Reducing the Spinup Time of Ocean Models

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Reducing the Spin-up Time of Ocean Models

• Erik Bernsen Henk Dijkstra
• EGU 2007

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Outline

• Introduction
• Model
• Method
• Results
• Conclusion

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Introduction
SST, present day, 710 ppm CO2
SST, present day, 280 ppm CO2

• CCSM 1.4
• Atmosphere model
• Land surface model
• Ocean model
• Sea ice model
• Spinup
• Repeat three times
• 20 yr coupled run
• 20 yr ocean run
• 200 yr coupled run
• CPU time
• 4?20,000 hr 80,000 hr
• on Teras.

SST, late oligocene (26 Myr ago) , 710 ppm CO2
SST, early miocene (20 Myr ago), 710 ppm CO2
Von der Heydt and Dijkstra oligocene/miocene
ocean circulation, Paleoceanography, vol 21, 2006
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Model (I) Planetary Geostrophic Ocean Model

• Advection-diffusion equation for temperature and
  salinity (only prognostic variables).
• Linear equation of state.
• Momentum equations Geostrophic balance with
  linear friction, hydrostatic balance.
• Continuity equation.
• Ekman top layer.
• Convective adjustment ?v ?v(??/?z)
• Forcing
• Restoring boundary conditions for temperature and
  salinity.
• Windstress.

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Model (II) Results
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Method (I) Jacobian Free Krylov Newton Method
(JFKN)

• Timestepper Iterate
• untill is small.

Newton Iterate untill is
small.
Use GMRES method for solving linear systems.
Needed matrix-vector products
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Method (II) Preconditioning

• To speed up convergence of GMRES we use a
  preconditioner M-1
• with

• How to choose M-1?

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Method(III) Choice of preconditioner

• Write with
• Construct Jacobian
• Use MRILU to construct corresponding
  preconditioner M-1.
• Use this preconditioner for several Newton steps.

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Method(IV) Global Convergence

• Problem Newtons method gives local convergence,
  but no global convergence.

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Results
Spinup time- scale
Speed-up 20 times faster (for timestepping
run of 5000 yr.)
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Conclusion Future Work

• Using a JFKN method for spin up can reduce the
  spin-up time dramatically. One only needs
• Residual F(x).
• Dependencies for Jacobian matrix for construction
  of preconditioner.
• How does the method scale with resolution?
• How will this method work with more realistic
  models