2 MATERIALS AND METHODS

Transcription

1 2 MATERIALS AND METHODS 2.1. Sand Movement on Coral Cays Sand movement in Semak Daun cay was recognized by the monsoonal morphological change of the beach line. It is found that certain beach lines advanced in certain monsoonal condition, while in the other monsoonal condition, it reduced. Recent studies found that there are two main seasons in Seribu Islands region, which are influenced by the governing wind. Based on these recognitions, it is hypothesized that monsoonal wind was the main governing force in the area Monsoonal Wind In Seribu Islands region, the climate is caused by two monsoonal winds that blow in the area, that are quite stable that it would construct and keep the surface current in Java Sea (Lumingkewas 2009; Ilahude, 1980). In Figure 2.1, it could be seen that throughout the period 1948 to 2009, regional monthly winds vectors show evidence of a quite consistent bi-directional pattern (Poerbandono, 2012). Based on this bidirectional pattern, we could divide the wind force in to two types, which are the South-East (SE) and North-West (NW) wind. The peak of the SE Monsoon is in August, while the peak of the NW Monsoon is in January (see Table 2.1 and 2.2). Table 2.1 Mean monthly wind direction, in degrees (Poerbandono, 2012) SE Monsoon Apr May Jun Jul Aug Sep Oct Mean Direction Deviation NW Monsoon Nov Dec Jan Feb Mar Mean Direction Deviation Table 2.2 Mean monthly wind magnitude, in ms -1 (Poerbandono, 2012) SE Monsoon Apr May Jun Jul Aug Sep Oct Mean Magnitude Deviation NW Monsoon Nov Dec Jan Feb Mar Mean Magnitude Deviation

2 Figure 2.1 Period mean monthly wind energy resultant vector, (Poerbandono, 2012) Nodal Point Theory Surfing actions of wind-induced waves are considered as the primary control to the transport of cay beach sediments. When wind-induced waves from a direction strike a reef platform from the windward side, breaking may occur along the outer line of a reef platform. This will result in bending of wave rays along reef platforms, which are adjusted to the morphology of the reef platform itself. The pattern of wave rays tends to converge toward the leeward side of the cay. Upon change of direction of wind-induced waves, sands are eroded and transported as long-shore drift along the beach lines that are parallel to the direction of wind vectors and collected in the socalled nodal point (Flood, 1986), that could be seen in Figure

3 Figure 2.2 Nodal point accretion at cay's leeward under predominant wind-induced waves (Flood, 1986) It is known that there is a relationship between the seasonal incoming wind and the sediment dynamics defined by their positions on the cay. Changes of beach lines seem to follow the pattern of the wind direction. Sands in SE monsoon commonly found in the western and northern part of the cay, while in NW monsoon, the sands were commonly found on the southern part of the cay (Figure 2.3). In the western side of the cay, a nodal point is seen in term of sand spit.! (a) IKONOS July 2008 SE (b) World View December 2009 NW Figure 2.3 Semak Daun cay in two monsoonal seasons (Alodia et al., 2012) 8

4 Based on the understanding, there has been a proposed nodal point model for the dynamics of sediments in Semak Daun (Figure 2.4). Figure 2.4 Nodal point model proposed for ESE waves during SE monsoon in Semak Daun cay (Poerbandono, 2012) Evidence of Erosion Based on the documentations of prior research (Figure 2.5), it is found that coastal protection efforts have been done. Sea walls were found, indicating that based on the local people s understanding, erosion had occurred on the area. Erosion evidence was also found in term of beach line change, where can be seen some fallen trees and roots drowned by the seawater. From that evidence, it could be concluded that sediment dynamics were quite active in that area, because trees need media to grow on a proper level of sands, and in this case, the proper level of sands have been eroded. These evidences were found in the northern part of the cay. (a) Beach Wall (b) Beach Line Change Figure 2.5 Erosion evidences found in Semak Daun cay (Lumingkewas, 2009) 9

