Name_______________________
AOS 101-304
Homework 8
Due April 17
Instructions: Complete the following questions. Remember to show your work and, if
necessary, label your answers with units.
1. Below is a map of surface pressure with isobars every 4 hPa. The arrow (vector V) on
the map represents the wind at city A (denoted by the dot).

V
H
1012
A
L
1008
996
1000
1004
a.) Draw and label a vector representing the direction and relative magnitude of the
pressure gradient (PG) force at city A.
b.) Draw and label a vector representing the direction and relative magnitude of the
Coriolis force on the wind at city A.
c.) Draw and label a vector representing the direction and relative magnitude of the
frictional force on the wind at city A.
d.) Why must we consider friction in this case?
e.) If the isobars were to become closer together at city A, how would the magnitude of
the pressure gradient force and wind change?
2.) Below is a plot of 500 hPa height contoured every 60 meters with locations labeled A,
B and C.
C
L
A
B
a.) For each of the three locations (A, B and C) draw and label:
1.) Wind vectors
2.) Pressure gradient force vectors
3.) Coriolis force vectors
Remember that vectors with relatively larger magnitudes should be denoted with
longer arrows (e.g. if the pressure gradient force is stronger at one location than
another, the vector should be longer for that location).
b.) At what location would you expect the weakest 500 hPa winds? Why?
c.) At which location would the centrifugal force be the largest? Why?
3.) A hurricane is characterized by
strong pressure gradients and strong,
circular winds. The winds of a mature
hurricane are typically in cyclostrophic
balance where the PG, Coriolis and
centrifugal forces all balance.
In this figure, the pressure at the center
of the hurricane is 960 hPa (96,000
Pa). At a 200 km (200,000 m) radius
the pressure is 990 hPa (99,000 Pa).
The wind speed at 200 km is 50 m/s.
For simplicity, let ρa = 1 kg/m3 and f =
5 x 10-5 s-1. The units for each force
magnitude should be m/s2.

V
P2 = 990 hPa
D = 200 km
|V| = 50 m/s
P1 = 960 hPa
a.) Find the magnitude of the pressure gradient force using the equation (D must be in

1 | P2  P1 |
meters, and P1, P2 must be in Pascals): FPG 
a D


b.) Find the magnitude of the Coriolis force using the equation: Fcor  f | V |
c.) Find the magnitude of the centrifugal force using the equation (D must be in meters):


Fcen  | V | 2 / D
d.) Using these values and what you know about each force, draw and label vectors on
the figure above representing how each force acts on the parcel. The length of the arrow
should correspond to each force’s relative magnitude. Do the forces balance?