tss\ 
 
 NBS 
 
 
 NOAA TR NESS 58 
 
 A UNITED STATES 
 DEPARTMENT OF 
 COMMERCE 
 PUBLICATION 
 
 X' 
 
 35 
 
 NOAA Technical Report NESS 58 
 
 U.S. DEPARTMENT OF COMMERCE 
 
 National Oceanic and Atmospheric Administration 
 
 National Environmental Satellite Service 
 
 The Airborne ITPR 
 Brassboard Experiment 
 
 WASHINGTON, D.C. 
 March 1972 
 
 W. L. Smith 
 
 D. T. Hilleary 
 
 E. C. Baldwin 
 W. Jacob 
 
 H. Jacobowitz 
 G, Nelson 
 S. Soules 
 D. Q. Wark 
 
NOAA TECHNICAL REPORTS 
 
 National Environmental Satellite Service Series 
 
 The National Environmental Satellite Service (NESS) is responsible for the estab- 
 lishment and operation of the National Operational Meteorological Satellite System and of 
 the environmental satellite systems of NOAA. The three principal Offices of NESS are 
 Operations, Systems Engineering, and Research. The NOAA Technical Report NESS series is 
 used by these Offices to facilitate early distribution of research results, data handling 
 procedures, systems analyses, and other information of interest to NOAA organizations. 
 
 Publication of a Report in NOAA Technical Report NESS series will not preclude later 
 publication in an expanded or modified form in scientific journals. NESS series of NOAA 
 Technical Reports is a continuation of, and retains the consecutive numbering sequence of, 
 the former series, ESSA Technical Report National Environmental Satellite Center (NESC) , 
 and of the earlier series, Weather Bureau Meteorological Satellite Laboratory (MSL) Report. 
 Reports 1 to 37 are listed in publication NESC 56 of this series. 
 
 Reports 1 to 50 in the series are available from the National Technical Information 
 Service, U.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, Va. 
 22151. Price: $3.00 paper copy; $0.95 microfiche. Order by accession number, when 
 given, at end of each entry. Beginning with 51, Reports are available through the Super- 
 intendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. 
 
 ESSA Technical Reports 
 
 NESC 38. Angular Distribution of Solar Radiation Reflected from Clouds as Determined 
 
 from TIROS IV Radiometer Measurements, I. Ruff, R. Koffler, S. Fritz, J. S. 
 
 Winston, and P. K. Rao, March 1967. (PB 174 729) 
 NESC 39. Motions in the Upper Troposphere as Revealed by Satellite Observed Cirrus 
 
 Formation, H. McClure Johnson, October 1966. (PB 173 996) 
 NESC 40. Cloud Measurements Using Aircraft Time-Lapse Photography, L. F. Whitney, Jr., 
 
 and E. Paul McClain, -April 1967. (PB 174 728) 
 NESC 41. The SINAP Problem: Present Status and Future Prospects. Proceedings of a 
 
 Conference held at the National Environmental Satellite Center, Suitland, 
 
 Md., January 18-20, 1967, E. Paul McClain, Reporter, October 1967. (PB 176 570) 
 NESC 42. Operational Processing of Low Resolution Infrared (LRIR) Data from ESSA 
 
 Satellites, Louis Rubin, February 1968. (PB 178 123) 
 NESC 43. Atlas of World Maps of Long-Wave Radiation and Albedo -- For Seasons and 
 
 Months Based on Measurements from TIROS IV and TIROS VII, J. S. Winston and 
 
 V. Ray Taylor, September 1967. (PB 176 569) 
 NESC 44. Processing and Display Experiments Using Digitized ATS-1 Spin Scan Camera 
 
 Data, M. B. Whitney, R. C. Doolittle, and B. Goddard, April 1968. (PB 178 424) 
 NESC 45. The Nature of Intermediate-Scale Cloud Spirals, Linwood F. Whitney, Jr., and 
 
 Leroy D. Herman, May 1968. (AD-673 681) 
 NESC 46. Monthly and Seasonal Mean Global Charts of Brightness From ESSA 3 and ESSA 5 
 
 Digitized Pictures, February 1967-February 1968, V. Ray Taylor and Jay S. 
 
 Winston, November 1968. (PB 180 717) 
 NESC 47. A Polynomial Representation of Carbon Dioxide and Water Vapor Transmission, 
 
 William L. Smith, February 1969. (PB-183 296) 
 NESC 48. Statistical Estimation of the Atmosphere's Geopotential Height Distribution 
 
 From Satellite Radiation Measurements, William L. Smith, February 1969. (PB 183 297) 
 NESC 49. Synoptic/Dynamic Diagnosis of a Developing Low-Level Cyclone and Its Satellite- 
 Viewed Cloud Patterns, Harold J. Brodrick and E. Paul McClain, May 1969. 
 
 (PB 184 612) 
 NESC 50. Estimating Maximum Wind Speed of Tropical Storms from High Resolution Infrared 
 
 Data, L. F. Hubert, A. Timchalk, and S. Fritz, May 1969. (PB 184 611) 
 NESC 51. Application of Meteorological Satellite Data in Analysis and Forecasting, R. K. 
 
 Anderson, J. P. Ashman, F. Bittner, G. R. Farr, E. W. Ferguson, V. J. Oliver, 
 
 and A. H. Smith, September 1969. (AD-697 033) 
 NESC 52. Data Reduction Processes for Spinning Flat-Plate Satellite- Borne Radiometers, 
 
 Torrence H. MacDonald, July 1970. 
 
 (Continued inside back cover) 
 
.<<°'% 
 
 S *TES O* + 
 
 U.S. DEPARTMENT OF COMMERCE 
 Peter G. Peterson, Secretary 
 
 NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION 
 
 Robert M. White, Administrator 
 
 NATIONAL ENVIRONMENTAL SATELLITE SERVICE 
 David S. Johnson, Director 
 
 NOAA Technical Report NESS 58 
 
 The Airborne ITPR 
 Brassboard Experiment 
 
 W. L. Smith 
 
 D. T. Hilleary 
 
 E. C. Baldwin 
 W. Jacob 
 
 H. Jacobowitz 
 G. Nelson 
 S. Soules 
 D. Q. Wark 
 
 o 
 
 Q 
 
 -a 
 
 
 \n 
 
 
 
 r, 
 o 
 
 WASHINGTON, D.C. 
 MARCH 1972 
 
UDC 551 . 508 . 25 : 551 . 507 . 352 : 551 . 507 . 362 . 2 
 
 551.5 Meteorology 
 
 .508 Instruments 
 
 .25 Radiance measurement 
 
 .507 Instrument carriers 
 
 .352 Aircraft observations 
 
 .362.2 Satellite observations 
 
 The inclusion of the name or description 
 of any product does not constitute an en- 
 dorsement by the NOAA National Environmental 
 Satellite Service. Use for publicity or 
 advertising purposes of information from this 
 publication concerning ' proprietary products 
 or the tests of such products is not author- 
 ized. 
 
 
 li 
 
CONTENTS 
 
 Acknowledgements iv 
 
 I. Introduction (W. L. Smith, S. D. Soules , and D. Q. Wark) 1 
 
 Ob j ect ives 1 
 
 The CV-990 Expedition 2 
 
 II. Engineering description and evaluation 
 
 (D. T. Hilleary and G. J. Nelson) 2 
 
 The instrument 2 
 
 Aircraft installation and flight testing 18 
 
 III. Measurement characteristics (W. L. Smith) 19 
 
 IV. Data reduction and accuracy (W. L. Smith, W. J. Jacob, 
 
 and E . C . Baldwin ) 21 
 
 Introduction 21 
 
 The calibration equations 21 
 
 V. Clear-column radiance determination (W. L. Smith) 24 
 
 Introduction 24 
 
 Analytical solution 24 
 
 Aircraft test results 26 
 
 Conclus ion 28 
 
 VI. Aircraft-deduced atmospheric transmittances (W. L. Smith) 28 
 
 Introduction 28 
 
 Mathematical solution 32 
 
 Computational procedure 34 
 
 Results 38 
 
 Summary 44 
 
 VII. Determination of cloud transmittance (H. Jacobowitz) 44 
 
 Introduction - 44 
 
 iii 
 
Numerical method 45 
 
 Results of the aircraft measurements 48 
 
 Conclusions and recommendations 55 
 
 References 59 
 
 Appendix Flight plan and ITPR data for June 12, 1970, (flight 7) 60 
 
 I Flight plan 60 
 
 II Flight data 61 
 
 Acknowledgements 
 
 We would like to express our sincere gratitude to Earl Peterson and his 
 staff at the Airborne Science Office of the NASA Ames Research Center, and 
 William Nordberg of the NASA Goddard Space Flight Center for their 
 collaboration which enabled the successful accomplishment of the Airborne 
 ITPR Experiment. We also acknowledge the assistance L. Mannello , 
 P. Pellegrino, and R. Ryan in the reduction and analysis of the data. 
 
 IV 
 
THE AIRBORNE ITPR BRASSBOARD EXPERIMENT 
 
 W. L. Smith, D. T. Hilleary, E. C. Baldwin, W. Jacob, H. Jacobowitz, 
 G. Nelson, S. Soules , and D. Q. Wark 
 
 National Environmental Satellite Service 
 
 National Oceanic and Atmospheric Administration 
 
 Washington, D.C. 
 
 ABSTRACT. A preprototype (brassboard model) Infrared 
 Temperature Profile Radiometer (ITPR) was tested on 
 the NASA Convair-990 aircraft expedition during June 
 1970. The objectives of the airborne ITPR experiment 
 were to obtain data to test various techniques planned 
 for deriving temperature soundings from spaceborne 
 ITPR measurements and to specify the transmission 
 characteristics of the atmosphere and clouds. This 
 paper describes the instrument and shows various 
 results obtained from the airborne measurements . 
 
 I. INTRODUCTION 
 
 Objectives 
 
 A preprototype (brassboard model) Infrared Temperature Profile Radio- 
 meter (ITPR) was tested on the NASA Convair-990 aircraft during June 1970. 
 The ITPR measures the earth-atmosphere upwelling radiance in five narrow 
 spectral channels whose detailed spectral characteristics are summarized in 
 Section II of this report. The spectral intervals were chosen to obtain 
 radiance observations similar to those collected by spacecraft instruments 
 designed for sounding the distribution of the atmosphere's temperature and 
 water vapor. A spacecraft version of the ITPR is assembled for the Nimbus 5 
 spacecraft to be launched in 1972. The objective of the airborne ITPR brass- 
 board experiment was to provide data for detailed study of various problems 
 of atmospheric remote sensing. The specific objectives of the ITPR experi- 
 ment in the CV-990 were: 
 
 (1) To obtain data to test a proposed technique for the deduction of 
 clear-column radiances , and hence the atmospheric profile down to 
 the earth's surface, from cloud-contaminated remote observations. 
 (Section V summarizes some of the results of this test.) 
 
 (2) To obtain radiance measurements in a cloudless atmosphere so that 
 the atmospheric transmission characteristics of the ITPR spectral 
 intervals could be determined. (Section VI summarizes these results.) 
 
 (3) To obtain radiance measurements through various types of clouds so 
 that the spectral transmittance characteristics of clouds could be 
 studied. (Section VII summarizes these results.) 
 
The CV-990 Expedition 
 
 The ITPR was flown aboard the NASA Convair-990 during the June 1970 
 meteorological expedition conducted by the Goddard Space Flight Center and 
 the Airborne Science Office of the Ames Research Center. The CV-990 
 meteorological expedition consisted of 10 flights, each with a duration of 
 about 5 hours. Figures 1-1, 1-2, 1-3, and 1-4 show the date, time, and 
 ground track of each flight. The expedition covered a wide range of latitude 
 (28°N-80°N) and terrain (desert, mountains, vegetated land, ocean, and ice); 
 a wide variety of weather conditions was also sampled.. The 10 flights 
 collected a sample of airborne radiance data almost as diverse as radiance 
 data obtained by earth-orbiting satellites. This report describes the ITPR 
 instrument, its airborne radiance measurements, and the application of these 
 data to solutions of various atmospheric radiative transfer problems. 
 
 II. ENGINEERING DESCRIPTION AND EVALUATION 
 
 The Instrument 
 
 The preprototype Infrared Temperature Profile Radiometer (ITPR) is a five- 
 channel filter radiometer. Each channel measures radiances in a different 
 spectral interval. The channel spectral characteristics and the pertinent 
 atmospheric absorption bands are shown in Table II-l. Figure II-l shows the 
 measured transmittance of the spectral filters in channels 1 through 5. 
 
 The instrument collects infrared energy with five identical optical 
 telescopes , all of which are oriented to view a common field via a scan 
 mirror. Table II-2 is a summary of the ITPR optical characteristics, figure 
 II-2 is a system block diagram of the instrument electronics, and figure II-3 
 shows the optical design of a typical channel. 
 
 The radiation beams sensed by the five telescopes are chopped by a 
 common mechanical chopper operating at 23.5 Hz, and are then spectrally 
 filtered. A thermistor bolometer detector behind each telescope converts 
 the chopped radiation energy into a proportional AC electrical signal. The 
 signals are amplified and processed through separate electronic channels , 
 each including a synchronous demodulator and a post-demodulation filter. 
 
 The ITPR is. composed of two units: the optics unit (fig. II-4) which 
 contains the scan mirror drive assembly, optics deck, a.c. amplifiers, a 
 thermistor bolometer bias power supply, and a housing calibration surface; 
 and the electronics unit , which contains the channel demodulators , scan 
 logic, temperature monitor circuits, clocks, command relays, and an instru- 
 ment power supply. 
 
 The optics deck (fig. II-5) contains the channel telescopes, an optical 
 chopper assembly, and the detectors. In the chopper assembly an arrangement, 
 utilizing a galium arsenide light-emitting diode and a photo transistor, 
 generates a phase reference signal for the synchronous demodulator of each 
 channel. 
 
 The ITPR analog signal channel (the preamplifier, amplifier, and 
 
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 Figure 1-2. — Ground-tracks for Convair-990 Flights No. 4 and 7. 
 

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Table II-l. — Summary of ITPR spectral characteristics 
 
 Channel 
 
 Energy-weighted 
 central 
 wavenumber 
 cm~l 
 
 Half-power 
 bandwidth 
 cm - -'- 
 
 Absorption 
 band 
 
 1 
 
 532.5 
 
 (18.8um) 
 
 30 
 
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 2 
 
 898.5 
 
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 80 
 
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 3 
 
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 Table II-2. — Summary of ITPR optical characteristics 
 
 Number of channels 
 Optical FOV (half power) 
 Objective optics 
 
 Entrance aperture diameter 
 
 Focal length 
 
 Optical speed 
 Effective aperture 
 Condensing optics 
 
 Scan mirror 
 
 Five, each with separate telescope 
 3.0° 
 
 Aspheric Cassegranian 
 4.52 cm 
 
 14.50 cm 
 
 f/3.2 
 
 11.9 cm 2 
 
 Refractive 
 
 (Entrance aperture imaged on 
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 Flat Ni-plated aluminum alloy 
 substrate-overcoated with Al and 
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 Figure II-5.--ITPR optics deck containing the channel telescopes 
 
12 
 
 synchronous demodulator) is a modified version of the circuitry designed for 
 the NIMBUS 4 SIRS (Wark et al. 1970). The input stage is a differential 
 amplifier in the Middlebrook configuration using a matched pair of Field 
 Effect Transistors selected for low noise and high transconductance 
 (Middlebrook and Taylor/1961). As in the NIMBUS 4 SIRS, the three-stage 
 amplifier section is capable of producing total gains of 1.4 x 10^. Indivi- 
 dual hybrid voltage regulators are used to decouple each amplifier from the 
 power supply to reduce noise and to limit channel crosstalk to better than 
 -60db. A thermistor mounted on the detector case, but electrically a part 
 of the feedback loop of the amplifier second stage, is used to adjust the 
 gain to compensate for the change of detector responsivity as a function of 
 temperature (Barnes Engineering Company/1958) . ITPR had a gain compensation 
 to within 2 percent. 
 
 One of the problems inherent in a radiometer in which an opaque 
 mechanical chopper is used to modulate incoming scene radiances is the need 
 to correct the signal component caused by sensed radiant energy emitted by 
 the chopper. Since the modulated energy reaching the detector is basically 
 a function of the difference between the temperatures of the scene and the 
 chopper, the instrument channel calibrations are affected by changes in the 
 chopper temperature. In the ITPR, the chopper temperature is sensed by a 
 thermistor embedded in a "radiation coupler plate" adjacent to the chopper. 
 The thermistor is designed into a compensation network (chopper offset 
 generator) which produces ad.c„offset signal. The offset signal is summed 
 with the radiation difference signal to reduce the dynamic range of the 
 measurement and optimize signal telemetry. The offset signals generated for 
 each ITPR channel compensate the output signals for the spectral radiance of 
 the chopper to within 2 percent. A more detailed description of the chopper 
 offset generator and its function appears below. 
 
 The following radiometric analysis indicates how a channel calibration 
 should change as a function of varying instrument component temperatures. 
 Each channel senses the chopped radiation (or the difference in radiant 
 power at the detector which results from opening the chopper). The first 
 equation below applies when a chopper port passes all of the sensed beam, 
 and the second equation is applicable when the chopper completely obscures 
 the beam. 
 
 P, = A Q n Av [0.74 p p , p rn0 B(T o ) + 
 1 ms ml m2 s 
 
 0.26 p m2 B(T ) + 0.74 p^p^ e ms B(T ms ) + 
 
 ' 74 p m2 £ ml B(T ml> + e m2 B ( Tm 2 )] + P a (H-D 
 
 P 9 = A Q n Av B(T ) + P a (II-2) 
 
 where 
 
 Pn is the radiative power reaching the detector with the chopper com* 
 pletely open and P 2 is the radiative power reaching the detector 
 with the chopper completely closed; 
 
13 
 
 A = it D 2 /4 and D is the outside diameter of the effective primary 
 mirror stop (11.9 cm^); 
 
 ft is the solid angle of the "half power" field of view of the channel 
 (2.16 x 10~ 3 steradian); 
 
 n is the effective transmission of the filter and lenses weighted for 
 the associated spectral bandwidth; 
 
 T f and T-. are the spectral transmissions of the filter and lenses, 
 respectively; 
 
 B(T) is the effective blackbody radiance in the spectral interval Av 
 at blackbody temperature T and 
 
 n Av B(T) = / TfT-L B(v, T) dv ; 
 
 T and T are the effective blackbody temperatures of the scene and the 
 chopper, respectively; 
 
 T is the blackbody temperature of the channel components whose 
 
 emissions reach the detector via the central portion of the primary 
 aperature obscured by the secondary mirror; 
 
 Tj-ji, T 2» T are temperatures of the primary, secondary, and scan 
 mirrors, respectively; 
 
 p-.i, p m 2 , P are reflectances of the primary, secondary, and scan 
 mirrors ; 
 
 P is the sensed radiation emitted by components on the detector side 
 of the chopper" 
 
 The numerical constant 0.74 is necessary because 26 percent of the 
 channel entrance aperture, A, is obscured by the secondary mirror and 
 spider as shown in figures I I- 3 and I I- 5. The second term in the brackets 
 occurs because the detector views the obscured portion of the aperature. It 
 senses radiation emitted by the cylindrical baffle tube and other components 
 in reflections from the central part of the secondary mirror. 
 
 The other terms in equation (II-1) represent radiation emitted by the 
 mirrors. The radiation power, P , emitted by components on the detector 
 side of the chopper and reaching the detector is eliminated by subtracting 
 equation (II-2) from equation (II-1). Equation (II-3) was written in terms 
 of the root -mean-square value of the chopped radiant power on the detector. 
 Matched mirror reflectances and equal primary and secondary mirror tempera- 
 tures have been assumed. 
 
