NASA Contractor Report 181818 

MODELING AND CHARACTERIZATION 

OF THE EARTH IlADIATION BUDGET EXPERIMENT (ERBE) 

NONSCANNER AND SCANNER SENSORS 

(NASA-CE-181618) WODELING AND I89- 24772 

CHARACTERIZATION OF THE EBRTA RADIATION 

BUDGET EXPEBIHENT t15BBE) NOISCANNER AN 1; 

SCANNER SENSORS Final Report (Information and Control Systems] 182 p CSCI. O4B (33147 0205450 

Unclas 

Nesim Halyo 

Dhirendra K. Pandey 

Deborah B. Taylor 

INFORMATION & CCINTROL SYSTEMS, INCORPORATED 

28 MMRCH DRIVE 

HAMJTON, VIRGINIA 23666 

CONTRACT NASI-18018 

March 1989 

. NASA 

National Aeronautcs and 

Space Ad rn i n is t ra t ton 

Langley Research Center 

Hampton. Vtrginia 23665 
FOREWORD 

I 

The work described in this report was performed by lnformation & Control Systems, 

Incorporated under Contract Number NAS1-18018 for the National Aeronautics and Space 

Administration, Langley Research Center, Hampton, Virginia. Mr. Robert J. Keynton 

was the NASA Technical Representative for this contract. Dr. Nesim Halyo directed the 

technical effort at ICs. 

/ 

4 

i 
TABLE OF CONTENTS 

PaSe 

Foreword ......................................................... i1 

c 

List of Figureli .................................................. vi 

List of Tables ................................................... x 

PART I: MODELING AND CHARACTERIZATION OF THE EARTH RADIATION 

BUDGET EXPERIMENT (ERBE) NONSCANNER SENSORS ............. 1 

1 . Introdl~ction ............................................ 1 

2 . Nonscwiner Sensors ...................................... 3 

2.1 De. scription ........................................ 3 

2.1.1 Basic Operations ............................ 3 

2.1.2 Sensor Modeling ............................. 11 

2.2 Toi:al Wavelength Channels .......................... 15 

2.2.1 Active Cavity Power Balance ................. 15 

2.2.2 Active Heater Electronics ................... 

2.2.3 Reference Cavity ............................ 

2.3 Shoi-twave Channels ................................. 

2.4 Sensor Data Interpretation Algorithm Development ... 

2.4.1 Steady-State Sensor Models .................. 

2.4.2 Total Wavelength Channels ................... 

2.4.3 Shortwave Channels .......................... 

2.5 Sensor Data Output Interpretation Algorithm ........ 

2.5.1 Total Wavelength Channels ................... 

2.5.2 Shortwave Channels .......................... 

PRECEDGNG PAGE BLANK NOT FILMED 

17 

20 

20 

24 

24 

25 

31 

34 

34 

36 

iii 
TABLE OF CONTENTS (CONTINUED) 

Page 

3 . Ground Calibration ...................................... 37 

3.1 Description of Calibration Sources ................. 37 

3.1.1 Master Reference Blackbody (MRBB) ........... 37 

3.1.2 Integrating Sphere (IS) ..................... 41 

3.2 Count Conversion Equations ......................... 41 

3.3 Calibration Data Background ........................ 42 

3.3.1 ERBS Calibration Data ....................... 42 

3.3.2 NOAA-9 Calibration Data ..................... 42 

3.3.3 NOAA-10 Calibration Data .................... 43 

3.4 Ground Count Conversion Coefficients Results ....... 43 

4 . In-Flight Calibration ................................... 48 

4.1 In-Flight Calibration Sources ...................... 48 

4.2 In-Flight Count Conversion Equations ............... 48 

4.2.1 Total Channels .............................. 48 

4.2.2 Shortwave Channels .......................... 50 

4.2.3 Dome Degradation Factor ..................... 50 

4.2.4 A, Term of NOAA-9 Shortwave Channels ........ 57 

4.3 Total Channel Offsets .............................. 57 

4.4 Shortwave Channel Offsets .......................... 59 

4.4.1 NOAA-10 Shortwave Offsets Determination ..... 66 

4.5 Final In-Flight Count Conversion Coefficients ...... 83 

4.5.1 ERBS Nonscanner Results ..................... 83 

4.5.2 NOAA-9 Nonscanner Results ................... 93 

4.5.3 NOAA-10 Nonscanner Results .................. 93 

iv 
TABLE OF CONTENTS (CONCLUDED) 

Page 

Reference~i .................................................. 103 

Appendix A Configuration Factor ............................. 104 

Appendix B BMRBB-IBB Correction Factor ...................... 106 

Appendix C Solar Calibration Data ........................... 107 

PART 11: MODELING AND CHARACTERIZATION OF THE EARTH RADIATION 

BUDGET EXPERIMENT (ERBE) SCANNER SENSORS ............... 114 

. I . Introduction .......................................... 114 

I1 . Scanner Description and Model1 ng ...................... 117 

A . Spectral Considerations ........................... 122 

B . Scanner Dynamic Model ............................. 130 

C . Ef'fective Point Spread Function ................... 139 

D . Interpretation Algorithms (Count Conversion) ...... 151 

I11 . Calibration ........................................... 153 

A . Calibration Sources ............................... 153 

B . Calibration Procedures ............................ 157 

1 . Total and Longwave Channels ................... 159 

2 . Shortwave Channels ............................ 161 

C . In-E'light Offset Stability ........................ 162 

D . SWICS Stability ................................... 162 

E . 'Striping" Algorithm .............................. 167 

References .................................................. 170 

V 
LIST OF FIGURES 

PART I: CALIBRATION AND INTERPRETATION OF THE EARTH RADIATION 

BUDGET EXPERIMENT (ERBE) NONSCANNER SENSORS 

Figure 2.1 Nonscanner Total Channel ............................. 4 

Figure 2.2 Nonscanner Shortwave Channel ......................... 5 

Figure 2.3a Electronic Block Diagram ............................. 7 

Figure 2.3b Active Cavity Feedback ............................... 8 

Figure 2.3~ Nonscanner Electronics (ACR) ......................... 

Figure 2.4 Angle Conventions .................................... 

Figure 2.5 Transmission of lmm SUPRASIL-W ....................... 

Figure 3.1 ERBE Calibration Chamber ............................. 

Figure 3.2 Cross section of Master Reference Blackbody (MRBB) ... 

Figure 3.3 Integrating Sphere ................................... 

Figure 4.1 Nonscanner Elevation Positions ....................... 

Figure 4.2 Solar Measurement vs Calibration Day For ERBS MFOVSW 

Sensor ............................................... 

Figure 4.3 Solar Measurement vs Calibration Day For ERBS WFOVSW 

Sensor ............................................... 

Figure 4.4 Solar Measurement vs Calibration Day For NOM-9 

MFOVSW Sensor ........................................ 

Flgure 4.5 Solar Measurement vs Calibration Day For NOAA-9 

WFOVSW Sensor ........................................ 

Figure 4.6 Solar Measurement vs Calibration Day For NOAA-10 

MFOVSW Sensor ........................................ 

Figure 4.7 Solar Measurement vs Calibration Day For NOAA-10 

WFOVSW Sensor ........................................ 

Figure 4.7a MFOVSW (Nighttime) Energy vs MFOVSW FOVL 

Temperature. T. ...................................... 

9 

13 

22 

38 

39 

40 

49 

51 

52 

53 

54 

55 

56 

58 

vi 
LIST OF FIGURES (CONTINUED) 

Figure 4.8 Ofl'set Variation Obtained By Using IBB Data vs 

Ca1.ibration Day For ERBS MFOVT Channel..... .......... 60 

Figure 4.9 Off'set Variation Obtained By Using IBB Data vs 

Calibration Day For ERBS WFOVT Channel........ ....... 61 

Figure 4.10 Offset Variation Obtained By Using IBB Data vs 

Calibration Day For NOAA-9 MFOVT channel............. 62 

Figure 4.11 Offset Variation Obtained By Using IBB Data vs 

Calibration Day For NOAA-9 WFOVT channel............. 63 

Figure 4.12 Offset Variation Obtained By Using IBB Data vs 

Calibration Day For NOAA-10 MFOVT Channel............ 64 

Figure 4.13 Offset Variation Obtained By Using IBB Data vs 

Calibration Day For NOAA-10 WFOVT Channel ............ 65 

Figure 4.14 Estimated Shortwave Energy (Orbital Average) From 

Darkside Data Analysis For ERBS MFOVSW Channel For 

Aprll 1985.. ......................................... 69 

Figure 4.15 Esttmated Shortwave Energy (Daily Average) From 

Darkside Data Analysis For ERBS MFOVSW Channel For 

April 1985.................... ....................... 70 

Figure 4.16 Finiil Offset Term For ERBS MFOVSW Channel For April 

1985....................................... .......... 71 

Figure 4.17 Esthated Shortwave Energy (Orbital Average) From 

Darkside Data Analysis For ERBS WFOVSW Channel For 

Aprll 1985. .......................................... 72 

Figure 4.18 Estimated Shortwave Energy (Daily Average) From 

Darkside Data Analysis For ERBS WFOVSW Channel For 

April 1985 ........................................... 73 

Figure 4.19 Final Offset Term For ERBS WFOVSW Channel For April 

1985.. ............................................... 74 

Figure 4.20 Estimated Shortwave Energy (Orbital Average) From 

Darkside Data Analysis For NOAA-9 MFOVSW Channel For 

April 1985....... .................................... 75 

Figure 4.21 Estinated Shortwave Energy (Daily Average) From 

Darkside Data Analysis For NOAA-9 MFOVSW Channel For 

April 1985........................................... 76 

vii 
LIST OF FIGURES (CONTINUED) 

Figure 4.22 Final Offset Term For NOAA-9 MFOVSW Channel For April 

1985... .............................................. 77 

Figure 4.23 Estimated Shortwave Energy (Orbital Average) From 

Darkside Data Analysis For NOAA-9 WFOVSW Channel For 

April 1985....... .................................... 78 

Figure 4.24 Estimated Shortwave Energy (Daily Average) From 

Darkside Data Analysis For NOAA-9 WFOVSW Channel For 

April 1985........................................... 79 

Figure 4.25 Final Offset Term For NOAA-9 WFOVSW Channel For April 

1985...................................... ........... 80 

Figure 4.26 Differences In Offset Levels By Looking At Different 

Data Sources for ERBS WFOVSW Channel.......... ....... 81 

Figure 4.27 Differences In Offset Levels By Looking At Different 

Data Sources for NOAA-9 WFOVSW Channel............... 82 

Figure 4.28 Differences In Offset Levels By Looking At Different 

Data Sources for ERBS MFOVSW Channel................. 85 

Figure 4.29 Differences In Offset Levels By Looking At Different 

Data Sources for NOAA-9 MFOVSW Channel....... ........ 86 

Figure A.l Representation of Configuration ...................... 104 

PART 11: CALIBRATION AND INTERPRETATION OF THE EARTH RADIATION 

BUDGET EXPERIMENT (ERBE) SCANNER SENSORS 

Figure 1. ERBE Scanner with Contamination Covers Open.. ........ 116 

Figure 2. ERBE Scanner... ...................................... 118 

Figure 3. Scan Pattern ......................................... 119 

Figure 4. Precision Aperture Shape ............................. 121 

Figure 5. Detector Bridge Diagr am.............................. 123 

Figure 6. Scanner Electronics Block Diagr am.................... 124 

Figure 7. ERBE Scanner Spectral Response ....................... 126 

viii 
LIST OF FIGURES (CONCLUDED) 

Figure 8 . 

Figure 9 . 

Figure 10 . 

Figure 11 . 

Figure 12 . 

Figure 13 . 

Figure 14 . 

Figure 15 . 

Figure 16 . 

Figure 17 . 

Figure 18 . 

Figure 19 . 

Figure 20 . 

Figure 21 . 

Figure 22 . 

Figure 23 . 

ERBE Scanner Spectral Response ....................... 127 

ER:3E Scanner Spectral Response ....................... 128 

Spc?ctral Considerations .............................. 129 

Scanner Heater Controller Model ...................... 132 

Siniulation of ERBE Total Scanner Thermal and 

E1e:ctrical Variables ................................. 136 

Spa.tia1 Frequency Response of the Optics ............. 145 

Shape and Spatial Frequency Response of the Detector 

Aperture ............................................. 147 

Frequency Response of the Electronics as a Function 

of Cycles/Degrees .................................... 148 

Effective Spatial Frequency Response Function of ERBE 

Sca ..ners ............................................. 149 

Effective Spatial Response of ERBE Scanners .......... 150 

ERBE Calibration Chamber ............................. 154 

Cross Section of Master Reference Blackbody (MRBB) ... 155 

Integrating Sphere ................................... 156 

Actjve Measurements of the ERBE Shortwave Scanner 

Instrument Scanning the ERBE Integrating Sphere ...... 158 

NOAA-9 SWICS Amp Output .............................. 166 

NOAA-9 Scanner SW Channel: SWICS Data ............... 168 

ix 
LIST OF TABLES 

PART I: CALIBRATION AND INTERPRETATION OF THE EARTH RADIATION 

BUDGET EXPERIMENT (ERBE) NONSCANNER SENSORS 

Table 3.1 

Table 3.2 

Table 3.3 

Table 4.1 

Table 4.2 

Table 4.3 

Table 4.4 

Table 4.5 

Table 4.6 

Table 4.7 

Table 4.8 

Table 4.9 

Table 4.10 

Table 4.11 

Table 4.12 

ERBS Flight Model One (FM1) Ground Count Conversion 

Coefficients.......................................... 44 

NOAA-9 Flight Model Two (FM2) Ground Count Conversion 

Coefficients........................ .................. 45 

NOAA-10 Proto-Flight Model (PFM) Ground Count 

Conversion Coefficients......... ...................... 47 

ERBS Shortwave Offset Determination For April 6, 1985 

Using Darkside Data Analysis .......................... 

NOAA-9 Shortwave Offset Determination For April 6, 

1985 Using Darkside Data Analysis. .................... 68 

NOAA-10 WFOVSW Offsets................................ 84 

ERBS MFOV Total In-Flight Count Conversion 

Coefficients.......................................... 87 

ERBS WFOV Total In-Flight Count Conversion 

Coefficients........ .................................. 88 

ERBS MFOV SHORTWAVE In-Flight Count Conversion 

Coefficients.......... ................................ 89 

ERBS WFOV Shortwave In-Flight Count Conversion 

Coefficients.......... ................................ 91 

NOAA-9 MFOV Total In-Flight Count Conversion 

Coefficients .......................................... 94 

NOAA-9 WFOV Total In-Flight Count Conversion 

Coefficients....... ................................... 95 

NOAA-9 MFOV Shortwave In-Flight Count Conversion 

Coefficients .......................................... 96 

NOAA-9 WFOV Shortwave In-Flight Count Conversion 

Coefficients...................... .................... 98 

NOAA-10 MFOV Total In-Flight Count Conversion 

Coefficients.......................................... 100 

67 

X 
LIST OF TABLES (CONCLUDED) 

I 

i 

Table 4.13 NOAA-10 WFOV Total In-Flight Count Conversion 

Coel'flcients .......................................... 100 

Table 4.14 NOAIL-10 MFOV Shortwave In-Flight Count Conversion 

Coefficients .......................................... 101 

Table 4.15 NOM.. 10 WFOV Shortwave In-Flight Count Conversion 

Coef'flclents .......................................... 101 

Table A.l Conf'iguration Factors ................................. 105 

Table B.l BMRB8 IBB Correction Factors .......................... 106 

Table C.l ERBS MFOVSW Solar Calibration Data .................... 108 

- 

Table C.2 EXBS WFOVSW Solar Callbration Data .................... 109 

Table C.3 NOAA-9 MFOVSW Solar Calibration Data .................. 110 

Table C.4 NOAA-9 WFOVSW Solar Calibration Data .................. 111 

Table C.5 NOAA-10 MFOVSW Solar Calibration Data ................. 112 

Table C.6 NOAA-10 WOVSW Solar Callbration Data ................. 113 

PART 11: CALIBRATION AND INTERPRETATION OF THE EARTH RADIATION 

BUDGEr EXPERIMENT (ERBE) SCANNER SENSORS 

Table 1 . Scannw Electronics .................................... 133 

Table 2 . NOM-(1 Count Conversion Equations ...................... 160 

Table 3 . ERBE ERBS (FM1) Scanner Data Interpretation 

Coefflcients ........................................... 163 

Table 4 . ERBE h'OAA-10 (FM2) Scanner Data Interpretation 

Coefficients ........................................... 163 

Table 5 . ERBE hOAA-9 (PFM) Scanner Data Interpretation 

Coefficients ........................................... 163 

Table 6 . ERBS Scanner Offset Stability .......................... 164 

Table 7 . ERBS Total Scanner ..................................... 165 

xi 
PART I 

MODELING AND CHARACTERIZATION OF THE 

EARTH RADIATION BUDGET EXPERIMENT (ERBE) 

NONSCANNER SENSORS 

1. INTRODUCTION 

Three Earth Radiation Budget Experiment (ERBE) satellites, namely ERBS, NOAA9 and NOAA-10 were launched on October 5, 1984, December 5, 1984, September 17,1986 

respectively to measure the radiances from the sun and reflected and emitted radiances 

from the earth-atmosphere system. The first spacecraft, ERBS, which has a non-sunsynchronous trajectory, is favorable for mid and low latitudes. The other two satellites, 

NOAA-9 and NOAA-10, which have sun-synchronous trajectories, are favorable for high 

altitudes. A general overview of the concept behind the three-satellite ERBE radiometric 

system and its instrume:nts has been described in many internal NASA documents, such 

as the Science Team Meeting Minutes and Contractor Status Reports, as well as in journal 

publications [l]. 

Each ERBE satellite has five nonscanner sensors with active cavity radiometer detectors. Four of them are aimed to measure the radiances leaving the earth-atmosphere 

system, while the fifth sexor, known as the Solar Monitor, measures the solar incident radiance. One wide and one medium field-of-view sensor make measurements across the total 

spectral band, while the the other two measure the Earth’s reflected radiation, which is 

then subtracted from the total measurements to determine the Earth’s emitted radiation. 

The fifth instrument, the Solar Monitor, uses the same type of Active Cavity Radiometer 

(ACR) that is used by the nonscanners. Details of these sensors can be found elsewhere 

PI - 141. 
This report describes the development of governing equations, calibration procedure 

and interpretation of calibration data to determine the Ground and In-Flight Count Conversion Coefficients for the nonscanner active cavity radiometers. Chapter 2 details the 

nonscanner instruments and mathematical developments, while Chapters 3 and 4 describe 

the Ground and In-Flight Count Conversion Coefficients, respectively. 

I 2 
2. NONSCANNER SENSORS 

2.1 Description 

The ERBE Non-Scanning sensors are state-of-the-art active cavity radiometers (ACR) 

designed for high accuracy and stability. Each of the three Non-Scanner instruments consists of four sensors. Two of the sensors have a wide field-of-view (WFOV) which provides 

limb-t-limb coverage of the top of the atmosphere (TOA) plus a "space ring" to accommodate small deviations in spacecraft roll angle and possible installation misalignments. The 

other two Non-Scanners have a medium field-of-view (MFOV) covering a circular area with 

a diameter corresponding to about 10" Earth Central Angle at the top of the atmosphere, 

The WFOV and MVOV sensors each consist of a Shortwave (SW) and a Total (T) 

sensor, measuring the spcctral bands from 0.2pm to 5pm and from 0.2pm to 50 + pm, respectively. In comparison to the Total channels, the Shortwave channels contain a suprasil 

dome filter to filter out the incoming longwave radiation. A schematic diagram showing 

the major elements of the MFOV-T and the WFOV-SW sensors is shown in Figs. 2.1 and 

2.2, respectively. A more detailed description of the ERBE Non-Scanner Instruments can 

be found in [I] - [3]. 

2.1.1 Basic Operation. 

As shown in Figs. 2.1 and 2.2, the active and reference cavities are cylindrical near 

the primary aperture and conical near the bottom. The active and reference cavity heater 

wires are wound around the bottom or conical part of the cavities. Temperature sensing 

wires are wound around the cylinders which hold the cavities, and thermally connect the 

cavities to the copper hea.: sink, shown as node 2 in the schematic diagrams. 

The copper heatsink is maintained at a constant temperature by resistance heater 

windings, as shown in Figs. 2.1 and 2.2. The resistance heater windings extend somewhat 

3 
1 I 

ACTIVE CAVITY 

Cu HEAT SINK 

REFERENCE CAVITY 

AI HEAT SINK 

BASE PLATE 

FOV LIMITER 

A1 HEAT SINK 

APERTURE 

H HEATER 

P TEMPERATURE PROBE 

I 4 Figure 2.1 Nonscanner Total Channel 
i 

1 

i9T - 8 - 8 I 

1 

2 

3 

4 

5 

6 

7 

8 

9 

H 

P 

ACTIVE CAVITY 

Cu HEAT SINK 

REFERENCE CAVITY 

A1 HEAT SINK 

BASE PLATE 

FOV LIMITER 

A1 HEAT SINK 

APERTURE 

SW FILTER DOME 

HEATER 

TEMPERATURE PROBE 

Figure 2.2 Nonecanner Shortwave Channel 

5 
beyond the copper heatsink, also adding heat to the two aluminum heatsinks corresponding 

to nodes 4 and 7. The heatsink has three set temperatures of operation, although normal 

operation is around 34 "C. 

In the normal operation modes, the reference cavity maintains a constant temperature 

nearly equal to the heatsink temperature. The reference cavity has a conductive path to 

the copper heatsink; its radiative exchange is mainly with the aluminum heatsink and to a 

lesser degree with the copper heatsink and the active cavity. In the Earth-looking modes, 

the reference cavity heater is off, so that the only source of heat to the cavity comes from 

the current flowing in the temperature sensor wire around the cavity. Since all these effects 

remain essentially constant, the reference cavity remains at a constant temperature. 

On the other hand, the activity cavity has two extra major sources of energy: the 

radiation arriving through the primary aperture (node 8), and the Joule heating produced 

by the active cavity heater windings. The radiation arriving through Joule heating produced by the active cavity heater windings. The radiation arriving through the primary 

aperture consists of radiation arriving through the sensor field-of-view (FOV), or the secondary aperture, which is the signal to be measured, radiation emitted by or reflected from 

the field-of-view limiter (FOVL) and the baseplate (node 5). The radiative exchange with 

the primary aperture itself must also be considered. 

On the other hand, the active cavity heater, through a feedback control circuit shown 

in Fig. 2.3, maintains the active cavity temperature approximately "C above the reference 

cavity temperature. Since the reference cavity temperature remains constant, so does 

the active cavity temperature. When the radiation arriving from the primary aperture 

increases, the active cavity heater reduces its heat input by the same amount to maintain 

the active cavity at a constant temperature. The active cavity heater voltage, in digital 

format, constitutes the sensor output from which the desired signal is to be estimated. 

