Trends are tricky

The blue bars here show the average surface temperature of the Earth, year by year, with the 1950-1980 average subtracted out.  The difference is called the temperature anomaly.  You can see the anomaly is about 0.5 Celsius now, or 0.9 Fahrenheit.  

The green curve is an attempt to smooth out the data and extract meaningful trends.  This is where it gets tricky!   This particular curve was obtained using a cubic spline, built piece by piece from a bunch of cubic polynomials.  But doing this requires some choices: adjusting a smoothing parameter lets us build a curve that fits the data very closely and wiggles a lot, or a curve that's very smooth but doesn't stay so close to the data.

How do we pick the 'right' smoothing parameter?  What does 'right' even mean?  The answers depend on what you want to know.

In this particular curve, generalized cross-validation was used to pick the smoothing parameter.  For more on that, and an intro to other curve-fitting techniques, read  +Jan Galkowski's post:

Next, the orange curve shows the slope of the green curve.  So, it's a way to see how fast the Earth is warming.  It shows the Earth is warming less fast since 1998... but still getting warmer.

Of course, different ways of smoothing the data would give different answers here... and that's why trends are tricky.

It's also crucial to combine statistics with knowledge of the climate, and climate physics.  Jan's post is mainly a tutorial on curve-fitting... but it's important to know that 1998 was an El Niño year, and thus especially hot worldwide.  We haven't had a strong El Niño since then. This might explain why the orange curve, the rate of warming, goes down after 1998. 

It might not, but it's an example of what I mean: it's important to go beyond the simple graphs and dig into the actual science! 

On the other hand, it's also important to learn statistics, and Jan's post can help you there.  It's pretty advanced, so don't be shy about asking questions, either here or on the blog.
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