A HYBRID BULK-BIN APPROACH TO MODEL WARM-RAIN PROCESSES

1. A HYBRID BULK-BIN APPROACH TO MODEL WARM-RAIN PROCESSES Wojciech W. Grabowski OdileTouron, Jean-Pierre Pinty, and Jean-Louis Brenguier National Center for Atmospheric Research Boulder, Colorado (at CNRM in Toulouse until October 2009) (paper submitted to JAS)

2. bulk warm-rain microphysics: cloud is always at water saturation; • - bin warm-rain microphysics: cloud droplets are activated and they grow according to the predicted supersaturation.

3. bulk warm-rain microphysics: cloud is always at water saturation; • - bin warm-rain microphysics: cloud droplets are activated and they grow according to the predicted supersaturation. • But supersaturation is really needed only for the activation because the amount of condensate differs insignificantly between bulk and bin models. • So if one applies activation parameterization (and most LES models should), why bother predicting supersaturation?

4. This is starting point for the hybrid bulk-bin approach: we predict spectral evolution of the activation spectrum, adjusting always to water saturation inside the cloud. NB: this approach has already been used in a bin model of Brenguier and Grabowski (JAS 1993) for condensation only…

5. This is starting point for the hybrid bulk-bin approach: we predict spectral evolution of the activation spectrum, adjusting always to water saturation inside the cloud. Bin model: we predict S, then calculate droplet growth/evaporation (change of the spectrum); this gives condensation rate. Hybrid model:we predict condensation rate from saturation adjustment, then calculate evolution of the droplet spectrum.

6. C – condensation rate from saturation adjustment. If evaporation, then it is applied only to cloud droplet part of the spectrum (say, below 40 microns). E – drizzle/rain evaporation rate. Applied only to drizzle/rain part of the spectrum. NOTE: C=0 when E≠0.

7. Q: How to derive spectral change given the known condensation rate?

8. Q: How to derive spectral change given the known condensation rate? A: Through the “bogus supersaturation” approach!

9. Validation in the framework of the adiabatic rising parcel: comparing bin model with the hybrid model – see the paper…

10. Application to the multidimensional framework (condensation only).

11. The key issue: numerical problems near the cloud-environment boundaries Klaassen and Clark JAS 1985 (bulk model) Grabowski JAS 1989 (bin model) Kogan et al. JAS 1995 (bin model) Grabowski and Smolarkiewicz MWR 1990 (bulk model) Stevens et al. MWR 1996 (2-moment scheme) Grabowski and Morrison MWR 2008 (2-moment scheme) 1D advection-condensation problem (Grabowski and Smolarkiewicz MWR 1990)

13. Tests with hybrid bulk-bin scheme

14. quasi-analytic solution

15. quasi-analytic solution

16. iord=2 monotone MPDATA

17. The results are consistent with the view that gridboxes are homogeneous – this results to the “super-adiabatic” growth or cloud droplets. But this is inconsistent with the analytic solution! adiabatic cloud cloud-free Is there any solution to this problem?

18. Homogeneous gridboxes adiabatic cloud cloud-free Heterogeneous gridboxes

19. homogeneous spectral change heterogeneous spectral change (e.g., increasing cloud fraction) A caveat: heterogeneous spectral change should not increase droplet concentration beyond what is allowed by activation.

20. How to decide between homogeneous and heterogeneous spectral change? Using additional model variable: “cloud fraction”, β. (Jarecka et al., JAS 2009, in press)

21. Source/sink : -resets β from 0 to 1 for initial condensation -resets β to 0 for total evaporation - increases/decreases β in partially-cloudy gridboxes: already adjusted bulk cloud water bin cloud water to be adjusted

22. iord=2 monotone MPDATA with homo/hetero logic

23. iord=2 monotone MPDATA with homo/hetero logic

24. It appears that introduction of homogeneous and heterogeneous logic leads to the solution which is consistent with the analytic solution.

25. Example of an application to warm precipitating convection: idealized problem of 2D moist spherical thermal rising from rest, producing cloud water and eventually rain.

26. Results at t=20 min: Cloud water qc Rain water qr Cloud fraction β

27. Drop mass spectra in the center of the domain z=2.5 km (inside cloud) z=2.0 km (outside cloud)

28. Conclusions: A new scheme has been developed based on the observation that supersaturations inside clouds are small and bulk condensation rate provides sufficiently accurate prediction of spectral changes. When condensation first occurs (e.g., near the cloud base), activation parameterization inserts activated droplets near the low end of the spectral representation. Subsequent growth by diffusion of water vapor is represented by shifting the spectrum towards larger sizes so that the spectral changes match the bulk condensation rate. Growth by collision/coalescence leads to formation of drizzle and eventually rain as in the bin scheme. The hybrid bulk-bin approach eliminates the need for supersaturation prediction, which is numerically cumbersome, especially near cloud edges, and typically requires high spatial and temporal resolution (e.g., near the cloud base where droplet activation takes place).

29. Conclusions, cntd: A simple approach is proposed to deal with numerical artifacts near cloud boundaries. The key point is to recognize the need for both homogeneous and heterogeneous advection-condensation processes. Predicting the “cloud fraction” β guides the selection of either homogeneous or heterogeneous numerical representation. Tests in a multidimensional cloud model illustrate consistency of the hybrid bulk-bin approach. Work to include the hybrid scheme into French Meso-NH model is underway…