Thus, the active cavity heater input varies with the energy variations from all other 

sources. To obtain an estimate of the desired signal (i.e., the radiation arriving through 

6 
. 

I- 

; 

U 

d 

W 

I 

f W!! a& 

5s 

oa 

t 

w 

a 

4 

Id > 

L 

W 

c 

4 

9 

U 

.cI -a 

El Y 

7 

7 
Active Cavity = Qrl 

Heat Feedback 

n Tj - TI 

(v1,rlcl)Tl = Rji + 441 + Qel 

j=l 

Figure 2.3b Active Cavity Feedback 

I 8 
00 

L 3 

9 
the secondary aperture), it is necessary to carefully eliminate the effects from the other 

energy sources such as variations due to the field-of-view limiter baseplate, the dome filter 

and other component temperatures, the energy loss through the conductive path to the 

Cu heatsink, etc. When all of these effects, most of which are second order, are carefully 

accounted for and subtracted from the active cavity heater input, the remaining energy is 

due to absorbed radiation arriving through the sensor field-of-view, which is the desired 

signal. In the following sections, the radiative, conductive and electrical interactions of the 

various elements of the radiometers are modeled and investigated in detail to obtain the 

best estimate of the desired incoming flux. 

All the nonscanner sensors have field-of-view limiters and baseplates with specular, 

characteristics to the extent possible. As the FOVL’s are hemispherical with their origin 

at the center of the primary aperture, this specular characteristic tends to minimize the 

amount of reflected radiation which enters the active cavity through the primary aperture. 

This effect may be somewhat reduced in the shortwave channels due to the presence of the 

dome filter between the FOVL and the active cavity. 

As mentioned earlier, in Earth-looking modes, the reference cavity heater is turned 

off, so that the cavity temperature is nearly equal to the heatsink temperature. However, 

the sensors can also be operated at three other levels of reference cavity heater voltage. At 

each of these modes, a higher amount of constant heat is provided to the reference cavity. 

While some of this energy is emitted, and some conducted to the copper heatsink, the 

cavity temperature settles at a level higher than the one reached during the normal Earthlooking mode. Thus, the reference cavity temperature reaches a temperature higher than 

the heatsink temperature. The feedback control electronics drives the active cavity heater 

input to the level necessary to maintain the active cavity temperature slightly higher than 

that of the reference cavity. 

In these modes, although the active and reference cavities are both at higher temperatures, the principle of operation remains the same at the new operating point. The 

10 
* 

active cavity temperature is maintained at a constant, albeit higher, temperature by the 

feedback control law which compensates exactly for the variations in absorbed energy arriving through the precision aperture. These modes of operation where the active cavity 

temperature differential over the heatsink temperature is higher, substantially increase the 

dynamic range of the scmors with no change in the sensitivity of the sensor. In particular, 

solar calibration, where the signal measured is significantly higher than the one experienced 

during Earth-looking modes, is performed at a non-zero reference cavity heater voltage. 

The field-of-view limiter and the baseplate are thermally isolated from the detector 

which consists of nodes 1,2, 3,4, 7,8 and 9 shown in the sensor schematic in Figs. 2.1 and 

2.2. The baseplate is connected to the detector by a bolt using thermal insulation, but it 

is connected to the elev'ation beam through a conductive link to minimize signal induced 

variations in the FOVL and baseplate. 

While the discussion above provides the basic operation of the non-scanning ERBE 

sensors and describes the major elements of the ACR's, many of the significant details 

involved in the design and assembly of the sensors are too numerous to be mentioned here. 

A more detailed description of the sensors is given in [l] - (31. 

2.1.2 Sensor Modeling. 

The main objective in modeling the ERBE sensors has been to obtain a thorough 

understanding of the various interrelationships and interactions among the components 

of the sensors. This involves modeling the radiative exchange, thermal conduction and 

electronic interactions to form the overall model describing the significant behavior of the 

sensors. Since the sensors cannot be characterized and calibrated in the actual conditions 

of orbital operations, it is necessary to infer the sensor response in normal operation from 

calibration data rneasure,d under somewhat different conditions, namely the calibration 

chamber. A thorough unc:erstanding of the sensor under as wide a variety of conditions as 

possible provides a most .reliable approach to achieve this inference with the aid of flight 

calibration data. Furthermore, ascertaining the stability of the sensors, and interpreting 

11 
actual changes in the sensors themselves during the life of the sensors also necessitate a 

good understanding of the sensors. 

While a thorough understanding of the significant sensor response is indispensable, 

practical considerations limit the level of detail that can be included in a model before 

extraneous effects, possibly caused by numerical difficulties, limit the usefulness of the 

model. Therefore, for a given application, a trade-off of the level of detail needed to model 

what is considered significant in the sensor response is necessary. 

As mentioned in the Introduction, the quantity desired is the irradiance, or flux, 

reaching a point at satellite altitude through the sensor’s designated field-of-view and 

spectral waveband. Using the angle conventions shown in Fig. 2.4, let LEX(Z,Y;$,~) be 

the spectral radiance leaving the top of the atmosphere and arriving at the point (z,y) 

on the primary aperture from the direction ($J,x). Let niT be the solid angle formed by 

the secondary aperture at the center of the primary aperture, i.e., at the origin (O,O), for 

the ith Total waveband sensor. For example, ~WT corresponds to the FOV of the Wide 

Field-of-View Total channel. Similarly, OMS corresponds to the FOV of the Medium 

Field-of-View Shortwave channel. 

The desired radiant incidence, or flux, at the point (0,O) arriving from the top of the 

atmosphere within the sensor’s spectral band and FOV is given by 

RiT niT 

Qis 

where Lb;(z,y;$,x) is the radiance at (z,y), and 

Ideally, we would like to measure the radiant incidence, E;T, at an infinitesimally small 

I 12 
% 

0 

x 

'I 

0 

II 

3 

13 
area or a point. From satellite orbit, it is possible to closely approximate this condition, 

by spatial averaging over the small primary aperture. Thus, in the Earth-looking modes, 

the desired irradiance can be expressed as 

~- 

AiT nil' 

1 

Eis 1 Ais J/ JJL' LEX(Z,y;$,X)dXdfIdA= - Ais Pis 9 (2.5) 

Ais nis 

where Air, Ais are the areas of the primary aperture opening for the appropriate sensors, 

and PiT, pis represent the power absorbed by an ideal flat plate collector with spectral 

absorptivity and transmissivity of 1 and perfect cosine angular response over the appropriate field-of-view and spectral band, and over the collector area of AiT or Ais according 

to the sensor. 

Having defined the desired signals, mathematical models which describe the significant 

sensor behavior and which lead to simple algorithms for estimating the desired fluxes will 

be developed. 

The basic approach taken in modeling the sensors is to develop a lumped-parameter 

thermal-electronic model by partitioning the sensor into a set of appropriately selected 

nodes [SI. The selection of nodes used in the model is shown in Figs. 2.1 and 2.2 for the 

Total and Shortwave channels, respectively. 

The energy balance for the jth node can then be expressed as 

where 5, yj and cj are the volume, density and specific heat capacity of the it'' node, 

Rjk is the thermal resistance between the jth node, and kth nodes, Ai is the area of 

radiant interaction for the jth nodre, 4, is the net flux absorbed by the it" node, Ti the 

temperature of the jth node and Qj the total power of all heat sources acting on the 

14 
jth node. Writing a power balance equation for each node of the sensor, it is possible to 

obtain a thermal model for the radiative and conductive exchange among the sensor nodes. 

When a model of the tdectrical processing and control circuits is adjoined to the thermal 

exchange, a complete dynamic model of the sensor is obtained. 

2.2 Total Wavelength Channels 

2.2.1 Active Cavity Power Balance. 

The active cavity is the most important node of the sensors 

the thermal and 

be expressed as 

electrical systems. The power balance equation 

as it is the focus of both 

for the active cavity can 

+P 9 

where Qa is the power provided by the active cavity heater windings, QJ~ the Joule heat 

power produced by thc current flowing in temperature sensor wires, and p the power 

absorbed by the cavity due to radiation arriving through the primary and secondary apertures. The effects of the radiative interchange between the active cavity and the remaining 

nodes is modeled here through the distribution factors Djk. The distribution factors can 

be obtained by Monte C'arlo simulation using ray-tracing techniques by standard radiative 

exchange equations in a cavity using diffuse-grey assumptions or by the coupled-enclosure 

radiative exchange method developed for approximating complicated cavity geometries. 

The active cavity heater power Ga and the sensor wire Joule heating term QJ~ will 

be discussed in more detail subsequently. First consider the absorbed power, PiT, by the 

ifh Total sensor, which contains information about the desired irradiance EiT given by Eq. 

(2.1). Let AiT denote the area of the primary aperture opening of the ith Total sensor and 

Lx(z, y; +, x) the spectral radiance arriving through the secondary aperture and entering 

15 
the active cavity at the point (z,y) from the direction ($J,x). Then p~ can be expressed 

as 

where fli~(z,y) is the solid angle formed by the secondary aperture at the point (z,y) 

for the ith Total sensor. Except for machining tolerances, the primary aperture for all 

channels have the same dimensions and edge characteristics, so that 

Q;T(X) is the effective spectral absorptivity of the inside of the active cavity of the it" 

sensor, and giT($,x) represents the angular response characteristics of the it" sensor to 

radiation arriving from the direction ($,x). It has been assumed that the spectral and 

angular characteristics of the sensor are separable; i.e., that the product of a function 

of X and a function of ($,x) can describe the sensor's combined spectral and directional 

characteristics. 

It should be noted that the effective spectral absorptivity of the active cavity includes 

the effect of multiple bounces of entering radiation at several points inside the cavity. 

The selection of the dimensions of the cylindrical and conical portions of the cavities was 

based on the results of where it is shown that incoming radiation must have at least three 

bounces before leaving the cavity. Thus, if the cavity paint has an absorptivity of .9, then 

the effective cavity absorptivity would be .999, or, for all practical purposes, unity. 

The geometry and radiative properties of the surfaces of the FOV limiter and baseplate 

are designed to minimize the amount of reflected radiation that enters the cavity. However, 

due to imperfections and the finite (non-zero) opening of the primary aperture, some 

angular nonuniformity in response may occur. The term si($, x) accounts for deviations 

. 

16 
from the ideal “cosine response”; so that for an ideal sensor with a cosine response gi($J, x) 

would be unity for all angles ($, x). 

Comparing Eqs. (2!.4) and (2.9), it is seen that the actual absorbed power PIT depends 

on the actual spectral absorptivity and angular response, as opposed to the ideal absorbed 

power in Eq. (2.4). 

2.2.2 Active Heater Electronics. 

As mentioned earl’ier, the active cavity temperature is maintained at a constant level 

above the reverence ca.vity temperature. This is achieved by the control circuit shown 

in Fig. 2.3b. The functional block diagram in Fig. 2.3a shows that the bridge configuration produces a signal proportional to the difference between the active and reference 

cavity temperatures with an additional offset. This signal is then amplified and fed into 

a proportional-integra1 (PI) controller which provides the voltage that drives the current 

through the active cavity heater windings, thus closing the feedback loop. The voltage is 

sampled every 0.8 seconds and translqlitted to Earth through a down-link, providing the 

main radiometer sensor output. 

To model the electronics, first consider the bridge. The active and reference sensor 

wires provide two legs of the bridge, while the other two legs are set to constant resistance 

values. If the active 01’ reference cavities change in temperature the bridge goes out of 

balance thus forcing the controller to add more or less heat to the active cavity and 

maintain its temperature. 

Now note that the bridge output voltage AV is given by 

(2.11) 

(2.12) 

where Rl(T1) and R3(T3) are the sensor wire electrical resistances for the active and 

17 
I 

l 

reference cavities, respectively, and Rz and R4 are the electrical resistances of the copper 

and aluminum heatsinks, respectively. Linearizing the sensor wire resistance in terms of 

its temperature, assume that within a small temperature range, 

Rl(T1) = a1 +blG Y R3(T3) = a3 + 63 T3 . 

It may further be noted that, when the sensor wires are exactly matched, 

AV KB(T~ - T3 - bE) , 

I where T2 is the copper heatsink temperature and KB, bE are given by 

VB b KB = - 

4R 

(2.13) 

(2.14a) 

(2.14b) 

(2.14~) 

I where second order terms have been neglected. So that the bridge will come to balance 

when the active cavity temperature is slightly higher than that of the reference cavity. 

Although the sensor wires are selected to have as close characteristics as possible, perfect 

matching is not essential to the basic operation. After some manipulation, it can be shown 

that the bridge balance will occur when 

(2.15) 

It is seen that appropriate selection of the electronic bias term BE by tuning the 

resistances RZ and Rq, can produce any desired offset between the active and reference 

cavity temperatures. 

It should also be noted that any drift in the sensor wire resistance versus temperature 

I parameters or other bridge impedances will alter the bridge balance and result in slightly 

I 18 
different temperature 1,elationship between TI and T3. 

Further note that since the resistance versus temperature characteristics depend on 

the operating heat sink temperature, T2. The Cu heat sink temperature is, therefore, 

very tightly controlled. To date, the data show that noticeable variations of the heat sink 

temperature are rare and do not exceed 0.01 "C. 

To obtain a dynamic model of the amplifier and proportional-integral (PI) controller 

feedback the following equations can be added to the energy (power) balance equations. 

1 

73 

710 = -[Tg - Ti0 + ri(K~ KE AV + KE n~)] (2.17) 

(2.18) 

v = T11 + n, (2.19) 

where Ts, T10,T11 are variables representing electrical quantities rather than temperatures, 

nE and nu represent random noise introduced by the electronics, and u is the sensor output 

voltage which is applied to the active cavity heater windings. 

Thus, the active cavity heater closes the loop according to 

Qo=u2/Ro , (2.20) 

where R, is the electrical resistance of the active heater windings, and Q, the power added 

to the active cavity in Eq. (2.7). 

19 
2.2.3 Reference Cavity. 

The reference cavity power balance can be written according to the general Eq. (2.6). 

mm n 

(2.21) 

In the case of the reference cavity, the heater, is not in the feedback loop, but is 

driven by a constant voltage, Ur, when the appropriate operation mode is selected. Thus, 

(2.22) 

Using the general energy balance equation in Eq. (2.6), each note temperature can be 

modeled by a differential equation. The combined set of these coupled ordinary differential 

equations forms a dynamic model of the sensor. The results of a sensitivity analysis based 

on a computer simulation of this thermal-electronic model is shown in 181. 

2.3 Shortwave Channels 

The model of the Shortwave sensors differs from that of the Total wavelength sensors 

only for the active cavity, the dome filter and the primary aperture to which the dome 

filter is attached. The form of the energy balance equation for the other nodes remains 

unchanged, except that radiative interaction among the field-of-view limiter, baseplate, 

primary aperture and the active cavity is now included. 

The major effect of the quartz dome is to filter out longwave radiation before it 

is absorbed by the active cavity. Thus, longwave radiation is partially absorbed and 

partially reflected by the dome filter with no transmission occurring. This produces a 

secondary but non-negligible effect in the radiative exchange. When the longwave radiation 

in the observed scene increases, more heat is absorbed by the dome. So that the dome 

temperature, hence the radiation emitted by the dome increases. Accordingly, when the 

observed longwave radiation increases, the active cavity receives more (longwave) energy 

20 
with a lag, even if the scene shortwave radiation is unchanged. Therefore, the model of the 

Shortwave sensors must account for this secondary effect so that a variation in longwave 

radiation is not interpreted as a variation in shortwave radiation. 

The power balance for the active cavity can be expressed as 

(2.23) 

where the number of nodes m for the Shortwave channels include the dome filter and 

exceeds the number of nodes for the total wavelength channels by one. 

For the active cavity, the absorbed power, p, with appropriate subscripts for the 

channel, is highly depmdent on the spectral transmissivity of the dome filter, as can be 

seen in Fig. 2.2. Thus, the expression for the absorbed power becomes 

Pia = // // 1- (z, 9; $9 x) 7ia(~) aia(A) gis(+, x> d~ d~ (2.24) 

where Ria(Z, y) is the solid angle formed by the secondary aperture when viewed from the 

point (5,~) on the prirnary aperture opening and is the spectral transmissivity of the 

dome filter for ith shor,;wave sensor. 

Ai, Ri,(z,y) 

The spectral transmissivity of the fused quartz dome filter used in the ERBE shortwave 

sensor is shown in Fig. 2.5. As can be seen from the plot, the transmission of the filter 

after 5pm is negligible, as these measurements do not show a noticeable “longwave leak” 

after 50pm. It should be noted, howcvcr, that the approach takcn here in determining 

the shortwave channel coefficients would automatically include the effects of any longwave 

transmission. 

To model the dome filter heating effects, the power balance for the dome, or node 9, 

can be expressed as 

(2.25) 

21 
ln 

T 

m 

N 

.I 

Q-4 

0 

Y 

cy 

0, 

k 

z 

iz 

% 

22 
where pf is the power arriving through the secondary aperture which is absorbed by the 

dome filter. This power can be expressed in a form similar to the power absorbed by the 

active cavity. 

where aif(X) is the spectral absorptivity of the dome filter and gir(x,$) the angular 

response of the filter relative to a cosine response for the ith sensor. Similarly Aif is the 

outer surface area of the dome which sees the secondary aperture, and Rif(z,Y) is the 

solid angle formed by the secondary aperture when viewed from the point (2, y) on A;f. 

The power balance equation for the dome shows the effect of absorbed longwave 

radiation on the dome temperature. It should be noted that the FOV limiter and baseplate 

temperatures are influenced by the variations in absorbed energy from the scene and 

participate in the radiative exchange with the dome filter. However, the FOV limiter 

and baseplate are conductively linked to the box beam, whereas the dome filter is a poor 

conductor and is thermally insulated from the primary aperture to which it is glued. 

Thus, the temperature of the dome filter varies with the longwave content of the scene and 

the temperature of the FOVL, baseplate and the primary aperture which is conductively 

coupled to the heat sink. However, the dome temperature lags the incoming longwave flux 

as can be seen by Eq. 1:2.25). Linearizing the power balance equation, the time constant 

for this differential equation can be found to be 

(2.27) 

where 2'90 is the nomin.31 dome temperature. 

For the shortwave, or filtered, channels it is seen that when the longwave radiation is 

a ramp of 1 W/m2 sec, the shortwave channel output has a lag of about 40 sec. 

23 
2.4 Sensor Data Interpretation Algorithm Development 

The dynamic sensor models discussed in the preceding section are coupled nonlinear differential equations which describe the dynamic response of the sensors to incoming 

radiation under given conditions. On the other hand, to interpret the sensor output (radiometric and housekeeping data) in normal operation, what is required is a (sensor) data 

interpretation algorithm (SDIA) which estimates the magnitude of the incoming radiation 

from the sensor’s radiometric and housekeeping data input. Viewing the sensor as a transformation from the set of incoming radiation signals into the set of sensor outputs, it is 

necessary to determine the inverse transformation which maps the sensor output back into 

the corresponding input irradiance. 

The determination of this inverse transformation for the dynamic (Le., time dependent) models is a complex process which results in a rather complex algorithm to implement. Therefore, the approach taken here is to determine the steady-state model of the 

sensor, then invert this model to obtain an algorithm for interpreting the sensor output. 

In most cases, as the non-scanner footprint, hence the incoming radiation signal, changes 

slowly in comparison to the sensor settling time, neglecting the transient behavior in the 

normal Earth-looking modes introduces little error. In modes of operation where the sensor 

transient response has not died down, the steady-state assumption should not be used. 

2.4.1 Steady-State Sensor Models. 

The steady-state sensor response is obtained by allowing sufficient time for the sensor’s transient response to decay to negligible levels while the incoming radiation remains 

constant. In this condition, the temperature of each node reaches a constant value; however, thermal gradients are still present in the steady-state response. Thus, the energy or 

power balance equation for the steady-state condition is obtained by simply setting the 

time derivative of the node temperatures, Y’j, to zero in Eq. (2.6); i.e., 

24 . 
(2.28) 

2.4.2 Total Wavelength Channels. 

The active cavity power balance in steady-state can be written as follows using Eq. 

(2.7) and Eq. (2.20): 

(2.29) 

where p with appropr',ate subscripts is given by Eq. (2.9) and represent the steady-state 

signal power absorbed by the active cavity, and u is the steady-state voltage output of the 

sensor. 

Now, for a given amount of absorbed power, the active heater control electronics 

reacts, as described in the previous section, in a way to maintain the active cavity temperature, TI, at a fixed level above the reference cavity temperature, T3. This is achieved 

by balancing the bridge output voltage AV in Eq. (2.11). As shown in Eq. (2.15), in 

steady-state, the bridge is balanced, so that TI and T3 satisfy 

Tl=a+bT3 , (2.30) 

(2.31) 

where a and b are constants which depend on the resistance versus temperature characteristics of the temperature sensing wires wound around the active and reference cavities. 

On the other hand, the reference cavity temperature is given by 

(2.32) 

Substituting Eq. (2.32) and Eq. (2.30) into Eq. (2.29), we obtain 

25 
(2.33) 

Thus, Eq. (2.33) and Eq. (2.9) provide a nonlinear steady-state description of the 

Total channels. In this model, the independent variables other than the incoming radiance 

are the Cu heatsink temperature, T2, the reference cavity heater voltage, u,, and the box 

beam temperature, TB, which is conductively coupled to the baseplate. It should be noted 

that the thermal resistances R12 and R32 are nearly equal, and that b is close to unity. 

This thermal and electrical balancing has a tendency to reduce the effect of many terms in 

Eq. (2.33) by reducing many of the coefficients. However, exact cancellations do not occur 

since the balance is not perfect. The cancellation tendency is nevertheless beneficial, as 

the sensitivity to some parameters is reduced. 

The temperatures of the copper heatsink, 2'2, the field-of-view limiter, T6, the primary 

aperture, Ts, and the reference cavity heater voltage, ur, are measured and telemetered I 

I to Earth along with housekeeping data and the main radiometric output voltage, u. The 

remaining temperatures are not measured, but can be estimated. Due to the close conductive and radiative coupling of these nodes to the Cu heatsink whose temperature is tightly 

controlled, the temperatures of the aluminum heatsinks, and the reference and active cavities are assumed to be constant when the Cu heatsink temperature is constant. Note that 

the temperatures need not be, and in fact are not, equal; they simply are assumed to remain constant at their respective values. On the other hand, the baseplate temperature is 

only assumed to maintain a constant temperature of the field-of-view limiter. It should be 

noted that, due to the geometry and surface finish, the amount of radiation emitted from 

the baseplate which enters the cavity through the primary aperture is extremely small, as 

explained in the previous section. 

