Surface temperature and atmospheric temperature near the surface may be estimated through a method that uses data from common types of airborne thermal infrared imager or other radiometric device having a narrow field of view. The method accounts for effects of atmospheric attenuation, surface emissivity, reflected cloud and clear sky radiance, and sensor response to various levels of approximation. Required meteorological measurements are the temperature of the intervening atmosphere and possibly the cloud base. Data acquired by other investigators suggest accuracies approaching ±1 K for certain surfaces such as water and that similar accuracies in atmospheric temperature may be expected for certain vegetated surfaces.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Emissivities of Several Surfaces at Thermal Infrared Wavelengthsa
Surface
∊
Wavelength (μm)
Water
0.97–0.99
2–15
Melting snow
0.99
8–14
Peat
0.99
8–14
Sandy soil
0.92–0.98
8–13
Sand
0.90–0.92
8–14
0.91–0.94
8–12
Red clay
0.96
8–14
Desert
0.90–0.93
8–14
Asphalt paving
0.96
8–12
Concrete (dry)
0.97
8–12
Granite
0.82
8–12
Basalt
0.90
8–12
Leaves
0.90–0.97
8-13
0.86–0.96
3–5
Leaves (orange)
0.99
8–14
Bark
0.94–0.97
8–13
0.87–0.90
3–5
Grass (meadow fescue-dry)
0.88
8–13
0.82
3–5
Grass (dead)
0.97
8–14
Grass (live)
0.99
8–14
∊ is given to the nearest 0.01, and the nadir angle is 0° (vertical view). Mean values are shown. Sources for this table are Refs. 8 and 11–15.
Table II
Input and Output Variables for the Estimation of Effective Surface Temperature a
Input
Output
(1)
Altitude Z in meters
(1)
Effective or apparent temperature Te of the surface in kelvins
(2)
Nadir (or zenith) angle η in degrees
(3)
Radiance measured by the sensor Rm in Wm−2 sr−1
(4)
Volume extinction coefficient k in km−1 for the RPV-to-ground layer
(5)
Mean atmospheric temperature Ta in kelvins for the RPV-to-ground layer
(6)
Sensor filter function values ϕi for each wavelength increment
(7)
Fraction of cloud in reflected sky radiance f
(8)
Radiance temperature of clear sky Ts in kelvins
(9)
Radiance temperature of cloud Tc in kelvins
Effective temperature is the apparent radiative temperature of the surface, taking into account atmospheric attenuation, surface emissivity, sensor filter function, and reflected cloud and clear sky radiance, as discussed in the text.
Table III
Values of Te Computed for Different Values of Certain Input Variablesa
∊
k (km−1)
Ta (K)
Te (K)
0.98
0.1
270.0
303.86
0.98
0.1
280.0
303.45
0.98
0.1
290.0
303.00
0.98
0.09
280.0
303.35
0.98
0.1
280.0
303.45
0.98
0.11
280.0
303.56
0.97
0.1
280.0
303.94
0.98
0.1
280.0
303.45
0.99
0.1
280.0
302.97
0.7
0.1
280.0
320.74
0.8
0.1
280.0
313.43
0.9
0.1
280.0
307.47
The computations assume that Z = 500 m, η = 10°, Rm = 6.4 Wm−2 sr−1, λ1,λ2 = 10,11 μm, f = 0,Ts = 240 K, and values of ∊i = 0.3,0.8,1.0 0.8, 0.3 over the wavelength interval. The iteration parameters (a and b) were 0.02 Wm−2 sr−1 and 0.1 K. Calculations for Z = 1000 m (not shown) produced changes in Te of about twice those listed for the different k and Ta. Variables are explained in the text.
Table IV
Values of Te Computed for Different Values of Certain Cloud Parametersa
∊c
f
Tc (K)
Te (K)
1.0
0.5
285.0
309.79
0.9
0.5
285.0
310.12
0.8
0.5
285.0
310.44
0.7
0.5
285.0
310.77
0.6
0.5
285.0
311.09
0.5
0.5
285.0
311.41
1.0
0.3
285.0
311.09
1.0
0.5
285.0
309.79
1.0
0.7
285.0
308.48
1.0
0.5
275.0
310.70
1.0
0.5
285.0
309.79
1.0
0.5
295.0
308.77
The computations assume that k = 0.1 km−1, ∊ of the surface = 0.8, and Ta = 290 K. The values of the other unlisted variables were the same as in Table III.