5 2.2. Characteristic of Hydrodynamics in Study Area The hydrodynamics characteristics that will be explained in this study are mainly focused on the tidal and current conditions. From recent studies, it is found that the hydrodynamics were influenced by the monsoonal conditions. In SE monsoon, the current flows to the east with the magnitude of ms -1, while in the NW monsoon, it flows to the west with the magnitude of ms -1 (Lumingkewas, 2009; Wyrtki, 1961). The characteristic of hydrodynamics in study area is also defined by prior field observation. The data from the field observation contains of tidal and current data in a specific point around Semak Daun area Field Observation The tide and current from the prior observation data was obtained by deploying a 600kHz Acoustic Wave And Current profiler (AWAC) in the survey area from 25 June to 2 July 2008 (Poerbandono et al., 2009), which was on the SE Monsoon. AWAC was stationary deployed on the seabed and facing up-ward. The recording was configured at an acquisition rate of 900s with 1m vertical resolutions. The approximate depth of deployment was 11m. The observation point coordinate was (678311, ) m, with the projection of UTM-48, southern hemisphere Analysis of Observation Data The data from the field observation (Poerbandono et al., 2009) indicates that the tidal type in Seribu Islands is diurnal tide. In the beginning of the observation, the tide was in the period of neap tide, until the end of the observation, the tide changes into spring tide. The spring tide high water is 0.54m, while the neap tide high water is 0.24m. The net current from the observation point was 0.008m/s, with the direction of 230. The maximum value of current magnitude in the observation point was 0.392m/s and the minimum value was 0.003m/s, so we could say that the speed of the current that flows in the study area was quite low Numerical Simulation Setup Numerical simulations were carried out to understand the hydrodynamics and sand transport pattern in the region. The module chosen for the simulation was Flow Model Flexible Mesh (FM) in MIKE21. The simulation in the Flow Model FM 10

6 module needs an input of flexible mesh. The flexible mesh was created in the Mesh Generator Module in MIKE Zero Mesh Generation A flexible mesh consists of a number of nodes and a number of elements. It is based on a node-element structure with values defined either as element average/element center values, or on the nodes. Elements can have many different forms in general. The nodes and elements are defined in each their own table. In the two horizontal dimensions, the elements can be triangles, quadrilateral, and a mix of the two. The bathymetric data for the mesh generation were compiled from one-minute grid of GEBCO bathymetry, bathymetric chart of Semak Daun cay (2004), and bathymetric chart of Panggang, Karya, and Pramuka cay in (2009) with the projection of UTM 48 South zone. The coastline data was obtained by inserting the simulation domain data from GEBCO to the NOAA Coastline Extractor. Before the mesh generation, the bathymetric charts were geo-referenced in ArcGIS. In this research, the simulation domain consists of two land boundaries (Sumatra and Java) and three open boundaries (Figure 2.6). The bathymetric character of the simulation domain can be seen in the domain wire frame (Figure 2.7), which could be noticed that the simulation domain is quite flat. For the efficiency of the simulation, the maximum number of nodes in the domain must be defined. In this simulation, the maximum number of the nodes is This number could be obtained by simplifying the coastline geometries. When the meshing finished, a natural neighbor interpolation was executed to obtain the morphology of the seabed in the simulation area. The interpolation requires values only at the mesh nodes and will base the interpolation solely on the scatter data. 11

7 Figure 2.6 Model domain and observation points 12

8 Figure 2.7 Domain wire frame 2.4. Sensitivity Analysis Sensitivity analysis is the study of how the variation in the output of a model (numerical or otherwise) can be apportioned, qualitatively or quantitatively, to different sources of variation (EAS, 2012). This analysis is very useful when attempting to determine the impact of the actual outcome of a particular variable will have if it differs from what was previously assumed. In this sensitivity analysis test, there are three scenarios for two different variables, which are bed resistance and wind forcing. The sensitivity test was executed at the same point and time of the deployment to compare the variety of the tide and current due to the change of those two variables Scenario of Bed Resistance Chezy number (m 1/2 s -1 ) 50 is used for normal the bed resistance variable. The other scenarios were to change this Chezy number to 30 and 70. The idea was to indicate the change of the tide and current in the area if the bottom stress was reduced or increased, since the bottom stress,! b, is determined by a quadratic friction law:! b = c f u b u b (1) 13

9 where in this case, c f = g C 2 (2) where c f is the drag coefficient, u b is the depth-average velocity, g is the gravitational force, and the drag coefficient in this research is determined from Chezy number, C. Figure 2.8 Sensitivity of tide simulation due to bed roughness Figure 2.9 Sensitivity of the current simulation due to bed rougness From this comparison, could be concluded that the change of the bed resistance in this simulation was not that significant for the tidal condition, but quite significant for the current velocity. As can be seen in Figure 2.8, the values of the water level with different Chezy numbers was almost remain the same, while in Figure 2.9, the current velocity is averagely increased if the Chezy number were also increased. This could mean that a rough seabed is an indicator of a strong current condition. 14

