Cycle Mania and Hadcrut3

From the fun school of posts here are a couple of plots that reconstruct hadcrut3v from a series of sine waves.
One shows reconstruction from cycles only; this has problems getting a good fit in the 1800s but shows rhat the next few years should be a period of reducing temperatures. The long period controlling the plot is 317 year long
The other is constructed round a smooth increasing trend. A better fit in the 1800s and still shows that despite the trend the temperatures will be flat for a few more years before increasing with a vengance. The underlying trend is defined by this polynomial
y = 2.40389E-07x3 - 1.34093E-03x2 + 2.49320E+00x - 1.545547E+03

Do either have any predictive skills. = NO

The most importasnt thing shown is in the the trending plot where  despite an ever increasing trend there is still a period where temperatures appear not to increase - from 1998 to 2018. this is due to an underlying 60year period being on a down part of the cycle. This is something that the "skeptics" cannot seem to grasp - CO2 is increasing so why is temperature static?.

The all cycle:

317 year and 60.1 year cycles controlling the "trend"

The trend+cycle plot

Trend and 59.75 year cycle controlling trend

So what curve are we "following" - only another 4 or so years will tell!.

Earlier posts:
http://climateandstuff.blogspot.co.uk/search/label/simulation

Reconstructions with limited signals

Firs Set is using trend and the second is using cycles only
The minimum amplitude used is 0.03

Period years	amplitude	Offset months
0.5012	0	8.47
0.8395	0	2.82
0.8907	0	1.13
1.7692	0	0.92
1.9373	0	2.77
1.9906	0	5.72
2.0417	0	9.62
2.1095	0	10.57
2.2567	0	9.57
2.3139	0	6.72
2.5418	0	4.42
2.6735	0	2.47
2.7608	0	4.97
2.8737	0	2.52
3.1647	0	0.98
3.2734	0	6.37
3.4699	0	9.59
3.5777	0	3.07
3.7684	0	3.37
4.0192	0	6.87
4.7240	0	6.64
5.1020	0	5.57
5.2675	0	9.87
5.8528	0	6.67
5.9782	0	1.77
6.2558	0	4.37
6.6195	0	3.07
7.5727	0	3.22
8.3954	0	3.07
10.1027	0.034637599	6.87
11.0000	0.043331925	-75
11.8786	0	4.27
12.6922	0	4.77
14.8995	0.033178542	4.87
21.1000	0.046919237	4.37
35.0832	0	3.42
59.7500	0.107447989	3.07
110.2417	0	5.37
118.5000	0.048809315	95.17
290.2778	0	134.32
310.3644	0	-6.58
2508.2497	0	4.17
2508.3333	0	4.12

Period years	amplitude	Offset months
0.5012	0.036054	8.3
0.8395	0	2.9
0.8910	0	1.23
1.7692	0	0.95
1.9373	0	2.7
1.9911	0	5.8
2.0409	0	9.55
2.1091	0	10.55
2.2569	0	9.55
2.3139	0	6.75
2.5418	0	4.4
2.6714	0	2.35
2.7608	0	5
2.8746	0	2.55
3.1638	0	0.96
3.2734	0	6.55
3.4699	0	9.64
3.5794	0	3.15
3.7684	0	3.35
4.0150	0	6.75
4.7240	0	6.68
5.1061	0	5.5
5.2466	0	9.55
5.7274	0	6.65
5.9782	0	1.85
6.2516	0	4.35
6.6153	0	3
7.5693	0	3.2
8.4272	0	3.25
10.0693	0.030061	6.7
11.0000	0.038659	-69
11.7532	0	3.85
12.6336	0	4.55
14.9497	0.030069	5
21.2083	0.048414	4.45
35.6852	0	3.75
60.0833	0.119432	3.05
101.8333	0	96.15
110.2167	0	5.35
290.2778	0	134.3
317.0533	0.395701	2.3
2508.1661	0	4.15
2508.3333	0	4.1

The Total Cycle thing repeated

"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk".
Attributed to von Neumann

The spreadsheet is available on request (11MB)


A plot of all the amplitudes and frequencies used. The 11 year cycle is TSI The scatter of low frequency low amplitude signals gives the noise

300 year and 60 year cycles superimposed on the constructed temperature record

A check to see if volcanic activity can be seen in the difference between actual HADCRUT3 and reconstruct



Remaider HADCRUT3-reconstruct with the used trailing moving average filtered and offset TSI

The reconstructed signal extended beyond the 2 ends of hadcrut3 note that the little ice age becomes a warm period using the 300year cycle

Acomparison of reconstruced cosines with no tren and reconstructed cosines + trend

Frequency/amplitude and phases of cosines + tsi used

Period years	amplitude	Offset months
0.5012	0.036054	8.3
0.8395	0.00624	2.9
0.8910	0.011773	1.23
1.7692	0.011506	0.95
1.9373	0.012512	2.7
1.9911	0.020375	5.8
2.0409	0.012712	9.55
2.1091	0.010769	10.55
2.2569	0.015195	9.55
2.3139	0.017313	6.75
2.5418	0.017742	4.4
2.6714	0.017162	2.35
2.7608	0.011035	5
2.8746	0.027285	2.55
3.1638	0.019767	0.96
3.2734	0.015463	6.55
3.4699	0.01479	9.64
3.5794	0.02302	3.15
3.7684	0.025772	3.35
4.0150	0.019124	6.75
4.7240	0.028562	6.68
5.1061	0.020193	5.5
5.2466	0.020888	9.55
5.7274	0.01294	6.65
5.9782	0.024963	1.85
6.2516	0.024229	4.35
6.6153	0.016764	3
7.5693	0.021827	3.2
8.4272	0.019945	3.25
10.0693	0.030061	6.7
11.0000	0.038659	-69
11.7532	0.013485	3.85
12.6336	0	4.55
14.9497	0.030069	5
21.2083	0.048414	4.45
35.6852	0.026464	3.75
60.0833	0.119432	3.05
101.8333	0.02669	96.15
110.2167	0	5.35
290.2778	0	134.3
317.0533	0.395701	2.3
2508.1661	0	4.15
2508.3333	0	4.1