1 Numerical Weather Prediction Parametrization of diabatic processes Convection I Peter Bechtold and Christian Jakob

2 Convection Lectures: –The nature of convection –Parametrisation of convection –The ECMWF mass-flux parametrisation and Tracer transport –Forecasting of Convection –Wavelets, Neural Networks and EOFs (in preparation) Exercises –The big secret !!!

3 Convection Aim of Lectures: The aim of the lecture is only to give a rough overview of convective phenomena and parameterisation concepts in numerical models. The student is not expected to be able to directly write a new convection code- the development and full validation of a new convection scheme takes time (years). There are many details in a parameterisation, and the best exercise is to start with an existing code, run some offline examples on Soundings and dig in line by line ….. there is already a trend toward explicit representation of convection in limited area NWP (no need for parameterization) but for global we are not there yet, and still will need parameterizations for the next decade Offline convection Code: Can be obtained from

4 Convection Parametrisation and Dynamics - Text Books Emanuel, 1994: Atmospheric convection, OUP Houze R., 1993: Coud dynamics, AP Holton, 2004: An introduction to Dynamic Meteorology, AP Bluestein, 1993: Synoptic-Dynamic meteorology in midlatitudes, Vol II. OUP Peixoto and Ort, 1992: The physics of climate. American Institute of Physics Emanuel and Raymond, 1993: The representation of cumulus convection in numerical models. AMS Meteor. Monogr. Smith, 1997: The physics and parametrization of moist atmospheric convection. Kluwer Dufour et v. Mieghem: Thermodynamique de l’Atmosphère, 1975: Institut Royal météorologique de Belgique Bohren and Albrecht, 1998: Atmospheric Thermodynamics.OUP AP=Academic Press; OUP=Oxford University Press

5 How does it look like ?

6 African Squall lines Moist convection : Global IR GOES METEOSAT 7/04/2003 SPCZ ITCZ at 10ºN Deep and shallow convection Intense deep Sc convection

7 Convection and role of water vapor Interaction of Tropics and midlatitudes: Dry air intrusions modulate convection (Rossby wave breaking)

8 Convection and upper-level Divergence (determine divergence from variation of cold cloud top areas) M c is the convective mass flux (see later)

9 Outline General: Convection and tropical circulations Midlatitude Convection Shallow Convection Useful concepts and tools: Buoyancy Convective Available Potential Energy Soundings and thermodynamic diagrams Convective quasi-equilibrium Large-scale observational budgets

10 about 3 mm/day is falling globally, but most i.e. 5-7 mm/day in the Tropics Convection and tropical circulations (1) It’s raining again… 2000/2001 rainfall rate as simulated by IFS CY30R2 and compared to GPCP obs

11 Model Tendencies – Tropical Equilibria Above the boundary layer, there is an equilibrium Radiation-Clouds-Dynamics-Convection for Temperature, whereas for moisture there is roughly an equilibrium between dynamical transport (moistening) and convective drying. - Global Budgets are very similar Nevertheless, the driving force for atmospheric dynamics and convection is the radiation

12 Convection and tropical circulations (2) proxy distribution of deep and shallow convective clouds as obtained from IFS

13 Shallow Convection (1) Field of tropical oceanic Cumuli

14 Shallow Convection (2) Convective bands and open cells in cold air outbreak – J. v. Mayen Island

15 Shallow (Boundary-Layer) Convection (5) Basic physics of the trade-cumulus boundary layer Emanuel, 1994

16 Shallow (Boundary-Layer) Convection (4) Mean thermodynamic profiles, buoyancy and turbulent kinetic energy Note the different stability at cloud base: a well-mixed layer for the Sc, and a subcloud-layer that is largely decoupled from the cloud layer for the Cu and Cu under Sc regime.