I 

I In order to simplify the expression in Eq. (2.33) and to obtain a simpler algorithm 

26 
with which to interpret, the sensor output using only the available, or meaured, data, some 

terms can be grouped together. First, recall the identity 

where Tko is the nominal node temperature and AT& is the change in the temperature, 

Tk. For a peak-to-peak temperature variation of 4 OK, and a nominal node temperature of 

300"K, if the linear term in AT& is about 2 W/m2, the error that may be introduced by 

32 = Tio + 4T,",(Tk - Tko) + 6Ti0(Tk - Tko)2 

+ 4Tk0(Tk - Tk0)3 + (Tk - TkO)l (2.34) 

I 

v2 R32 v," 

Ra 

2 dkATk + 6- - 

R12 Rr p==--- 

k= 1 

R12 

-t - 

k= 1 

-. ( QJ1 - b*QJ3)] R12 (2.36. a) 

(2.36.b) 

If all the node teinperatures, hence ATk, were known precisely, then these values 

could be used in Eq. (2,36.a) or Eq. (2.33) to compute the absorbed power. However, since 

only some of these terr.peratures are measured, it is necessary to estimate the remaining 

node temperatures. Since the heatsink temperature, 2'2, is tightly controlled about its 

set temperature, and clue to the high conductive coupling of the detector nodes, it will 

be assumed that the only temperatures directly influenced by the incoming radiation are 

27 
the FOVL and the baseplate. The FOVL and baseplate are structurally attached to, but 

thermally insulated from the detector, and are conductively coupled to the instrument 

boxbeam which tempers any variations caused by the absorption of incoming radiation. 

Although thermally insulated, some minimal conductive coupling between the detector 

and the baseplate may be present and will be accommodated. 

First consider the change in the node temperatures, ATk, due to a change in the 

reference heater voltage from zero to vo volts. From Eq. (2.32), it can be seen that 

(2.37) 

In this mode, the active cavity heater will increase the active cavity temperature until the 

bridge is balanced; from Eq. (2.31), it follows that 

ATizbAT3 , (2.38) 

where b is given by Eq. (2.31). Neglecting any temperature changes in the other detector 

nodes, and solving for AT3, 

(2.39) 

Now let TF and ATF be the FOVL temperature and the change from the nominal 

FOVL temperature, respectively; let ATk represent the total change in the kfh node temperature from the nominal, and 

where fk accounts for any correlation between ATk and ATF due to conductive or radiation 

interactions, gk accounts for changes in Tk due to u, when T2 is constant, and I?k represents 

the sensor noise and effects not explicitly modeled here, such as AQJ~. Since most of the 

I 

I 

28 
node temperatures are constant, fk and ek are negligible for most nodes. Substituting Eq. 

(2.37) into Eq. (2.36), 

(2.41) 

(2.42) 

(2.43) 

(2.44) 

Eq. (2.41), coupled with Eq. (2.9), provide a simple steady-state model, where the 

coefficients CF, cr and c, are given by Eqs. (2.42), (2.43) and (2.44). With some exceptions, 

this model still maintains most of the significant relationships among the various system 

parameters . 

From the expression for co in Eq. (2.44), it can be shown that, when the Cu heatsink 

temperature, T,, is conestant, c, will remain constant. Since the nominal temperatures 

are constant by definition, it remains to show that the Joule heating term arising from 

the current flowing in the temperature sensitive sensor wires wound around the active and 

reference cavities is also constant. From the bridge model obtained in the preceding section 

in Eq. (Z.ll), it is seen that in stead-state the bridge will be balanced at 

(2.45) 

After some manipulation, it can be shown that the Joule heating produced by the 

bridge can be expressed as 

29 
(2.46) 

(2.47) 

where the arguments of R1 and R3 have been dropped for convenience. 

The beneficial effects of thermal and electrical balancing can clearly be seen in Eq. 

(2.48). Perfect balance would imply 61 = b3, and R32 = R12, which would result in the 

complete cancellation of this term. Although perfect balancing is not likely, the term in 

brackets on the RHS of Eq. (2.48) becomes quite small, so that the effect of the term is 

considerably smaller than otherwise. Furthermore, the sensitivity of the term to variations 

I in R3 is also of second order, as this term would be of order 0((l/R3)~). As R3 is near 

2200 R, the change in the Joule heating term due to a 1 fl change in R3 would be less 

than an easily negligible 0.05 %. The sensitivity of the term to expected variations in BE, 

bl and b3 are also small, although not always negligible. 

The major sensitivity of c, is to variations in the bridge resistances and to variations 

in the boxbeam and satellite temperatures. The former effect is clearly seen from Eq. 

(2.48) and Eq. (2.31) where an extremely small variation in BE, u1, a3, bl or b3 can 

produce a noticeable change in c,. The latter effect is due to the fact that ambient satellite 

temperature may, in steady-state, produce thermal gradients in the aluminum heatsink, 

node 7, near the reference cavity. This may then change the reference cavity temperature 

by an extremely small amount, which then results in a similar change in the active cavity 

temperature. Even though the temperature variation in either cavity temperature may 

be small, the high sensitivity of the sensor to such changes requires careful consideration. 

For example, a change of 0.001" C in the active cavity may be interpreted as a change 

I 

I 

I 30 
of about 3 W/mZ in the incoming flux. Similarly, a change of 0.01 fl in the resistance of 

any of the bridge components may be interpreted as a change of 8 W/mZ in the incoming 

flux. To minimize such changes, the temperature sensing wires of the ERBE sensor were 

painstakingly processed using a heating treatment, and the heatsink temperature was 

tightly controlled about its set value. 

Equation (2.9) and Eqs. (2.41) - (2.44) provide a steady-state model which describes 

the sensor behavior under the assumptions stated. It should be noted that a variety of 

measurement conditioils can be obtained by appropriate treatment of Eq. (2.9) to obtain 

the incoming flux. This will be done in the following sections for the Earth-looking modes, 

as well as for the measurement conditions encountered in ground and flight calibrations. 

2.4.3 Shortwave Channels. 

The only significant difference between the Shortwave and Total sensors is the presence 

of the dome filter in the former sensors which filters out longwave radiation. Otherwise 

the sensors are designed to operate in the same way. Thus, most of the steady-state model 

development for the Tctal sensors is also valid for the Shortwave sensors, when the number 

of nodes, n, is replaced by the number of Shortwave sensor nodes, m, which simply includes 

the filter dome as an additional node. Since the interactions among the detector nodes 

and the electronics are the same, Eqs. (2.29) - (2.39) continue to hold. 

Now, if all the node temperatures, including the dome filter temperature, were precisely known, the power absorbed by the cavity could be computed using Eq. (2.33) or Eq. 

(2.36.a). Whereas measuring the dome temperature for use in the interpretation of the 

sensor response would be desirable, the placement of a temperature sensor in the dome filter would modify the uniformity of the filter as well as add to the manufacturing challenge. 

Thus, it is necessary to estimate the dome temperature. 

From Fig. 2.2, it can be seen that the only nodes directly influenced by incoming 

radiation are the FOVL, the baseplate, the dome filter and the primary aperture, excluding 

the active cavity whose temperature is controlled. The steady-state change in the dome 

31 
temperature due to incoming radiation can be obtained by manipulating Eq. (2.25). 

(2.49.a) 

(2.49.b) 

where it has been assumed that only the change in the FOVL and the baseplate are the 

same in steady-state, and that the nodes which do not directly see the incoming radiation 

remain unchanged. 

The effect of the reference cavity heater voltage, vr, on the dome filter temperature 

is only seen through the change in the emitted radiation from the active cavity. As for 

the Total channels, the change in the cavity temperatures due to the reference cavity 

heater voltage can be seen to be directly proportional to the added heat, hence to v:, by 

combining Eq. (2.38) and Eq. (2.39). 

The total change in the node temperatures can be expressed in the form 

where ek represents sensor noise and effects which are not explicitly modeled shown in Eq. 

(2.50). It should be noted that while this expression allows a linear relationship between 

the power absorbed by the filter, pf, and all the node temperatures for generality, in fact 

hfk ought to vanish except for k = 9; Le., the dome filter itself. Similar comments apply 

to the other coefficients. 

Substituting Eq. (2.50) into Eq. (2.36.a), 

(2.51) 

i 32 
m m 

m 

(2.53) 

(2.54) 

(2.55) 

k=l 

where TF, is the nominal FOVL temperature and the Joule heating terms aJ1 and 053 

are given by Eq. (2.46:) and Eq. (2.47), respectively. 

From Eq. (2.51), it is seen that the form of the steady-state model for the Shortwave 

and Total channels is essentially the same, when the LHS is interpreted as the power 

absorbed by the activc cavity, including the extra power emitted by the dome filter into 

the cavity. It should be noted, however, that the values of the coefficients CF, c, and c, 

are different for the two sensors. 

Since the power emitted by the FOVL and baseplate is largely longwave radiation 

which is filtered by the dome, the active cavity does not receive this radiation directly. 

However, the indirect effect of increased dome filter emission will be felt by the active 

cavity. As this is a very small effect, the dominating tendency is not clearly determined. 

The steady-state model for the Shortwave channels can thus be expressed in the form of 

Eqs. (2.51) - (2.55), Eq. (2.24) and Eq. (2.26). At this stage, the model is sufficiently general 

to accommodate the tj'pe of measurement conditions which will be normally encountered 

during the Earth-looking mode as well as the ground and flight calibration conditions. 

33 
2.5 Sensor Data Output Interpretation Algorithm 

Using the steady-state models developed, simple algorithms which can be used to 

interpret the operational data during the normal Earth-looking modes are obtained in this 

section. The specialization of the models to the ground and flight calibration conditions 

will be performed in the following sections. 

The steady-state models developed can be used to obtain power absorbed by the active 

cavity. However, the desired quantity is the flux originating within the sensor’s field-ofview and spectral band, as given in Eq. (2.1) and Eq. (2.2). The desired fluxes can be 

estimated from the absorbed power using standard approximations. 

2.5.1 Total Wavelength Channels. 

For the Total channels, the power absorbed by the active cavity is given by Eq. (2.9). 

Let RiE(z, y) be the solid angle subtended by the portion of the top of the atmosphere 

seen through the secondary aperture at the point (z,y) on the primary aperture opening. 

Note that 

This is due to the fact that, for the MFOV channels, the Earth (or the TOA) fills the 

sensor’s field-of-view completely; whereas the WFOV channels include a space ring beyond 

the TOA so that all of the TOA can be seen through the secondary aperture at every point 

of the primary aperture opening. Therefore, in the Earth-looking modes, the WFOV 

sensors’ fields-of-view are not completely filled with the TOA, as no significant signal is 

contributed by the solid angle formed by the space ring, under normal conditions, i. e., 

where the sun or the moon is not in the space ring. 

I The power absorbed by the active cavity can now be approximated as 

(2.57) 

I 34 
where 6iT is the effective absorptivity of the active cavity, F;E the standard configuration 

factor from the prim2.r~ aperture opening to the portion of the TOA %een", GiE an 

angular response factor and &iT the estimate of the radiant incidence, or flux, arriving 

from the TOA within the appropriate field-of-view. 

(2.58) 

It should be noted that the angular response factor, Gi,q,tria to account for a sensor 

response which is different than the standard cosine response using a single factor. When 

the sensor has a perfect cosine response, so that giT($, x) is unity for all directions ($, x) 

of interest, GiE reduces to the standard geometric configuration factor, and the term in 

parenthesis in Eq. (2.5'7) reduces to unity; i.e., 

when the sensor has small deviations in angular response, the average effect of these 

deviations can be accounted for by this angular response factor. When large deviations 

are present, it is necessary to include the angular response into the process of inverting 

the flux from satellite altitude to the TOA. The flux estimate obtained here is given by 

(2.61) 

Combining the steady-state sensor model in Eq. (2.41) with Eq. (2.57), and solving 

for the estimated flux, we obtain a simple algorithm of the form 

35 
(2.63) 

(2.64) 

where the subscripts denoting the channel are not explicitly shown, for convenience. 

With this simple algorithm, it is possible to estimate the desired flux when the coefficients A,, AF, A, and B are determined. While the expressions given for the coefficients 

provide an understanding of the trends and relationships among the system parameter, 

they are not intended for use in determining the actual values of these coefficients. 

The determination of the actual coefficient values for each sensor is described in the 

following section on ground calibration. In this context, calibration is the process of 

determining the values of the algorithm coefficients needed to interpret the digital sensor 

output by using measurements obtained by each sensor under well-controlled calibration 

conditions and well-established calibration sources traceable to accepted standards. 

2.5.2 Shortwave Channels. 

For the Shortwave channels, the power absorbed by the active cavity due to the 

incoming radiation can be obtained similarly as 

where AEET is due to the longwave dome heating effects. 

(2.65) 

36 
3. GROUND CALIBRATION 

This chapter describes the ground calibration sources, procedures and analysis for 

determining the count conversation coefficients for total and shortwave nonscanner sensors. 

Further, the results arle tabulated for each sensor. 

3.1 Description of Calibration Sources 

Figure 3.1 shows the ERBE calibration chamber, which is an 8 foot diameter cylinder 

containing a Master Reference Blackbody (MRBB) at one end and an Integrating Sphere 

(IS) on the other end. The Solar Simulator can project a beam through a quartz window 

onto an instrument mounted on a carousel in the middle of the chamber. The chamber 

walls, chilled with liquid nitrogen (LNz), are used as a Space Reference Source for scanner 

calibration. 

3.1.1 Master Reference Blackbody (MRBB). 

The ERBE Master Reference Blackbody (MRBB), shown in Fig. 3.2, is traceable to the 

IPTS68. The radiating surface is a concentrically grooved piece of aluminum with a black 

anodized face. Six calibrated platinum resistance thermometers (PRTs) are mounted on 

the back of the groove LO determine its temperature. The temperature stability is attained 

by placing the aluminiim in a thermally controlled housing. The instrument Fields-Ofview are completely filled by the blackbody. To simulate the energy exchange to space 

that occurs during flight operation of the instruments, the instrument is placed at the 

narrow end of the cone where a grooved ring is cooled by the liquid nitrogen. 

The absorptivity 0.- the grooved surface, measured at the Naval Ocean Systems Center, 

is found to be 0.991. The grooved surface temperature variations measured by an infrared 

radiometer appear to be less than f 0.01 K over the operating range of the MRBB (-80°C 

to 75°C). The thermal control is accurate to f 0.01 K over this temperature range. 

37 
ALBEDO PLATE 

Figure 3.1 ERBE Calibration Chamber 

38 
Figure 3.2 Cross section of Master Reference Blackbody (MRBB) 

39 
Figure 3.3 Integrating Sphere 
3.1.2 Integrating Sphere (IS). 

The Integrating Sphere, shown in Fig. 3.3, is used to calibrate the nonscanner shortwave sensors. The 23 inch diameter sphere is illuminated by four 250 watts tungsten 

lamps through projection optics system that reflects the light off a mirror and then transmits through a piece of flashed opal glass to the interior of the sphere. 

The inside wall of'the Integrating Sphere is coated first by 3M White Velvet and then 

by barium sulfate. A uniform angular radiance for the Sphere's interior coat is found within 

a few percent. Further, the silicon photodiode (SiPD) is used to measure the shortwave 

radiation. The Integra.ting Sphere is also maintained thermally stable by circulating water 

and alcohol in a pipe wound around its outside. 

3.2 Count Conversion Equations 

Following the development of sensor modeling detailed in Chapter 11, one can rewrite 

the Count Conversion Equation for Total Channel as 

(34 ET = AVI I 72 + A&(TF - TF~) + ALTH + A~TA + AkVi + Bits 

where ET = CUT~,V,TF,TF,,TH,TA and VR are known variables. Here the emissivity, 

C, is considered to be one. Sigma, u, is the Stefan-Boltzmann constant. T is the source 

temperature. The unlcnown ground coefficients like At, Ab, AL, Ah, A:, and Elics are 

determined by performing the multi-regression analysis. Note that the contributions of 

primary aperture and heat sink are found negligible due to a very small temperature 

variations. Therefore, the terms A~TH and AkTA are dropped form the above equation. 

Thus, Eq. (3.1) reduces to 

BT = ALV2 + A>(TF - TF~) + AkVi + Bits (34 

Similarly, the Comt Conversion Equation for Shortwave Channel can be rewritten 

from Eq. (2.65) as 

41 
Es = ALV2 + A~(TF - Tp0) + ALVi + Bits + (ALET) (3.3) 

This equation is very similar to the above Eq. (3.2), except for a last term, A',&-, 

which is due to the longwave dome heating effects. The unknown coefficients are determined again by performing multi-regression analysis. Silicon Photodiode (SiPD) is 

calibrated using the procedure outlined in [lo]. 

3.3 Calibration Data Background 

Calibration data for total and shortwave sensors were obtained by looking at the 

Master Reference Blackbody (MRBB) and Integrating Sphere (IS) sources described in 

the previous section. Internal Blackbody (IBB) sources are used to monitor the changes 

in the nonscanner sensors during In-Flight operation. Therefore IBB ground data is used 

as a transfer standard for total channels from MRBB to IBB. This section describes the 

important features of the data selected for determining the ground Count Conversion 

Coefficients. 

3.3.1 ERBS Calibration Data. 

Details about the calibration data sets are given in [SI. It is important to note that the 

calibration testing was interrupted by power outages and a failure in the elevation drive. 

As a result, there are three types of data sets available: (1) Pre-recovery, (2) Recovery and 

(3) Restart. Each data set is analyzed in this study. 

3.3.2 NOAA-9 Calibration Data. 

There are two types of data sets available. One is available in the preliminary calibration report and the other is documented in the final calibration report (61. Note that the 

heat sink temperature reported in the preliminary report is 38.8"C which is different from 

the final calibration report, 33.58"C. The Integrating Sphere (IS) data for Medium Fieldof-View Total (MFOVT) Channel, which is needed to calibrate the Silicon Photodiode 

(SiPD) is not available. 

42 
3.3.3 NOAA-10 Calibration Data. 

There are two calibration data sets: one is documented in (71 and the other is available 

in loose form. The important point to be mentioned is that the WFOVT channel calibrated 

in May 1983 was replaced by a new WFOVT channel calibrated in May 1984. After a 

thorough analysis, the following conclusions are drawn: 

(1) Total channels sliould be calibrated using May 1984 data sets because of the availability of May 1984 IBB data. Note that May 1983 IBB data is not reported. 

(2) Shortwave channels are calibrated using May 1983 data sets. Silicon Photodiode 

(SiPD) was calibrated by Total channels count conversion coefficients determined from 

May 1983 data sets. Note that the May 1984 Integrating Sphere (IS) data for Total 

channels is not reported. 

3.4 Ground Count Conversion Coefficients Results 

Count Conversioii Coefficients for total and shortwave channels were obtained by 

using multi-regression analysis. Table 3.1 displays the ERBS Nonscanner ground count 

conversion coefficients with the number of data points used in this analysis and standard 

deviation of error in watt/m2. Coefficients for total channels are computed using MRBB 

pre-recovery period data. Silicon Photodiodes (SiPD) are calibrated using IS data of total 

channels. Using SiPD’s gain and AEL given in Table 3.1, count conversion coefficients for 

Shortwave channels are obtained using MRBB and IS data (excluding VR = 6.77 data). 

The Shortwave channcl gains are recalibratcd using solar calibration in orbit. Note that 

the A> term of MFOk’SW is found to be positive which contradicts the theoretical value 

obtained neglecting conductive thermal transfer. 

NOAA-9 Nonscanner ground count conversion coefficients are given in Table 3.2. 

Count conversion coeflicients for MFOVT and WFOVT channels are determined using 

MRBB data from final and preliminary calibration reports respectively. Numerous runs 

were also made with thle available data and the coefficients found are not very different. As 
Table 3.1 ERBS Flight Model One (FM1) 

Ground Count Conversion Coefficients 

SYMBOLS MFOVT WFOVT 

- 58.454 

-0.03641 

2.799 

66.4883 

2984.17 

293.6555 

g = 34.4596 

AEL = 3.9127 

24 

2.95 

MFOVSW I WFOVSW 

-28.2194 

-0.02902 

-0.7097 

29.2817 

1234.19 

293.4491 

g = 21.1822 

AE, = 5.1004 

28 

1.53 

Ak 

B:cs 

PFo 

SiPD (GAIN 

k OFFSET) 

DATA POINTS 

aof ERROR 

( watt/m2) 

44 

59.2633 30.0461 

2487.64 1560.32 

292.4233 292.56 14 

17 14 

1.63 0.14 
T'able 3.2 NOAA-9 Flight Model Two (FMZ) 

Ground Count Conversion Coefficients 

.. 

SYMBOLS MFOVT WFOVT MFOVSW WFOVSW 

At -94.4978 -27.5846 - 105.3788 -30.6239 

Ale -0.03561 -0.03384 

AI, -2.2093 -0.4799 -20.2739 -6.1145 

AI, 100.18 14 29.8788 119.9772 35.506 

%s 4559.82 1609.58 4822.18 1543.95 

TFO 292.702 1 293.3871 293.4 132 

aof ERROR 0.88 7.27 4.47 

I I 1 J 

Due to the unavaihbility of MFOVT data for the integrating sphere, the MFOVSW channel 

SiPD gain and offset were not obtained by the established procedure. Details are given in the text. 

45 
we know that the calibration of Shortwave channels require the behavior of SiPD, which is 

gain (9) and offset (AEL). For MFOVSW channel, the behavior of SiPD is not known due 

to the unavailability of IS data for MFOVT channel. To resolve this problem, the SiPD 

gains of all Shortwave sensors were compared and found that the SiPD’s gain of NOAA-9 

WFOVSW was greater by 5.3% than the SiPD gain of ERBS WFOVSW. With this conclusion, the SiPD gain for MFOVSW channel was computed as g = 24.0911, which is 5.3% 

higher than the ERBS MFOVSW SiPD gain. Thus the count conversion coefficients for 

MFOVSW was computed using MRBB and IS ground data. Further, note that the AF 

term of MFOVSW is negative which is opposite to ERBS MFOVSW channel. 

Table 3.3 describes NOAA-10 Nonscanner ground count conversion coefficient results. 

MFOVT channel is calibrated using May 1984 MRBB data (excluding V, = 6.77 data). 

In addition, the count conversion coefficients for MFOVT channel using May 1983 MRBB 

data (excluding V, = 6.77 data) are not found to be very different from the coefficients 

given in Table 3.3. Similarly, the count conversion coefficients for WFOVT channel is determined. Further, the count conversion coefficients for MFOVS W and WFOVS W channels 

are obtained using May 1983 MRBB and IS calibration data. Note that the AP term for 

each channel is found to be negative, which is consistent with the NOAA-9 Nonscanner 

semors. 

