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

2. 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

3. Turbulence - Principle Turbulence - Principle
v=0 _ u _ y
laminar
turbulent
Deviation from the mean can transport matters
decomposition
with:
but: 3 3 3

4. 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)

5. 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

6. 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

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

8. 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

9. 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

10. 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), ≤ mm
Ice/snow The roughness length:
→ 1 mm
klev

11. 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

12. 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

13. 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.

14. 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

15. 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

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

17. 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

18. 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

19. 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