VOL. 2, NO. 2, March 2012
ISSN 2225-7217
ARPN Journal of Science and Technology
©2011-2012. All rights reserved.
http://www.ejournalofscience.org
Impact of tsunami on Tamil Nadu Monsoon Rainfall
1
1
G. Helen Ruth Joice and 2 K. Thamilharazan
Department of Physics, Thiru Kollanjiappar Arts and Science College Viruthachalam
2
Department of Physics, Sir Theagaraya College, Chennai
E-Mail: [email protected]
ABSTRACT
In 2004 Tamil Nadu was severely affected by Tsunami. After the incident Tamil Nadu has been experiencing erratic
rainfall. The effect of the Tsunami on the atmospheric circulation related to the monsoon rainfall is investigated in this
paper. The qualitative analysis is done by Poincare map and the quantitative analysis is done by calculating the Lyapunov
exponent. The Poincare map was analysed and the ratio SD1/SD2 for Tamil Nadu. The Poincare value of the southeast
monsoon rainfall before and after Tsunami was found to be 0.307 and 0.418. The Lyapunov exponent was calculated to be
0.285 and 0.799 respectively. North East monsoon rainfall was found to be 0.679 before Tsunami and 0.834 after Tsunami.
The Lyapunov Exponent was found to be 0.5604 before Tsunami and 0.8606 after Tsunami. The values of Poincare and
Lyapunov suggest that the Tamil Nadu North East monsoon rainfall has certainly been disturbed for the past few years.
Keywords: rainfall, monsoon, lyapunov exponent, poincare map.
1. INTRODUCTION
The oceans play a major part in creating conditions for life
on land. Together with the atmosphere, oceans regulate
global temperatures, shape weather and climate patterns.
The ocean and the atmosphere are intimately connected.
Changes in the pattern of sea surface temperature are
linked with changes in the atmospheric circulation. They
affect the incidence of extreme weather and are precursors
of climatic variability on inter-annual and longer
timescales. The enormous thermal inertia of the ocean
implies that any systematic change of climate will be of
long duration.
The tsunami disaster of 26 December 2004 demonstrated
the awesome destructive power of the ocean. More
gradually, the oceans exert a profound impact on the
global biosphere through their influence on weather and
climate.
Rainfall pattern of Tamil Nadu
Tamil Nadu has a long coastline of over 1000 km and the
climate is basically tropical thus it experiences very
peculiar system of the monsoon rainfall. Both the South
West and North East monsoon gives rainfall to Tamil
Nadu. Tamil Nadu receives an annual average rainfall of
977 mm. approximately 33% of this is from the Southwest
Monsoon and 48% from the Northeast Monsoon. Though
the State receives its rainfall from both Southwest and
Northeast Monsoons, the Northeast Monsoon provides the
major part of the precipitation to the State. The Climatic
season for the State of Tamil Nadu can be broadly
classified into i) Winter Season (January-February), ii)
Summer Season (March-May), iii) Southwest Monsoon
(June-September), iv) Northeast Monsoon (OctoberDecember). The Table-1 gives the average annual rainfall
distribution of Tamil Nadu [1].
Table-1. The Annual rainfall pattern of Tamil Nadu.
Season
Southwest
Monsoon
Northeast Monsoon
Average Rainfall
Months
Normal Rainfall
in mm
Percentage of
annual Rainfall
June-September
October - December
-
322.00
470.00
977.00
32.96%
48.10%
100.00%
The present paper is aimed at investigating the changes in
the rainfall pattern of Tamil Nadu after the December 26th
2004 Tsunami. We have incorporated a qualitative
analysis and a quantitative analysis to method to study the
Rainfall pattern. Poincare method is followed for
qualitative analysis. The Lyapunov Exponent calculation
is done for quantitative analysis.
2. DATA
The Tamil Nadu rainfall data form 1994-2010 was
obtained from Regional Meteorological centre, Chennai.
The rainfall pattern is analysed for the different seasons of
Tamil Nadu as mentioned in Table-1. All the data are split
into two parts. The rainfall data before Tsunami
occurrence and the rainfall data after the Tsunami
occurrence.
3. METHODOLOGY
The rainfall data of Tamil Nadu is subjected to both
qualitative and quantitative analysis.
