Colombe Siegenthaler - Le Drian

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Presentation transcript:

Colombe Siegenthaler - Le Drian Turbulent vertical diffusion in ECHAM5 (vdiff.f90) Colombe Siegenthaler - Le Drian 21th April 2010 1 1 1 1 1

Layout Importance of turbulence in GCM? Parametrisation of turbulence Coupling to the surface Surface fluxes Brief technical overview Overlook on structure vdiff.f90 Turbulent flow are characterized fluctuating dynamical quantities in space and time in a “disordered” manner (Monin and Yaglon,1973) 2 2 2 2

Turbulence - Principle Turbulence - Principle v=0 _ u _ y laminar turbulent Deviation from the mean can transport matters decomposition with: but: http://ocw.mit.edu/OcwWeb/Civil-and-Environmental-Engineering/1-061Fall-2004/LectureNotes/ 3 3 3

In the atmosphere Tropopause Free troposphere 1-2 km PBL The PBL is the layer close to the surface within which vertical transports by turbulence play dominant roles in the momentum, heat and moisture budget. (ECMWF training course, 'planetary boundary layer', May 2007)

Flux parametrisation - I Governing equations (conservation of momentum, heat, moisture,...) : Parametrisation... Fluxes: are sub-grid scale process, need to be parametrised 'Boundary layer meteorology and Air pollution modelling', M. Rotach, ETH lecture 5

Flux parametrisation - II Very common: analogy with molecular viscosity, diffusion With example: stable condition gives negative flux Simple approach But often fails when large eddies (non-local turbulence) 6

Different parametrisations of K It exists a lot of different parametrisations An introduction to Boundary layer Meteorology, Stull, 1988 7

m states for momentum, h for heat and in ECHAM5..... 1.5 order closure introduction of a TKE equation m states for momentum, h for heat : turbulence kinetic energy (TKE) computed prognostically for each time step : mixing length, depends on the stability, vertical position ~“ measure of the average distance a parcel moves in the mixing process that generates flux” 8

vdiff.f90: Central point Compute : tracers, variance(Tompkins) For Where Differential equation: need boundary conditions → Surface fluxes Cm: drag coefficient Ch: transfert coefficient Lowest model level Surface value → Surface fluxes: tracers emissions

Surface fluxes – momentum diffusion for Richardson number (stability) Roughness length Rougher surface are likely to cause more intense turbulence, which increases drag and transfer rates (Stull, 1988) The roughness length: Land → function of the subgrid-scale orography and vegetation (prescribed in surface initial file), ≤1m Sea → depends on the friction velocity (for waves), ≤ 1.5 10 -2 mm Ice/snow The roughness length: → 1 mm klev

Surface fluxes – heat/moisture diffusion Sensible heat flux Latent heat flux Land Surface energy balance Total surface downward radiation Sea Prescribed SST or coupling with mixed layer ocean or coupled with full ocean model H H Rn LE LE Ts G

Latent heat flux over land → relative humidity at surface (different to 1 only above bare soil) → simulates transpiration of vegetation (different to 1 only above vegetation) vegetation lake snow bare soil One grid box Total latent heat flux is computed as the area weighted average of the four component above

Surface fluxes and vegetation Latent heat flux Interaction with the vegetation: resistance formulation (the big leaf approximation): aerodynamic resistance with canopy resistance stomacal resistance of a single leaf leaf area index klev H LE 'Parameterization of land-surface processes in NWP', G. Basalmo, ECMWF training courses, May 2007.

Technically...the tri-diagonal algorithm Solution: with Method : Discretize Mathematical algorithm (tri-diagonal algorithm) to compute vertical profile of variable after diffusion: loop from top to ground surface values used (computed from surface fluxes) Loop from ground to top of the atmosphere

Surface layer coefficients Computed: Surface layer coefficients Vertical profiles : Wind shear buoyancy Ri mixing length Each time: Loop from top to bottom Ground boundary condition (update surface temperature) Loop back from bottom to top Tri-diagonal algorithm (3x) : TKE (e) u,v qv,ql,qi,s (=cpT+gz), variance, tracers Incrementation Tendencies qv,ql,qi,T, tracers Diagnostics: Surface fluxes (evaporation, latent and sensible heat) 2 meters dew point 10 meters maximum wind, etc

As a conclusion... klev-3/2 klev-1 klev-1/2 klev H LE Ts

Good to know working with vdiff... Each turbulent flux (as well as the TKE) is computed on interface level Interface levels are not numbered the same way as in the rest of the model (beginning from index 0 going to index 31) TKE lower boundary condition depends on the square of the frictional velocity The first level from the ground is assumed to be entirely the surface layer (similarity theory is used) Each coefficient computed for the surface layer is computed 3 times (land, water and ice). A mean using the sea-land mask is sometimes computed afterwards. Tracers are diffused with the same eddy diffusivity as moisture (water vapour is kind of a tracer) 17 17 17 17

Usefull references for vdiff J. P. Schultz et al., 2000: On the Land Surface-Atmosphere Coupling and Its Impact in a Single-Column Atmospheric Model, J. Applied Meteor. → implicit coupling with the surface, tri-diagonal algorithm S. Brinkop and E. Roeckner, 1995: Sensitivity of a general circulation model to parameterizations of cloud-turbulence interactions in the atmospheric boundary layer, Tellus → TKE scheme 18 18 18 18

TKE scheme robust on resolution ? 3 hours simulation of a nocturnal Stratocumulus, idealisation based on ASTEX campaign very high resolution (LES) SCM resolution L31 In the low resolution experiment, the structure of the TKE is not well represented, particularly at the cloud top Lenderink and Holtslag, 1999, ‘Evaluation of the Kinetic Energy Approach for modeling turbulent fluxes in stratocumulus’, Mon. Wea. Rev.) 19