METR 446 Test # 1 September 18, 2001
Name: Solution
1) (15 pts) On the axes below draw and label curves representing equilibrium vapor pressure over a pure water droplet and the equilibrium vapor pressure over two solution drops, one that contains

Sample problems for test # 4
1) If the ground behaves as a black-body, will the net irradiance between the ground and an overlying cooler cloud be greater if the cloud is a black-body or a gray-body? You can assume that no significant absorption (or

METR 446 Test # 4 December 7, 2001
Name: Solution
1) (10 pts) Describe in words what flux transmittance is.
Flux transmittance is simply the ratio of the irradiance leaving a layer of the atmosphere to the irradiance entering it.
2) (5 pts) To de

Metr 446 Homework # 1 Due Tuesday, September 11
1. Assume that all of the aerosol particles in the air are exactly the same size, and are composed of either pure NaCl, pure (NH4)2SO4, or pure NH4NO3. As these aerosols enter a cloud, only one type tur

Metr 446 Homework # 2 Due Tuesday, September 25
1. (20 pts) Calculate the growth rate of 10 and 50 m radius droplets due to i) condensation, and ii) coalescence. Assume a temperature of 5 oC, and a supersaturation of 0.3%. Also assume that the cloud

Metr 446 Homework # 3 and 4 Due Friday, October 5
1) Calculate the minimum cloud height necessary for a 5 m droplet introduced into the base of the cloud to reach sufficient size to fall back out of the cloud as a precipitation drop. Also calculate t

METR 446 Homework # 5 Due Tuesday, November 6
1. (20 pts) If the maximum monochromatic radiance at a wavelength of 550 nm is 450 W m-2 m-1 sr-1 at the surface of the earth when the sun is directly overhead, what is the average absorption coefficient

METR 446 Homework # 6 Due Friday, November 9 (before 5:00 pm)
1. (10 pts) Determine the solar monochromatic irradiance at the top of the atmosphere given the following set of monochromatic (0.5 m) irradiance measurements made throughout the day at th

METR 446 Homework # 7 Due Tuesday, December 4
1) (15 pts) Using the skew-T diagram below, calculate the rate of radiational warming (or cooling) at a reference level of 600 mbar that results from the presence of water vapor. Use 50 mbar intervals for

METR 446 Test # 1 September 18, 2001
Name: _
1) (15 pts) On the axes below draw and label curves representing equilibrium vapor pressure over a pure water droplet and the equilibrium vapor pressure over two solution drops, one that contains twice a

For water : J kg K J L = 2.5 10 6 kg N = 0.075 m kg w = 1000 3 m m2 D = 2.5 10 -5 s J = 0.023 smK g m w = 18 mol Rw = 461
Common aerosol species : kg = 1760 3 m g m s = 132 ( NH 4 ) 2 SO4 (ammonium sulfate) mol dissociates into 3 ions

Sample problems for test # 1
1) Calculate the minimum relative humidity necessary to cause condensation on each of the particles shown below, where r = 0.2 m. Assume a temperature of 298 K. Metal cube (nonhygroscopic) Solution droplet that formed on

Sample problems for test # 4
1) If the ground behaves as a black-body, will the net irradiance between the ground and an overlying cooler cloud be greater if the cloud is a black-body or a gray-body? You can assume that no significant absorption (or

Formulas :
= =
c
A r2 d = 2 sin d E= d 2Q = L cos d = L(if isotropic ) dAdt 0
2
E = E d
0
L = L d
0
a + r + = 1 a = L = Lo e -u a = 1 - e - u u = k c dx
0 x
L* =
2hc 2
5 (e - 1)
hc k T
E * = T 4
Constants : c = 3.0 108
m

METR 446 Test # 2 October 16, 2001
Name: _
1) (30 pts) If a spherical ice crystal and a spherical liquid drop with the same radius are in a cloud with a supersaturation with respect to water of 0.3% and a temperature of 20 oC, how much faster will

For water : Rw = 461 J kg K
6
J Lvap = 2.5 10 kg J Lsub = 2.83 10 6 kg kg w = 1000 3 m m2 D = 2.5 10 -5 s g mw = 18 mol Equations :
Other constants : e = 1.6 10 -19 C Rearth = 6.38 10 6 m
air = 1.8 10 -5
g = 9.81 sm 2
kg ms
4DC (e - eo )

Sample problems for test # 2
1) Considering the expressions relating settling velocity to droplet radius, what is the range in the value of the exponent, a, in wt ra? 2) Approximately what is the ratio of the concentration of cloud condensation nucl

Test # 2 sample problem solutions
1) Considering the expressions relating settling velocity to droplet radius, what is the range in the value of the exponent, a, in wt ra?
24 8r w g 2 From the exp ressions in HW 3 & 4 for Re < 0.1 wt2 2 w r =

METR 446 Test # 2 October 16, 2001
Name: Solution
1) (30 pts) If a spherical ice crystal and a spherical liquid drop with the same radius are in a cloud with a supersaturation with respect to water of 0.3% and a temperature of 20 oC, how much faste

METR 446 Test # 3 November 13, 2001
Name:
1) (25 pts) Assume the ocean is a gray-body with a wavelength-independent absorptance of 0.85. If the temperature of the ocean is 20 oC, at what solar zenith angle will the absorbed solar irradiance be equa

Formulas :
= =
c
A r2 d = 2 sin d d 2Q = L cos d = L(if isotropic ) E= dAdt 0 E = E d
0 2
L = L d
0
a + r + = 1 a = L = Lo e -u a = 1 - e - u u = k c dx
0 x
Constants : c = 3.0 108
m s
L =
*
2hc 2
h = 6.63 10 -34 J s k =

Sample problems for test # 3
1) What is the peak monochromatic radiance from an object (black-body) in this room at 25 o C? 2) The ocean has an albedo (reflectivity) of about 0.1. What is the irradiance of the ocean if its temperature is 15 oC? 3) If

Solutions to sample problems for test # 3
1) What is the peak monochromatic radiance from an object (black-body) in this room at 25 o C? This is a two-step problem. First it is necessary to determine the wavelength at which the radiance is greatest,

METR 446 Test # 3 November 13, 2001
Name: Solution
1) (25 pts) Assume the ocean is a gray-body with a wavelength-independent absorptance of 0.85. If the temperature of the ocean is 20 oC, at what solar zenith angle will the absorbed solar irradianc

METR 446 Test # 4 December 7, 2001
Name:
1) (10 pts) Describe in words what flux transmittance is.
2) (5 pts) To derive an expression for the equilibrium ozone number density, we assumed that some of the reactions taking place in the stratosphere

Answers to sample problems for test # 1
1) Cube: RH = 100% pure water : RH = 2(0.075 N )( NJm ) 2 ec m = 1.0055 = 100.55% = exp = exp kg -6 R Tr (461 kgJK )(1000 3 )(298 K )(0.2 10 m) es w w m
2 imw s rp3 2 ehc 3imw M = exp so