Name______Homework 8
AOS 101-304Due 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).
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.
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.
a.) Find the magnitude of the pressure gradient force using the equation (D must be in meters, and P1, P2 must be in Pascals):
b.) Find the magnitude of the Coriolis force using the equation:
c.) Find the magnitude of the centrifugal force using the equation (D must be in meters):
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?