Primal 4D-Var

• 4D-Var Concepts
• Primal 4D-Var
• Incremental Approach Used in ROMS (I4D-Var)

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The Mechanics of 4D-Var

• The Conjugate Gradient and Lanczos Algorithms
• Preconditioning
• Covariance Modeling

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Tutorial 1: Explanation of CPP Options, ocean.in, s4dvar.in (Arango, 30 mins)

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Run Exercise 1 - I4D-Var (PDF)

• Using a 30 km resolution model of California Current system (CCS), running I4D-Var, with 1 outer-loop, 50 inner-loops, 4 day assimilation cycle, and observations in the form of SST, SSH, Argo and hydrographic sections.

Tutorial 2: Multiple Outer Loops (Moore, 15 mins)

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Run Exercise 2 - I4D-Var with Multiple Outer-loops (PDF)

• Same as exercise 1, but running multiple outer-loops

Tutorial 3: Discussion of Exercises 1 and 2 (Moore, 30 mins)

• 4D-Var output, comparison of circulation from exercises 1 and 2

Tutorial 4: Calculation of prior error standard deviations (Moore & Arango, 30 mins)

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Homework 1: Building the standard deviation file for user model configuration.

Dual 4D-Var

• 4D-Var Recap
• Dual 4D-Var (4D-PSAS and R4D-Var)
• The Basic R4D-Var and 4D-PSAS Algorithm
• Weak Constraint 4D-Var

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4D-Var Diagnostics

• Posterior Error Estimates
• Hypothesis Tests and Degrees of Freedom
• Array Modes
• Clipping

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Tutorial 5: Explanation of CPP Options, ocean.in, s4dvar.in (Arango, 15 mins)

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Run Exercise 3 - R4D-Var and 4D-PSAS for a Single Outer-loop (PDF)

• Running CCS R4D-Var and 4D-PSAS

Tutorial 6: Semi-variograms (Milliff, 30 mins)

• A practical method for estimating decorrelation length scales.
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Run Exercise 4 - R4D-Var and 4D-PSAS subject to the weak constraint (PDF)

• Same as exercise 3 but subject to weak constraint.

Tutorial 7: Discussion of exercise 3 (Moore, 30 mins)

• 4D-Var output, posterior error, posterior EOFs, comparison of circulation estimates with I4D-Var from exercise 1.

Run Exercise 5 - Array Modes (PDF)

• Computation of array modes using the output from R4D-Var and 4D-PSAS.

Tutorial 8: Discussion of exercises 4 and 5 (Moore, 30 mins) Tutorial 9: Computing normalization coefficients for covariance models (Moore & Arango 30 mins)

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Homework 2: Building the file of normalization coefficients for the prior error covariance matrix for user model configuration.

Observation Impact and Sensitivity

• Observation Impacts
• Adjoint 4D-Var
• Observation Sensitivity

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Tutorial 10: Setting up the impact/sensitivity functional, build script, cpp options and s4dvar.in (Moore, 45 mins)

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Run Exercise 6 - Observation impact calculations (I4D-Var, R4D-Var and 4D-PSAS) (PDF)

• computation of the impact of the observations on the 4D-Var increments in CCS transport.

Tutorial 11: Discussion of exercise 6. (Moore, 30 mins) Run Exercise 7 - Observation sensitivity calculation (R4D-Var and 4D-PSAS) (PDF)

• computation of the sensitivity of the 4D-Var increments in CCS transport to changes in the observations or observation array.

Tutorial 12: Discussion of exercise 7. (Moore, 30 mins) Tutorial 13: Building your observation files. (Arango & Powell, 60 mins)

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Homework 3: Build observation file for user model configuration.

Tutorial 15: Configuring I4D-Var for your model (Various, 60 mins)

• (ini file, don't use restart files, etc)

• Discussion of results.

Workshop Adjourns