International Journal of Current Research and Review
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IJCRR - 4(4), February, 2012

Pages: 06-09

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DETRENDED FLUCTUATION ANALYSIS OF CYCLONIC DISTURBANCE OVER THE NORTH INDIAN
OCEAN

Author: R.Samuel Selvaraj, R.Uma

Category: General Sciences

Abstract:Tropical cyclones are among the most destructive natural disasters of the world. The long coastline of peninsular India is frequently affected by cyclonic storms originating in the Bay of Bengal and Arabian Sea resulting in loss of life and property in the affected region. Hence there is a need for prediction and forecasting methods for minimizing the disastrous effects of tropical cyclones. The time series data of the annual cyclonic disturbance records (for the time period 1901 - 2004) over the North Indian Ocean (comprising of Bay of Bengal and Arabian Sea) has been analyzed. It is found that the behavior of the cyclonic intensity exhibits perfect power law behavior. Local changes of scaling exponents are examined. It is found that the calculated scaling exponent is larger than 0.5 indicating that cyclonic disturbance data have long-range correlations.

Keywords: Detrended Fluctuation Analysis (DFA), north Indian Ocean, cyclone, power law, long-term correlation, etc.

Full Text:

INTRODUCTION
Tropical cyclones are primarily products of the long-term characteristics of the tropical general circulation of the atmosphere. Their annual frequency of occurrence over the globe is quite steady. About 80 tropical cyclones with wind speeds equal to or greater than 34 knots form in the world‘s waters every year (McBridge, J. L., 1995). Of these about 6.5% develop in the Bay of Bengal and Arabian Sea (Neumann, C. J., 1993).Tropical cyclones over the Bay of Bengal are generally higher both in terms of their frequency and intensity. The share of Bay of Bengal comes out to be 5.5%. The principal damaging forces associated with tropical cyclone that has impacts on people and environment are the strong and violent winds, high seas and storm surge and flooding caused by heavy rain. Out of these three destructive elements a sudden rise in sea level which is termed as ?Storm surge‘ is responsible for nearly 90% of loss of life and property in the case of tropical cyclonic disasters. The periodicity of the tropical cyclones from 1890 to 1969 was studied by Raghavendra (1973) and found that the annual frequency to have a trend of 30 to 45 years. Rao and Jayaraman (1958) have analyzed the frequency data of tropical cyclones for the period of 1890-1955 employing statistical methods but found to have no trend. Prediction of the frequency of Tropical cyclones over the Oceanic region are very important as they would be helpful for both short term and long term planners towards disaster mitigation. Orun, M. and Koçak, K. (2009) used Detrended fluctuation analysis (DFA) to calculate scaling exponent of daily mean temperature, daily maximum temperature, daily minimum temperature and daily temperature differences for 52 stations in Turkey. The Detrended Fluctuation Analysis (DFA) technique was introduced to investigate long-range power-law correlations. J. Alvarez-Ramirez et al. (2008) proposed an extension of the R/S method to estimate the Hurst exponent of high dimensional fractals and also commented that due to the simplicity in implementation, the DFA is now becoming a widely used method in physics and engineering. A. Sarkar and P. Barat (2005) investigated long time series of the rainfall records for All India and different regions of India and succeeded in finding evidence for power law distributions of the rainfall quantity. Peters et. al. (2002) has presented a power law behavior in the distribution of rainfall over at least four decades. In this paper, an attempt is being made to calculate the scaling exponent using the Detrended Fluctuation Analysis (DFA) for the cyclonic disturbances over the north Indian Ocean.

MATERIAL AND METHODS The Detrended Fluctuation Analysis (DFA) technique is used to calculate the scaling exponent for the cyclonic disturbance includes depression, cyclonic storm and severe cyclonic storm over the north Indian Ocean for the period from 1901 to 2004. The first step in the Detrended Fluctuation Analysis (DFA) procedure is to calculate the time series x(i) of length N.

k Y (k) = Σ [x(i) - ]
           i=1

Here x indicates the mean value of x(i) ‘s. Next, the profile Y(k) is divided into N [N / n] n which is the non overlapping segments of equal length n . In the next step, the local trend for each segment is calculated by a least square fit of the data. The ycoordinate of the fitted line is denoted by Y (k)n. Then the Detrended time series for the segment duration ?n‘ as Ys (k) =Y(k) -Yn (k). The root-mean square fluctuation of the original time series and the Detrended time series is calculated by

N F(n) = {[(1/N)∑(Y(k)-Yn(k))2 } 1/2
                      k=1

By repeating this calculation to all segment sizes, a relationship between F(n) and n is obtained. Finally the double logarithmic plot of F(n) versus n is used to calculate the slope, which gives the scaling exponent β. The value of the scaling component β is interpreted as follows.

