[ the Reflectance and Scattering, [ of Solar Radiation by the Earth | 1967016633-002

i 05863-II-T

I r_,CDAD'f'lCOLLEGEUiCkl'r r OF , ENGINEERI-_-**l- g-,,,,,, ...... NG - u,_.,_nnlmL_l ,.Jr _CR_,Jr_Lc I::rfbiNl::l:l(INl_

] HiGHALTITUDEENGINEERINGLABORATORY

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s [ The Reflectance and Scattering, [ of Solar Radiation by the Earth | 1967016633-002

THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Aerospace Engineering High Altitude Engineering Laboratory i

i Technical Report

i THE REFLECTANCE AND SCATI_ING OF SOLAP RADIATION BY THE EARTH

Fred L. Bartman I"

." ORA Project 05863 s

D under contract with:

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CO_T_ACTNO. NaSr-_4(03) WASHINGTON, D.C.

administered through:

OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR

._ February 1967 1967016633-003

_ s report was also a dissertation submitted in parti_l fulfillment of the requirements for the degree of Doctor of Phi!osophy in The University of Michigan, 1967. 1967016633-004

ACKNOWLEDG_NTS 6 I The autnor wishes to thar_ all of the many people who have assisted him in this study. The advice, and help of Professor Edward S. Epstein, I Chairman of the Doctoral Committee, is particularly appreciated. The author is also grateful to Professors Leslie M. Jones, Robert M. Howe,

La_Tence L. Rauch, and Aksel Wiin-Nielsen, for serving as members of the Committee and for their help and suggestions during the course of the work. i The constant interest aad encouragement of Professors Wilbur Nelson and L. M. Jones in the early stages of the work, before the Committee was

Ii. formed, arealsogratefullyacknowledged. The help of all my colleagues in the High Altitude Engineering Lab- _" oratory in carrying out preparations and field operations for the balloon " flight measurements is also acknowledged. Of these, the work of Mr. r Michael Surh, on radiometez calibration, and Messrs. Leo W. Csrls, Paul A. Titus, Wan Y. Lee, and David Hartzig on field operations and radiometer data processing is particularly appreciated.

i The financial support received from the National Aeronautics and Space Administration under Contract NASr-94(03) is also gratefully ac- ° knowledged. Ntur.erousdiscussions of radiometer calibrations and the man- nero _ interpretation of radiometer data with Dr. William Nordberg, Mr. William Bandeen and other members of the Staff of Goddard Space Flight r Center, and of Mr_ Frank Malinowski of Santa Barbara Research Corpora- i tion have also been very he1_ful. T 1967016633-005

TABLE OF CONTENTS

Page

, LIST OF TABLES v

LIST OF ILLUSTRATIONS vii

I ._ NOMENCLATURE xiv

ABSTRACT xxiii

CHAPTER

I. INTRODUCTION 1

II. DEFINITIONS 9 A. The Geometry of Scatterin_ and Reflecbion 9 B. Reflectanc,_ 9 C. Scattering Jh_le lO D. Earth's Albedo ll E. Planetary Albedo, Bond's Definition 16

IIl. A REVIEW OF RESEARCH RELATED TO EARTH'S ALBEDO 23 A. Earth's Albedo from Measurements of Earthlight on the Moon 23 B. Earth's Albedo Measurements from Satellites and Spacecraft 29 C. Reflectance of the Earth's Surface 27 D. The Reflectance of Clouds 28 E. The Scattering of Solar Radiation by Air Molecules and Aerosols 28 F. Estimates of Earth's Albedo 33 G. Discussion: Models of the Earth for Albedo Purposes 33

IV. B_LOON FLIGHT MEASUREMENTS OF EARTH REFLECTANCE 36 A. Introductory Notes 36 B. The Balloon Flight Measurement System 37 C. Radiometer Measurements: Calibration and Interpretation 43 . i. Calibration of the radiometers 14"3 2. Interpretation of the radiometer data 57 D. Data Obtained on Three Flights 63 t i. The 2 June, 1962 Balloon Flight 63 2. The 26 June,1963 Balloon Flight 78 3. The i0 March, 1969 Balloon Flight 84 ,, E. Discussion of Data Obtained 92 i i. Nonisotropic earth reflectance i00 2. The wavelength dependence of earth re-

i fiectance i01

1 iii 1967016633-006

TABLE OF CONTENTS (Continued)

CIIAFTER Page

V, A MODEL OF THE EARTH FOR ALBEDO PURPOSES 107 A. Geometrical Characteristics 107 B. Physical Characteristics t08 C. Illustrative Example 110

