Cloud Resolving Models: Their development and their use in parametrization development

1. Cloud Resolving Models:Their development and their use in parametrization development Richard Forbes, forbes@ecmwf.int (with thanks to Adrian Tompkins)

2. Outline • Why were cloud resolving models (CRMs) conceived? • What do they consist of? • How have they developed? • To which purposes have they been applied? • What is their future?

3. E.G: Warner (1952) Limited coverage of a few variables Why were cloud resolving models conceived? • In the early 1960s there were three sources of information concerning cumulus clouds • Direct observations

4. Turner (1963) Realism of laboratory studies? Difficulty of incorporating latent heating effects Why were cloud resolving models conceived? • In the early 1960s there were three sources of information concerning cumulus clouds • Direct observations • Laboratory Studies

5. Why were cloud resolving models conceived? • In the early 1960s there were three sources of information concerning cumulus clouds • Direct observations • Laboratory Studies • Theoretical Studies Linear perturbation theories. Quickly becomes difficult to obtain analytical solutions when attempting to increase realism of the model.

6. Why were cloud resolving models conceived? • Obvious complementary role for Numerical simulation of convective clouds • Numerical integration of complete equation set • Allowing more complete view of ‘simulated’ convection • In the early 1960s there were three sources of information concerning cumulus clouds • Direct observations • Laboratory Studies • Theoretical Studies

7. Outline • Why were cloud resolving models conceived? • What do they consist of ?

8. GCM Grid cell ~100km What is a CRM?The concept GCM grid too coarse to resolve convection - Convective motions must be parametrized In a cloud resolving model, the momentum equations are solved on a finer mesh, so that the dynamic motions of convection are explicitly represented. But, with current computers this can only be accomplished on limited area domains, not globally - yet!

9. IR SW dynamics microphysics turbulence surface fluxes What is a CRM?The physics radiation 1. Momentum equations 2. Turbulence Scheme 3. Microphysics 4. Radiation? 5. Surface Fluxes

10. 4 1 5 3 2 What is a CRM?The Issues 1. RESOLUTION: Dependent on application. 2. DOMAIN SIZE: Purpose of simulation. 3. LARGE-SCALE FLOW? Reproduction of observations? Lateral BCs. 4. DIMENSIONALITY: 2 or 3 dimensional dynamics? 5. TIME: Length of integration.

11. W Lateral Boundary Conditions Early models used impenetrable Lateral Boundary Conditions LCloud development near boundaries affected by their presence No longer in use Periodic Boundary Conditions JEasy to implement JModel boundaries are ‘invisible’ LNo mean ascent is allowable (W=0) Open Boundary Conditions JMean vertical motion is unconstrained LVery difficult to avoid all wave reflection at boundaries LDifficult to implement, also need to specify BCs

12. 1. Deep convective updraughts ~30 minutes 3. O(10km) 2. Turbulent Eddies 3. Anvil cloud associated with one event 2. O(100m) 1. O(1km) 4. Mesoscale convective systems, Squall lines, organised convection 4. O(1000km) days-weeks Spatial and Temporal Scales?

13. What do they consist of ? SUBGRID-SCALE TURBULENCE MICROPHYSICS (ice and liquid phases) RADIATION (sometimes - Expensive!) DYNAMICAL CORE Open or periodic Lateral BCs Lower boundary surface fluxes Upper boundary Newtonian damping (to prevent wave reflection) BOUNDARY CONDITIONS

14. Prognostic equations for u,v,w,q,rv,(p) affected by, advection, turbulence, microphysics, radiation, surface fluxes... DYNAMICAL CORE Prognostic equations for bulk water categories: rain, liquid cloud, ice, snow, graupel… sometimes double moment schemes or bin models (number concentrations). HIGHLY UNCERTAIN!!! MICROPHYSICS (ice and liquid phases) Attempt to parametrizeflux of prognostic quantities due to unresolved eddies Most models use 1 or 1.5 order schemes ALSO UNCERTAIN!!! SUBGRID-SCALE TURBULENCE What do they consist of ?

