1. © Crown copyright Met Office Length scales and anisotropy Isabelle Mirouze and NEMOVAR groups members NEMOVAR Steering Group meeting – 16 January 2012

2. © Crown copyright Met Office Length scales and anisotropy Zonal length scales estimated from an ensemble (Daget,2008) degree

3. © Crown copyright Met Office Length scales and anisotropy Horizontal correlations for SST errors in the AMM7 model (J. While)

4. © Crown copyright Met Office 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

5. © Crown copyright Met Office 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)

6. © Crown copyright Met Office 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

7. © Crown copyright Met Office 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

8. © Crown copyright Met Office 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…

9. © Crown copyright Met Office 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?