The modulated annual cycle: An alternative reference frame for climate anomalies

  • Wu Z
  • Schneider E
  • Kirtman B
 et al. 
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In climate science, an anomaly is the deviation of a quantity from its
annual cycle. There are many ways to define annual cycle. Traditionally,
this annual cycle is taken to be an exact repeat of itself year after
year. This stationary annual cycle may not reflect well the intrinsic
nonlinearity of the climate system, especially under external forcing.
In this paper, we re-examine the reference frame for anomalies by
re-examining the annual cycle. We propose an alternative reference frame
for climate anomalies, the modulated annual cycle (MAC) that allows the
annual cycle to change from year to year, for defining anomalies. In
order for this alternative reference frame to be useful, we need to be
able to define the instantaneous annual cycle: we therefore also
introduce a new method to extract the MAC from climatic data. In the
presence of a MAC, modulated in both amplitude and frequency, we can
then define an alternative version of an anomaly, this time with respect
to the instantaneous MAC rather than a permanent and unchanging AC.
Based on this alternative definition of anomalies, we re-examine some
familiar physical processes: in particular SST re-emergence and ENSO
phase locking to the annual cycle. We find that the re-emergence
mechanism may be alternatively interpreted as an explanation of the
change of the annual cycle instead of an explanation of the interannual
to interdecadal persistence of SST anomalies. We also find that the ENSO
phase locking can largely be attributed to the residual annual cycle
(the difference of the MAC and the corresponding traditional annual
cycle) contained in the traditional anomaly, and, therefore, can be
alternatively interpreted as a part of the annual cycle phase locked to
the annual cycle itself. In addition to the examples of reinterpretation
of physics of well known climate phenomena, we also present an example
of the implications of using a MAC against which to define anomalies. We
show that using MAC as a reference framework for anomaly can bypass the
difficulty brought by concepts such as ``decadal variability of summer
(or winter) climate{''} for understanding the low-frequency variability
of the climate system. The concept of an amplitude and frequency
modulated annual cycle, a method to extract it, and its implications for
the interpretation of physical processes, all may contribute potentially
to a more consistent and fruitful way of examining past and future
climate variability and change.

Author-supplied keywords

  • Alternative reference frame
  • Climate anomaly
  • Decadal climate variability of winter (summer) temperature
  • ENSO phase locking to annual cycle
  • Empirical mode decomposition
  • Ensemble empirical mode decomposition
  • Extrinsic annual cycle
  • Intrinsic annual cycle
  • Modulated annual cycle
  • Nonlinear non-stationary time series
  • Reemergence
  • Traditional annual cycle

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