(i) if 0 < β < 0.5 then the time series is long-range anti-correlated
(ii) if β > 0.5 then the time series is longrange correlated
(iii) β = 0.5 corresponds to Gaussian white noise
(iv) while β = 1 indicates the 1/ f noise, typical of systems in a Self Organized Criticality (SOC).

Cyclonic disturbance data is obtained from IMD Cyclone E- Atlas. We have considered the annual frequency of cyclonic disturbance over the north Indian Ocean for a period of 104 years (1901- 2004). Table I illustrates the log value of the segment duration ?n‘ and log value of the root-mean square fluctuation of the original time series and the Detrended time series F(n) for the cyclonic storms (including depression, cyclonic storms and severe cyclonic storms) over the north Indian Ocean from 1901-2004. Fig 1 illustrates the number of annual frequency of cyclonic storms (including depressions, cyclonic storms and severe cyclonic storms) over the North Indian Ocean for the period 1901-2004. Fig 2 illustrates the Detrended fluctuation analysis of the cyclonic disturbance data over the north Indian Ocean.

RESULTS AND DISCUSSIONS
The goal of Detrended Fluctuation Analysis (DFA) is to assess the long range correlation of the data involved. The long term time series of the cyclonic disturbance over the north Indian Ocean has been investigated. The value of the scaling exponent β is found to be greater than 0.5. The time series is long-range correlated (Orun, M. and Koçak, K. (2009)). We have found an evidence for power law distributions of the cyclonic behavior over the north Indian Ocean. This supports the view that atmospheric dynamics is governed by self-organized criticality.

CONCLUSION
The scaling exponent for the cyclonic disturbances over the north Indian Ocean for the period from 1901 to 2004 is calculated using the Detrended Fluctuation Analysis (DFA) technique. The value of the scaling exponent β is found to be greater than 0.5. The time series is longrange correlated.

ACKNOWLEDMENTS
Authors acknowledge the immense help received from the scholars whose articles are cited and included in references of this manuscript. The authors are also grateful to authors/editors/publishers of those articles, journals and books from where the literature of this article has been reviewed and discussed

References:

1. Jose Alvarez-Ramirez, Juan C. Echeverria and Eduardo Rodriguez, 2008. Performance of a highdimensional R/S method for Hurst exponent estimation, Physica A 387, 6452–6462.

2. McBride, J. L., 1995. Tropical cyclones in a warmer world, Report, WMO/TD-No. 693, No. TCP-38, WMO, Geneva, pp. 63–105.

3. Neumann, C. J., 1993. Global Overview - Chapter 1, Global Guide to Tropical Cyclone Forecasting, WMO / TC-No. 560, Report No. TCP-31, World Meteorological Organization; Geneva, Switzerland.

4. Orun, M. and Koçak, K. (2009), Applicat?on of Detrended fluctuation analysis to temperature data from Turkey, International Journal of Climatology, 29, 2130–2136.

5. O. Peters, C. Hertlien, and K. Christensen, (2002). A complexity view of Rainfall, Phys. Rev. Lett. 88, 018701, 1-4.

6. Raghavendra, V. K., 1973. A statistical analysis of the number of tropical storms and depressions in the Bay of Bengal during 1890-1969, Ind. J. of Met & Geophys., 24, 125-130.

7. Rao, K. N. and Jayaraman, S., 1958. A statistical study of frequency of depressions/cyclone in the Bay of Bengal, Ind. J. of Geophys., 9, 233- 250.

8. A. Sarkar and P. Barat, 2005. Analysis of Rainfall records in India: Self Organized Criticality and Scaling, cdsweb.cern.ch/record/918484/files/05 12197.pdf


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