I 46 
Table 3.3 NOAA-10 Proto-Flight Model (PFM) 

Ground Count Conversion Coefficients 

SYMBOLS MFOVT 

Ab -97.2831 

Aj, 

A:, -8.3056 

Ak 93.8456 

%CS 4544.25 

FFO 293.9253 

SiPD (GAIN 

&OFFSET) 

DATA POINTS 17 

aof ERROR 1.56 

(watt/m2) 

WFOVT MFOVSW WFOVSW 

-27.1754 -103.2228 - 27.6993 

-0.02232 -0.02859 

-0.5087 -13.9002 - 1.4872 

28.7406 120.1269 32.6115 

1392.75 4307.47 1264.18 

294.1156 293.5307 293.72460 

g = 32.2839' 

AEL = 4.3029 

18 15 41 

g = 34.4596 

AEL = 3.9127 

0.61 4.59 2.67 

g and AEt for WFOVSW channel were computed by using May 1983 IS data for WFOVT 

channel. 

47 
4. IN-FLIGHT CALIBRATION 

This chapter describes the in-flight calibration sources, count conversion equations, 

calibration procedures and analysis for determining the final in-flight count conversion 

coefficients for total and shortwave sensors. 

4.1 In-Flight Calibration Sources 

Figure 4.1 shows the nonscanner elevation beam positions. The nonscanner sensors 

are mounted in the elevation beam, which can be rotated to observe the Earth, the sun, or 

the internal blackbodies. Thus, the in-flight calibrations for total channels are maintained 

through the use of internal blackbody sources and space-look data during solar calibration, while shortwave channels are calibrated using solar calibration data, space-look data, 

SWICS lamps-off, and SWICS lamps-on data. Further, the dark side of the Earth data 

can be used to determine the shortwave channels offsets. 

4.2 In-Flight Count Conversion Equations 

The development of in-flight count conversion equations for total and shortwave channels are given in this section. 

4.2.1 Total Channels. 

In-flight count Conversion equations for total channels can be obtained by multiplying 

the ground count conversion equations with a configuration factor, f. Thus, the Eq. (3.1) 

becomes 

where ET = fE!,., Av = fA',, AF = fA',, AR = fAk, and BEDMT = f (Bits - A',TF,,). 

The configuration factor, f, for each sensor is given in Appendix A. Note that Av, AF, 

48 
. 

. . -. .’ --. \ .’ EARTH VIEWING 

SOLAR CALIBRATION 

INTERNAL CALIBRATION .- 

[STOW POSIT ION 1 

Figure 4.1 Nonscanner Elevation Positions 

49 
AR and BEDMT are known coefficients determined from the ground MRBB calibration 

data. These coefficients would remain unchanged except the offset term, BEDMT, which 

would be determined by utilizing in-flight calibration data. This will be discussed in the 

next sect ion. 

4.2.2 Shortwave Channels. 

Similarly, the count conversion equations for the shortwave channels can be obtained 

by multiplying Eq. (3.3) by a configuration factor, f, as follows. 

Es = AvV2 + AFTF + ARV~ + AEET + BEDMT (44 

where Av = fAb , AF = fA', , AR = fAk and BEDMT = f(B;,, - A~TF~). These 

coefficients are determined from the ground MRBB and IS data. 

Due to the use of dome for preventing the longwave radiation from getting into the 

active cavity, the determination of count conversion coefficients for shortwave channels are 

not straight forward like it is for total channels. The dome's transmissivity is decreasing, 

which may be due to ultraviolet energy in the solar spectrum. As a result, both the gain 

and offset are varying with time during in-flight operations. Methods to determine the 

gain and offset are described in the next subsection. 

4.2.3 Dome Degradation Factor. 

Dome degradation factor (DF) is required to upgrade the in-flight count conversion 

coefficients, Eq. (4.2), determined directly from the ground calibration data. This factor, 

which can be computed from the solar measurements data, is defined as 

where X is a day in question and R is a reference day. S(X) and S(R) are computed from 

an equation fitted to solar measurements data. Note that the use of such equation would 

reduce sensor noise and error in the solar measurements. Further, al, (Av/(1 - AE)) 

50 
0 

In 

rrl 

X 

d 

n 

u 

51 
+ 

% 

9 

b 

00 

0 

0 

I 

I I I I I I I I r 

X 

s rd 

7- ' 

0 

Z 

0 

n 

fl 

0 

52 
X 

s 

d 

h 

d 

53 
e 

x 

d 

0 .d .. 4 

cd 

-d 

u 

54 
c 

+ “f 

-ja 7- 

0 

si, 

c. 3 c 

X 

s 

d 

a 

0 *d 

Y 

E 

FI 

55 
I I I I 1 

0 

0 8 3 8 hl c F c 

X 

s 

d 

A 

0 

cd 

*d 

.r 

k 

4 

u 

56 
values for ERBS and NOAA-9 shortwave sensors on the first day of solar calibration are 

found to be 2-3% higher than the a1 values determined from the ground data. 

Figures 4.2 to 4.7 show the solar measurements with curve fit equation of 2nd order. 

Note that January 1, 1.984 is considered as a reference day (X=l). This equation is used 

to compute the degradation factor. Data used in Figs. 4.2 to 4.7 are given in Appendix C. 

4.2.4 AF Term of NIOAA-9 Shortwave Channels. 

In analyzing the instrument validation (IVT) tapes, a strong correlation between 

MFOVSW (night-time,) energy and FOVL temperature was found. Figure 4.7a shows 

this correlation for April 6, 1985. This procedure has been repeated for many days. In 

conclusion, the A= te1,m is changed from -4.8983 to 0.7092 to remove the effects of this 

correlation. Similar analysis was performed on the WFOVSW channel where the value of 

the AF term changed liom -5.1897 to -0.354. 

Further, such analyses were performed on the ERBS and NOAA-10 shortwave sensors, 

where no strong correlations were found. 

4.3 Total Channel Offsets 

The offset for tot,al channels can be estimated by using internal blackbody sources 

(IBB) or space-look data. It is found that IBB data is more stable than the space-look 

data. Therefore, the IBB source data is used to determine the offset in this study. The 

offset term, BEDMT, can be estimated as 

BEDMT = f (Bits - AB + BMRBB-IBB) 

where Bits is the grocnd offset given in Tables 3.1 - 3.3. AB is a change in offset obtained 

by looking at IBB source data. AB can be expressed as 

AB = €0~14~~ -E; 

57 
58 
where E and TZBB are the surface emissivity and temperature of the internal blackbody 

source. The emissivity, E, is considered to be unity. E& is the estimated energy computed 

by using ground count conversion coefficients given in Tables 3.1 - 3.3. BMRBB-IBB is a 

correction factor detailed in Appendix B. 

Figures 4.8 and 4.9 show offset variation, AB, in MFOVT and WFOVT channels 

of ERBS, respectively. One can note from these figures that there is a distinct jump in 

offset shown by a solid circle. The clear cause of this jump is not known. However, the 

temperature transients caused by a full-sun condition on the satellite may have been a real 

reason. At this point, this condition is not fully investigated and modeled. Therefore, the 

data points belonging to hot orbit conditions are excluded in determining the final AB 

term. 

Figures 4.10 and 4.11 show the changes in offset determined by using IBB data for 

NOAA-9 MFOVT and WFOVT channels, respectively. Note that the MFOVT channel 

is drifting continuously in a quadratic form. An equation to represent the IBB data for 

MFOVT channel is obtained by using the least square method. This equation is displayed 

in Fig. 4.10 and used to compute the offset for every day. On the other hand, NOAA-9 

WFOVT channel, shown in Fig. 4.11, does not depict a similar trend. Therefore, the AB 

is computed by taking an average over a small portion of data to reduce the uncertainty. 

Figures 4.12 and 4.13 represent the offset variations for NOAA-10 MFOVT and 

WFOVT channels respectively. AB of both channels seems to be fluctuating and drifting. 

Total channels’ offset tcrms for December 1986 and January 1987 are estimated by taking 

the average over small data points. Results are discussed in the next section. 

4.4 Shortwave Channel Offsets 

All nonscanner shclrtwave channels except WFOVSW of NOAA-10, observe the darkside of the Earth. Assuming zero shortwave energy during night time, the offset term, 

BEDMT, can be compt.ted by using degraded in-flight count conversion coefficients as 

59 
0 

0 

n 

--- 

?Yo ,iu 

';O 

I 1 I I c 

0 In 0 * 0 

m 

0 

cv 

0 

7 

4 

7 

7 

It 

4 

It 

LL 

7 

a 

Z 

0 

v) 

4: 

7 

7 

I 

4: 

I 

LL 

7 

a 

Z 

0 

0 

I\ 

00 

a, 

7 

a 

00 

a, 

7 

: 

m 
1 

0 

b 

0 

a 

7- 

n 

z 

0 

7- 

0 
000000000000 

000000000 00 000hCDmnmcv7 

62 
1 l 

8 0 

j: c 

0 

04 

I 

0 

rn 

I 

0 

-4- 

I 

0 

ro 

I 

0 

co 

I 

-¶ 

11 

< 

Xh 

00 

vl 

< 

-¶ 

7 

x 

< 

ace 

00 

7- 

P 

z 

0 

n- 
b, ,io 

do* 

".o 

2 

0' 

b 

6 

6 

0' 

0 

I 

t! 

? 

I 

d 

6 

I); 

I 

0 / 0' 

0'' 

I 

b 

I I I I I I I I I 

0 0 0 00 .- N m du, 

I I I I I 

00 0 0 0 *m N 7 

00 

00 

m - 

I 

A 

a* 

u 

E! 

Y 

0 

. 

64 
I 

0 0 0 0 0 

cn F c\( rr) * 

cv c\( cv cv 

I I I I I I I I 

<' 0 

0 0 0 

(b b a l-- ? F .- cv I 

4 

a 

0 

z 

0 

z 

0 

Y 

b, 

tn" 

0 

M 

: 

65 
i Each term of the right hand side of Eq. (4.3) is known. Darkside data are stripped 

from ID1 (telemetry) tapes. Sun blips data on WFOVSW are excluded in this analysis. 

Note that the data selected here is considered to be free from temperature transients, 

Le., mid-night time data. The solar zenith angle, 6,, is greater than 120 '. Tables 4.1 

and 4.2 show typical examples of April 6, 1985 darkside analysis for ERBS and NOAA-9 

nonscanner shortwave sensors respectively. Figures 4.14 and 4.15 show the variation of m 2 

watt/m2 shortwave energy for ERBS MFOVSW channel obtained from the darkside data 

analysis with degraded count conversion coefficients, for April 1985. Figure 4.16 shows the 

final offset term for ERBS MFOVSW channel obtained after subtracting the estimated 

shortwave energy given in Fig. 4.15 from the degraded in-flight offset. Similar analyses are 

performed with ERBS WFOVSW (Figs. 4.17 - 4.19) channel, which is found to be more 

stable than the ERBS MFOVSW channel. This procedure is employed to determine the 

NOAA-9 nonscanner shortwave offsets for April 1985, which are shown in Figs. 4.20 - 4.25. 

Note that NOAA-9 shortwave channels are more stable than ERBS shortwave channels. 

Further, the procedure detailed above is used to determine final in-flight shortwave offsets 

of ERBS and NOAA-9 nonscanner channels for other months discussed later. 

I 

4.4.1 NOAA-10 Shortwave Offsets Determination. 

NOAA-10 is a terminator orbital satellite which leads WFOVSW channel to only a 

few days of darkside data in a whole year. To overcome this problem, the WFOVSW offsets 

are determined using SWICS lamps-off and space-look data. However, it is appropriate 

to perform similar analyses first on ERBS and NOAA-9 shortwave channels to find a 

, 

1 

I correlation, if any exists, between darkside and SWICS lamps-off data. Figures 4.26 and 

4.27 show the differences in offset levels obtained by analyzing the SWICS lamps-off, spacelook and darkside data with the same in-flight count conversion coefficients. One can note 

I 66 
Table 4.1 XIWS Snortwave Offset Determination 

For April 6, 1985 Ueing Darkside Data Analyst 

DnmSlI @MY515 OF ID1 TM€ WIDS 

ERBE. ERBS(R11) "ER 

SHMlltYWE CMEL NIGHT LHLY ESTINYITES (ultW2)) 

TAPE BEGItNING WTE : U 6/85 TIM : 0: I: I JU.M : 2446161,51113l9672SS 

TAPE ENDING DATE : U 6/8S TINE : 23:59:28 JULlrW : 2446162.49964l598893 

COW CWJERSIN COEFFlClENlS : I2'19/8S 

NWBER OF RECS M WK2115 : 2711 

WTA WGWDCI 8 CNSTM = 1273.576736 

CMSTMS FOR WW-N aywDL 

BMSn 1295,41311 #&U = -1.39681 MRT = .1111 

MTG = -22.78731 AHIW .IO111 ACALHT = 26.11611 

AEMn = .IO101 TNHL(6) : 292.561429 lNWQ(8) = 316.841429 

BMSn = 1127.32100 AFWf = -.64821 MPERT = .10111 

KJOLTG = -25.77581 AHTW = ,81181 ACALHT = 26.74611 

AEMll = -.13174 lNMIL(6) a 293.449091 TN(rm(8) 8 

WTA W6ENENl 8 C[NSTW = 1317.533711 

HEDIUi FIELD-W-'JIEU SHORNlWE 

ORBIT RECORD RECORD WPLE MPLE NO OF NO OF 

HW STWOAEt NlNlHW WlHW WPLES RECORDS 

ONIATIM 

1 

2 

3 

0 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

-8431 

-.5286 

-. 7483 

.3622 

.3338 

-.E828 

-1,1843 

.I343 

,8403 

-.2153 

-2.2563 

-2,2350 

-,E247 

-1.8324 

.486l 

.&I 

.996 

-811 

.525 

,636 

.789 

.59s 

.952 

.87l 

,586 

I .459 

,961 

.742 

.75l 

1 ,135 

-3.4440 

-5.1741 

-I. 2237 

-6.1613 

-5.4936 

-6.1519 

-8.1456 

-5.2121 

-4.5198 

-4 * 7979 

-8.1812 

-7.4982 

-5.W14 

-6.4591 

-9.1619 

4.1347 

4.6872 

3.5751 

7.6393 

4.7131 

4.3317 

4.1823 

4.9165 

7.5193 

4.5653 

2.6958 

2.9421 

3,1537 

2.2236 

5.1782 

721 36 

92) 44 

921 46 

920 46 

920 46 

921 46 

911 45 

921 46 

921 44 

921 46 

921 44 

911 45 

921 44 

921 44 

901 45 

TMALS -.5320 1.306 -9.1619 7.6393 13541 677 

316.872273 

UI# FIELD-OFYIEU SHDM 

RECORD RECORD WlE WlE NO OF NO OF ORBIT 

t(E#( STMD HlNlHW WININ WPLES RECORDS w) 

DEUlATlM TINE 

8.2766 

7.3912 

7.6714 

7.9141 

7,8186 

7.5361 

7.6746 

7.4361 

7.3998 

7,3388 

7.2512 

7.1039 

7.4572 

7.5229 

7 I 8552 

I .I95 

,613 

1748 

1.187 

1.168 

,817 

.755 

,813 

,862 

.856 

,735 

0611 

.721 

,981 

.83a 

6.3784 

5.3256 

5.1951 

5.1221 

5.4165 

5.4159 

5.5293 

5.1116 

5.1389 

4.9754 

5.0193 

%1122 

5.4156 

5.4428 

5.4884 

18.61S3 

9.1423 

9,5348 

9.9247 

9.9871 

9.5361 

9.3235 

9.5119 

9.3411 

9.1734 

9.3774 

8.8126 

9.5494 

9.1958 

I 1 * I 381 

?21 36 

921 44 

921 46 

921 46 

921 46 

921 46 

901 45 

921 46 

92l 46 

921 44 

921 44 

911 45 

921 44 

921 46 

911 45 

61 .SO48 

61.5719 

61.6309 

61.7l63 

61.7733 

41 .8418 

41.9078 

61 .P748 

62.1422 

42. I I93 

42.1767 

62.2437 

42.3118 

62.3782 

62.4452 

7,5711 ,898 4.1754 ' 18.6153 13541 677 (RECORDS) 

67 

8EOM HFOV SU WLUE = 1118.5383 

BlMl UFUJ SU WlUE = 1309.9627 
Table 4.2 NOAA-9 Shortwave Offset Determination 

For April 6, 1985 Uehg Darkside Data Analysis 

KN511 * 10:6.280@J MOVE = -.52740 WfRT * .OW00 

AVOLIb 8 -22.SYbO AHTSNK .!IO000 ACALHT a 23.913JO 

lyHAll I IyOIvU(6l * ?92.702105 lWlb(L(81 a .000000 

MAT1 IIAYAGEIKNT B CollsTAltl * 

COMSTAIITS FUR ffW-SY CHML 

1415.430042 

SCwSTl = 1049.uouoO AfOWf * ,70920 AAPERT ,00000 

AWL16 i -25.45990 AHlSNK * .OOOUU ACALHT a 28,98700 

ClCHAl : -.Ob04 TWL16l = 293.413230 Ty)Io1LI81 a I oooooo 

RDIUH FIELD-OF-JIEY SHORTMAVE 

WIT AfCORO RECORD SARPLE SARPLE M GF it0 OT 

NAN STMDAiD MlNlHM MAllHUH SAHPLES RECDRDS 

DEVlll IO1 

I 

2 

3 

k 

5 

b 

1 

8 

9 

10 

11 

12 

13 

I4 

.690 

.440 

.36B 

I388 

* 427 

.37: 

.510 

,44? 

.:2: 

.:52 

. bil 

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from these figures that the magnitude of differences are found within f 6 watt/m2 with 

mixed signs. However, the important point to be mentioned here is that the standard error 

with SWICS lamps-off - darkside is smaller than the other cases. 

A similar analysis procedure is also performed on NOAA-10 WFOVSW channel. Table 

4.3 details the offset terms for the NOAA-10 WFOVSW channel using SWICS lamps-off 

and darkside data. It is very clear from this table that the WFOVSW offset can be 

determined using SWICS lamps-off data within 2 watt/m2. Also, note that the offset 

difference between SWICS lamps-off and space-look data is approximately 7 watt/m2. 

At this juncture, it may be appropriate to use SWICS lamps-off data to determine the 

NOAA-10 WFOVSW offset term. 

Further, the offset term for MFOVSW channel can also be determined using SWICS 

lamps-off data. Figs. 41.28 and 4.29 show the differences in offset terms for ERBS and 

NOAA-9 MFOVSW channels, respectively. Similar conclusions may be drawn as we have 

for WFOVSW channel. NOAA-10 MFOVSW channel sees the darkside of the Earth. 

Therefore one can always estimate the offset term for the MFOVSW channel from the 

Merge reports. However, the NOAA-10 MFOVSW channel offset can be determined by 

using the equation given below: 

BEDMT = B (SWICS LAMPS-OFF) - (e 12watt/m2) 

Final in-flight count conversion coefficients are given in the next section. 

4.5 Final In-Flight Count Conversion Coefficients 

This section describes the final in-flight count conversion coefficients for ERBS, NOAA9 and NOAA-10 nonscanner channels produced using the procedures detailed earlier. 

4.5.1 ERBS Nonscanner Results. 

In-flight count conversion coefficients for total channel with their corresponding offset 

numbers are given in Tables 4.4 and 4.5. Tables 4.6 and 4.7 show the in-flight count 

83 
Table 4.3 NOAA-10 WFOVSW Offsets 

CALIBRATION DAY 

December 10, 1986 

January 21, 1987 

February 4, 1987 

April 15, 1987 

June 10, 1987 

June 24, 1987 

July 22, 1987 

August 19, 1987 

September 2, 1987 

December 23, 1987 

January 20, 1988 

BEDMT 

DARKSIDE 

DATA 

- 

- 

- 

- 

1453.30 

1453.30 

1457.60 

1461.20 

- 

- 

BEDMT 

SWICS LAMPS-OFF 

DATA 

1420.02 

1427.11 

1430.81 

1441.65 

145 1.80 

1451.80 

1456.30 

1460.60 

1463.96 

1469.77 

1472.28 

BEDMT 

SPACELOOK 

DATA 

1414.24 

1418.54 

1423.63 

1433.82 

- 

- 

- 

1452.65 

1456.14 

1462.77 

1465.40 

84 
a 

II II II 

bbb 

II II II 

.. 

n 

$: 

h-) 

85 
h 

II II II 

bbb 

d II II II 7 

0 

I 

I 

I 

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I 

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86 
Table 4.4 ERBS MFOV Total In-Flight 

: 

Count Conversion Coefficients 

-22.7093 -0.923 25.1276 

APPLICABLE PERIOD 

11/01/84 - 11/30/84 

01/01/85 - 01/31/85 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

08/01/85 - 08/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

BEDMT 

1273.547 

1273.577 

1273.577 

1274.130 

1274.130 

1274.130 

1275.450 

1275.450 

1275.450 

87 
Table 4.5 ERBS WFOV Total In-Flight 

Count Conversion Coefflcients 

I -22.7873 1 -1.3968 1 26.1161 1 

1 APPLICABLE PERIOD 

11/01/84 - 11/30/84 

01/01/85 - 01/31/85 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

08/01/85 - 08/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

BEDMT 

1703.070 

1704.063 

1704.063 

1704.020 

1704.020 

1704.020 

1705.050 

1705.050 

1705.050 

88 
Table 4.6 ERBS MFOV SHORTWAVE In-Flight 

Count Conversion Coefficients 

APPLICABLE :PERIOD 

11/01/84 - 11/30/84 

01/01/85 - 01/31/85 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

08/01/85 - 08/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

AV 

-25.5337 

-25.5458 

-25.5630 

-25.5791 

-25.5843 

-25.5942 

- 25.6082 

-25.6490 

- 25.6520 

AE 

-0.0375 1 

-0.03753 

-0.03755 

-0.03758 

- 0.03 758 

-0.03760 

-0.03762 

-0.03 768 

-0.03768 

AF 

1.2227 

1.2233 

1.2241 

1.2248 

1.2251 

1.2256 

1.2262 

1.2282 

1.2283 

AR 

29.0431 

29.0570 

29.0765 

29.0948 

29.1007 

29.1120 

29.1279 

29.1744 

29.1778 

1 

89 
DATE NOV84 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

1012.954 

m.o0o 

oooo.o0o 

oooo.o0o 

1015.710 

1010.248 

10 14.967 

1013.115 

1014.760 

10 13.666 

1013.572 

101 1.629 

1010.580 

1010.010 

1007.262 

1008.794 

1010.408 

1014.129 

1015.225 

1015.357 

1012.055 

1 006.4 84 

1007.126 

1005.381 

1006.273 

1008.439 

1008.118 

1007.739 

1007.395 

1008.575 

-- 

Table 4.6 (Continued) 

