EAS 447: Tropical Meteorology

1. EAS 447: Tropical Meteorology The Effects of a Small Coriolis Parameter, Hadley Cell characteristics, Barotropic and Inertial Instabilities, and a few miscellaneous introductory topics

2. Scale analysis • Scale the Navier-Stokes equation governing fluid motion in the x-direction (y-direction is very similar) • du/dt – fv + f*w + uw/a – uvtanϕ/a = - 1/ρ delP + ν del2u • For mean motions in the Hadley Cell, we are interested in large-scale balance.

3. Navier-Stokes Equation in X-dir du/dt – fv + f*w + uw/a – uvtanϕ/a = -(1/ρ) (δp/δx) + ν (δ2u/δ2z) • T = L/U, • L = 1000 km = 106 m (these should be unitless, but I am putting units for you to explicitly understand) • U, V = 10 ms-1 • ϕ = latitude (say, 10° for simplicity) • f = 2Ω sinϕ = 2*(2 π/86400 s)* sinϕ ~ 10-5 s-1 (we are in the tropics, remember that f is small!) • f* is 2Ω cosϕ • W is small at large scales- try 1 x 10-2 ms-1 • a is the radius of earth, set at 1 x 107 m for ease

4. Scale analysis U2/L – fV + f*W + UW/a – UVtanϕ/a = -(1/ρ) (δP/L) + ν (δ2U/δ2Z) • ρ = air density, let it be 1 kg/m3 • H = 104 m • ν = dynamic viscosity of air, which is 9.49 x 10-6 m2/s or ~1x10-5 m2/s at 250 K. So, the last term is tiny, at about 10-12 m/s2.

5. Scale analysis U2/L fV f*W UW/a UVtanϕ/a = (1/ρ) (δP/L) + F • U2/L~10-4 fV~10-4f*W~10-6 UW/a~10-8 UVtanϕ/a~10-6 = (1/ρ) (δP/L)~10-4F~10-12

6. Scale analysis U2/L - fV = - (1/ρ) (δP/L) This leaves us with gradient wind balance on synoptic length scales in the tropics, since f is small. Pressure gradient was chosen to balance left side of equation. It is about 102 Pa / 1000 km, meaning about 1 mb per 1000 km. Since the Coriolis acceleration is weak, synoptic scale pressure gradients are small. Plotting surface pressure in the tropics is not a particularly useful analysis in general. Convergence and rotation of winds important to tropical circulations, so streamline analysis is of greater use than plotting pressure on a constant height surface, especially at low levels. Same concepts are applicable for the y-momentum equation.

7. Scale analysis Synoptic scale temperature gradients, like pressure gradients, are small: T = δψ / Rd ~ δP / Rd Ψ = geopotential fluctuation scale T = 102 / 287 ~ 0.3 K So, for scales of 106 m, temperature and pressure variations are very small in the tropics.

10. Rossby Radius of Deformation • LR = (NH) / (ζ+f)1/2 ((2Vθ/r)+f)1/2 • N=Brunt-Viasala frequency, H = scale height pertaining to wave, Vθ = tangential wind speed • If r < LR : Mass adjusts to wind. Inertially unstable. High values of relative vorticity and tangential wind speeds will do this. Coriolis acceleration is small in this case, so this is for rather small systems usually, where Ro > 1 (that is, U/foL > 1). They can be larger in the tropics, since f is small. For example, UL Div can significantly alter mass and circulation fields.

11. Rossby Radius of Deformation • LR = (NH) / (ζ+f)1/2 ((2Vθ/r)+f)1/2 • If r > LR : Wind adjusts to mass • Typical of midlatitude baroclinic waves. Also, think of the general circulation: Temperature differences tend to create pressure differences Pressure differences help drive the wind… and this brings us to the Hadley Cell circulation!

