Ocean Dynamics

, Volume 61, Issue 8, pp 1107–1120 | Cite as

Preliminary results of a finite-element, multi-scale model of the Mahakam Delta (Indonesia)

  • Benjamin de BryeEmail author
  • Sébastien Schellen
  • Maximiliano Sassi
  • Bart Vermeulen
  • Tuomas Kärnä
  • Eric Deleersnijder
  • Ton Hoitink
Part of the following topical collections:
  1. Topical Collection on Joint Numerical Sea Modelling Group Workshop 2010


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.


Finite element Model Mahakam River Multi-scale Tide Hydrodynamics 



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 ( Eric Deleersnijder is a research associate with the Belgian National Fund for Scientific Research (F.R.S-FNRS).


  1. 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. Google Scholar
  2. 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.CrossRefGoogle Scholar
  3. 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):850–863CrossRefGoogle Scholar
  4. 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):229–267Google Scholar
  5. Deleersnijder E, Lermusiaux P (eds) (2008) Multi-scale modeling: Nested-grid and unstructured-mesh approaches. Ocean Dyn 58:335–498 (Special Issue)CrossRefGoogle Scholar
  6. 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):691–702CrossRefGoogle Scholar
  7. Egbert G, Bennett A, Foreman M (1994) TOPEX/Poseidon tides estimated using a global inverse model. J Geophys Res 99(C12):24,821–24,852CrossRefGoogle Scholar
  8. 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):1309–1331CrossRefGoogle Scholar
  9. Gordon A, Susanto R, Ffield A (1999) Throughflow within Makassar Strait. Geophys Res Lett 26:3325–3328CrossRefGoogle Scholar
  10. Haidvogel DB, McWilliams JC, Gent PR (1991) Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J Phys Oceanogr 22(8):882–902CrossRefGoogle Scholar
  11. 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):265–275CrossRefGoogle Scholar
  12. 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):W11406CrossRefGoogle Scholar
  13. 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 77:437–431CrossRefGoogle Scholar
  14. 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 Google Scholar
  15. 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):229–233Google Scholar
  16. Lambrechts J, Comblen R, Legat V, Geuzaine C, Remacle J-F (2008a) Multiscale mesh generation on the sphere. Ocean Dyn 58(5):461–473CrossRefGoogle Scholar
  17. 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 79:143–151CrossRefGoogle Scholar
  18. 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):1344–1356CrossRefGoogle Scholar
  19. 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):900–921CrossRefGoogle Scholar
  20. Mandang I, Yanagi T (2008) Tide and tidal current in the Mahakam Estuary, East Kalimantan, Indonesia. Coast Mar Sci 32(1):1–8Google Scholar
  21. Millenium Ecosystem Management (2005) Ecosystems and human well-being: biodiversity synthesis. World Resources Institute, Washington, DCGoogle Scholar
  22. 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–S36CrossRefGoogle Scholar
  23. Okubo A (1971) Oceanic diffusion diagrams. Deep-Sea Res 18:789–802Google Scholar
  24. Pawlowicz R, Beardsley B, Lentz S (2002) Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput Geosci 28:929–937CrossRefGoogle Scholar
  25. 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 125–145Google Scholar
  26. Roe PL (1981) Approximate Riemann solvers, parameters vectors and difference schemes. J Comput Phys 135:250–258CrossRefGoogle Scholar
  27. 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)Google Scholar
  28. Simpson J (1997) Physical processes in the ROFI regime. J Mar Syst 12:3–15CrossRefGoogle Scholar
  29. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
  30. Smith SD, Banke EG (1975) Variation of the sea surface drag coefficient with wind speed. Q J R Meteorol Soc 101:665–673CrossRefGoogle Scholar
  31. Storms JE, Hoogendoorn RM, Dam RA, Hoitink A, Kroonenberg S (2005) Late-Holocene evolution of the Mahakam Delta, East Kalimantan, Indonesia. Sediment Geol 180:149–166CrossRefGoogle Scholar
  32. Susanto R, Gordon A (2005) Velocity and transport of the Makassar Strait throughflow. J Geophys Res 110(C1):C01005CrossRefGoogle Scholar
  33. Toro E (1997) Riemann solvers and numerical methods for fluid dynamics, a practical introduction. Springer, BerlinGoogle Scholar
  34. Waworuntu JM, Garzoli SL, Olson DB (2001) Dynamics of the Makassar Strait. J Mar Res 59:313–325CrossRefGoogle Scholar
  35. 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):141–151CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Benjamin de Brye
    • 1
    • 3
    Email author
  • Sébastien Schellen
    • 1
    • 3
  • Maximiliano Sassi
    • 2
  • Bart Vermeulen
    • 2
  • Tuomas Kärnä
    • 3
  • Eric Deleersnijder
    • 1
    • 4
  • Ton Hoitink
    • 2
  1. 1.Institute of Mechanics, Materials and Civil Engineering (IMMC)Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Hydrology and Quantitative Water Management Group, Department of Environmental SciencesWageningen UniversityWageningen, GldThe Netherlands
  3. 3.Georges Lemaître Centre for Earth and Climate Research (TECLIM)Université catholique de LouvainLouvain-la-NeuveBelgium
  4. 4.Earth and Life Institute (ELI), Georges Lemaître Centre for Earth and Climate Research (TECLIM)Université catholique de LouvainLouvain-la-NeuveBelgium

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