The Formation of Tropical Cyclones 1

David J. Raymond

Physics Department and Geophysical Research Center New Mexico Tech Socorro, NM, USA

1Work supported by US National Science Foundation and Oﬃce of Naval Research What is a tropical cyclone?

I Closed circulation at all levels

I Warm core

I Maximum wind near surface

I Strong meridional secondary circulation with convection and rain Tropical cyclone tracks 1985-2005 (Wikipedia) Annual average sea surface temperatures (NOAA) Annual average atmospheric precipitable water (NASA) Spontaneous formation of TCs (RCE modeling) 2

“In some cases, tropical cyclones are found to form spontaneously from random convection. This formation is due to a cooperative interaction between large-scale moisture, long-wave radiation, and locally enhanced sea-surface ﬂuxes, similar to the aggregation of convection found in previous studies.” But it takes about two weeks ... occurs more rapidly from pre-existing disturbance

2Nolan, Rappin, and Emanuel (2007) Barotropic instability

Charney-Stern theorem latitudinal vorticity gradient changes sign latitude strip of relative vorticity

absolute vorticity

dζ ∂v ∂v a = 0; ζ = y − x + f dt a ∂x ∂y Conclusion...

I Barotropic instability is a key mechanism for generating tropical storms.

I But, why???

I Barotropic instability rearranges pattern of absolute vorticity, but does not increase it.

I The vorticity disturbances produced by baroclinic instability generally result in regions with closed circulations (in the moving reference frame of the disturbance). Protective “pouch” in a wave3

I The closed circulation in a pouch prevents the ingestion of dry air, allowing convection to moisten the pouch.

I This is only eﬀective if pouches at diﬀerent levels are vertically aligned ⇒ low wind shear.

3Dunkerton, Montgomery, and Wang (2009) Where do tropical cyclones form?

I Moist tropical regions with sea surface temperatures in excess of 26◦C.

I Away from equator – need non-zero Coriolis parameter.

I Develop out of pre-existing tropical weather disturbances, often produced by barotropic instability.

I Low wind shear. Convective Instability of the Second Kind (CISK) 4

convective heating in rotating flow lower surface warms env, lowers pressure causes surface pressure cyclonic circulation

frictional convergence forces convection

4Charney and Eliassen (1964) Critique of CISK 5

“... [T]he existence of a linear instability of the type envisioned by Charney and Eliassen (1964) would imply that weak tropical cyclones should be ubiquitous and not conﬁned to maritime environments.” “All numerical simulations of tropical cyclones reveal the essential importance of latent (and perhaps sensible) heat ﬂux from the sea surface, as proposed originally by Riehl (1954).”

5Emanuel (1986) Actual dynamics of spin up

downdrafts can cause surface divergence

surface fluxes radial flow may not be alter thermodynamics in Ekman balance

Flux form of vorticity equation:

∂ζa = −∇h· v hζa − ζ vz + kb × F = vort conv+tilting+frict ∂t h Ekman (im)balance

I Ekman balance in boundary layer (tilting not important there): vort conv + frict = 0

I Spin up cannot occur when Ekman balance holds!

I Understanding of spin up requires independent determination of vorticity convergence and hence mass convergence:

vort conv ≈ vorticity × mass conv Observations of tropical cyclone formation 6

I Proto-cyclones ﬁrst develop a vortex at middle levels in the troposphere.

I Only then does a smaller surface vortex form beneath the mid-level vortex.

6Ritchie and Holland (1993, 1997); Harr et al. (1996a,b); Simpson et al. (1997); Bister and Emanuel (1997); Raymond, López, and López, 1998) Examples from recent field programs 7

I TCS-08: August-September 2008, Guam, West Paciﬁc

I PREDICT: August-September 2010, St. Croix, Western Atlantic, Caribbean

I Dense array of dropsondes deployed into candidates for tropical cyclogenesis

I Area-average vorticity tendency obtained from 3-D Var analysis for:

I Hagupit2: Non-developing wave (developed into typhoon one week later)

I Nuri1: Intensifying tropical wave.