13. Things to remember about the Tropics… • Easterly trade winds near the surface • Westerly winds at upper levels • Generally need condensation for instability • Heat exported polewards • Direct thermal circulation of Hadley cell greater than eddies at heat and momentum transport • Easterly and westerly waves

14. Lorenz energy cycle • Tropics are different from the midlatitudes in that the direct thermal circulation from the Hadley Cell largely converts mean available potential energy into mean kinetic energy through the averaged vertical heat flux term, wT. • Midlatitude processes typically covert eddy kinetic energy into mean kinetic energy as a result of product of the eddy momentum flux and mean meridional shear of planetary extratropical waves u’v’(du/dy).

15. Heat Absorbed v Emitted to Space

16. Intertropical Convergence Zone • ITCZ: solar heating strongest at the surface over the course of the year. Instability (moisture and lift aided by low level convergence once a circulation established). • Moist convection and LH release effectively warm mid and upper troposphere • DTC and transport heat upward and poleward • Updraft reaches tropopause and increasing static stability. Air diverges aloft, due to stability and higher pressure aloft relative to higher latitudes due to expansion of air column via convective heating. Air heads poleward and then also eastward due to Earth’s rotation.

17. Intertropical Convergence Zone • LL convergence and UL divergence • Moist and warm climates (tropical wet) • Average yearly position in Northern Hemisphere; penetrates to relatively high latitude over land in summer hemisphere

18. Average ITCZ position Jan & July:

19. Intertropical Convergence Zone • Most ITCZ lightning over land: -more heating over land (more instability, higher updraft speed) and clouds get higher (colder temperatures) CAPE = §ELZ w dw/dz = g ((T’ – T)/T) dz w2/2 = §LNBZ (T’-T)/T dz -drier midlevel air (promotes cooling) -more aerosols • Deep convection needs moisture, instability, & lift • Lift is the largest limiting factor in the tropics overall- forcing is often subtle & localized

20. Tropical Moist Convection • Heavy precipitation thunderstorms common due to high precipitable water levels and generally low vertical wind shear • Relatively moist adiabatic environment over much of the tropics as well, especially over the oceans • High BRNs, mostly • Most common type of severe weather would be high winds from squall lines, which may result from local effects, such as topographical or moisture gradients

21. Small Scale Tropical Phenomena • Water spouts often form along lines of cumulus congestus or cumulonimbus clouds • Warm center (perturbation about 0.3 K), 1-10 mb P deficit, cyclonic or anticyclonic rotation; typically most intense lowest 1000 m near surface; winds generally < 30ms-1 • High SST; too strong of a thunderstorm downdraft typically kills waterspout • Dust devils actually quite similar in values to water spouts listed above; unstable airmass, often dry

22. Tropical Savannah Climates • Typically experience a well-defined dry and wet season over the course of the year • Usually wet in summer and early fall season, with a dry winter and early spring • Increased moisture helps also increase instability during local summer, generally leading to better chances of precipitation then

24. Subtropical Highs • Air at upper levels turns poleward and eastward; dries, becomes dense, and sinks; can only go so far north due to conservation of angular momentum. Viscous dissipation and energy conversion may also be factors. • Dominated by slow subsidence • Large aerial expanse, typically centered near 30° latitude • Often produce arid climates; often deserts (Sahara, Atacama, Kalahari, Arabia, Outback, Mexico and SW US)

25. Subtropical Highs • Surface flow returns from subtropical highs to ITCZ. Goes equatorward and turns westward due to Coriolis acceleration. • Air has been warmed and dried by subsidence. Also heated from surface below, though cools upwards in PBL. Often, a subsidence inversion forms above PBL, which may have stratus below the inversion. • Cool sea surface temperatures, especially on east side of ocean basin- reduce PBL temperatures and often reinforce inversion.

27. Subtropical Highs- Trade Wind Inversion • Cold Sea surface temperatures on east side of ocean basin along with conservation of potential vorticity lead to a stronger trade wind inversion on east side of ocean basin. • Colder low levels east side: h decreases • Shallow water PV = (ζ + f ) / h • Coriolis parameter, f, decreases from North Pole to equator, so air flowing south will see a decrease in f. Relative vorticity, ζ, may also decrease to adjust for decrease in h.

