1. a) The spectra of intensity of infrared radiation measured from orbit above the Sahara Desert and above Antarctica are shown in Figures la and 1b. Explain why there is a relative minimum for wavelengths in the range 13 - 17 um above the Sahara Desert, but there is a relative maximum for the same wavelengths above Antarctica. b) Figure 1c shows the spectrum of infrared radiation measured above the Pacific Ocean when the atmosphere was cloud free and also above a thick thunderstorm anvil outflow cloud. Estimate the height of the anvil cloud top assuming that the lapse rate was 6° C per km throughout the troposphere.
1. a) The spectra of intensity of infrared radiation measured from orbit above the Sahara Desert and above Antarctica are shown in Figures la and 1b. Explain why there is a relative minimum for wavelengths in the range 13 - 17 um above the Sahara Desert, but there is a relative maximum for the same wavelengths above Antarctica. b) Figure 1c shows the spectrum of infrared radiation measured above the Pacific Ocean when the atmosphere was cloud free and also above a thick thunderstorm anvil outflow cloud. Estimate the height of the anvil cloud top assuming that the lapse rate was 6° C per km throughout the troposphere.
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
Related questions
Question
![Wien's displacement Law: Ap=2898/Tum
Kirchoff's Law: absorptivity = emissivity
Flux of solar Radiation at Earth: F, = T1370 Watts/m²
Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K
Beer's Law: 1(x) = 1(0) exp[-x]; x = kpdx = fondx
Optical cross section: k in
Force of buoyancy: Fg = g
kg
Ideal Gas Law: P = pRT; R = 287 J Kg¹ K
Ideal Gas Law: P = nkT; k=1.381x 1023 J/K
Ideal Gas Law for Water Vapour: e=p, R, T; R = 461.5 J Kg¹ K-¹
Hydrostatic Equation:=-pg
Barometric Law: P(z) = P(0) exp(-); H = RT/g; P. = 100 × 10³ Pa; g = 9.81 m/s²
(Po-P)
(T-T₂)
P
To
dT
Adiabatic Lapse Rate:
dz
or o in-
m²
molecule
Cp
= g
First Law of Thermodynamics: &q= c₂ dT + P da or 8q = cp dT - 1 dp
Specific Heat Capacity for Air: c=1005;
CAPER
-9.8 °C/km
EL
So
LFC
Potential Temperature: 0 = T
Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = 98
=
0 dz
Latent Heat of Condensation for water: 2535 J/g
Latent Heat of Sublimation for water: 2834 J/g
Les
Clausius-Clapeyron Equation: dT
R₂T²
Solution to C-C equation: ()
eso
Joules
kg-deg C
= exp
{ (- Đ
Saturated (Wet) Adiabatic Lapse Rate: I'
at To 0 °C (273 K), eso = 611 Pa
Equivalent Potential Temperature: 0 = 0 exp
Adiabatic liquid/ice water content: x = -
Velocity: v² v² = 2a(z-zo); a is acceleration
(T-T₂) dinPo
dT
dz
LWS
1+
L dws
Cp dr
Information (as provided on 2021 final exam)
Earth-Sun mean distance: 149.598 x 10⁹ m
Radius of Sun: 6.96 x 10³ m
Radius of Earth: 6371 x 10³ m
Effective temperature of Sun: 5770 K
Cross sectional area of a sphere: R²
Surface area of a sphere: 4R²
Solid Angle: 2 = Area on sphere/R²; d = sine de do
Albedo of the Earth: A = 0.3
Plank Function: B(A,T) =
2hc²
hc
As ekXT-1
Plank's constant: h = 6.626 × 10-³4 Js
Boltzmann's constant: k = 1.381x 1023 J/K
Speed of light: c = 3 x 10³ m/s
Flux: F = f I cose d
Watts
m² μm-ST
Watts
m²
Stephan's constant: = 5.67 × 108 Wm² K-4
Net flux upward or downward for isotropic radiation: F = al
Stephan-Boltzmann Law: F = 6T4
-Aws(); or x = - Δρ. (mg)
kg
m³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd28de0e5-9c94-4bd5-a9be-fdd69ffbee6a%2Fb45995e1-f022-4405-b38c-9f028c59b9bc%2F6pgx2kt_processed.png&w=3840&q=75)
Transcribed Image Text:Wien's displacement Law: Ap=2898/Tum
Kirchoff's Law: absorptivity = emissivity
Flux of solar Radiation at Earth: F, = T1370 Watts/m²
Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K
Beer's Law: 1(x) = 1(0) exp[-x]; x = kpdx = fondx
Optical cross section: k in
Force of buoyancy: Fg = g
kg
Ideal Gas Law: P = pRT; R = 287 J Kg¹ K
Ideal Gas Law: P = nkT; k=1.381x 1023 J/K
Ideal Gas Law for Water Vapour: e=p, R, T; R = 461.5 J Kg¹ K-¹
Hydrostatic Equation:=-pg
Barometric Law: P(z) = P(0) exp(-); H = RT/g; P. = 100 × 10³ Pa; g = 9.81 m/s²
(Po-P)
(T-T₂)
P
To
dT
Adiabatic Lapse Rate:
dz
or o in-
m²
molecule
Cp
= g
First Law of Thermodynamics: &q= c₂ dT + P da or 8q = cp dT - 1 dp
Specific Heat Capacity for Air: c=1005;
CAPER
-9.8 °C/km
EL
So
LFC
Potential Temperature: 0 = T
Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = 98
=
0 dz
Latent Heat of Condensation for water: 2535 J/g
Latent Heat of Sublimation for water: 2834 J/g
Les
Clausius-Clapeyron Equation: dT
R₂T²
Solution to C-C equation: ()
eso
Joules
kg-deg C
= exp
{ (- Đ