Tables (4)
Table I
Emissivities of Several Surfaces at Thermal Infrared Wavelengthsa
Surface
∊
Wavelength (μm)
Water
0.97–0.99
2–15
Melting snow
0.99
8–14
Peat
0.99
8–14
Sandy soil
0.92–0.98
8–13
Sand
0.90–0.92
8–14
0.91–0.94
8–12
Red clay
0.96
8–14
Desert
0.90–0.93
8–14
Asphalt paving
0.96
8–12
Concrete (dry)
0.97
8–12
Granite
0.82
8–12
Basalt
0.90
8–12
Leaves
0.90–0.97
8-13
0.86–0.96
3–5
Leaves (orange)
0.99
8–14
Bark
0.94–0.97
8–13
0.87–0.90
3–5
Grass (meadow fescue-dry)
0.88
8–13
0.82
3–5
Grass (dead)
0.97
8–14
Grass (live)
0.99
8–14
∊ is given to the nearest 0.01, and the nadir angle is 0° (vertical view). Mean values are shown. Sources for this table are Refs. 8 and 11–15.
Table II
Input and Output Variables for the Estimation of Effective Surface Temperature a
Input
Output
(1)
Altitude Z in meters
(1)
Effective or apparent temperature Te of the surface in kelvins
(2)
Nadir (or zenith) angle η in degrees
(3)
Radiance measured by the sensor Rm in Wm−2 sr−1
(4)
Volume extinction coefficient k in km−1 for the RPV-to-ground layer
(5)
Mean atmospheric temperature Ta in kelvins for the RPV-to-ground layer
(6)
Sensor filter function values ϕi for each wavelength increment
(7)
Fraction of cloud in reflected sky radiance f
(8)
Radiance temperature of clear sky Ts in kelvins
(9)
Radiance temperature of cloud Tc in kelvins
Effective temperature is the apparent radiative temperature of the surface, taking into account atmospheric attenuation, surface emissivity, sensor filter function, and reflected cloud and clear sky radiance, as discussed in the text.
Table III
Values of Te Computed for Different Values of Certain Input Variablesa
∊
k (km−1)
Ta (K)
Te (K)
0.98
0.1
270.0
303.86
0.98
0.1
280.0
303.45
0.98
0.1
290.0
303.00
0.98
0.09
280.0
303.35
0.98
0.1
280.0
303.45
0.98
0.11
280.0
303.56
0.97
0.1
280.0
303.94
0.98
0.1
280.0
303.45
0.99
0.1
280.0
302.97
0.7
0.1
280.0
320.74
0.8
0.1
280.0
313.43
0.9
0.1
280.0
307.47
The computations assume that Z = 500 m, η = 10°, Rm = 6.4 Wm−2 sr−1, λ1,λ2 = 10,11 μm, f = 0,Ts = 240 K, and values of ∊i = 0.3,0.8,1.0 0.8, 0.3 over the wavelength interval. The iteration parameters (a and b) were 0.02 Wm−2 sr−1 and 0.1 K. Calculations for Z = 1000 m (not shown) produced changes in Te of about twice those listed for the different k and Ta. Variables are explained in the text.
Table IV
Values of Te Computed for Different Values of Certain Cloud Parametersa
∊c
f
Tc (K)
Te (K)
1.0
0.5
285.0
309.79
0.9
0.5
285.0
310.12
0.8
0.5
285.0
310.44
0.7
0.5
285.0
310.77
0.6
0.5
285.0
311.09
0.5
0.5
285.0
311.41
1.0
0.3
285.0
311.09
1.0
0.5
285.0
309.79
1.0
0.7
285.0
308.48
1.0
0.5
275.0
310.70
1.0
0.5
285.0
309.79
1.0
0.5
295.0
308.77
The computations assume that k = 0.1 km−1, ∊ of the surface = 0.8, and Ta = 290 K. The values of the other unlisted variables were the same as in Table III.