4. Atmospheric transport Forces in the atmosphere: Gravity g Pressure-gradient a p 1/ dp / dx for x-direction (also y, z directions) Coriolis ac 2 v sin to R of direction of motion (NH) or L (SH) Angular velocity = 2/24hh Friction a f kv Wind speed v Equilibrium of forces: Latitude Friction coefficient k In vertical: barometric law

ap In horizontal: geostrophic flow parallel to isobars v P P + P ac In horizontal, near surface: flow tilted to region of low pressure ap af v

ac P P + P The Coriolis force GEOSTROPHIC FLOW: equilibrium between pressure-gradient and Coriolis forces Isobar ap ac

steady parallel to isobars speed ~ pressure gradient ap ap ac N hemisphere example Circulation around Highs and Lows How Highs and Lows affect surface weather

air rises precipitation Surface Low air sinks dry weather Surface High Great red spot of Jupiter: lack of friction allows persistence of Highs and Lows Questions 1. The Coriolis force responsible for anticyclonic and cyclonic motions (rotation

around Highs and Lows) applies only when viewing motions from the perspective of the rotating Earth. Then how come we can see rotating hurricanes (strong cyclones) from weather satellites? 1. What happens to tropical cyclones when they cross the Equator? Do they start turning the other way? Satellite in geostationary orbit Cyclone tracks, 1985-2005 The Hadley circulation (1735): global sea breeze COLD Trade winds

HOT COLD Explains: Intertropical Convergence Zone (ITCZ) Wet tropics, dry poles Easterly trade winds in the tropics But Direct meridional transport of air between Equator and poles is not possible because of Coriolis force Hadley circulation only extends to about 30o latitude

Easterly trade winds in the tropics at low altitudes Subtropical anticyclones at about 30o latitude Westerlies at mid-latitudes Climatological surface winds and pressures (January) Climatological surface winds and pressures (July) Time scales for horizontal transport (troposphere) 1-2 months 2 weeks 1-2 months

1 year VERTICAL TRANSPORT: BUOYANCY Consider an object (density ) immersed in a fluid (density ): ap Fluid () Object ( g z+z z Buoyancy acceleration (upward) :

For air, Ma p RT p(z) > p(z+z) pressure-gradient force on object directed upward ab = a p - g g so as T

Barometric law assumes T = T ab = 0 (zero buoyancy) T T produces buoyant acceleration upward or downward ATMOSPHERIC LAPSE RATE AND STABILITY Lapse rate = -dT/dz Consider an air parcel at z lifted to z+dz and released. It cools upon lifting (expansion). Assuming lifting to be adiabatic, the cooling follows the adiabatic lapse rate : z stable

unstable = 9.8 K km-1 z dT g 9.8 K km -1 dz C p What happens following release depends on the local lapse rate dTATM/dz: ATM inversion

-dTATM/dz > upward buoyancy amplifies (observed) initial perturbation: atmosphere is unstable unstable -dTATM/dz = zero buoyancy does not alter perturbation: atmosphere is neutral T -dTATM/dz < downward buoyancy relaxes initial perturbation: atmosphere is stable dTATM/dz > 0 (inversion): very stable The stability of the atmosphere against vertical mixing is solely determined by its lapse rate. WHAT DETERMINES THE LAPSE RATE OF THE ATMOSPHERE?

An atmosphere left to evolve adiabatically from an initial state would eventually tend to neutral conditions (-dT/dz = at equilibrium Consider now solar heating of the surface. This disrupts the equilibrium and produces an unstable atmosphere: z z z ATM

ATM T Initial equilibrium state: - dT/dz = initial T Solar heating of surface: unstable atmosphere final

T buoyant motions relax unstable atmosphere back towards dT/dz = Fast vertical mixing in an unstable atmosphere maintains the lapse rate to Observation of -dT/dz = is sure indicator of an unstable atmosphere. Typical summer afternoon vertical profile over Boston 4 Altitude, km

3 cloud 2 planetary boundary layer (PBL) 1 0 -20 -10 0

10 Temperature, oC 20 30 IN CLOUDY AIR PARCEL, HEAT RELEASE FROM H2O CONDENSATION MODIFIES Wet adiabatic lapse rate W = 2-7 K km-1 z T RH Latent heat release

as H2O condenses RH > 100%: Cloud forms 100% W W2-7 K km-1 9.8 K km -1

SUBSIDENCE INVERSION typically 2 km altitude DIURNAL CYCLE OF SURFACE HEATING/COOLING: ventilation of urban pollution z Planetary Boundary Layer (PBL) depth Subsidence inversion MIDDAY

1 km Mixing depth 0 NIGHT MORNING T NIGHT

MORNING AFTERNOON VERTICAL PROFILE OF TEMPERATURE Mean values for 30oN, March Altitude, km Radiative cooling (ch.7) - 3 K km-1 +2 K km-1 Radiative heating: O3 + hO2 + O

O + O2 + M O3+M heat Radiative cooling (ch.7) - 6.5 K km-1 Latent heat release Surface heating TYPICAL TIME SCALES FOR VERTICAL MIXING tropopause (10 km) 10 years

1 month planetary 2 km boundary layer 0 km 1 day Questions A sea-breeze circulation often results in an inversion. Explain why. A classic air pollution problem is fumigation where a location downwind of a tall smokestack will experience a sudden burst of high pollution from that smokestack in mid-morning. Can you explain this observation on the basis of atmospheric stability?