17 A third convective mode Recent studies indicate, that there is a third important mode of convection (besides deep and shallow) in the tropics consisting of mainly cumulus congestus clouds terminating near the melting level at around 5 km. Johnson et al., 1999, JCL

18 Convection and tropical circulations (3) ITCZ and the Hadley meridional circulation : the role of trade-wind cumuli and deep tropical towers

19 Convection and tropical circulations (4) The Walker zonal Circulation From Salby (1996)

20 Convection and tropical circulations (5) Tropical waves: Rossby, Kelvin, Gravity, African easterly waves a Squall line

21 Convection and tropical circulations (7) 50/50 rotational/divergent 50/50 KE/PE Strong zonal wind along the Equator Symmetric around the Equator Eastward moving ~18 m/s The KELVIN wave

22 Convection and tropical circulations (8) The Kelvin wave, OLR composite

23 Convection and tropical circulations (9) Symmetric KE>PE KE max at Equator,PE max off the Equator Westward moving ~ 5 m/s The (n=1) Equatorial Rossby wave

24 Convection and tropical circulations (10) The Equatorial Rossby wave, OLR composite

25 African easterly waves African easterly waves have periods of 2-6 days, typical wavelengths of about 2500 km and propagation speeds around -8 m/s. These waves are thought to originate from barotropic and baroclinic instability, but the effects of diabatic (Cumulus) heating, the diurnal cycle and orography also modulate the waves. For instability to exist, the quasi-potential vorticity gradient must change sign in the domain, i.e for tropical North Africa it must become negative. Although the shear instability associated with the jet is present throughout the rainy season, the waves appear to contribute to the development of rainfall systems only during late summer as only then the can access the necessary moisture in the low-level monsoon flow. The exit region of the Tropcial easterly Jet – which is the consequence of the outflow=divergence due to the Asian Monsoon - might also have an effect on convection over tropical North Africa The waves are generally confined to a latitudinal zone close and south of the Jet Further reading: Diedhiou et al. (1998, GRL), Nicholson and Grist (2003,J. Clim), Hsieh and Cook (2004, MWR), Grist (2002, MWR)

26 West-African meteorology – easterly waves Monsoon flow,Easterly waves, and midlatitude-tropical mixing Low-level Monsoon flow Mid-level dry “Harmattan” Upper-level easterlies

27 Reminder : useful relations for the Streamfunction expressing the rotational (non divergent part) of the horizontal wind field Streamfunction like vorticity is a scalar function that allows to describe the flow (i.e. both u and v) Streamfunction and vorticity: Geostrophic Streamfunction and Geopotential: Nota: Streamfunction ≠ Streamline which is defined by

28 Analysis from a series of 2-day Forecasts Hovmoeller plots as an easy way to plot wave (propagation) Comparison Analysis – Forecast for African easterly waves. No filtering required

29 Convection and tropical circulations Summary of tropical motions and scales There are still uncertainties concerning our knowledge about the interaction between convective and synoptic scales in the Tropics. Horizontal temperature fluctuations in the Tropics are small w ~ -.5 cm/s In the absence of condensation heating, tropical motions must be barotropic and cannot convert PE in KE. Therefore they must be driven by precipitating disturbances or lateral coupling with midlatitude systems. When precipitation takes place, heating rates are strong; e.g. 100 mm/day precip ~ energy flux of 2900 W/m2 or an average 30 K/day heating of the atmospheric column => w ~ 8.6 cm/s. However, this positive mean motion is composed of strong ascent of order w ~ 1 m/s in the Cumulus updrafts and slow descending motion around (“compensating subsidence”) when analysing the vorticity equation it appears that in precipitating disturbances the vertical transport of vorticity (momentum) through Cumulus is important to balance the divergence term

30 Midlatitude Convection (1) Convection associated to synoptic forcing, orographic uplift, and/or strong surface fluxes A Supercell over Central US, Mai 1998, flight level m

31 Midlatitude Convection (2) It’s raining again… Europe climatology ( Frei and Schär, 1998 ) In Europe most intense precipitation is associated with orography, especially around the Mediterranean, associated with strong large-scale forcing and mesoscale convective systems

32 Midlatitude Convection (3) European MCSs ( Morel and Sénési, 2001 ) Density Map of Triggering ….. over Orography

33 Midlatitude Convection (4) European MCSs ( Morel and Sénési, 2001 ) Time of Trigger and mean propagation European (midlatitude) MCSs essentially form over orography (convective inhibition –see later- offset by uplift) and then propagate with the midtropospheric flow (from SW to NE)

34 Midlatitude Convection (5) along the main cold frontal band and in the cold core of the main depression – 17/02/97 during FASTEX A Supercell over Central US, Mai 1998, flight level m

35 Midlatitude Convection (6) Forcing of ageostrophic circulations/convection in the right entrance and left exit side of upper-level Jet Thermally direct circulation Thermally indirect circulation Acceleration/deceleration of Jet Total energy is conserved: e.g. at the exit region where the Jet decelerates kinetic energy is converted in potential energy

36 Midlatitude Convection (7) Conceptual model of a Squall line system with a trailing stratiform area (from Houze et al. 1989) Evaporation of precipitation creates negatively buoyant air parcels. This can lead to the generation of convective-scale penetrative downdraughts. In the stratiform part there is heating/cooling couple with an upper-level mesoscale ascent, and a lower-level mesoscale downdraught, due to the inflow of dry environmental air and the evaporation of stratiform rain.