15. Basic Equations • Continuity: This is known as the anelastic approximation, where horizontal and temporal density variations are neglected in the equation of continuity. Horizontal pressure adjustments are considered to be instantaneous. This equation thus becomes a diagnostic relationship. This excludes sound waves from the equation solution, which are not relevant for atmospheric motions, and would require small timesteps for numerical stability. Based on Batchelor QJRMS (1953) and Ogura and Phillips JAS (1962) Note: Although the analastic approximation is common, some CRMs use a fully elastic equation set, with a full or simplified prognostic continuity equation. See for example, Klemp and Wilhelmson JAS (1978), Held et al. JAS (1993). Reference: Emanuel (1994), Atmospheric Convection

16. Basic Equations DYNAMICAL CORE Pressure Gradient • Momentum: Coriolis Diabatic terms (e.g. turbulence) Mixing ratio of vapour and condensate variables Buoyancy Where: Overbar = mean state Since cloud models are usually applied to domains that are small compared to the radius of the earth it is usual to work in a Cartesian co-ordinate system The Coriolis parameter if applied, is held constant, since its variation across the domain is limited

17. Basic Equations • Thermodynamic: • Diabatic processes: • Radiation • Diffusion • Microphysics (Latent heating) Equation of State: Moisture: Microphysics terms Condensation Evaporation

18. SUBGRID-SCALE TURBULENCE All scales of motion present in turbulent flow. Smallest scales can not be represented by model grid - must be parameterised. Assume that smallest eddies obey statistical laws such that their effects can be described in terms of the “large-scale” resolved variables. Progress is made by considering flow, u, to consist of a resolved component, plus a local unresolved perturbation: Doing this, eddy correlation terms are obtained: e.g.

19. SUBGRID-SCALE TURBULENCE Many models used “First order closure” (Smagorinsky, MWR 1963) Make analogy between molecular diffusion: and likewise for other variables: v,r, etc… • K are the coefficients of eddy diffusivity • K set to a constant in early models • Improvements can be made by relating K to an eddy length-scale l and the wind shear. Reference Cotton and Anthes, 1989 Storm and Cloud Dynamics Dimensionless Constant = 0.02 -0.1

20. SUBGRID-SCALE TURBULENCE Length scale of turbulence related to grid-length Further refinement is to multiply by a stability function based on the Richardson number: Ri. In this way, turbulence is enhanced if the air is locally unstable to lifting, and suppressed by stable temperature stratification First order schemes still in use (e.g. U.K. Met Office LEM) although many current CRMs use a “One and a half Order Closure” - In these, a prognostic equation is introduced for the turbulence kinetic energy (TKE), which can then be used to diagnose the turbulent fluxes of other quantities. Note: Krueger,JAS 1988, uses a more complex third order scheme Reference: Stull(1988), An Introduction to Boundary Layer Meteorology See Boundary Layer Course for more details!

21. Microphysics • The condensation of water vapour into small cloud droplets and their re-evaporation can be accurately related to the thermodynamical state of the air. • However, the processes of precipitation formation, its fall and re-evaporation, and also all processes involving the ice phase (e.g. ice cloud, snow, hail) are: • Not completely understood • Operate on scales smaller than the model grid • Therefore parameterisation is difficult but important

22. qtotal qrain Warm - Bulk qvap qrain qliq qsnow qgraup qice Ice - Bulk Ice - Bin resolving Different drop size bins From Dare 2004, microphysical scheme at BMRC Microphysics Different approaches to microphysical parameterization. “Bulk” single-moment, double-moment, bin resolving.

23. Microphysics - numerics Often processes are considered to be resolved by the O(1-10s) timesteps used in CRMs, and therefore a simple explicit solution is used. If sinks result in a negative mass, some models reset to zero (i.e. not conserving). Not many papers mention numerics!