 P rms = C l (P 1 " P 2 ) = C l A fi n Av C0 ' 7U p3 B(T S } + 
 0.26 p B(T Q ) + 0.74 p 2 e B(T ms ) 
 (1.74e - 0.74e 2 ) B(T ml ) - B(T )] 
 
 0.26 p B(T Q ) + 0.74 p 2 e B(T ms ) + (II-3) 
 
14 
 
 C-i is a factor to convert the amplitude of the radiant power wave- 
 form (P-^ - P2) s to its root-mean- square, P . The factor 
 depends upon the shape of the radiant power waveform created by 
 the chopper port passing through the sensed beam and depends 
 upon the relative sizes of the beam and the port. 
 
 The higher order emissivity term has been dropped from equation (II-4). 
 This equation has been arranged to show that the channel must be considered 
 to measure not only the differences between the chopper radiance and that of 
 the scene, but also to some extent the differences between the chopper radi- 
 ance and the obscuration and mirror radiances. 
 
 P rms = c i A fi n Av {[0.74 - 2.22e] [B(T S ) - B(T c )3 
 + [0.26 - 0.26e] [B(T ) - B(T_)] 
 + 0.74e CB(T ms ) - B(T C )] 
 + 1.74e [B(T ,) - B(T )]} 
 
 (II-4) 
 
 , where e = 1 - p 
 
 The relative sensitivities of the signal to target radiances , and to 
 mirror emissions, can be estimated by assuming mirror reflectances and 
 emissivities. The ITPR mirror surfaces are aluminum overcoated with a 0.15- 
 micron thickness of silicon monoxide. Reflectivities of 96 percent and 
 emissivities of 4 percent were assumed to obtain equation (II-5). These 
 values may be pessimistic, but the cleanliness of the mirrors could not be 
 maintained during the flight test program. 
 
 P rms = C x A fl n Av {0.65 [B(T S ) - B(T C )] 
 
 + 0.25 [B(T Q ) - B(T C )] + 0.03 [B(T ms ) - B(T C ) (II-5) 
 
 + 0.07 CB(T ml ) - B(T C )]} 
 
 It is apparent that the instrument calibration can be affected signi- 
 ficantly by temperature changes in the chopper, obscuration, telescope 
 mirror, and scan mirror. The chopper temperature is indirectly sensed in the 
 ITPR. The rotating chopper is radiatively coupled to a "radiation coupler 
 plate" which contains thermistor temperature sensors. One thermistor cir- 
 cuit output is used only as a monitor; another is used with the chopper off- 
 set generator circuitry mentioned above. 
 
 The chopper temperature monitor was calibrated indirectly. The optics 
 deck was mounted in a temperature-controlled fixture and set up to measure 
 spectral radiances from a blackbody source. The optical path was purged with 
 nitrogen. The amplitudes of the AC signals were brought to zero, at the out- 
 put of the amplifiers, by adjusting the blackbody temperature. This proce- 
 dure was repeated for several instrument temperatures. In each instance, the 
 instrument and source were allowed to reach thermal equilibrium. 
 
 The relationship of the channel output signal to the chopped radiance 
 
15 
 
 can be simplified to the following equation: 
 
 S dc = C 2 R(T d ) GjL (T d ) H G 2 P rms + X(T C ) (II-6) 
 
 where : 
 
 S-, is the do c. volt age at the analog electronic channel output. 
 
 R(Tj) is the single flake thermistor bolometer responsivity in volts 
 
 rms/watt rms (including all harmonic components) which is a function 
 of detector temperature (Barnes Engineering Company 1958). 
 
 C 2 is a constant factor necessary to adjust the single flake responsiv- 
 ity specified by the bolometer manufacturer. It corrects the 
 responsivity for the bolometer bias voltage, the chopping frequency, 
 and the signal loading by the compensating thermistor flake 
 (Barnes Engineering Company 1958). 
 
 Gj_(T d ) is the a . c .amplifier gain which has been made a function of 
 
 detector temperature so that the product R(T, ) G-,(T d ) is approxi- 
 mately constant (Barnes Engineering Company 1969). 
 
 H is a factor which relates the DC output of the synchronous demodula- 
 tor to the rms of the AC signal waveform. The amplifier bandwidth 
 passes all of the significant signal components. 
 
 Q>2 is the effective signal gain in the post-demodulation filter which 
 includes a DC amplifier. 
 
 X(T C ) is the chopper-offset-generator signal component as measured at 
 the channel output. 
 
 Combining (H-5) and (II-6): 
 
 S dc = Cjl C 2 A fl n Av R(T d ) G 1 (T d ) H G 2 
 
 {0.65 B(T ) + 0.25 B(T ) + 0.07 B(T ml ) 
 
 + 0.03 B(T ms ) - B(T C )} + X(T C ) (II-7) 
 
 The changes of detector responsivity with temperature are partially 
 
 compensated as mentioned above. The circuitry was adjusted empirically 
 
 to make the product of detector responsivity and AC amplifier gain 
 constant, within +2 percent, over the temperature range 10° to 40°C. The 
 
 slope of each channel's output versus the pertinent spectral radiance of a 
 blackbody test source was determined from instrument temperatures of 10°, 25° 
 and 40°C. The 10° and 40°C slopes were finally equalized by adjusting the 
 value of a resistor in series with the thermistor. The slope at 25°C was 
 about 2 percent greater than at other temperatures. 
 
 The chopper offset generator signal is expressed in equations (II-6) and 
 (II-7) in terms of its effect at the channel output, because the d.c„ 
 
16 
 
 amplifier actually amplifies the fixed offset signal component, the variable 
 offset signal component, and the synchronous demodulator output signal by 
 different factors. Different input resistors are used at the summing junc- 
 tion of the d.coperational amplifier for the various signal components. 
 
 Equation (II-8) shows the desired offset term assuming that T = T . 
 Equations (II-9) and (11-10) show the form of the offset signals generated 
 by the chopper offset generator circuitry shown in figure II-6. 
 
 X(T C ) = 0.74 p 3 A a n Av R(T d ) G 1 (T d ) H G> 2 B(T C ) 
 
 X(T C ) = 
 
 R^ 
 
 El 
 
 R 
 
 6 T + Rr 
 R 6 + R T 
 
 Rp = R exp 3 (L_ - L.) 
 1 O T T 
 c o 
 
 + G^ E 1 / R 3 + R4 + R 5 \ 
 
 ^ R 2 + R 3 + R 4 + R 5 J 
 
 (II-8) 
 
 (II-9) 
 
 (11-10) 
 
 where : 
 
 G is the d.c. amplifier gain for the variable chopper offset signal. 
 
 G^ is the d.c. amplifier gain for the fixed chopper offset signal. 
 
 R- and Ry are resistances as indicated in figure II-6. 
 
 R™ is the resistance of thermistor temperature sensor mounted on the 
 radiation coupler plate. R Q is its resistance at temperature T . 
 
 3 is a property of the thermistor material. 
 
 The chopper offset term has not been combined with other terms in equa- 
 tion (II-7) because of the manner in which the flight data were processed. 
 The fixed voltage E and the variable voltage corresponding to the bracketed 
 portion of equation (II-9) were separately digitized and recorded with the 
 channel output data and used to compute X(T ) from equation (II-9). The 
 computed X(T C ) was then subtracted from the recorded channel output, S dc . 
 In practice, the offset generator circuitry only served to compress the 
 range of the recorded data. The proper performance of the generator circu- 
 itry was checked by comparing the variable portion of X(T ) against the 
 values of T measured by the monitoring thermistor. 
 
 It can be shown from equation (II-7) that the primary and secondary 
 mirror temperatures could be allowed to change about 1.5°C, or that the scan 
 mirror temperature could change about 3°C before the spectral radiances 
 deduced from an initial instrument calibration would err by more than 0.25 
 ergs /cm 2 s sr cm" -*-. The mirror temperatures were not measured. 
 
 Variations in the chopper and obscuration temperatures would be much 
 more serious. The temperature of the radiation coupler plate was measured 
 
17 
 
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 Q 
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 "I 
 
 r 
 
 
 O 
 
 CO 
 
 
 h- 
 
 _l 
 
 
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 CT 
 
 
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 UJ 
 
 
 111 
 
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 X 
 
 r- 
 
 
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 A 
 
 ro 
 
 
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 UJ 
 
 
 UJ 
 
 UJ 
 
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 X 
 
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 v/W^^Vv^WW^^-aMZ-WW^ — Ml 
 
 
 ro 
 
 
 10 
 
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 CL 
 
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 UJ 
 
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 UJ 
 
 CD 
 
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 4-> 
 
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 Pj 
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 CD 
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 CD 
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 -P 
 CD 
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 CD 
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18 
 
 but could not be considered a satisfactory indicator of chopper or obscura- 
 tion temperature except when the instrument temperature was not changing. 
 
 Aircraft Installation and Flight Testing 
 
 The instrument, attached to a special frame which included a remotely 
 controlled door assembly, was mounted in the forward cargo compartment of 
 the aircraft. The NASA Convair-990 is fitted with windows near the bottom of 
 its cargo compartments. A tubular section of the frame penetrated the air- 
 craft fuselage through a mating sleeve in a dummy window plate, allowing the 
 radiometer a clear view of the earth beneath the aircraft. O-ring seals 
 between the instrument and frame and the tube and window sleeve maintained 
 the pressure integrity of the cargo compartment. 
 
 Two blackbody radiation sources were installed with the radiometer. 
 The scan mirror indicated in figure II- 3 could be rotated on command so that 
 the channels viewed (1) the earth beneath the aircraft, (2) a warm blackbody 
 operated at about 50°C, (3) the instrument's housing calibration surface, or 
 (4) a cold blackbody operated at a temperature between 0° and -40°C. The 
 radiating surfaces of the blackbodies consisted of V-grooves milled into 
 copper plates and coated with 3M401 "Black Velvet" paint. 
 
 f The cold blackbody was designed as an integral part of a small 5-liter 
 dewar and was cooled by liquid nitrogen (LN 2 ). A larger (45-liter) 
 storage dewar contained enough LN 2 for flights of 4 to 6 hours . Thermistors 
 sensed the liquid level in the small blackbody dewar, and a liquid level 
 controller automatically valved LN 2 from the larger dewar when it was 
 required. Nitrogen gas boiled off from the small dewar was used to purge 
 the instrument's optical path prior to opening the remotely controlled door, 
 and to cool the warm blackbody thermal sink. 
 
 The blackbody temperatures were controlled to about 0.2°C. Commercial 
 thermocouple deviation amplifiers were used to sense the blackbody tempera- 
 tures and to drive temperature controllers which provided signals to Silicon 
 Control Rectifier power units that powered the blackbody resistance heaters. 
 Thermistors embedded in the radiator plates were used to read out the radia- 
 tor temperatures. The thermistors were calibrated in situ against certified 
 thermocouples, also embedded in the plates; however, these thermocouples 
 were not read out during the flights. 
 
 During the flight attempts were made to determine the channel calibra- 
 tions (using two blackbody temperatures) whenever the instrument temperature 
 changed significantly. The housing calibration surface proved to be unre- 
 liable for calibration because of internal thermal gradients. 
 
 The instrument, the blackbodies, the LN„ supply, and other auxiliary 
 equipment were controlled and monitored from a console located in the air- 
 craft passenger cabin. The instrument's infrared and housekeeping data were 
 multiplexed, digitized, formatted, and recorded on a digital tape recorder. 
 An auxiliary multiplexer and analog-to-digital converter transferred data to 
 a paper tape printer which generated an inflight printout of the infrared 
 data and selected housekeeping data. 
 
19 
 
 III. MEASUREMENT CHARACTERISTICS 
 
 The spectral radiance, I v (p-t)> measured in any spectral channel of 
 the airborne ITPR at the pressure level, p. over a cloudless atmosphere is 
 given by the radiative transfer equation 
 
 ivo<Pt)= b Vo ( Po )x vo ( Pt , Po ) - /° B vo ( P ) dT vo ( Pt>P> d m p (ni-i) 
 
 F t d In p 
 
 where B (p) is the Planck radiance source function at pressure level p and 
 the channel central wave number, vo. x (p t »p) is the mean spectral 
 transmittance of the atmosphere between the pressure levels defined by 
 
 \, (p t ,p) = V v %(P t »P)dv// o %dv (III-2) 
 
 where (L is the channel response function. The Planck radiance is given by 
 
 B VQ (p) = 2hc 2 v o 3 /{exp(hc vo /k T(p))-1} (III-3) 
 
 where h = 6.6237 X 10~ 27 erg sec, c = 2.99791 X 10" 10 cm sec -1 and 
 k = 1. 38024 X 10~16 erg deg~l. T(p) is the atmospheric temperature at the 
 pressure level p. The equivalent blackbody (brightness) temperature sensed 
 by any channel is 
 
 T5 (p t ) = hcv Q /k in {2hc 2 v o 3 /I vo (p t )+l} (III-4) 
 
 Channel 1 (v Q = 532.5 cm - -'-) measures the radiation upwelling from the 
 earth and atmosphere within a semitransparent spectral region of the rota- 
 tional water vapor band. The radiance measured in this spectral interval 
 can be interpreted in terms of the total amount of water vapor in the 
 atmospheric column below the instrument sensor. 
 
 Channel 2 (v = 898.0 cm -1 ) measures most of the radiation emitted from 
 the earth's surface and clouds below the sensor. The radiation measured in 
 this "atmospheric window" channel is only slightly attenuated by atmospheric 
 gases (primarily water vapor) and so can provide a good measure of cloud- 
 top and surface temperatures as well as cloud cover. Channels 3 
 (v Q = 747.0 cm -1 ), 4- (v Q = 732.5 cm" 1 ), and 5 (v = 708.0 cm -1 ) sense the 
 radiation upwelling in semitransparent regions of the 15um CO2 band. Since 
 the atmospheric CO2 distribution is known, these spectral measurements can 
 be interpreted in terms of the temperatures of lower , middle , and upper 
 layers of the atmosphere below the instrument. 
 
 Figure III-l shows the variation of the effective radiating altitude 
 for each channel at varying aircraft altitudes. The "effective-radiating- 
 altitude" is defined here as that atmospheric level where the air temperature 
 is equal to the measured equivalent blackbody temperature. Channel 5 
 measurements provide a good means for determining the air temperature at 
 aircraft level (i.e., the effective radiating pressure equals the aircraft 
 pressure) up to about 5,000 ft. The window channel, channel 2, senses 
 temperatures at and close to the earth's surface, even under fairly moist 
 
300 
 
 at 
 
 => 400 
 </> 
 
 o 
 
 z 
 
 < 
 a 
 
 2 
 
 500 
 
 700 
 
 JlJ 850-- 
 
 1000 
 200 
 
 20 
 
 ALTITUDE (THOUSAND FEET) 
 
 29.0 15.0 
 
 7.5 
 
 0.5 
 
 T 
 
 CV-990 ITPR 
 JUNE 9,1970 
 75°N 121 D W 
 
 : -29.0 
 
 CHANNELS 
 
 532.5cm" 
 
 (1) 
 
 898.0cm" 
 
 (2) 
 
 747.0cm" 
 
 (3) 
 
 732.5cm" 
 
 (4) 
 
 708.0cm" 
 
 (5) 
 
 "(41 
 
 --.15. 
 
 a 
 
 z 
 < 
 
 CO 
 
 o 
 
 x 
 
 300 
 
 400 
 
 500 
 
 700 850 
 
 1000 
 
 PRESSURE ALTITUDE (MB) 
 
 300 
 
 40.1 
 
 ALTITUDE (THOUSAND FEET) 
 
 27.7 20.1 15.0 10.0 
 
 T 
 
 T 
 
 5.0 1.0 
 
 CV-990 ITPR 
 JUNE 18, 1970 
 28°N 93°W 
 
 -27.7 rr 
 
 1000 
 200 
 
 300 400 500 700 
 PRESSURE ALTITUDE (MB) 
 
 Figure III-l. — Variation of effective altitude with aircraft altitude for 
 five channels of ITPR. High latitude (Top), Subtropical 
 (Bottom). 
 
21 
 
 atmospheric conditions. At high aircraft altitudes, the water vapor channel 
 senses radiances originating lower in the atmosphere than any of the CCU 
 channels. However, from low aircraft altitudes, the water vapor channel does 
 not probe as deeply into the atmosphere as channels 3 or 4, because of the 
 relatively large concentrations of water vapor near the surface. 
 
 IV. DATA REDUCTION AND ACCURACY 
 
 Introduction 
 
 There were almost continuous temperature variations of the ITPR optics 
 unit because of large variations in the environmental air temperature during 
 the CV-990 flights. Therefore, accurate determination of scene spectral 
 radiance from a channel output required that the instantaneous thermal state 
 of the instrument be taken into account in the output voltage-to-radiance 
 transformation. Pref light calibration relations could not be applied to 
 inflight data because they were not obtained for the thermal conditions 
 encountered during flight . Furthermore , inflight calibrations , obtained by 
 viewing the warm and cold blackbody reference targets , could not be applied 
 directly to subsequent scene data unless the thermal environment remained 
 constant. The CV-990 experiments generally required almost continuous 
 variations in aircraft altitude so it was impossible to have specific 
 inflight calibration data for every thermal situation. As a consequence, a 
 multivariable calibration relationship had to be formulated for each channel 
 to account for all the thermal energy transfer processes affecting the out- 
 put signal. The coefficients of the calibration equations were determined 
 by least-square multiple regression from the entire sample of inflight cali- 
 bration data. The inflight calibrations were conducted under thermal condi- 
 tions covering the entire range of those encountered during scene measure- 
 ments . 
 
 The Calibration Equations 
 
 As discussed in section II, the ITPR electronics were designed so that 
 the output of each channel would vary linearly with the spectral scene 
 radiance when the instrument was in thermal equilibrium. That is 
 
 B(T S ) = A Q + A x S dc (IV-1) 
 
 As indicated in equations (II-7) - (11-10), A and At, are functions of the 
 detector responsivity , the chopper radiation, and any radiation from compon- 
 ents located in front of the chopper (e.g. , the mirrors and portions of the 
 instrument reflected in the cassegrain obscuration), as well as the chopper 
 offset generator variable. Expressing the detector responsivity in terms of 
 a cubic function of the detector temperature, the chopper radiation in terms 
 of the Planck function of the chopper temperature, and the remaining radia- 
 tion in terms of the Planck function of the housing temperature, then 
 
 6 6 
 
 A = C + I C-f., and A, = d_ + E d.f 
 o o . =i x !> 1 o . =i x J 
 
 2 3 
 where the C's and d's are constants, f, = T d , f 2 = T d , fg = T d , 
 
 (IV-2) 
 
22 
 
 fn = B(T C ), f 5 = B(T h ), and f g = X(T c ). (The symbols are defined in section 
 II.) The Planck function of the housing temperature, T^, is used to account 
 for all other radiation components because the mirror temperatures were not 
 measured. Substituting (IV-2) into (IV-1) yields the calibration equation 
 for each channel 
 
 B <V = ilo f i (C i + d i S dc> < IV - 3 > 
 
 where f is equal to unity. 
 
 The cold and warm blackbody calibration data obtained throughout all 10 
 CV-990 flights were used to obtain the 14 coefficients of (IV-3) by multi- 
 ple regression. B(T S ) is merely the Planck radiance of the thermistor- 
 measured blackbody temperature when viewing a calibration blackbody. All the 
 fj*s and blackbody temperatures were measured and telemetered simultaneously 
 with S^ c , permitting the empirical determination of (IV-3) and its applica- 
 tion to scene radiance data. 
 
 The resulting calibration equations were tested by application to the 
 calibration channel outputs, S^ c , from which they were derived. They 
 permitted specification of blackbody temperatures by the output of each 
 channel to within 0.5°C rms of that obtained independently by the blackbody 
 thermistors. The root-mean- square error of the blackbody thermistor temper- 
 atures were judged to be about 0.4°C. The random error of the channel out- 
 put derived scene temperatures were found to be about 0.3°C for an indivi- 
 dual M— second sample. 
 
