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

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

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

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

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

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

Environmental TKE from BOMEX Linearly decreases with increasing height

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

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)

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

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

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)

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

Questions?