- VI. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 124

A. Conclusions 124 B. Further Research 126

APPENDIX A. EARTH'S ALBEDO FROM MEASUREMENTS OF EARTHLIGHT ON THE MOON 128

I. The Work of Dan Jon 128 2. The Work of Bakos 131 3. The Work of Dubois 137

APPENDIX B. EARTH'S ALBEDO MEASUREMenTS FROM SATELLITES AND SP_ CECRAFT 140

I. The Low Resolution Measurements 140 2. The Medium Resolution Measurements 158 3. The Mariner 2 Measurements 183

APPENDIX C. REFLECTanCE OF THE EARTH'S SURFACE 187

i. Spectral Reflectance 187 2. Angular Distribution of Reflectance 200 3. Total Directional Reflectance 209

APPENDIX D. THE REFLECTANCE OF CLOUDS 2]8

i. Spectra] Reflectance 218 2. Angular Distribution of Reflectance 218 3. Total Directional Reflectance 219

APPENDIX E. THE SCATTERING OF SOLAR RADIATION BY AIR MOLECULES AND AERObOLS 225

i. Molecular Scattering 225 2. Aerosol Scattering 232 3. Summary 237

APPENDIX F. ESTIMATES OF EARTH'S ALBEDO 238

APPENDIX G. DESCRIPTIO]_ OF COORDINATE SYSTEM8 U8ED 249

REFERENCES 250

iv [1 196701663g-007

LIST OF TABLES

Ii Tabl_ Page I. Earth's Albedo From Measurements of Earthlight on the

I Moon 2h 2. Earth's Albedo Me,..surementsFrom Satellites and Space-

craft 26 3. Summary of Reflectance Data For Earth Surface Features 29

Summary I 4. of Reflectance Data for Clouds 30 5. Summary of Data for Molecular and Aerosol Scattering 32

1 6. Summary of Earth Albedo Estimates 34

[," 7. Cloud Cover Viewed by Radiometer,2 June 1962 Balloon I Flight 63 8. Theoretical F-I MRIR _eflectance Measurements 10h

L 9. Illustrative Example, Values of "Jk 117

i0. Illustrative(ooooG_) Example, Values of _:kJ For GILA= 180.3e 118

ii. l(12lluoost:'ativeGMT) Example, Values of _'k_ For GHA = 0.23° n9

12. Illustrative Example, Values of _ For GHA m 180.3° (ooooOMT) _ 12o i3. Illustrative Example, Values of [ For GHA = 0.23°

(1200 GMT) i 121 14. Earthshine Photometer Stations 132

15. Long;itudiualVariation of Cloud Cover 135 16. Monthly Variations of the Brightness of the Earthshine 135

17. Values _f Absorptivity for Varloue Coatings i_2

18. No3 maninald 5 Characteristics of Tiros Radi_eter Channels 160

19. Nominal Characteristics of F-_ MRIR (0.2-_.O-Micron Channe_ 168

20. Final Seasonal and Annual Values of Long- and Short- Wave Radiation 182 n v II 1967016633-008

LIST OF TABLES (.Concluded)

Table Page

21. Bidirectional Luminous Reflectance of Terrain Back- grounds for Moderately High S_n 203

22. Bidirectional Luminous Reflectance of Terrain for Low Sun Angles 206

,_3. Bidirectional Luminous Reflectance of Terrain Back- grounds Under Overcast 207

2h. Dependence of Cloud Total Reflectance on Underlying Surface 223

25. Wavelength Dependence of Normal Optical Thickness of Earth's Molecular Atmosphere Above Sea Level "._30

26. Reflectance of Solar Radiation, _ _40

27, Data Used to Obtain Albedo of Northern Hemisphere 243

28. Seasonal Distribution of Planetary Albedo Components Due to Atmosphere Sc%tterlng and Ground Reflectance 245 %

vi t,, 1967016633-009

# I

LIST OF ILLUS,"_TIONS

Figure Page

I i. Geometry of reflection and scattering. 6 2. Distribution of reflected radiation for a perfectly

I diffuse (Lambert)reflector. 9 3. Distribution of reflected radiation for imperfectly i diffusefor threereflector,angles ofi/,incidence:0(Bo,¢o,8,0¢)°, coshO°,Bandis plotted60°. I0

4. Geometry for calculating earth's albedo. 12

I 5. Planetary albedo-geometrical relations. 17

I 6. Cperfompaerisonctly diffuseof DanJohn'somogenphaseeousfunctionearth. with that of a 25

i 7. Balloon flight confi_tLration. 39 8. Balloon gondola used on 2 June,!'962balloon flight. 39

