• Emissivity• Kirchoff’s Law• Thermal Inertia, Thermal Capacity, and Thermal Conductivity• Review for Midterm

• Reminder: Midterm Exam on Monday! Review sheet is posted.

Thermal IR (cont’d)

• No objects in the world are true blackbodies; rather, they are selectively radiating bodies.• Emissivity (є) is the ratio between the radiant flux exiting a real world selective radiating body (M r) and a blackbody at the same temperature (Mb)

• A graybody outputs a constant emissivity that is less than one at all wavelengths

Emissivity

• All selectively radiating bodies have emissivities ranging from 0 to <1 that fluctuate depending upon the wavelengths of energy being considered. A graybody outputs a constant emissivity that is less than one at all wavelengths.

• Some materials like distilled water have emissivities close to one (0.99) over the wavelength interval from 8 - 14 m. Others such as polished aluminum (0.08) and stainless steel (0.16) have very low emissivities.

• All selectively radiating bodies have emissivities ranging from 0 to <1 that fluctuate depending upon the wavelengths of energy being considered. A graybody outputs a constant emissivity that is less than one at all wavelengths.

• Some materials like distilled water have emissivities close to one (0.99) over the wavelength interval from 8 - 14 m. Others such as polished aluminum (0.08) and stainless steel (0.16) have very low emissivities.

EmissivityEmissivity

Spectral emissivity of a blackbody, a graybody,

and a hypothetical selective radiator

Spectral emissivity of a blackbody, a graybody,

and a hypothetical selective radiator

2x reduction2x reduction

1

0.5

0.1

0.1 1 10 100

0.1 100

100101

102

104

106

108

Wavelength, m

Wavelength, m

Spec

tral

Em

issi

vity

,

Spec

tral

Rad

iant

Exi

tanc

e

W m

-2

m-1

selective radiator

blackbody

6,000 ÞK blackbody = 1.0

graybody

6,000 ÞK graybody = 0.1

6,000 ÞK selective radiator

a.

b.

1

0.5

0.1

0.1 1 10 100

0.1 100

100101

102

104

106

108

Wavelength, m

Wavelength, m

Spec

tral

Em

issi

vity

,

Spec

tral

Rad

iant

Exi

tanc

e

W m

-2

m-1

selective radiator

blackbody

6,000 ÞK blackbody = 1.0

graybody

6,000 ÞK graybody = 0.1

6,000 ÞK selective radiator

a.

b.

Spectral radiant exitance distribution of

the blackbody, graybody, and

hypothetical selective radiator

Spectral radiant exitance distribution of

the blackbody, graybody, and

hypothetical selective radiator

Spec

tral

Em

issi

vity

, eSp

ectr

al R

adia

nt E

xita

nce

W m

-2 u

m-1

Two rocks lying next to one another on the ground could have the same true kinetic temperature but have different apparent temperatures when sensed by a thermal radiometer simply because their emissivities are different. The emissivity of an object may be influenced by a number factors, including:

• color

• surface roughness

• moisture content

• wavelength

• viewing angle

Two rocks lying next to one another on the ground could have the same true kinetic temperature but have different apparent temperatures when sensed by a thermal radiometer simply because their emissivities are different. The emissivity of an object may be influenced by a number factors, including:

• color

• surface roughness

• moisture content

• wavelength

• viewing angle

EmissivityEmissivity

• Water, distilled 0.99• Asphalt 0.95• Vegetation 0.96 to 0.98• Snow 0.83 to 0.85• Concrete 0.71 to 0.90• Stainless Steel 0.16• Aluminum 0.05 to 0.08

* From Table 8-1 (p. 258)

Emissivity of Selected Materials

• The Russian physicist Kirchhoff found that in the infrared portion of the spectrum the spectral emissivity of an object generally equals its spectral absorptance, i.e. ~ . This is often phrased as:

“good absorbers are good emitters and

good reflectors are poor emitters”.

• The Russian physicist Kirchhoff found that in the infrared portion of the spectrum the spectral emissivity of an object generally equals its spectral absorptance, i.e. ~ . This is often phrased as:

“good absorbers are good emitters and

good reflectors are poor emitters”.

Kirchoff’s Radiation LawKirchoff’s Radiation Law

• Thermal capacity (c) is the ability of a material to store heat. It is measured as the number of calories required to raise a gram of material (e.g. water) 1 ˚C (cal g-1 ˚C-1).

• Thermal conductivity (K) is the rate that heat will pass through a material and is measured as the number of calories that will pass through a 1-cm cube of material in 1 second when two opposite faces are maintained at 1 ˚C difference in temperature (cal cm-1 sec-1 ˚C).

• Thermal capacity (c) is the ability of a material to store heat. It is measured as the number of calories required to raise a gram of material (e.g. water) 1 ˚C (cal g-1 ˚C-1).

• Thermal conductivity (K) is the rate that heat will pass through a material and is measured as the number of calories that will pass through a 1-cm cube of material in 1 second when two opposite faces are maintained at 1 ˚C difference in temperature (cal cm-1 sec-1 ˚C).

Thermal Properties of TerrainThermal Properties of Terrain

• Thermal inertia (P) is a measurement of the thermal response of a material to temperature changes and is measured in calories per square centimeter per second square root per degree Celsius (cal cm-2

sec -1/2 ˚C-1). Thermal inertia is computed using the equation:

P = (K x p x c)1/2

where K is thermal conductivity, p is density (g cm-3), and c is thermal capacity. Density is the most important property in this equation because thermal inertia generally increases linearly with increasing material density.

• Thermal inertia (P) is a measurement of the thermal response of a material to temperature changes and is measured in calories per square centimeter per second square root per degree Celsius (cal cm-2

sec -1/2 ˚C-1). Thermal inertia is computed using the equation:

P = (K x p x c)1/2

where K is thermal conductivity, p is density (g cm-3), and c is thermal capacity. Density is the most important property in this equation because thermal inertia generally increases linearly with increasing material density.

Thermal InertiaThermal Inertia

There is an inverse relationship between having high spatial resolution and high radiometric resolution when collecting thermal infrared data.

There is an inverse relationship between having high spatial resolution and high radiometric resolution when collecting thermal infrared data.

Thermal Infrared Remote SensingThermal Infrared Remote Sensing