... Is it a Trend (edited)

The second half of "it's all cycles" post

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

The elephant has been constructed!!

The spreadsheet is available on request (11MB)

This post examines the reconstruction of the HADCRUT3V temperature trend using cycles and a polynomial trend.

Over the HADCRUT period the fit is very sligtly better than cycles only
TSI has NOT been inverted to give the best fit (there is a definite minimum error - set to the levels used here) both a 10 year and 11 year further cycle is required to produce the best fit. The fit is chosen with various filter values applied to the TSI. A 38 month trailing average gives the best fit.

Note that TSI has been extended to the future by repeating an earlier cycle.
 
Also included here is a comparison plot where the cycles only and trend out put are compared. Divergence occurs pre 1850 and post 2010

So assuming these plots accurately predict the  future!!!! the next 5 or so years should show which is "truth"

Long Term Plot

Comparison of plot with and without TSI (volcanic forcings also shown)

The Poynomial is:

y =0.00000024008x^3-0.00134007x^2 + 2.49324x -1546.54
X= date eg. 1850.167

Period years	amplitude	Offset months
0.5012	0.02791257	8.47
0.8395	0.006504311	2.82
0.8907	0.012030142	1.13
1.7692	0.011135157	0.92
1.9373	0.012108253	2.77
1.9906	0.019817414	5.72
2.0417	0.012781876	9.62
2.1095	0.010343775	10.57
2.2567	0.014687976	9.57
2.3139	0.016754467	6.72
2.5418	0.017169878	4.42
2.6735	0.017438215	2.47
2.7608	0.010679424	4.97
2.8737	0.026304239	2.52
3.1647	0.020652313	0.98
3.2734	0.016460943	6.37
3.4699	0.015744304	9.59
3.5777	0.022220303	3.07
3.7684	0.023943458	3.37
4.0192	0.019582555	6.87
4.7240	0.027640318	6.64
5.1020	0.02182499	5.57
5.2675	0.021641714	9.87
5.8528	0	6.67
5.9782	0.02566776	1.77
6.2558	0.022759327	4.37
6.6195	0.016595394	3.07
7.5727	0.02370424	3.22
8.3954	0.02139623	3.07
10.1027	0.034637599	6.87
11.0000	0.043331925	-75
11.8786	0.013113219	4.27
12.6922	0.021194863	4.77
14.8995	0.033178542	4.87
21.1000	0.046919237	4.37
35.0832	0.022348787	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	0.016579178	-6.58
2508.2497	0	4.17
2508.3333	0	4.12