 Figure IV-1 shows a sample of calibration data obtained for channel 3. 
 The dots are values of channel 3 output dc voltage, S ( j c , obtained by viewing 
 the warm blackbody whose radiance was calculated from the thermistor-moni- 
 tored temperatures. There is generally a 10 . ergs/cm 2 s sr cm~l disparity 
 of blackbody radiance for a given output voltage of the channel. The X's 
 show the same output voltages transformed into scene radiance by equation 
 (IV-3). The 10.0 ergs/cm 2 s sr cm~l disparsity has been reduced to well 
 within 1.0 ergs/cm 2 s sr cm~l after accounting for the thermal conditions 
 of the instrument by means of equation (IV-3). 
 
 As mentioned above, the random error of a M~ second radiance sample 
 obtained by any channel was found to be about 0.5 ergs/cm 2 s sr cm"-'- (i.e., 
 0.3°C of scene temperature). Comparisons of the calibrated output radiances 
 indicated interchannel relative accuricies of better than 0.5 ergs/cm 2 s sr 
 cm~T. 
 
 The absolute accuracy of channel output radiance is more difficult to 
 assess because it depends upon the effective emissivity of the blackbodies 
 as well as on the absolute accuracy of the blackbody thermistors . An esti- 
 mate of the absolute accuracy of the output radiance was obtained by compar- 
 ing the scene brightness temperature, measured by channel 5, the most opaque 
 CO2 channel, with the temperature, measured by the aircraft platinum-wire 
 thermometer. The brightness temperature measured by channel 5 at low alti- 
 tides, where the atmosphere is opaque to 15-ym radiation, or within opaque 
 clouds, should be close to the environmental air temperature. Figure IV-2, 
 
23 
 
 8.3- 
 
 8.2 
 
 8.1 
 
 80 
 
 M 
 
 1 7.9 
 
 i- 
 p 
 
 7.8- 
 
 O 
 
 7.6 
 7.5 
 7.4 
 7.3 
 
 — i — i — i — r~| — i — i — i — i — | — i — r 
 
 * CALIBRATED OUTPUT VOLTAGE 
 
 VS WARM BB RADIANCE 
 
 • RAW OUTPUT VOLTAGE 
 
 VS WARM BB RADIANCE 
 
 ft 
 
 i — I — r 
 
 s . 
 
 J I L_L 
 
 J I L 
 
 J I L 
 
 175 
 
 170 E 
 
 165 _ 
 
 3 
 
 a. 
 i— 
 
 O 
 
 Q 
 111 
 »- 
 < 
 
 -160 = 
 
 155 
 
 155 160 165 170 
 
 WARM BLACKBODY RADIANCE (ergs/cm 2 s sr cm" 1 ) 
 
 Figure IV-1. — Warm blackbody calibration data obtained for ITPR channel 3 
 (13.4-ym). 
 
 ?<?0 
 
 280 
 
 270 
 
 260 
 
 250 
 
 240 
 
 230* 
 
 • CLOUD TEMPERATURE 
 
 ALOW LEVEL AIR TEMPERATURE 
 
 230 
 
 240 
 
 250 260 270 
 
 AIR TEMPERATURE (°K) 
 
 280 
 
 2*0 
 
 Figure IV-2. — ITPR channel 5 (14.1-um) measurements of cloud temperature and 
 low level air temperature vs. Rosemont measured air temperature, 
 
24 
 
 which shows the comparison of the two independent air temperature measure- 
 ments , indicates that the absolute accuracy of the ITPR brightness tempera- 
 ture measurements is within the 1°C absolute accuracy of the Rosemont thermo- 
 meter measurements. The apparent achievement of 1 percent absolute accuracy 
 and 1/2 percent relative accuracy for radiance observations in the highly 
 unstable aircraft environment is considered remarkable. 
 
 Finally, figure (lV-3) is an example of a computer plot of measured 
 brightness temperatures for a small portion of flight 3 over the eastern 
 Pacific. Low stratus clouds existed during the observation period. The 3- 
 step "staircases" are measurements of the temperatures of the cold housing, 
 and warm blackbody calibration targets. The other "brightness temperatures" 
 are the earth-atmosphere scene temperatures. The high relative accuracy of 
 the brightness temperatures measured by ~:he various channels is clear from 
 the calibration data. The stability of the observations is indicated by the 
 lack of significant variation in brightness temperatures in the atmospheric 
 window channel (channel 2) during large variations in aircraft altitude. At 
 low altitudes all channels observe the same brightness temperature because 
 there is little vertical temperature variation in the atmosphere beneath 
 the aircraft, and the ocean and air temperatures are nearly the same. The 
 close examination of the ITPR data, a sample of which is given in the 
 appendix, will permit the reader to judge for himself the reliability of the 
 airborne ITPR radiance observations. 
 
 V. CLEAR-COLUMN RADIANCE DETERMINATION 
 
 Introduction 
 
 Future Nimbus satellites will carry an Infrared Temperature Profile 
 Radiometer (ITPR)» and ITOS weather satellites a similar Vertical Temperature 
 Profile Radiometer (VTPR) instrument to measure vertical profiles of 
 temperature and water vapor in the earth's atmosphere. The radiation from 
 clear columns of air is required for the derivation of temperature and mois- 
 ture profiles from high in the atmosphere to the earth's surface. Because 
 most of the earth is covered by varying amounts of clouds , a method is needed 
 for estimating the equivalent clear-column radiance for the many areas where 
 the radiometer's field of view is partially filled by clouds. A method for 
 
 calculating the clear-column radiance from the observed total radiance has 
 been suggested previously (Smith, 1968). One of the primary objectives of 
 NASA Convair-990 brassboard ITPR flights during June 1970 was to collect 
 data to test this technique. 
 
 Analytical Solution 
 
 The solution for calculating the clear-air radiance contribution to the 
 total radiance measured over a partly cloudy atmosphere was presented by 
 Smith (1969). Briefly, the clear-column radiance for any frequency, v, is 
 obtained from two spatially independent radiance measurements through the 
 solution of 
 
 I clr (v ) = ^0_- _N*I 2 (v) (V-l) 
 
 (1-N*) 
 
25 
 
 23 ID 23 20 
 
 hSc <H)i*Cal*K Bro ,H<ciM~Sc © ^h St ©^fCal^H Overcast Stratus St©— ft: aH* St © *fCaH 
 Stratocumulus 
 
 280 L 
 
 J i I , L 
 
 •L 
 
 ., 
 
 J i 1 i I 22R. 
 
 CH I TEMP 
 1 
 
 21 SO 22 22 10 22 20 22 30 22 40 22 50 23 
 
 TIME (GMT) 
 
 23 10 23 20 
 
 Figure IV- 3. --Computerized plot of measured brightness temperature for 
 all ITPR channels during a portion of Flight 3. 
 
26 
 
 where I c i r ( v ) is "the clear-column radiance and Ij_(v) and Io(v) are the two 
 spatially independent radiance measurements. The parameter N* is the ratio 
 of the fractional cloud covers of the two fields of view. N* is determined 
 from corresponding atmospheric "window" radiometric observations, I(w). It 
 follows from (V-l), applied to the window region, that 
 
 N* = H = I G lr (w > - flfo) (V_ 2 ) 
 
 N 2 I clr^ w ^ " J 2^^ 
 
 where the clear-air radiance for the window region is assumed known. I c i r ( w ) 
 will be determined from the simultaneous ll-ym and 3.7-ym window measurements 
 to be obtained by the spacecraft version of the ITPR (Smith and Jacob, 1972). 
 Elements 1 and 2 are chosen so that Ij_(w)>l2(w) , which restricts N* to 
 1>N*>_0 . 
 
 The above solution for the clear-column radiance is valid only when the 
 geographical variation of observed radiance is due to a variation of frac- 
 tional cloud cover in the adjacent fields sampled. A variation of either 
 atmospheric temperature or cloud height would produce erroneous values of N* 
 and I c -i r ( v )« Therefore, the two spatially independent observations should be 
 geograpnycally close to each other so that variations in the observed radi- 
 ance will tend to be caused only by cloud cover variations. The ITPR and 
 VTPR are designed for high spatial resolution and contiguous sampling to 
 ensure geographically close observations, to increase the probability of 
 clear fields of view, and to produce a large number of independent estimates 
 of clear-air radiance for a given geographical area. 
 
 The "noise" level of the deduced clear-air radiances will be larger than 
 the measurement noise. It can be seen from equation (V-l) that the clear- 
 air radiance noise level is about 1/(1-N") times as large as the measurement 
 noise. Consequently, the instrument noise level must be kept relatively low. 
 On the other hand, the spatial resolution must be sufficiently high so that 
 most of the N* values will be much less than unity. The satellite versions 
 of the ITPR and VTPR temperature sounding radiometers have been designed to 
 scan spatially and contiguously with instantaneous resolutions of 21 and 30 
 n.mi., respectively, and to achieve noise levels of less than 0.5 percent 
 of the signal levels (i.e., 200/1 signal-to-noise ratios). 
 
 Aircraft Test Results 
 
 On June 12, 1970, high-altitude (41,000 ft) ITPR radiance observations 
 were obtained above broken altocumulus and stratocumulus clouds over the 
 Pacific Ocean at 46°N, 133°W. Clear-air measurements were obtained on 
 either side of the broken cloud region, and clear-air radiances were calcu- 
 lated from the cloud- contaminated observations. 
 
 Figure V-l shows the measured window radiances (ergs/cm z s sr cm - - 1 -) 
 during the period. Clear observations were obtained near 23:37:20 and 
 23:44:20 GMT. The actual clear-air radiance measured by channel 2 was about 
 84.0 ergs/cm 2 s sr cm~l (279°K). Cloud-contaminated radiances measured in 
 the window channel were as low as 50 ergs/ cm 2 s sr cm~l (250°K). 
 
27 
 
 JUNE 12, 1970 ITPR Channel 2 (ll.l^.m) 
 
 Figure V-l. — "Window" radiances measured by ITPR 11.1-ym C0 2 channel, 
 
 JUNE 12, 1970 ITPR 
 
 23:34 :35 :36 .37 :38 :39 :40 :41 :42 :43 :44 23:45 
 
 TIME 
 
 Figure V-2. — N* distribution calculated for adjacent fields of view from 
 11.1-ym radiance measurements. 
 
28 
 
 Assuming a clear-air window spectral radiance of 84.0, we calculated N* 
 for the adjacent fields of view which were observed about 4 seconds apart. 
 Figure V-2 shows the resulting distribution of N*. Values of the clear- 
 column radiances were then calculated from the adjacent observed radiances 
 in the three-temperature-sounding CO2 channels. The values for N*>0.8 are 
 shown together with the measured radiance distributions in figures V-3, V-4, 
 and V-5. 
 
 It can be seen from figures V-3, V-4, and V-5 that some of the infrared 
 clear-air radiances are erroneous, particularly in the region where a large 
 amount of cloudiness exists (e.g., 23:38 to 23:44 GMT). Some erroneous 
 values were calculated because N* is relatively high (greater than 0.5 
 between 23:38 and 23:44 GMT), and in some cases the variation in radiance 
 probably resulted from variations in cloud heights rather than differences 
 in cloud amounts (the field of view contained both altocumulus and strato- 
 cumulus ) . However, many of the estimates of clear-column radiance are in 
 fair agreement with the observed clear-air radiances measured at 23:37:20 and 
 23:44:20 GMT. 
 
 Figures V-6, V-7, and V-8 show histograms of the clear-column radiances 
 deduced from the cloud- contaminated radiances measured between 23:38 and 
 23:44 GMT. The values of the most frequently occurring estimates agree 
 closely with the observed clear-air radiances. The mean clear-column radi- 
 ance values, I c j-p( v ) 5 defined as the frequency-weighted average of the mode 
 value and values of the two adjacent class intervals, agree with the measured 
 values of clear-air radiance quite well considering the instrument noise. 
 
 Conclusion 
 
 The aircraft test results presented here indicate that the clear-air 
 radiance contribution to radiances observed with a partial cloud cover 
 within the field of view can be deduced with the accuracy needed for calcu- 
 lating temperature profiles down to the earth's surface. (This conclusion 
 is also borne out by other examples not presented here.) Since the earth's 
 atmosphere, when viewed on a synoptic scale (i.e., horizontal scale of 300 
 to 500 km), is covered by broken clouds, this method applied to appropriate 
 satellite measurements should make possible the determination of atmospheric 
 temperature distribution on a synoptic scale over almost the entire globe. 
 
 VI. AIRCRAFT-DEDUCED ATMOSPHERIC TRANSMITTANCES 
 
 Introduction 
 
 Vertical profiles of upwelling (or downwelling) radiance, as observed 
 by an airborne radiometer, can be used to determine the transmittance of the 
 atmosphere to the sensed radiation. The solution for atmospheric trans- 
 mittance from the radiance profile is obtained through a solution of the 
 differential equation of radiative transfer. The inference of the physical 
 properties of the atmosphere (e.g., distribution of its temperature and water 
 vapor) from satellite radiance observations requires knowledge of the 
 atmosphere's transmission as a function of optical depth, pressure, and 
 temperature. The observation of the radiative transmittance properties of 
 
29 
 
 JUNE 12, 1970 ITPR Channel 3 (l3.4yu.rn) 
 
 90 r 
 
 85 
 
 80 
 
 75 
 
 LU 
 
 u 
 z 
 
 < 70 
 
 a 
 < 
 
 Of 
 
 65 
 
 60 
 
 55 
 
 50 L 
 
 Observed Radiance 
 
 • Calculated Clear-Column Radiance 
 
 23:34 :35 
 
 :36 
 
 .37 
 
 :38 
 
 :39 :40 
 
 TIME 
 
 :41 
 
 :42 :43 :44 23:45 
 
 Figure V- 3. --Observed radiances (solid line) and calculated clear- column radi- 
 ance (dots) for the ITPR 13.4-um C0 2 channel. 
 
 JUNE 12, 1970 ITPR Channel 4 (l3.7yum) 
 
 50 Li 
 
 Observed Radiance 
 
 • Calculated Clear-Column Radiance 
 
 23:34 :35 :36 .37 :38 :39 :40 
 
 TIME 
 
 •41 
 
 :42 :43 :44 23:45 
 
 Figure V-4. — Observed radiances (solid line) and calculated clear- column 
 (dots) for the ITPR 13.7-um C0 2 channel. 
 
30 
 
 
 JUNE 12, 1970 ITPR Channel 5 (M.ljum) 
 
 n i i 1 1 i 1 1 | [- 
 
 
 
 Observed Radiance 
 
 
 
 • Calculated Clear-Column Radiance 
 
 
 65 
 
 _ 
 
 
 H 60 
 u 
 z 
 < 
 
 at 
 
 • 
 
 - 
 
 50 
 
 
 - 
 
 45 
 
 
 - 
 
 40 
 
 l 1 I I i l I I 1 1 
 
 I l 
 
 23:34 :35 
 
 :36 
 
 .27 
 
 :38 
 
 :39 :40 
 
 TIME 
 
 .41 
 
 :42 
 
 :43 
 
 :44 23:45 
 
 Figure V-5. — Observed radiances (solid line) and calculated clear-column 
 
 6? 
 
 u 
 
 z 
 
 UJ 
 
 oc 
 ac 
 
 3 
 U 
 U 
 
 O 
 
 >- 
 u 
 
 z 
 
 UJ 
 
 o 
 
 radiance (dots) for the ITPR 14.1-ym CCU channel, 
 
 35 
 
 30 
 
 25 
 
 20 
 
 15- 
 
 10 
 
 TIME INTERVAL: 23:38 -23:44 GMT 
 TOTAL NUMBER = 21 
 
 I CLR (3) = 83.4 ergs/cm 2 s sr cm" 1 
 
 CLEAR AIR RADIANCE MEASURED AT 
 23:37:20 = 83.3 ergs/cm 2 s sr em -1 — 
 23:44:20 = 83.8 ergs/cm 2 s sr cm" 1 
 
 80 
 
 81 
 
 82 
 
 83 
 
 84 
 
 85 
 
 — r~ 
 86 
 
 —r~ 
 87 
 
 88 
 
 89 
 
 90 
 
 CLEAR COLUMN RADIANCE 
 
 Figure V-6. --Histogram of clear- column radiances deduced from cloud-contami- 
 nated radiances measured in the 13.4- ym CO2 channel. 
 
31 
 
 u 
 
 z 
 
 UJ 
 
 ee. 
 
 OL 
 
 Z> 
 U 
 U 
 
 O 
 
 >- 
 u 
 
 z 
 
 o 
 
 UJ 
 
 OL 
 
 35 
 
 30 
 
 25 
 
 20 
 
 15 
 
 10- 
 
 5- 
 
 TIME INTERVAL: 23:38-23:44 GMT 
 TOTAL NUMBER ■ 21 
 
 70 
 
 71 
 
 72 
 
 ICLR (4) = 73.3 ergs/cm 2 s sr cm" 1 
 
 CLEAR AIR RADIANCE MEASURED AT 
 23:37:20 = 72.7 ergs/cm 2 s sr cm" 1 
 23:44:20 = 73.8 ergs/cm 2 s sr cm -1 
 
 
 73 
 
 74 
 
 75 
 
 — r— 
 76 
 
 77 
 
 78 
 
 79 
 
 —I 
 80 
 
 CLEAR COLUMN RADIANCE 
 
 Figure V- 7. --Histogram of clear-column radiances deduced from cloud-contami- 
 nated radiance measured in the 13.7^um C0~ channel. 
 
 35i 1 1 1 1 1 — i 1 1 — i 
 
 z 
 
 UJ 
 
 ae 
 ee 
 
 3 
 <J 
 O 
 
 O 
 
 u 
 
 z 
 
 UJ 
 
 o 
 
 30 
 
 25 
 
 20 
 
 TIME INTERVAL: 23:38-23:44 GMT 
 TOTAL NUMBER =21 
 
 ICLR (5)= 61.2 ergs/cm 2 s sr cm" 1 
 -CLEAR AIR RADIANCE MEASURED AT 
 
 23:37:20 = 61.4 ergs/cm 2 s sr cm *1 
 23:44:20 = 61.7 ergs/cm 2 s sr cm"' 
 
 15- 
 
 10 
 
 55 
 
 56 
 
 — r~ 
 57 
 
 — r- 
 58 
 
 59 
 
 60 
 
 T" 
 
 61 
 
 62 
 
 63 
 
 64 
 
 65 
 
 CLEAR COLUMN RADIANCE 
 
 Figure V-8. --Histogram of clear-column radiances deduced from cloud contami- 
 nated radiances measured in the 14.1-um CO2 channel. 
 
32 
 
 the real atmosphere has obvious advantages over the estimation of atmospheric 
 transmission solely from theory or laboratory measurements. 
 
 Mathematical Solution 
 
 The differential equation of radiative transfer, known as Schwarzchild's 
 Equation, can be written for an atmosphere in local thermodynamic equilibrium 
 
 as 
 
 dl v = k v (B v - I v ) du (VI-1) 
 
 where I v is the monochromatic radiance, B is the monochromatic source func- 
 tion which is the Planck radiance for a medium in thermodynamic equilibrium, 
 and k v is the monochromatic mass absorption coefficient. The incremental 
 optical path length 
 
 du = pdz (VI-2) 
 
 where p is the density of absorbing medium and dz is the incremental geo- 
 metric path length. 
 
