Thermodynamics of Atmospheres and Oceans
Worksheet 8.2
1. If the imaginary part of the index of refraction nim=0, then
a) there is no scattering, only absorption
b) there is no absorption, only scattering
c) there is both absorption and scattering
2. Do ice particles or water particles absorb more radiation at the following wavelengths (refer to figure 8.11 in text):
a. 3.7 m ice
b. 1.6 m ice
c. 10 m ice/water are about same
3. Calculate the size parameter, x, for a drop of radius 20 m for
a) wavelength 0.5 m
b) wavelength 100 m
a) x=2πr/λ = 251.32
b) x=1.26
4. Qext~2 for
a) geometric optics regime
b) Rayleigh regime
c) none of the above
5. Qext~x4 for
a) geometric optics regime
b) Rayleigh regime
c) none of the above
6. If Qabs = 0.2 and Qext = 2.0 for a given ice crystal size and wavelength, what is Qsca?
Qsca=Qext-Qabs=2.0-.2=1.8
7. A cloud drop size distribution has the form
n(r) = No r -(+1)
over the radius range r=0 to R, where No and are constant. For a cloud having a geometric depth h and assuming that Qabs(x)=1 in the infrared, write an expression for the infrared absorption optical depth. Follow these steps.
7. Write an expression for the volume absorption coefficient, abs, for a distribution of cloud drops
8. What are the units for abs?
m-1
9. Integrate the expression for abs, assuming the drop size distribution given above
10. Write an expression for the absorption optical depth of a cloud of depth h
11. Evaluate the optical depth for the value of abs determined in 9.
12. Clouds (increase, decrease) the amount of solar radiation reaching the surface
Decrease clouds have a highly reflective to solar radiation
13. Low-level clouds (increase, decrease) the amount of infrared radiation reaching the surface
increase
14. Clouds absorb more (visible, near infrared) radiation
Near infrared
15. Shortwave reflectivity of a cloud is (larger, smaller) for greater liquid water path.
larger
16. Shortwave reflectivity of a cloud is (larger, smaller) for larger dropsize.
smaller
17. Longwave emissivity of a cloud is (larger, smaller) for greater liquid water path.
larger
18. Longwave emissivity of a cloud is (larger, smaller) for larger dropsize.
smaller
19. What is a typical value for the shortwave absorptivity of clouds?
10% *Note this value is not actually listed in the text but from Fig. 8.13
20. The expression
is true for
a) all circumstances
b) geometric optics regime x>1
c) rayleigh regime x<1
21. Cloud drop size distributions are determined from aircraft measurements using a FSSP (Forward Scattering Single Probe) instrument, which determines drop sizes and concentrations by using optical techniques. The FSSP typically gives counts of particles in fifteen different size bins, with r = 1.5 m. These counts can then be converted into concentrations 1.5 m (# cm-3 1.5 m-1) by taking into account aircraft velocity, etc. One dropsize distribution, n(r), determined from the FSSP during the Arctic Stratus Experiment is given below, from the middle of a stratus deck. The values of the droplet radii given at the top of the table represent the average radius of the 1.5 m size bin.
r (m): 1.6 3.1 4.7 6.3 7.8 9.4 11.0 12.5 14.1 15.7 17.2 18.8 20.4
n(r): 94 103 105 94 23 23 0.6 0.1 0 0 0 0 0
a) Compute the following for the above dropsize distribution:
N: total number concentration of droplets (# cm-3)
wl: liquid water mixing ratio (g kg-1)
: mean dropsize radius (m)
re: droplet equivalent radius (m)
ext: volume extinction coefficient for solar (shortwave) radiation (m-1)
b) Assuming that the cloud is 300 m deep and that the microphysical properties are homogeneous vertically, compute , the liquid water path (g m-2)
c) For shortwave radiation, compute ext, the cloud optical depth for shortwave radiation
You should probably do this problem with some software. Excel should be fine
Because we are dealing with solar radiation λ=.5μm smallest raindrop is 1.6μm. So that the size parameter is much greater than 1 and we are in geometric optics regime. Hence Qext =2
b)
c)