Presentation on theme: "Richard Forbes, email@example.com Cloud Resolving Models: Their development and their use in parametrization development Richard Forbes, firstname.lastname@example.org."— Presentation transcript:
1Richard Forbes, email@example.com Cloud Resolving Models: Their development and their use in parametrization developmentRichard Forbes,Adrian Tompkins
2Outline 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?Cloud Resolving Models
3Why were cloud resolving models conceived? In the early 1960s there were three sources of information concerning cumulus cloudsDirect observationsE.G: Warner (1952)Limited coverage of a few variables
4Why were cloud resolving models conceived? In the early 1960s there were three sources of information concerning cumulus cloudsDirect observationsLaboratory StudiesRealism of laboratory studies?Difficulty of incorporating latent heating effectsTurner (1963)
5Why were cloud resolving models conceived? In the early 1960s there were three sources of information concerning cumulus cloudsDirect observationsLaboratory StudiesTheoretical StudiesLinear perturbation theoriesQuickly becomes difficult to obtain analytical solutions when attempting to increase realism of the model
6Why were cloud resolving models conceived? In the early 1960s there were three sources of information concerning cumulus cloudsLaboratory StudiesTheoretical StudiesAnalytical StudiesObvious complementary role for Numerical simulation of convective cloudsNumerical integration of complete equation setAllowing more complete view of ‘simulated’ convection
7Outline Why were cloud resolving models conceived? What do they consist of ?Cloud Resolving Models
8What is a CRM? The concept GCM Grid cell ~100kmGCM grid too coarse to resolve convection - Convective motions must be parametrizedIn 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!
9What is a CRM? The physics radiationSWIR1. Momentum equations2. Turbulence Schemedynamics3. Microphysics4. Radiation?microphysicsturbulence5. Surface FluxessurfacefluxesCloud Resolving Models
10What is a CRM? The Issues1. RESOLUTION: Dependence on turbulence formulation.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.43152Cloud Resolving Models
11Lateral Boundary Conditions Early models used impenetrable Lateral Boundary ConditionsL Cloud development near boundaries affected by their presenceNo longer in usePeriodic Boundary ConditionsJ Easy to implementJ Model boundaries are ‘invisible’L No mean ascent is allowable (W=0)Open Boundary ConditionsJ Mean vertical motion is unconstrainedL Very difficult to avoid all wave reflection at boundariesL Difficult to implement, also need to specific BCsW
12Spatial and Temporal Scales? 1. O(1km)1. Deep convective updraughts~30 minutes3. O(10km)3. Anvil cloud associated with one event2. O(100m)2. Turbulent Eddies4. O(1000km)4. Mesoscale convective systems, Squall lines, organised convectiondays-weeksCloud Resolving Models
13What do they consist of ? MICROPHYSICS SUBGRID-SCALE TURBULENCE (ice and liquid phases)SUBGRID-SCALETURBULENCERADIATION(sometimes - Expensive!)DYNAMICAL COREOpen or periodic Lateral BCsLower boundary surface fluxesUpper boundary Newtonian damping (to prevent wave reflection)BOUNDARYCONDITIONS
14(ice and liquid phases) What do they consist of ?DYNAMICAL COREPrognostic equations for u,v,w,q,rv,(p)affected by, advection, turbulence, microphysics, radiation, surface fluxes...MICROPHYSICS(ice and liquid phases)Prognostic equations for bulk water categories: rain, liquid cloud, ice, snow, graupel… sometimes also their number concentration.HIGHLY UNCERTAIN!!!SUBGRID-SCALETURBULENCEAttempt to parameterize flux of prognostic quantities due to unresolved eddiesMost models use 1 or 1.5 order schemesALSO UNCERTAIN!!!