10 Scenario of Wind Forcing The original values from Table 2.1 and Table 2.2 were used as normal wind condition. The other scenarios were to multiply and to divide the magnitude values by 5. The idea was to indicate the change of the tide and current in the area if the surface stress was reduced or increased, since the surface stress,! s, is determined by the following empirical relation:! s = " a c d u w u w (3) where ρ a is the density of air, c d is the drag coefficient of air, and! u w = (u w, v w ) is the wind speed 10m above the sea surface. Figure 2.10 Sensitivity of tide due to wind speed Figure 2.11 Sensitivity of current due to wind speed 15

11 From this comparison, it could be concluded that the change of the wind speed in this simulation was more significant than the change of the bed resistance, both for the tidal and current conditions. It could be seen in Figure 2.10 that although the values were quite similar, there was slight differences difference between the results of the scenarios. The current condition itself was concerned as highly affected by the wind. As can be seen in Figure 2.11, the current velocity experienced a very high average rise when the wind velocity was multiplied, and experienced an average drop when the wind velocity was divided. This could mean that the wind was a major governing variable of hydrodynamics phenomenon in Seribu Islands region, because it caused a major change, especially on the current velocity Calibration and Validation The method used to calibrate the simulation data with the observed data is by comparing simulated tide and current with observed water level and current from the field observation of Poerbandono et al (2009) Verification of Tidal Data The verification of tidal data was executed by comparing the tidal data from the model and from the observation (Figure 2.12 and Figure 2.13). The simulation was executed from 20:00:00 06/25/2008 to 20:00:00 07/01/2008 with 1 hour interval. Figure 2.12 Time series comparison between observed water level and simulated tide 16

12 Figure 2.13 Equality line of observed and simulated water level From the comparison time series and scatter plot of Figure 2.12, can be seen that there is a similar trend between the tendency of the model and observed tide, and it already represented neap and spring tide. There are quite big discrepancies on the beginning of the time series because the instrument had just been deployed in the mean time and the model was run with no initial condition. The MSL was 0.9m. The RMS of the simulation was 6.59%. The number obtained by subtracting the water level values of the observation to the model. The subtracted values were then divided by the water level values. The divided values were then averaged to a percentage. The result showed that the water level heights from the model represented the water level from the field. Based on the number, the modelling result is considered valid Verification of Current Velocity Data The verification of current velocity data was also executed by comparing the tidal data from the model and from the observation. The discrepancy factor of 2 is 54% (Figure 2.14). It was discovered that the model were overestimated. This could 17

13 happen because the current, as described in the sensitivity analysis section, is affected by several variables. One of the most influential variables is the bathymetry. Figure 2.14 Comparison of observed and simulated velocity The observation point was located in a lagoon, where the current that flows through it was quite small, while in the simulation domain, the same location was represented by bathymetric mesh that did not match the whole morphological feature from the field. This happened because the bathymetric mesh were simplified, so that the depth changing in the location of the deployment were not that high, while in the reality, the depth changing in lagoon area is actually quite high, due to the steep reef. This simplified depth changing affected the current velocity, because the energy transferred in a flat zone is bigger than the energy transferred in a steep zone. Based on this understanding, the overestimated model could be concluded as the impact of the simplified bathymetric mesh Hydrodynamics Simulation The hydrodynamics simulation is setup for two monsoonal conditions (SE and NW monsoon) with the period of 7 days each. This period is used to represent one neap tide and one spring tide condition. The simulation run in August as a representation 18

14 of SE monsoon, while the NW monsoon represented by running the simulation in the month of January Terms and Definition Hydrodynamics simulation is a simulation of current that flows in an area. The simulation could be executed in one or multi point(s), one line, or one area. The current obtained from the simulation is resulted from a series of numerical functions, with the input of parameters such the simulation domain, simulation time, solution technique, flood and dry conditions, density, eddy viscosity, bed resistance, coriolis forcing, wind forcing, ice coverage, tidal potential, precipitation-evaporation, wave radiation, sources, structures, initial conditions, boundary conditions, decoupling, and the output of the simulation Governing Equations The simulation is based on the numerical solution of the two-dimensional shallow water equations the depth-integrated incompressible Reynolds averaged Navier- Stokes equations in the Cartesian coordinate, which is defined as (DHI, 2011):!h!t +!hu!x +!hv!y = hs (4) and the two horizontal momentum equations for the x- and y- component, respectively:!hu!t +!hu 2!x +!hvu!! = fvh " gh!y!x " h!p a!x " gh2!" 2!x + # sx " # bx " 1 #!s xx!x +!s xy % $!y!hv!t & (+! '!x (ht xx )+!!y (ht xy)+ hu s S +!huv!x +!hv 2!! = fuh " gh!y!y " h!p a!y " gh2!" 2!y + # sy " # by " 1 #!s yx!x +!s yy % $!y & (+! '!x (ht xy)+!!y (ht yy)+ hv s S (5) (6) 19

