ECMWF Training Course 02 May 2000 Numerical Weather Prediction Parametrization of diabatic processes Convection II The parametrization of convection Peter Bechtold, Christian Jakob, David Gregory (with contributions from J. Kain (NOAA/NSLL) Moist Processes

Outline Aims of convection parametrization ECMWF Training Course 02 May 2000 Outline Aims of convection parametrization Overview over approaches to convection parametrization The mass-flux approach Moist Processes

Task of convection parametrisation(1) total Q1 and Q2 ECMWF Training Course 02 May 2000 Task of convection parametrisation(1) total Q1 and Q2 To calculate the collective effects of an ensemble of convective clouds in a model column as a function of grid-scale variables Recall: these effects are represented by Q1-QR, Q2 and Q3 Hence: parametrization needs to describe CONVECTIVE CONTRIBUTIONS to Q1/Q2: condensation/evaporation and transport terms and their vertical distribution. Moist Processes

ECMWF Training Course 02 May 2000 Task of convection parametrization (2) Convective contributions to Q1 and Q2 Conservation: Vertical integral of Q1 convective = surface convective precipitation Moist Processes

Task of convection parametrisation: in practice this means: ECMWF Training Course 02 May 2000 Task of convection parametrisation: in practice this means: Determine occurrence/localisation of convection Trigger Determine vertical distribution of heating, moistening and momentum changes Cloud model Determine the overall amount of the energy conversion, convective precipitation=heat release Closure Moist Processes

Constraints for convection parametrisation ECMWF Training Course 02 May 2000 Constraints for convection parametrisation Physical remove convective instability and produce subgrid-scale convective precipitation (heating/drying) in unsaturated model grids maintain a realistic vertical thermodynamic and wind structure produce a realistic mean tropical climate maintain a realistic variability on a wide range of time-scales produce a realistic response to changes in boundary conditions (e.g., El Nino) be applicable to a wide range of scales (typical 10 – 200 km) and types of convection (deep tropical, shallow, midlatitudinal and front/post-frontal convection) Computational be simple and efficient for different model/forecast configurations (T511, EPS, seasonal prediction) Moist Processes

Types of convection schemes ECMWF Training Course 02 May 2000 Types of convection schemes Schemes based on moisture budgets Kuo, 1965, 1974, J. Atmos. Sci. Adjustment schemes moist convective adjustement, Manabe, 1965, Mon. Wea. Rev. penetrative adjustment scheme, Betts and Miller, 1986, Quart. J. Roy. Met. Soc., Betts-Miller-Janic Mass-flux schemes (bulk+spectral) entraining plume - spectral model, Arakawa and Schubert, 1974, J. Atmos. Sci. Entraining/detraining plume - bulk model, e.g., Bougeault, 1985, Mon. Wea. Rev., Tiedtke, 1989, Mon. Wea. Rev., Gregory and Rowntree, 1990, Mon. Wea . Rev., Kain and Fritsch, 1990, J. Atmos. Sci., Donner , 1993, J. Atmos. Sci., Bechtold et al 2001, Quart. J. Roy. Met. Soc. episodic mixing, Emanuel, 1991, J. Atmos. Sci. Moist Processes

ECMWF Training Course 02 May 2000 The “Kuo” scheme Closure: Convective activity is linked to large-scale moisture convergence Vertical distribution of heating and moistening: adjust grid-mean to moist adiabat Main problem: here convection is assumed to consume water and not energy -> …. Positive feedback loop of moisture convergence Moist Processes

Adjustment schemes e.g. Betts and Miller, 1986, QJRMS: ECMWF Training Course 02 May 2000 Adjustment schemes e.g. Betts and Miller, 1986, QJRMS: When atmosphere is unstable to parcel lifted from PBL and there is a deep moist layer - adjust state back to reference profile over some time-scale, i.e., Tref is constructed from moist adiabat from cloud base but no universal reference profiles for q exist. However, scheme is robust and produces “smooth” fields. Moist Processes

Procedure followed by BMJ scheme… 1) Find the most unstable air in lowest ~ 200 mb 2) Draw a moist adiabat for this air 3) Compute a first-guess temperature-adjustment profile (Tref) 4) Compute a first-guess dewpoint-adjustment profile (qref)

Adjustment schemes: The Next Step is an Enthalpy Adjustment First Law of Thermodynamics: With Parameterized Convection, each grid-point column is treated in isolation. Total column latent heating must be directly proportional to total column drying, or dH = 0.

