Roel Neggers 1 , Philipp Griewank 1 , Thijs Heus 2

1. Using LES as a non-hydrostatic testing ground for developing scale-adaptive and stochastic parameterizations for the grey zone • Roel Neggers1, Philipp Griewank1, Thijs Heus2 • 1 Research group on Integrated Scale-Adaptive Parameterization and Evaluation (InScAPE) Institute of Geophysics and Meteorology, University of Cologne (IGMK), Germany 2 Cleveland State University, Cleveland, Ohio, USA This research is supported by the U.S. Department of Energy’s Atmospheric System Research, an Office of Science, Office of Biological and Environmental Research program, under Grant DE-SC0017999

2. Towards high resolution in NWP and climate simulations The grey zone problem: What to do with convective parameterizations? One solution is to introduce scale-adaptivity and stochasticity This is a new game, and we need new methods to make progress Question: How can we best develop, test and evaluate these schemes? Two possible approaches: Top-down: Adopt existing GCMs and increase resolution Bottom-up: Adopt LES models and decrease resolution

3. Using an LES code as a non-hydrostatic testing ground for convective parameterizations in the grey zone The idea: • Implement new convection schemes as subgrid schemes in an LES code • Test their scale-adaptivity and stochasticity by performing simulations at a range of resolutions spanning the grey zone • GZM: Grey Zone Model • Advantages: • Simple configuration (periodic boundaries, homogeneous forcing, etc) • LES is already fully non-hydrostatic • Resolved scales can naturally respond to parameterized physics: •  Interactive cloud-circulation coupling • If a convection scheme is not properly scale-adaptive, you will know very quickly! • Simple diffusive LES-type subgrid schemes can form the basis of next-generation convection schemes

4. Simulation modes: FCMs and MCMs Few Column Model (FCM) Multi Column Model (MCM) resolved circulation 100 m - 100 km : geopotential height (resolved)

5. Illustration with ED(MF)n Neggers et al. (JAMES, 2015) Spectral EDMF: A multiple mass flux scheme formulated in terms of discretized size distributions • In a nutshell: • Plume macrophysicalproperties are assumed to be size-dependent • Associated size densities are discretized into a limited number of bins • Profiles of each bin are independently estimated using a rising plume model • Bulk properties like cloud fraction and mass flux transport thus become “resolved”: They can simply be diagnosed at every height from the reconstructed spectrum / PDF • Indirect size-interactions can take place through the mean state • The number density still requires closure

6. Implementation of ED(MF)n into DALES Work started by ThijsHeus when at MPI Hamburg Continued at InScAPE (University of Cologne): PhD work of MarenBrast Current status: • Implementation completed, ED(MF)nis now a subgrid option in DALES • DALES can now be run as a GZM at large grid spacings (~100km) and long time-steps (~300 to 900 sec) • Testing for prototype cases is completed • Optimization of ED(MF)n in progress, using LASSO LES and ARM SGP data •  See Philipp Griewank’s poster on Wednesday

7. Testing the scheme in FCM mode 8x8 microgrid, discretized at x=y=100 km, z=40 mand t=300 s Prescribed plume number density (single powerlaw up to 1000m) Results for classic prototype cumulus cases: RICO ARM SGP Note: These are results from a single grid column

8. New prototype cases: GASS-DCP GoAmazon 1 LASSO 11 June 2016 Indirect interactionss between plumes of different sizes are responsible for equilibration & smooth responses to large-scale forcings(Neggers et al, JAMES 2015)

9. Grey zone test I FOOKIE: Filter On/Off Kumulus Impact Experiment Filter out all EDMF plumes larger than the grid spacing

10. Subgrid (EDMF) vs resolved transport across a range of resolutions: Total Subgrid Resolved dx [m] Brast, Schemann and Neggers, 2018: Investigating the scale-adaptivity of a size-filtered mass flux parameterization in the grey zone of shallow cumulus convection. J. Atmos. Sci., doi:10.1175/JAS-D-17-0231.1

11. First signs of true scale-adaptivity: Transport and clouds are (more or less) conserved across the grey zone Subgrid Resolved Total dx [m]

12. The Honnert / Dorrestijn metric for scale-adaptivity is reproduced (solid line): Spread in EDMF flux across grid-columns (dashed line) Low spread in subgrid flux at large grid-spacings: ED(MF)n is more or less doing the same thing in every grid column

13. With decreasing resolution ED(MF)n starts to “fill in” the power spectrum: Reference high-res LES Resolved ED(MF)n Collapse of the resolved scales! Are we missing variability?