 The monochromatic transmittance of the medium is given by 
 
 x v = exp (-/k v du) (VI-3) 
 
 thus (VI-1) may be written as 
 
 T v ( P } dIv(p) + CB v (p) - I v (p)] dT v (p) = (VI-4) 
 
 d In P d In p 
 
 where lnp, the natural logarithm of pressure, has been chosen as the verti- 
 cal coordinate. Integrating (VI-4) over the frequency interval sensed by a 
 particular channel of the ITPR we have 
 
 f dl v (p) ^dv + r [B v (p)-I v (p)] dT v<P> <J> v dv = (VI-5) 
 
 d In p d In p 
 
 where <jk is the spectral response function (see figure II-l). 
 
 Consider the following definitions for a spectral mean of any quantity, 
 
 % 
 
 Q = /Jq, % dv/r ^dv, (vi-6) 
 
 and the departure of the quantity from its mean; 
 
 QJ = % - Q ; (vi-7) 
 
 such that , 
 
 r Q'v* v dv = 0. (VI-8) 
 
33 
 
 Making use of (VI-6), (VI-7), and (VI-8), Equation (VI-5) may then be 
 written as 
 
 dl(p) + CB(p) - Kp)] d In x(p) 
 
 d In p d In p Up; 
 
 where 
 
 C(p) = 
 
 IJ(p) dT v (p) - BMp) dT v (p) - K d] v ,(p) 
 d In p d In p d In p 
 
 (VI-9) 
 
 We wish to solve (VI-9) for x given observations of I and B as functions 
 of In p. The solution, however, is complicated by the fact that the covari- 
 ance terms on the right of (VI-9) are not observed. Let us for the moment 
 assume no variation of monochromatic transmittance with frequency so that the 
 right-hand side of (VI-9) becomes zero. This case yields a first order 
 approximation of the mean transmittance, denoted as x . Integrating (VI-9), 
 with C(p) = 0, gives 
 
 T (P ,P) = exp {/ 
 
 1 dI<P> d in p[ 
 
 P ° CB( P )-T( P )] d ln P 
 
 (VI-10) 
 
 where p is any boundary pressure level. By definition, t (p ,p ) = 1. The 
 first order approximation of the transmittance profile, x (p p ), can be cal- 
 culated directly from a measured radiance and temperature (Planck radiance) 
 profile. 
 
 The actual transmittance profile, i(p ,p), in which C(p)^o, is then 
 
 T (P >P) = T (P 'P) ex P {j ". 
 
 CJjlL 
 
 J o [B(p)-I(p)] 
 
 d ln p} 
 
 (VI-11) 
 
 The exponential factor can be thought of as a correction term. Since the 
 covariance term, C(p), is not observable, it must be estimated from theo- 
 retical principles. The correction term is estimated from theoretically 
 calculated radiances and transmittances . Using (VI-9), 
 
 C(p) « dl(p) + [B(p) - I(p)] d ln t(p) 
 d ln p d ln p 
 
 (VI-12) 
 
 where the circumflex (a) indicates a calculated value. Combining (VI-9), 
 (VI-11), and (VI-12) yields 
 
 (VI-13) 
 
 x~(p ,p)=exp -/ P — L. / d[I(p)-I(p)]- [B(p)-I(p)] d ln 7(p) (d In p] 
 
 ° L Po [B(p)-Kp)] 1 dlnp dlnp ) J 
 
 Equation (VI-13) is used to calculate the atmospheric transmittance pro- 
 files pertaining to the ITPR spectral intervals from the observed radiance 
 and temperature (Planck radiance) profiles. 
 
34 
 
 Computational Procedure 
 
 The ITPR aboard the CV-990 measured the upward radiance, I , as a func- 
 tion of pressure in its five spectral channels. Other instrumentation pro- 
 vided measures of air temperature and relative humidity. Vertical profiles 
 were obtained over a cloudless sea on three occasions, during flights 1, 8, 
 and 9. The observational procedure was one of flying 5-minute legs at 
 various altitudes above a specific earth location. Table VI-1 summarizes the 
 average values of radiance, air temperature, and relative humidity for each 
 altitude leg of the three vertical profiles. 
 
 Each profile variable was interpolated to 100 levels equally spaced in 
 the natural logarithm of pressure, in order to ensure accurate quadrature in 
 the numerical computations. Air temperature and relative humidity were 
 interpolated linearly with respect to lnp. The measured radiances were inter- 
 polated on the basis of the theoretically calculated radiances by assuming 
 that the discrepancy between measured and calculated radiance within each 
 layer is linear with respect to the logarithm of pressure. 
 
 The theoretically calculated radiances are obtained from the equation 
 of radiative transfer in integral form; 
 
 I(p a )=B(p )t( P ,p ) - / Ps B(p) dx(p a ,p) , (VI-14) 
 
 p d in p 
 
 d In p 
 
 where p a and p are the pressures at the instrument and surface altitudes , 
 respectively. 
 
 The transmission of atmospheric water vapor, for the rotational H2O 
 band, is assumed to be given by the "Random Band Model", 
 
 Vp a ,p) = expi -(S/6)Uw ) (Vi-15) 
 
 (V 1 + (S/TTCOUW j 
 
 where S is the mean line strength, 6 is the mean line spacing and o is the 
 mean half-width of the lines. The path length of water vapor 
 
 n = i / P w(p) dp (VI-16) 
 
 g Pa 
 
 where g is the acceleration of gravity and w is the water vapor mixing ratio. 
 
 The transmission of the atmospheric carbon dioxide for the 15-um C0„ 
 band is assumed to be given by the "Ordered Band Model" , 
 
 x c (p a ,p) = 1-erf |V(m*S/6 2 )U c \ (VI-17) 
 
 The path length of carbon dioxide. U (p), is assumed to be a constant 0.24-7 
 atm cm/mb. Assuming no selective absorption, the transmission in the 11-ym 
 "window" spectral region is expressible in terms of the continuum absorption 
 
35 
 
 Table VI-1. — Measured radiances, temperature, and relative humidity 
 
 Pressure 
 
 J (mb) 
 
 Measure 
 
 d Radiances (erg 
 
 s/cm^ s 
 
 sr cm 1) 
 
 Temp 
 
 Rel. Hum. 
 
 
 
 
 Ch 1 
 
 Ch 2 
 
 Ch 3 
 
 Ch 4 
 
 Ch 5 
 
 °K 
 
 Percent 
 
 FLT-1 (44°N, 
 
 129 
 
 D W) 
 
 
 997 
 
 
 
 134.93 
 
 100.94 
 
 121.94 
 
 124.49 
 
 126.82 
 
 289.1 
 
 73 
 
 970 
 
 
 
 136.00 
 
 100.15 
 
 122.42 
 
 125.30 
 
 128.10 
 
 291.0 
 
 48 
 
 926 
 
 
 
 137.08 
 
 100.78 
 
 123.07 
 
 125.95 
 
 129.39 
 
 292.0 
 
 5 5 
 
 854 
 
 
 
 136.81 
 
 101.41 
 
 123.07 
 
 125.78 
 
 128.25 
 
 291.0 
 
 39 
 
 698 
 
 
 
 131.99 
 
 99.37 
 
 118.57 
 
 119.68 
 
 119.55 
 
 284.0 
 
 35 
 
 573 
 
 
 
 124.62 
 
 97.97 
 
 110.88 
 
 109.28 
 
 105.64 
 
 271.0 
 
 50 
 
 466 
 
 
 
 120.99 
 
 97.63 
 
 105.10 
 
 100.95 
 
 94.93 
 
 262.0 
 
 29 
 
 337 
 
 
 
 120.99 
 
 97.22 
 
 99.63 
 
 91.31 
 
 81.44 
 
 246.0 
 
 22 
 
 FLT-8 (34°N, 
 
 130< 
 
 >W) 
 
 
 
 
 
 
 
 
 1017 
 
 
 
 138.05 
 
 100.80 
 
 124.35 
 
 126.90 
 
 129.72 
 
 290.0 
 
 85 
 
 1003 
 
 
 
 136.74 
 
 100.17 
 
 123.62 
 
 125.85 
 
 128.54 
 
 289.6 
 
 63 
 
 932 
 
 
 
 132.84 
 
 100.25 
 
 120.86 
 
 122.79 
 
 124.00 
 
 285.0 
 
 6 2 
 
 754 
 
 
 
 129.41 
 
 99.40 
 
 117.87 
 
 118.92 
 
 119.08 
 
 281.3 
 
 45 
 
 505 
 
 
 
 113.87 
 
 98.19 
 
 105.74 
 
 102.34 
 
 97.82 
 
 264.0 
 
 35 
 
 238 
 
 
 
 104.43 
 
 95.09 
 
 91.81 
 
 82.05 
 
 70.00 
 
 224.0 
 
 13 
 
 FLT-9 (28°N, 93°W) 
 
 1017 
 
 153.61 
 
 120.10 
 
 144.39 
 
 146.21 
 
 148.98 
 
 301.5 
 
 100 
 
 983 
 
 150.53 
 
 119.41 
 
 141.94 
 
 142.73 
 
 145.20 
 
 299.0 
 
 88 
 
 853 
 
 140.33 
 
 115.98 
 
 134.88 
 
 133.87 
 
 132.81 
 
 292.9 
 
 60 
 
 716 
 
 131.59 
 
 112.94 
 
 126.34 
 
 123.68 
 
 120.95 
 
 285.0 
 
 47 
 
 601 
 
 125.79 
 
 110.95 
 
 119.36 
 
 115.28 
 
 109.48 
 
 275.2 
 
 30 
 
 490 
 
 122.28 
 
 109.79 
 
 113.21 
 
 107.02 
 
 98.72 
 
 265.0 
 
 22 
 
 365 
 
 119.96 
 
 108.64 
 
 106.46 
 
 96.64 
 
 84.94 
 
 249.0 
 
 20 
 
 209 
 
 117.15 
 
 107.82 
 
 98.03 
 
 84.14 
 
 67.51 
 
 218.6 
 
 37 
 
36 
 
 coefficient, 3, by 
 
 x wD (p a ,p) - exp )- kU w [ (VI-18) 
 
 where k is the continuum absorption coefficient. The temperature and 
 pressure dependence of the line parameters S, a, and k is assumed to be 
 accounted for by the usual forms (Smith, 1969) 
 
 '"«)'"*'"«) 
 
 S/T^ < ' - ;•. | J oV'/lV:\ m (vr-19 
 
 where S , a , and k Q are fixed values for standard temperature and pressure, 
 T Q and p , values of 273°K and 1000 mb. The effective temperature and 
 pressure, T e and p , of an absorbing layer (p a »p) are defined by 
 
 T e = £ T du dp // du dp 
 
 F a dp y & dp 
 
 p a /r p 
 
 P ^u dp // 
 
 a dp *a dp 
 
 (VI-20) 
 
 P e = ' p P du dp // du dp 
 
 Howard, Burch , and Williams (1955) showed from empirical data that (VI-15) 
 can be expressed as , 
 
 t w (p a ,p) = exp -1.97LU W (VI-21) 
 
 \\j 1 + 6 . 57LU W ) 
 
 for a given temperature and pressure, where L is a generalized absorption 
 coefficient. It then follows from (VI-15), (VI-19), and (VI-21) that 
 
 * w (p a>P ) - exp( - 1 " 97 L o ( W n »w | (VI-22) 
 
 a j _ 
 
 I V 1 + 6.57L (T e /T ) n+1/2 (p e /p )^U w ) 
 
 where L is the generalized absorption coefficient for standard pressure and 
 temperature. In a similar manner (VI-17) can be expressed as 
 
 A 
 
 T c (p a ,p) =1- erf IWLl^r /^.\ m U 
 
 W(k) 
 
 (VI-23) 
 
 and (VI-18) by 
 r wd ( Pa 
 
 5-dCPa.P) ~- e *P ■ L n /M ' /Pe\ m U, I (VI-24) 
 
 ft) " fe) ' " 
 
 where in (VI-23) the -1/2 temperature exponent has been absorbed by the n. 
 
37 
 
 Thus the atmospheric transmissions for spectral channels 1 and 2 are calcu- 
 lated by equation (VI-22) and (VI-24). The atmospheric transmissions for 
 the 15-ym carbon dioxide channels, (3), (4), and (5), which are influenced 
 by H2O as well as CO2 lines, are calculated as the product of (VI-22) and 
 (VI-23), (i.e., t = T-,. T ). The transmission model parameters (L_ s n, and 
 m) were determined from the theoretical data given by Moller and Raschke 
 (1963) and are presented in table VI-2 below. 
 
 Table VI-2. — Theoretical transmission model parameters 
 
 Water vapor Carbon dioxide 
 
 Channel L m n L m 
 o o 
 
 1 3.550 0.72 1 - 
 
 2 0.158 1.00 - 
 
 3 0.347 .72 0.003 .66 7 
 
 4 0.380 .72 0.010 .66 6 
 
 5 0.437 .72 0.028 .66 5 
 
 As mentioned earlier, the measured radiances were interpolated to levels 
 within a measurement layer assuming that 
 
 A 
 
 d[I(p) - I(p)3 = K = constant (VI-25) 
 
 d In p 
 
 Integrating (VI-25) between the limits pl and p, where P L is the layer base 
 pressure, gives the interpolated measured radiances 
 
 T(p) = I(p) + [I(p L ) - I (p L )] + K In (p/p L ) (VI-26) 
 
 The slope K is found from (VI-26) for p=p u where p u is the pressure at the 
 top of the layer. 
 
 K = [T(p u ) - I(p u )] - CT(p L ) - I(p L )] (VI-27) 
 
 ln (Pu/PL) 
 
 To ensure that the calculated radiance profile will be a close approximator 
 of the true profile, the generalized water vapor absorption coefficients for 
 channels (1) and (2) and the generalized CO2 absorption coefficients for 
 channels (3), (4), and (5) were specified for each flight as those values 
 which yielded agreement between I(p) and I(p) for the highest level of the 
 profile . 
 
38 
 
 The transmission for each layer was computed on the basis of the 
 measured and calculated radiance profiles using (VI-13) written in its 
 
 numerical form 
 
 ( N-l. A A 
 
 x(p L ,p u )=exp 1-Z )[I(i+l)-I(i+l)]-[I(i)-I(i)]-[B(i+l/2) 
 
 .-i(i+l/2)][lnT(I+l)-lnT(i)]iaBU+l/2>-I(I+l/2)}( (vi-28) 
 
 where N is the number of the quadrature levels for the layer and 
 
 Q(i+l/2) E [Q(i) + Q(i+l)]/2 (VI-29) 
 
 where Q denotes any quantity. 
 
 Results 
 
 Table VI-3 lists the atmospheric transmittances computed from the mea- 
 sured radiances and the corresponding optical properties of the observed 
 layers. The pure CO2 transmittances for channels 3, 4, and 5 were obtained 
 by dividing the total transmittance values by the model-determined water 
 vapor transmittances . It is somewhat difficult to assess the reliability of 
 these transmittances. One immediately questions their dependence upon the 
 theoretically calculated .values used in (VI-13). To assess this dependence, 
 the transmittances for flight 9 were recomputed using different absorption 
 coefficients in the theoretical band models. Table VI-4 shows the results. 
 The first-order approximation, t q , is independent of the model transmittance 
 and calculated radiance profile except for their minor influence (<.001 per- 
 cent) on the measured radiance interpolation. As may be seen from table 
 VI-4, the final transmittance values are only weakly dependent upon the model 
 values used. 
 
 Figures VI-1 through VI-5 shows plots of the radiance derived H2O and CO2 
 transmittance values versus the pressure and temperature scaled mass of these 
 gases. Here the pressure exponent was assumed to be unity. The temperature 
 exponent was assumed to be zero for channels 1 and 2. 
 
 For channels 3, 4, and 5 the temperature exponent and the generalized 
 absorption coefficients of the ordered band model were determined by a non- 
 linear least-squares procedure. The result minimizes the rms difference 
 between the observed transmittances and those calculated using the ordered 
 band model. 
 
 The scatter revealed in these figures appear to be due primarily to 
 inaccuracies in the estimated water vapor path lengths. This is because the 
 scatter becomes successively smaller for those spectral channels which are 
 less affected by water vapor. For instance, channel 1, whose radiation is 
 completely dependent on the water vapor distribution, has the greatest 
 amount of scatter. On the other hand, channel 5, whose radiation is almost 
 independent of water vapor, has the least amount of scatter. Channel 3, 
 whose radiation is due to both water vapor and carbon dioxide, has an 
 
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 CD 
 
 m 
 
 cD 
 
 CO 
 
 co 
 
 m 
 
 CD 
 
 CO 
 
 =t 
 
 cD 
 
 d 
 
 CD 
 
 cD 
 
 &-< 
 
 L^s 
 
 1 
 
 1 
 
 CD 
 
 1 
 
 CD 
 
 1 
 
 CO 
 
 H 
 
 CO 
 
 Eh 
 
 CD 
 
 1 
 
 CD 
 
 1 
 
 CD 
 
 i 
 
 m 
 
 1 
 
 m 
 
 O 
 
 J 
 
 ro 
 
 ro 
 
 ro 
 
 CD 
 
 CD 
 
 c~- 
 
 J 
 
 ro 
 
 J 
 
 O 
 
 O 
 
 O 
 
 CD 
 
 CD 
 
 CD 
 
 U4 
 
 ro 
 
 co 
 
 ro 
 
 d 
 
 d- 
 
 LO 
 
 Pl. 
 
 CM 
 
 Ph 
 
 CM 
 
 CM 
 
 CM 
 
 co 
 
 CO 
 
 J" 
 
40 
 
 Table VI-4. — Transmittances computed from flight 9 radiance data using two 
 different model transmittance values (t-j_, t 2 ) for the 209- to 
 365-mb layer and their differences (6 ). 
 
 1st- order Model Final 
 
 Channel approx. (t q ) Eq (10) Value (x) Value (t) Eq (13) 
 
 x 1 0.934 0.903 0.902 
 
 T 2 .933 .866 .897 
 
 6 T .001 .037 .005 
 
 T, .988 .997 .988 
 
 ^2 .988 .994 .988 
 
 6 .000 .003 .000 
 
 T 1 .836 .798 .772 
 
 12 .836 .811 .773 
 
 6 .000 -.013 -.001 
 
 •1 
 
 T 2 
 
 ,693 .653 .639 
 
 x _2_ .694 .661 .638 
 
 6 -.001 -.008 .001 
 
 379 .394 .401 
 
 T _2_ .378 .446 .392 
 
 6^ .001 -.052 .009 
 
41 
 
 0.3 
 0.4 
 0.5 
 0.6 
 0.7 
 0.8 
 0.9JA 
 
 1.0 
 0.01 
 
 I I I I I II I I 
 
 T 1 — I I I I I 
 
 O 
 O 
 
 
 A 
 A 
 
 © © 
 
 J I I l I I I I 
 
 532.5cm- 1 (Ch. 1) 
 Flight 1 © 
 Flight 8 D 
 Flight 9 A 
 
 I I I I I I 1 
 
 0.03 0.05 0.07 0.1 
 
 u w (p/p ) 
 
 0.3 0.5 0.7 1.0 
 
 Figure VI-1. — Radiance-derived ^0 transmittance values for channel 1, 
 
 0.88 
 
 TTT 
 
 T 1 I I I I I 
 
 0.90 
 
 
 0.92 
 
 
 0.94 
 
 
 0.96 
 
 
 0.98 
 
 & 
 
 100 
 
 i 
 
 
 
 01 
 
 o 
 
 A 
 A 
 
 © 
 
 898.0cm- 1 (Ch. 2) 
 Flight 1 © 
 Flight 8 □ 
 Flight 9 A 
 
 © 
 
 0.03 0.05 0.07 0.1 0.3 0.5 0.7 1.0 
 
 U w (p/ Po ) 
 
 Figure VI-2. — Radiance-derived H2O transmittance values for channel 2, 
 
42 
 
 0.0 
 
 L 
 
 1 1 
 
 1 1 1 1 1 1 1 
 
 1 
 
 t 
 
 r ■ " 
 
 i i i 
 
 I.I. 
 