15 where t is the time; x, y and z are the Cartessian co-ordinates; η is the surface elevation; d is the still water depth; h = η + d is the total water depth; u, v and w are the velocity components in the x, y and z direction; f = 2Ωsinϕis the Coriolis parameter (Ω is the angular rate of revolution and ϕ is the geographic latitude); g is the gravitational acceleration; ρ is the density of water; s xx, s xy, s yx and s yy are components of the radiation stress tensor; v t is the vertical turbulent (or eddy) viscosity; p a is the atmospheric pressure; ρ 0 is the reference density of water. S is the magnitude of the discharge due to point sources and (u s, v s ) is the velocity by which the water is discharged into the ambient water. The governing equation mentioned above is based on the partial differential equation. It could be seen that the equation is still in a continuum condition. To obtain the result, the equation must be discretized by the boundary conditions and initial condition, so the Δt, Δx, Δy, could be defined. The over-bar indicates a depth average value. For example, u and v are the depthaveraged velocities defined by: hu =! " udz (7)!d and hv =! " vdz (8)!d Parameters of Simulation The hydrodynamics simulation contains more than one parameter, which are: 1. Simulation Domain The domain used for this simulation is the flexible mesh created in the Mesh Generator Module. The mesh file is an ASCII file including information of the geographical position and bathymetry for each node point in the mesh. The time integration method 20

16 2. Solution Technique The time integration method used in this simulation is the low order method. 3. Flood and Dry Conditions This simulation included flood and dry conditions with default values, which are drying depth of 0.005m, flooding depth 0.05m, and wetting depth 0.1m. 4. Density The density is assumed to be a function of salinity and temperature. This simulation used barotropic density type, where both temperature and salinity (TS) will be constant and the density will not be updated during the simulation. 5. Eddy Viscosity The eddy type of the simulation is governed by Smargorinsky formula (1963), where the sub-grid scale eddy viscosity is given by: A = c s 2 l 2 2S ij S ij (9) where c s is a constant, l is a characteristic length and deformation rate is given by: S ij = 1 "!u i +!u % j 2 $ #!x j!x ' (i,j = 1,2) (10) i & where the format of the formulation is constant, with the value of 0.28 and the eddy viscosity range is from 1.8x10-6 to m 2 s Bed Resistance The bottom stress was determined by the quadratic friction law with the value of Chezy number of 50m 1/2 s

17 7. Coriolis Forcing The Coriolis type used in this simulation is varying in domain, where the Coriolis force will be calculated based on the geographical information given in the mesh file. 8. Wind Forcing The wind forcing data used in this simulation were taken from the mean monthly wind direction and magnitude from 1948 to 2009 (Poerbandono, 2012), with constant value of wind friction. The August wind represented the SE monsoon, and the January wind represented the NW monsoon. 9. Boundary Conditions The study area domain consists of two land boundaries (Sumatera and Java Island) and three open boundaries. Along the land boundaries normal fluxes are forced to zero for all variables, and the open boundary condition were specified in form of the surface elevation for the hydrodynamic equation. The three open boundaries were provided on Tidal Prediction of Heights in MIKE21 Toolbox. 10. Initial Condition The initial condition type of this simulation is constant. The initial data of the surface elevation, u-velocity, and v-velocity is Other Conditions In this simulation, ice coverage, precipitation and evaporation, wave radiation, structures, decoupling, and tidal potential were excluded. 12. Output The output of this simulation is a 2D hydrodynamics simulation in the form of area series. The treatment occurred in flood and only real wet area. In the treatment of only real wet area, where the output file will contain delete values for points where the water depth is less than the wetting depth. The map projection will still be in UTM-48, Southern hemisphere. 22