Large-scale disturbances and convection Željka Fuchs, University of Split
Huatulco airport
Tropical disturbances Tropical cyclones Monsoons Easterly waves Madden-Julian oscillation Convectively coupled equatorial waves
Convectively coupled equatorial waves Correspond to Matsuno solutions in dry atmosphere Primitive equations Linearize, analytical model not a real world Close the system - assumptions
Convectively coupled equatorial waves Closures/destabilization mechanisms: CAPE closure CIN closure Moisture closure WISHE
Thermodynamics RF the strength of convective inhibition saturation fraction of the troposphere, GMS Cloud-radiation interactions surface moist entropy fluxes earlier work - CAPE
Gross moist stability The gross moist stability relates the net lateral outflow of moist entropy or moist static energy from an atmospheric convective region to some measure of the strength of the convection in that region. Convective profile: max mass flux in lower troposphere lateral flow imports moist entropy GMS negative - increases saturation fraction Stratiform profile: max mass flux in upper troposphere lateral flow exports moist entropy GMS positive decreases saturation fraction (moisture divergence generally negative in convectively active regions)
Thermodynamics RF 2007 and 2010 Model Physics Precipitation rate = P 1 + P 2 Precipitation due to precipitable water and GMS: P 1 = a h 0 q(z)dz Precipitation due to CIN: P 2 = m CIN [e s e t ] e s is moist entropy in the boundary layer e t is saturated moist entropy just above the boundary layer
Convectively coupled Kelvin waves and the moisture mode Assume x and t dependance 2D vertical structure
Vertical structure The first baroclinic mode structure of simple quasiequilibrium models does not capture the observed complex vertical structure of the temperature, heating and vertical velocity for convectively coupled equatorial Kelvin waves. The vertical structure influences the dynamics of Kelvin waves and as such should be an important part of the models.
Why not simply calculate the vertical structure? Fuchs and Raymond (2007) and Raymond and Fuchs (2007) developed a vertically resolved model that calculates the observed complex vertical structure of convectively coupled Kelvin waves from a simple, sinusoidal vertical heating profile.
2007 Model - Dynamics RF07 model non-rotating atmosphere, vertically resolved model heating profile B sinm 0 z where m 0 = p/ h
Im(w) (1/day) Re(w)/k (m/s) 2007 Results B sinm 0 z CCKW, free KW and MM 50 25 0-25 -50 A - phase speed 0.3 0 B - growth rate -0.3 0 5 10 15 20
More on vertical structure different heating and moisture profiles heating profile: the effects of top and bottom heavy vertical heating profiles moisture profiles are varied to produce different values of the gross moist stability (GMS) the essential results of the models can be obtained without assuming change in vertical heating profile with wave phase.
2010 Model - Dynamics New model NEW HEATING PROFILE B exp(m 0 cz) sin(m 0 z) varying c gives stratiform, deep or shallow convective heating
Im(w) (1/day) Re(w)/k (m/s) CCKW different heating profiles Convectively coupled Kelvin wave - different heating profiles 25 A - phase speed 20 15 10 5 0 bottom heating middle heating top heating 1 0.5 B - growth rate 0-0.5-1 0 5 10 15 20 l
Im(w) (1/day) Re(w)/k (m/s) CCKW different heating profiles Kelvin waves with top heavy heating profile for different CIN values 50 A - phase speed 25 0-25 CIN = 12 CIN = 6 CIN = 3 CIN = 1 CIN = 0-50 1 0.5 B - growth rate 0-0.5-1 0 5 10 15 20 l
Im(w) (1/day) Re(w)/k (m/s) Moisture mode different heating profiles Moisture mode - different heating profiles 10 A - phase speed 5 0-5 -10 top heating middle heating bottom heating 0.5 0 B - growth rate -0.5 0 5 10 15 20 l
Im(w) (1/day) Re(w)/k (m/s) Moisture mode different GMS GMS equal to 0 (solid line), -0.07 (longdash), -0.14 (mediumdash), and -0.21 (shortdash) 1 A - phase speed 0-1 0.3 B - growth rate 0.2 0.1 0 0 5 10 15 20 l
z/h z/h Temperature perturbation and heating anomaly CCKW 1 1 0.5 0.5 0 west east 0 0.2 0.4 0.6 0.8 1 x/l 0 west east 0 0.2 0.4 0.6 0.8 1 x/l
Conclusions vertically resolved model different heating (top to bottom) and moisture profiles (GMS) convectively coupled Kelvin waves are favored by top heavy heating profiles with positive GMS moisture modes are produced whenever the GMS is negative (MJO)
Your task Derive the dispersion relation starting with the linearized system of equations much like in the paper http://www.pmfst.hr/~zeljka/research.html find: Raymond, D. J., and Z. Fuchs, 2007: Convectively coupled gravity and moisture modes in a simple atmospheric model. Tellus, 59A, 627-640. You will neglect the surface fluxes and radiation to make your life easier so your dispersion relation will be different than in this paper. Give a 5 minute intro into the subject and present the derived dispersion relation briefly discussing the results that can be obtained from it. The newest paper on the subject if you want to do some more reading is http://physics.nmt.edu/~raymond/publications.html find: Fuchs, Z., S. Gjorgjievska, and D. J. Raymond, 2012: Effects of varying the shape of the convective heating profile on convectively coupled gravity waves and moisture modes, J. Atmos. Sci., 69, 2505-2519.