 0.1 
 
 * c =l-erf 
 
 V L >/Po>( T /T )"U c 
 
 0.2 
 
 . = .00582 
 
 
 
 J 
 
 
 0.3 
 
 
 
 
 
 
 
 c 0.4 
 
 _ 747.0cm" 1 (Ch. 3) 
 
 
 
 
 
 
 O 
 
 Flight 1 
 
 
 
 °s 
 
 . 
 
 0.5 
 
 D 
 
 Flight 8 
 
 
 o 
 
 
 _ 
 
 
 A 
 
 Flight 9 
 
 j. 
 
 
 
 - 
 
 0.6 
 
 
 
 
 
 
 - 
 
 
 
 D 
 
 •£a 
 
 
 
 - 
 
 0.7 
 
 
 >^± 
 
 
 
 
 - 
 
 0.8 
 
 
 1 l i i4j*<i« A 
 
 1 
 
 
 1 1 1 
 
 1 1 1 
 
 
 1 3 5 7 10 30 50 70 100 
 
 U c (P/P )(T/T ) 4,5 
 
 Figure VI- 3. — Radiance-derived CO2 transmittance values for channel 3, 
 0.0 
 
 1 3 5 7 10 30 50 70 100 
 
 U C (P/P )(T/T ) 2 ' 5 
 
 Figure VI-4. --Radiance-derived CO2 transmittance values for channel M-, 
 
 
43 
 
 0.0 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.61- 
 
 0.7 
 
 708.0cm" 1 (Ch. 5) 
 O Flight 1 
 O Flight 8 
 A Flight 9 
 
 0.8 
 
 rr 
 
 j i i i i i i i i 
 
 i i i i i i i 
 
 1 3 5 7 10 30 50 70 100 
 
 U c (p/p ) (T/T ) 4 ' 7 
 
 Figure VI- 5. --Radiance-derived CCU transmittance values for channel 5, 
 
44 
 
 intermediate amount of scatter. (It is noted that for channels 1 and 2 the 
 scatter is caused by errors in U while for channels 3, 4, and 5 the scatter 
 shown is due to errors in x caused by erroneous estimates of t w . ) In all 
 cases the scatter produced by errors of t, which are due to radiance errors 
 and temperature profile errors , appear to be small compared to the scatter 
 produced by errors in the estimated water vapor path lengths. 
 
 Summary 
 
 This study shows that atmospheric transmittances can be determined from 
 airborne radiance profiles through a solution of the differential equation 
 of radiative transfer. Band models may be used to account for the non- 
 monochromatic characteristics of the measured radiation in the solution. 
 
 The objective of the transmittance observations is the formulation of 
 models that can be used to estimate atmospheric transmission as a function of 
 absorbing gas concentration, temperature, and pressure for the particular 
 spectral regions sensed by satellite-borne sounding radiometers. Accurate 
 knowledge of the atmospheric transmission functions is needed to determine 
 the temperature and water vapor profiles of the atmosphere from the satellite- 
 measured radiances . 
 
 This study indicates that highly accurate water vapor observations are 
 needed to formulate adequate transmission functions for spectral regions 
 whose radiation is absorbed by that gas. The inaccurate water vapor esti- 
 mates available for this study prevented the formulation of transmission 
 functions for the two spectral regions dominated by water vapor absorption. 
 
 It is proposed to use airborne experimental methods, similar to those 
 described here, to help define the atmospheric transmission functions of the 
 spectral channels of future satellite sounding radiometers. The necessary 
 aircraft measurements should be obtained with preflight models of the 
 satellite instruments. This method should decrease much of the current 
 uncertainty about the transmission functions caused by the extrapolation of 
 theory and laboratory observations to the real atmosphere. 
 
 VII. DETERMINATION OF CLOUD TRANSMITTANCE 
 
 Introduction 
 
 The determination of the temperature distribution within the atmosphere 
 to the earth's surface from satellite measurements of the upwelling radiance 
 requires that the atmospheric radiation be emitted from and pass through 
 cloud-free columns of air. However, because the earth always has some cloud 
 cover, it is necessary to estimate an equivalent "clear-column" radiance in 
 the presence of clouds . To aid in the development of procedures for making 
 such estimates it is useful to have information on the spectral transmission 
 characteristics of clouds. 
 
 As part of the experimental ITPR testing program, measurements were made 
 of the radiance profile and ambient temperature through various types of 
 clouds with the hope that some of their spectral transmission characteristics 
 
45 
 
 could be determined. Although it was not possible to make an extensive 
 study of these transmittances , two cases were studied in some detail; these 
 cases probably represent high- and middle-level clouds. Many more measure 
 ments will be needed for more extensive studies; however, the few results 
 obtained are encouraging, since they indicate that such radiance measure- 
 ments from aircraft can be utilized in studying the transmittance character- 
 istics of clouds. 
 
 Numerical Method 
 
 The Schwarzchild equation of radiative transfer in the absence of 
 scattering is generally written in the form, 
 
 d] v = ^ - 2^ (VII-1) 
 
 dty 
 
 where 1^ is the intensity of the radiation field, B. the intensity of the 
 blackbody radiance source, t^ is the optical path length in the medium, and 
 v is the wavenumber of the radiation. The optical path length t^ is given 
 by, 
 
 t v =/* k v (z») dz' (VII-2) 
 
 where k^ is the attenuation coefficient and z is the path length in the 
 medium. 
 
 For monochromatic radiation, the transmittance in the medium is 
 
 t(z) = e-f Z k (z») dz' = e" 1 ^ (VII-3) 
 
 V O V 
 
 Therefore, the optical path length in terms of the transmittance is 
 
 dT v = -T v dt^ (VIM) 
 
 Substituting this expression into eq (VII-1), the equation of radiative 
 transfer takes the form 
 
 \ dt v ' V\, = "^ dT v (VII-5) 
 
 Integrating eq (VII-5) over a bandwidth Av , the result is 
 
 (rdl - Id t) + ( T v ' d ^ ' - V dt v ')=-BdT- V dx v ' (VII-6) 
 where 
 
 OO OO 00 
 
 I 3 f o % v &> , B = ^o <KA ^ , 7 = / o Vv dv , 
 
 K^- 1 * T v ,=T v - 7 ' and 
 
 4^ is the instrumental response function. While the correlation terms 
 
46 
 
 in equation VII-6 are important in cloud-free regions of the atmosphere, the 
 scattering and absorption of radiation by water and ice particles in clouds 
 tend to supress the correlation. Therefore, they shall be neglected in the 
 information. Equation (VII-6) can then be written, 
 
 dx(p .,p) dl(p) (VII-7) 
 
 =t 
 
 (p ,p) Kp)-B(p) 
 
 o 
 
 where the explicit dependence upon the pressure levels is shown, p is a 
 reference level, such as the top or base of the cloud. 
 
 Integrating both sides of equation (VII-7) from p to p we obtain 
 
 
 In x(p ,p) - In T(p o ,P Q ) = + / dKpM/dp' dp (VII-8) 
 
 Pc 
 
 Kp')-B(p') 
 
 Since x(p ,p )=1, we obtain as a final result, 
 ^o o ' 
 
 x(p -p) = exp |-/ P dKpM/dp' dp I (VII-9) 
 
 Po_ 
 
 B(p')-Kp') 
 
 Equation (VII-9), therefore, enables one to determine the transmittance 
 x from a knowledge of the radiance profile, l(p), and the ambient tempera- 
 ture profile, T(p) (i.e., "B~(T(p))). In the experiment on the CV-990 flight, 
 the radiances and ambient temperatures were measured at a number of levels 
 in the cloud. Therefore, for practical applications one must approximate 
 equation (VII-9) for a finite number of pressure levels. The approximation 
 that was used may be written, 
 
 I 
 
 7(p Q ,p £ ) ■■ exp Z Cl(p m ) - Kp m _l)] / (VII-10) 
 
 m=l — •£" 
 
 [l(Pm>P m -i) - ^Pm'Pm-l )] 
 
 h u , '^^Vl 5 „*, , B(p b ) + B(p ) 
 
 where Kp^P^) = and B(p m ,p in _ 1 ) = g 
 
 In this form the transmit tances can be readily approximated directly from the 
 measurements . 
 
 When scattering cannot be neglected, equation (VII-1) must be generalized 
 
to 
 
 47 
 
 ydl v (y) =-I v (u)+w v / p(y,y')I v (n')dy' 
 dt ~ 
 
 + (1-%)B V 
 
 (VII-11) 
 
 where 
 
 1 / p(y,y' ) du' =1 (VII-12) 
 
 2 _1 
 
 p(y,y') is the scattering phase function which describes how the scattered 
 
 radiation is distributed with direction, y' and y are, respectively, the 
 
 cosines of the zenith angles of incidence and emergence, and oj is the frac- 
 
 . . . v 
 
 tion of incident radiation that is scattered by a small volume element. 
 
 Since the upward intensity of the radiation was measured, y=l in 
 equation (VII-11). Because the size of the scatterers is of the same order 
 as the wavelengths of the radiation, the major contributions to the integral 
 in equation (VII-11) occur in the vicinity of y'=l, when y=l. As a result 
 of this and the fact that I (y T ) varies only slightly with angle in the 
 angular region near y'=l, equation (VII-11) can be approximately written 
 
 dl^ = (l-oo )(B - I ) (VII-13) 
 
 dt 
 
 Similar to the derivation of the transmissivity for the case when 
 scattering was neglected, the transmissivity that results in the presence 
 of scattering is given approximately by 
 
 Po 
 
 x(p ,p) = exp -] 1 / [dl(p')/dp' 3( (VII-14) 
 
 1-W 
 
 I(p» )-B(p» ) 
 
 where _ f°° w a dv 
 
 (VII-15) 
 
 Jsing equation (VII-9), equation (VII-14) may be written 
 
 T(p„,p) = t (p o ,p) l-oo (VII-16) 
 
 Another useful form that equation (VII-16) may be written is obtained 
 by defining t (p ,p) to be the transmissivity through the cloud- free 
 atmosphere and "aT to be the value of lo in the absence of the gaseous 
 
48 
 
 constituents of the atmosphere. Then, 
 
 7(p o> p) =/l>a!£l p (VII " 17) 
 
 \x a (p o ,p)"o/ 
 
 Results of the Aircraft Measurements 
 
 The Convair-990 experimental program included 10 flights. On some of 
 these, measurements of the radiances and ambient temperatures were made as 
 the aircraft flew separate legs above, through, and below one or more cloud 
 decks . In this way we hoped to gather sufficient data to study the spectral 
 transmission characteristics of the clouds. However, because of insufficient 
 data, only two case studies could be examined in detail. 
 
 In the first case (flight 2), measurements were made of a deck of clouds 
 described as cirrus. These clouds in the vicinity of Spokane, Wash., had 
 tops at 27,200 feet and bases at about 15,000 feet. The first leg of the 
 cloud study portion of the flight was made beneath the cloud deck, the 
 second and third legs through the deck, and the fourth leg above the deck. 
 This effectively divided the cloud deck into three sublayers. 
 
 As the aircraft flew these legs , measurements of the radiances in five 
 separate channels were made every 0.03 seconds, and ambient temperature was 
 measured every minute. ' The mean radiance for each channel and the mean 
 value of the ambient temperature were computed for each flight leg. These 
 values and the equivalent blackbody temperatures corresponding to the meas- 
 ured radiances are listed in table VII-1. The blackbody radiances corre- 
 sponding to the ambient temperatures also are shown. 
 
 These radiances were then used in equations (VII-10) and (VII-16) to 
 compute estimates of the cloud transmittances , T ca . The transmittances 
 obtained are shown in figure VII-1 for w =0 and in figure VII-2 for TO" =0.5 
 as a function of the elevation from the base of the cloud. The trans- 
 mittances for each channel are connected by a smooth curve. While such 
 curves as shown in figure VII-2 are good representations of the actual vari- 
 ations of T Qa in most of the cloud, the variations at the base of the 
 cloud are questionable. It is quite possible that the transmittances approach 
 unity more quickly than indicated and then level off in a manner similar to 
 that shown for the top of the cloud . 
 
 Note that values of T ca in the window channel (2) are significantly 
 higher than those for the other channels, while channel 5, the most opaque 
 CO2 band, has quite low values. It is interesting that, toward the base of 
 the cloud, transmittances in the water vapor band (1) are lower than those 
 in the CO^ channels (3 and 4), while the values for channel 1 fall between 
 those of the two COo channels at higher levels. This is probably because of 
 the higher concentration of water vapor at the base. 
 
 To isolate the effects of water vapor and CCU on the transmittance 
 characteristics of the clouds , estimates were made of transmittances for 
 conditions of zero water vapor and zero CO2 concentrations. These 
 
49 
 
 pq 
 
 pq 
 
 CO 
 
 pq 
 
 CN 
 
 pq 
 
 pq 
 
 fJ 
 
 u 
 
 CD 
 (X 
 
 £ 
 
 Eh 
 
 CO 
 W 
 
 (X. 
 
 •H 
 
 C 
 
 o 
 •H nd 
 
 ■H 3 
 
 td o 
 
 > H 
 
 I 
 
 w 
 M 
 
 H 
 
 o 
 o 
 
 CD 
 
 en 
 
 CO 
 
 en 
 
 LO 
 
 en 
 
 CO 
 
 o 
 
 d 
 
 en 
 
 CM 
 
 cn 
 
 St 
 
 H 
 H 
 
 CO 
 
 en 
 
 CO 
 CM 
 
 en 
 
 d 
 
 H 
 
 en 
 
 co 
 d 
 
 CO 
 
 co 
 
 LO 
 
 LO 
 
 cO 
 co 
 
 t> 
 
 co 
 
 co 
 
 CO 
 
 d 
 
 CO 
 
 d 
 
 o 
 H 
 
 d 
 CM 
 
 l> 
 
 CO 
 
 lo 
 
 o 
 
 CM 
 
 q-i 
 o 
 
 CO 
 
 a +j 
 
 CO 0) 
 
 O 
 
 4-> 
 
 CM 
 
 CO 
 
 CO 
 
 d 
 
 CO 
 
 o 
 
 CO 
 
 CM 
 CO 
 
 CM 
 
 o 
 
 CM 
 
 CO 
 
 LD 
 
 d 
 
 H 
 
 o 
 H 
 
 CD 
 
 CD 
 CM 
 
 CO 
 CO 
 
 d- 
 
 o 
 d 
 
 co 
 
 CD 
 
 CD 
 
 LO 
 
 O 
 CD 
 
 CD 
 
 co 
 
 co 
 
 LO 
 
 CN 
 
 H 
 d 
 
 CD 
 CO 
 
 00 
 
 CM 
 
 H 
 
 H 
 d 
 
 CM 
 
 LO 
 
 CM 
 CO 
 
 CO 
 
 CO 
 
 H 
 
 CM 
 
 CD 
 
 d- 
 
 CM 
 H 
 
 d 
 
 LO 
 
 en 
 o 
 H 
 
 co 
 
 CM 
 
 O 
 CM 
 H 
 
 CO 
 CM 
 
 O 
 l> 
 
 d 
 
 CM 
 
 H 
 
 LO 
 
 CM 
 
 d 
 
 o 
 
 l> 
 
 CM 
 
 CO 
 
 en 
 
 • 
 LO 
 CO 
 CM 
 
 en 
 en 
 
 en 
 
 CM 
 
 CO 
 
 H 
 
 d- 
 
 o 
 
 CO 
 
 CN 
 
 O 
 CO 
 CM 
 
 CO 
 
 
 H 
 H 
 
 LO 
 
 o 
 
 CM 
 CM 
 
 H 
 
 CD 
 CD 
 
 en 
 o 
 
 LO 
 
 o 
 
 en 
 
 CO 
 CD 
 CM 
 
 CD 
 [> 
 CM 
 
 CM 
 
 d 
 H 
 
 CO 
 
 Csl 
 
 d 
 
 co 
 
 LO 
 
 en 
 
 CN 
 
 O 
 
 d 
 
 CM 
 
 CN 
 
 O 
 CO 
 
 cn 
 co 
 
 o 
 co 
 
 H 
 
 cn 
 
 LO 
 
 CM 
 
 CO 
 CT> 
 
 CO 
 
 d 
 
 co 
 
 o 
 
 CD 
 
 CD 
 O 
 
 CO 
 CD 
 CM 
 
 en 
 d 
 
 CD 
 CD 
 CM 
 
 LO 
 CM 
 
 en 
 CD 
 CM 
 
 en 
 
 CM 
 
 d 
 
 CO 
 
 LO 
 
 CD 
 CM 
 
 CO 
 LO 
 
 co 
 
 CO 
 
 LO 
 
 LO 
 
 CD 
 CD 
 
 en 
 
 CD 
 
 co 
 
 CO 
 
 co 
 
 CD 
 
 CO 
 
 d 
 
 CM 
 
 d 
 
 LO 
 
 CM 
 
 LO 
 
 CM 
 
 H 
 
 O 
 
 CD 
 LO 
 CM 
 
 LO 
 
 co 
 l> 
 
 CD 
 CM 
 
 LO 
 LO 
 CM 
 
 H 
 
 I 
 
 > 
 
 0) 
 H 
 
 ■a 
 
 CD 
 
 U 
 
 co 
 
 CO 
 
 d) 
 
 Ih 
 
 Ph 
 
 r- 
 
 co 
 
 LO 
 
 o 
 
 CM 
 
 LO 
 
 CO 
 00 
 
 d 
 
 CM 
 
 CO 
 
 co 
 
50 
 
 ca 
 
 U» = 0.0 
 
 o 
 
 Channel 
 
 1 532.5cm- 1 
 
 2 898.0cm" 1 
 
 3 747.0cm- 1 
 -l 
 
 -l 
 
 H (THOUSAND FEET) 
 
 Figure VII-1. — Cloud trarismittance (x ) vs the elevation (H) above the base 
 of the cloud (Flight 2). 
 1.0! 
 
 CO 
 
 I — '— 
 
 Channel 
 
 1 532.5cm- 1 
 
 2 898.0cm" 1 
 
 3 747.0cm" 1 
 
 4 732.5cm" 
 
 5 708.0cm~ 1 
 
 Figure VII-2.- 
 
 H (THOUSAND FEET) 
 
 ■Cloud trarismittance (t__) vs the elevation (H) above the base 
 of the cloud (Flight 2). 
 
51 
 
 transmittances we shall denote x . The transmittances for the cloud-free 
 
 c 
 regions adjoining the region of measurement were computed for the CO2 band. 
 
 These we shall call T a . Before the first leg of the flight was made below 
 
 the cloud deck, the aircraft made a steady descent in the clear air adjacent 
 
 to the cloud. During this time, radiances were measured, and the clear-air 
 
 radiance values corresponding to the elevations of the legs were obtained. 
 
 Using the program discussed in section VI, which is a generalization of 
 
 Equation (VII-10), transmittances through the cloud-free atmosphere were 
 
 computed. They are shown in figure VII-3. 
 
 The values of t _ for the cloud for w =0.5 in the three C0 o channels 
 ca o *■ 
 
 were then plotted against the corresponding values of x as shown m figure 
 
 VII-4. Curves for each cloud level were then extrapolated to where the 
 value of x became unity. The transmittances in the cloud corresponding to 
 these extrapolated values, therefore, are the desired "pure" cloud trans- 
 mittances, x c . The resulting variations of these transmittances with eleva- 
 tion in the cloud are shown in figure VII-5. 
 
 Since there is only one channel for the water vapor band and one for 
 the "window", the "pure" cloud transmittances at these spectral intervals 
 must be approximated in a different manner. By assuming that 
 
 x ca s x c x x a (VII-18) 
 
 the "pure" cloud transmittances may be estimated. The resulting values are 
 also shown in figure VII-5. 
 
