 PPM. This is close to how cold the earth would be if we didn’t have CO2 as a control knob (to use Lacis’ term ).
Yet the ECS of 3C for doubling of CO2 is enough to keep Earth’s troposphere warm and fit enough to support biological life.
That is why it is important to understand and advance climate science.
The analysis in this presentation is not that complex — many people are following the same path that I outlined above  .