37 Midlatitude Convection (8a) Conceptual model of a rotating mesoscale convective system – tornadic thunderstorm (from Lemon and Doswell, 1979) Forward Flank downdraft induced by evaporation of precipitation Rear Flank Downdraft induced by dynamic pressure perturbation: Interaction of updraft with shear vector of environment: The linear part of the dynamic pressure perturbation is proportional to the horizontal gradient of the vertical velocity perturbation (updraft) times the environmental shear vector

38 Midlatitude Convection (8b) Origin and mechanism of generation of vertical vorticity Conversion of horizontal vorticity at surface frontal boundary in vertical vorticity by tilting in updraft A useful quantity in estimating the storm intensity is the “bulk” Richardson number R=CAPE/S 2, where CAPE is the convective available energy (see later) and S is the difference between the mean wind vector at 500 and 925 hPa

39 Summary: What is convection doing, where does it occur Convection transports heat, water vapor, momentum … and chemical constituents upwards …. Water vapor then condenses and falls out -> net convective heating/drying Deep Convection (precipitating convection) stabilizes the environment, an approximate not necessarily complete picture is to consider it as reacting to the large-scale environment (e.g. tropical waves, mid-latitude frontal systems) =“quasi-equilibrium”; shallow convection redistributes the surface fluxes The tropical atmosphere is in radiative(cooling) / convective(heating) equilibrium 2K/day cooling in lowest 15 km corresponds to about 5 mm/day precipitation. The effect of convection (local heat source) is fundamentally different in the midlatitudes and the Tropics. In the Tropics the Rossby radius of deformation R=N H/f (N=Brunt Vaisala Freq, f=Coriolis parameter, H=tropopause height) is infinite, and therefore the effects are not locally bounded, but spread globally via gravity waves – “throwing a stone in a lake”

40 What we have not talked about Organization of convection: Squall lines, Mesoscale convective systems, tropical superclusters, and the influence of vertical wind shear The diurnal cycle of convection over land (see lecture Notes) Follow some Tools and Concepts !

41 Buoyancy - physics of Archimedes (1) Body in a fluid Assume fluid to be in hydrostatic equlibrium Forces: Top Bottom Gravity Net Force: Acceleration: Emanuel, 1994

42 Buoyancy (2) Vertical momentum equation: Neglect second order terms

43 Buoyancy (3) == = B - buoyancy acceleration

44 Buoyancy (4) Contributions Buoyancy acceleration: Dry air: Often (but not always):Then Hence

45 Buoyancy (5) Contributions Cloudy air: effects of humidity and condensate need to be taken into account In general all 3 terms are important. 1 K perturbation in T is equivalent to 5 g/kg perturbation in water vapor or 3 g/kg in condensate

46 Non-hydrostat. Pressure gradient effects CRM analysis of the terms Physics: Vector field of the buoyancy pressure- gradient force for a uniformly buoyant parcel of finite dimensions in the x-z-plane. (Houze, 1993, Textbook) Guichard and Gregory P Z (km) (ms -2 ) B

47 Convective Available Potential Energy (CAPE) Definition: CAPE represents the amount of potential energy of a parcel lifted to its level of neutral buoyancy. This energy can potentially be released as kinetic energy in convection. Example: Much larger than observed - what’s going on ?

