Abstract

The Earth Radiation Budget Experiment consists of an array of radiometric instruments placed in earth orbit by the National Aeronautics and Space Administration to monitor the longwave and visible components of the earth’s radiation budget. Presented is a dynamic electrothermal model of the active cavity radiometer used to measure the earth’s total radiative exitance. Radiative exchange is modeled using the Monte Carlo method and transient conduction is treated using the finite element method. Also included is the feedback circuit which controls electrical substitution heating of the cavity. The model is shown to accurately predict the dynamic response of the instrument during solar calibration.

© 1989 Optical Society of America

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References

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  1. B. R. Barkstrom, “The Earth Radiation Budget Experiment (ER BE),” Bull. Am. Meteorol. Soc. 65, 1170 (1984).
    [CrossRef]
  2. R. B. Lee, B. R. Barkstrom, R. D. Cess, “Characteristics of the Earth Radiation Budget Experiment Solar Monitors,” Appl. Opt. 26, 3090 (1987).
    [CrossRef]
  3. L. P. Kopia, “The Earth Radiation Budget Experiment Instrument Design Status,” in Proceedings, Fourth Conference on Atmospheric Radiation, Toronto (16–18June1981).
  4. L. P. Kopia, “The Earth Radiation Budget Experiment Scanner Instrument,” Rev. Geophys. Space Phys. 24, (1986).
    [CrossRef]
  5. M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
    [CrossRef]
  6. N. E. Tira, “Dynamic Simulation of Solar Calibration of the Total, Earth-Viewing Channel of the Earth Radiation Budget Experiment (ERBE),” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (Dec.1987).
  7. L. D. Eskin, “Application of the Monte Carlo Method to the Transient Thermal Modeling of a Diffuse-Specular Radiometer Cavity,” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (1981).
  8. J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

1987 (1)

1986 (2)

L. P. Kopia, “The Earth Radiation Budget Experiment Scanner Instrument,” Rev. Geophys. Space Phys. 24, (1986).
[CrossRef]

M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
[CrossRef]

1984 (1)

B. R. Barkstrom, “The Earth Radiation Budget Experiment (ER BE),” Bull. Am. Meteorol. Soc. 65, 1170 (1984).
[CrossRef]

Barkstrom, B. R.

R. B. Lee, B. R. Barkstrom, R. D. Cess, “Characteristics of the Earth Radiation Budget Experiment Solar Monitors,” Appl. Opt. 26, 3090 (1987).
[CrossRef]

B. R. Barkstrom, “The Earth Radiation Budget Experiment (ER BE),” Bull. Am. Meteorol. Soc. 65, 1170 (1984).
[CrossRef]

Cess, R. D.

Cooper, J. E.

M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
[CrossRef]

Eskin, L. D.

L. D. Eskin, “Application of the Monte Carlo Method to the Transient Thermal Modeling of a Diffuse-Specular Radiometer Cavity,” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (1981).

Gardiner, B. D.

J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

Kopia, L. P.

L. P. Kopia, “The Earth Radiation Budget Experiment Scanner Instrument,” Rev. Geophys. Space Phys. 24, (1986).
[CrossRef]

L. P. Kopia, “The Earth Radiation Budget Experiment Instrument Design Status,” in Proceedings, Fourth Conference on Atmospheric Radiation, Toronto (16–18June1981).

Kowary, F.

J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

Lee, R. B.

Luther, M. R.

M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
[CrossRef]

Mahan, J. R.

J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

Taylor, G. R.

M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
[CrossRef]

Tira, N.

J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

Tira, N. E.

N. E. Tira, “Dynamic Simulation of Solar Calibration of the Total, Earth-Viewing Channel of the Earth Radiation Budget Experiment (ERBE),” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (Dec.1987).

Appl. Opt. (1)

Bull. Am. Meteorol. Soc. (1)

B. R. Barkstrom, “The Earth Radiation Budget Experiment (ER BE),” Bull. Am. Meteorol. Soc. 65, 1170 (1984).
[CrossRef]

Rev. Geophys. Space Phys. (2)

L. P. Kopia, “The Earth Radiation Budget Experiment Scanner Instrument,” Rev. Geophys. Space Phys. 24, (1986).
[CrossRef]

M. R. Luther, J. E. Cooper, G. R. Taylor, “The Earth Radiation Budget Experiment Nonscanner Instrument,” Rev. Geophys. Space Phys. 24, 391 (1986).
[CrossRef]

Other (4)

N. E. Tira, “Dynamic Simulation of Solar Calibration of the Total, Earth-Viewing Channel of the Earth Radiation Budget Experiment (ERBE),” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (Dec.1987).