ERBS MFOV Shortwave In-Flight Offsets, BEDMT 

JAN 85 

1010.674 

1012.960 

1014.819 

1014.003 

1012.919 

1011.541 

101 1.072 

1011.067 

1010.279 

101 1.750 

1012.113 

1011.877 

101 1.877 

1011.887 

1012.132 

1012.102 

1012.217 

10 12.964 

1012.597 

1011.969 

1011.810 

10 12.065 

1012.373 

1012.174 

1011.539 

1011.239 

1011.529 

101 1.443 

1010.649 

1010.795 

1010.933 

-- 

APRIL 85 

1014.669 

1016.341 

1015.056 

10 16.909 

1017.394 

1018.602 

1020.088 

1018.463 

1018.026 

1018.389 

1018.275 

1018.490 

1019.857 

1019.065 

1018.721 

1017.232 

101 7.3 70 

1018.667 

1019.814 

1020.130 

1019.083 

1016.483 

1016.146 

1016.527 

101 7.047 

1016.946 

1017.429 

1017.124 

1017.277 

1016.729 

---_- 

JULY 85 

1018.715 

1019.416 

1019.621 

1019.562 

1019.724 

1017.932 

1017.316 

1016.120 

1015.958 

1015.770 

1016.442 

1016.644 

1016.577 

1016.307 

1016.558 

1017.584 

1016.527 

1016.365 

1016.899 

1016.988 

1016.202 

1016.524 

1015.872 

10 15.150 

1015.459 

1015.810 

10 15.964 

1015.289 

10 15.800 

1016.135 

1017.722 

AUG 85 

1019.746 

1021.483 

1021.902 

102 1.779 

1020.792 

1018.769 

101 6.905 

1016.131 

1016.090 

1016.006 

1016.342 

1016.981 

1017.167 

1016.906 

1017.488 

1017.689 

1017.405 

1014.810 

1014.432 

101 1.831 

1008.237 

1001.268 

1003.013 

1005.929 

1009.120 

1012.149 

1016.676 

1018.798 

1019.052 

1018.619 

1019.084 

OCT 85 

10 19.06 1 

1018.814 

1019.177 

1019.238 

1019.875 

1019.256 

1018.490 

1018.205 

1017.859 

1017.536 

101 7.986 

1018.222 

1018.088 

1017.430 

1017.180 

1017.932 

1019.620 

1019.578 

1020.139 

1019.905 

1019.336 

1020.540 

1018.795 

1017.471 

1016.403 

1016.069 

1015.970 

1016.525 

1016.468 

1016.845 

101 7.036 

JAN 86 DEC 86 

1030.008 

1030.288 

1030.197 

1028.391 

1028.023 

1026.633 

1026.716 

1026.241 

1026.791 

1027.021 

1027.172 

1027.167 

1027.533 

1026.397 

1026.265 

1025.840 

1026.265 

1026.673 

1026.818 

1025.998 

1025.890 

1025.601 

1026.015 

1026.694 

1028.265 

1028.593 

1028.936 

1030.129 

1030.623 

1030.082 

1029.654 

1029.495 

1029.622 

1029.003 

1027.463 

1025.923 

1021.665 

102 1.427 

1023.207 

1024.885 

1025.483 

1025.279 

1025.321 

1024.391 

1022.702 

1020.854 

1023.104 

1027.556 

1030.739 

1032.437 

1032.501 

103 1.792 

1032.094 

1031.806 

1031.374 

1033.027 

1033.444 

1034.936 

1035.641 

1035.873 

1035.456 

1035.769 

JAN 87 

1036.5 18 

1036.544 

1036.880 

1036.799 

1036.397 

1036.022 

1036.146 

1035.343 

1034.831 

1034.173 

1034.127 

1034.197 

1033.206 

1033.32 1 

1034.098 

1034.223 

1033.891 

1033.814 

1034.207 

1035.025 

1034.714 

1034.975 

1035.906 

1036.457 

1036.745 

1037.520 

1037.076 

103 7.049 

1036.726 

1036.706 

1036.706 

90 
Taible 4.7 ERBS WFOV Shortwave In-Flight 

Count Conversion Coefficients 

11/01/84 - 11/30/84 

01/01/85 - 01/31/85 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

08/01/85 - 08/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

AV 

-25.5824 

-25.6867 

-25.7758 

- 25.9090 

-25.9663 

-26.0224 

-26.1480 

-26.4821 

-26.5086 

AE 

-0.03051 

-0.03064 

-0.03074 

-0.03090 

-0.03097 

-0.03104 

-0.03119 

-0.03159 

-0.03 162 

AF 

-0.6434 

-0.6460 

-0.6482 

-0.6516 

-0.6530 

-0.6544 

- 0.65 76 

-0.6660 

-0.6666 

AR 

26.5454 

26.6537 

26.7461 

26.8844 

26.9438 

27.0020 

27.1323 

27.4790 

27.5065 

91 
Table 4.7 (Continued) 

ERBS WFOV Shortwave In-Flight Offsets, BEDMT 

DATE NOV84 JAN85 APRIL85 JULY85 AUG85 OCT85 JAN86 DEC86 JAN87 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

1304.592 

oooo.o0o 

oooo.o0o 

oooo.oO0 

1303.967 

1304.012 

1303.830 

1303.737 

1303.592 

1303.336 

1303.085 

1302.592 

1302.952 

1302.715 

1302.503 

1302.182 

1302.025 

1302.031 

1302.266 

1302.5 18 

1302.393 

1301.998 

1301.595 

1301.380 

1301.326 

130 1.830 

130 1.94 1 

1302.078 

1302.208 

1302.196 

1305.4 10 

1306.28 1 

1306.863 

1306.778 

1306.558 

1305.943 

1305.729 

1305.765 

1305.815 

1305.931 

1306.079 

1306.184 

1306.345 

1306.486 

1306.604 

1306.476 

1306.378 

1306.277 

1306.332 

1306.157 

1305.978 

1305.638 

1305.720 

1305.559 

1305.446 

1305.071 

1305.006 

1304.838 

1304.969 

1305.019 

1305.244 

13 11.386 

1311.064 

1310.654 

1310.489 

13 10.196 

1 309.94 3 

1309.733 

1309.599 

1 309.4 8 6 

1309.319 

1309.129 

1308.900 

1308.745 

1308.405 

1308.297 

1308.46 1 

1308.8 12 

1309.39 1 

1309.924 

1310.079 

1309.968 

1309.165 

1308.830 

1309.006 

1309.252 

1309.4 56 

1309.601 

1309.832 

1309.880 

1309.920 

1316.677 

13 17.OOO 

13 17.136 

1317.259 

1316.939 

1316.818 

1316.047 

1315.959 

13 15.932 

1315.964 

1316.333 

13 16.409 

13 16.440 

13 16.48 1 

1316.539 

1316.681 

1316.740 

13 16.748 

1316.735 

13 16.624 

1316.475 

1316.254 

13 16.060 

1315.835 

1315.883 

13 15.648 

1315.411 

1315.276 

1315.276 

1315.731 

1316.258 

13 19.660 

1320.111 

1320.300 

1320.150 

1320.029 

1319.733 

1318.684 

1318.131 

1317.955 

1318.023 

1318.184 

1318.431 

1318.617 

1318.833 

1318.953 

1319.068 

1319.332 

1319.412 

1319.450 

1319.430 

1319.439 

1319.439 

1319.439 

1319.439 

1319.439 

1319.439 

1319.439 

1318.879 

1318.755 

1318.783 

1318.568 

1323.42 1 

1323.458 

1322.920 

1322.595 

1322.168 

1322.028 

132 1.948 

132 1.68 1 

1321.371 

132 1.28 7 

1320.978 

1320.776 

1320.59 1 

1320.815 

132 1.170 

1322.047 

1322.435 

1323.161 

1322.890 

1322.968 

1323.116 

1322.593 

1322.022 

1321.904 

1321.475 

1321.249 

1321.641 

1321.832 

1321.932 

1322.240 

mi.22a 

1330.460 

1330.417 

1330.477 

1330.554 

1330.428 

1329.713 

1329.405 

1329.171 

1329.066 

1329.055 

1329.153 

1329.186 

1329.446 

1329.42 1 

1329.645 

1329.698 

1329.594 

1329.576 

1329.249 

1329.072 

1328.941 

1328.710 

1328.702 

1328.881 

1329.149 

1329.251 

1329.559 

1330.097 

1330.168 

1330.069 

1330.163 

1347.622 

1347.903 

1348.473 

1348.516 

1348.516 

1348.516 

1348.516 

1348.516 

1348.516 

1348.516 

1348.516 

1348.5 16 

1348.516 

1348.516 

1348.516 

1348.516 

1348.516 

1348.279 

1348.318 

1348.051 

1347.929 

1347.616 

1347.611 

1347.636 

1348.316 

1348.695 

1349.031 

1349.1 64 

1349.226 

1349.130 

1349.352 

1351.197 

135 1.076 

1351.131 

1351.272 

1351.094 

1351.152 

1351.214 

1350.727 

1350.725 

1350.659 

1350.474 

1350.312 

1350.3 13 

1350.397 

1350.399 

1350.365 

1350.286 

1350.083 

1350.123 

1350.300 

1350.25 1 

1350.568 

1350.454 

1350.803 

1350.885 

1350.74 7 

1350.692 

1350.718 

1350.715 

1350.922 

1 3 50.7 2 7 
conversion coefficients respectively. Offsets for shortwave channels are determined using 

the darkside data. 

4.5.2 NOAA-9 Nomicanner Results. 

In-flight count conversion coefficients for MFOVT channel are given in Table 4.8. This 

channel is found to be drifting in quadratic equation form. Therefore, the offset, BEDMT, 

is determined for every day. However, WFOVT channel, displayed in Table 4.9, seem 

very constant over the month period. 

Further, in-flight count conversion coefficients for MFOV and WFOV shortwave channels are tabulated in Tables 4.10 and 4.11, respectively. The dome’s transmissivity of the 

WFOVS W channel has decreased approximately 2% in one year while, the MFOVS W channel has not degraded significantly. Offset terms of the shortwave channel are determined 

for everyday using the darkside data. 

4.5.3 NOAA-10 Noriscanner Results. 

Tables 4.12 and 4.1.3 display the in-flight count conversion coefficients for MFOVT and 

WFOVT channels, res.pectively. These coefficients will remain unchanged except for the 

offset term BEDMT. T:ie offset terms are determined using the in-flight internal calibration 

blackbody (IBB) data. 

Further, Tables 4.14 and 4.15 detail the in-flight count conversion coefficients for 

the shortwave channels. These coefficients vary depending on the dome’s transmissivity 

determined from the scllar measurements data. Note that the change in the dome’s transmissivity for the MFOVSW channel is negligible in comparison to the WFOVSW channel, 

which has degraded almost 4.5% in one year. 

The MFOVSW offset term is determined by analyzing darkside data, while the WFOVSW’s 

offset term is computed using SWICS lamps-off data. The offset term for MFOVSW for 

December 1986 is the average of two darkside data points, i.e., December 10, 1986 and 

December 24, 1986. 1%; is important to note that there is no darkside observed by the 

93 
Table 4.8 NOAA-9 MFOV Total In-Flight 

Count Conversion Coefficients 

NOAA-9 MFOV Total Channel In-Flight Offsets, BEDMT 

DATE APRIL 85 JULY 85 OCT 85 JAN 86 DEC 86 JAN 87 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

1211.54 

1211.36 

1211.18 

1211.01 

1210.83 

1210.65 

1210.48 

1210.30 

1210.13 

1209.95 

1209.77 

1209.60 

1209.42 

1209.25 

1209.07 

1208.90 

1208.72 

1208.55 

1208.3 7 

1208.20 

1208.02 

1207.85 

1207.67 

1207.50 

1207.32 

1207.15 

1206.97 

1206.80 

1206.63 

1206.45 

1195.89 

1195.72 

1195.55 

1195.38 

1195.22 

1195.05 

1194.89 

1194.72 

1194.55 

1194.43 

1194.22 

1194.05 

1193.89 

1193.72 

1193.56 

1193.39 

1193.23 

1193.06 

1192.90 

1192.73 

1192.57 

1192.40 

1192.24 

1192.07 

1191.91 

1191.74 

1191.58 

1191.4 1 

1191.25 

1191.09 

1190.92 

1180.98 

1180.82 

1180.66 

1180.5 1 

1180.35 

1180.19 

1180.04 

11 79.88 

1179.72 

1179.57 

1179.41 

1179.25 

1179.10 

1178.94 

1178.79 

1178.63 

1178.48 

1178.32 

1178.17 

1178.01 

1177.86 

1177.70 

1177.55 

1177.39 

1177.24 

117i.08 

1176.93 

1176.77 

1176.62 

1176.47 

1176.31 

1166.99 

1166.84 

1166.69 

1166.55 

1166.40 

1166.25 

1166.11 

1165.96 

1165.81 

1165.67 

1165.52 

1165.37 

1165.23 

1165.08 

1164.94 

1164.79 

1164.65 

1164.50 

1164.36 

1164.21 

1164.07 

1163.92 

1163.78 

1163.63 

1163.49 

1163.34 

1163.20 

1163.05 

1162.91 

1162.77 

1162.62 

1123.93 

1123.82 

1123.71 

1123.60 

1123.48 

1123.37 

1123.26 

1123.15 

1123.04 

1122.93 

1122.82 

1122.71 

1122.61 

1122.50 

1122.39 

1122.28 

1122.17 

1122.06 

1121.95 

1121.84 

1121.73 

1 12 1.62 

1121.52 

1121.41 

1121.30 

1121.19 

1121.08 

1120.98 

1120.87 

1120.76 

1120.65 

1120.55 

1120.44 

1120.33 

1120.22 

1120.12 

1120.01 

11 19.90 

11 19.80 

1119.69 

1119.58 

1119.48 

1119.37 

1119.26 

1119.16 

1119.05 

1118.95 

11 18.84 

11 18.73 

1118.63 

1118.52 

1118.42 

1118.31 

1118.21 

11 18.10 

11 18.00 

1117.89 

1117.79 

1117.68 

1117.58 

1117.48 

11 17.37 
Table 4.9 NOAA-9 WFOV Total In-Flight 

Count Conversion Coefficients 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

t-i-+"i -22.8621 -0.3977 24.7635 

1475.43 

14 75.97 

1477.63 

1479.35 

1482.41 

1482.41 

APPLICABLE PERIOD I BEDMT 

95 
Table 4.10 NOAA-9 MFOV Shortwave In-Flight 

Count Conversion Coefficients 

AF 

0.7092 

0.7096 

0.7100 

0.7104 

0.7118 

0.7119 

AR 

28.9870 

29.0027 

29.0186 

29.0344 

29.0911 

29.0963 

APPLICABLE PERIOD AV 

04/01/85 - 04/30/85 -25.4599 

07/01/85 - 07/31/85 -25.4737 

10/01/85 - 10/31/85 -25.4877 

01/01/86 - 01/31/86 -25.5015 

12/01/86 - 12/31/86 -25.5513 

01/01/87 - 01/31/87 -25.5559 i 

. 

AE 

-0.03604 

-0.03606 

-0.03608 

-0.03610 

-0.03617 

-0.03618 

I 96 
Table 4.10 (Continued) NOAA-9 MFOV Shortwave In-Flight Offsets, BEDMT 

DATE APRIL 85 JULY 85 OCT 85 JAN 86 DEC 86 JAN 87 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

841 .i'03 

841.578 

841.985 

84O.i'02 

840.i.63 

840. i'4 2 

840.845 

840.972 

840.907 

840.2128 

840.951 

84O.f;88 

841.1 47 

841.1 73 

84 1 SI92 

84 1.01 3 

840.063 

841 .(I63 

841.078 

841.1 43 

841.195 

841.1 79 

841.1 60 

841.338 

841.1 55 

841.1 46 

841.1 79 

841.2106 

84 1.2170 

841.2056 

842.784 

842.788 

842.598 

842.740 

842.768 

842.729 

842.805 

842.739 

842.857 

842.333 

840.883 

840.94 1 

840.970 

841.135 

841.038 

841.055 

84 1.104 

84 1.14 1 

841.177 

841.260 

841.338 

841.337 

841.405 

843.234 

845.545 

845.501 

845.540 

845.507 

84 5.590 

845.456 

845.366 

846.971 

847.855 

846.868 

846.797 

846.728 

846.812 

846.880 

846.698 

846.857 

847.356 

846.964 

846.914 

847.124 

847.089 

847.076 

847.309 

845.880 

846.040 

845.963 

846.066 

846.179 

846.168 

846.228 

846.276 

846.209 

846.353 

846.330 

846.307 

846.803 

847.298 

846.279 

847.169 

847.273 

847.408 

847.371 

847.440 

847.407 

847.432 

847.430 

847.433 

847.611 

847.690 

847.684 

847.696 

847.738 

847.797 

847.852 

847.878 

847.888 

847.848 

847.901 

847.921 

848.402 

847.873 

847.913 

847.845 

847.911 

847.682 

847.609 

847.616 

847.575 

847.555 

852.443 

852.482 

852.529 

852.505 

852.564 

852.574 

852.578 

852.623 

852.468 

853.021 

852.929 

852.909 

852.902 

853.000 

853.028 

852.995 

852.996 

853.082 

853.069 

853.024 

853.104 

853.107 

853.097 

853.276 

852.787 

852.792 

852.850 

852.862 

852.837 

852.916 

852.883 

853.044 

853.051 

853.223 

853.114 

853.109 

853.116 

853.116 

853.116 

853.116 

853.1 16 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

852.925 

853.347 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 

853.116 
Table 4.11 NOAA-9 WFOV Shortwave In-Flight 

Count Conversion Coefficients 

APPLICABLE PERIOD AV AE 

04/01/85 - 04/30/85 

07/01/85 - 07/31/85 

10/01/85 - 10/31/85 

01/01/86 - 01/31/86 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

AF 

-0.3540 

-0.3562 

-0.3583 

-0.3603 

-0.3664 

-0.3668 

AR 

30.1311 

30.3192 

30.4989 

30.6680 

31.1862 

31.2263 

-25.9880 

-26.1503 

-26.3053 

-26.4511 

-26.8980 

-26.9326 

98 

-0.03465 

-0.03487 

-0.03507 

-0.03527 

-0.03586 

-0.03591 
Table 4.11 NOAA-9 (Continued) WFOV Shortwave In-Flight Offsets, BEDMT 

DATE APRIL 85 JULY 85 OCT 85 JAN 86 DEC 86 JAN 87 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

1359.474 

1359.412 

1359.929 

1359.8 66 

1359.729 

1359.764 

1359.952 

1359.754 

1359.744 

1359.6 78 

1359.561 

1359.445 

1359.656 

1359.555 

1359.589 

1359.577 

1359.644 

1359.411 

1359.446 

1359.563 

1359.642 

1359.4 18 

1359.565 

1359.500 

1359.571 

1359.906 

1360.047 

1360.003 

1359.971 

1359.853 

1367.569 

1367.608 

1367.732 

1367.705 

1367.684 

1367.674 

1367.619 

1367.678 

1367.559 

1366.908 

1366.032 

1366.063 

1366.182 

1366.337 

1366.178 

1366.129 

1366.102 

1366.091 

1366.080 

1366.208 

1365.966 

1366.132 

1366.245 

1367.928 

1370.306 

1370.318 

1370.283 

1370.278 

1370.490 

1370.48 1 

1370.577 

1377.714 

1378.496 

1378.206 

1378.113 

1378.366 

1378.440 

13 78.380 

1378.797 

1378.278 

1378.513 

1378.397 

1378.503 

1378.467 

13 78.383 

13 78.543 

1377.78 1 

1375.950 

1375.896 

1375.849 

1375.897 

1375.726 

13 76.032 

1375.848 

13 75.926 

1375.951 

1376.059 

1376.133 

1376.207 

1376.519 

1376.830 

1376.145 

1384.154 

1383.89 1 

1384.099 

1384.285 

1384.401 

1384.290 

1384.293 

1384.203 

1384.347 

1384.555 

1384.380 

1384.26 1 

1384.332 

1384.426 

1384.550 

1384.658 

1384.565 

1384.537 

1384.395 

1384.415 

1384.555 

1384.866 

1384.443 

1384.338 

1384.342 

1384.407 

1384.411 

1384.347 

1384.337 

1384.470 

1384.494 

1411.863 

141 1.955 

14 1 1 -962 

1412.124 

14 12.117 

1412.049 

1412.140 

1412.212 

1412.558 

14 12.992 

1412.910 

1412.938 

1412.999 

1413.079 

1413.133 

14 13.284 

14 13.169 

14 13.603 

1413.362 

14 13.250 

1413.212 

14 13.336 

14 13.429 

14 13.526 

14 12.976 

14 12.875 

14 12.89 1 

14 12.967 

14 12.842 

14 12.842 

14 12.850 

1414.768 

14 14.838 

14 14.842 

1414.845 

14 14.856 

14 14.946 

1414.946 

14 14.946 

14 14.946 

14 14.946 

14 14.946 

1414.946 

1414.946 

14 14.946 

1414.946 

1414.946 

14 14.946 

1414.946 

1414.946 

1415.093 

14 15.378 

14 14.946 

1 4 1 4.946 

1414.946 

1414.946 

1414.946 

14 14.946 

14 14.946 

1414.946 

14 14.946 

1414.946 

99 
Table 4.12 NOAA-10 MFOV Total In-Flight 

Count Conversion Coemcients 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

I 1 I 1 

1668.74 

1669.70 

* -23.22 15 - 1.9825 22.4009 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

I APPLICABLEPERIOD I BEDMT I 

1432.85 

1432.85 

Table 4.13 NOAA-10 WFOV Total In-Flight 

Count Conversion Coefficients 

1-22.5230 1 -0.4216 1 23.8202 1 

1 APPLICABLEPERIOD 1 BEDMT 1 

100 
Table 4.14 NOAA-10 MFOV Shortwave In-Flight 

Count Conversion Coefficients 

-24.3501 

-24.4643 

1 APPLICABLE PERIOD 

-0.03032 -1.3074 28.6683 1417.18 

-0.03047 -1.3135 28.8028 1422.56 

12/01/86 - 12/31/86 

01/01/87 - 01/31/87 

Table 4.15 NOAA-10 WFOV Shortwave In-Flight 

Count Conversion Coefficients 

12/01/86 - 12/.31/86 

01/01/87 - 01/431/87 
WFOVS W channel during December 1986 and January 1987. 

. 
REFERENCES 

1. Barkstrom B. R. and J. B. Hall, Jr., "Earth Radiation Budget Experiment (ERBE): 

An Overview," J. Energy, Vol. 6, pp. 141-146, 1982, 

2. Barkstrom, B. R., "The Earth Radiation Budget Experiment (ERBE)," Bulletin of 

the American Meteorological Society, Vol. 65, pp. 1170-1185, 1984. 