14. A simple stochastic plume number generator The number of plumes of size in a domain of horizontal size x is estimated using Lotka-Volterra equations: Inspired by Nober and Graf (ACP, 2005) Death rate: Birth rate: (infinite domain) : plume life-cycle timescales : nearest neighbour spacing between clouds of equal size No interaction matrix (yet)

15. Offline test: Episodic behavior Number of plumes of size 50m for various domain sizes: Plume birth events get much rarer at smaller

16. Grey zone test II STOOKIE: Stochastics On/Off Kumulus Impact Experiment The stochastic number generator is implemented into DALES-ED(MF)n Results from three 8x8 RICO runs at various are compared Note: The real gridspacing =10 km in all experiments km km km Shaded: Total mass flux [m/s] by all condensed plumes in the spectrum, at a single gridpoint

17. A closer look at the largest plume in the spectrum ( m): km km km Shaded: Relative area fraction [%] covered by the largest plumes in the spectrum, at a single gridpoint The increasing variability reflects that the population becomes subsampled at smaller The largest plumes feel this first, given their large neighbor spacing. They then only rarely occur but can occupy a relatively large area of the gridbox.

18. Top-down view of the variability on the () grid in the number of largest plumes: km km km Shaded: Relative area fraction [%] covered by the largest plumes in the spectrum, at a single gridpoint

19. A closer look at the number density: • The typical powerlaw shape of the number density is reproduced • The number of plumes of a given size becomes highly variable when approaches the nearest-neighbor spacing km km km

20. How does the variability in plume number for a given size depend on ?

21. This powerlaw scaling in the variability in plume number matches results of recent subdomain analyses of large-domain LES fields and satellite images: LES RICO (51.2x51.2km, x=25 m) Cloud mask (black) Normalized standard deviation Subdomain size / cloud size Neggers, Griewank and Heus, 2019: Powerlaw scaling in the internal variability of cumulus cloud size distributions due to subsampling and spatial organization. J. Atmos. Sci., https://doi.org/10.1175/JAS-D-18-0194.1

22. The resolved “circulation” shows signs of responding to the subgrid stochastic noise:

23. Summary and conclusions LES codes can be a useful testing ground for scale-adaptive and stochastic parameterizations This GZM-approach was illustrated using grey zone experiments with ED(MF)n implemented in DALES Size filtering in discretized spectral models introduces true scale-adaptivity The new stochastic plume number generator reproduces powerlaw scaling behavior as diagnosed in LES and as observed in nature. This concerns the shape of the number density, but also its internal variability. In the grey zone the stochastic generator increases variability in convective transport on the grid. Responses in the resolved fields are identified.

24. Outlook • Experiments with , check out power spectra, learn how the resolved circulation responds to subgridstochastics • COOKIE tests: Make subgrid EDMF clouds visible for radiative transfer • Solve problems with LES microphysics at large time-steps • Optimization of ED(MF)n using ARM data & LASSO simulations • Represent direct size-interactions in the LV equations • Use MCM mode to study cloud-circulation coupling in the Trades  See Philipp Griewank’s poster on Wednesday

25. Closure of the birth rate Number of expected births of clouds of size : Number of subdomains:  Chance that a cloud is born in a single subdomain: Discretized birth rate, summed over N subdomains: where is a uniform random number between 0 and 1

26. Using MODIS band 1 reflectance (x=250m) in the Atlantic Trades (EUREC4A area): Deviation from -1 exponent reflects spatial organization  A new metric Borg This expresses that small clouds start to “live” on top of larger-scale thermo-dynamic structures (cold pools), favouring or inhibiting their formation.