28. Subtropical Highs • On average, colder climate than ITCZ annually since winters are significantly cooler on average. • Stronger mass circulation in winter due to increased temperature gradient in winter hemisphere. • Wider expanse of subtropical high coverage in winter and early spring hemisphere as ITCZ is then located in opposite hemisphere.

29. Average surface pressure and associated winds for January Figure 18.16 A

30. Average surface pressure and associated winds for July Figure 18.16 B

32. Hadley Cell Structure • Subtropical ridge and ITCZ tilt equatorward with height; towards cooler air with height (tropical tropopause is higher and colder) • Equatorial region often actually experiences subsidence in area: 3 ½ cell model by Asnani • mT air equatorward of ITCZ; cT air poleward of ITCZ

33. Tropical Upper Tropospheric Troughs (TUTTs) TUTTs appear to originate from midlatitude troughs, though not certain. Common in Western and Central Pacific and North Atlantic though present in other basins, too. Common in North Atlantic June-September. Typically increase vertical wind shear and may increase static stability by cooling most of the troposphere except above 300 hPa. Often, convective coverage is rather low.

34. Global Pressure Tides in the Tropics • These waves are global in nature but strongest in the tropics. • Diurnal pressure wave (weaker): maximum surface pressure around 5 AM; minimum around 5 PM • Semi-diurnal pressure wave (stronger): 10 AM and 10 AM maximum surface pressures; 4 AM and 4 PM minima

35. Global Pressure Tides in the Tropics As a result, we have a strong diurnal minima in surface pressure for the tropics for a given location at slightly after 4 PM local time, with the strongest maximum slightly before 10 AM. A weaker minimum is around 4 AM and a weaker maximum is slightly after 10 PM. These fluctuations are on the order of 1-2 mb.

36. Barotropic and Inertial Instabilities • Barotropic instability results in vortical flow oriented about a vertical axis, while inertial stability results in flow around a horizontal axis. • Barotropic Instability: • β - δ2u/δ2y <0 or Δη/Δy <0 where η = f + ζ ζ = δv/δx - δu/δy. Focus on - δu/δy since we are interested in meridional changes.

37. Inertial Instability • Inertial Instability: • δM/δy < 0: unstable δM/δy = (1/a) δ/δ ϕ (u cosϕ + Ωa cos2ϕ) Plug in δy = a δϕ and manipulate to find: δM/δy = -a cos ϕ (- δu/δy + u tanϕ / a + f) δu/δy > f + (u tanϕ/a) => Unstable case

38. Where do we find these two types of instabilities? • Equatorward side of westerly jet stream or poleward side of easterly jet stream, at least in the Northern Hemisphere. • Often, jets are not peaked enough to exhibit instability. • Vortices may exhibit this, such as tornadoes and the inner core of hurricanes.

40. Held-Hou Model • I will give you an end result of their findings. • They find the meridional extent of the Hadley Cell, ϕH, to be determined by the following: ϕH = (5/3) (g H ΔH / Ω2a2) Factors such as increased temperature gradients increase the meridional extent of the Hadley Cell, which makes sense since the circulation is largest and most vigorous in the cold season, when equatorial to subtropical high temperature gradients are greatest. Also, momentum argument fairly straightforward.

41. END Section • Next section is ocean circulation and monsoons.

42. Scale analysis- Vertical N-S Eq dw/dt – f*u – (u2 + v2) /a = -(1/ρ) (δP/δz) -g + ν (δ2w/δ2z) • Same numbers as before, except δP is much different as, δP/δz >> δP/δx

43. Scale analysis- Vertical N-S Eq dw/dt – f*u – (u2 + v2) /a = -(1/ρ) (δP/δz) -g + ν (δ2w/δ2z) UW/L f*U 2U2 /a = -(1/ρ) (δP/δz) -g + F 10-7 10-3 10-5 = 1 (δP/104) 10 10-12