3. Carman, S. I., "E:RBE Nonscanner Instrument Operations Manual," No. D04608A, 

September 8, 1982. 

4. Lee, R. B., III, B. R. Barkstrom and R. D. Cess, "Characteristics of the Earth Radiation Budget Experiment Solar Monitors," App. Opt., Vol. 26, pp. 3090-3096, 1987. 

5. Castineiras, A., "Final Calibration Report on ERBE Flight Model One Nonscanner 

Instrument," No. 1106904, August 15, 1984. 

6. Castineiras, A., "F'inal Calibration Report on ERBE Flight Model Two Nonscanner 

Instrument," No. 1106906, October 19, 1984. 

7. Castineiras, A., "Final Calibration Report on ERBE Protoflight Model Nonscanner 

Instrument," No. 1106908, December 20, 1984. 

8. Halyo, N., S. H. Choi, D. A. Chrisman, Jr. and R. W. Samms, "Development of 

Response Models for the Earth Radiation Budget Experiment (ERBE) Sensors: Part 

I - Dynamic Models and Computer Simulations for the ERBE Nonscanner, Scanner 

and Solar Monitor Sensors," NASA CR-178292, March 20, 1987. 

9. Halyo, N. and S. H. Choi, "Development of Response Models for the Earth Radiation 

Budget Experiment (ERBE) Sensors: Part IV - Preliminary Nonscanner Models and 

Count Conversion Algorithms," NASA CR-178295, March 20, 1987. 

10. Halyo, N. and D. €1. Taylor, "Explicit Solution of the Spectral Radiance in Integrating Spheres with Application to the Earth Radiation Budget Experiment Ground 

Calibration," J. Opt. SOC. Am. A, Vol. 5, pp. 520-534, 1988. 

103 
APPENDIX A 

Configuration Fact or 

The configuration factor, f, is required by Eq. (4.1) to obtain the in-flight count 

conversion coefficients. This factor depends on the geometry of the field-of-view limiter 

(FOVL) and the primary aperture. With known radius of FOVL and primary aperture, 

one can compute f using the well known equation given below. 

where 

1+RT z=1+ 

R22 

r1 and r2 are radius and h is the gap between two discs as shown in Fig. A.l. 

i 

Primary Aperture FT 0 h 

FOVL pJl 

0 . Figure A.l Representation of Configuration 

104 
Table A.1 displays the configuration factor, f for each nonscanner sensor used in 

this work. ERBS nomcanner configuration factors are found in agreement with TRW’s 

results reported in [5], except for the WFOVT channel. The configuration factor for ERBS 

WFOVT channel is computed by taking non-cosine response function into account. The 

configuration factors for NOAA-9 and NOAA-10 for nonscanner sensors, given in Table A.l 

are computed using the design data given in [3]. Note that the present results are not in 

agreement with TRW’s configuration factors reported in [6] - [7). The author has not been 

able to locate the data, points used by TRW for NOAA-9 and NOAA-10. Furthermore, 

the configuration factors for NOAA-9 and NOAA-10 given in Table A.l, were reproduced 

by several independent investigators. 

- 

SE:NSORS ERBS NOAA-9 

Table A.l Configuration Factors 

NOAA-10 

MFOVT 

WFOVT 

MF OVS W 

WF‘OVS W 

- 1 

I I I I 

0.4240 0.2387 0.2387 

0.8692 0.8288 0.8288 

0.4240 0.2387 0.2387 

0.8797 0.8288 0.8288 

105 
APPENDIX B 

BMRBB- IBB Correction Factor 

SENSORS 

MFOVT 

WFOVT 

This factor is required to determine the final in-flight offset term, BEDMT, for total 

channels. This factor is based on the assumption that the count conversion coefficients 

may have drifted. To determine a correct offset term for the in-flight IBB source, a 

BMRBB-IBB factor was determined using the ground IBB data with ground count conversion coefficients based on MRBB data. Table B.l displays the BMRBB-IBB correction 

factor for each nonscanner sensor. Note that the correction factor for NOAA-9 MFOVT 

channel is determined after performing error budget analysis and scanner-nonscanner intercomparisons (a technique developed by the inversion group) at satellite altitude. Also 

note that the correction factor for NOAA-10 WFOVT is negative. At this point the actual 

cause of this negative value is unknown, but it is worth mentioning that the NOAA-10 

WFOVT channel was replaced by another WFOVT channel prior to launch. In the future 

more scanner-nonscanner intercomparisons at satellite altitude may answer such questions. 

ERBS NOAA-9 NOAA-10 

5.010 20.444 11.664 

5.187 4.796 -4.349 

Table B.l BMRBB-IBB Correction Factors 
APPENDIX C 

Solar Calibration Data 

Solar calibration data are used to determine the degradation factor, DF which is 

required to upgrade the in-flight count conversion coefficients for shortwave channels. Data 

for ERBS, NOAA-9 and NOAA-10 Shortwave sensors are given below. 

107 
I 108 

Table C.1 ERBS MFOVSW Solar Calibration Data 

CALIBRATION SOLAR 

SAMPLE DATE X(DAY) MEASUREMENTS 

1 

2 

3 

4 

5 

6 

7 

9 

10 

11 

12 

13 

14 

15 

10 

17 

19 

20 

21 

22 

23 

24 

25 

26 

27 

29 

30 

31 

32 

33 

34 

35 

30 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

80 

61 

a 

ia 

2a 

io/25/a4 

iop6fa4 

1 i/oi/a4 

1 i/os/ar 

i I/ 12/61 

1 i/mfa4 

ii/zs/ar 

iz/os/ar 

121 lo/ar 

i2/17/a4 

iz/za/ar 

oi/23/a5 

oyoefas 

02/m/a5 

cu/os/as 

04/17/85 

05/01/85 

05/29/85 

oe/a~/as 

oa/o7/a5 

os/2i/as 

os/or/as 

091iaia5 

10/29/84 

03/06 f 85 

03/20/85 

05/08/85 

071 10 f 85 

07/21 f 85 

10/02/85 

101 16/85 

10/31/85 

11/13/85 

ii/27/a5 

n/ia/a5 

iz/zs/as 

oi/n/a6 

02/05/a6 

01/07/86 

03/05/86 

031 19/86 

04/02/86 

04/16/80 

04/30/86 

05/14/86 

0 5 12 8 18 6 

06/04/86 

061 19/86 

06/25/86 

07/09/86 

07/23/86 

09/03/80 

09/17/86 

10/15/86 

10/29/86 

11/12/80 

11/26/86 

12/24/86 

01/07/87 

oelnlas 

io/oi/as 

299. 

300. 

303. 

306. 

310. 

317. 

325. 

331. 

345. 

352. 

363. 

389. 

403. 

417. 

431. 

445. 

459. 

473. 

487. 

494. 

515. 

543. 

557. 

571. 

599. 

013. 

627. 

641. 

655. 

070. 

683. 

097. 

725. 

738. 

753. 

767. 

795. 

809. 

823. 

837. 

851. 

865. 

879. 

880. 

901. 

907. 

921. 

935. 

980. 

977. 

991. 

1005. 

1019. 

1033. 

1047. 

1061. 

1089. 

1103. 

338. 

585. 

718. 

1363.8oooO 

1362.5oooO 

1304.80000 

1363.50000 

1364.I)0000 

1365.00000 

1304.7oooO 

1363.2oooO 

1365.80000 

1304.00000 

1364.4oooO 

1304.30000 

1361.7oooO 

1304.30000 

1363.20000 

1304.60000 

1361.60000 

1363.2oooO 

1362.60000 

1363.1oooO 

1360.4oooO 

1361.80000 

1362.1oooO 

1361.80000 

1362.1oooO 

1302.80000 

1302.90000 

1359.50000 

1380.80000 

1360.50000 

1361.00000 

1360.4ooOO 

1360.40000 

1359.00000 

1359.90000 

1361.4oooO 

1360.7oooO 

1359.4oooO 

1359.50000 

1362.3oooO 

136 1.2ooOO 

1360.80000 

1380.7oooO 

1359.30000 

1358.7oooO 

1359.50000 

1358.50000 

1359.30000 

1359.90000 

1358.80000 

1359.7oooO 

1358.90000 

1357.30000 

1358.90000 

1358.50000 

1359.80000 

1359.50000 

1358.00000 

1355.7oooO 

1358.90000 

i35a.m 
1 

. 

~~ 

'Ihblet C.2 ERBS WFOVSW Solar Calibration Data 

- 

CALIBRATION SOLAR 

SAMPLE DATE X(DAY) MEASUREMENTS 

I_ 

1 

2 

3 

4 

5 

0 

7 

8 

9 

10 

11 

12 

13 

14 

15 

10 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

80 

61 

10/25/84 

10/26/84 

10/29/84 

11/01/84 

11/05/84 

11/12/84 

11/20/84 

11/28/84 

12/03/84 

12/10/84 

12/17/84 

12/28/84 

01/23/85 

02/06/85 

02/20/85 

03/06/85 

03/20/85 

04/03/85 

041 17/85 

05/01/85 

05/08/85 

05/29/85 

06/26 f 85 

071 10185 

08/07/05 

0812 1/85 

09/04/85 

09/18/85 

lO/O2/85 

lOll6f85 

10/31/85 

11/13/85 

11/27/85 

12/18 f85 

12/25/85 

01/07/80 

01/22/88 

02/05/86 

03/05/86 

03/19/80 

04/02/80 

041 16/86 

04/30/86 

05/14/80 

05/28/80 

06/04/86 

061 19 f 86 

06/25/86 

07/09/86 

07/23/88 

08/17/86 

09/03/88 

09/17/80 

1010 1/86 

10/15/80 

10/29/86 

11/12/86 

11/28/86 

12/24/86 

01/01/81 

07/24/85 

299. 

300. 

303. 

308. 

310. 

317. 

325. 

331. 

338. 

345. 

352. 

363. 

389. 

403. 

417. 

431. 

445. 

459. 

473. 

487. 

494. 

515. 

543. 

557. 

571. 

585. 

599. 

613. 

627. 

641. 

855. 

670. 

683. 

697. 

718. 

725. 

738. 

753. 

767. 

795. 

809. 

823. 

837. 

851. 

865. 

879. 

886. 

901. 

907 * 

921. 

935. 

980. 

977. 

991. 

1005. 

1019. 

1033. 

1047. 

1061. 

1103. 

1089. 

1364.30000 

1363.2oooO 

1363.20000 

1362.80000 

1362.20000 

1362.30000 

1361.7oooO 

1359.30000 

1358.90000 

1357.50000 

1356.2oooO 

1356.80000 

1355.20000 

1354.20000 

1351.40000 

1351.80000 

1352.1oooO 

1349.4oooO 

1350.40000 

1349.00000 

1347.90000 

1348.20000 

1345.7oooO 

1344.7oooO 

1344.50000 

1344.80000 

1343.60000 

1339.10000 

1340.2oooO 

1338.00000 

1338.4oooO 

1337.00000 

1338.30000 

1335.20000 

1333.20000 

1334.00000 

1332.80000 

1332.10000 

1331.90000 

1330.2oooO 

1331.3oooO 

1327.3oooO 

1329.8oooO 

1327.7oooO 

1326.7oooO 

1327.90000 

1326.80000 

1325.90000 

1320.2oooO 

1323.00000 

1323.4oooO 

1323.30000 

1321.40000 

1320.2oooO 

1320.00000 

1318.1oooO 

1319.7oooO 

1318.90000 

13 16.90000 

1314.4oooO 

1316.00000 

109 
Table C.3 NOAA-9 MFOVSW Solar Calibration Data 

CALIBRATION SOLAR 

SAMPLE DATE X(DAY) MEASUREMENTS 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

01/23/85 

01/25/85 

01/27/85 

01/30/85 

02/06/85 

02/13/85 

02/20/85 

03/06/85 

03/20/85 

04/03/85 

04/17/85 

05/08/85 

05/29/85 

06/12/85 

06/26/85 

07/10/85 

07/24/85 

08/07/85 

0812 1/85 

09/18/85 

10/02/85 

10/ 16/65 

10/30/85 

111 13/85 

11/27/85 

121 11/85 

01/22/86 

02/05/86 

021 19/86 

03/05/86 

031 19/86 

04/02/86 

04/30/86 

051 14/86 

05/28/86 

061 11/86 

07/09/86 

07/23/86 

08/06/86 

08/20/86 

09/03/86 

091 17/86 

101 15/86 

10/29/86 

111 12/86 

11/26/86 

01/21/87 

09/04/85 

389. 

391. 

393. 

396. 

403. 

410. 

417. 

431. 

445. 

459. 

473. 

494. 

515. 

529. 

543. 

557. 

571. 

585. 

599. 

613. 

627. 

641. 

655. 

669. 

683. 

697. 

711. 

753. 

767. 

781. 

795. 

809. 

823. 

851. 

865. 

879. 

893. 

921. 

935. 

949. 

963. 

977. 

991. 

1019. 

1033. 

1047. 

1061. 

1117. 

1363.2oooO 

1365.60000 

1362.8oooO 

1362.40000 

1365.60000 

1365.80000 

1365.40000 

1365.40000 

1364.50000 

1364 .90000 

1364.70000 

1362.50000 

1365.20000 

136 1.10000 

1363 .WOO 

1362.20000 

1364.50000 

1362.40000 

1362.80000 

1362.10000 

1364 .00000 

1364.00000 

1362.50000 

1360.70000 

1362 .00000 

1361.50OOO 

1362.00000 

1362.10000 

1360.70000 

1360.5oooO 

136 1.90000 

136 1.20000 

1361.70000 

1362.70000 

1360.30000 

1361.90000 

136 1.60000 

1360.10000 

1361.10000 

1359.00000 

1360.40000 

1360.50000 

1359.50000 

1359.50000 

1358.90000 

1358.7oooO 

1359.80000 

1359.40000 

I 110 
Table C.4 NOAA-9 WFOVSW Solar Calibration Data 

CALIBRATION SOLAR 

SAMPLE DATE X(DAY) MEASUREMENTS ____ -- 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

le1 

17' 

It1 

11, 

20 

2 I. 

2;1 

2<6 

24 

25 

21i 

2:' 

2t1 

2!) 

30 

3 :l 

32 

33 

34 

35 

3I3 

3'7 

323 

3'3 

41) 

41 

42 

43 

44 

45 

46 

47 

48 

.I 

01/23/85 

01/25/85 

01/27/85 

01/30/85 

02/06/85 

02/13/85 

02/20/85 

03/06/85 

03/20/85 

04/03/85 

04/17/85 

05/08/85 

05/29/85 

06/12/85 

06/26/85 

07/10/85 

07/24/85 

08/07/85 

08/21/85 

09/04/85 

091 1818 5 

10/02/85 

10/16/65 

10/30/85 

11/13/85 

11/27/85 

12/11/85 

01/22/86 

02/05/86 

021 19/86 

03/05/86 

03/19/86 

04/02/86 

04/30/86 

05/14/86 

05/28/86 

0611 1/86 

07/09/86 

07/23/86 

08/06/86 

08/20/86 

09/03/86 

09/17/86 

10/15/86 

10/29/86 

11/12/86 

11/26/86 

01/21/87 

389. 

391. 

393. 

396. 

403. 

410. 

417. 

431. 

445. 

459. 

473. 

494. 

515. 

529. 

543. 

557. 

571. 

585. 

599. 

613. 

627. 

641. 

655. 

669. 

683. 

697. 

711. 

753. 

767. 

781. 

795. 

809. 

823. 

851. 

865. 

879. 

893. 

921. 

935. 

949. 

963. 

977. 

991. 

1019. 

1033. 

1047. 

1061. 

1117. 

1364.20000 

1366.10000 

1363.80000 

1362.60000 

1363.20000 

1363.10000 

1362.10000 

1361.80000 

1359.50000 

13 57.60000 

1357.90000 

1350.90000 

1355.50000 

1345.90000 

1349.60000 

1344.20000 

1349.50000 

1343.30000 

1345.20000 

1343.30000 

1345.40000 

1344.80000 

13 39.10000 

1335.60000 

1336.30000 

1333 .WOO0 

1335.70000 

1333.40000 

133 1.30000 

1328.30000 

1332.30000 

1329.80000 

1329.OOOOO 

1330.40000 

1325.30000 

1325.30000 

13 25.50000 

1322.70000 

132 1.30000 

1319.70000 

13 18.80000 

1317.90000 

13 16.50000 

13 15.50000 

1315.40000 

13 11.00000 

13 12.10000 

1307.90000 

111 
Table C.5 NOAA-10 MFOVSW Solar Calibration Data 

- 

CALIBRATION SOLAR 

SAMPLE DATE X(DAY) MEASUREMENTS 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

10122186 

10/25/86 

lO/29/86 

11/01/86 

11/05/86 

11/12/86 

11/26/86 

121 10186 

12/24/86 

01/21/87 

02/18/87 

03/04/87 

031 18/87 

04/01/87 

041 15/87 

04/29/87 

08/19/87 

09/02/87 

091 16/87 

09/30/87 

10/14/87 

10128167 

11/11/87 

11/25/87 

12/09/87 

12/23/87 

01/06/88 

01/23/88 

02/03/88 

02/04/87 

1026. 

1029. 

1033. 

1036. 

1040. 

1047. 

1061. 

1075. 

1089. 

1117. 

1131. 

1145. 

1159. 

1173. 

1187. 

1201. 

1215. 

1327. 

1341. 

1355. 

1369. 

1383. 

1397. 

1411. 

1425. 

1439. 

1453. 

1467. 

1484. 

1495. 

1371 .OOOOO 

1373.20000 

13 73.60000 

1373.80000 

1370.oooOO 

1371.10000 

1370.10000 

1371 .WOO0 

1369.10000 

1371.40000 

137 1 .OOOOO 

1369.10000 

1369.OOOOO 

1370.10000 

1372.10000 

1367.70000 

1368.70000 

1375.20000 

1375.10000 

1374.80000 

1368 .OOOOO 

1368.10000 

1373.10000 

1373.20000 

1374.20000 

1370.80000 

1366.60000 

1368.80000 

1365.60000 

1366.80000 

112 I 
Table C.13 NOAA-10 WFOVSW Solar Calibration Data 

C A L IBR AT10 N SOLAR 

SAMPLE DATE X (DAY) MEASUREMENTS 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

10122186 

10/25/86 

10/29/86 

11/01/86 

11/05/80 

11/12/86 

11/26/86 

121 10/86 

12/24/86 

01/21/87 

02/04/87 

021 18/87 

03/04/87 

03/18/87 

04/01/87 

04/15/87 

04/29/87 

08/19/87 

09/02/87 

091 16/87 

09/30/87 

10/14/87 

10128167 

11/11/87 

11/25/87 

12/09/87 

12/23/87 

0 110618 8 

01/23/88 

02/03/88 

1026. 

1029. 

1033. 

1036. 

1040. 

1047. 

1061. 

1075. 

1089. 

1117. 

1131. 

1145. 

1159. 

1173. 

1187. 

1201. 

1215. 

1327. 

1341. 

1355. 

1369. 

1383. 

1397. 

1411. 

1425. 

1439. 

1453. 

1467. 

1484. 

1495. 

1361.90000 

1359.00000 

1357.20000 

1354.50000 

1356.50000 

1354.60000 

1352.10000 

1346.90000 

1345.30000 

1338.50000 

1335.90000 

1335.10000 

1334.00000 

1328.90000 

1324.80000 

1327.90000 

1325.40000 

1308.90000 

1305.90000 

1302.40000 

1306.10000 

1303.90000 

13OO.20000 

1296.90000 

1295 .00000 

1297.20000 

1296.60000 

1293.50000 

1292.60000 

1292.90000 
PART I1 

MODELING AND CHARACTERIZATION OF THE 

EARTH RADIATION BUDGET EXPERIMENT (ERBE) 

SCANNER SENSORS 

I. INTRODUCTION 

The accurate measurement of the total radiative energy flux (radiant exitance) at 

the top of the atmosphere provides one the most important elements in understanding 

the various climatic relationships of the earth-atmosphere system. For example, top of the 

atmosphere measurements of the reflected solar and the emitted radiative energy with high 

I 

I 

I absolute accuracy can validate the actual occurrence of the Greenhouse effect and provide 

quantitative relationships among increasing levels of atmospheric constituents and the I 

I earth’s climate. In establishing long-term trends and relationships, the absolute accuracy 

and stability of the sensors and the interpretation of the sensor output are of critical 

importance. 

This paper describes the calibration and interpretation of the Earth Radiation Budget 

Experiment (ERBE) scanner sensors. The Earth Radiation Budget Experiment provides 

measurements of the earth’s outgoing radiative flux as seen from the three satellites: ERBS, 

NOAA-9 and NOAA-10. Each satellite contains two instruments: a narrow field-of-view 

scanning instrument and a wide field-of-view nonscanning instrument. Each of the NFOV 

, 

I 

scanning instruments contains three scanner sensors which measure the radiation in three 

wavelength bands. The shortwave scanner measures the spectral radiance within the band 

from 0.2 pm to 5.0 pm, the longwave scanner the band from 5.0 pm to 50 pm and the total I 

114 
scanner the band from 0.2 pm to 50 pm. Figure 1 shows the ERBE scanner instrument 

with the contamination covers open. 

The ERBS satellite was launched in near-earth-orbit during mission 41-G by the space 

shuttle Challenger on October 5, 1984. After the required orbital transfer maneuver, ERBS 

attained its orbit at an altitude near 610 km with an inclination angle 57". The NOAA-9 

and NOAA-10 satellites are both sun-synchronous satellites and have been placed in orbits 

with an inclination anglc of 99" and an altitude near 860 km. NOAA-9 has an equatorial 

crossing time of 1430 LT for the ascending (northward) node, while NOAA-10 has an 

equatorial crossing time of 0730 LT producing a three-satellite system with high local time 

sampling. 

The basic objectiveas of the ERBE are to determine: 1) the monthly average radiation budget on a global, zonal and regional scale, 2) the average diurnal variation of the 

radiation budget on a regional and monthly scale, and 3) the equator-to-pole transport 

gradient. A zone is defined to be an area covering 10" ECA, and a region is defined as 

an area of 250 km x 250 km. A more detailed description of the ERBE objectives can be 

found in [l], [2]. 

c 

115 
116 
11. SCANNER DESCRIPTION AND MODELING 

The ERBE scanner instrument is shown in Fig. 1 with open contamination covers. 

Figure 2 is a schematic diagram showing the principal components of the scanner. The 

scanner detectors are thermistor bolometers with an active and reference flake placed in a 

balanced bridge configuration for accurate detection of small signals. 

