Analysis in Terms of EOF's
EOF analysis has been applied to the atmospheric data for long time.
Here, we make reference to "Physics of Climate" (Peixoto and Oort, 1992)
for EOF analysis introduction:
"The empirical orthogonal function(EOF) analysis, sometimes referred to
as eigenvector or principal components analysis, provides a convenient method
for studing the spatial and temporal variability of long time series
of data over large areas.This method splits the temporal variance of the data
into orthogonal spatiaL patterns called empirical eigenvectors. "
"This approach enables one to identify a set of orthogonal spatial modes,
such that, when ordered, each successive eigenvector explains the maximum
amount possible of the remaining variance in the data.Each eigenvector
pattern is associated with a series of time coefficients that described the
time evolution ofthe particular spatial mode. The eigen vector patterns that
account for a learge fraction of the variance are, in general, considered to be
physically meaningful and connected with important centers of action." "The
principal advantages of the eigenfunctions are that they provide the most
efficient way of compressing geophysical data in both space and time and they
may be regarded as uncorrelated (independent) modes of variability of the
Peixoto, J.P., and A.H. Oort, 1992: Physics of Climate. American Institute
of Physics New York.
EOF Analysis of TRMM Precipitation Data
TRMM TMI data--We use the monthly mean precipitation rate derived from
TRMM3B31 algorithm.Data are of 5x5 degree resolution.(more description
about the data needed).
TRMM 3A25 data-- The TRMM Precipitation Radar (PR), the first of its kind
in space, is an electronically scanning radar, operating at 13.8 GHz that
measures the 3-D rainfall distribution over both land and ocean, and defines
the layer depth of the precipitation.The primary objective of algorithm 3A25
is to compute the monthly rainfall
vertical structure and various statistics of rainfall and related
variables measured by PR.In the following discussion we use monthly
mean surface rain rate of TRMM 3A25 with 5x5 degree resolution.For the
details of the TRMM 3A25 algorithm, please link here.
Reference:Meneghini, R., J.A., Jones, T. Iguchi, K. Okamoto, and
J. Kwiatkowski,2001: Statistical Methods of Estimating Average Rainfall
over Large Space-Time scales Using Data from the TRMM Precipitation Radar,
J. Applied Meteorology .
The first four EOFs (figure below) and their respective time series (figure
following) were derived from TRMM 3B31(TMI) precipitation data. The data used are the subset overthe region of
The percentage of explained totalvariance is labeled on the top of each
panel. As described in the method description, you need to know the physics of
the field to interpret the patterns.The number one EOF, which explains 23.5%
of the total variances, depicts a dipole pattern extending zonally and
symmetrically with respect to the equator. It mainly reflects the annual cycle
of surface solar radiationenergy.The values shows the correlation field
between precipitation value (that has been normalized in the process) andthe
first EOF.The time series of the first EOF (the top panel of thenext
Figure) shows a regular annual cycle.Combining the patterns with the time
series, the precipitation annual variation is clear:over the Northern
Hemisphere, precipitation amount is high during the summer and is low during
the winter; the precipitation over the Southern Hemisphere is of the opposite
phase, high during the Northern Hemisphere winter, and low during the Northern
The second EOF shows a broad tongue extending from the equatorial eastern
Pacific to the central Pacific.It is asymmetric with respect to the equator,
and is accompanied by two centers with the opposite site directly over the two
sides.The centers over the Australia and the maritime islands are of opposite
sign too.The time seriesshows this pattern is of annual cycles too, but
there is about 3 month phase lag between this annual cycle and the first one.
This mode denotes the annual evolution of warm SST tongue which develops on
about late spring and diminishes on later summer.
The physical explanation
of the third EOF is not obvious, though the time series shows a clear annual
cycle.The fourth EOF's time series shows a semi-annual cycle, in general,
indicating the monsoon precipitation activity. Since this subset data does not
includethe Southern America and the whole India the monsoon region did not
come outclearly in the EOF pattern.
The ENSO signature is not clearly isolated out.However the abnormal
amplitudes of the four time series during the early 1998 probably reflect the
ENSO events.In general, TRMM data are too short for climatological signal
It is found that there are noticeable differences in the overall averaged
precipitation estimation between TMI and PR.By using EOF to the difference
field of TMI and PR, we decompose the difference into main spatial patterns
which vary with time.Before the EOF computation, the seasonal mean comparison
may provide the baseline for the later discussion on the EOF results.
- 1. Both TMI and PR precipitation estimation has similar spatial patterns.
PR precipitation (TRMM 3A25) estimate is systematically lower than that of
TMI over the high precipitation region, but higher than TMI data over
the low precipitation region.
- 2. For most of the areas, the difference is not dramatic.The differences
are big over the heavy precipitation region, small over the light precipitation
- 1. Both TMI and PR precipitation estimation has similar spatial patterns
in terms of the first four prominent modes) and similar time scales.
- 2. PR precipitation estimation is consistently lower than TMI over the
high precipitation regions, and higher over the dry region.
- 3. The time series of the second EOF of the difference field shows
clearly an annual cycle as that of the TRMM3B31 reflecting the annual cycle
of warm SST tongue.But the spatial pattern shows the difference occuring
mainly at the north side of the tongue (see the second EOF of TRMM 3B31) and
the southeastern side of the tongue.
- 4. The difference field show large scale coherence in the first three
EOF modes.The first three EOFs can explain
51% of the total variance,probably indicating the coherent spectral feature
of the difference field.