Low Frequency Modulation of

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Low Frequency Modulation of Annual and
Sub-annual Cycle Precipitation and Temperature in
the Western United States
Balaji Rajagopalan and Subhrendu Gangopadhyay
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Objective
How does the low frequency components of the
climate system (e.g., ENSO, PDO, etc.) modulate
high frequency components of the climate system,
namely, regional annual and sub-annual cycles of
precipitation and temperature. Study Area
Western United States
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Study Area and Data

• 11 states (AZ, CA, CO, ID, MT, NV, NM , OR, UT,
  WA, WY)
• total, 84 climate divisions
• 106 years (1895-2000) of monthly precipitation
  and
• temperature data for each climate division

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Methodology

• Uses the technique MTM-SVD (multi-taper method
  using singular-
• value decomposition).
• Identify significant frequencies from the MTM
  spectrum.
• Do space-time reconstruction at these
  significant frequencies.
• Use the space-time reconstructions to analyze
  temporal evolution
• of these significant frequencies, and phase
  shifts.
• Finally, use spectral-coherence to relate low
  frequency components
• with precipitation and temperature at the
  annual and sub-annual
• frequencies.

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MTM Spectrum Joint Precip. and Temp.

• Low Frequency
• 0.0 to 0.5 cycles/yr
• High Frequency
• 0.5 to 6.0 cycles/yr

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MTM Spectrum Only Precipitation

• Significant frequencies (cy/yr) at 95 confidence
  level
• 0.0674
• 0.1875 ( 5 yr cycle)
• 0.3721 ( 3 yr cycle)
• 1.0000 (annual cycle)
• 2.0000 (sub-annual cycle)
• other harmonics

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Temporal Evolution of Frequencies Joint
P-T Moving Window MTM-SVD at 90
Observations- - ENSO and decadal oscillations
are patchy - enhanced ENSO post 1980 -
annual and sub-annual cycles significant all
throughout
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Spatial Reconstruction at Significant Frequencies
LOW Frequencies, P and T
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Spatial Reconstruction at Significant Frequencies
HIGH Frequencies, P and T
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Spatial Reconstruction of ANNUAL Cycle Using a
20-year Moving Window Precipitation
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Spatial Reconstruction of ANNUAL Cycle Using a
20-year Moving Window Temperature
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Phase Shift of ANNUAL Cycle P and T 1950-1975
1975-2000
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Phase Shift of SUB-ANNUAL Cycle P and
T 1950-1975 1975-2000
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Diagnosis of Space-time Reconstructions and Phase
Shifts

• For precipitation, Pacific Northwest and
  Arizona are out of phase
• ( we know that these two regions have the
  opposing ENSO signal
• for winter precipitation), the shifts are of
  the order of /- 50 days
• (positive is early and negative is late).
• With temperature, all the shifts in temperature
  are positive and in
• the mid-latitudes this implies for example an
  early Spring. Such
• shift in temperature for example in the
  Pacific Northwest we can
• expect that winter precipitation comes more
  as rain-on-snow type
• events.

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Diagnosis of Space-time Reconstructions and Phase
Shifts

• Also in case of precipitation, there are very
  little shifts in the rest
• of the study region.
• Wherever the annual cycle is weak, primarily in
  the desert regions
• (in particular, California-Nevada border,
  southern Utah, western
• Montana) there seems to be a shift in the
  annual cycle close to 100
• days. This apparently is a very large shift
  but to some extent makes
• sense because these are desert regions a
  little precipitation goes a
• long way to show significant shifts.

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Diagnosis of Space-time Reconstructions and Phase
Shifts

• With the 6-month cycle, we observe that for
  precipitation,
• the shifts are nearly halved and for
  temperature the shifts
• are nearly double that of the annual cycle.

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Spectral Coherence
Next plots -
Spectral coherence between January through April
SST (sea surface temperature) first principal
components (refereed in the figures as PC1B1
PC1B2 and PC1B3 are the extra-tropic SST PCs) and
spatially averaged MTM projections
time-reconstructed for both the annual and
sub-annual cycles
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Spectral Coherence Annual Cycle
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Spectral Coherence Annual Sub-annual
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Low Frequency Modulation of Annual and
Sub-annual Cycle Precipitation and Temperature in
the Western United States
Balaji Rajagopalan and Subhrendu Gangopadhyay