The Importance of Convection from a Large Scale ... - IMAGe
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The Importance of Convection from a Large Scale ... - IMAGe

The Importance of Convection from aLarge Scale Dynamical PerspectiveDargan M. W. FriersonUCAR/University of Chicago2 November 2005

2 November 2005 1Some Motivation

2 November 2005 2Talk Outline◮ A Simplified Moist GCM – model description◮ A Simple Convection Scheme• Formulation• Effect on Zonally Averaged CirculationHadley circulation (energy and mass transports),tropical precipitation• Effect on Transient Dynamics/Equatorial WavesSpeed/strength of equatorial Kelvin waves

2 November 2005 3◮ Goal:A Simplified Moist GCM• Design a simplified GCM that incorporates thedynamical effect of moisture in the simplest possiblemanner, while remaining fully modular with full GCMphysical parameterizations whenever possible◮ The model:• Primitive equations: up to T170 resolution, 25 levels• Gray radiative transfer (next slide)• Aquaplanet slab mixed layer oceanClosed system in terms of energetics (atmosphereperforms all the energy transports)• Simplified Monin-Obukhov surface flux scheme, K-profileboundary layer scheme

2 November 2005 4Radiation Scheme◮ Gray radiation: Water vapor, clouds, other tracers have noeffect on radiation.◮ Parameters: longwave optical depths, shortwave heating0LW optical depths400SW heating of surface200300Pressure400600800W/m 22001001000−50 0 50Latitude0−50 0 50Latitude◮ All shortwave (solar) heating into surface

2 November 2005 5Moisture/Convection◮ No condensate, no microphysics, no freezing◮ Simplest convection scheme: no convection scheme!(large scale condensation (LSC) only)• Precipitation occurs when a gridbox becomessaturated• Model can be integrated with this• Revaporate precipitation into unsaturated areas• Similar in practice to moist convective adjustment

2 November 2005 6No Convection Scheme Simulations◮ Instantaneous precip, T85 and T170 resolutionsT85x 10 −32Latitude500−501.510.50 50 100 150 200 250 300 3500T170x 10 −32Latitude500−501.510.50 50 100 150 200 250 300 350Longitude0

2 November 2005 7No Convection Scheme Simulations◮ Precipitation is concentrated at the grid scale in the tropics◮ Tropics are sensitive to resolution in this model: howevermidlatitudes are not◮ This version of the model used in studies of moisture effectson midlatitude static stability, eddy scales, energy fluxes,and jet latitude. (Frierson, Held and Zurita-Gotor 2006a, b)◮ Also used in a nonhydrostatic GCM to study the“hypohydrostatic” rescaling (Garner et al 2006)

2 November 2005 8A Simplified Betts-Miller (SBM) ConvectionScheme◮ Basic principle: relax temperature, humidity to somepost-convective equilibrium profile (Betts 1986, Betts andMiller 1986, see also Arakawa 2004)δT = − T − T eqτ c, δq = − q − q eqτ c◮ Equilibrium temperature profile: moist adiabat from surfaceparcel (relax up to LZB)◮ Equilibrium humidity profile: specified relative humidity withrespect to the equilibrium temperature◮ First complication: enthalpy conservation(− R δqdp/g = R c pδTdp/g, or drying must equal heating)L

2 November 2005 9Enthalpy Conservation◮ Shift reference temperatures by a uniform amount in heightto satisfy enthalpy conservation (simplest method that iscontinuous, similar to real Betts-Miller scheme)∆k =1∆pZ pLZBp 0T eq2 = T eq − ∆kc p−(c p δT + Lδq)dp◮ If the column is too dry, the temperature correction isnegative (rough simulation of downdrafts)◮ Implies precipitation is no longer correlated with CAPE.◮ Second complication: what if predicted precipitation afterthis adjustment is negative?

