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Length scales and anisotropyIsabelle Mirouze and NEMOVAR groups members

NEMOVAR Steering Group meeting – 16 January 2012

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Length scales and anisotropy

Zonal length scales estimated from an ensemble (Daget,2008)

degree

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Length scales and anisotropy

Horizontal correlations for SST errors in the AMM7 model (J. While)

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Length scales and anisotropy

Questions:1. How do the length scales vary in space and time?

2. How strong is the anisotropy, in which area?

3. How do the length scales vary according to the resolution of the model?

Issues:• How to estimate length scales and anisotropy• Accounting for static / flow-dependent length scales• Accounting for anisotropy

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Estimate and/or parameterise

Parametrise:• Rossby radius• Depending on T/S gradient • Depending on bathymetry• Depending on the mixed layer depth• …

Estimate from an ensemble of unbalanced errors:• Diagonal and off-diagonal terms of the tensor (Belo

Pereira and Berre, 2006)• Ratio of the length scales (main directions) and

rotation angles (Chorti and Hristopulos, 2008)

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Estimate from an ensemble

ECMWF:• 5 members, 12/1957 to 02/2011, ORCA1, 10-day• Unbalanced part of the errors • Variances for every cycles and every 3 months • Gradient of the unbalanced errors

Met Office:• NMC errors, 01/2007 to 12/2008, ORCA025, 1-day

Options:• Climatologic length scales, ~9500 / ~730 members• Season length scales, ~2400 / ~180 members• Cycle (or other) length scales 5 members

• filtering issues

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Accounting for the estimate

Static isotropic length scales• Climatologic estimate + related normalization factors• Season estimate + related normalization factors

=> PrepIFS / SCS modifications

Flow dependent isotropic length scales• Parameterization• Static estimate + parameterization• Estimate from an ensemble at every cycles (possibly

associated with static estimate)

=> Normalization issue

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Accounting for the estimate

Anisotropy• 1D implicit diffusion model

• Hexad and triad (Purser et al, 2003)• Change of spatial coordinate (Yann Michel)

C = D F F* D*

F is a isotropic correlation model

D is a deformation operator• Full 2D and/or 3D implicit diffusion model

• Issues to handle…

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Suggesting plan

• Stage 1• Estimate climatologic length scales for ORCA1 using

ensemble errors (NMC errors?)

• Stage 2• Estimate climatologic length scales for ORCA025,

AMM7 and regional models using NMC errors• Compare the different resolutions

• Stage 3• Take into account the diagonal elements of the

tensor. What is the impact?