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# GEOtop 0.9375Kmackenzie

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

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### GEOtop 0.9375Kmackenzie

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