Abstract
The Mahakam is a 980-km-long tropical river flowing in the East Kalimantan province (Borneo Island, Indonesia). A significant fraction of this river is influenced by tides, the modelling of which is the main subject of this study. Various physical and numerical issues must be addressed. In the upstream part of the domain, the river flows through a region of three lakes surrounded by peat swamps. In the lowland regions, the river is meandering and its hydrodynamics is mostly influenced by tides. The latter propagate upstream of the delta, in the main river and its tributaries. Finally, the mouth of the Mahakam is a delta exhibiting a high number of channels connected to the Makassar Strait. This article focusses on the flow in the delta channels, which is characterised by a wide range of time and space scales. To capture most of them, the depth-integrated and the section-integrated versions of the unstructured mesh, finite-element model Second-Generation Louvain-la-Neuve Ice-Ocean Model are used. Unstructured grids allow for a refinement of the mesh in the narrowest channels and also an extension of the domain upstream and downstream of the delta in order to prescribe the open-boundary conditions. The Makassar Strait, the Mahakam Delta and the three lakes are modelled with 2D elements. The rivers, from the upstream limit of the delta to the lakes and the upstream limit of the domain, are modelled in 1D. The calibration of the tidal elevation simulated in the Mahakam Delta is presented. Preliminary results on the division of the Eulerian residual discharge through the channels of the delta are also presented. Finally, as a first-order description of the long-term transport, the age of the water originating from the upstream limit of the delta is computed. It is seen that for May and June 2008, the time taken by the water parcel to cross the estuary varies from 4 to 7 days depending on the channel under consideration.
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References
Comblen R, Lambrechts J, Remacle J-F, Legat V (2010) Practical evaluation of five partly discontinuous finite element pairs for the non-conservative shallow water equations. Int J Numer Methods Fluids 63(6):701–724. http://dx.doi.org/10.1002/fld.2094
Comblen R, Legrand S, Deleersnijder E, Legat V (2009) A finite element method for solving the shallow water equations on the sphere. Ocean Model 28:12–23.
de Brye B, de Brauwere A, Gourgue O, Kärnä T, Lambrechts J, Comblen R, Deleersnijder E (2010) A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI. Coastal Eng 57(9):850–863
Deleersnijder E, Campin JM, Delhez EJM (2001) The concept of age in marine modelling: I. Theory and preliminary model results. J Mar Syst 28(3–4):229–267
Deleersnijder E, Lermusiaux P (eds) (2008) Multi-scale modeling: Nested-grid and unstructured-mesh approaches. Ocean Dyn 58:335–498 (Special Issue)
Delhez EJM, Heemink AW, Deleersnijder E (2004) Residence time in a semi-enclosed domain from the solution of an adjoint problem. Estuar Coast Shelf Sci 61(4):691–702
Egbert G, Bennett A, Foreman M (1994) TOPEX/Poseidon tides estimated using a global inverse model. J Geophys Res 99(C12):24,821–24,852
Geuzaine C, Remacle J-F (2009) GMSH a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J Numer Methods Eng 79(11):1309–1331
Gordon A, Susanto R, Ffield A (1999) Throughflow within Makassar Strait. Geophys Res Lett 26:3325–3328
Haidvogel DB, McWilliams JC, Gent PR (1991) Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J Phys Oceanogr 22(8):882–902
Hoekman DH (2007) Satellite radar observation of tropical peat swamp forest as a tool for hydrological modelling and environmental protection. Aq Cons Mar and Freshw Ecosyst 17(3):265–275
Hoitink A, Buschman F, Vermeulen B (2009) Continuous measurements of discharge from a horizontal acoustic Doppler current profiler in a tidal river. Water Resour Res 45(11):W11406
Kalnay E, Kanamitsua M, Kistlera R, Collinsa W, Deavena D, Gandina L, Iredella M, Sahaa S, Whitea G, Woollena J, Zhua Y, Leetmaaa A, Reynoldsa R, Chelliahb MW, Ebisuzakib HW, Janowiakb J, Mob KC, Ropelewskib C, Wangb J, Jennec R, Joseph D (1996) The NCEP/NCAR 40-Year Reanalysis Project. Bull Am Meteorol Soc 77:437–431
