The diagram below shows a Morlet Wavelet Transform of the winter (North Pacific Index) NPI index.
The North Pacific (NP) Index is the area-weighted sea level pressure over the region 30°N-65°N, 160°E-140°W. The NP index is defined to measure interannual to decadal variations in the atmospheric circulation.
Reference: Shoshiro Minobe
GEOPHYSICAL RESEARCH LETTERS, VOL. 26, No. 7, Pages 855-858, APRIL, 1, 1999
Resonance in bidecadal and pentadecadal climate oscillations over the North Pacific: Role in climatic regime shifts
Superimposed on this plot are the times of Jupiter-Saturn Conjunction (when these two planets are on opposite sides of the Sun) which are spaced by 19.86 years, and the times of Jupiter-Saturn Opposition (when the two planets are aligned on the same side of the Sun), also spaced by 19.86 years.
This result is supported by a comparable figure from:
ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 20, NO. 5, 2003, PP. 694–710 694
Joint Propagating Patterns of SST and SLP Anomalies in the
North Pacific on Bidecadal and Pentadecadal Timescales
ZHU Yimin and YANG Xiuqun
What we see in these figures is a remarkable match between the phase and period of Jupiter-Saturn conjunctions and oppositions and the bi-decade cycle in the winter NPI index. This match is best between the years of 1947 and 1991.
It is also apparent that groups of three bi-decadal cycle in the Winter NPI index are nested in phase inside a penta-decadal cycle of roughly 55 years in length. You can see one complete penta-decadal cycle starting with a Jupiter-Saturn opposition in 1922 and ending three Jupiter-Saturn oppositions later in 1981.
Amazingly, the Sun's motion about the Barycentre (i.e. center-of-mass) of the Solar System undergoes one orbital loop from one Jupiter-Saturn conjunction (or opposition) to the next every 19.86 years. Each orbital loop of the Sun about the Barycentre rotates by roughly 120 degrees with respect to the stars, compared to its previous orbital loop. Hence, it takes three orbital loops (i.e 3 x 19.86 = 59.6 years) for the Sun's Barycentric motion to rotate once with respect to the stars.
This means that solar inertial motion (SIM) about the Barycentre mimics the three bi-decadal cycles nested [in-phase] inside a longer penta-decadal cycle. The synchronization between these two phenomenon is quite remarkable and suggests that there may be an underlying physical link.