Enthalpy is not conserved for first-guess profiles for this sounding! Must shift Tref and qvref to the left…

Imposing Enthalpy Adjustment:

Adjustment scheme: Adjusted Enthalpy Profiles:

The mass-flux approach ECMWF Training Course 02 May 2000 The mass-flux approach Condensation term Eddy transport term Aim: Look for a simple expression of the eddy transport term Moist Processes

The mass-flux approach ECMWF Training Course 02 May 2000 The mass-flux approach Reminder: with Hence = and therefore Moist Processes

The mass-flux approach: Cloud – Environment decomposition ECMWF Training Course 02 May 2000 The mass-flux approach: Cloud – Environment decomposition Cumulus area: a Fractional coverage with cumulus elements: Define area average: Total Area: A Moist Processes

ECMWF Training Course 02 May 2000 The mass-flux approach: Cloud-Environment decomposition (see also Siebesma and Cuijpers, JAS 1995 for a discussion of the validity of the top-hat assumption) With the above: Average over cumulus elements Average over environment and Use Reynolds averaging again for cumulus elements and environment separately: and = Neglect subplume correlations Moist Processes

The mass-flux approach ECMWF Training Course 02 May 2000 The mass-flux approach Then after some algebra (for your exercise) : Further simplifications : The small are approximation Moist Processes

The mass-flux approach ECMWF Training Course 02 May 2000 The mass-flux approach Then : Define convective mass-flux: Then Moist Processes

The mass-flux approach ECMWF Training Course 02 May 2000 The mass-flux approach With the above we can rewrite: To predict the influence of convection on the large-scale with this approach we now need to describe the convective mass-flux, the values of the thermodynamic (and momentum) variables inside the convective elements and the condensation/evaporation term. This requires, as usual, a cloud model and a closure to determine the absolute (scaled) value of the massflux. Moist Processes

Mass-flux entraining plume cloud models ECMWF Training Course 02 May 2000 Mass-flux entraining plume cloud models Continuity: Heat: Specific humidity: Entraining plume model Cumulus element i Moist Processes

Mass-flux entraining plume cloud models ECMWF Training Course 02 May 2000 Mass-flux entraining plume cloud models Simplifying assumptions: 1. Steady state plumes, i.e., Most mass-flux convection parametrizations today still make that assumption, some however are prognostic 2. Bulk mass-flux approach Sum over all cumulus elements, e.g. with e.g., Tiedtke (1989), Gregory and Rowntree (1990), Kain and Fritsch (1990) 3. Spectral method e.g., Arakawa and Schubert (1974) and derivatives Important: No matter which simplification - we always describe a cloud ensemble, not individual clouds (even in bulk models) Moist Processes

Large-scale cumulus effects deduced using mass-flux models ECMWF Training Course 02 May 2000 Large-scale cumulus effects deduced using mass-flux models Assume for simplicity: Bulk model, Combine: Moist Processes

Large-scale cumulus effects deduced using mass-flux models ECMWF Training Course 02 May 2000 Large-scale cumulus effects deduced using mass-flux models Physical interpretation (can be dangerous after a lot of maths): Convection affects the large scales by Heating through compensating subsidence between cumulus elements (term 1) The detrainment of cloud air into the environment (term 2) Evaporation of cloud and precipitation (term 3) Note: The condensation heating does not appear directly in Q1. It is however a crucial part of the cloud model, where this heat is transformed in kinetic energy of the updrafts. Similar derivations are possible for Q2. Moist Processes

Deducing mass-flux model parameters from observations (1) ECMWF Training Course 02 May 2000 Deducing mass-flux model parameters from observations (1) The mass-flux entraining plume models (both bulk and spectral) have been used to interpret observations of Q1 and Q2. (in all following figures M is defined in units of omega!) Yanai and Johnson, 1993, Meteor. Monogr. Moist Processes

ECMWF Training Course 02 May 2000 Deducing mass-flux model parameters from observations (2) - use cloud model Yanai and Johnson, 1993 Moist Processes

Deducing mass-flux model parameters from observations (3) ECMWF Training Course 02 May 2000 Deducing mass-flux model parameters from observations (3) Mass flux models can also be applied to convective downdraughts Yanai and Johnson, 1993 Moist Processes

Caniaux, Redelsperger, Lafore, JAS 1994 ECMWF Training Course 02 May 2000 Deducing convective and stratiform heating profiles from Cloud Res. Model (1) Heat Budget of Squall Line important: Q1c is dominated by condensation term The convective and stratiform parts are computed by partitioning the whole domain as function of rainfall and/or updraft intensity Caniaux, Redelsperger, Lafore, JAS 1994 Moist Processes

ECMWF Training Course 02 May 2000 Deducing convective and stratiform heating profiles from Cloud Res. Model (2) Heat Budget of Squall Line but for Q2 the transport and condensation terms are equally important Note again that the stratiform (mesoscale) heating maximum occurs above the convective maximum Caniaux, Redelsperger, Lafore, JAS 1994, Guichard et al. 1997 Moist Processes