 It is interesting to note that the transmittances for the CO2 and water 
 vapor bands are very nearly the same, while those for the window channel are 
 considerably greater in magnitude. 
 
 The results presented in figure VII-5 can be explained if the predomi- 
 nant phase of the cloud particles is liquid. Although the cloud was 
 reported as cirrus , it seems quite unlikely that ice particles predominate 
 at levels as low as 15,000 feet. Therefore, assuming that most of the cloud 
 was composed of liquid water drops, the agreement between the transmittances 
 in the CO2 and water vapor bands can be explained by the fact that the values 
 of the liquid water absorption coefficients are fairly close in the two 
 bands. On the other hand, the magnitude of the absorption coefficient for 
 the window region is less than half that for either the water vapor or C0 2 
 band. This explains the larger values of x c for this channel. The same 
 conclusion may be reached by comparison of the extinction efficiency factors 
 (ratio of the extinction cross section to the geometric cross section) for 
 10-um drops. Again, the values for the water vapor and CO2 bands are close, 
 in value while that for the window region is considerably smaller. Table 
 VII-2 lists the absorption coefficients and extinction efficiency factors 
 for the three spectral regions. 
 
 The second case for which cloud transmittances were computed was derived 
 from data gathered from cirrus clouds with tops at 37,800 feet and bases at 
 27,000 feet (flight 10). Table VII-3 lists information on mean radiances and 
 temperatures, similar to that listed in table VII-1. Only one leg of the 
 
52 
 
 H (THOUSAND FEET) 
 
 Figure VII-3. — Clear-air transmittance (x a ) vs the elevation (H) in the clear 
 air above the cloud base (Flight 2). 
 
 ca 
 
 0.5 
 
 0.4 
 
 0.3 
 
 0.2- 
 
 0.1 
 
 0.0 
 0.0 
 
 i — ■ — r 
 
 i — ' — i ' — r 
 
 OJ Q = 0.5 
 
 p=587mb to p=520mb 
 
 .*— t 
 
 0.1 0.2 0.3 0.4 
 
 0.6 
 
 p=587mb to p-332mb 
 
 Smm it— *■■<■ — I 
 0.7 0.8 0.9 1.0 
 
 Figure VII-4. --Cloud transmittance (t ca ) vs the clear-air transmittance (x a ) 
 (Flight 2). 
 
 ■ I 
 
53 
 
 r c 
 
 H (THOUSAND FEET) 
 
 Figure VII-5. — "Pure" cloud transmit tance (t c ) vs the elevation (H) above the 
 base of the cloud (Flight 2). 
 
 Table VII-2. — Absorption and extinction factors for liquid water 
 
 
 
 Absorption coeff 
 
 Channel 
 
 Mean wavelength 
 
 in water 
 
 
 um 
 
 cm _J - 
 
 1 
 
 18.78 
 
 2633 
 
 2 
 
 11.13 
 
 1296 
 
 3 \ 
 
 
 
 4 / 
 
 13.72 
 
 3083 
 
 5 ] 
 
 
 
 Extinction efficiency 
 factor 
 
 2.628 
 1.789 
 
 2.284 
 
54 
 
 o 
 H 
 
 +-> 
 Xi 
 bO 
 
 •H 
 
 H 
 
 4-1 
 
 bO 
 
 C 
 
 •H 
 
 T3 
 
 GO 
 
 =1 
 O 
 H 
 O 
 
 C 
 
 T3 
 
 & 
 
 d 
 w 
 
 rtf 
 0) 
 S 
 
 ra 
 
 a> 
 o 
 c 
 
 iD 
 •H 
 
 c 
 
 (D 
 
 nj 
 & 
 
 0) 
 
 I 
 I 
 
 rrj 
 
 l-l 
 H 
 > 
 
 H 
 
 ■a 
 
 LO 
 
 
 CO 
 
 pq 
 
 CN 
 
 CQ 
 
 H 
 
 CD 
 
 +-> 
 
 (0 
 ft 
 
 B 
 
 0) 
 Eh 
 
 to 
 
 a 
 
 •H 
 
 c 
 o 
 
 ■H T3 
 
 to o 
 
 > H 
 
 0) O 
 
 H 
 
 M 
 
 CN 
 
 S 
 O 
 
 ra 
 bo 
 
 (0 
 
 o 
 
 LO 
 
 UD 
 
 CN 
 
 o 
 
 co 
 
 UD 
 
 CT> 
 CM 
 
 CM 
 
 CO 
 
 CO 
 
 LO 
 
 CN 
 
 H 
 
 CO 
 
 CO 
 
 o 
 
 [> 
 
 LO 
 
 d 
 
 co 
 
 d- 
 
 LO 
 
 o 
 r-- 
 
 CN 
 LO 
 
 H 
 
 UD 
 
 co 
 
 H 
 
 P- 
 
 CN 
 
 LO 
 d 
 
 co 
 
 UD 
 
 CN 
 
 co 
 
 d 
 
 CD 
 
 CD 
 CN 
 
 
 o 
 
 CD 
 
 CN 
 
 H 
 
 zf 
 d 
 CM 
 
 UD 
 
 co 
 CM 
 
 d 
 CM 
 CM 
 
 d 
 H 
 co 
 
 d 
 
 CM 
 
 o 
 H 
 
 CN 
 
 O 
 M 
 
 rd 0) 
 
 w a> 
 
 o 
 
 -t- 1 
 
 CO 
 LO 
 
 co 
 co 
 
 LO 
 
 d* 
 
 Eh 
 
 co 
 
 CN 
 Eh 
 
 H 
 
 to 
 
 P-i 
 
 en 
 CT> 
 
 LO 
 
 CO 
 
 CD 
 
 LO 
 
 CN 
 O 
 
 H 
 H 
 
 (D 
 CO 
 
 UD 
 
 co 
 
 CD 
 
 CN 
 
 cn 
 CN 
 
 O 
 UD 
 CN 
 
 OD 
 CO 
 
 d- 
 
 CN 
 
 d 
 d 
 
 LO 
 
 co 
 
 CN 
 
 UD 
 LO 
 
 O 
 
 H 
 co 
 
 LO 
 CO 
 
 p» 
 
 CM 
 
 o 
 
 CN 
 
 co 
 
 LO 
 
 co 
 
 CO 
 
 L-* 
 
 OD 
 CO 
 
 o 
 o 
 
 d- 
 
 co 
 
 o 
 
 cn 
 
 d 
 
 CN 
 
 oo 
 C- 
 
 o 
 
 UD 
 CN 
 
 LO 
 
 co 
 oo 
 
 UD 
 CN 
 
 LO 
 LO 
 
 cn 
 co 
 
 CN 
 
 d 
 
 00 
 
 UD 
 CM 
 
 O 
 CO 
 
 CD 
 LO 
 
 o 
 
 ID 
 
 CN 
 CD 
 
 CD 
 
 co 
 
 d- 
 
 UD 
 
 cn 
 O 
 
 LO 
 
 UD 
 
 co 
 
 cn 
 
 co 
 
 CO 
 
 d 
 
 r- 
 
 LO 
 
 co 
 
 CN 
 
 co 
 
 CD 
 CO 
 
 d 
 
 CN 
 
 O 
 UD 
 
 d 
 
 CN 
 
 d 
 
 UD 
 CN 
 
 d 
 d" 
 
 UD 
 
 d 
 
 CN 
 
 d 
 H 
 co 
 
 d 
 
 CM 
 
 O 
 
 H 
 
 CN 
 
55 
 
 flight was made within the cirrus. Computation results are shown in figures 
 VII-6 and VII-7. 
 
 Note that here the window and water vapor channels have transmit tances 
 very nearly the same in value. This is probably because of the smaller 
 amount of water vapor at the higher levels . 
 
 Since no data from cloud-free regions near the cloud area were avail- 
 able, another means for estimating the "pure" cloud transmittances was used. 
 A relative measure of the absorption coefficients in the CC>2 band were 
 obtained from flight 2 data. By plotting the values of x ca against the 
 absorption coefficients, one could obtain t c by extrapolating the curves to 
 points where the absorption coefficients became zero. 
 
 The transmittance values, x , computed for flight 2 were used to esti- 
 mate an absorption coefficient k for the band, assuming the relation, 
 
 x a ( Po ,p) = e- k (Po-P } (VII-19) 
 
 from which 
 
 k = - ln T a(Po>P) 
 Po-P 
 
 Since (p -p) is a common factor to all the values of the absorption coeffi- 
 cients, plots of T ca for w = 0.5 for this case study were made against -In x_ 
 determined for the thickest layer from flight 2 (See figure VIIr8). The 
 values of x were then extrapolated to a value of zero for -lnx . The 
 values of x obtained were the desired values of x ; these are plotted in 
 figure VI I- 9. 
 
 The "pure" cloud transmittances for channels 1 and 2 were assumed to be 
 the same as the transmittances with water vapor present. For comparison 
 with the curves of x c for the CO2 band, they are shown in figure VII-9. 
 That the transmittances are much closer in value for all the channels than 
 those for flight 2 can be explained by the fact that ice particles are much 
 larger than cloud water drops. Thus, nearly all the radiation refracted 
 into the crystals is absorbed, and differences in the absorption coefficients 
 are unimportant. For large particles the extinction efficiency factors all 
 tend toward a value of 2. Probably, the small variations in this parameter 
 give rise to the differences in the transmittance curves of figure VII-9. 
 
 Conclusions and Recommendations 
 
 The results of the cloud transmittances determined from measurements 
 obtained by the airborne ITPR brassboard instrument indicate that much can 
 be learned about the radiative properties of clouds by using such measure- 
 ments. Although not many cases were studied in quite so great detail as 
 would have been desirable, the results definitely do point toward what can 
 be achieved on future flights . 
 
 Therefore, on the basis of this study, we recommend that more extensive 
 
56 
 
 ca 
 
 1 — ' — r 
 
 Channel 
 
 1 
 
 532.5cm" 1 
 
 2 
 
 898.0cm -1 
 
 3 
 
 747.0cm" 1 
 
 4 
 
 732.5cm" 1 
 
 5 
 
 708.0cm" 1 
 
 o.ol 1 1 
 
 I ,1 L 
 
 8 10 12 14 
 
 H (THOUSAND FEET) 
 
 Figure VII-6. — Cloud transmittance (t c ^) vs the elevation (H) above the base 
 of the cloud (Flight 10). 
 
 ca 
 
 10 12 
 
 H (THOUSAND FEET) 
 
 Figure VII-7.--Cloud transmittance (t ca ) vs the elevation (H) above the base 
 of the cloud (Flight 10). 
 
57 
 
 ca 
 
 u.« 
 
 i — 
 
 1 ' 
 
 , 1 1 1 
 
 
 0.3 
 
 — #— 
 
 
 p=314 to p=274mb 
 
 - 
 
 0.2 
 
 - 
 
 c3 =0.5 
 
 
 
 0.1 
 
 
 
 
 
 
 
 
 p=314mb to p=210mb 
 
 
 0.0 
 
 i 
 
 1 . 1 
 
 1 i 1 i 
 
 
 0.0 
 
 0.5 
 
 1.0 
 
 1.5 
 
 2.0 
 
 2.5 
 
 InT 
 
 Figure VII-8. — Cloud transmittance (^ ca ) for flight 10 vs the negative of the 
 logarithm of the clear air transmittance (-In x a for the 
 thickest layer in flight 2. 
 
 1.0 
 
 0.8 - 
 
 0.6- 
 
 0.4- 
 
 0.2 
 
 0.0 
 
 I ' 
 
 1 ■ 1 1 1 
 
 1 1 ' 1 
 Channel 
 
 i 
 
 
 
 1 
 
 532.5cm" 
 
 
 — w 
 
 
 ___ 2 
 
 898.0cm" 
 
 1 — 
 
 * vV 
 
 
 3 
 
 747.0cm" 
 
 1 
 
 V % 
 
 
 4 
 
 732.5cm" 1 
 
 1 
 
 
 
 5 
 
 708.0cm" ! 
 
 
 \ 
 
 ^ OJ = 
 
 0.5 
 
 
 - 
 
 — 
 
 
 1,2 
 
 
 - 
 
 1 
 
 3,4,5 
 
 1 i 1 
 
 1 
 
 i 
 
 _i _ 
 
 10 
 
 12 
 
 H (THOUSAND FEET) 
 
 Figure VII-9. - J 'Pure" cloud transmittance (t c ) vs the elevation (H) above the 
 base of the cloud (Flight 10). 
 
58 
 
 measurements be made for a variety of cloud situations to assess the 
 accuracy of current results. These measurements should provide for flying a 
 greater number of legs (perhaps six or more) within the clouds and in the 
 adjoining clear regions to permit better definition of transmittance curves. 
 Also, the study of a larger number of cases should lead to a clearer under- 
 standing of the factors that influence the transfer of radiation through 
 clouds . 
 
59 
 
 References 
 
 Barnes Engineering Company, "Thermistor Infrared Detectors," Reprinted 
 from NAVORD 549 5, June 1, 19 58. 
 
 Barnes Engineering Company, "Satellite Spectrometer, Phase II, 1st Quarterly 
 Report 4596 to Contract Cwb 10-419," November 15, 19 59. 
 
 Howard, J. N. , Burch, D. L. , and Williams, D. , Near- Infrared Transmission 
 Through Synthetic Atmospheres , Geophysical Research Papers No. 40 
 (AFCRC-TR-55-213, Cambridge Research Center, U.S.A.F., November 19 55, 
 244 pp. 
 
 Middlebrook, R. D. , and Taylor, A. D., "Differential Amplifier with Regulator 
 Achieves High Stability, Low Drift," Electronics Magazine , Vol. 34, 
 July 28, 1961, pp. 56-59. 
 
 Moller, R. , and Raschke, E. , Evaluation of TIROS III Radiation Data, 
 
 Ludwig-Maximilians - Universitat , Meteorologisches Institut , Munchen , 
 Germany, NASA Research Grant, NSG-305, July 1963, 114 pp. 
 
 Smith, W. L. , "An Improved Method for Calculating Tropospheric Temperature 
 and Moisture from Satellite Radiometer Measurements," Monthly Weather 
 Review , Vol. 96, No. 6, June 1968, pp. 387-396. 
 
 Smith, W. L. , "A Polynomial Representation of Carbon Dioxide and Water Vapor 
 Transmission," ESSA Technical Report NESC 47, February 1969 (Available 
 from the National Technical Information Service), 20 pp. 
 
 Smith, W. L. , "The Improvement of Clear-Column Radiance Determination with a 
 Supplementary 3.8-ym Window Channel," ESSA Technical Memorandum NESCTM- 
 16, U. S. Department of Commerce, National Environmental Satellite 
 Service Center, Washington, D. C. , July 1969, 17 pp. 
 
 Smith, W. L. , and Jacob, W. J., "Multi-Spectral Window Determination of 
 Surface Temperature and Cloud Properties," (to be submitted for 
 publication). 
 
 Wark, D. Q. , Hilleary, D. T. , Anderson, S. P., and Fischer, J. C. , "NIMBUS 
 Satellite Infrared Spectrometer Experiment," IEEE Transactions on 
 Geoscience Electronics , Vol. GE-8, No. 4, October 1970, pp. 264-270. 
 
60 
 
 APPENDIX 
 
 Flight plan and ITPR data for June 12, 1970 (flight 7) 
 
 Flight Plan 
 
 The flight plan is to leave Eielson AFB for a point 
 southeast of Fairbanks and execute a pass over the 
 glacier Gloco at 14 K. After Anchorage is passed, 
 the aircraft will proceed to a point of 4-9° N. and 
 150° W. at 31 K in order to pass over a front. The 
 aircraft will then turn left at Medford, Oregon, 
 pass over the cold section of the front, there 
 execute a 30-minute delay. The aircraft will then 
 attempt to reach the cirrus shield associated with 
 the warm front, and if time permits, to execute a 
 15-minute delay with clear skies below the cirrus. 
 Afterwards , the aircraft will go down the coast 
 about 200 miles offshore until Moffett AFB is reached. 
 
61 
 
 II. Flight Data 
 
 DATA FORMAT 
 
 Time: Hours: Minutes: Seconds (GMT) 
 
 Pressure Altitude (mb) 
 
 Brightness Temperatures (°K) 
 
 Tl (532.5 cm -1 ) 
 
 T2 (898.5 cm" 1 ) 
 
 T3 (747.0 cm" 1 ) 
 
 T4 (732.5 cm" 1 ) 
 
 T5 (708.0 cm" 1 ) 
 
62 
 
 6/ 12/ 70 
 
 HP !• N St". .11 T Tl 
 
 _L£_ 
 
 T.3 
 
 Oil t__. 
 
 ■.6 57 
 
 -*___i__ 
 
 1.7 37 
 
 28_- 261.60 2 8 3.i' 
 
 ?6 C 260.31 77 7.2 
 
 236 260.6* 271. ?' 
 
 '■17 ?6n.?. 27-_-___: 
 
 353.56 25*. 63 2^3 . S <♦ 
 ._2.60.___9.. 25.1__.aJ 2-.2.__>.2-.. 
 
 261..H. 251. 69 21.3. C 1 
 
 .____5.9___.___L. 251 . ,15 _2_i2_.___2_ 
 
 296 258.51 277.11 268.31 21,9.93 2*1.92 
 
 '<' 759.P. 773.76 75Q.H1 251.11. _2__l3-_'J a 
 
 2>)7 257.97 277.21. 257.99 ?*9.12 21.2.21 
 
 2.6 8 253. °0 2 7..1. 252.6a 2*5.97 2*0.37 
 
 23? 259.23 277.65 253.95 251.07 2*3.03 
 
 .2.86 25_»_, S3- 225_-2 _. 2_-__J__. _25a.il. 2„_2_.7_2_.. 
 
 '54 261.73 285.71. 76*. 72 251.. 03 21,3.75 
 
 37 761 .5"' 273. 1.9 7_?.r jfi 253.10 73*. 02 
 
 60.1.6 277. nC 260.7". 252.1.. 7,3.73 
 
 '36 f57.0 1 767.76 7C1..H 7*6.91 .2*3.0.1. .. 
 
 239 25",. 31. 259. '-i. 251.11 21,7.27 21,2.1,7 
 
 ai__2____-__L_. 269. -35- 251.67_2.!i2__7.a 232J.6.5 
 
 29' 253.86 266. 13 257.86 71.7.1.1 2,1.58 
 
 23i__2.i_2_-C--_ 2-5.3. f 6 __-3-..-J- -__1_-.J. 2.3 9. 2 2 . 
 
 25_ 21,9.00 262. (1 ?35. c '7 237.27 21,0.37 
 
 . 2_i6 . 2__6, 16 2.52.i6_233,-.5. 232.5 3 239. 9", 
 
 287 21,9.93 255. F. 237..? ?£._,.!_, 2,0.96 
 
 _2Jl5.2-t._L_.an 753.57 j>*f..3;> ?**.l.7 230.99 
 
 '36 71,8.1,2 251.66 7*5.29 21,3. 16 2>»0.36 
 
 731 71,9.11 ,-57.°', 71.6.73 7*3.6' 71.0.63 . 
 