2 November 2005 10Shallow Convection◮ When predicted precipitation is negative, set precip tozero and perform “shallow convection”◮ Three methods of doing this:• No adjustment of temperature and humidity: baselinefor comparison (δT = δq = 0)• Change humidity profile by uniform fraction (Choose f qin q eq2 = f q q eq such that net drying equals zero): “qref”• Lower depth to where net drying equals zero (Choosep shall such that 0 = R p shallp(− q−q ref0 τ c)): “shallower”

2 November 2005 11Sensitivity to Shallow Scheme◮ Simulations with τ c = 2h, RH SBM = .7, instantaneousprecipLSC onlyx 10 −4SBM with no shallow convectionx 10 −4Latitude500−5042Latitude500−50420 100 200 300SBM with qref0x 10 −40 100 200 300SBM with shallower0x 10 −4Latitude500−5042Latitude500−50420 100 200 300Longitude00 100 200 3000◮ With no shallow convection scheme, the convectionscheme is much less effective◮ Two shallow schemes are qualitatively similar

2 November 2005 12Hadley Circulation◮ Moist static energy fluxes by Hadley circulation (30N-30S):321Flux, PW0−1−2−3−30 −20 −10 0 10 20 30Latitude◮ Equatorward transport by Hadley circulation for LSC only◮ Two SBM shallow convection schemes are similar◮ LSC has 50% larger mass flux compared with SBM!

2 November 2005 13Precipitation◮ Zonal mean precip (30N-30S):500450400shallowerqrefLSCno shallow350Precip, W/m 2300250200150100500−30 −20 −10 0 10 20 30Latitude◮ ITCZ precip scales with Hadley circulation strength (largerfor LSC and no shallow)◮ Increased precip within ITCZ in LSC and no shallow casesare accompanied by reduction within subtropics (totalprecip remains similar)

2 November 2005 14Ability to Build Up CAPE◮ Claim: key categorization of convection schemes is abilityto build up and rapidly release CAPE (abruptness ofconvective trigger)◮ Time series of precip and CAPE along the equator:8000LSC8000SBM, no shallow60006000400040002000200000 10 20 30 40 5000 10 20 30 40 5040003000shallower40003000qrefPrecipCAPE200020001000100000 10 20 30 40 50Days00 10 20 30 40 50Days

2 November 2005 15Ability to Build Up CAPE◮ Test with a more stringent convective criteria: RH SBM = .832shallowerqrefLSCno shallow1Flux, PW0−1−2−3−30 −20 −10 0 10 20 30Latitude◮ Two shallow schemes begin to diverge◮ No shallow scheme looks more like LSC only simulations

2 November 2005 16Shallow Convection Summary◮ Properties of schemes that have abrupt release of CAPE(LSC, or SBM with no shallow scheme):• Smaller energy transports by Hadley cell• Larger Hadley circulation mass flux• Smaller/negative “gross moist stability” = mv¯v• Larger eddy moisture fluxesGMS, K302520151050 shallowerqref−5 LSCno shallow−10−30 −20 −10 0Latitude10 20 30• More resolution dependence

2 November 2005 17Effect of Convective Relaxation Time◮ Vary relaxation time: τ c = 1h, 2h, 4h, 8h, 16h◮ Significant effects on many aspects of the circulation:transients, relative humidity, fraction of convection, etc◮ However there is no effect on Hadley circulation system(provided large scale precip does not occur)32Flux, PW10−1−2−3−30 −20 −10 0 10 20 30Latitude◮ Mass transport and ITCZ precip are within 2 % for first 4cases (then an abrupt increase of 35%)

2 November 2005 18Effect of Convective Relaxation Time◮ How is the circulation so insensitive to relaxation time?◮ Rewrite the precipitation expression:¯q = ¯q eq + τ c PHumidity adjusts to keep precip the same.◮ This same adjustment occurs in simple models such asFrierson, Majda and Pauluis 2004.◮ Sensitivity to RH SBM is more complicated due to changesin surface budget, but circulation is still relatively insensitive

2 November 2005 19Tropical Waves◮ Method of Wheeler and Kiladis (1999):• Fourier transform over the tropics in space and time• Separate into eastward and westward propagation• Take out “background spectrum”• Observations show Kelvin waves, Rossby waves, etcwith reduced phase speeds

2 November 2005 20◮ Dry wave equation:Gross Moist Stability∂u∂t∂T∂t= − ∂T∂x(1)= −∆s ∂u∂x + P (2)where ∆s is dry stability◮ But precip is correlated with convergence (P = −∆q ∂u∂x )∂T∂t = −∆m∂u ∂xwith ∆m = ∆s − ∆q, the gross moist stability◮ Phase speed goes as √ ∆m

2 November 2005 21Tropical Waves◮ Wheeler-Kiladis diagram for precip for simulation withτ c = 2h, RH SBM = .6Frequency0.−time spectrum0−15 −10 −5 0 5 10 15Wavenumber◮ Strong, persistent Kelvin wave dominates the spectrum◮ Speed ≈ 20 m/s (40 m equivalent depth), only slightly fasterthan observations. What sets speed? Sensitive toconvection scheme parameters?

