I gave theory for the operators previously. The basic plan here is to apply them, particularly second derivative (acceleration) to see if it helps clarify break points, and the general pattern of temperatures. The better smoothing might seem contrary to detecting breakpoints, since it smooths them. But that actually helps to avoid spurious cases. I'll show here just the analysis of GISS Land/Ocean.
I'll start with the spectrum of acceleration below. As I said in Part 1, you can actually get much the same results by differencing the smooth (twice for accel), or smoothing the difference. But the combined operator shows best what is happening in the frequency domain.
Spectrum of accelerationHere is a plot of the spectra for acceleration, as with trend in part 1.
- Each of the operators is now quadratic for low frequencies, as differentiation requires. As the frequency (1/width) = 10 /Cen is approached, the response again starts to taper. This is the effect of smoothing at higher frequencies.
- Each operator then has pronounced band-pass character, slightly more so than with trend. This will show in their behaviour.
- You can still see the increasing order of roll-off, though each is slower than the corresponding trend spectrum.
Gradient plotsThe active plot below shows gradients with 10,20 and 30 year filters, on 13 different datasets. Each plot shows the three different tapers ("Regress" (red) is just OLS). You can use the buttons at the top to change data set or filter length.
The plot you see first here is GISS Land/Ocean monthly, 30 year filters. The filter is centered, so you see an estimate of the derivative at the year marked on the axis. There is no padding, so the plot stops at 2000. Some notes:
- The trend is mostly positive (warming).
- As the smoothing increases, there is more pronounced amplification around the filter period (30 yrs). Inevitably, most of that is noise. But it happens even with the OLS trend.
- There is no radical change as smoothing increases, but the blue curve strips away high frequency detail, which probably had little meaning.
- What remains are the familiar features - warming 1910 to near 1940, then a hiatus, then warming from about 1975 on, with a max trend (not a pause) at about 2000. Some sign of deceleration there, although it could be just the amplification of the 30 yr band.
Acceleration plotsNow we are estimating second derivative, which should be mostly the derivative of the above. This will be clearer with the W2 blue curve. The main thing to look for are spikes (+ or -) to indicate break points, where the derivative changes.
- The spikes aren't very pronounced. There is conflict between the want to remove HF noise, and preserving the spike. So the smoothest line shows smoothish spikes, but that is abtually the meaningful part. It isn't really better without smoothing. So here we see 1910 and 1940 as the most prominent features, with a reasonable peak around 1972 (it's really hard now to pin down a year, as it should be). At this resolution, no sign of a peak at 2000.
- Going to shorter periods doesn't really reveal more. There is just more noise at about the periodicity of the filter length.
More about the datasets
- HadCRUT - HADCRUT 4 Land/Ocean
- GISSlo - GISS Land/Ocean
- NOAAlo - NOAA Land/Ocean
- UAH5.6 - UAH Lower Troposphere
- RSS.MSU - RSS Lower Troposphere
- TempLSgrid - Land/Ocean
- BESTlo - Land/Ocean
- C.Wkrig - Cowtan and Way kriging Land/Ocean
- TempLSmesh - Land/Ocean
- BESTla - Land Only
- GISS.Ts - Met stations
- CRUTEM - Land Only
- NOAAla - Land Only
- HADSST3 - Sea Surface
- NOAAsst - Sea Surface