 237 251.lt 256.67 2*8.23 21.6.57 21,1.63 
 
 _256_ 25___.7*. 25.__._L__.2k7 _62 2*5..12_.2*-1 . 3 5 
 
 23° 21.8.91 251.-3 21.6. ,0 2*3.3) 2.0. .33 
 
 _-.__i_2i-7-.9SL.25_l. LI _2-._-._fl2 21,2.2.3 2*11.35 
 
 78 7 21,5.72 2*. .89 71.7.16 21,1.35 239.13 
 
 .-__37-___**_-__--2*2.-.3_-!-_.-L32_._L5_ 23t_-.9 5.23J! . 8 8 
 
 731, 21,3. °3 -.6. P. '31.76 239.6. 213.23 
 
 -285- ?3-_..6..-2 31.,*.1 232.J29 2.1.-3 .33.83 
 
 337 21,3. .2 71.6.27 2.5.51 7'9.77 233.03 
 
 _2_5 7.3.0 6 7I.6. 75 7.39. 111 2_.__._3 J. 237.53 
 
 21.2.61. 239.32 
 __L_2_t3__ia. 2 -2._-_2.239.. 32 
 
 ?....') 238. .J 
 
 19 
 
 1_L 
 
 19 
 
 19 
 
 19 
 
 286 21,7.02 751. 7< 
 
 232_-2_i_6.65._2-*.._, 
 5. 37 737 21,1,. 82 2lt7.bg 7.1. .2 
 
 5-3 1,9 . . 236_ 245_. 16 _« . _3 .2m. .6 2*1. OJ 238.57 
 
 55 237 2.3.67 21,5. VI 7. ".61 2*0.21 237.96 
 
 55 l__-._2_L*_.2i_2.-ll_2.**. __L. 220.18 238.99 2 37.11 
 
 55 75 ?1> 2.2.1.2 7.H.H 739.36 239.25 737.27 
 
 55 '7 7.1F 7* 3.7* ?*7.'6 73.1.66 2.*.0._.3 237.9. 
 
 55 1,9 73" 21,6.11 2.9.1."' 21,7.1-3 21.2.73 239. J 3 
 & _0. 237 2*7.28 259.39. 23.3.53 2.3.53 239.37 
 
 56 13 23° 2.7.-7 7 5 . ' 7 2**. 18 21,3.11 239.73 
 56 25 .236 2Jt7, **.251. -5.2-5. 13 23?.6) 2*0. Qil. 
 56 35 23F 21,8.08 252. 6 . 7.5.33 2. ..05 ?'.9.9* 
 
 -___--__ 2-___-_it_L_.t2__2.i__-. -__— 7_-_..__-___--3-.J. J..239.3 3. 
 
 56 59 735 2*5.65 2*.. 36 733.29 ?.'.. I 239.20 
 67 in .. _-J6-___-__52. _7fc9.f,5.Zi L3_.35._2-i-t.!tS. 2 59.3 6 
 57"23 297 2*7.75 251.11 ?V..'^ ?>.",.. '.ill Jj 1 
 
 57 35 78 5 2*6 .90 250. p 6 ___-.*-_0.1 2*' 
 
 57 1.7 737 21,7.91 251. :• 2 23. .92 2'.' 
 _5 Z _59 . 239 2*7 .39 752.53 _?3 5. 3 1 23 . 
 
 58 61 236 21,1,. 76 71.7.63 ",1.77 23" 
 
 59 3 237 21.5.21. 2.7.73 n,?. lf 
 
 ALT 
 287 
 286 
 285 
 2£7 
 288 
 282- 
 287 
 ______ 
 
 287 
 .286 
 766 
 28.8 
 2 6-, 
 288 
 286 
 286 
 286 
 288 
 285 
 2-6. 
 287 
 
 2ee 
 
 288 
 .290 
 265 
 286 
 286 
 285 
 
 2es 
 
 268 
 269 
 288 
 286 
 
 286 
 
 288 
 
 2.6 
 
 266 
 
 288 
 265 
 267 
 267 
 287 
 285 
 289 
 787 
 286 
 265 
 266 
 287 
 286 
 
 -__-_ 
 
 _L_ 
 
 T - 
 
 tl T 
 
 li. 
 
 T 7 
 
 13. 
 
 ______ 
 
 _____ 
 
 ...TJ I_ 
 
 255.62 265.61 251.61 21.7. .5 232.02 286 260.82 279.17 261.03 252.01 2.3.03 
 
 25.3.8.9. .27S..35 -__■--, -_i_. _L5-_-__t-2_2.-_-_n-_2_-.---.26J_. *1 217 -.27 759.57 750.99 7. 7. 6.3 
 
 259.65 276.32 259.73 250.10 2.2. .7 289 259.57 273.1,5 258.01 250.36 21.2.61 
 
 2__a._--t-27_L___3.__2__l__6L_-_5_..5i____Z___J 783 763.119 761.+- 76 1.13 751.61. 71.7.53 
 
 257.33 275.26 25b. 31 21.8.95 232.16 289 253.50 277.0') 257.62 21,9.86 232.35 
 
 25.9-.56 .73. J 9 759.5. 751;. .7 737.93 73? 758.55 776.35 757.91 750.07 7*7.5? 
 
 .6. 2.33.5 9 
 
 .0 5 2,0.3 
 .-91 7 + 0.0 6 
 .6 3 2 18.8 3 
 2*3.23 739.1. 
 
 236 21,5.81' 238.65 232. "9 231.13 219.37 
 
 23" 233. °6 237.2? 737.13 2*1 .63 238.95 
 
 217 233.92 236.15 231.32 731.31 238.62 
 
 233. 231. 67 233. c. 236 .95 236. *9 237.7 3. 
 
 23* 2,0.55 233.21 7?7.«6 237.55 216.63 
 
 ?1^ 2, 0.63 233.'5 ?i7.66 736.36 2. 16,3 6 
 
 733 239.76 232.22 737.17 736.77 256.25 
 
 283.23 0.21 737. 1.1 737.50 23 7 , J.5_ 2 36. 3 3 
 
 781. 2,1.89 233.ro 239.36 238.23 257.31 
 
 287 231.69 733.37 733.37 238.99 237.25 
 
 236 232.7' 233.17 230.26 233.99 237.61 
 
 237 7,6. 09 239. 1-3 733.36 232. 81 239.33 . 
 23' 733.81 736.1.7 '31.28 230.16237.69 
 2_86_233.°5 2*7._7__ ?31._._5 230.53 236.53 
 787 236.29 731.37 ?*?. 39 231.31 239.36 
 i37 237.35 250. '.7 733 .71 237.2.2 239.9.3. 
 7,3= 237.51 751.7. 233.73 237.72 230.18 
 
 89 737.57 251.. . 733.22 232.63 2___9 ..i ... 
 
 717 239.68 253.6? 71,7.15 ?33.32 230.8.) 
 
 267 737.06 ..51.29 2,3. 15- 232.09 2.5.-J, 5 6. 
 
 233 236.36 2... 'I 233.1" 731.31 239.21 
 
 _285 7.5.57 233.38 ' 37.3 3 230.37 2.38.8.3. 
 
 287 251, ,1 755.2' '36.59 235.71 231.19 
 
 7 17 75 1.7' 756.31 73". 36 236.37 732.13 
 
 20 6 59 79" 250.58 255. "'1 736.38 235.86 232. 3* 
 
 _70 7.11. 217 751..01 256.76 2* Q ..22 236...1 6 _232 . 3 7. 
 
 20 7 2C 21 1 2*8.18 253.27 7*5.96 733.17 7,0.95 
 
 70 7 3 3 2.1.1 25Q. f], 256.2° 2*6.90 236.16 ZJtZjZZ. 
 
 20 7 35 28. 2*6.52 751.73 73*. 18 2*2.57 2*0.11 
 
 70 7 57 787 7*6.35 7*9. .3 733. 3 2 232.3) . -_-.___--. _ 
 
 28° 236.17, 250.32 7*3.96 2*2.3* 2*9.2* 
 
 2C 
 
 -.0 
 ?0 
 
 ?: 
 
 _-_?__ 
 
 8 33 
 ___*__. 
 
 '1" ?37.57 251. ■ 7 2,F. 11 2*_7_.90 2.0.9* 
 
 79- 2*6.79 259.63 '33.51 7*2.83 2*0.56 
 
 ___}?_ 2*6. * 6 2*9.1.5 7*7.76 2*2.2.9 .2*0.07 
 
 28°. 2,6.** 2*9..3 2*3.72 2*2.7) 2*0.31 
 
 233 2*6. Fl 2*9. f . ?**.;* 2*7.61 2*U.18 
 
 20 9 21 237 2*6.09 251.26 2*5.9" 2*3.91 2*1.05 
 
 20 9 33 266 2* 9.20 253 .11 ?*'.*! 2**^9 . -2*1.7.1 
 
 20 9 35 235 2*8.97 252.71 237.93 233.6, 2*1. *1 
 
 -___ ____7- _'35„__i-_,_i < __-_____.._______.6_..?.3. 2* *.5) 2*1.28 
 
 20 10 8 285 2*8.59 252. ,7 236.?' 233.31 7*1.32 
 
 .'11 10. '1 2.6 2*8.7 5 ,251. "9 7*6. *7 2**. 27 2*1.19 
 
 11 
 ___-_*___ 
 
 237 2*8.91+ 452.61 2*6.75 2**. 67 2*1.72 
 2.7-£<__--6. 25-7-.-Jt--2_t-!-_2_.-2»-i,-.*7- 2*1. *_5 
 
 286 
 287 
 267 
 266 
 
 „2_68 
 785 
 267 
 285 
 760 
 28 7 
 
 ..2.0 - 
 288 
 268 
 266 
 267 
 287 
 
 _-«__ 
 
 .ee' 
 
 ?_86 
 2 87 
 2_8_6 
 287 
 2 85 
 286 
 266 
 286 
 287 
 285 
 
 ______ 
 
 286 
 267 
 265 
 2 86 
 286 
 2.88. 
 287 
 7*7 
 787 
 267 
 268 
 
 _<_. 6_ 
 269 
 286 
 286 
 28.6 
 286 
 286 
 
 256. 6C 
 
 25__.9_ 
 
 259.79 
 
 258.9.2- 
 
 261.25 
 
 .26Q..23_ 
 755.33 
 257.77 
 253.20 
 255.65 
 239.10 
 2 3Z..3S. 
 2,9.62 
 
 .23. .52 
 238.61 
 23-. 63 
 236.27 
 2 39.53 
 251.73 
 23.9.8 3 
 238.70 
 237.30 
 235.83 
 
 -233.09 
 232. 95 
 2*5.63 
 2,3.33 
 2.35.09 
 23.. 37 
 236.22 
 2,5.73 
 236.21 
 232.53 
 232.37 
 2*2. *3 
 2*3,96 
 2*6.91 
 2*7.63 
 2*7.02 
 2*7.79 
 2*7.33 
 2*7....__>. 
 235.93 
 2*7,_5_ 
 2*1.11 
 2 3__-2-3. 
 237.82 
 219.-53 
 233.62 
 2 3 6j 3-5- 
 235.53 
 233.6* 
 2*3.72 
 2*1.31 
 2nj.59 
 23.0.53- 
 239.35 
 231.66 
 2*1.99 
 2*2.83 
 2*2.26 
 
 _2_33_.9 7 
 
 _ 2 3?. 8, 
 2*5.6* 
 2*6.0 
 
 -2*7. *1_. 
 2*7.26 
 23_9-_3 C- 
 2 38.9 7 
 236.2* 
 2*E.30 
 .2**.. 76. 
 251.20 
 Z. U.-1 3. 
 251. *3 
 250.2* 
 2*9.** 
 250.73 
 2*7.09 
 2.36-..Q--. 
 2*7. *0 
 2*6.56 
 2*C.*1 
 2*6,03 
 2 36.69 
 2 36.. 98_ 
 2,1.63 
 2_38.86 
 2*6.63 
 2. .3.8 j ,6-6- 
 238.3* 
 ._-___._._. 
 
 277.17 257.71 239.31 231.33 
 
 279.9,8 -25a_-5* 251.J_L.-_3___.__2 . 
 
 ?79.63 260.1* 251.50 2*2.98 
 
 775.7F. 756.116 751 . fl 7*3.7 5 
 
 282.29 262.99 253.36 2*3.56 
 
 281 256.93 278.1* 257.61 2*9.11 2*1.19 
 
 .247 260. *1 212.*5 267.00 252.*5 2*3.13 
 
 285 251.26 275.93 257.27 250.20 2*2.71 
 
 286 761.97. 262. __a -2-62.56 
 286 251.55 280.5* 262.65 253.31 2*3.91 
 
 ZZ7 _.7 _,. 2b_ 
 
 -.33.66 783 76 1.30 779. .15 767.07 75.3.70 7*3.1* 
 
 269.55 251.21 2*7.28 2*2.50 
 
 27-3--23 .2-_.fa._J. 2_-__.___-233.26 
 
 259.06 250.80 2*7.25 2*2.67 
 
 261. 9. .252. 19 2*__.09..2*2 .9* 
 
 25*. 09 2,5.67 2*2.12 2*0.15 
 
 251.18 ?**■*" 7*7.*5 739.90 
 
 753.9* 2*6.06 2*3.-9 2*L'.5* 287 2*9. 3u 253.18 2*6.1* 2*3.55 2*0.66 
 
 .5 3.5* 2 3.6.19 -23.3. _»-2_.a_-72__-2_l.Z-25_-.-72-256_, 63 737.59 733.67 7*1.0 6 
 
 289 255.56 260.52 252.00 2*7.71 2*2.72 
 2fl_L_2S_____._2__5_i.7_- 252.2* 2*7. 9* 7*2.65 
 267 25*. 60 259.10 251.22 2*7.51 2*2.60 
 28_1.2SS.-6C - 2-66^ 3-* _25 3 -5-6- -2-3 a _52- 232_-~6. 
 286 2*8. *6 252.38 2*5.69 2*2.9* 2*0.01 
 -28- 2_-___ 6.- ---S-L-SS. -____3-_2 7 2*1.99 239.55- 
 
 255.07 2*5.53 2*2. )2 2*0.16 
 
 £52.9* 2*6.5.3 _23itxll-..2_---..87. 
 
 251.60 2**. 13 2*2.13 2*0.22 
 
 252.91 ?,ft.*. ?**. 7 3 7* 11.99 
 
 759.01 2*6.82 2*5.78 2*1.67 
 
 253.79. 2*6-.7-l .2*3. ,8- 2*Q..93 
 
 251. *9 2*5.56 2*3.11 2*0.82 
 
 251.38 2*3__33. 2*2.51.233.7.9 
 
 237.66 2*2.71 231.55 239.20 
 
 _i7-.-0 7 _2.ij._L.-bC . 7 39..1U -23-1-.27.. 
 
 236.73 233.36 239.56 238. Cd 
 
 2*1.95. 2*2.3. Z31..15 239.98 
 
 2*5.71 2*1.16 239.97 237.7* 
 
 -*8.73 2,2.03 23.Q-.17..238.6-3 
 
 250.3* 2*3.55 2*2.12 239.13 
 
 2*9.38 231.-3&. 2_.2._-5-23_L___e.. 
 
 2*1. 2J 2*2.3- 2*1. *6 236.9* 
 
 2*7.79 2*2.3. 2*1. ,1 236.86 
 
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 20 16 2 238 271.21 279.2" 267.13 257.18 21.1.39 238 271.12 279.11 267.66 257.59 211.28 238 271.11 279.37 267.37 257.16 211.38 
 
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 20 16 25 233 270.75 273.71 267.18 257.13 2H.16 238 271.03 278.81 267.22 257.36 211.62 210 270.85 278.91 267.01 257.19 211.36 
 
 20 16 37 239 P70.69 278.75 267.28 257.1] 211.63 237 270.71 £78.60 266 . 78 257.11 211.33 239 271.07 279.01 267.36 257.65 211.80 
 
 20 16 19 239 270.77 273.17 266.82 257.21 211.29 239 270.80 278.96 267.21 257.57 211.61 210 270.61 278.66 267.05 257.20 211.11 
 
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 20 17 19 239 270.60 279.42 267.52 257.71 211.71 239 270.11 273.95 267.21 257.18 211.12 238 270.59 279.15 267.51 257.62 211.71 
 
 20 18 239 270.52 279.21 267.27 257.43 211.55 239 270.55 279.09 267.31 257.41 211.51 237 270.17 278.79 267.17 257.29 211.22 
 
 20 48 13 Pun 270.66 279.15 267.60 257.63 241.72 238 270.56 273.76 267.06 257.42 211.11 239 270.72 279.12 267.16 257.68 211.65 
 
 20 18 25 24(1 270.69 273.96 267.20 257.12 241.51 238 270.62 278.86 267.20 257.59 211.10 239 270.78 278.86 267.37 257.59 211.65 
 
 20 18 37 711 270.83 278.63 267.05 257.55 241.61 237 27U.78 273.47 266.94 757.31 211.17 239 270.81 279.03 267.20 257.62 21U.77 
 
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 20 19 13 233 270.81 278.73 267.11 257.55 211.15 239 270.76 279.03 267.17 257.53 211.58 239 270.51 278.78 267.33 257.17 211.51 
 
 20 19 25 211 270.66 278. °2 267.33 257.6* 211.63 236 270.19 273.57 266.90 257.25 211.30 23/ 270.91 279.19 267.81 257.98 211.99 
 
 20 19 35 239 270.56 279. CI 267.00 257.27 211.13 237 267.30 274.78 265.09 256.43 211.11 210 267.12 271.91 261.27 255.95 213.83 
 
 20 56 53 238 267.00 274.13 261.31 255.55 213.61 228 266.93 274.11 261.12 255.50 213.67 238 267.05 271.59 263.89 255.31 213.60 
 
 20 57 1 23? 267.13 275.02 261.17 255.34 213.86 238 267.06 274.53 263.65 251.90 213.15 210 267.07 271.27 263.81 255.13 213.57 
 
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 20 57 29 239 267.26 271.87 261.03 255.26 213.62 239 267.22 271.33 263.29 251.70 213.25 238 267.19 271.13 263.15 251.85 213.51 
 
 20 57 10 238 267.05 273.51 262.99 251.14 243.16 239 267.11 273.60 263.14 251.61 213.39 210 267.02 273.57 263.07 751.57 21.3.31 
 
 20 57 53 211 267.27 271.10 263.35 251.88 213.56 211 267.09 273.19 262.89 251.59 213.17 211 267.51 271.30 263.73 255.07 213.60 
 
 7 58 u. 71? 767.13 773.91 763.13 751.63 ?13.?1 713 767.60 271.19 263.13 255.09 213.72 211 267.33 7,71. 16 263.21 251.96, 213.51 
 
 20 58 17 211 267.11 273.82 263.17 255.15 213.76 213 267.21 £73.21 262.89 251.82 213.50 211 267.55 273.18 263.21 251.99 2U3.70 
 
 20 58 29 243 267.11 273.31 262.82 251.73 2l3.6b 211 267.51 273.72 263.16 255. J8 213.97 215 267.31 273.03 263.18 251.87 213.70 
 
 20 58 39 216 267.61 273.63 263.23 255.02 213.83 216 267.62 273.95 263.73 255.19 213.88 215 267.18 273.85 263.35 255.01 213.81 
 
 20 53 51 71ft 767.56 273.61 763.49 255.23 21U.09 217 267.10 £73.79 263.29 755.12 211.08 215 267.57 773.55 263.10 255.09 213.86 
 
 20 S° 3 246 267.67 273.66 263.67 255.43 214.17 217 267.58 273.12 263. 13 255.13 213.96 216 267.61 273.52 263.35 255.17 213.91 
 
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 20 59 27 217 267.69 273.85 263.59 255.35 211.09 218 267.36 273.19 263.53 255.20 213.87 218 267.32 271.01 263.52 255.29 2<»<..13 
 
 20 59 39 219 267.11 271.56 263.91 255.11 211.29 216 267.16 271.66 263.52 P55.25 211.07 253 267.59. 271..B1 261.06 255.62 211.11 
 
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 71 3 251 767.66 276.59 265.09 256.17 211.13 251 267.51 £77.17 P65.51 756.78 P11.3? 250 267.66 277.22 265.39 256.30 211.13 
 
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 21 2 13 262 265.31 273.23 263.12 255.37 211.11 261 265.30 273.11 263.12 255.56 211.56 261 265.38 273.11 263.31 255.15 2I.1.1.6 
 
