Download Global circulation and Coriolis force/ Hadley cell - IUP

Prof. Dr. J.P. Burrows
Institute of Environmental Physics
Atmospheric Physics, WS 2007/2008
Exercise 10
10.1 Atmosphere as a heat engine
(3pts) 1. Describe an atmospheric heat engine. Illustrate in term of cycles (involving warm and
cold air) how work is done by air parcels.
(5pts) 2. An air parcel at an initial temperature of 300K and pressure 1000hPa ascends along an
isentropic surface to the 500hPa surface. It remains on that pressure surface and slowly
cools by emission of radiation to space by 20K. It then descends following an isentropic
surface to the 1000hPa surface. There it slowly warms back to its initial temperature
R as
a result of heat added from the underlying surface. Calculate ∆h , ∆u, ∆w, ∆q, and dq
T
for each step of the cycle.
10.2 Global circulation and Coriolis force
(4pts) 1a. Sketch and label a diagram showing the idealized three-cell model of global circulation.
In your diagram, kindly label with arrows the direction of flow, label also where warm,
cold, moist or dry air occurs. Please indicate properly if air is descending or rising.
(2pts) 1b. How does the Coriolis force affect these cells? How do these cells form trade winds?
(3pts) 1c. What are the climatic zones for each cell? Describe briefly each climatic zone.
10.3 Hadley cell
(4pts) 1. Draw a diagram to describe a Hadley atmospheric circulation cell. (a) vertically (tropospherestratosphere) (b) horizontally (equator-poles) What is ITCZ? What pattern of surface
winds causes it? In your diagram (vertical case), kindly label with arrows the direction of
flow, label also where warm, cold, moist or dry air occurs.
Kindly indicate properly if air is descending or rising, i.e. at which latitudes are upward/downward air motions dominant?
(3pts) 2. What does the circulation of the Hadley cell have to do with the location of tropical
rainforests and deserts in North and South America? Which of these two terrestrial biomes
generates more biomass?
(4pts) 3. Explain how the following factors impact or influence Hadley circulation.
(a) precipitation
(b) effect of the topography
(c) effect of the proximity of the oceans to the distribution of precipitation
(d) prevailing wind directions
(e) effect of the seasons
10.4 Atmospheric dynamics
(2pts) 1. Explain the following terms as drivers of atmospheric motions - (a) pressure and temperature gradients, (b) gravity, (c) friction, (d) Coriolis force
(2pts) 2. If a baseball player throws a ball a horizontal distance of 100m at 30◦ N latitude in 4s, by
how much is it deflected laterally as a result of the rotation of the earth?
(4pts) 3. The thermal advection equation for the adiabatic motion of air parcel to the east is
∂T
∂T
= −u
∂t
∂x
(a) What is the magnitude of the rate of change of temperature in degrees/second if the
zonal wind is 10 m/s and the temperature gradient is 2 K per 100 km?
(b) What is the magnitude in degrees/day?
(4pts) 4. Given the constant angular velocity ω on how fast a tornado rotates, show that the surface
pressure at the center of the tornado is given by
ω 2 r02
p = p0 exp −
2RT
where p0 , r0 , and T are the surface pressure, distance r0 from the center, and temperature
(assumed constant). If the temperature is 288 K and pressure and wind speed at 100 m
from the center are 1000 hPa and 100 m/s, respectively, what is the central pressure?
2
Hint: Rewrite the cyclostrophic balance equation vr = ρ1 ∂ρ
in terms of the pressure
∂r
gradient rather than geopotential gradient. Then use ideal gas law to replace the density
term with T and p. Solve the equation relating r, ω, and T .
Return date: Monday, 2. Feb. 2008, 17:00, Post Box 100
Tutor: Joseph Pagaran, Room: S4300, Tel. No.: 0421-218-8265, email: [email protected]
Additional info: http://www.iup.uni-bremen.de/~ pagaran/AP0708.html