| on Mar 31, 2008, 12:48 PM E.S.T.
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In Part I,
we presented evidence of a noticable periodicity in globally averaged
temperatures when filtered with Hodrick-Prescott smoothing. Using a
default value of lamda of 100, we saw a bidecadal pattern in the rate
of change in the smoothed temperature series that appears closely
related to 22 year Hale solar cycles. There was also evidence of a
longer climate cycle of ~66 years, or three Hale solar cycles, corresponding to slightly higher peaks of cycles 11 to 17 and 17 to 23 shown in Figure 4B. But how much of this is attributable to value of lambda (λ). Here is where lambda (λ) is used in the Hodrick-Prescott filter equation:
The first term of the equation is the sum of the squared deviations dt = yt − τt which penalizes the cyclical component. The second term is a multiple λ
of the sum of the squares of the trend component’s second differences.
This second term penalizes variations in the growth rate of the trend
component. The larger the value of λ, the higher is the penalty.
For the layman reader, this equation is much like a tunable bandpass filter used in radio communications, where lambda (λ) is
the tuning knob used to determine the what band of frequencies are
passed and which are excluded. The low frequency component of the
HadCRUT surface data (the multidecadal trend) looks almost like a DC
signal with a complex AC wave superimposed on it. Tuning the waves with
a period we wish to see is the basis for use of this filter in this
excercise.
Given an appropriately chosen, positive value of λ, the low frequency trend component will minimize. This can be seen in Figure 2 presented in part I, where the value of lambda was set to 100. Read rest of story...
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