Volterra Algorithm for Modelling Sea Surface Current Circulation from Satellite Altimetry Data

This work introduces a new approach for modelling sea surface current from AVISO/Altimeter satellite data. This is based on utilizing of the Volterra series expansion in order to transform the time series of Merged Sea Level Anomaly satellite altimetry data into a real ocean surface current. The basic equation of hydrodynamic has been solved by first order Volterra model. Then, the Volterra kernel inversion used to obtain the sea surface current velocity. The purpose of Volterra model was to reduce the impact of Coriolis parameter especially in such low latitude zone as Malaysia. The discretization of inverse Volterra algorithm done by Lax-Wendrof scheme. Valeport electromagnetic current meter was used to acquire in situ sea surface current measurements along the east coast Of Malaysia. The result shows that the integration between Volterra model and Lax-Wendroff scheme is good tool to model sea surface current pattern from AVISO/Altimeter satellite data. 1.INTRODUCTION The study of the dynamics of ocean surface is always a challenging and intriguing process. In fact, features of ocean surface are complex. It is not to easy to understand ocean surface dynamics because there are many factors controlling them (Maged 1994 and 2000). Most scientists identify the forces which induce sea surface dynamics to be the wind, tide, Corolois force and other factors such as density differences between water masses and usually cause vertical movements (Maged 1994). However, scientists cannot study these factors separately as this will give them imperfect scenario of coastal water hydrodynamics. Traditional methods which are involving in situ measurements by using sophisticated equipments are not able to study coastal water hydrodynamics within large scale size of the South China Sea for instance. Remote sensing technology which is based on altimeter sensors is able to provide excellent information of coastal hydrodynamics (Mohd et al.2005) At present, few studies have been utilized different altimeter sensors for the sea surface investigations in the South China Sea (Mohd et al. 2005). Hu et al. (2001) investigated the sea surface height with a period of 3-6 months using six years TOPEX/POSEIDON altimeter data. They reported that the sea surface height variations are associated strongly with current and eddies features. Imawaki et al. (2003) introduces a new technique for acquiring high-resolution mean surface velocity by combined use of TOPEX/POSEIDON and ERS-1/2 altimeter data and drifter data obtained from 1992 through 2001 to detect the undulation of mean-surface dynamic topography down to the oceanic current. In fact, the ocean current associated with geoid by the amount of sea surface dynamic topography is different compared to the mean –surface height acquired from satellite altimeter. In order to improve the hydrodynamic equation solutions of the mean sea-surface to invert accurate pattern of sea surface current we need to obtain altimeter data that is both more accurate and more widely distributed in time. Furthermore, we need to improve our knowledge of the long wavelength geoid so that its errors are substantially smaller than the corresponding values of the sea surface topography. The main contributions of this work is to design scheme to reduce the impact of Coriolis parameter in continuity equation. In fact low latitude zone such as Malaysia is dominated by weak Coriolis parameter. In this context, the geostrophic current might be produced must be weak. According to this prospective, this study attempts to implement the Volterra model and Lax-Wendroff scheme to suppress the numerical solution of geostrophic continuity equation. 2-DATA AND STUDY AREA The study area is located the South China Sea and SCS is an equatorial, semi-enclosed sea with a complex topography that includes large shallow regions. The SCS is located between the Asian continent, Borneo, the Philippines, and Taiwan (Figure 1 ). The northeastern part adjoins a deep sea basin, while the southern part is a shelf sea with depths less than 200 m. The SCS has two features that have very important and interesting effects on the general circulation: (1) the Coriolis force decreases to zero at the equator where both nonlinear and frictional forces become very important; and (2) the monsoon regime exerts a strong effect on the SCS circulation. Neither of the above phenomena are studied in coastal regions of the world ocean at the present time (Wrytki 1962). Figure 1. Location of the South China Sea. The AVISO/Altimeter data of Merged Sea Level Anomaly (MSLA) were acquired on October 2003 and March 2005, respectively. The study area was between 102° E to 114° E and 1 ° N to 10° N. In fact the in situ sea surface current measurements are collected between 102° 5’E to 105° 10’E and 2° 5’N to 6° 10’N (Figure 2). The in situ current measurements were collected by using Valeport electro-magnetic current meter which was lowered down from the sea surface to water depth of 50 m. The in situ sea surface current measurement were conducted by the research vessel UNIPERTAMA VII. Figure 2. Location of In Situ Measurements along east coast of Malaysia. 3MODEL DESCRIBITION 3.1 Volterra Model The Volterra model can be used to express the geostrophic current velocity obtained from AVISO altimeter data as a series of nonlinear filters on the ocean surface current. This means that the Volterra model can be used to study the geostrophic current energy variation as a function of parameters such as the current direction, or the current waveform. A generalized, nonparametric framework to describe the input–output x and y geostrophic current components relation of a time-invariant nonlinear system. In discrete form, the Volterra series for input, X(n), and output, Y(n) as given by Inglada and Garello (1999) can be expressed as: ) ( .... )......... ( ) ( ) ,........, , ( .... .......... .......... ) ( ) ( ) ( ) , , ( ) ( ) ( ) , ( ) ( ) ( ) ( 2 1 2 1 1 1 1 3 2 1 3 2 1 1 1 1 3 2 1 2 1 1 1 2 1 1 1 1 0