Characteristic of Tidal Currents in the Lombok Strait Using 3D FVCOM Numerical Model

The Lombok Strait located between Bali Island and Lombok Island, Indonesia. Lombok Strait is complex area because influence by Indonesian Throughflow and influence by Tidal Current. For this case want to research about tidal current circulation and simulated using a three-dimensional baroclinic hydrodynamic numerical modelling method by Finite Volume Coastal Ocean Model (FVCOM). The study was simulated during 1-year on 2004, February. The model just simulated by barotropic condition and only influence by elevation tide in open boundary. The verification of ocean current (u and v components) from the model compare with observation data has a high coefficient of determination, i.e., 0.9, respectively. This verification result shows good agreement between model and observation data. For the result model, in the Lombok strait dominant influence by M2 semidiurnal component from Indian Ocean and K1 diurnal component from Pacific Ocean. The current circulation in the near surface dominant movement pattern from southern to northern. On the other hand, for the vertical current in 100 – 600 meter is different with near surface. The current movement from northern to southern. In the sill area have upwelling phenomenon in the north side of the sill and downwelling in south of the sill.


Introduction
The water mass condition in the Lombok Strait is influenced by the water mass from the Pacific Ocean to the Indian Ocean. This is due to the difference in sea level between oceans. The Pacific Sea level is higher than the Indian Ocean, which is one of the drivers of Indonesian Throughflow (ITF). The condition of this sea-level difference varies seasonally [1,2,3].
Besides being affected by the ITF, the waters of the Lombok Strait are waters with a complex coastline and are influenced by the tide phenomenon [4,5]. A previous study conducted on the waters of the Lombok Strait conducted by Hatayama [6] still using a rough grid resolution of 1/12 x 1/12 degree. Several studies have investigated the ITF and internal waves in the waters of the Lombok Strait, but rarely discuss the characteristics of tidal currents in the waters of the Lombok Strait. In this paper, we will discuss the characteristics of tidal currents in the waters of the Lombok Strait using numerical calculations. Furthermore, it will be analysed horizontally and vertically with 1-year time simulation.

Model Design
The location of the model simulation covers the Lombok Strait area, and detail can be seen in Figure 1. The specifications of parameters and notes related to the model can be seen in Table 1. The model is barotropic. This model does not consider other parameters like wind stress, atmospheric pressure, heat flux, and freshwater flux. It is reasonable to investigate the impacts of stratification to add baroclinic tides into our future model. Furthermore, the ITF, which is not resolved in this model, has not interacted with the tides and alters tidal dynamics in this region. In the future model, the ITF will be used to evaluate the effect of the throughflow on the tidal fields.

Hydrodynamic Model
This study using numerical modelling Finite Volume Coastal Ocean Model (FVCOM). FVCOM using two modes (external and internal), which are calculated separately with the hydrodynamic model equations consist of continuity and momentum equations (1 -3), temperature (4), salinity (5), and density (6) [7] as follows: Where , , and σ are directions for east and west, north and south, and also vertical in the Cartesian coordinate system; , , and ω are the components of the current velocity for the , , and σ directions; T is the temperature; S is salinity; ρ is the density while ρ 0 is the reference density; f is the Coriolis force; g is gravity; Km is the vertical eddy viscosity; and K h is the thermal vertical eddy diffusion coefficient. F x , F y , F t , and F s represent friction in the and directions, thermal, and salinity diffusion; D is the total depth of the water column; is the absorption of radiation into the water column; ζ is the height of the water surface elevation.

Model Verification
The u and v component of current model will be validated with observation data taken in 2004 (1-29 February) using the Acoustic Doppler Current Profiler (ADCP) from INSTANT (International Nusantara Stratification and Transport) program. Locations of observation points for verification of current, can be seen in Figure 2.
To verify between model result and observation data, correlation analysis and root mean square error (RMSE) were carried out, which were written in equations (7) and (8) as follows: where r is the correlation coefficient, n is the number of samples, ∑ x is the total number for the item variable x, and ∑ y is the total number for the item variable . While in the RMSE equation, X insitu is the value of the observations and X model is the value obtained from the model results, and n is the amount of data.

Verification of Hydrodynamic Model Result
The comparison of the current verification between the model results and observations for u and v components can be seen in Figure 3. The calculation of the correlation between the u and the v components shows a significant correlation value of 0.9, respectively. This value implies a good agreement current pattern between model and observation data. Meanwhile, the Root Mean Square Error (RMSE) calculation between the model and observations for u and v components i.e. 0.006 m/s and 0.025 m/s, respectively. The current conditions in the model can describe conditions in the field.

Dynamic of Vertical Current Circulation
The cross-sectional study area was carried out in the Lombok Strait with analysis from a depth of 0 m -600 m; more details can be seen in Figure 7-8. The characteristics of the waters on transect A-A' show different current velocity conditions from 0 -100 m the current come from south to the north, and 100 -600 m the water mass come from north to the south. From 0 -100 m, the water mass influence by the M2 component from the Indian Ocean; on the other hand, from 100 -600 m, the water mass influence by the K1 component from the Pacific Ocean.

Figure 7. Cross-section study area A-A' in Lombok Strait
The water mass movement in-depth 100 -600 m is very strong from northern to southern. This situation affects the occurrence of upwelling and downwelling in the sill area. As seen in Figure 8, there is a strong upwelling and downwelling phenomenon in the sill area. Strong upwelling occurs north of the sill, with a maximum current of 1.2 m/s. Meanwhile, downwelling occurs in the south of the sill, with a maximum speed of 2 m/s. The high downwelling current velocity in the southern area of the sill is due to intense friction between the descending water mass and the irregular sill surface. The condition of the vertical current is almost the same on average 15 days, 30 days, and one year.
In addition, previous studies conducted by Hendrawan and Asai [4] also found the same results, where strong upwelling and downwelling phenomena were found in the north and south sills. The presence of the M2 component influences the upwelling and downwelling phenomena in the area, then the high downwelling current velocity in the southern area due to the influence of short internal tidal waves. In addition, the movement of high upwelling currents in the northern part of the sill allows particles to rise rapidly. As for the southern sill area, strong downwelling allows the particles to descend more quickly. After one cycle of the M2 tidal period, particles on the northern side of the Lombok sill were swiftly flowing upward; some of these particles on the northern side of the sill only needed one cycle of the M2 tidal period to reach the upper layer [4].