POINCARE MAP-QUALITATIVE ANALYSIS
One commonly used nonlinear method that is simple to
interpret is the so-called Poincare [2] plot. It is a graphical
representation of the correlation between successive
rainfall data i.e., plot of X i+1 as a function of Xi. The
standard deviation of the point’s perpendicular to the lineof identity denoted by SD1 describes short-term variability
which is mainly caused by rainfall data. The standard
deviation along the line-of-identity denoted by SD2, on the
other hand, describes long-term variability. The standard
Poincar´e plot can be considered to be of the first order
[3].
96
VOL. 2, NO. 2, March 2012
ARPN Journal of Science and Technology
ISSN 2225-7217
©2011-2012. All rights reserved.
http://www.ejournalofscience.org
LYAPUNOV EXPONENT-QUANTITATIVE
ANALYSIS
The Lyapunov exponent gives the quantitative value for a
non linear dynamical system. A positive largest Lyapunov
exponent indicates chaos. It is thus useful to study the
mean exponential rate of divergence of two initially close
orbits using the formula [4, 5].
λ < 0 Negative Lyapunov exponents are characteristic of
dissipative or non-conservative system
λ = 0 A Lyapunov exponent of zero indicates that the
system is in steady state mode or conservative.
λ > 0 A large positive Lyapunov exponent indicates the
system is unstable and chaotic.
The values obtained from the qualitative and quantitative
analysis of the Tamil Nadu Rainfall pattern are tabulated
in Table-2.
This number, called the Lyapunov exponent "λ", is useful
for distinguishing among the various types of systems. It
works for discrete as well as continuous systems
Table-2. Qualitative and Quantitative Values of Tamil Nadu rainfall.
Season
Southwest Monsoon
Northeast Monsoon
Average
Rainfall Before Tsunami
Rainfall After Tsunami
Poincare
0.307
0.679
0.555
Poincare
0.418
0.834
0.808
4. RESULT
The Poincare map for Southwest and Northeast monsoon
data for a period of 1993 - 2003 was and the Standard
deviation data SD1 and SD2 were calculated and the ration
of SD1/SD2 was found to be 0.432 and 0.679 respectively.
The value of SD1/SD2 ratio for a period of 2004-2010 was
calculated to be 0.782 and 0.834 respectively. When the
two rations are compared the ratio, the southwest and
northeast monsoon rainfall of Tamil Nadu after tsunami
are showing a higher ratio values indicating that the
rainfall pattern is disturbed. The qualitative value from
Poincare map is then further confirmed by calculating the
Lyapunov exponent for the southwest and northeast
monsoon rainfall. The Lyapunov exponent value for the
southwest and northeast monsoon before Tsunami is
0.307and 0.418 respectively. After Tsunami the Lyapunov
Exponent was found to be 0.285 and 0.799. Thus after
tsunami the southwest rainfall and the northeast rainfall of
Tamil Nadu are showing a chaotic behaviour.
5. CONCLUSIONS
The occurrence of Tsunami in Tamil Nadu in the year
2004 has disturbed the oceanic atmospheric circulation
conditions which in turn has caused changes in the
Rainfall pattern over the state. The qualitative and the
quantitative analysis of rainfall also emphasis this
condition
Lyapunov
0.285
0.560
0.5367
Lyapunov
0.799
0.8606
0.826
REFERENCES
[1] Tamil Nadu Annual Report on Natural Calamities
2005-06.
Revenue
Administration,
Disaster
Management and Mitigation Department Chennai 600
005.
[2] A practical method for calculating largest Lyapunov
exponents from small data sets Michael T. Rosenstein,
James J. Collins, and Carlo J. De Luca, Neuro
Muscular Research Center and Department of
Biomedical Engineering, Boston University.
[3] Numerical Calculation of Lyapunov Exponents,
Marco Sandri, University of Verona, Italy. The
Mathematical Journal. 6(3): 78-84.
[4] Computing Accurate Poincare maps,
Tucker, Physica D 171(2002)127-137.
Warwick
[5] S. Lynch and Z. G. Bandar, Bistable neuromodules,
Nonlinear Anal. Theory Methods Appl. 63(2005),
669-677.
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