Alternatives to the entraining plume model - Episodic mixing ECMWF Training Course 02 May 2000 Alternatives to the entraining plume model - Episodic mixing Observations show that the entraining plume model might be a poor representation of individual cumulus clouds. Therefore alternative mixing models have been proposed - most prominently the episodic (or stochastic) mixing model (Raymond and Blyth, 1986, JAS; Emanuel, 1991, JAS) Conceptual idea: Mixing is episodic and different parts of an updraught mix differently Basic implementation: assume a stochastic distribution of mixing fractions for part of the updraught air - create N mixtures Version 1: find level of neutral buoyancy of each mixture Version 2: move mixture to next level above or below and mix again - repeat until level of neutral buoyancy is reached Although physically appealing the model is very complex and practically difficult to use Moist Processes

Closure in mass-flux parametrizations ECMWF Training Course 02 May 2000 Closure in mass-flux parametrizations The cloud model determines the vertical structure of convective heating and moistening (microphysics, variation of mass flux with height, entrainment/detrainment assumptions). The determination of the overall magnitude of the heating (i.e., surface precipitation in deep convection) requires the determination of the mass-flux at cloud base. - Closure problem Types of closures: Deep convection: time scale ~ 1h Equilibrium in CAPE or similar quantity (e.g., cloud work function) Boundary-layer equilibrium Shallow convection: time scale ? ~ 3h idem deep convection, but also turbulent closure (Fs=surface heat flux, ZPBL=boundary-layer height) Grant (2001) Moist Processes

CAPE closure - the basic idea ECMWF Training Course 02 May 2000 CAPE closure - the basic idea large-scale processes generate CAPE Convection consumes CAPE Moist Processes

CAPE closure - the basic idea ECMWF Training Course 02 May 2000 CAPE closure - the basic idea Surface processes also generate CAPE (difficult to include in closure) Convection consumes CAPE Downdraughts Moist Processes

Fs is surface moist static energy flux ECMWF Training Course 02 May 2000 Boundary Layer Equilibrium closure (1) as used for shallow convection in the IFS Assuming boundary-layer equilibrium of moist static energy hs What goes in goes out Therefore, by integrating from the surface (s) to cloud base (LCL) including all processes that contribute to the moist static energy, one obtains the flux on top of the boundary-layer that is assumed to be the convective flux Mc (neglect downdraft contributions) Fs is surface moist static energy flux Moist Processes

Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook ECMWF Training Course 02 May 2000 Boundary Layer Equilibrium closure (2) – as suggested for deep convection Postulate: tropical balanced temperature anomalies associated with wave activity are small (<1 K) compared to buoyant ascending parcels ….. gravity wave induced motions are short lived Convection is controlled through boundary layer entropy balance - sub-cloud layer entropy is in quasi-equilibrium – flux out of boundary-layer must equal surface flux ….boundary-layer recovers through surface fluxes from convective drying/cooling Fs is surface heat flux Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook Moist Processes

ECMWF Training Course 02 May 2000 Summary (1) Convection parametrisations need to provide a physically realistic forcing/response on the resolved model scales and need to be practical a number of approaches to convection parametrisation exist basic ingredients to present convection parametrisations are a cloud model and a closure assumption the mass-flux approach has been successfully applied to both interpretation of data and convection parametrisation ……. Moist Processes

ECMWF Training Course 02 May 2000 Summary (2) The mass-flux approach can also be used for the parametrization of shallow convection. It can also be directly applied to the transport of chemical species The parametrized effects of convection on humidity and clouds strongly depend on the assumptions about microphysics and mixing in the cloud model --> uncertain and active research area …………. Future we already have alternative approaches based on explicit representation (Multi-model approach) or might have approaches based on Wavelets or Neural Networks Moist Processes

  Trigger Functions Moist. Conv. Sub-cloud Mass conv. Cloud-layer   CAPE Cloud Depth CIN Moist. Conv. Sub-cloud Mass conv. Cloud-layer Moisture ∂(CAPE)/∂t BMJ (Eta)  Grell (RUC, AVN) KF (Research) Bougeault (Meteo FR) Tiedtke (ECMWF) Bechtold Emanuel (NOGAPS ,research) Gregory/Rown (UKMO) 

Closure Assumptions (Intensity)   CAPE Cloud-layer moisture Moisture Converg. ∂(CAPE)/∂t Subcloud Quasi-equil. BMJ (Eta)  Grell (RUC, AVN) KF (Research) Bougeault (Meteo FR) Tiedtke (ECMWF) shallow Bechtold Emanuel Gregory/Rown (UKMO) 

Vertical Distribution of Heat, Moisture Entraining/Detraining   Entraining/Detraining Plume Convective Adjustment Buoyancy Sorting Cloud Model BMJ (Eta)  Grell (RUC, AVN) KF (Research) Bougeault (Meteo FR) Tiedtke (ECMWF) Bechtold Emanuel Gregory/Rowntree (UKMO) 