24. Outline • Why were cloud resolving models conceived? • What do they consist of? • How have they developed?

25. 3km Warm air bubble 3km 100m HISTORY:1960s • One of the first attempts to numerically model moist convection made by Ogura JAS (1963) • Same basic equation set, neglecting: • Diffusion - Radiation - Coriolis Force • Reversible ascent (no rain production) • Axisymmetric model domain • 3km by 3km • 100m resolution • 6 second timestep

26. Axi-symmetric Slab Symmetric r z z x Possible 2D domain configurations Motions function of r and z + Pseudo-”3D” motions (subsidence) - No wind shear possible - Difficult to represent cloud ensembles • Use continued mainly in hurricane modelling Motions functions of x and z + Can represent ensembles of clouds - Lack of third dimension in motions - Artificially changes separation scale • Still much used to date For reference see Soong and Ogura JAS (1973)

27. Ogura 1963 7 Minutes 14 Minutes Cloud reaches domain top by 14 Minutes Cloud occupies significant proportion of model domain Liquid Cloud

28. History:

29. Outline • Why were cloud resolving models conceived? • What do they consist of? • How have they developed? • To which purposes have they been applied?

30. Use of CRMs • 1990s really saw an expansion in the way in which CRMs have been used: • Long term statistical equilibrium runs. • Investigating specific process interactions. • Testing assumptions of cumulus parametrizationschemes. • Developing aspects of parametrizations. • Long term simulation of observed systems. • All of the above play a role in the use of CRMs to develop parametrization schemes

31. Radn cooling = = convective heating surface rain = moisture fluxes Uses: Radiative-Convective equilibrium experiments Long term integrations until fields reach equilibrium • Sample convective statistics of equilibrium, and their sensitivity to external boundary conditions • e.g Sea surface temperature • Also allows one to examine process interactions in simplified framework • Computationally expensive since equilibrium requires many weeks of simulation to achieve equilibrium • 2D: Asai J. Met. Soc. Japan (1988), Held et al. JAS (1993), Sui et al. JAS (1994), Grabowski et al. QJRMS (1996), 3D: Tompkins QJRMS (1998), J. Clim. (1999)

32. USE CRM TO INVESTIGATE A CERTAIN PROCESS THAT IS PERHAPS DIFFICULT TO EXAMINE IN OBSERVATIONS UNDERSTANDING THIS PROCESS ALLOWS AN ATTEMPT TO INCLUDE OR REPRESENT IT IN PARAMETRIZATION SCHEMES Uses: Investigating specific process interactions • Large scale organisation: • Gravity Waves: Oouchi, J. Met. Soc. Jap (1999) • Water Vapour: Tompkins, JAS, (2001) • Cloud-radiative interactions: • Tao et al. JAS (1996) • Convective triggering in squall lines: • Fovell and Tan MWR (1998)

33. CRM – Large Scale Forcing • CRMs respond to the imposed “large-scale forcing” • Relies on argument of scale separation (as do most convective parametrization schemes) • Care must be taken in calculating large-scale forcing from observations. With periodic BCs must have zero mean vertical velocity. Normal to apply terms: W CRM domain

34. Example: 350m resolution 3D CRM simulation used in a variety of parametrization ways Animation of convective temperature perturbations in a periodic CRM Used to understand coldpool triggering Used to set closure parameters for a simplified cloud model Tompkins JAS 2001 Di Giuseppe & Tompkins JAS 2003 Used as a cloud-field proxy to develop parametrization to correct radiative geometrical biases Used to justify PDF decision in cloud scheme of ECHAM5 Tompkins JAS 2002 90 km Di Giuseppe & Tompkins JGR 2003, JAS2005 Tompkins & di Giuseppe 2006

35. Uses: Testing Cumulus Parametrization schemes • Parametrizations contain representations of many terms difficult to measure in observations • e.g. Vertical distribution of convective mass fluxes for mass-flux schemes • Assume that despite uncertain parametrizations(e.g. microphysics, turbulence), CRMs can give a reasonable estimate of these terms. • Gregory and Miller QJRMS (1989) is a classic example of this, where a 2D CRM is used to derive all the individual components of the heat and moisture budgets, and to assess approximations made in convective parametrization schemes.

