The best
fit sine wave has a period of 67.7 + / - 7.2 years.
What I did was to
fit a sine wave of various periods to the data, and record the amplitude of the best fit.
% of 2 Saw4 24.98 years 75.2 % of 3 Saw5 20.01 years 80.1 % of 4 I am using the «PAST» program to
fit the sine waves.
Not exact matches
There are other modes of vibration as well —
sine curves in which more than one
wave fits into the length of the string, known to musicians as harmonics.
The software produces a
sine wave from a «best
fit» solution.
He used the Lomb - Scargle routine in IDL to determine the most significant periodicity in the data (= 3.2 days), and then used this as input into a least - squares
sine wave fit to produce the
fitted curve shown.
The
fit was much better, suggesting it really was two
sine waves.
(c) even an R2 fantastically close to 1 is no guarantee at all of future behavior, as evidenced by my favorite example of this, namely a curve that's an equally good
fit to the peak of a Gaussian and the peak of a
sine wave.
I found that F3 (HadCRUT3) could be
fitted accurately with
sine waves of frequency nf for n = 1 to 5, each involving 2 coefficients (amplitude and time - shift), plus one more for frequency f (= 1 / ToothW) for a total of 11 coefficients.
This was an alternative hypothesis, so to test it I tried
fitting two
sine waves instead of one.
fit a few
sine waves to residual 4.
I then performed a joint
fit of one
sine wave to the residual (joint with CS as a parameter), noticed it was not a great
fit but that the residual bore a strong resemblance to the result of two
sine waves beating, and tried two
sine waves.
This is easily refuted by
fitting the top of a gaussian to the top of a
sine wave, or vice versa (depending on which one you propose to extrapolate from).
Were that the case, that is, if this were just a random
fit of
sine waves, I most certainly would not have bothered submitting to AGU, it would be completely vacuous.
I
fitted to LN [CO2](using a CE of 1.4 for 2x [CO2]-RRB- Sato's aerosol 550 nm * minus 0.58 degrees and a sinewave I have a
sine wave of 57 years + / - 0.122
The r - squared of a linear trend line of this partial
Sine wave is 0.88... 88 % of the data
fit the trend line.
fitting only to least sum squares (blue dots) I get a change in temperature that looks like a
sine -
wave with a peak to peak of 60 - 70 years.
A cyclic
fit based on a
sine wave of combinations of
sine waves could make sense of there are cyclic phenomena going on (as is the fact, orbits etc).
Girma for a bit of fun I reconstructed the hadcrut3V global tempreature series from
sine waves of different frequencies amplitudes and phases (I think it is pretty good
fit over 1850 to 2010 — and beyond!).
and you can have a high degree of
fit to the modern temperature record with a long term process represented by a periodic but stationary
sine wave.
Using just 4
sine waves in a periodic but stationary function will give a pretty good
fit to the modern day temperature decomposition you showed without invoking any AGW at all.
The periodic functions you
fit are fairly clear — I have run my own tests using GISS (up to 2008) to look for the
sine wave function with the best
fit.
Any
sine wave with a period longer than the length of the time series (in the case of GISS, about 130 years) will give a
fit almost indistinguishable from a straight line
fit.
Instead what I did was take your result from Loehle 2007 which gives a 2000 year reconstruction and perform the same analysis — what is the
sine wave with the best
fit to the 2,000 year data?
In fact, you can get a very good
fit with actual temperature by modeling them as three functions: A 63 - year
sine wave, a 0.4 C per century long - term linear trend (e.g. recovery from the little ice age) and a new trend starting in 1945 of an additional 0.35 C, possibly from manmade CO2.
The linear trends as well as the
sine wave period and amplitude were adjusted to make the
fit work.