2 November 2005 22Control Simulation Kelvin Wave Composite◮ Method of Wheeler, Kiladis, and Webster: take Kelvinfiltered time series at a point on the equator, regress thisagainst other fieldsLongitudeLongitudeLongitude20100−10−2020100−10−2020100−10−20Precip and surface windsOmega(500 mbar)−80 −60 −40 −20 0 20 40 60 80p surf−80 −60 −40 −20 0 20 40 60 80−80 −60 −40 −20 0 20 40 60 80Latitude2001000−1000−0.05−0.11000−100−200

2 November 2005 23Control Simulation Composite◮ P, E, u surf on the equator:600PrecipitationW/m 24002000250Evaporation−80 −60 −40 −20 0 20 40 60 80W/m 2200150100505Surface zonal wind−80 −60 −40 −20 0 20 40 60 80m/s0−5−10−80 −60 −40 −20 0 20 40 60 80Longitude◮ Evaporation leads and provides strength for wave:evaporation-wind feedback is energy source(E = C D |u|(q s − q))

2 November 2005 24Control Simulation Composite◮ Shallow convection leads and propagates moistureupwards600PrecipitationW/m 240020000Omega−80 −60 −40 −20 0 20 40 60 80Pressure−500−10000Humidity−80 −60 −40 −20 0 20 40 60 80Pressure−500−1000−80 −60 −40 −20 0 20 40 60 80Longitude

2 November 2005 25Sensitivity to Relaxation Time◮ Wheeler-Kiladis diagram for different τ c (2 h, 4 h, 8 h)0.8ST for ps, tau=2h40.8ST for ps, tau=4h40.8ST for ps, tau=8h40.63.530.63.530.63.530.−10 0 101.50−10 0 101.50−10 0 101.5◮ Longer relaxation time causes additional convectivedamping (Emanuel 1993)

2 November 2005 26Relaxation Time Composites◮ Kelvin wave composite of P, omega, q for τ c = 2h, 4h:600Precip, τ = 2h600Precip, τ=4 h500500W/m 24003004003002002001000−50 0 50Omega1000−50 0 50OmegaPressure−500−500−10000−50 0 50Temp−10000−50 0 50TempPressure−500−500−1000−50 0 50Longitude−1000−50 0 50Longitude◮ Temperature more out of phase with vertical velocity withlonger relaxation time

2 November 2005 27Simulations With Some Large Scale Precip◮ Next increase RH SBM from the control value to causesome large scale precip to occur (with τ = 4h here)0.8RH=.60.8RH=.80.8RH=.9Frequency0.60.40.2Frequency0.60.40.2Frequency0.60.40.20−10 0 10Wavenumber0−10 0 10Wavenumber0−10 0 10Wavenumber◮ Percent of large scale precip: (0%, 18%, 99%)◮ When there’s mostly large scale precip, no Kelvin wave◮ With some large scale precip, the variability is enhanced,and the propagation speed becomes slower

2 November 2005 28Composites◮ Composites of RH=.6 and .8 casesPrecip, RH = .6Precip, RH = .8W/m 2700600500400300200700600500400300200100−50 0 50100−50 0 500Omega0Omega−200−200Pressure−400−600−800−400−600−800−1000−50 0 50Longitude−1000−50 0 50Longitude

2 November 2005 29Gross Moist Stability◮ Vertical advection of moist static energy divided byvertical advection of dry static energy:0.40.35Gross moist stability ratioRH=.6RH=.80.3ratio0. 206004002000Precipitation−80 −60 −40 −20 0 20 40 60 80−80 −60 −40 −20 0 20 40 60 80LongitudeRH=.6RH=.8

2 November 2005 30Conclusions◮ Convection can have significant effect on zonallyaveraged tropical circulation◮ Key classification of convection schemes: ability to buildup and rapidly release CAPE◮ Relative insensitivity to convection scheme parameters,provided LSC precip is not allowed to occur◮ LSC precip enhances and slows simulated equatorial Kelvinwaves◮ Concurrent and future work• 2-D Walker cell – within this model and full GCM• Quantitative theory for gross moist stability• Fully moist Hadley circulation theory

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