48 Thermodynamic diagrams Tephigram Dry adiabat Constant mixing ratio Moist adiabat Constant temperature Constant pressure

49 Convection in thermodynamic diagrams (1) using Tephigram/Emagram Idealised Profile LCL LFC LNB CIN CAPE

50 Convection in thermodynamic diagrams (2) using equivalent Potential Temperature and saturated equivalent Potential Temperature θ Θ e (T,q) Θ esat (T) Θ e is conserved during moist adiabatic ascent CAPE Note that no CAPE is available for parcels ascending above 900 hPa and that the tropical atmosphere is stable above 600 hPa (θ e increases) – downdrafts often originate at the minimum level of θ e in the mid-troposphere. GATE Sounding

51 Importance of choice of moist adiabat in CAPE calculations Reversible moist adiabat: Condensate remains in parcel at all time. Consequences:Water loading (gravity acting on condensate) Condensate needs to be heated - different heat capacity than dry air Phase transition from water to ice leads to extra heating Irreversible moist adiabat (Pseudo-adiabat): Condensate is removed from parcel instantly

52 Importance of choice of moist adiabat in CAPE calculations CAPE - reversible adiabat without freezing vs. irreversible adiabat Emanuel, 1994 Reversible CAPE much smaller, typically by a factor of 2 with respect to irreversible

53 Mixing Reason: Convective draughts undergo mixing with environment Observations: Condensate content (here w) measured in convection is much smaller than the adiabatic value (denoted here w a ) Warner, 1970, JAS

54 Mixing and 3D flow subcloud and cloud-layer Circulations From high-resolution LES simulation (dx=dy=50 m) Vaillancourt, You, Grabowski, JAS 1997

55 Mixing models undiluted after Raymond,1993 entraining plume cloud top entrainmentstochastic mixing

56 Effect of mixing on parcel ascent No dilution Heavy dilution Moderate dilution

57 In convective regions these terms will be dominated by convection Large-scale effects of convection (1) Q 1 and Q 2 Thermodynamic equation (dry static energy) : Define averaging operator over area A such that: and Apply to thermodynamic equation, neglect horizontal second order terms, use averaged continuity equation: “large-scale observable” terms “sub-grid” terms why use s and not T s =C p T+gz ds/dz= C p dT/dz+g If dT/dz=-g/C p (dry adiabatic lapse rate), then ds=0

58 Large-scale effects of convection (2) Q 1 and Q 2 This quantity can be derived from observations of the “large-scale” terms on the l.h.s. of the area-averaged equations and describe the influence of the “sub-grid” processes on the atmosphere. Define: Apparent heat source Analogous: Apparent moisture sink Apparent momentum source Note that : withMoist static energy

59 Large-scale effects of convection (3) vertical integrals of Q 1 and Q 2 Surface Precipitation flux Surface Precipitation Surface sensible Heat flux Surface latent Heat flux

60 Large-scale effects of convection (3) Deep convection Tropical Pacific Yanai et al., 1973, JAS Tropical Atlantic Yanai and Johnson, 1993 Note the typical tropical maximum of Q1 at 500 hPa, Q2 maximum is lower and typically at 800 hPa

61 Large-scale effects of convection (5) Shallow convection Nitta and Esbensen, 1974, MWR Q2Q2 Q1Q1 QRQR (K/day) P(hPa) q-difference of simulation without and with shallow convection. Without shallow boundary-layer is too moist and upper- troposphere too dry !

62 Effects of mesoscale organization The two modes of convective heating Structure Effects on heating (K/day) convective mesoscale total P(hPa) 300

63 Zonal average convective Q1 in IFS P (hPa) Latitude

64 Convective quasi-equilibrium (1) Arakawa and Schubert (1974) postulated that the level of activity of convection is such that their stabilizing effect balances the destabilization by large-scale processes. Observational evidence: v (700 hPa)  hPa  Precipitation GARP Atlantic Tropical Experiment (1974) Thompson et al., JAS, 1979

65 Summary (1) Convection is of crucial importance for the global energy and water balance Convection generates and/or influences a number of phenomena important to forecasting (thunderstorms, heavy precipitation, hurricanes) On large horizontal scales convection is in quasi-equilibrium with the large-scale forcing An important parameter for the strength of convection is CAPE Convection affects the atmosphere through condensation / evaporation and eddy transports

66 Summary (2) The effect of convection on the large scale depends on type of convection and synoptic situation Shallow convection is present over very large (oceanic) areas, it determines the redistribution of the surface fluxes and the transport of vapor and momentum from the subtropics to the ITCZ Q1, Q2 and Q3 are quantities that reflect the time and space average effect of convection (“unresolved scale”) and stratiform heating/drying (“resolved scale”)