I Nuri2: Rapidly developing tropical depression (typhoon two days later)

7Raymond, Sessions, and L´opez (2011); Gjorgjievska and Raymond (2014) Hagupit2: Not intensifying at this time

Hagupit 2

14 14 14 convergence 12 12 tilting 12 friction 10 10 10 net

8 8 8

6 6 6 height (km) 4 4 4

2 2 2

0 0 0 0.00 0.05 0.10 0.15 0.20 0.1 0.0 0.1 0.2 0.3 0.03 0.00 0.03 0.06 0.09 1 1 1 2 vorticity (ks− ) vort tend (ks− day− ) mass flux (kg/m /s)

Both convergence and frictional tendencies are negative, resulting in spin-down. Nuri1: Intensifying wave

Nuri 1

14 14 14 convergence 12 12 tilting 12 friction 10 10 10 net

8 8 8

6 6 6 height (km) 4 4 4

2 2 2

0 0 0 0.00 0.05 0.10 0.15 0.20 0.1 0.0 0.1 0.2 0.3 0.03 0.00 0.03 0.06 0.09 1 1 1 2 vorticity (ks− ) vort tend (ks− day− ) mass flux (kg/m /s)

Spin up tendency from convergence strongest at mid-levels. Nuri2: 24 hr later, rapidly intensifying depression

Nuri 2

14 14 14 convergence 12 12 tilting 12 friction 10 10 10 net

8 8 8

6 6 6 height (km) 4 4 4

2 2 2

0 0 0 0.00 0.05 0.10 0.15 0.20 0.1 0.0 0.1 0.2 0.3 0.03 0.00 0.03 0.06 0.09 1 1 1 2 vorticity (ks− ) vort tend (ks− day− ) mass flux (kg/m /s)

Spin up tendency at surface far exceeds frictional spin-down tendency. Mass ﬂux proﬁle and vorticity tendency height height

top−heavy mass flux profile bottom−heavy mass flux profile

But what controls mass flux profile??? Thermodynamic effect of a vortex

Hagupit2 Nuri2 warm

PV anomaly warm cool PV anomaly Nuri2 vs. Hagupit2

Temperature difference: nuri2 - hagupit2 10 z vs dtemp z vs dtvirt 8

4 height (km)

0 1.5 1.0 0.5 0.0 0.5 1.0 temp diff (K) Two key indices

Saturation fraction: Schematic of instability index Z trop Z trop ∗ SF = rdp r dp 12 surf surf 10 instability index Instability index: 8

6 ∗ ∗ ∗

II = ∆s = s − s height (km) 1−3km 5−7km 4 Saturated moist entropy: 2 0 saturated entropy ∗ ∗ s = Cp ln θe Instability index for Nuri and Hagupit

Entropy (dashed) and saturated entropy (solid) profiles 10 Hagupit2 -- II = 27, SF = 0.82 Nuri1 -- II = 17, SF = 0.81 8 Nuri2 -- II = 11, SF = 0.88

4 height (km)

0 200 220 240 260 280 300 320 entropy (J/K/kg) Mass ﬂux proﬁle and vorticity tendency

normal SF, II larger SF, smaller II height height

top−heavy mass flux profile bottom−heavy mass flux profile Instability index vs. saturation fraction8

green -- TS in 0-48 hr 40

20 instability index (J/K/kg) 15

10 0.65 0.70 0.75 0.80 0.85 0.90 saturation fraction 8Raymond, Sessions, and L´opez (2011); Gjorgjievska and Raymond (2014) Mid-level vorticity vs. instability index

green -- TS in 0-48 hr 0.14 N2

0.12 ) 1 − 0.10

0.08

0.06 H2 mid-level vort (ks

0.04

0.02 10 15 20 25 30 35 40 instability index (J/K/kg) Low-level vorticity tendency vs. instability index

green -- TS in 0-48 hr 2.0

N2 1.5 ) 2 − s k

( 1.0

d n e t

r 0.5 o v

l H2 e v

e 0.0 l - w o l 0.5

1.0 10 15 20 25 30 35 40 instability index (J/K/kg) Pathway to cyclogenesis

enhanced top-heavy mid-level vorticity smaller II and greater SF tropical convection results in reduced result in bottom-heavy in tropical disturbance instability index convection and low-level spinup

mid-level vortex reduced instability tropical cyclogenesis spins up index results in increased saturation fraction References...

I Bister, M., and K. A. Emanuel, 1997: The genesis of hurricane Guillermo: TEXMEX analyses and a modeling study. Mon. Wea. Rev., 125, 2662-2682.

I Burpee, R. W., 1972: The origin and structure of easterly waves in the lower troposphere of North Africa. J. Atmos. Sci., 29, 77-90.

I Charney, J. G. and A. Eliassen, 1964: On the growth of the hurricane depression. J. Atmos. Sci., 21, 68-75.