Kärnä T, de Brye B, Gourgue O, Lambrechts J, Comblen R, Legat V, Deleersnijder E, (2010) A fully implicit wetting–drying method for DG-FEM shallow water models, with an application to the Scheldt estuary. Comput Meth Appl Mech Eng. doi:10.1016/j.cma.2010.07.001
Kishimoto-Yamada K, Itioka T (2008) Consequences of a severe drought associated with an El Nino–Southern Oscillation on a light-attracted leaf-beetle (Coleoptera, Chrysomelidae) assemblage in Borneo. J Trop Ecol 24(Part 2):229–233
Lambrechts J, Comblen R, Legat V, Geuzaine C, Remacle J-F (2008a) Multiscale mesh generation on the sphere. Ocean Dyn 58(5):461–473
Lambrechts J, Hanert E, Deleersnijder E, Bernard P-E, Legat V, Remacle J-F, Wolanski E (2008b) A multiscale model of the whole Great Barrier Reef hydrodynamics. Estuar Coast Shelf Sci 79:143–151
Legrand S, Deleersnijder E, Delhez E, Legat V (2007) Unstructured, anisotropic mesh generation for the northwestern European continental shelf, the continental slope and the neighbouring ocean. Cont Shelf Res 27(9):1344–1356
Liu W-C, Chen W-B, Cheng RT, Hsu M-H, Kuo AY (2007) Modeling the influence of river discharge on salt intrusion and residual circulation in Danshuei River estuary, Taiwan. Cont Shelf Res 27(7):900–921
Mandang I, Yanagi T (2008) Tide and tidal current in the Mahakam Estuary, East Kalimantan, Indonesia. Coast Mar Sci 32(1):1–8
Millenium Ecosystem Management (2005) Ecosystems and human well-being: biodiversity synthesis. World Resources Institute, Washington, DC
Muller H, Blanke B, Dumas F, Lekien F, Mariette V (2009) Estimating the Lagrangian residual circulation in the Iroise Sea. J Mar Syst 78(Supplement 1):S17–S36
Okubo A (1971) Oceanic diffusion diagrams. Deep-Sea Res 18:789–802
Pawlowicz R, Beardsley B, Lentz S (2002) Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput Geosci 28:929–937
Roberts HH, Sydow J (2003) Late quaternary stratigraphy and sedimentology of the offshore Mahakam Delta, East Kalimantan (Indonesia). In: Sidi FH, Nummedal D, Imbert P, Darman H, Posamantier HW (Eds) Tropical deltas of Southeast Asia; sedimentology, stratigraphy, and petroleum geology, vol 76. SEPM special publication. SEPM, Tulsa, pp 125–145
Roe PL (1981) Approximate Riemann solvers, parameters vectors and difference schemes. J Comput Phys 135:250–258
Sassi M, Hoitink A, Vermeulen B, Hidayat H (2011) Discharge estimation from H-ADCP measurements in a tidal river subject to sidewall effects and a mobile bed. Water Resour Res (in press)
Simpson J (1997) Physical processes in the ROFI regime. J Mar Syst 12:3–15
Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99–164
Smith SD, Banke EG (1975) Variation of the sea surface drag coefficient with wind speed. Q J R Meteorol Soc 101:665–673
Storms JE, Hoogendoorn RM, Dam RA, Hoitink A, Kroonenberg S (2005) Late-Holocene evolution of the Mahakam Delta, East Kalimantan, Indonesia. Sediment Geol 180:149–166
Susanto R, Gordon A (2005) Velocity and transport of the Makassar Strait throughflow. J Geophys Res 110(C1):C01005
Toro E (1997) Riemann solvers and numerical methods for fluid dynamics, a practical introduction. Springer, Berlin
Waworuntu JM, Garzoli SL, Olson DB (2001) Dynamics of the Makassar Strait. J Mar Res 59:313–325
Wei H, Hainbucher D, Pohlmann T, Feng S, Suendermann J (2004) Tidal-induced Lagrangian and Eulerian mean circulation in the Bohai Sea. J Mar Syst 44(3–4):141–151
Acknowledgements
The present study was carried out in the framework of the project “Taking up the challenges of multi-scale marine modelling”, which is funded by the Communauté Française de Belgique under contract ARC 10/15-028 (Actions de recherche concertées) with the aim of developing and using SLIM (www.climate.be/slim). Eric Deleersnijder is a research associate with the Belgian National Fund for Scientific Research (F.R.S-FNRS).
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Responsible Editor: Phil Peter Dyke
This article is part of the Topical Collection on Joint Numerical Sea Modelling Group Workshop 2010
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de Brye, B., Schellen, S., Sassi, M. et al. Preliminary results of a finite-element, multi-scale model of the Mahakam Delta (Indonesia). Ocean Dynamics 61, 1107–1120 (2011). https://doi.org/10.1007/s10236-011-0410-y
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DOI: https://doi.org/10.1007/s10236-011-0410-y