36. Updraught, Downdraught, non-convective and net cloud mass fluxes Gregory and Miller QJRMS 1989 They compared these profiles to the profiles assumed in mass flux parameterization schemes - concluded that the downdraught entraining plume model was a good one for example.

37. CC CC cloud cover relative humidity cloud mixing ratio Uses: Developing aspects of parametrization schemes • The information can be used to derive statistics for use in parametrizationschemes • E.g. Xu and Randall, JAS (1996) used CRM to derive a diagnostic cloud cover parameterisation where:

38. CRMs OBSERVATIONS Uses: Developing Parametrization Schemes PARAMETRIZATION GCMs - SCMs Validation (and development) Validation (and development) Validation (and development) Provide extra quantities not available from data

39. OBSERVATIONS Validation CRMs For example, Grabowski (1998) JAS performed week-long simulations of convection during GATE, in 3D with a 400 by 400 km 3D domain. Simulation Observations Simulation All types of convection developed in response to applied forcing - Could be considered a successful validation exercise?

40. Use observations to evaluate parameterizations of subgrid-scale processes in a CRM Step 1 Step 2 Evaluate CRM results against observational datasets Use CRM to simulate precipitating cloud systems forced by large-scale observations Step 3 Step 4 Evaluate and improve SCMs by comparing to observations and CRM diagnostics PARAMETERISATION GCMS - SCMS GCSS - GEWEX Cloud System Study(Moncrieff et al. Bull. AMS 97) CRMs OBSERVATIONS

41. GCSS: Validation of CRMsRedelsperger et al QJRMS 2000SQUALL LINE SIMULATIONS Simulations from different models (total hydrometeor content) Observations - Radar Open BCs Periodic BCs Open BCs Open BCs Conclude that only 3D models with ice and open BCs reproduce structure well

42. CRM GCSS: Comparison of many SCMs with a CRMBechtold et al QJRMS 2000 SQUALL LINE SIMULATIONS

43. Issues of this approach Confidence is gained in the ability of the SCMs and CRMs to simulate the observed systems Sensitivity tests can show which physics is central for a reasonable simulation of the system… But… Is the observational dataset representative? What constitutes a good or bad simulation? Which variables are important and what is an acceptable error? Given the model differences, how can we turn this knowledge into improvements in the parameterization of convection? Is an agreement between the models a sign of a good simulation, or simply that they use similar assumptions? (Good example: microphysics)

44. Outline • Why were cloud resolving models conceived? • What do they consist of? • How have they developed? • To which purposes have they been applied? • What is their future?

45. Future - Issues • Fundamental issues remain unresolved: • Resolution? • At 1 or 2 km horizontal resolution much of the turbulent mixing is not resolved, but represented by the turbulence scheme. • CRM ‘solutions’ have often not converged with increasing horizontal resolution at 100m. Need higher resolutions? • Dimensionality • 2D slab symmetric models are still widely used, despite contentions to their ‘numerical cheapness’. • Representation of microphysics? • Representing interaction with large scale dynamics? • Re-emergence of open BCs?

46. Cloud Resolving Convective Parametrization 2D CRMs in a global model • Grabowski and Smolarkiewicz, Physica D 1999. Places a small 2D CRM (roughly 200km, simple microphysics, no turbulence) in every grid-point of the global model • Still based on scale separation and non-communication between grid-points • Advantages and Disadvantages? From Khairoutdinov, illustrating multimodelling framework developed at CSU

47. Cloud Resolving Convective Parametrization 2D CRMs in a global model CAM CRCP OBS Improves diurnal cycle and tropical variability?

48. Convective-scale Limited Area NWPExample of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005

49. Convective-scale Limited Area NWPExample of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, 13 UTC Model simulated OLR and surface rain rate Meteosat low resolution infra-red and radar-derived surface rain rate

50. Convective-scale Limited Area NWPExample of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, 13 UTC MODIS 13:10 UTC Model simulated OLR and surface rain rate MODIS high resolution visible image