I Dunkerton, T. J., M. T. Montgomery, and Z. Wang, 2009: Tropical cyclogenesis in a tropical wave critical layer: Easterly waves. Atmos. Chem. Phys., 9, 5587-5646. References continued...

I Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones: Part I: Steady state maintenance. J. Atmos. Sci., 43, 585-604.

I Ferreira, R. N., and W. H. Schubert, 1997: Barotropic aspects of ITCZ breakdown. J. Atmos. Sci., 54, 261-285.

I Gjorgjievska, S., and D. J. Raymond, 2014: Interaction between dynamics and thermodynamics during tropical cyclogenesis. Atmos. Chem. Phys., 14, 3065-3082.

I Harr, P. A., M. S. Kalafsky, and R. L. Elsberry, 1996: Environmental conditions prior to formation of a midget tropical cyclone during TCM-93. Mon. Wea. Rev., 124, 1693-1710. References continued...

I Harr, P. A., R. L. Elsberry, and J. C. L. Chan, 1996: Transformation of a large monsoon depression to a tropical storm during TCM-93. Mon. Wea. Rev., 124, 2625-2643.

I Maloney, E. D., and D. L. Hartmann, 2001: The Madden-Julian oscillation, barotropic dynamics, and north Paciﬁc tropical cyclone formation. Part I: Observations. J. Atmos. Sci., 58, 2545-2558.

I Molinari, J., D. Knight, M. Dickinson, D. Vollaro, and S. Skubis, 1997: Potential vorticity, easterly waves, and eastern Paciﬁc tropical cyclogenesis. Mon. Wea. Rev., 125, 2699-2708. References continued...

I Nolan, D. S., E. D. Rappin, and K. A., Emanuel, 2007: Tropical cyclogenesis sensitivity to environmental parameters in radiative-convective equilibrium. Quart. J. Roy. Meteor. Soc., 133, 2085-2107.

I Raymond, D. J., S. L. Sessions, and C. L´opez Carrillo, 2011: Thermodynamics of tropical cyclogenesis in the northwest Paciﬁc. J. Geophys. Res., 116, D18101, doi:10.1029/2011JD015624.

I Ritchie, E. A. and G. J. Holland, 1993: On the interaction of tropical-cyclone-scale vortices II. discrete vortex patches. Quart. J. Roy. Meteor. Soc., 119, 1363-1379.

I Ritchie, E. A. and G. J. Holland, 1997: Scale interactions during the formation of Typhoon Irving. Mon. Wea. Rev., 125, 1377-1396. References continued...

I Simpson, J., E. Ritchie, G. J. Holland, J. Halverson, and S. Stewart, 1997: Mesoscale interactions in tropical cyclone genesis. Mon. Wea. Rev., 125, 2643-2661.

I Wang, C.-C., and G. Magnusdottir, 2005: ITCZ Breakdown in three-dimensional ﬂows. J. Atmos. Sci., 62, 1497-1512.

I Wang, C.-C., and G. Magnusdottir, 2006: The ITCZ in the central and eastern Paciﬁc on synoptic time scales. Mon. Wea. Rev., 134, 1405-1421. Origin of African easterly waves ...

“This study shows that the African waves are directly related to the mid-tropospheric easterly jet that is found within the baroclinic zone to the south of the Sahara. During the same season that the waves are observed, the gradient of the monthly mean potential vorticity vanishes along the isentropic surfaces. Charney and Stern have shown that this is a necessary condition for instability of the jet provided that the amplitude of the waves is negligible at the ground. Results show that the horizontal [south] and vertical [north] shear of the mean zonal wind are acting as nearly equal sources of energy for the perturbations. The role of convection in the origin of these waves has not yet been determined.” ... and their role in TC formation 9

“From June to early October these waves propagate across the Atlantic and occasionally reach the eastern Paciﬁc. Although only a few of these disturbances actually intensify after reaching the Atlantic, they account for approximately half of the tropical cyclones that form in the Atlantic.”

9Burpee (1972) Barotropic instability in SW Caribbean and E Paciﬁc 10

Potential vorticity (0.1 PVU) on 310 K isentropic surface, 15 June through 30 September, 1991.

10Molinari et al. (1997) ITCZ dynamics

vorticity decreases ITCZ height vorticity increases

latitude ITCZ breakdown (low-level wind, vorticity) ...... and rollup 11

11Ferreira and Schubert, 1997; Wang and Magnusdottir (2005, 2006) MJO and East Paciﬁc Hurricanes 12

12Maloney and Hartmann (2001)