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GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
GEOtop 0.9375Kmackenzie
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GEOtop 0.9375Kmackenzie

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A brief description of the theory of GEOtop 0.9375KMackenzie is here explained.

A brief description of the theory of GEOtop 0.9375KMackenzie is here explained.

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Transcript

  • 1. GEOtop 0.9375KMackenzie
  • 2. Structure
    • Input data and options
    • Meteo data calculation
    • Energy balance (if wanted)
    • Water balance (if wanted)
    • Output writing
  • 3. Meteo
    • I) wind, T, RH: Micromet or uniform values
    • II) precipitation: Micromet or simple kriging
    • III) SWin: Micromet (from T, RH) or theoretic-measured values (cloudiness)
    • IV) LWin: Micromet (from 500 mbar curve) or formulae with ground values
  • 4. Energy balance
    • Integration heat equation (snow-soil)
    • Phase change
    • Boundary conditions:
      • Atmosphere exchange (surface layer)
      • Constant flux at the bottom
  • 5. Water balance
    • Vertical - Lateral - Surface flow SOLVED SEPARATELY
    • Variables: Psi - h (mm)
    • When can this work?
    Dt ?
  • 6. Lateral-vertical
    • Most crucial
    • Strong coupling
    • Key: find Dt at which the fluxes can be solved decoupled?
    • Dt proportional to C/k
    • Since C goes to 0 for saturated soil, this method does not work
  • 7. But….
    • We cannot afford solving a full implicit 3D problems, as we are modelling large basins with limited simulation times ….
    • Precision required - Spatial scale - Simulation time constraint
    • Compromise decided by the user
  • 8. Overcoming the problem
    • Prevent C from going to 0, using the ‘soil elasticity’ concept
    • Choice on admitting a maximum Dpsi after one time step of the integration of the lateral flow (the lower the more precise), otherwise the time step is reduced - index of numerical stability
    • Minimum time step allowed
  • 9. Vertical flow
    • Solved with the time step decided by lateral flow
    • Picard method
    • Problems:
      • Instability of the boundary condition
      • Not fully conservative (there is a mass loss….)
  • 10. Overcome instability
    • Fix a maximum value of psi of the first layer (if a large value is obtained, psi is set at the max value assuming exfiltration)
    • Iteration (Picard) and switching between 2 cases
    • Convergence more difficult to reach the more constraint we set - we have to use very simple conditions
  • 11. Switching
    • All Pnet infiltrates - Psi is free to vary
    • Psi at the first layer set at its maximum (saturation) value and infiltration is found so that it maintains the 1st layer Psi value
    • Switching should sharply occur when 1st layer reaches saturation - however a tolerance on Psi is set (the higher the faster - the lower the more precise)
  • 12. Time step
    • … is reduced in order to
      • Reach convergence
      • Maintain mass error below a tolerance
    The user decides: convergence tolerance mass errors acceptable minumum time steps
  • 13. Other instabilities
    • Occur when soil is very dry (or frozen) and infiltration occurs
    • If this occurs, the water content of the 1st layer is updated and Richards’ equation is not solved
  • 14. Surface flow
    • Solved with the time step decided by lateral flow
    • Water path as many cells as needed (not only one like before…)
    • No constraint on time step
  • 15. Channels
    • No pure channel pixels exist
    • Channels are located in mixed pixels
    • Problems of deciding how much water goes to the channels via surface (h) and via sub-surface (Psi)

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