How to represent subgrid atmospheric processes in Climate |Models

1. How to represent subgrid atmospheric processes in Climate |Models A. Pier Siebesma siebesma@knmi.nl Faculty for Applied Sciences Climate Research Regional Climate Division Multiscale Physics

2. Landsat 65km LES 10km ~1mm-100mm ~mm ~1m The Climate System: A Multiscale Challenge: Earth 107 m Courtesy: Harm Jonker, TU Delft

3. No single model can encompass all relevant processes mm 10 m 100 m 1 km 10 km 100 km 1000 km 10000 km Cloud microphysics  turbulence Cumulus clouds Cumulonimbus clouds Mesoscale Convective systems Extratropical Cyclones Planetary waves DNS Subgrid Large Eddy Simulation (LES) Model Cloud System Resolving Model (CSRM) Numerical Weather Prediction (NWP) Model Global Climate Model

4. Architecture of a Global Climate Model

5. Unresolved (subgrid) Processes in Climate Models Source: ECMWF Model documentation

6. Climate Model Sensistivity estimates of GCM’s participating in IPCC AR4 Source: IPCC Chapter 8 2007 • Spread in climate sensitivity: • concern for many aspects of climate change research, assesment of climate extremes, design of mitigation scenarios. • What is the origin of this spread? • Radiative Forcing, Climate feedbacks,

7. Relative Contributions to the uncertainty in climate feedbacks Cloud feedback Surface albedo feedback Water vapor feedback Radiative effects only Source: Dufresne & Bony, Journal of Climate 2008 Uncertainty in climate sensitivity mainly due to (low) cloud feedbacks

8. Governing Equations for incompressible flows in the atmosphere Continuity Equation (incompressible) with NS Equations gravity term coriolis term Heat equation Moisture equation Condensed water eq. Gas law

9. Large scale subsidence Vertical turbulent/ convective transport Filtered Equations for the Thermodynamic Variables subgrid resolved Radiative heating Precipitation Net Condensation Rate Large scale advection

10. turbulence Resolved Scales convection clouds radiation ~ 250 km Small scales Large scales Schematic View of how scales are connected in traditional GCM’s Depiction of the interaction between resolved and parameterized unresolved cloud-related processes (convection, turbulence, clouds and radiation) in present-day climate models. (from Siebesma et al, Perturbed Clouds in our climate system MIT) Which are the problems, errors and uncertainties that we have to face with this approach?

11. 1. Inherent lack of understanding of certain physical processes [100,600mm] < 100 mm >800mm • Uncertainties in ice and mixed phase microphysics: • Supersaturation • Liquid vs ice • Habits • Size distribution • Sedimentation • Interaction with radiation No fundamental equations available describing these properties and processes. Source : Andrew Heymsfield

12. 2. Non-linear character of many cloud related processes Example 1: Autoconversion of cloud water to precipitation in warm clouds : Kessler Autoconversion Rate (Kessler 1969) With: ql : cloud liquid water ql : critical threshold H : Heaviside function A : Autoconversion rate Autoconversion rate is a convex function: Larson et al. JAS 2001

13. qsat(T) . (T,qt) qt qt qsat T Example 2: Cloud fraction and Cloud liquid water (Thijs Heus TU Delft/KNMI) LES Cloud fraction: Cloud liquid water:

14. Plane parallel cloud Scu Cloud albedo x a x a(LWP) < a(LWP) Liquid water path (LWP) Example 3: Cloud Albedo Bias Neglecting Cloud inhomogeneity causes a positive bias in the cloud albedo.

15. These biased errors slowly go away when increasing model resolution: • Typically allowed if x < 100m , i,e, at the LES model scale • So for all models operating at a coarser resolution additional information about the underlying Probability Density Function (pdf) is required of temperature, humidity (and vertical velocity). For Example: So if only….. we would know the pdf .

16. turbulence Resolved Scales convection clouds radiation ~ 250 km Small scales Large scales 3. Interactions between the various subgrid processes • Subgridprocesses strongly interact with each other while in (most) GCM’s they only interact indirectly through the mean state leading to inconsistencies and biases.

17. 4. Statistical versus Stochastic Convection • Traditionally (convection) parameterizations are deterministic: • Instantaneous grid-scale flow and mean state is taken as input and convective response is deterministic • One to one correspondency between sub-grid state and resolved state assumed. • Conceptually assumes that spatial average is a good proxy for the ensemble mean. ~500km

18. 4. Statistical versus Stochastic Convection Stochastic Convection That takes into account fluctuations so that the ensemble mean is not satisfied each timestep but more in a canonical sense Statistical ensemble mean Deterministic convection parameterization Microcanonical limit Convection Explicitly resolved 100m 1km 100km 1000km resolution

19. New Pathways

20. turbulence convection clouds radiation Resolved Scales 3.5 km Pathway 1: Global Cloud Resolving Modelling (Brute Force) NICAM simulation: MJO DEC2006 Experiment 3.5km run: 7 days from 25 Dec 2006 • Short timeslices • Testbed for interactions: • deep convection and the large scale • Boundary clouds, turbulence, radiation still unresolved MTSAT-1R NICAM 3.5km Miura et al. (2007, Science)

21. Resolved Scales (b) turbulence 2D CRM convection 5 km 250 km clouds radiation Pathway 2: Superparameterization

22. Pathway 2: Superparameterization What do we get? • Explicit deep convection • Explicit fractional cloudiness • Explicit cloud overlap and possible 3d cloud effects • Convectively generated gravity waves But….. A GCM using a super-parameterization is three orders of magnitude more expensive than a GCM that uses conventional parameterizations. On the other hand super-parameterizations provide a way to utilize more processors for a given GCM resolution Boundary Layer Clouds, Microphysics and Turbulence still needs to be parameterized

23. Pathway 3: Consistent pdf based parameterizations Remarks: turbulence Resolved Scales convection Resolved Scales clouds radiation Large scales Unresolved scales ~100 km Increase consistency between the parameterizations! How? Let’s have a closer look at the subgrid variability and the way this is treated in tradiational parameterizations

24. qsat(T) . qt (T,qt) T Statistical Cloud Schemes (1): • Estimate ac and ql using the subgrid variability:

25. Statistical Cloud Schemes (2): Convenient to introduce: “The distance to the saturation curve” Normalise s by its variance: So that ac and ql can be written in a single variable PDF: What to choose for G(t) ???

26. Statistical Cloud Schemes (3): Gaussian Case: Cloud cover and liquid water function of only one variable!!!! Sommeria and Deardorf (JAS,1976)

27. Verification (with LES) Cloud cover Bechtold and Cuijpers JAS 1995 Bechtold and Siebesma JAS 1999

28. Verification (with Observations) Wood and Field (unpublished)

29. Correct limit: if and the scheme converges to the all-or-nothing limit • Parameterization problem reduced to finding the subgrid variability, i.e. finding . Remarks:

30. Convective transport in Shallow Cumulus: Characteristics Courtesy Bjorn Stevens LES Heus TU Delft

31. Horizontal Variability Upward transport by moist buoyant cumulus cores Typical Mean Profiles

32. less distinct updrafts in subcloud layer

33. a a a Strong bimodal character of joint pdf has inspired the design of mass flux parameterizations of turbulent flux in Large scale models (Betts 1973, Arakawa& Schubert 1974, Tiedtke 1988) wc

34. e d M How to estimate updraft fields and mass flux? Betts 1974 JAS Arakawa&Schubert 1974 JAS Tiedtke 1988 MWR Gregory & Rowntree 1990 MWR Kain & Fritsch 1990 JAS And many more…….. The old working horse: Entraining plume model: Plus boundary conditions at cloud base.

35. Standard transport parameterization approach: This unwanted situation can lead to: • Double counting of processes • Inconsistencies • Problems with transitions between different regimes: • dry pbl  shallow cu • scu  shallow cu • shallow cu deep cu

36. Intermezzo (2) Remarks: turbulence Resolved Scales convection Resolved Scales clouds radiation Large scales Unresolved scales ~100 km Increase consistency between the parameterizations! How?

37. zinv Eddy-Diffusivity/Mass Flux approach : a way out? • Nonlocal (Skewed) transport through strong updrafts in clear and cloudy boundary layer by advective Mass Flux(MF) approach. • Remaining (Gaussian) transport done by an Eddy Diffusivity (ED) approach. Advantages : • One updraft model for : dry convective BL, subcloud layer, cloud layer. • No trigger function for moist convection needed • No switching required between moist and dry convection needed

38. LeMone & Pennell (1976, MWR) Cumulus clouds are the condensed, visible parts of updrafts that are deeply rooted in the subcloud mixed layer (ML)

39. The (simplest) Mathematical Framework : zinv

40. Cumulus Topped Boundary Layer Neggers, Kohler & Beljaars accepted for JAS 2009 alternatives: Lappen and Randall JAS 2001 Rio and Hourdin JAS 2008 Figure courtesy of Martin Koehler Moist updraft Dry updraft K diffusion Flexible moist area fraction Top 10 % of updrafts that is explicitly modelled

41. Assume a Gaussian joint PDF(ql,qt,w) shape for the cloudy updraft. • Mean and width determined by the multiple updrafts • Determine everything consistently from this joint PDF An reconstruct the flux: • Remarks: • No closure at cloud base • No detrainment parameterization • Pdf can be used for cloud scheme and radiation

42. Convection and turbulence parameterization give estimate of ss radiation scheme : Cloud scheme : • Subgrid variability (at least the 2nd moment) for the thermodynamic variables needs to be taken into acount in any GCM for parameterizations of convection, clouds and radiation in a consistent way. • At present this has not be accomplished in any GCM.

43. But… Many open problems remain Conceptually on process basis • Convective Momentum Transport • Influence of Aerosols/Precipitation on the (thermo)dynamics of Scu and Cu • Mesoscale structures in Scu and Shallow Cu • Transition from shallow to deep convection (deep convective diurnal cycle in tropics) Parameterization • Vertical velocity in convective clouds • Convection on the 1km~10km scale. (stochastic convection) • Microphysicis (precip) • Transition regimes. Climate Determine and understand the processes that are responsable for the uncertainty in cloud-climate feedback.

44. A slow, but rewarding Working Strategy See http://www.gewex.org/gcss.html Large Eddy Simulation (LES) Models Cloud Resolving Models (CRM) Single Column Model Versions of Climate Models 3d-Climate Models NWP’s Global observational Data sets Observations from Field Campaigns Development Testing Evaluation

45. SCM LES Tested for a large number of GCSS Cases……………….. l qsat qt Cloud fraction Condensate

46. A slow, but rewarding Working Strategy See http://www.gewex.org/gcss.html Large Eddy Simulation (LES) Models Cloud Resolving Models (CRM) Single Column Model Versions of Climate Models 3d-Climate Models NWP’s Global observational Data sets Observations from Field Campaigns Development Testing Evaluation