L. D. Eskin, “Application of the Monte Carlo Method to the Transient Thermal Modeling of a Diffuse-Specular Radiometer Cavity,” M.S. Thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute & State U., Blacksburg, VA (1981).

J. R. Mahan, F. Kowary, N. Tira, B. D. Gardiner, “Transient Conduction-Radiation Analysis of an Absolute Active Cavity Radiometer Using Finite Elements,” in Proceedings, International Symposium on Thermal Problems in Space-Based Systems, ASME HTD-83, Boston, MA (14–18Dec.1987).

L. P. Kopia, “The Earth Radiation Budget Experiment Instrument Design Status,” in Proceedings, Fourth Conference on Atmospheric Radiation, Toronto (16–18June1981).

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Figures (7)

Fig. 1
Fig. 1

ERBE total, wide field-of-view radiometer configured for solar calibration.

Fig. 2
Fig. 2

Electrical substitution heater feedback control circuit.

Fig. 3
Fig. 3

Collimated solar radiation entering cavity through solar port.

Fig. 4
Fig. 4

Radiation distribution factors for a collimated beam incident at angles of (a) 7.7°, (b) 5.5°, (c) 3.3°, and (d) 1.1°.

Fig. 5
Fig. 5

Nonequivalence for a narrow beam as a function of angle of incidence to the cavity aperture.

Fig. 6
Fig. 6

(a) Comparison of predicted and observed electrical substitution heater power for the solar calibration event of 28 Dec. 1984, and (b) the corresponding variation of predicted RTD temperature with time.

Fig. 7
Fig. 7

(a) Comparison of predicted and observed electrical substitution heater power for the solar calibration event of 31 Oct. 1985, and (b) the corresponding variation of predicted RTD temperature with time.

Tables (1)

Tables Icon

Table I Results of Various Tests on the Overall Error and Performance of the Model

Equations (32)

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Q j θ = H D j θ i   =   1 N A i p .
D j θ = i   =   1 N ( A i p K i j K i ) i   =   1 N A i P ,
x ( k T x ) + y ( k T y ) + G = ρ c T t ,
Q rad  , j = Q rad  , j in Q rad  , j out .
Q rad  , j in = Q C B , j + Q cav , j + Q S F , j + Q V , j ,
Q C B , j = H D j θ k   =   1 N A k p ,
Q cav , j = i   =   1 n ε A i σ T i 4 D i j ,
ε i A i D i j = ε j A j D j i .
Q cav , j = i   =   1 n ε A j σ T i 4 D j i .
Q S F , j = ε A j F A a D j a  ,
Q V , j = V D j ( l , m ) ,
Q rad , j in = H D j θ k   =   1 N A k p + i   =   1 n ε A j σ T i 4 D j i + ε A j F A a D j a + V D j ( l , m ) .
Q rad , j out = ε A j σ T j 4 .
Q rad , j = H D j θ k   =   1 N A k p + i   =   1 n ε A j σ T i 4 D j i + ε A j F A a D j a + V D j ( l , m ) ε A j σ T j 4 .
G rad  , j = 1 A j δ H D j θ k   =   1 N A k p + 1 δ i   =   1 n ε σ T i 4 D j i + 1 A a δ ε F D j a + 1 A j δ V D j ( l , m ) 1 δ ε σ T j 4 .
E 1 = E 0 ( R 1 R 1 + R 4 R 2 R 2 + R 3 ) ,
R 1 = R + Δ R 1 ,
E 1 = E 0 4 ( R 1 R 1 )  .
R 1 = R [ 1 + α ( T 1 T h s ) ]  ,
E 1 = α 4 E 0 ( T 1 T h s ) .
d E 2 d t = E b E 1 τ ,
d E 2 d t = E b τ α 4 τ E 0 ( T 1 T h s ) .
E b = α 4 E 0 Δ T ,
d E 2 d t = α 4 τ E 0 [ Δ T + ( T h s T 1 ) ] .
E 2 p   + 1 = E 2 p + Δ t α 4 τ E 0 [ Δ T + ( T h s T 1 ) ] .
Q elec = E 2 2 R h w ,
G elec , j = Q e 1 ec A h w δ ,
G elec , j = E 2 2 R h w A h w δ .
G elec , j p   +   1 = 1 R h w A h w δ { E 2 p + Δ t α 4 τ E 0   [ Δ T + ( T h s T 1 ) ] } 2 .
Q e 1 ec in + Q rad in = Q emit out + Q cond out .
err = ( 1 Q out / Q in ) × 100 % ,
NE = ( 1 Q elec / Q rad max ) × 100 % ,

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