For Graduate students, please do Exercises #2, 3, 4, 5, and 6 in Hartmann Book (Chapter 4), page 114.
#2 10 points
#3 25 points
#4 20 points
#5 30 points
#6 15 points
The following two exercises are optional and they are designed for any students who want to practise their programming skills.
E#1: Write a program to compute the Ekman spiral for u and v from z=0 to z=2000 m at an interval of 100 m. KM=12.5, Vg=10 ms-1, Φ=45°N, f = 2 Ω sin Φ, and Ω = 7.292 ×10-5 rad/s. Based on your calculations, plot the Ekman spiral. Use u = Vg [1 - exp(-a0 z) cos(a0 z)], v = Vg exp(-a0 z) sin(a0 z), where a0 = [f / (2 KM]1/2.
E#2: Write a program to compute diurnal variations of soil temperatures every two hours at a 0.1 m interval from 0 to 0.5 m for a dry and a wet soil. Based on your calculations, plot the results in the same fashion as given in Figure 4.2. Soil temperatures are given by T(z,t)=T+A0 exp(-z/D) sin(Ωt - z/D), where z is the soil depth (m), t is time (seconds), D is the damping depth = (2κ/Ω)1/2, Ω = 7.292 ×10-5 rad/s, κ=K/(ρcp). Assuming T = 20°C, A0 = 8°C. For a dry soil, the specific heat cp = 890 J/kg/K, the density ρ=1600 kgm-3, the thermal conductivity K = 0.25 W/m/K. For a wet soil, the specific heat cp = 1550 J/kg/K, the density ρ=2000 kgm-3, the thermal conductivity K = 1.58 W/m/K.
For Undergraduate students, please do the following.
1. (20 points) Exercise #6 in Hartmann Book, page 114. Give the reasons why the net radiation at the surface at Flagstaff is greater than the net radiation at Yuma during summer [Fig. 4.16(c,d)]. [See also the notes on Feb 18 lecture or GPC_CH4b.ppt ]
2. (80 points) Refer to Figure 2.4, page 28 in Hartmann Book,
(1) Find out the values (in Wm-2) for the downward solar radiation at the surface, reflected solar radiation at the surface, net solar radiation, downward longwave radiation at the surface, upward longwave radiation at the surface, and net longwave radiation. [Assuming the surface is a blackbody.]
(2) Determine the surface albedo. Is this value higher or lower than the planetary albedo for Earth? Why?
(3) Find out the latent heat flux and the sensible heat flux.
(4) Calculate the net radiation at the surface and compare it with the sum of latent and sensible heat fluxes.
(5) Calculate the Bowen ratio?
(6) Convert the latent heat flux in Wm-2 into the evaporation rate in mm/day.