Home > Natural Variability, Statistics > Lines, Sines, and Curve Fitting 14 – more extrapolation revisited

## Lines, Sines, and Curve Fitting 14 – more extrapolation revisited

2012 February 16

A year ago, I was working through some curve fitting exercises. Girma was advancing his line+sine model as superior to climate modeling partially based on its hight correlation. He had allowed that an equally simple model with a higher correlation than his would be a superior model. I demonstrated 3 variations of an exp+sine model, one for each surface record, each had higher correlation than his. Neither one of us dealt with autocorrelation.

I thought I would make a quick update on that original post. Nothing fancy, just adding the data points for the 2011 annual surface temperature record indexes.

The coefficients for the equations came from Feb 2010 datasets for GISTEMP, HadCRUT3, and NCDC. GISTEMP changes over time due to their backcast for UHI adjustments and I noticed slight variations in calculated statitistics for it. In all three cases the correlation ticked up slightly. The coefficients were found as the best match (highest correlation) for the exp+sine function based on a brute force search of the parameter space for 1901-2000 data points. These are repeated below:

-a/100 + b/100 * exp((k/10000)*(x-1880))+ A * sin(((x-B)/T)*(2*pi)

```    a         b          k           A         B         T
GIS 39.39528 11.34487 158.5761 0.08123327 1857.690 66.71628
CRU 58.50143 17.07027 132.0417 0.11238451 1801.812 61.63521
NOA 37.78438 12.43439 150.1897 0.10528688 1863.281 62.17947```

To better see the recent decades, we can zoom into a 1976-2025 50-year chart.

Curve fitting is fun if not exactly physical. You can even get published doing it as evidenced by Scafetta 2012 Testing an astronomically based decadal-scale empirical harmonic climate model versus the IPCC (2007) general circulation climate models. From the abstract …

We compare the performance of a recently proposed empirical climate model based on astronomical harmonics against all CMIP3 available general circulation climate models (GCM) used by the IPCC (2007) to interpret the 20th century global surface temperature. The proposed astronomical empirical climate model assumes that the climate is resonating with, or synchronized to a set of natural harmonics that, in previous works (Scafetta, 2010b, 2011b), have been associated to the solar system planetary motion, which is mostly determined by Jupiter and Saturn. … By combining this corrected trend with the natural cycles, we show that the temperature may not significantly increase during the next 30 years mostly because of the negative phase of the 60-year cycle … The results of this paper reinforce previous claims that the relevant physical mechanisms that explain the detected climatic cycles are still missing in the current GCMs and that climate variations at the multidecadal scales are astronomically induced and, in first approximation, can be forecast.

I have to admit that I’m not as familiar with Scafetta as I would like. But really? Earth’s climate is resonating with Jupiter and Saturn? Really? I need to find a mode that would allow me to publish “The proposed climate model assumes a resonance mode when Jupiter aligns with Mars“.

In my previous curve-fitting work, I warned that this exercise is interesting but without a connection to one or more physical process, it’s not physics. And, at least without reading further, I can’t really count Scafetta’s comments as a connection to physical processes. But there is something closer to Earth (literally) that has been proposed: The Atlantic Multi-decadal Oscillation. The AMO is not a driver of the climate, but appears as a response to changes in the Atlantic Meridional Overturning Circulation (AMOC). Medhaug and Furevik 2011 North Atlantic 20th century multidecadal variability in coupled circulation noted that while models were able to reproduces the overall structure of the circulation fairly well, they were unable to match the phase and duration of the observed 20thC AMO and concluded that the AMOC is not actually driven by external forces but rather by natural variability. But it could be a persistent feather of the Holocene. Knudsen 2011 Tracking the Atlantic Multidecadal Oscillation through the last 8,000 years looked at the AMO in ice records and conjectured “that a quasi-persistent ~55- to 70-year AMO, linked to internal ocean-atmosphere variability, existed during large parts of the Holocene.. Tamino demurred politely. Even more skeptically, Vince 2011 posed the question Is the Atlantic Multidecadal Oscillation (AMO) a statistical phantom?

There are alternate theories for the high 1940s temps (aerosols, changes in temp recording methodologies) and the low 70s (low aerosols due to clean air regs). And for the apparent slowing of the warming trends in this last decade (decline in TSI, more aerosols (this time cooling)). But I think poor resolution of global climate models has caused a more dismissive attitude towards AMOC/AMO discussion than is currently warranted.