Using high-res simulations to optimise EDMF cloud-parameterization schemesAndrew Williams1, Yair Cohen2 and Tapio Schneider2,3

1. University of Oxford, UK 2. California Institute of Technology, Pasadena, CA, US 3. Jet Propulsion Lab, Pasadena, CA, US

EDMF parameterization

•Unified representation of turbulence andconvection in one SGS model by decomposing thegrid box of a global climate model into two areafractions:

Figure 1: The problem of convective parameterization in globalmodels, with a EDMF decomposition of the flow and a bi-modaldistribution as typically found in LES cloud simulations (Fig. 3).

The EDMF assumption

•The EDMF model combines turbulence andconvection in a single SGS model, neglecting thecontribution from updraft variance (see Eq. 1).

•Requiring the first term in Eq. 1 to be negligibletranslates to an upper bound on individualupdraft variance, given by Eq. 2.

Figure 2: Illustrating the effect of the EDMF assumption on thedistribution obtained by the parameterization.

EDMF equations

Variance of scalar field φ in EDMF scheme - decomposed into updraft/environment components:

< φ′φ′ >︸ ︷︷ ︸grid variable

= aφ′φ′u︸ ︷︷ ︸Neglected

(EDMF assumption)

+(1− a)φ′φ′e + a(1− a)(φu − φe)2 (1)

The maximum variance of individual updrafts can be determined by applying the EDMF assumption toEq. 1.

=⇒ φ′φ′uindividual = (1− a)φ′φ′e + a(1− a)(φu − φe)2

number of updrafts(2)

Research question

How many individual updrafts - each modelled asGaussians with a standard deviation σ2 = φ′φ′,Eq.2) - is optimal in recreating the updraft distribu-tion from a high-resolution Large-Eddy Simulation(LES)?

Figure 3: Schematic research methodology.

Methods

•Using passive tracers we identified coherentupdrafts in high resolution LES simulation ofconvection. We used the PyCLES model (PythonCloud LES: Pressel et al., 2015), which is anatmospheric large eddy simulation model able tosimulate boundary layer turbulence, shallow anddeep convection.

•The scikit-learn Python package was used toperform Kernel Density Estimation (KDE) inorder to fit a number of individual updrafts to theupdraft distribution diagnosed from LES.

•The Kolmolgorov-Smirnov error between theconstructed updraft distribution and the updraftdistribution from LES was minimized to obtainthe optimal number of updrafts Noptimal. Thiswas done for different convective cases anddomain sizes (i.e. GCM resolutions).

Results

Figure 4: K-S error as a function of the number of updrafts usedin the fitting. Results for RICO, half-domain. *

Convective case Domain size Noptimal

Rico * Half 5Rico Norm 7Rico Double 9

Bomex Half 3Bomex Norm 7Bomex Double 9

Figure 5: Table of Noptimal for various convective cases anddomain sizes (relative to some default domain, ‘Norm’). RICO:Rain In Cumulus over the Ocean. BOMEX: Non-precipitatingshallow cumulus over ocean.

Conclusion

•We found that in all cases tested there exists anNoptimal which minimizes theKolmolgorov-Smirnov error between LES andKDE distributions.

•Noptimal was found to vary strongly with domainsize (i.e. GCM resolution), but weakly betweenthe two convective cases tested (with/withoutprecipitation). See Table 5.

•The dependence on domain size is reasonable, asLES simulations show updraft variance increasingwith domain size, thus more individual updraftsare required to capture this.

•The lack of dependence of Noptimal on convectivecase is not yet understood and requires furtherinvestigation.

•Further research could extend these results bytesting the effect of multiple updrafts in anoperational EDMF scheme.

References

[1] Schneider, T. et al. (2017): Climate goals and computingthe future of clouds. Nature Climate Change, 7.

[2] Tan, Z.et al. (2018): An extended eddy-diffusivitymass-flux scheme for unified representation of subgrid-scaleturbulence and convection. Journal of Advances inModeling Earth Systems, 10, 770-800.

[3] Pressel, K. et al. (2015): Large-eddy simulation in ananelastic framework with closed water and entropybalances. Journal of Advances in Modeling EarthSystems, 7, 1425-1456.

Acknowledgements

Thanks is due to the Caltech Summer Undergraduate ResearchFellowship (SURF) for supporting this work financially and toYair Cohen and Tapio Schneider for their advice and guidancethroughout the project.