Low Frequency Modulation of

Annual and Sub-annual Cycle

Precipitation and Temperature in the

Western United States

Balaji Rajagopalan and Subhrendu Gangopadhyay

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

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

NM

CA

NV

ID

MT

WY

UT

AZ

CO

OR

WA

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.

MTM Spectrum – Joint Precip. and Temp.

• Low Frequency

-0.0 to 0.5 cycles/yr

• High Frequency

-0.5 to 6.0 cycles/yr

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

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

Spatial Reconstruction at Significant Frequencies – LOW Frequencies, P and T

Spatial Reconstruction at Significant Frequencies – HIGH Frequencies, P and T

Spatial Reconstruction of ANNUAL Cycle

Using a 20-year Moving Window – Precipitation

Spatial Reconstruction of ANNUAL Cycle

Using a 20-year Moving Window – Temperature

Phase Shift of ANNUAL Cycle P and T

1950-1975; 1975-2000

Phase Shift of SUB-ANNUAL Cycle P and T

1950-1975; 1975-2000

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.

Diagnosis of Space-time Reconstructions andPhase 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.

Diagnosis of Space-time Reconstructions andPhase 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.

Spectral Coherence

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

Next plots :-

Spectral Coherence – Annual Cycle

Spectral Coherence – Annual + Sub-annual

Low Frequency Modulation of

Annual and Sub-annual Cycle

Precipitation and Temperature in the

Western United States

Balaji Rajagopalan and Subhrendu Gangopadhyay