**"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk".**

Attributed to von Neumann

Following on from comments The frequencies etc of the original plots have been tweaked.

Note no attribution of the frequencies found is offered!

Method:

All frequencies and TSI were removed leaving just the polynomial.

a frequency was fitted to the main humps of the HADCRUT data (59Years)

Amplitude and phase of this were matched to the temperature record

The residuals were obtained and a simple curve fit added.

This showed a period of about 100 years.

A Further frequency was fitted to this curve fit changing phase and amplitude and frequency to give a near zero curve fit too the residual

This produces a good low resolution fit.

An attempt was made then to further reduce the residuals by subtracting TSI:

This does not lower residuals significantly.

All frequencies are then re-instated and phase and freq of the 2 frequencies and TSI adjusted for minimum residuals:

A reasonable fit! Note that this is significantly better fit than the previous post around the twitch in 1945. This is because of the artificially input 60 year and 100 year waves.

The future |

None of the frequencies discovered produced the current rise so this has been trended with the following equation:

temp anom = 2.40389E-07(date)^3 - 1.34093E-03(date)^2 + 2.49320E+00(date) - 1.545547E+03

This trend produces the correct fit - It may be CO2 or something else. But I cannot see how a further cyclical parameter could produce the current rise.

Assuming that the trend is correct it produces the following prediction:

I DO NOT CLAIM THIS IS ACCURATE!!!!

However a very important point is that the trend is positive the whole of the time period. But the 2 major cycles 60 years and 100 years produce a substantially flat temperature from 2001 to 2023. During this period the trend continues rising and will add significantly to the 60 and 120 year cycles when they go positive.

This will allow "skeptics" 22 years of "I told you there was no warming" followed by an unfortunate, unexpected (to them) temperature rise.

TSI source still unknown but has little effect. The TSI has been extended to the future by splicing in data from 1900 a low level similar to this cycle?

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All "sums" are done on monthly data and plots are filtered using a Hodrick Prescott filter (from the same source as the band pass filter) to remove high frequency components (HP filter gives a better end filter than moving average which has to terminate within 1/2 the averaging period from the end dates - in my opinion!)

The trend line is given by this polynomial:

y = 2.40389E-07x^3 - 1.34093E-03x^2 + 2.49320E+00x - 1.545547E+03

This trend fits the near horizontal 1800s and the increases since the 1960s

This could of course be a long period sine but if so then since the 1800s we have only gone perhaps half way through its cycle. this will only become visible in the next few decades if temperatures begin to decline.

The overall response with the increasing polynomial shows recent flatlining and even drops over the last year. The future prediction is for a decline for the next few years (the trend is still increasing remember!) as the 60y and 100y cycles go into a low period.

The frequency table (Frequency that would reconstruct the TSI data (9 years to 14 years + 21 years) has been artificially set to zero. The 2500 year data below is set to give 0 amplitude (no frequency found).

Period years | amplitude | Offset months |

0.5012 | 0.023174092 | 6.60 |

0.8420 | 0.006750249 | 4.05 |

0.8900 | 0.010820097 | 0.59 |

1.7684 | 0.006095148 | 0.75 |

1.9373 | 0.006963534 | 2.85 |

1.9924 | 0.005092903 | 5.85 |

2.0384 | 0.004105465 | 9.20 |

2.1070 | 0.004651939 | 10.50 |

2.2649 | 0.007415539 | 10.35 |

2.3139 | 0.009177612 | 6.50 |

2.5418 | 0.006009001 | 4.50 |

2.6756 | 0.007867544 | 2.45 |

2.7458 | 0.004892064 | 4.65 |

2.8746 | 0.010417192 | 2.65 |

3.1555 | 0.005246582 | 0.56 |

3.2692 | 0.004667568 | 6.65 |

3.4699 | 0.004344144 | 9.34 |

3.5794 | 0.008309031 | 3.25 |

3.7750 | 0.008219473 | 3.90 |

3.9908 | 0.005512257 | 5.70 |

4.7031 | 0.005653949 | 6.25 |

5.1270 | 0.004919605 | 6.20 |

5.2257 | 0.004829187 | 9.05 |

5.7274 | 0.002816915 | 6.75 |

5.9866 | 0.004839718 | 2.05 |

6.2976 | 0.00394786 | 4.55 |

6.5986 | 0.002294266 | 3.50 |

7.5860 | 0.002836881 | 3.50 |

8.4414 | 0.002737653 | 3.35 |

10.0785 | 0 | 6.75 |

11 (TSI) | 0.014289 | 72.00 |

11.4522 | 0 | 3.25 |

12.3828 | 0 | 4.05 |

14.7992 | 0 | 4.35 |

21.1787 | 0 | 4.45 |

35.8859 | 0.001785871 | 4.65 |

59.4167 (not Found By filtering) | 0.041468451 | 3.35 |

103.5000 (not Found By filtering) | 0.017897547 | 101.05 |

110.1917 | 0 | 5.15 |

2508.3333 | 1.56572E-06 | 4.15 |

2508.3333 | 1.56572E-06 | 4.10 |

2508.3333 | 1.56572E-06 | 4.10 |

So if I'm following this correctly, by removing a 60 year and 100 year sine, you have improved the 11y TSI fit to the residuals. (Which begs the question - what are these sine waves?)

ReplyDeleteAlso, I found it a bit hard to read your amp/year chart as a point chart. It would be easier to read as a line chart.

I haven't even touched the surface of Scafetta, yet.

http://www.fel.duke.edu/~scafetta/pdf/scafetta-JSTP2.pdf

TSI seems to be irrelevant - the fit provides no fitting to the hadcrut data over the whole of the time. Alignments of peaks in one place give misalignment in others.

ReplyDeleteThe mass of other frequencies inmprove the wiggle fitting significantly - but this is only at the year level. The 60 and 100 year are more significant for matching the record.

The final plot extends the time scale to 2055.

It is noticable that we have gone throgh a period of cooling but by 2029 significant warming begins again! This will give the sceptics a good talking point until then!! but by 2060 it will be about a 2C rise - all assuming that the trend is correct of course!

Mike

But what is the physical basis of the 60? Ocean cycles? Ice feedbacks? Or something solar? Which is why I keep pushing Scaffeta at you. I have no great confidence that he is right - but I haven't even found the time to read him and evaluate his 60 year solar claims.

ReplyDeleteBUT the thing is it does not matter All the frequencies added in ar cyclicle. IE they do not produce a trend. The trend equation is the danger:

ReplyDeletetemp anom = 2.40389E-07(date)^3 - 1.34093E-03(date)^2 + 2.49320E+00(date) - 1.545547E+03

Yhe sorce of tis is the important search.

Solar input (TSI) is really insignificant For the solar input to have an effect it would have to be much larger energy input than TSI. This would surly have been measurable on the earth?

Mike

ReplyDeleteFor the solar input to have an effect it would have to be much larger energy input than TSI.Or a feedback? Recall that there is "direct" forcing by CO2 and then there is the feedback. Climate sensitivity is function of both the forcing and the feedback.

If I have this right, the solar guys are claiming cloud feedbacks based on gamma rays or some such.

Don't get me wrong. I'm not trying to convince you that there is a significant solar component is recent warming. But discounting "direct TSI" (while true and important) is missing the argument that the solar guys are advancing. In a sense, its attacking a straw man.

So I'm hoping to get a better understanding of exactly what it is that Scaffata and West are arguing. That is why I keep pointing you in that direction. Not to convince you one way or the other.