Here is a beautiful photograph of our planet. The climate of earth is what makes it our home and able to support all of us. Water dominates the climate as it covers most of the surface. As a liquid it readily absorbs sunlight, but at both low and high temperatures it changes into a state that reflects more sunlight.

After energy from sunlight is absorbed, it must be removed from the earth. If it didn't then the earth would become too hot. If too much sunlight were reflected or the atmosphere did not abosrb sunlight, then the earth would become cold and the oceans would freeze.

The overall temperature of the earth is governed by physical science. The applicable physical laws existed before humans gave them names. The basic equation for the climate of Earth is the Stephan-Boltzamm law which states that temperature is proportional to the forth power of the amount of radiation energy:

Surface Temperature (Kelvin) = Constant * Radiation Energy^0.25 Stephan-Boltzmann Constant = 5.6704 x 10^-8 Watt/m^2 K^2 Radiation Energy (watts/meter^2)

The amount of Radiation Energy is a function of Total Solar Irradiance (TSI), how much is not reflected (1-albedo) and how easily energy is emitted (emissivity).

Radiation Energy = TSI * Fraction not reflected * Emissivity

Total Solar Irradiance (typically 1365.5 Watts/second-meter^2) Albedo (unitless, typically 0.3 for earth) Emissivity (unitless, tpically 0.81)

Combining both equations together with typical values yields:

Surface Temperature = 287K = 14.3 C = 57.5 F

I’m going to concentrate on 2) because it accounts for the changing amplitude of the cycle (eg a day with clear skies will have a warmer day/cooler night than a day with cloudy skies, comparing midday with midday wouldn’t work as well).

So you keep measuring the temperature day after day, starting in July and by December you’re really confused. It looks like you’re cooling. Global warming must be wrong again!

Obviously not; you’re in the Northern Hemisphere so you’re going into winter. Another pesky natural cycle has ruined your trend. So repeat 2), average over 12 months and you can compare years.

It’s ridiculous to compare night with day, or summer with winter; so why do some people compare an El Nino year with a La Nina year? Or a strong El Nino with a weak El Nino (this is like comparing midday with clouds to midday without clouds). You can’t extract any useful information about trends from this data!

To show you that this works, I’m going to make up a temperature record using just 3 things – greenhouse gases, the solar cycle & El Nino Southern Oscillation. These are 3 of the biggest factors affecting temperature, so it should look something like the real temperature record.

Figure 1 – Components of temperature series

To make up my ‘toy’ temperature series I add these together and get figure 2. It does a reasonable job of looking like the real temperature record for the last ~40 years and that’s what you’d expect for a period of roughly constant average solar output & El Nino.

Figure 2 - Toy temperature series built from GHG, ENSO and solar components.

There is definite global warming from greenhouse gases, but there are still periods when you get a negative trend. Figure 3 is from a 9 year period in the graph for example.

Figure 3 – Example negative trend from toy temperature series. Years 24-32.

So how do you decide what average to take? Well, you start by averaging over at least one period of the cycle; eg to cancel out day/night you take 24 hours, for summer/winter 12 months and for the solar cycle 11 years.

In a real data series without knowing all of the cycles, a scientist would do something called a ‘Fourier Transform’ – a clever bit of maths which tells you how long the cycles are. Here I know the periods: they are 4-8 years (El Nino) and 11 years (solar cycle). I’m going to take a 10 year average (remember, you can do this at home and try any average period you want to see what happens!), which is close enough to 11 that it should filter out most of the cycles.

Figure 4 shows there’s some little wiggles because 10 years doesn’t perfectly capture the periods but the interesting thing is the trend; it’s very close to the data and it thinks that there’s a warming trend of +0.017C/year.

Figure 4 – Running mean 10 year average temperature.

This is exactly what I put into my toy model as the greenhouse gas warming. I tried the same trick with a quadratic equation and yet again, the averaging trick works and calculates very close to the underlying trend – try for yourself!

How could you use this trick to work out underlying trends in real temperature data? Follow the steps: