How to represent subgrid atmospheric processes in Climate |Models Multiscale PhysicsRegional Climate DivisionA. Pier Siebesmasiebesma@knmi.nlFaculty for Applied SciencesClimate Research

The Climate System: A Multiscale Challenge:Earth 107 m Courtesy: Harm Jonker, TU Delft

10 m100 m1 km10 km100 km1000 km10000 kmturbulenceCumuluscloudsCumulonimbuscloudsMesoscale Convective systemsExtratropical CyclonesPlanetary wavesLarge Eddy Simulation (LES) ModelCloud System Resolving Model (CSRM)Numerical Weather Prediction (NWP) ModelGlobal Climate ModelNo single model can encompass all relevant processesDNSmmCloud microphysics

Architecture of a Global Climate Model

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

Climate Model Sensistivity estimates of GCMs participating in IPCC AR4Source: 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,

Relative Contributions to the uncertainty in climate feedbacksSource: Dufresne & Bony, Journal of Climate 2008Radiative effects onlyWater vapor feedbackSurface albedo feedbackCloud feedbackUncertainty in climate sensitivity mainly due to (low) cloud feedbacks

Governing Equations for incompressible flows in the atmosphereContinuity Equation (incompressible)NS EquationsHeat equationMoisture equationGas lawwithgravitytermcoriolistermCondensed water eq.

Large scale advectionNet Condensation RateFiltered Equations for the Thermodynamic VariablesRadiative heatingPrecipitationresolvedsubgrid

Schematic View of how scales are connected in traditional GCMsDepiction 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?

1. Inherent lack of understanding of certain physical processes< 100 mm[100,600mm]>800mmSource : Andrew HeymsfieldUncertainties in ice and mixed phase microphysics:SupersaturationLiquid vs iceHabitsSize distributionSedimentationInteraction with radiation

No fundamental equations available describing these properties and processes.

2. Non-linear character of many cloud related processesWith:ql : cloud liquid waterql : critical thresholdH : Heaviside functionA : Autoconversion rate

: Kessler Autoconversion Rate (Kessler 1969)Example 1: Autoconversion of cloud water to precipitation in warm cloudsAutoconversion rate is a convex function: Larson et al. JAS 2001

Example 2: Cloud fraction and Cloud liquid water(Thijs Heus TU Delft/KNMI) LESCloud fraction:Cloud liquid water:

Neglecting Cloud inhomogeneity causes a positive bias in the cloud albedo.Example 3: Cloud Albedo Bias

These biased errors slowly go away when increasing model resolution:Typically allowed if x < 100m , i,e, at the LES model scaleSo 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 .

3. Interactions between the various subgrid processesSubgrid processes strongly interact with each other while in (most) GCMs they only interact indirectly through the mean state leading to inconsistencies and biases.

4. Statistical versus Stochastic Convection

~500km

Traditionally (convection) parameterizations are deterministic:Instantaneous grid-scale flow and mean state is taken as input and convective response is deterministicOne to one correspondency between sub-grid state and resolved state assumed.Conceptually assumes that spatial average is a good proxy for the ensemble mean.

4. Statistical versus Stochastic Convection

resolution100m1km1000km100kmConvectionExplicitly resolvedStatistical ensemble meanDeterministic convection parameterizationStochastic ConvectionThat takes into account fluctuations so that the ensemble mean is not satisfied each timestep but more in a canonical senseMicrocanonical limit

New Pathways

Pathway 1: Global Cloud Resolving Modelling (Brute Force)NICAM simulation: MJO DEC2006 ExperimentMTSAT-1RNICAM 3.5kmMiura et al. (2007, Science)3.5km run: 7 days from 25 Dec 2006Short timeslicesTestbed for interactions: deep convection and the large scaleBoundary clouds, turbulence, radiation still unresolved

Pathway 2: Superparameterization

Pathway 2: SuperparameterizationWhat do we get?Explicit deep convectionExplicit fractional cloudinessExplicit cloud overlap and possible 3d cloud effectsConvectively generated gravity wavesBut..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

Remarks:Resolved Scalesturbulenceconvectioncloudsradiation~100 kmLarge scalesUnresolved scalesResolved ScalesPathway 3: Consistent pdf based parameterizationsIncrease consistency between the parameterizations!How?Lets have a closer look at the subgrid variability and the way this is treated in tradiational parameterizations

Statistical Cloud Schemes (1):Estimate ac and ql using the subgrid variability:

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

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

Verification (with LES)Cloud coverBechtold and Cuijpers JAS 1995Bechtold and Siebesma JAS 1999

Verification (with Observations)Wood and Field (unpublished)

Remarks:

Convective transport in Shallow Cumulus: Characteristics

Courtesy Bjorn StevensLESHeusTU Delft

Typical Mean Profiles

wcStrong 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)

The old working horse:Entraining plume model:Plus boundary conditionsat cloud base.How to estimate updraft fields and mass flux? Betts 1974 JASArakawa&Schubert 1974 JASTiedtke 1988 MWRGregory & Rowntree1990 MWRKain & Fritsch1990 JASAnd many more..

Double counting of processesInconsistenciesProblems with transitions between different regimes: dry pbl shallow cu scu shallow cu shallow cu deep cu

This unwanted situation can lead to:Standard transport parameterization approach:

Remarks:Resolved Scalesturbulenceconvectioncloudsradiation~100 kmLarge scalesUnresolved scalesResolved ScalesIntermezzo (2)Increase consistency between the parameterizations!How?

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 neededNo switching required between moist and dry convection neededEddy-Diffusivity/Mass Flux approach : a way out?

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

zinvThe (simplest) Mathematical Framework :

Figure courtesy of Martin Koehler Cumulus Topped Boundary LayerNeggers, Kohler & Beljaars accepted for JAS 2009alternatives: Lappen and Randall JAS 2001 Rio and Hourdin JAS 2008Dry updraftMoist updraftK diffusionTop 10 % of updrafts that is explicitly modelledFlexible moist area fraction

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 PDFRemarks:No closure at cloud baseNo detrainment parameterizationPdf can be used for cloud scheme and radiationAn reconstruct the flux:

Convection and turbulence parameterization give estimate of ssCloud scheme :radiation 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.

But Many open problems remainConvective Momentum TransportInfluence of Aerosols/Precipitation on the (thermo)dynamics of Scu and CuMesoscale structures in Scu and Shallow CuTransition from shallow to deep convection (deep convective diurnal cycle in tropics)

Conceptually on process basisParameterizationVertical velocity in convective cloudsConvection on the 1km~10km scale. (stochastic convection)Microphysicis (precip)Transition regimes.ClimateDetermine and understand the processes that are responsable for the uncertainty in cloud-climate feedback.

A slow, but rewarding Working StrategyLarge Eddy Simulation (LES) ModelsCloud Resolving Models (CRM)Single Column ModelVersions of Climate Models3d-Climate ModelsNWPsObservations from Field CampaignsGlobal observationalData setsDevelopmentTestingEvaluationSee http://www.gewex.org/gcss.html

lqtqsatCloudfractionCondensateTested for a large number of GCSS Cases..

A slow, but rewarding Working StrategyLarge Eddy Simulation (LES) ModelsCloud Resolving Models (CRM)Single Column ModelVersions of Climate Models3d-Climate ModelsNWPsObservations from Field CampaignsGlobal observationalData setsDevelopmentTestingEvaluationSee http://www.gewex.org/gcss.html