15Reference: Emanuel (1994), Atmospheric Convection Basic EquationsContinuity: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 ConvectionCloud Resolving Models
16Basic Equations Momentum: DYNAMICAL CORE Pressure Gradient Coriolis Diabatic terms(e.g. turbulence)Mixing ratio of vapour and condensate variablesBuoyancyWhere:Overbar = mean stateSince 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 limitedCloud Resolving Models
17Basic Equations Thermodynamic: Equation of State: Moisture: Diabatic processes:RadiationDiffusionMicrophysics (Latent heating)Equation of State:Moisture:Microphysics termsCondensation EvaporationCloud Resolving Models
18All scales of motion present in turbulent flow SUBGRID-SCALETURBULENCEAll scales of motion present in turbulent flowSmallest 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 variablesProgress 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.Cloud Resolving Models
19Dimensionless Constant = 0.02 -0.1 SUBGRID-SCALETURBULENCEMany 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 diffusivityK set to a constant in early modelsImprovements can be made by relating K to an eddy length-scale l and the wind shear.Reference Cotton and Anthes, 1989Storm and Cloud DynamicsDimensionless Constant =Cloud Resolving Models
20Reference: Stull(1988), An Introduction to Boundary Layer Meteorology SUBGRID-SCALETURBULENCELength scale of turbulence related to grid-lengthFurther 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 stratificationFirst 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 schemeReference: Stull(1988), An Introduction to Boundary Layer MeteorologySee Boundary Layer Course for more details!Cloud Resolving Models
21MicrophysicsThe 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 understoodOperate on scales smaller than the model gridTherefore parameterisation is difficult but importantCloud Resolving Models
22From Dare 2004, microphysical scheme at BMRC MicrophysicsMost schemes use a bulk approach to microphysical parameterizationJust one equation is used to model each categoryqtotalqrainWarm - BulkqvapqrainqliqqsnowqgraupqiceIce - BulkIce - Bin resolvingDifferent drop size bins
23Microphysics For example: Fall speed of graupel Sources and sinks For Example, (Lin et al. 1983) snow to graupel conversionqsnow-crit = 10-3 kg kg-1S =0 below this thresholdT0 =0oCNot many papers mention numerics. Often processes are considered to be resolved by the O(10s) timesteps used in CRMs, and therefore a simple explicit solution is used; beginning of timestep value of qgraup used to calculate the RHS of the equation. If sinks result in a negative mass, some models reset to zero (i.e. not conserving).
24Outline Why were cloud resolving models conceived? What do they consist of?How have they developed?Cloud Resolving Models
25HISTORY:1960sOne of the first attempts to numerically model moist convection made by Ogura JAS (1963)Same basic equation set, neglecting:Diffusion - Radiation - Coriolis ForceReversible ascent (no rain production)Axisymmetric model domain3km by 3km100m resolution6 second timestep3kmWarm airbubble100m
26Possible 2D domain configurations Axi-symmetriczrSlab SymmetriczxMotions function of r and z+ Pseudo-”3D” motions (subsidence)- No wind shear possible- Difficult to represent cloud ensemblesUse continued mainly in hurricane modellingMotions functions of x and z+ can represent ensembles- Lack of third dimension in motions- Artificially changes separation scaleStill much used to dateFor reference see Soong and Ogura JAS (1973)
27significant proportion Ogura 19637 Minutes14 MinutesCloud reaches domaintop by 14 MinutesCloud occupiessignificant proportionof model domainLiquidCloud
29Outline Why were cloud resolving models conceived? What do they consist of?How have they developed?To which purposes have they been applied?Cloud Resolving Models
301990s really saw an expansion in the way in which CRMs have been used Use of CRMs1990s really saw an expansion in the way in which CRMs have been usedLong term statistical equilibrium runs -Investigating specific process interactionsTesting assumptions of cumulus parametrization schemesDeveloping aspects of parametrizationsLong term simulation of observed systemsAll of the above play a role in the use of CRMs to develop parametrization schemesCloud Resolving Models
31Uses: Radiative-Convective equilibrium experiments Long term integrations until fields reach equilibriumRadn cooling == convective heatingsurface rain = moisture fluxesSample convective statistics of equilibrium, and their sensitivity to external boundary conditionse.g Sea surface TemperatureAlso allows one to examine process interactions in simplified frameworkComputationally expensive since equilibrium requires many weeks of simulation to achieve equilibrium2D: 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)
32Uses: 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)USE CRM TO INVESTIGATE A CERTAIN PROCESS THAT IS PERHAPS DIFFICULT TO EXAMINE IN OBSERVATIONSUNDERSTANDING THIS PROCESS ALLOWS AN ATTEMPT TO INCLUDE OR REPRESENT IT IN PARAMETRIZATION SCHEMES
33Example: 350m resolution 3D CRM simulation used in a variety of parametrization ways Used to understand coldpool triggeringUsed to set closure parameters for a simplified cloud modelTompkins JAS 2001Di Giuseppe & Tompkins JAS 2003Used as a cloud-field proxy to develop parametrization to correct radiative geometrical biasesUsed to justify PDF decision in cloud scheme of ECHAM5Tompkins JAS 200290 kmDi Giuseppe & Tompkins JGR 2003, JAS2005Tompkins & di Giuseppe 2006
34Uses: Testing Cumulus Parametrization schemes Parametrizations contain representations of many terms difficult to measure in observationse.g. Vertical distribution of convective mass fluxes for mass-flux schemesAssume 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.
35Gregory and Miller QJRMS 1989 Updraught,Downdraught,non-convectiveand netcloud mass fluxesThey 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 – but note resolution issues.
