Pennsylvania State University
Department of Meteorology
Meteo 440W: Atmospheric Measurement Principles
Spring 2014
Problem Set # 2
Due: Monday, March 24, 2014 23:59 EDT
1. A cumulus cloud with cloud depth of 3 km and a circular diameter of 5 km has a liquid
water content of 2.1 g m-3. Prior to the cloud formation, the environmental temperature
was 273 K with a mean pressure of 585 mb. How much latent heat was released due to
the formation of this cloud? What is the new temperature of the air parcel? Specific heat
of air is 1.005 kJ kg-1 K-1
The cloud is the top half of an oblate spheroid, use V=(2/3)<PI>a2b
mH2O = V*2.1gm-3 = 3.299E8kg
E=mH2Ocpd<DELTA>T = 8.248E14 J
<DELTA>T = EmH2O-1cpd-1=6.997K
T = Ti+<DELTA>T = 279.997K
Energy (kJ):
Air Parcel Temperature After Cloud Formation (K):
8.248E14 kJ
279.997 K
2. The relative humidity was measured to be 82.3% at a temperature of 14.0°C and
pressure of 982 mb. What is the water vapor mixing ratio?
RH=w/ws*100
Ws = <EPSILON>es/P
Ws=<EPSILON>eoP-1exp{Rv-1[Lv0+([cpv-cL][T-T0])][(T0-1-T-1)]}
Ws = 9.967gkg-1
W = (RH/100)*ws
W = 8.203gkg-1
H2O vapor pressure (g H2O/kg air):
8.203 g/kg
3. At 0.2% supersaturation and 298 K, how much does a water cluster of radius
0.1μmneed to grow in order to form a raindrop?
R*=(2<SIGMA><NU>)/(kTln(S))
R* = 0.524m
<DELTA>R = r*-r = 0.524-(1E-7) = 0.524m = 524,000 <MU>m
This makes sense because it is not practical to make a water drop in this fashion.
Increase in radius (μm):
524,000
4. A mercury lamp, waveband selected to center about 254 nm, shines through a sample
and reference cell of length 37.84 cm. The reference cell contains an O3 scrubber
assumed to be 100% efficient. The measured intensities of light in the sample and
reference cells are 97.465 and 98.425 kHz, respectively. What is the O3 mixing ratio if
the absorption coefficient = 308 cm-1?
Fx2/Fx1 = exp[-baLC]
C = (-1/baL)ln(Fx2/Fx1)
C = 8.4E-7
O3 Mixing Ratio (ppm):
8.4E-7
5. A CO2 molecule absorbs radiation of 4.26 μm. At which wavelength would a passive
IR remote sensing instrument need to be sensitive to be able to detect CO2?
A molecule emits at exactly the same wavelength as it absorbs.
Wavelength (μm):
4. 26 μm
6. The mean global temperature of Earth is 14.5°C, the incoming solar irradiance is
1367 W m-2, and the albedo is 0.28. What is the radiative forcing due to greenhouse
gases?
P*=<SIGMA>T4
P*=388.4Wm-2
<DELTA>P=(S0/2)-P* <- ½ due to Earth only absorbing on half of its surface.
<DELTA>P=103.7Wm-2
RF (W m-2):
103.7 W/m2