The normal scanning direction is perpendicular to the satellite ground track. In this 

cross-track scan mode, the duration of a complete scan is 4 seconds. The scan starts with 

a space-look beyond the horizon and gradually scans the topof-the-atmosphere viewing 

the satellite nadir point ,md scans past the horizon on the other side of the track, before 

scanning to a position where the detector sees its corresponding internal calibration source. 

Then a fast retrace bring!; the scanner back to its original position beyond the horizon, thus 

completing a full normal scan, as shown in Fig. 3. Throughout the scan, the A/D converter 

samples the scanner output voltage every 33 msec. The sampled digital voltage during the 

space look, when viewing the earth and the internal calibration source is telemetered down 

to earth and constitutes the scanner's radiometric output; for example, the retrace samples 

are not transmitted. 

The ERBE scanner can also perform a normal scan sequence at any azimuth angle so 

that the scan direction is no longer in a cross-track direction. In fact, when the azimuth 

angle is commanded to be go", the scan direction is along the satellite ground track. Other 

scan modes are also available for specific purposes such as solar calibration through the 

mirror-attenuated-mosiac (MAM). 

The ERBE scanner: contain significant optical, thermal/radiative and electronic components. The incoming :;pectral radiance, LA, enters the scanner as shown in Fig. 2. The 

staircase shape of the field-of-view limiter (element 10) is designed to reflect back any radiation arriving from locations outside the desired footprint. The surface of the field-of-view 

117 
. 

118 
It9 
limiter is reflective black so that any outsf-field radiation will largely be reflected out of 

the scanner and some will be absorbed, thus not reach the detector. Since some of the 

radiation is absorbed, the temperature of the field-of-view limiter itself will vary slightly 

with the amount of incoming radiation. 

For the shortwave sensor, the incoming radiation passes through the shortwave suprasilW1 filter shown as element 14. A second shortwave filter (element 13) will cut-off any 

longwave radiation from reaching the detector. However, the first filter (element 14) cuts 

off longwave radiation before it reaches and heats other surfaces closer to the detector 

itself. Thus, the purpose of the first shortwave filter is to reduce thermal transients from 

unduly influencing the detector. The suprasil filter itself absorbs some of the incoming 

longwave and will vary in temperature. However, the impact will be smaller and will be 

further reduced by the shortwave filter. The longwave and total channels do not have a 

filter in element 14. 

The remaining radiation falls on the primary mirror, shown as element 6, and is reflected to the secondary mirror, shown as element 9, which reflects the radiation through 

the primary insert (element 5), the precision aperture (element 4) and through corresponding filters (element 13) according to the sensor onto the active flake (element 1). 

The primary and secondary mirrors form a Cassegrainian optical system with its focal 

distance corresponding to the precision aperture. Both primary and secondary mirrors are 

aluminized optical glass with a protective overcoat. 

I 

, The precision aperture has a hexagonal configuration as shown in Fig. 4. In the scan 

direction, the instantaneous field-of-view is 3", while along the track direction it reaches 

4.5'. The hexagonal shape of the aperture was selected to reduce aliasing errors and 

approximates a diamond aperture shape. A diamond aperture, when coupled with a lowpass electrical filter with a cut-off near the Nyquist frequency, can be shown to reduce 

aliasing errors in comparison to a circular aperture [3], [4]. 

The radiation which passes through the precision aperture falls on the active thermis- 
scan direction 

3" ---- 

I 

Figure 4. Precision Aperture Shape 

121 
tor flake (element 1) after passing through a filter (element 13). For the shortwave channel, 

the filter is suprasil-W1; the longwave channel has a diamond filter; the total channel has 

no filters. 

When the incoming radiation is absorbed by the active flake, its temperature rises. 

The change in temperature produces a corresponding change in the electrical resistivity of 

the flake. The active and reference flakes (elements 1 and 3) form two of the four legs of a 

balanced bridge, as shown in Fig. 5. When the temperature, hence resistivity, of the active 

flake varies, the resistance of the corresponding leg goes out of balance producing a signal 

proportional to the difference in the active and reference flake resistances. This signal is 

amplified in preamp and power amplification sections and is processed through a low-pass 

filter. The filter output is sampled, digitized and is telemetered to earth as the radiometric 

output of the sensor. Housekeeping data such as the reference flake temperature, T3, the 

detector bridge voltage, VB, etc. are also telemetered to earth every 4 seconds. 

To accommodate drifts in various thermal and electronic parameters, a drift balance 

mechanism is present, as shown in Fig. 6. When the average space look output voltage 

exceeds a specified value, the drift balance is activated in a direction to bring the space 

look readings within the specified margins. Otherwise, the drift balance is inactive. This 

mechanism maintains the dynamic range of the radiometric output in the presence of drifts. 

The detector is in a housing, element 8, which is kept at a constant temperature near 

38" C with the help of a heater driven by a PI controller. The heater tries to maintain 

all the detector components at a constant operating temperature so that the temperature 

variations in the active flake caused by the incoming radiation are reproduced by the 

sensor's radiometric output without distortion or error. 

A. Spectral Considerations. 

Each of the three ERBE scanners are ideally intended to measure the exact shortwave 

(0.2 pm - 5.0 pm), longwave (5.0 pm - 50.0 pm) or the total (0.2 pm - SO.+ pm) radiance 

in the incoming radiation, LA. However, the spectral properties of the materials used in 

1 122 
s" 

I 

123 
124 

t 
actual sensors produce a spectral response which differs from the ideal spectral response 

to varying degrees. In the ERBE scanners, non-ideal spectral behavior is largely due to 

the spectral characteristics of the following elements. 

1. Primary and secondary mirror spectral reflectivity, 

2. Shortwave and longwave filter transmissivity, and 

3. Active thermistor flake spectral absorptivity. 

The total channel is influenced only by the first and third factors above. The shortwave 

channel has two additic'nal suprasil-W1 filters, while the longwave channel has an additional 

diamond filter. Figurea 7, 8 and 9 show plots of the spectral response of the three ERBE 

scanners. While the essential tendency of each sensor is to measure the spectral radiance 

in its corresponding spectral band, the actual spectral responses fall somewhat short of 

the ideal and must be accommodated. 

Once absorbed by the active flake, the spectral characteristics of the incoming radiance 

no longer have any impact on the response of the sensor. Thus, it is useful to think of 

the sensor, as shown in Fig. 10, of a system with non-ideal spectral characteristics, .(A), 

followed by a system urhich is independent of spectral characteristics but depends only on 

thermal and electronic parameters. The input to this spectrally flat system is the portion 

of the incoming radiat',on, LA, which is absorbed by the active flake, say Ld. I 

Whether in viewkg calibration sources or in measuring top-of-the-atmosphere (TOA) 

radiances, the incomirg spectral radiance LA, is first transformed into absorbed heat at 

the active flake, Ld, and then transformed into an electrical voltage output as a digital 

signal. On the other hand, the ideal desired measurements would have been: 

125 
126 
- al 

C 

C 

0 

I 

0 a 

m 

I4 

a 

v1 

k 

i 

3 

v1 

127 
- al 

C 

C 

0 

L 

0 

al 

> 

0 

C 

0 

-I 

b a 

k 

*, 

x 

a 

m 

128 
129 
for the shortwave, longwave and total channels, respectively. 

It is clear that, in general, the shortwave radiance Lsw, cannot be determined from 

just Liw for arbitrary incoming radiation, LA. However, if Liw, Liw and Lz are known 

and these values are used to identify the observed scene type, then the incoming spectral 

radiance can be parametrized and a more accurate estimate of Lsw and LLw in terms of 

Lzw, Liw and Lz may be obtained using say a least-squares method. This approach is 

used in processing the ERBE data. 

Thus, the sensor interpretation algorithms produce an estimate of Lzw, Liw and 

Lz from the corresponding sensor radiometric outputs. Then, the “unfiltered” radiances 

Lsw, LLw are estimated by jointly processing these three measurements. In this paper, 

we will consider the algorithm which produce the estimates of Lzw, Liw and Lz. The 

algorithms used to estimate Lsw and LLw will be given in a future paper on the inversion 

algorithm. 

B. Scanner Dynamic Model. 

, As the radiation entering the scanner makes its way to the active flake, it is reflected 

from and absorbed by the various surfaces shown in Fig. 2. The absorbed energy raises I 

I 

the temperature of the elements and forms gradients and transients among the various 

I scanner components. For example, as the active thermistor flake absorbs the incoming radiative energy, Ld, its temperature rises and the temperature (hence resistance) differential 

between the active and reference flakes is detected by a balanced bridge. The expected 

behavior is that the reference flake temperature remains constant, as it does not see the 

incoming radiation and is placed in a cavity where the temperature is maintained at a 
c 

set constant temperature. However, the reference flake temperature cannot be directly 

measured. Thus, its actual behavior can only be determined by modeling and simulation. 

In conjunction with the thermal and radiative effects, the electrical signal processing 

also has significant impact on the scanner output. The heater electronics controlling the 

heat sink temperature has a direct thermal input. Figure 11 shows the transfer function 

of the heater controller. The heater controller dynamics can then be modeled as 

T8 9 

KH1 z7 = -- 27 - - 

KH1 

T7 + - 

TH 1 TH 1 TH I 

1 

KH1 7H2 

KAT2 KH2 TH1 KH2 ?HI KH2 781 

)x7 - - - T7+-- T8 9 

1. TH2 KH1 7H2 k* = (-- - 

where Tb is the set temperature at which the scanner heat sink is to operate, &(z8) is 

the Joule heating added to the heat sink to maintain the set temperature. 

The signal proces,sing performed by the ERBE scanner electronics is shown in Fig. 

6. The bridge, the preamp and the power amplifiers have rather small dynamic effects on 

the signal, as their cut-off frequencies tend to be much higher than the frequency content 

of the incoming radiation, Ld. However, the low-pass filter, a four-pole Bessel filter, has 

a significant effect on the signal as it has a lower cut-off frequency. In fact, the cut-off 

frequency is much lower than the Nyquist frequency, presumably to reduce noise rather 

than aliasing. However, this practice introduces some blurring effects and will be discussed 

in the following section. 

The electronics model for the detector bridge, preamp, power amp and the Bessel filter 

is detailed in Table 1 which also shows the parameter values for the electronic system. 

Augmenting the electronic model in Table 1 with the heat sink controller in (3), the 

complete electronic model can be expressed as 

131 I 
Figure 11. Scanner Heater Controller Model 

132 
Table 1. Scanner Electronics 

L 

BRIDGE: 

I 

Constants/Parameters sw LW Total 

K 3.4067 6.2067 2.32 

KB 0.0002623 0.0002652 0.0002583 

71 (sec) 1.4388 x 1.52698 x lo-' 1.35745 x 

TO("K) 311.16"K 31 1.16"K 31 1.16"K 

&I(= Rlo = R30 at 38" C 1.5 x lo5 1.5 x 105 1.5 x io5 

, 

Constants/Parameters 

Eo, (volt) 

CB (Amp) 

Kc 

72 (set) 

73 (set) 

S W 

25 x 

f2 x 10-9 ----- 

1.7578 x 

1.53743 x 

pi = 4 * (Ti - 293.16) + 3330 (OK) 

PREAMP: 

AMP & FILTER: 

sw 

LW 

25 x 

f2 x 10-9 ----- 

1.7578 x 

1.63298 x 

20.83 

8.51172 x 

1.05736 x lo2 

1.17485 x lo2 

1 .o 

0.62678 

9.4575 x 10-~ 

~ 

LW 

61.62 

8.51172 x 

1.05736 x lo2 

1.17485 x lo2 

1 .o 

0.62678 

9.4575 x 10-~ 

Total 

25 x lo-' 

f2 x 10-9 

----- 

1.7578 x 

1.45612 x loWs 

Tot a1 

13.03 

8.51172 x 

1.05736 x lo2 

1.17485 x lo2 

1 .o 

0.62678 

9.4575 x 10-3 

133 
Table 1. (Continued) Scanner Electronics 

ELECTRICAL SIGNAL PROCESSING MODEL 

24 = x3 

26 = x5 

where Z6 is going to be signals. 

134 
. 

. 

i = Az~ + BZT + B,,(E,, + n) + BUT, + b (4) 

where z is an 8-component state vector of electrical system variables, T is a 14-component 

vector of the thermal node element temperatures, E,, is an operating voltage, n is the 

total noise viewed at the preamp input and T, is the set temperature for the heat sink 

controller. A,, B,, B,,, and B, are appropriately dimensioned matrices. 

Using a lumped-;?arameter approach, the thermal conductive and radiative transfer 

among the elements shown in Fig. 2 can be expressed in terms of the node element temperatures, T;, forming, the vector T. 

where T4 represents i;he vector whose ith component is T:, Q8(z8) is the Joule heating 

power produced by the heat sink controller and L is the incoming radiation. 

Figure 12 shows the simulation results obtained using the dynamic model described 

by (4) and (5). The input radiance is a square wave with a 4 second period, one full scan 

of the ERBE scanner. During the first 2 seconds, no incoming radiation is present; e.g., a 

space look condition; during the last 2 seconds, the sensor sees a radiance of 175 W/m2-sr, 

before the cycle repeats. 

As seen in the plots in Fig. 12, the analog output (before sampling) produces a good 

replica of the incomin,g radiation. A more careful look shows that the output has a trapezoidal shape which is caused by the temporal processing due to the thermal and electrical 

transients. In other words, the scanner output lags its input largely due to the low-pass 

filter. 

The active flake temperature, TI, rises sharply in response to the leading edge of the 

square wave and then continues to rise at a slower rate, thus displaying the presence of 

multiple modes in the system. The response of the active thermistor flake clearly is not a 

135 
t b4&uia 

8 MWM n 

aoomal~yc n 

9 

0 

W 

w 

. 

. 

Figure 12. Simulation of ERBE Total Scanner Thermal and Electrical Variables 

136 
xa 

1 I 

-1.461~ I 

8.03 

, , 1 , , 

0 1.34 266 4.01 5.3s 6.69 

c 

c 

Figure 12. (Continued) Simulation of ERBE Total Scanner Thermal 

and Electrical Variables 

13 7 
Figure 12. (Concluded) Simulation of ERBE Total Scanner Thermal 

and Electrical Variables 

138 
replica of the incoming radiation as it continues to increase while the input is flat. However, 

the active flake conducts its heat to the detector assembly, Tz, which then conducts to the 

reference flake, T3. 

As the simulation shows, the reference flake temperature does remain constant during this period of time; rather it increases at about the same rate as the active flake 

temperature. As a result, the temperature difference between the active and reference 

flakes produce an excellent replica of the incoming radiation. The plot of this temperature 

difference, TI - 2'3, is seen to respond almost simultaneously to the leading edge of the 

square wave. On the c'ther hand, z6 which is the analog output voltage is slightly delayed. 

This behavior indicates that the thermal response of the flakes is quite fast, having a time 

constant of about 12 insec. 

Therefore, the lag in the scanner output is largely due to the low-pass filtering. Another conclusion is th2.t the balancing role of the reference is quite important to the proper 

operation of the scanner. Other simulations not presented here show a natural frequency 

of the combined radiative-thermal-electronic system with a period of about 24 sec., or a 4 

scan duration. Further, slower modes are also present although of less significance to the 

radiometric signal. Further simulation details can be found in (5). 

C. Effective Point !3pread Function. 

The instantaneous field-of-view (IFOV) of the scanner is largely determined by the 

precision aperture and the optic system. For the ERBE scanners, the precision aperture 

has a hexagonal shape with a 3" aperture in scan direction and up to 4.5O in the satellite 

track direction, as shown in Fig. 4. When the sensor input is not changing and the scanner 

SCCS the same footprint, the IFOV describes the point spread function (PSF). A d' iscrete 

step scanner which can stay at a given scan angle long enough for transients to die down 

would fall in this category, although it may have other disadvantages. 

As the simulation described in the last section shows, the scanner output is influenced 

by temporal processing (thermal, electronic) as well as spatial processing (IFOV). For 

139 
continuous scanners which have a low-pass filter, the sensor output will be a weighted 

average of the radiation arriving from the current and past locations of the footprint. To 

avoid excessive blurring and aliasing errors, it is desirable to use a low-pass filter with a 

cut-off near the Nyquist frequency [3]. 

It is possible to combine both spatial and temporal processing into an effective pointspread function which explicitly shows the weighting of each point in the scene in a given 

measurement by means of a convolution. This, however, turns out to correspond to an 

optical transfer function (OTF) which has non-zero phase characteristics, unlike most 

optical systems which have zero phase. In this case, the non-zero phase (or alternately 

complex-valued OTF) is being introduced by the causal nature of temporal processing, as 

can be seen from the following. 

I Effective Spatial Response 

To model the effects of electrical filtering (or processing) on the overall electro-optical 

system, we will consider a scanner where the scanning axis, say y, is perpendicular to the 

x-axis in which the relative motion of the scanner center of mass and the scene occurs. 

Other types of scanning strategies can be analyzed and modeled in a similar fashion, but 

will not be treated here. The electrical filtering is actually performed on the analog signal 

which is obtained by the optical system. Thus, the scanning axis, y, runs along the time 

axis. We will assume that the scanner’s relative motion along the x-axis is much slower in 

comparison to the scanning motion of the optical axis, or alternately, the scanning speed 

is assumed to be much faster than the relative motion of the device. 

I 

I 

I 

I 

l 

Let h,(t) be the impulse response of the electrical filter processing the signal obtained 

by the Optical Transfer Function (OTF), f0(v,w). Thus, the Electrical Transfer Function 

(ETF), he (w’), is given by the one-dimensional Fourier transform 

I 

c 

J -ca 

I 140 
where w‘ is the temporal frequency variable in units of cycles per sec. In most continuous 

scan systems, the electrical processing used is low-pass filtering with the ETF corresponding to standard low-pass filters such as the Butterworth, Tchebycheff, Bessel filters. 

The input-output relationship of the electrical filter is given by the one-dimensional 

convolution 

where i(t) and o(t) arc: the input and output signals, respectively. It is assumed here that 

transient effects due to initial conditions have died down to negligible levels. 

On the other hand, when the optical axis points along (z, y), the optical system inputoutput relationship is given by the two-dimensional convolution 

00 

g(z,y) = /w -00 / -w T0(5’,y’)L(z-z’,y-y’)dz’dy’ (8) 

where L(z,y) is the scene radiance input to the sensor and g(z,y) is the output, and 

~~(2, y) is the optical Point Spread Function (PSF) corresponding to the OTF, FO(v,u). 

Now suppose that, at time t, the optical axis points along (z(t),y(t)) producing the 

signal g(z(t),y(t)). Then, the analog output of the electrical filter is given by 

where the output of the electronics, s(z(t), y(t)), has been associated with the optical axis 

direction (~(t), y(t)) rzlther than simply time, t. 

As mentioned earlier, the scanning motion along y is much faster than the motion 

along x. Thus, we assume that y(t - t’) varies along the scan direction, while z(t - t’) 

remains essentially unchanged over the period of a scan; i.e., 

z(t - t’) = z(t) , 
I (11) y(t - t’) = y(t - t’) = yt - Yt 9 

I when t - t‘ is of the order of a scan period, but is much larger than the electrical filter 

time constants, and where y is the linear scan rate. Substituting (10) and (11) into (9) 

and manipulating, 

where 

y’ = yt’ , 

and 6(2) is the Dirac delta function. 

It is seen that the effect of the electrical filter in the spatial domain can be expressed 

by the PSF ~,(z’,y’) and a two dimensional convolution, as shown in (13). 

Taking the 2-D Fourier transform of (13), and using (8), 
where w is the spatial frequency variable corresponding to the scan direction; i.e., the 

y-axis. It should be noted that since ?e varies only with w and is independent of Y, we will 

treat it as a function of w alone to emphasize this fact. 

From (16) and (l?’), it is seen that the effective OTF for the combined electro-optical 

system is given by 

where fe is the temporal transfer function of the electrical filter, and y is the scan rate. 

Thus, given f,(w’) anld the scan rate, it is a simple matter to obtain the effective spatial 

OTF. 

Similarly, it can be shown that the effective system PSF, r(z,y), can be obtained as 

a one-dimensional convolution. 

which is the inverse Fourier transform of the effective system OTF, ?(Y,w). 

It is important to note that any temporal effects which can be expressed in terms of 

a convolution can be malyzed in this manner. For example, thermal dynamics which may 

be present in the sensors can be included in the term ie(w’) and analyzed in the same way 

as electrical processing. 

The most significant aspect of (18) is the fact that the effective OTF, ?(v,w), is now 

a complex-valued function. Whereas the optical transfer function, f0(v, w), is usually a 

real-valued function, the electrical transfer function, fe(W‘), is rarely, if at all, real-valued. 

Thus, in general, ?e(~~) and .i(v,w) now have magnitude as well as phase characteristics 

due to a non-zero imaginary part. 

The existence of non-zero and non-linear phase characteristics in the image-gatherhg 

system essentially produces a ”blurring” effect which adds to the blurring due to the 

143 
magnitude characteristics. Any known optical phase aberrations can also be included in 

fO(4 W). 

The transfer functions involved can be expressed in terms of their magnitude and 

phase in the form: 

(21) +,w) = lL(Yw')I It4V,W)le iIP. (tiw)+cpo (w)1 

From (20), it is seen that, when the optical system has no phase aberrations, the effective system OTF phase is precisely the electronic phase, while the magnitude effects are 

multiplicative and depend on both optical and electrical system characteristics. 

It should be noted that for causal, or non-anticipating, electrical filters, the impulse 

response is constrained by 

so that the filter can be implemented in real time. This causality condition simply requires 

that the output at time t depend only on the input till time t so that the current output of 

the filter does not depend on the future input. From (15), this causality condition requires 

that the effective PSF of the electrical filter satisfy the condition 

Now we can use (18) to obtain the effective spatial response of the ERBE scanners. 

The OTF of the ERBE scanner is determined by the combined effects of the Cassegrain 

optics and the aperture shape. Figure 13 shows the spatial frequency response of the 

Cassegrain optics at various wavelengths ranging from shortwave to longwave. For the 

144 

4 

L 
I / 

i 

I 

I 

I 

I 

I 

("'a)"# 

11 

i 

i 

I 

i 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

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I 

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n 

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A? 4 

m II n 

IY 

Qd 

00100 ???? 

wn 

145 
wavelengths of most interest, the OTF frequency response is quite flat and is not a limiting 

factor in the frequency domain. 

Figure 14 shows the frequency response of the hexagonal aperture used in the ERBE 

scanners. In comparison to the optics, it is clear that the combined optical transfer function 

will be dominated by the precision aperture OTF. 

The various electronic subsystem frequency response are shown in Fig. 15. Note that 

these are shown as spatial frequency responses according to (17). For this purpose, the 

detector bridge frequency response includes the thermal processing which occurs in the 

conductive paths between the active and reference flakes. As noted earlier, (18) is valid for 

any temporal processing whether it is electrical or thermal. The detector bridge effects, 

while not being completely negligible, are dominated by the frequency response of the 

4-pole Bessel filter. Further note that the imaginary parts of these OTF’s are non-zero. 

