Dipole Mode Index DMI Wavelet Transform

12 th Biennial Conference of Pan Ocean Remote Sensing Conference PORSEC 2014 04 – 07 November 2014, Bali-Indonesia 584 global climate. This is due to the complex sea bottom topography of the Indonesian seas, and also connecting the Pacific and the Indian Ocean Qu et al., 2005.From the numerical model and the field observation shows that a little change of SST in Indonesia could give a high change on the rainfall in the Indo-pacific Miller et al., 1992; McBride et al., 2003; Ashok et al., 2001; Neale, Slingo, 2003. The SST variability in Indonesia seas is also important for the ecology point of view, since the Indonesia Sea has a rich of the ocean biodiversity. Therefore the investigation of SST variability and its characteristics become a substantial work. In this study, we used the satellite data to make an investigation of SST variability and its characteristics in the southern of Java and the lesser Sunda. Remote sensing technology had been widely used to observe the ocean resources. The Moderate Resolution Imaging Spectroradiometer MODIS is one of the satellite imaging that can be used easily to make a periodic SST observation. Furthermore, the temporal analysis of SST data is done using wavelet transform, and hence the period and the time of the phenomenon can be analyzed.

1.1. Dipole Mode Index DMI

IODM signature are originally occurs in the Indian Ocean. It could be due to an increasing of SST in the western Indian Ocean 50 W - 70 W and 10 S - 10 N, and simultaneously decreasing of the SST in the eastern part of Indian Ocean 90 W – 110 W and 10 S - Equator Saji et al., 1999. The IODM is recognized by determining the Dipole Mode Index DMI, which is the difference of SST anomaly between the western part and eastern part of Indian Ocean Saji et al., 1999. Saji, et al. 1999 mentioned that the positive DMI above 0.7 is the indication of the positive IODM phenomenon, whereas the negative of the DMI below -0.7 is indicating the negative IODM phenomenon. The more positive the IODM, the higher SST in the western Indian Ocean will be. This makes the convection increase around the western part of the Indian Ocean. However, the eastern part of Indian Ocean will experience drought including some areas in Indonesia. The opposite phenomenon will occur during the negative IODM.

1.2. Wavelet Transform

The wavelet transform is useful to analyze time series data that contain non-stationary power at many different frequencies Foufoula-Georgiou and Kumar, 1995; Daubechies, 1990. Torrence, and Compo 1997 proposed a Morlet Wavelet that used as the mother wavelet Equation 1. Ψ η = π e ω η e η 1 Where is the non-dimensional frequency and was taken to be 6 in this study to satisfy the admissibility condition Farge, 1992. This is known as the scaled wavelet, which is defined by: Ψ ′ = Ψ ′ 2 Where s is the dilation parameter used to change the scale, and n is the translational parameters used as time shifting. The s- 12 is a normalization factor to maintain the total energy of the scaled wavelet constant. The continuous wavelet transform CWT of a discrete sequence x n is a convolution of x n with the scaled wavelet functions and translated from Ψ η Torrence and Compo, 1997: = ′ Ψ ′ 1 ′ = 0 3 It is possible to calculate the wavelet transform using equation 3, but it would be simpler and easier if it done in Fourier space. Hence, by using the convolution theorem, the wavelet transform is the inverse of Fourier transform of the product. 12 th Biennial Conference of Pan Ocean Remote Sensing Conference PORSEC 2014 04 – 07 November 2014, Bali-Indonesia 585 = Ψ 1 = 0 4 where the angular frequence is defined by: = 5 Hence, the value of power spectum wavelet | | can be found from the wavelet equation aboved.

2. Data and Method