Saturated (Wet) Adiabatic Lapse Rate: I'
at To 0 °C (273 K), eso = 611 Pa
Equivalent Potential Temperature: 0 = 0 exp
Adiabatic liquid/ice water content: x = -
Velocity: v² v² = 2a(z-zo); a is acceleration
(T-T₂) dinPo
dT
dz
LWS
1+
L dws
Cp dr
Information (as provided on 2021 final exam)
Earth-Sun mean distance: 149.598 x 10⁹ m
Radius of Sun: 6.96 x 10³ m
Radius of Earth: 6371 x 10³ m
Effective temperature of Sun: 5770 K
Cross sectional area of a sphere: R²
Surface area of a sphere: 4R²
Solid Angle: 2 = Area on sphere/R²; d = sine de do
Albedo of the Earth: A = 0.3
Plank Function: B(A,T) =
2hc²
hc
As ekXT-1
Plank's constant: h = 6.626 × 10-³4 Js
Boltzmann's constant: k = 1.381x 1023 J/K
Speed of light: c = 3 x 10³ m/s
Flux: F = f I cose d
Watts
m² μm-ST
Watts
m²
Stephan's constant: = 5.67 × 108 Wm² K-4
Net flux upward or downward for isotropic radiation: F = al
Stephan-Boltzmann Law: F = 6T4
-Aws(); or x = - Δρ. (mg)
kg
m³
![1. a) The spectra of intensity of infrared radiation measured from orbit above the Sahara Desert
and above Antarctica are shown in Figures la and 1b. Explain why there is a relative minimum
for wavelengths in the range 13 - 17 um above the Sahara Desert, but there is a relative
maximum for the same wavelengths above Antarctica.
b) Figure 1c shows the spectrum of infrared radiation measured above the Pacific Ocean when
the atmosphere was cloud free and also above a thick thunderstorm anvil outflow cloud. Estimate
the height of the anvil cloud top assuming that the lapse rate was 6° C per km throughout the
troposphere.
Radiance [mW/m² sr cm¹]
Radiance [mW/m² srcm
25
20 18
200 TTTTTTT
150
100
50
0
400
50
45
40
HANN
25
25
15
10
5
0
400
140
120
100
25
60
40
20
500
20 18
500
20 18
LITTER
15 14 13 12 11 10
600 700 800
15 14 13 12
TTT
600 700
800
Thunderstorm Anvil
Wavelength [um]
9
7
T
(a) Sahara Desert
15 14 13 12
P-J_____T
What y
900 1000 1100 1200 1300 1400 1500 1600
Wavenumber [cm]
Wavelength [um]
11 10
9
Ingolsyfontinentele
900 1000 1100 1200 1300
1300 1400 1500 1600
Wavenumber [cm]
Wavelength [um]
10 9
11
8
(b) Antarctic Ice Sheet
Clear
(c) Tropical Western Pacific
1
L
L
0
400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600
Wavenumber [cm]
Figure 1. Spectra of infrared radiation intensity measured from an orbiting satellite above (a) the
Sahara Desert (no clouds), (b) Antarctica (no clouds), and (c) the tropical western Pacific Ocean.
(c) includes a spectrum measured above clear air as well as a spectrum measured above a thick
thunderstorm anvil outflow cloud (as labelled). Plank function curves at various temperatures are
shown (dashed lines) for comparison.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd28de0e5-9c94-4bd5-a9be-fdd69ffbee6a%2Fb45995e1-f022-4405-b38c-9f028c59b9bc%2Frdfgha5_processed.png&w=3840&q=75)
Transcribed Image Text:1. a) The spectra of intensity of infrared radiation measured from orbit above the Sahara Desert
and above Antarctica are shown in Figures la and 1b. Explain why there is a relative minimum
for wavelengths in the range 13 - 17 um above the Sahara Desert, but there is a relative
maximum for the same wavelengths above Antarctica.
b) Figure 1c shows the spectrum of infrared radiation measured above the Pacific Ocean when
the atmosphere was cloud free and also above a thick thunderstorm anvil outflow cloud. Estimate
the height of the anvil cloud top assuming that the lapse rate was 6° C per km throughout the
troposphere.
Radiance [mW/m² sr cm¹]
Radiance [mW/m² srcm
25
20 18
200 TTTTTTT
150
100
50
0
400
50
45
40
HANN
25
25
15
10
5
0
400
140
120
100
25
60
40
20
500
20 18
500
20 18
LITTER
15 14 13 12 11 10
600 700 800
15 14 13 12
TTT
600 700
800
Thunderstorm Anvil
Wavelength [um]
9
7
T
(a) Sahara Desert
15 14 13 12
P-J_____T
What y
900 1000 1100 1200 1300 1400 1500 1600
Wavenumber [cm]
Wavelength [um]
11 10
9
Ingolsyfontinentele
900 1000 1100 1200 1300
1300 1400 1500 1600
Wavenumber [cm]
Wavelength [um]
10 9
11
8
(b) Antarctic Ice Sheet
Clear
(c) Tropical Western Pacific
1
L
L
0
400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600
Wavenumber [cm]
Figure 1. Spectra of infrared radiation intensity measured from an orbiting satellite above (a) the
Sahara Desert (no clouds), (b) Antarctica (no clouds), and (c) the tropical western Pacific Ocean.
(c) includes a spectrum measured above clear air as well as a spectrum measured above a thick
thunderstorm anvil outflow cloud (as labelled). Plank function curves at various temperatures are
shown (dashed lines) for comparison.
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