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 21 5 47 261 266.85 276.82 264.92 256.35 245.11 262 266.77 277.41 264. 91' 256.16 244.90 262 267.06 278.33 265.63 256.69 245.24 
 
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 21 6 10 261 266.41 274.40 263.52 255.70 244.67 261 266.59 274.21 264.12 256.14 245.07 26 3 266.17 273.20 263.33 255.48 244.60 
 
 ?1 6-23 267 766.45 274.17 767. B 4 755.79 745.05 760 ?6f.?3 773. 93 763.4? 255.62 244.94 264 266.33 773.67 763.61 755.82 744.99 
 
 21 6 35 259 266.44 273.49 263.60 255.75 244.89 263 266.38 273.97 263.69 255.87 245.06 262 266.43 274.08 263.60 255.69 244.98 
 
 _2_1 6 47 263 266.47 274.34 763.76 755.H4 ?44.74 261 2h£.37 2 7 4 .5Q 26,3.11 6 25 5. a ft 244 . 80 261 ?66.48 775.07 764.71 756.13 245.08 
 
 21 6 59 26? 266.85 275.13 264.56 256.35 245.20 261 266.70 275.50 264.60 256.20 244.90 263 266.89 275.74 265.08 256.36 245.12 
 
 _2J Z_lfl 261 266.57 275.52 ?64.62 256.11 244.84 263 267.18 275. 97 265.0 4 256.62 245.24 261 267.06 276.13 264.96 256.49 245.17 
 
 21 7 23 262 267.05 275.7? 264.91 256.46 245.09 262 266.68 275.18 264.57 256.18 244.98 263 267.07 275.82 264.76 256.39 244.96 
 
 _2J 7 35 261 267.04 275.77 265.18 256.63 245.00 261 266. 94 275.49 764.6? 756.11 744.85 761 267.06 776.14 264.91 756.78 745.06 
 
 21 7 47 ..'61 266.92 275.74 264.79 256.34 245.04 262 266.92 275.99 264.80 256.28 244.90 26 267.19 275.61 264.87 256.31 244.86 
 
 _2J 7 59 267 767.78 775.67 764.88 756.35 ?44.9? 260 267.02 275.47 ?64.6f 756.75 744.89 761 767.37 776.06 265.05 756.60 745.14 
 
 21 8 10 26" 267.05 275.80 264.86 256.21 244.88 265 267.45 275.83 265.21 256.63 245.17 261 267.35 275.76 264.97 256.41 245.06 
 
 _2_1 8 20 26? 267.17 276. T6 264.88 256.36 245.01 263 267.29 275.88 265.12 756.5? 745.17 761 267.11 775.61 264.76 756.22 244.90 
 
 21 8 33 261 267.34 275.85 265.10 256.36 245.09 261 267.34 276.00 264.97 256.46 245.03 260 267.26 275.49 264.72 256.30 244.82 
 
 _2J 8 45 263 267.37 275.8? 765.115 756.50 745.05 26_3_ 767.47 275 .78 ?65.?7 756.47 745.09 761 767.30 775.64 264.64 7 56.30 244.87 
 
 21 8 57 261 267.62 275.92 265.22 256.43 245.34 262 267.36 275.62 264.64 256.21 244.94 261 267.46 275.57 264.74 256.32 245.01 
 
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 21 9 20 261 267.40 275.65 264.86 256.50 245.20 263 267.77 276.17 265.33 256.73 245.37 262 267.30 275.72 264.87 256.26 244.94 
 
 _2J 9 33 ?61 267.45 275.94 265.14 256.67 245.36 263 267. 43 275.69 764.86 256.37 245.10 761 267.57 275.75 765.18 756.62 245.19 
 
 21 9 45 261 267.48 275.75 265.07 256.42 245.17 262 267.62 275.68 265.07 256.46 245.14 260 267.33 275.51 264.71 256.26 244.85 
 
 _2_1 9 57 26? 767.57 776.17 765.75 7 56.73 745.42 261 267. 25 275.45 264.8? 756.70 244.85 261 267.67 ?75.65 765.08 756.45 745.7? 
 
 21 10 8 263 267.34 275.69 264.76 256.27 245.07 262 267.54 275.48 265.07 256.53 245.20 261 267.57 275.65 264.61 256.30 245.01 
 
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 21 10 33 262 267.53 275.69 265.08 256.6!) 245.46 262 267.55 275.67 265.23 256.71 245.37 262 267.39 275.48 264.82 256.45 245.14 
 
 21 10 45 ?61 267. 57 275 .79 2 65. 3 3 256 . 9 5 245. 39 __2jl2 767.39 775.6 3 764.71 ?56.?B 744.91 26? ?67.74 776.08 765.3? 
 
 21 10 57 26' 267.37 275.87 264.92 256.59 245.19 262 267.21 275.54 264.80 256.59 245.10 260 267.28 275.69 264.79 256.45 245.20 
 
 21 11 9 263 267.39 275. B-Z 265.21 256.74 245.29 262 267. 18 275.99 26 4 . 75 256.43 245.07 262 267.6 776.5? 265.37 256.87 745.48 
 
 21 11 20 261 267.32 275.09 764.87 256.45 245.02 261 267.22 275.68 265.06 256.48 245.13 262 267.21 276.30 264.97 256.30 245.10 
 
 ?1 11 31 761 767.0Q 775.9" 765.17 756.66 745.17 76? 767.17 776.70 764.76 756.4B 745.10 76? ?67.47 776.35 765.74 756.63 745.3? 
 
 21 11 43 262 267.17 276.58 264.88 256.23 245.0 7 262 267.45 276.46 265.37 256.65 245.22 262 267.54 276.83 265.39 256.76 245.25 
 
 21 11 55 ?6. 267.41 276.50 765.74 756.59 745. 19 260 267. 78 776.15 765.06 756.5.1 745.14 761 ?67.53 777.37 765.61 7 56.90 745.16 
 
 21 12 7 262 267.48 277.81 265.63 256.7! 245.16 262 267.46 277.64 265.78 256.71 245.16 263 267.46 278.18 265.87 256.86 245.38 
 
 ?1 12 19 763 767.35 779.14 765.63 756.70 744.99 260 267.29 273.06 765.69 756.71 745.07 763 767.11 776.99 765.46 756.59 745.07 
 
 21 12 31 262 267.08 276.89 264.85 256.35 244.95 262 267.33 276.82 265.33 256.55 245.10 263 267.07 276.85 264.93 256.30 244.69 
 
 21 1? 43 ?6? 767.77 777.T9 765.77 756.55 745.0? 76? 2 n 7.12 ?77.57 765.79 756.17 744.94 76 7 ?67.4? 777.411 765. ?7 756.65 745.13 
 
 21 12 55 261 267.39 277.32 765.27 256.38 244.96 262 267.47 277.83 265.39 256.63 245.25 261 267.34 277.70 265.32 256.43 244.88 
 
 21 13 Z 26? 267.73 778.76 765.99 756.39 745.79 761 767.50 ?7,9.34 765.71 756.67 ?44.87 761 ?67.77 778.76 765.87 756.86 745.36 
 
 21 13 19 260 267.71 273.76 265.96 256.88 245.30 262 267.65 273.53 265.98 256.92 245.16 261 267.56 278.80 265.67 256.^6 24~5 .TO - 
 
 21 13 31 260 267.77 279. 91 266.11 257.07 245.39 262 267.77 279.06 266.02 257.30 245.17 262 267.90 279.01 266.01 256.97 245.26 
 
 21 13 43 26? 268.07 279.20 266.04 257.02 245.23 260 267.94 279.00 265.83 256.93 245.19 264 267.99 279.04 266.06 257.05 245.29 
 
 21 13 55 26' 267.82 273.81 266.04 256.39 245.05 263 268.11 279.14 2o6.66 257.28 245.47 264 267.67 278.92 265.81 256.91 245.06 
 
 21 14 7 262 267.95 278.99 266.18 257.27 245.36 261 267.74 279.24 266. 21 257.19 245.25 261 267.90 278.82 266.20 257.04 245.14 
 
 21 14 19 26" 267.85 279. C 7 766.04 257.06 245.22 261 268.13 279.12 266.55 257.30 245.35 263 267.58 278.58 265.86 256.64 245.03 
 
 21 14 31 26; 268.07 279.00 266.22 257.12 245.58 262 267.70 273.58 265.69 256.58 245.17 263 267.83 278.64 266.06 256.95 245.27 
 
 21 14 41 261 267.75 278.73 265.81 256.83 245.16 262 267.81 278.93 266.26 257.00 245.35 264 267.88 276.85 266.10 256.97 245.29 
 
 21 14 53 263 267.81 278.87 265.95 256.93 245.27 265 267.96 279.29 266.51 257.38 245.69 263 267.58 278.35 265.90 256.89 245.23 
 
 21 15 5 262 267.79 279.11 266.16 257.15 245.41 261 2b7.71 279.05 266.03 256.96 245.35 264 267.75 278.67 266.11 257.03 245.23 
 
 21 15 17 ?6? 267.78 278.93 266.10 257.02 245.51 263 267.89 279.05 266.44 257.23 245.61 262 267.82 279.01 265.84 256.72 245.37 
 
 ?1 15 29 ?6? 268.22 279.45 266.38 257.27 245.51 263 2b7.79 273.98 265.34 256.96 245.13 262 267.89 279.04 266.24 257.01 245.32 
 
 21 15 41 261 267.76 278.82 266.20 256.97 245.33 261 267.83 £79.07 266.16 257.19 245.36 262 267.99 278.91 266.05 256.98 245.31 
 
 21 15 53 263 268.17 279.37 266.57 257.33 245.66 2 62 267.85 279.82 266.13 256.90 245.14 263 268.11 279.18 266.19 257.09 245.43 
 
 21 16 4 261 257.94 279.74 266.00 256.92 245.17 261 268.25 279.24 266.48 257.23 245.56 262 268.03 278.76 266.10 256.84 245.14 
 
 ?1 16 17 2b? 268. '1 '79.77 '6 6. 58 7_5_7 . = 1 '45.7a ZJl 2o9.0'j 278.93 2 65 . 89 J56_i.ia_ 246 . 5_2 2_6_3 .2 63. h_0 279.34 2c6.26 2 i I . 11 245.41 
 
 21 16 29 261 268.10 279.85 266.02 256.80 245.10 264 268.28 279.19 266.24 257.19 245.48 263 268.27 278.97 266.22 257.12 245.46 
 
 ?1 16 40 263 263.22 279.03 266.27 257.22 245.36 260 263.38 279.33 266.33 257.15 245.51 260 268.42 279.22 266 .20 257.03 245.30 
 
 21 16 53 263 268.08 278.86 266.19 256.39 245.12 261 268. ie 279.29 266.47 257.23 245.47 262 268.10 278.82 266.06 257.02 245.25 
 
 21 17 4 262 268.12 279.01 265.93 257.11 245.17 26 2 _2_tcL. 34 27 9.2 7 266.52 257.36 245.65 262 267.97 279.07 265.69 256.90 245.21 
 
 21 17 17 267 268.23 279. CT 266.32 257.21 245.52 262 268.06 278.91 265.90 256.38 245.22 261 268.26 278.98 266.37 257.19 245.58 
 
 21 17 29 262 268.12 279.3? 266.31 257.23 245.72 263 268.20 278.93 2o6.54 257.26 245.45 263 263.12 279.05 266.15 257.04 245.38 
 
 21 17 41 263 268.32 279.10 2t-6.45 257.21 245.52 263 268.25 278.88 266.11 257.08 245.39 262 268.40 278.81 266.29 257.12 245.49 
 
 21 17 53 262 268.12 273.30 265.99 257. U5 245.39 261 268.28 279.13 266.28 257.70 245.57 261 268.07 27 8.34 266.16 256.95 245.32 
 
 21 18 3 267 268.79 279.24 266.50 257.26 245.58 262 266.01 273.97 266.02 256.90 245.25 262 268.21 279.20 266.57 257.25 245.81 
 
 ,21 18 15 263 268.11 279.12 266.06 257.03 245.42 263 268.05 278.77 266.18 257.07 245.38 263 268.07 278.88 266.03 257.01 245.61 
 
 21 18 27 262 268.08 279.63 265.90 257.0) 245.78 26.2 267.84 278.50 265.95 256.90 245.35 261 267.74 277.10 265.07 256.60 245.20 
 
 21 18 39 261 267.76 277.29 265.39 256.7? 245.57 261 267.48 276.31 265.08 256.34 245.27 262 267.73 276.36 265.08 256.60 245.63 
 
 21 18 51 267 267.55 275.15 264.72 256.41 245.40 263 267.42 276.05 264.75 256.42 245.18 261 267.54 276.23 265.24 256.75 245.42 
 
 21 19 3 263 267.51 276.77 265.06 256.72 245.29 260 267.70 277.07 265.31 256.74 245.46 261 267.87 278.13 265.76 256.82 245.49 
 
 21 19 15 261 267.59 277.55 255.51 256.78 245.33 262 267.48 277.36 265.29 256.68 245.44 262 267.58 277.11 265.21 256.49 245.39 
 
 21 19 27 263 267.72 276.62 265.53 256.81 245.63 261 267.45 276.45 264.64 256.42 245.31 263 267.70 276.69 265.36 256.31 245.73 
 
 21 19 39 261 267.31 276.50 264.75 256.51 245.44 263 267.49 277.16 265.40 256.37 245.33 262 267.45 276.72 265.32 256.64 245.38 
 
 21 19 51 264 267.60 277.38 265.38 256.97 245.63 261 267.43 277.30 265.57 256.35 245.52 263 267.53 277.22 265.52 257.00 245.70 
 
 21 20 3 262 267.51 277.71 265.46 256.82 245.55 261 267.47 277.53 265.40 256.79 245.73 263 267.05 276.62 265.09 256.51 245.37 
 
 21 20 15 267 267.27 277.00 265.39 256.71 245.46 261 267.39 277.10 265.45 256.75 245.62 262 267.32 277.21 265.39 256.7 7 245.49 
 
 21 20 27 264 267.58 277. C9 265.47 256.79 245.68 262 2o7.27 276.94 265.23 256.65 245.60 261 267.36 276.73 265.19 256.76 245.73 
 
 21 20 39 262 267.27 277.12 265.12 256.79 245.61 260 267.19 277.13 265.35 256.82 245.62 262 267.15 277.25 265.26 256.80 245.57 
 
 21 20 51 26? 267.25 277.96 265.59 256.96 245.33 262 267.52 278.63 265.94 257.97 245.63 261 267.39 278.57 265.64 256.88 245.66 
 
 21 21 3 263 267.72 278.81 266.13 257.23 245.83 259 267.43 273.36 265.86 256.96 245.60 261 267.38 278.76 265.87 257.00 745.48 
 
 21 21 13 263 267.44 278.62 265.74 256.98 245.55 261 267.51 278.86 266.10 257.17 245.55 263 267.25 278.29 265.49 256.76 245.43 
 
 71 21 25 26' 267.78 777.14 ?65.?9 756.8? 245.71 262 267.00 275.58 264.63 256.41 245.51 £63 267. 01 275. 13 264.49 25(1.40 245.45 
 
 21 21 37 264 266.95 276.17 264.40 256.23 245.53 260 267.08 275.75 264.72 256.33 245.32 262 267.05 276.53 264.59 256.36 245.38 
 
 21 21 49 262 267.26 276.64 264.94 256.46 245.43 261 266.83 275.23 264.30 256.17 245.41 £61 2.6,6 .7 1 274.68 264.22 256.21 245.30 
 
 21 22 261 267.11 275.82 264.48 256.29 245.43 261 266.95 275.37 264.57 256.28 245.33 262 266.79 275.66 264.51 256.24 245.27 
 
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 915 285.01 283.39 284.71 285.06 284.88 
 921 284.95 283.63 284.71 235.13 264.75 
 
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 926 265.19 283.19 2.94.64 284.39 234.97 
 
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 916 285.16 283.93 284.56 285.04 264.94 
 
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 929 285.20 283.21 284.50 294.78 284.84 
 
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 20 284.63 26.4.99 284.63 957 285.18 284.17 284.73 285.16 284.82 957 285.04 284.25 284.63 295.00 284.77 
 
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 980 ?85.?7 734.76 ?84.48 ?34.38 284.75 
 
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 92 282.61 283.03 283.54 
 
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74 
 
 FLIGHT NO 7 6/ 12/ 70 
 
 I 
 
 HR MB SC ALT Tl _ J2_ _ T3 Tk T5 ALT Tl T2 T3 TU T5 ALT Tl T2 T3 TU T5 
 
 11 31 71." 279.711 289.06 281.'. 35 282.12 277.98 71.5 280.16 289.68 285 . ll. 282 .",1. 278.13 750 280.52 292.13 286.68 283.1*9 278.56 
 
 11 1.3 75' ?8fl.6i< 791..1.5 786.55 787.1,5 773.86 7 55 78(1.99 291.58 786.8? 733.71 779.76 761. 780.79 789.71 785.85 783.18 77q.11 
 
 11 55 769 281.11. 288.88 285.1.1. 283.22 279.31. 772 282.30 292. 51. 287.66 285. ]". 280.1.1 771. 282.81 296.03 290.38 286.83 281.19 
 
 1? 7 73? 737.8? ?a?.(-8 288.61 786.05 781.1 M 78? 787.1.7 783.38 7 86.0 7 781.. 39 731.15 791 787.B3 789.N7 786.97 731..96 781.79 
 
 12 19 707 233.11 283. °7 286.83 285.39 281.90 810 233.09 288.06 286.60 285. 11. 282.19 810 283.51. 288.39 287.02 285.50 282.76 
 17 3T 3ia 731..77 789.31. 287.91. 786 .31 ?3^.36 876 73... 35 783.99 787.88 786.1.1 783.71 830 785.01. 78q.H8 788.63 737. H5 ?81..nq 
 
 12 1.3 833 235.88 291.28 289.77 238.08 285.09 81.5 286.00 291.1.9 290.01 288.31 285.15 6*7 285.96 290.79 289.77 238.26 285.32 
 12 55 35 2 236.53 290.7° 289.79 788.53 235.61 865 237.16 292.22 290.91 2 8 q.;a 286.1.8 B6f 738.70 297.10 29H.13 291.88 287.33 
 
 13 7 873 28B.70 296.87 291,. H. 292.07 287.39 875 288.09 29".. 08 292.63 291.03 287.1.1 877 288.86 29 It. 1.5 293.03 291.<t<t 287.82 
 13 19 887 290.21 297.15 295. Pit 293.03 738.79 891 29 0.98 3 00.00 297.08 291.. 58 289. it9 895 790.70 298.03 295.87 793.83 789.1.5 
 
(Continued from inside front cover) 
 
 NESC 53. Archiving and Climatological Applications of Meteorological Satellite Data, 
 
 John A. Leese, Arthur L. Booth, and Frederick A. Godshall, July 1970. 
 
 , (COM- 71-00076) 
 NESC 54. Estimating Cloud Amount and Height From Satellite Infrared Radiation Data, 
 
 P. Krishna Rao, July 1970. (PB-194 685) 
 NESC 56. Time Longitude Sections of Tropical Cloudiness (December 1966-November 1967) , 
 
 J. M. Wallace, July 1970. 
 
 NOAA Technical Reports 
 
 NESS 55. 
 
 NESS 57. 
 
 The Use of Satellite-Observed Cloud Patterns in Northern Hemisphere 500-mb 
 Numerical Analysis, Roland E. Nagle and Christopher M. Hayden. April 1971. 
 Table of Scattering Function of Infrared Radiation for Water Clouds, Giichi 
 Yamamoto, Masayuki Tanaka, and Shoji Asano, April 1971. (COM-71-50312) 
 
PENN STATE UNIVERSITY LIBRAPiPc 
 
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