Combining the optical, thermal and electrical transfer functions into an overall effective OTF results in the frequency responses shown in Fig. 16. In the scan direction, the 

response if dominated by the temporal response, rather than the aperture of the scanner. 

This is an indication that the filter cut-off is too low. For the ERBE scanner, the Nyquist 

frequency is 15 Hz or 0.225 cycles/O in the spatial domain. Thus, a desirable level for the 

I temporal frequency response would be e-’ at w = 0.225 cycles/O. Note that at this level, 

the aperture and electrical systems would roughly contribute equally to the effective PSF. 

While the 

response along track is not changed much, the response in the scan direction has been 

significantly altered. The most significant effects are that the effective PSF 1) is shifted 

in the scan axis, 2) is not symmetrical and displays a “tail” and 3) has a wider “effective 

footprint” than the aperture in the scan direction. 

Figure 17 shows the effective spatial response of the ERBE scanners. 

While these effects can be reduced significantly by dynamic processing, zero-memory 

type solutions are limited. 
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, 
D. Interpretation Algorithms (Count Conversion). 

In the previous sections, we have described the main characteristics of the ERBE 

scanners as combined optical-thermal-electrical systems. However, for calibration and data 

reduction purposes, what is desired is an algorithm which produces the scanner input (Le., 

the incoming radiation) when the system output is known. In other words, the processing 

performed by the optical, thermal and electrical systems must be inverted; i.e., the inverse 

operator of the scanner system is derived. 

On the other hand, from the standpoint of computational time, it is desired to have 

as simple an algorithm as possible, since the huge amount of data to be processed places 

a soft limit on the complexity of data reduction algorithms. A gain/offset type equation 

was typical. 

With the basic constraints mentioned above, dynamic processing in the algorithm was 

not considered desirahle, so that a steady-state view was taken. The following algorithm 

was selected to interpret the sensor’s radiometric output voltage, v(t). 

where O(tk) is the average value of the eight output samples during the space look at the 

beginning of the scan :stating at time tk, At is the scan duration of 4 sec., a(t) is an offset 

dependent on the sample during the scan and will be discussed in more detail later. The 

housckceping data Tlt(tk) and Vo(tk) are transmitted to earth once every scan and are not 

available during the scan. TH(t) is the heatsink temperature (more precisely, T7) which is 

used to drive the heatsink controller, and Vo(t) is the DAC drift voltage. 

An additive term in the detector bridge voltage VB(~) was considered then dropped as 

the calibration data showed practically no variation in v~(t) during the ground calibration. 

From the analysis of the electronic system, however, it is seen that the effect of variations 

151 
in VB is multiplicative rather than additive. Thus, the coefficients, A,, A,, AH and AD 

are implemented according to: 

where AV, AVA, AHA and AD are constants determined during ground calibration, and 

c is the digital to analog conversion factor. 

c = 409.5 counts/volt (25) 

The first term in (23) is the most important term, with the remaining terms playing 

a relatively smaller role. The input of the second term in (23) is to allow for small but 

systematic effects not included in the first term. Note that the space clamp difference and 

heatsink temperature difference are correlated. Thus, the coefficients for these terms are 

determined from ground calibration data to allow for unexpected effects which may not 

be constant during the scan, but occur in a systematic manner every scan. 

Finally, the effect of the temporal processing discussed in the last section is approximately accounted for by the delay 7 in (23). As mentioned, a dynamic algorithm would 

be required to reduce the distortion or blurring introduced. However, the delay at least 

recognizes that the scanner voltage output at time t is more representative of the IFOV 

at t - 7 than it is of the current IFOV. The value used is 46 msec. which corresponds to 

the most significant time constant of the temporal processing. Using some flight data, this 

delay was validated to within 10% and the value modified. 

152 
111. CALIBRATION 

A. Calibration Sources. 

The ERBE ground calibration was performed in a calibration chamber especially designed for obtaining the required measurements. The calibration chamber is shown in Fig. 

18. To achieve high accuracy, the ground calibration is performed in vacuum. The Calibration sources are the Master Reference Blackbody (MRBB), shown in Fig. 19, and the 

ERBE Integrating Sphere, shown in Fig. 20, placed at opposite ends of the ERBE calibration chamber. A Sola;: Simulator is also available to produce a radiation source similar to 

the solar spectrum and intensity. The MRBB provides a highly accurate longwave calibration source, while the integrating sphere provides a calibration with both shortwave and 

longwave radiation [6] - [9]. 

The MRBB has six calibrated platinum resistance thermometers (PRT) mounted at 

.selected points which verify the uniformity of its surface temperature and is traceable to 

the IPTS68. 

The ERBE integrating sphere provides a calibration source containing both shortwave and longwave radiation, thus producing a spectral content similar to earth’s. The 

shortwave radiation is obtained from four 250 W tungsten lamps through a projection 

optics system that re9ects the light off a mirror before entering the sphere through four 

entrance ports made Df flashed opal glass. The flashed opal glass are intended to diffuse 

the light uniformly onto the sphere wall thus producing an uniform sphere wall radiance. 

The sphere wall is coated by 3M White Velvet and then Barium Sulfate thus producing a 

uniform and diffuse reflectivity over the sphere wall. The sphere wall radiance is monitored 

by two silicon photodiodes (SiPD) with wide fields-of-view. For an uniform wall radiance, 

the intensity at an ar~itrary point of the sphere can be thus monitored. 

153 
a 

IU 

W 

c 

(L 

3 

8 

W 

m w 

w 

8 

154 
k 

Q, I 

155 I 
156 

W 

PO 
The intensity of the light entering the sphere can be varied by blocking part of the 

radiation from the entrance ports. Thus, various levels of shortwave radiation can be 

mixed with a given intensity of longwave radiation emitted by the sphere wall. The sphere 

wall temperature is controlled by circulating a water and alcohol mixture through a tubing 

around the outer wall of the sphere. By making measurements of the sphere wall radiance 

at various levels of shortwave (including lamps off or no shortwave) and longwave radiation 

whose intensity is known by the SiPD measurements, it is possible to calibrate the scanners 

by scanning the uniform sphere wall. 

During the ground calibration the integrating-sphere data showed the following characteristics: 

(1) The NFOV scaning sensors measure non-uniformities (8%) on the sphere wall after 

known sources of error are taken into account to the extent possible. 

(2) The MFOV nonscanner sensor consistently measures a higher irradiance than does 

the WFOV nonsciinner sensor for both longwave and shortwave radiation. 

(3) The integrating sphere photodiode response shows nonlinear characteristics relative 

to the nonscanner measurements. 

(4) With the lamps off, the nonscanner sensors measure a higher (longwave) irradiance 

than expected by about 10 - 20 W/m2. 

The non-uniforrni:y of the sphere wall can be seen in Fig. 21 which shows measurements of the ERBE shortwave sensor as it scans the sphere wall. As a result of the 

non-uniformity and the other unexpected phenomena, the SiPD measurements, having a 

wide field-of-view, do not provide the shortwave intensity. The causes of these effects are 

investigated and explained in 191 which also suggests a different procedure to calibrate the 

shortwave ERBE scani iers and nonscanners. 

B. Calibration Procedures. 

The objective of the calibration is to obtain the coefficients necessary for the interpretation of the sensor output, namely, obtaining the coefficients in the algorithm developed 

157 
H 

$ 

E 
. 

in Section II-D. These coefficients consist of AV, AVA, AHA and AD in (24) and the 

offsets a(t) which are then substituted into (23) to compute the estimate of the radiative 

power absorbed by the active flake. 

Originally, a constant offset throughout the complete scan had been expected. However, during the ground calibration, significant variations in the offset during a scan were 

noticed. When scanning a uniform wall, the scanner output tends to vary according to the 

sample number, repeating regularly in successive scans. As a result an offset, a(t), which 

depends on the sample number during the scan, but not on the particular scan, is included 

in the sensor interpretation algorithm (23). The precise cause of this variable offset is not 

determined; however, it is thought to be of electronic origin, possibly due to power supply 

ground reference variations, and electromagnetic pulse effects at different configurations 

during the scan, transients due to pulses which occur every scan, etc. 

For the scanner instrument on the NOAA-9 satellite, the transmission of the housekeeping data every scan (4 sec.) produced significant transients in the electronics. To avoid 

the contamination of the radiometric signal by this effect, the algorithm in (23) was slightly 

modified so that the housekeeping data is transmitted once every eight scans. Thus, the 

transient occurs only once every 32 seconds, and does not contaminate the remaining seven 

scans. The modified algorithm is shown in Table 2. 

1. Total and Lorigwave Channels 

The total and longwave channels are calibrated using MRBB data. The data is ob 

tained by scanning the MRBB inside the calibration chamber, after it has reached a uniform 

temperature set at varims levels. The temperatures generally have been varied from -60" 

C to +45" C at six or :even different temperature levels. 

The algorithm coeficients are determined directly by a least-squares method of (23) 

and (24) to determine AV, AVA, AHA and AD and a constant offset bias, say b, added 

to the offsets a,(t). The offsets aa(t) are obtained by scanning a uniform wall in air. The 

offset bias, b, represent:; the vacuum to air correction which is applied to the in-air-offsets, 

159 
Table 2. NOAA-9 Count Conversion Equations 

I 

COEFFICIENTS 

AV 1 AHA 

AB I AD 

AVA I 

I 

CC(I, J, K) = GAIN(J) * (RC(I, J, K) - COFF(J, K) - SC(I, J)) 

AVA(J) * OFFSTl(J) * MOD(I- 1,8) 

where 

TOTAL 

CHANNEL 

5493.6354 

-17.11888 

0.0 

2.048750 

-6302.2166 

I - Scan Counter 

J - Channel Indicator 

W - Sample Counter 

GAIN(J) = AV(J)/(VB * CVLT(J)) 

OFFSTl(J) = AHA(J) * THDIF(J) + AB(J) * ABDIF + AD(J) * VDDIF(J) 

OFFSET(I,J) = (AVA(J)/(VB * CVLT(J))) * (SCDIF(I,J) + OFFSTl(J)) 

3261.6735 

-3.90308 

0.0 

0.7042702 

- 8 5 34.5 1306 

CVLT(COUNTS/VOLTS) = 409.5 

4221.3476 

-15.963174 

0.0 

0.0816490 

- 2673.2286 

DELAY(7) = -046 Seconds 

160 
i.e., 

a(t) = a,(t) + 6 (25) 

On the other hand, the data id(t - 7) is obtained by its definition in (1): 

where Ls(X,T) is Planck's equation for a cavity at temperature T, TBB(~) is the average 

MRBB temperature at time t. 

2. Shortwave Channels 

Due to the unexplected non-uniformity, of the ERBE integrating sphere, the calibration procedure developed for this channel is significantly more complicated. The basic 

philosophy is to use the total and longwave channels as transfer standards, and calibrate 

the integrating sphere output using these two channels which have been MRBB-calibrated. 

The remaining step is to similarly use a least-squares approach to determine the algorithm 

coefficients. The shortwave channels were calibrated using the following procedure: 

(1) Check longwave output of integrating sphere (at nadir) using longwave channel MRBB 

calibrated count conversion coefficients, integrating sphere wall temperature and longwave spectral response 

00 

LSLw = I, rLW(X) LB(X,TUJ) 

(2) Estimate shortwave output of integrating sphere (at nadir) using total channel MRBB 

calibration. 

a) Obtain 

b) Obtain 

using MRBB count coefficient algorithm. 

- som TT(~) L*(x,T,) dX fi: s," TT(X) [CLdl] dX.. Ldl is output 

due to lamp. 

c) Solve for c. 

161 I 
~ (3) Compute LSsw 

00 

Lssw = 1 ?SW(X) [&AI + LB(X,T,)] dX 

(3) Assumption: integrating sphere output is 

(4) Use integrating sphere sample 41 data (thought to be clean) at different shortwave 

levels and many scans to obtain count conversion coefficients. 

The calibration coefficients thus obtained for the three ERBE satellites are shown in 

Tables 3, 4 and 5. 

C. In-Flight Offset Stability. 

The ERBS satellite provides a capability to test the sensor offsets for stability over 

a period of time. The offsets can be tested by a pitch-over maneuver where the satellite 

pitch angle is commanded to 180". In this position, the sensors scan space, one of the most 

uniform sources provided the sun or moon are not in the field-of-view. 

The stability of the scanner offsets is in question as it is related to power supply 

reference variations over long periods of time. Table 6 shows the variation of the offsets 

determined from two pitch-over maneuvers approximately one year apart, from October 

1984 to October 1985. The mean variations are less than 0.27 W/m2-sr. 

Table 7 shows in-flight calibration results analyzed to indicate the stability of the 

offsets. This also shows a relatively small variation in the offsets of as much as 0.9 W/m2- 

sr for the ERBS total scanner. 

D. SWICS Stability. 

The in-flight calibration source for the shortwave scanners, the SWICS, appears to 

indicate a drift in its SiPD amp output. This can be seen in Fig. 22 which shows the 

NOAA-9 SWICS amp output over time. The amplifier output is clearly drifting. 

162 

, 
Table 3. ERBE ERBS (FM1) Scanner Data Interpretation Coefficients 

COEFFICIENTS 

TOTAL LONGWAVE SHORTWAVE 

CHANNEL CHANNEL CHANNEL 

I 

AD 

AVA 

Table 4. ERBE NOAA-9 (PFM) Scanner Data Interpretation Coefficients 

5477.2314 3174.3511 4267.8746 

15.604489 9.5852644 - 11.568366 

0.0 0.0 0.0 

0.1164209 5.435 1765 5.665687 

-7810.8822 -8354.0546 -7968.1652 

t 

TOTAL 

COEFFICIEYTS CHANNEL 

AV 5695.2 

AB 0.0 

AD 182.30 

AVA -7265.6 

AHA 139.47 

SHORTWAVE 

CHANNEL 

4392.0 

-506.26 

0.0 

170.25 

-4445.8 

LONGWAVE 

CHANNEL 

3130.0 

-98.59 

0.0 

- 409.2 7 

-3985.7 

Table 5. ERBE NOAA-10 (FM2) Scanner Data Interpretation Coefficients 

COEFFICIENTS 

TOTAL LONGWAVE SHORTWAVE 

CHANNEL CHANNEL CHANNEL 

I AV ' 5773.01 

- 12.4677 

0.0 

11.6246 

-28 11.24 

I 3080.27 

70.84 66 

0.0 

- 11.1559 

-1001.32 

AHA 

AB 

AD I AVA -- - - - - 

4188.21 

0.0 

0.0 

0.0 

-494 1.1 1 
~ 

Table 6. ERBS Scanner Offset Stability 

LW 

1.62 

4.66 

4.60 

16 . 02 

17 . 33 

EBBS SCANNER OFFSETS: (AS CURRENTLY IMPLEMENTED) 

sw 

-6 09 

-7 63 

-6 . 76 

-4 48 

-3.61 

Position Total 

LW (1 a) (1d 

4.27 (4.63) -0.71 (3.62) 

6.18 (4.17) -8.65 (4.61) 

3.98 (3.73) -8.69 (4.63) 

14.39 (3.21) -7.69 (4.16) 

17.76 (3.37) -4.17 (3.46) 

26 

40 

r 

2.39 

2.08 

EBBS SCANNER OFFSETS: (AS DETERMINED FROM PITCHOVEB OCT. 85) 

800 8C-6 

1.97 (2.25) 

26 1 1.61 (2.23) 

40 

66 

0.66 (2.10) 

6.48 (2.18) 

66 1 7.92 (2.24) L I I 

n 1 -El diffil 

mean N i=l 

mean (counts) 1.616 1.408 2.202 

mean (W/m2 - sr) 0.243 0 . 134 0 271 

max (counts) 2.64 

max (~/m2 - ar) 0.423 

2.76 

0.26 

4.38 

0 6399 

164 
k 

Q 

d 

id 

m 

V 

d 

m 

Y 

8 

w 

0 H 

H 

w 

t.c 

4 

a 

165 
0 

0 

0 

B 

Q 

Q 

a 

l m a 

n 

.- 

t0 

0 

cv 

0 

166 
a 

However, this does not mean that the SWICS output itself is drifting. In fact, Fig. 

23 implies that the drift is actually in the SWICS photodiode output, rather than its 

own radiative output. Figure 23 which shows the NOAA-9 shortwave scanner looking at 

the SWICS with its lamps on shows no drift at all. Therefore, it is more likely that the 

NOAA-9 shortwave sensor and the SWICS are stable while the SiPD is drifting. 

E. “Striping” Algorithm. 

During flight, features which appear as stripes on the data charts were observed by 

investigators. Closer analysis shows that, occasionally, the space clamp seems to jump to 

a new value, stay there for several scans, then jump back to a new value. However, the 

earth-viewing portion of the scan did not appear to be influenced by this phenomenon. So 

that, at every jump of the space clamp, all the values would also show a jump with the 

appearance of a stripe. This “striping” phenomenon has been noted on the ERBS and 

NOAA-9 scanners, but not so far on NOAA-10. The following empirical algorithm has 

been implemented with significant reduction of this effect. 

1. Read a record from the telemetry tape. 

2. Calculate the zero radiance at the internal calibration position (sample 74). 

3. Compare this to the space clamp. 

4. If the difference between the space clamp and the zero radiance at the internal calibration position is greater than a threshold (x 5 counts), then check to see which 

value has the greatest dispersion (using a window which includes the value of interest 

and 4 values ahead and behind it). 

5. Replace the space clamp with the internal calibration radiance if the space clamp’s 

dispersion is greater than the zero radiance at internal calibration dispersion. (Note, 

the threshold and dispersion tests are bypassed for all 3 channels if the scanner is not 

in the normal scan mode and for the shortwave channel if the scanner is performing 

an internal calibration.) 

6. Store the revised telemetry record on a direct access file which resides on a removable 

167 
I 1 I I I I I I I 

9 9 

0 8 0, hl F 

N N F N c 

N P N 

9 

0 

9 

s M .- r 

N N 

9 

0 

9 

- .- 

0 

(4( 

;J cv 

8 

cy 

c 

8 

0 

r 

0 

0 

QD 

0 

0 

rD 

0 

3 

0 

0 

ru 

0 

. 

I 

1 

I68 
disk pack. (Note, this is a temporary file which is purged at the end of the run.) 

169 
REFERENCES 

1. Barkstrom, B. R., “The Earth Radiation Budget Experiment (ERBE),” Bull. Am. 

Meteorof. SOC., 65, (ll), 1170-1185, 1984. 

2. Barkstrom, B. R. and G. L. Smith, “The Earth Radiation Budget Experiment: Science 

and Implementation,” Rev. Geophys., 24, No. 2, 379-390, May 1986. 

3. Halyo, N. and S. T. Stallman, “A Parametric Study of Aliasing Error for a Narrow 

Field of View Scanning Radiometer,” NASA CR-3294, 1980. 

4. Huck, F. O., S. K. Park, N. Halyo and S. T. Stallman, “Aliased Noise in Radiometric 

Measurements,” NASA Tech. Pap. 1639, May 1980. 

5. Halyo, N., S. H. Choi, D. A. Chrisman, Jr. and R. W. Sam, “Development of 

Response Models for the Earth Radiation Budget Experiment (ERBE) Sensors: Part 

1 - Dynamic Models and Computer Simulations for the ERBE Nonscanner, Scanner 

and Solar Monitor Sensors,” NASA CR-178292, 1987. 

6. Carman, S. L., “Deep Concentric Groves Enhance Blackbody Spectral and Spatial 

Uniformity,” Proc. SPIE Int. SOC. Opt. Eng., 416, 178-186, 1983. 

7. Carman, S. L. and R. J. Hesser, “An Integrating Sphere as a Precision Radiometric 

Calibration Source,” Proc. SPIE Int. SOC. Opt. Eng., 416, 111-118, 1983. 

8. Kopia, L. P., “Earth Radiation Budget Experiment Scanner Instrument,” Rev. Geophys. 24, No. 2, 400-406, May 1986. 

9. Halyo, N. and D. B. Taylor, “Explicit Solution of the Spectral Radiance in Integrating Spheres with Application to the Earth Radiation Budget Experiment Ground 

Calibration,” J. Opt. SOC. Am. A, 5, No. 4, 520-534, April 1988. J 

170 
Report Documentation Page 

1. Report No. 

NASA CR-181818 

2. Government Accession No. 

4. Title and Subtitle 

Modeling and Characterization of the Earth Radiation 

Budget Experiment (ERBE) Nonscanner and Scanner Sensors 

17. Key Words (Suggested by Authorls)) 

Earth Radiation Budget Experiment , sensor modeling, 

calibration, characterisation, data reduction algorithm, 

7. Authorls) 

18. Distribution Statement 

Unclassified - Unlimited 

Nesim Halyo, Dhirendra K. Pandey, and 

Deborah B. Taylor 

19. Security Classif. (of this report) 20. Security Classif. lof this page) 21. No. of pages 

Unclassified Unc las si f ied 182 

9. Performing Organization Name and Address 

Information & Control Systems, Incorporated 

28 Research Drive 

Hampton, VA 23666 

22. Price 

A09 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Langley Research Center 

Hampton, VA 23665-5225 

3. Recipient's Catalog No. 

5. Report Date 

March 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

FR-688 104 

10. Work Unit No. 

665-45-30-0 1 

11. Contract or Grant No. 

NAS 1- 180 18 

13. Type of Report and Period Covered 

Contractor Report 

14. Sponsoring hgency Code 

15. Supplementary Notes 

Langley Technical Representative: Robert J. Keynton 

Final Report 

16. Abstract 

The Earth Radiation Budget Experiment (ERBE) is making high-absolute-accuracy measurements of the reiected solar and earth-emitted radiation as well M the incoming solar radiation from three satellites: ERBS, NOAA-9 

md NOAA-10. Each satellite has four earth-looking non-scanning radiometers and three scanning radiometers. A 

ifth non-scanner, the solar monitor, measures the incoming solar radiation. 

This report describes the development of the ERBE sensor characterisation procedures using the calibration data 

'or each of the earth-looking non-scanners and scanners. Sensor models for the ERBE radiometers are developed 

ncluding the radiative exchange, conductive heat flow and electronics processing for transient and steady state 

:ontlitions. The steady state models are used to interpret the sensor outputs, resulting in the data reduction 

rlgorithma for the ERBE instruments. 

Both ground calibration and flight calibration procedures are treated and analyred. The ground and flight 

:alibration coefficients for the data reduction algorithms are presented. 

I active cavity radiometer, non-scanning radiometer, 

thermistor bolometer, scanning radiometer, Subject Category 47 

. 

1 

NASA '626 OCT 86 For sale by the National Technical Information Service, Springfield, Virginia 22161-2171