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Fluvial Landscape Erosion

Fluvial Landscape Erosion. Kirsten Meeker, Bjorn Birnir, Terence Smith, George Merchant www.cs.ucsb.edu/~kmeeker/erosion.htm.

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Fluvial Landscape Erosion

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  1. Fluvial Landscape Erosion Kirsten Meeker, Bjorn Birnir, Terence Smith, George Merchant www.cs.ucsb.edu/~kmeeker/erosion.htm

  2. Modeling fluvial landscape evolution using a simple system of nonlinear conservation equations produces stages of evolution and stochastic results with characteristic statistical properties.

  3. Conservation Equations

  4. Flow Equations

  5. Boundary Conditions upper boundary (ridge) h = 0 qw = qs = 0 lower boundary (absorbing body of water) H = h0 = h Lateral boundaries (infinite extent) periodic

  6. System Properties • Ill-posed problem • Shocks develop in water flow • Results vary widely with initial conditions • Large Fourier components (smallest spatial scale) grow fastest, all modes grow exponentially • Nonlinearities saturate, producing colored noise • Statistical measures are invariant • width function

  7. Numerical Methods Water Equation: Forward-time center space scheme with upwind differencing, explicit O(Dx, Dt)

  8. Sediment Equation: Crank-Nicholson scheme, implicit O(Dx2, Dt2)

  9. Can be expressed in matrix form as Ax=b Solved using preconditioned biconjugate gradient method diag(A) used as preconditioner

  10. Parallel Program Partitioning

  11. References • Towards an elementary theory of drainage basin evolution: I. The theoretical basis. Terence R. Smith, Bjorn Birnir and George E. Merchant Computers & Geosciences 23(8), 811-822 • Towards an elementary theory of drainage basin evolution: II. A computational evaluation.Terence R. Smith, George E. Merchant and Bjorn Birnir Computers & Geosciences 23(8), 823-849 • The scaling of fluvial landscapes. Björn Birnir, Terence R. Smith and George E. Merchant , Computers & Geosciences 27(10), 1189-1216

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