36Uses: Developing aspects of parametrization schemes CCcloud coverrelative humiditycloud mixing ratioThe information can be used to derive statistics for use in parametrization schemesE.g. Xu and Randall, JAS (1996) used CRM to derive a diagnostic cloud cover parameterisation where
37Uses: Developing Parametrization Schemes GCMs - SCMsCRMsOBSERVATIONSValidation (and development)Validation(and development)Validation(and development)Provide extra quantities not available from data
38CRMsOBSERVATIONSValidationFor example, Grabowski (1998) JAS performed week-long simulations of convection during GATE, in 3D with a 400 by 400 km 3D domain.SimulationObservationsSimulationAll types of convection developed in response to applied forcing - Could be considered a successful validation exercise?
39Simulation of Observed Systems Still controversy about the way to apply “Large-scale forcing”Relies on argument of scale separation (as do most convective parametrization schemes)CRM domainWWith periodic BCs must have zero mean vertical velocity. Normal to apply terms:
40Simulation of Observed Systems An observational array measures the mean mass flux.If an observational array contains a convective event, but is not large enough to contain the subsidence associated with this event, then the measured “large scale” mean ascent will also contain a component due to the net cumulus mass flux McRadiosonde stationsmeasure
41GCSS - GEWEX Cloud System Study (Moncrieff et al. Bull. AMS 97) PARAMETERISATIONGCMS - SCMSGCSS - GEWEX Cloud System Study (Moncrieff et al. Bull. AMS 97)CRMsOBSERVATIONSUse observations to evaluate parameterizations of subgrid-scale processes in a CRMStep 1Evaluate CRM results against observational datasetsStep 2Use CRM to simulate precipitating cloud systems forced by large-scale observationsStep 3Evaluate and improve SCMs by comparing to observations and CRM diagnosticsStep 4
42Simulations from different models (total hydrometeor content) GCSS: Validation of CRMs Redelsperger et al QJRMS 2000 SQUALL LINE SIMULATIONSSimulations from different models(total hydrometeor content)Observations - RadarOpen BCsPeriodic BCsOpen BCsOpen BCsConclude that only 3D models with ice and open BCs reproduce structure well
43GCSS: Comparison of many SCMs with a CRM Bechtold et al QJRMS 2000 SQUALL LINE SIMULATIONS
44Issues of this approach Confidence is gained in the ability of the SCMs and CRMs to simulate the observed systemsSensitivity 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)
45Outline 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?Cloud Resolving Models
46Future - 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.Indications are that CRM ‘solutions’ have not converged with increasing horizontal resolution at 100m.Dimensionality2D 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?
47Cloud Resolving Convective Parametrization 2D CRMs in a global model Grabowski and Smolarkiewicz, Physica D Places a small 2D CRM (roughly 200km, simple microphysics, no turbulence) in every grid-point of the global modelStill based on scale separation and non-communication between grid-pointsAdvantages and Disadvantages?From Khairoutdinov, illustrating multimodelling framework developed at CSU
48Cloud Resolving Convective Parametrization 2D CRMs in a global model CAMCRCPOBSImproves diurnal cycleand tropical variability?
49Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005
50Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, UTCModel simulated OLR and surface rain rateMeteosat low resolution infra-red and radar-derived surface rain rate
51Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, UTCMODIS 13:10 UTCModel simulated OLR and surface rain rateMODIS high resolution visible image
52Global “CRMs”Global cloud resolving model simulations? Or at least cloud-permitting model simulations3.5 km resolution 7 day forecast of the NICAM global model on the Earth Simulator (FRCGC, JAMSTEC)Miura et al., (2007), Geophys. Res. Lett., vol. 34.Courtesy of M. Satoh
53SummaryCRMs have been proven as very useful tools for simulating individual systems and in particular for investigating certain process interactions.They can also be used to test and develop parametrization schemes since they can provide supplementary information such as mass fluxes not available from observational data.However, if they are to be used to develop parametrization schemes, it is necessary to keep their limitations in mind (turbulence, microphysics)not a substitute for observations, but complementaryCare should be taken in the experimental design!Large scale forcingThe distinctions between traditional CRMs, limited area NWP and even GCMs is beginning to blur!
54Summary - Feedback Welcome! firstname.lastname@example.org LECTURE 1: Discussed microphysical processes. Examined the basic issues that must be considered when considering cloud parameterisation.LECTURE 2: We focussed on cloud cover, and in particular on statistical schemes which diagnose cloud cover from knowledge of the subgrid- scale variability of T and qt .LECTURE 3: Overview of the ECMWF cloud scheme.LECTURE 4: We considered some different methods of cloud validation with their respective strengths and weaknesses.LECTURE 5: Discussed what Cloud Resolving Models are and how they have been used for parametrization development.Cloud Resolving Models