1. Analysis of Parameterization in Single-Column Model
Nicholas Trank
05/22/18

2. Background
SCAMPy uses an eddy-diffusivity mass-flux approach (EDMF) to represent turbulent and convective motions in the atmosphere
Prognostic TKE (turbulent kinetic energy) uses updraft “memory” terms and a systematic derivation of the budget of TKE
can explicitly represent nonlocal updrafts/downdrafts
Single Column Atmospheric Model Python

3. Background Extension of previous EDMF schemes:
Plume formulation includes downdrafts
Plumes are prognostic (explicit time derivatives) to represent life cycle of updrafts/downdrafts
Second-order moments (TKE and scalar variances) are partitioned between plumes and environment
Variable area fractions of updrafts

4. Goal
However, a lot of assumptions are made in using this approach, such as values of scalar coefficients of the eddy-diffusivity equations
Needed to check whether some of the assumptions were supported by LES data

5. Goal
Turbulent fluxes in the environment for an arbitrary conserved variable φ are assumed to be diffusive:
Current simulations set ck = 0.25 based on previous works

6. Goal
To verify the validity of this approximation, LES data was used to separately calculate each component of the equations for two variables:
total humidity qt
liquid water potential temperature θl

7. Environmental TKE from BOMEX
Linearly decreases with increasing height

8. Mixing length is calculated with the environmental TKE and Obukhov length
Approximately constant within the region of interest

9. Qt and θl fluxes calculated with two different methods:
direct calculation of environmental flux
subtract mass-flux au(Φu- Φ0)(wu-w0) contribution from total flux
Direct calculation: qt flux = qt-w correlation – (env qt mean) * (env w mean)

10. Method (2) marginally decreases the counter- gradient flux
Counter-gradient fluxes can be seen from about 500 to 2000 m

11. CK profiles when calculated using qt and θl correlations exhibit wrong sign
Method (2) helps keep the value of cK more constant in the cloud layer, but not 0.25

12. Varying the value of the scalar cutoff threshold (initially 1σ) did shift the plots slightly, but did not remove the counter-gradient fluxes
A larger m-value made the fluxes less counter-gradient up to a certain height
(more area included in environment, but smaller area fraction became limiting factor)

13. Conclusions
Using cK as a constant 0.25 is not supported by LES data, so perhaps a better formulation is needed for how to calculate environmental fluxes
The parameterization still captures many features of shallow cumulus convection
Future work: evaluating accuracy of TKE calculation, perhaps including gravity waves

14. Questions?