9. Airborne telemet,> ,,_ I mounted in gondola...... % and instrument programming unit 41

I i0. Inside _obile teiem_ry _ro,_ndstation. 42 ii. Instrument oper_tlon prc._ramfor i0 March,]965 ',_,'lon - flight, hh i 12. Calibration sour_es. 46

_ !_. TIROS #I03A radic_.,;e_,.hs._nel5 (0.55-0.75-_ ,:"m) calibration curves. 50

," i_. TIROS #I03A radiometer ch_._.,e_._ (0o:_-5. ,_.'ton) I. calibration curves. 51

15. Calibration curves for 0.55-O.85-mieron channel of ii F-1 MRIR radicaeter. 53 16. Calibration curves for 0.2-4.0-micron channel of ii F-i MRXR radiometer. ,_ 17. SBRC F-_ _IR calibration, 0.2-4.O-micron channel. 55

[i 18. University of Michigan F-h MRIR calibration data. |. 0,2-_.O-micron channel. 56

vii I' 1967016633-010

LIST OF ILLUSTRATYONS (Contlnue4)

F_ure Page

19. Weighting function, H .$J for 0.55-0.75-mlcron channel of TIROS #103A radiometer. 59

20. Weighting function, H .$J for 0.2-6.0-micron channel of TIROS #I03A radiomete_¢ ^ 60

21. Weighting funetlon, H ._ for 0.55 0.85-mlcron channcl of F-I MRI_ radlomete_ ^ 61

22. Weigbtlng function, H .¢: for C.2-4.0-micron channel of F-h MRIR radiometer, s^ ^ 62

23. Altitude-tlme curve fo,' 2 June, 1962 balloon flight. 64

24. Trajectory for 2 June, 1962 balloon flight. 64

25. Photographs of cloud co_er for 2 June, 1962 b,_lloon flight. 65

26. Bidirectional reflectance of stratocumulus clouds, p' for 0.55-0.75-micron channel of TIROS #103A radiometer, 2 Jun_ 1962 balloon fl_ght. 67

27. Bidirectional reflectance of stratocumulus clouds, p' for 0.2-5.5-micron chana_l of TIROS #103A radi_neter 2 June, 1962 balloon flight. 68

28. Bidirectional reflectance of stratocumuluc clouds as s function of sc_tterlng angle, average values. 70

29. Cor parlson of experimental measurements of bidirectiorml reflectance of stratocumulus c_oud with theoretical single scattering pattern of water cloud model. 71

?0. Model of bidirectional reflectance pattern of stratocumulus cloud. 72

31. T@ta directional reflectance of a stratocumulus cloud as a function of solar angle of e]evatlon. 7_

! ! ! • 32. Reflectance diagram, ratio D3/05 v_. 05 for 2 Jun_ 1962 balloon flight. All data taken-shove c_plete overcast or broken to scattered cloud conditi_nf. 75

33. Reflectance ratio vs. time for 2 Jun_1962 balloon flight. 77

3_. Altitude-time data and trace of bal mn traJecto_ f_r 26 Jun_ 1963 balloon flight. 79

viii i 1967016633-011

i" LIST OF ILLUSTRATIONS (Continued)

] Figure Page 35. Reflectance diagram, ratio ' ' p3/P5 vs. 0; for 26 June,

I 1963 balloon flight, TIROS #103A radiometer. 80

36° Reflectance diagram ratio P;/p; vs. O; for 26 June, 1963

balloon flight, NIMBUS MRIR F-I. 81 37. Reflectance ratio vs. time for 26 Jane, 1963 balloon flight, TIROS #103A radiometer. 82

38. Reflectance ratio vs. time for 26 June, 1963 balloon flight, NIMBUS MRIR F-1. 83

39. Altitude vs. time curve for i0 March, 1965 balloon flight. 85

40. Ground trace of balloon trajectory for i0 March, ]965 balloon flight. 86 41. Polar coordinate system for bidirectional reflectance I diagrams. 88 1 42. Bidirectional reflectance diagram obtained at 083;'- 0836 CST on I0 March, 1965 balloon fl_ght, e° = 72.2-

71.5 ° , pressure altitude = 20.0-16.5 mb. 89 : 43. Photos of model of 0832-0836 CST bidirectional re-

{] flectance pattern" e72"=2-71"5°'o 91 44. Bidirectional reflectance of snow-covered sarth and atmosphere in principal plane, i0 March, 1965 balloon

I; flight" eo = 72"2-71"5°" 92 45. Bidirectional r_flectance disgram obtained at 0855-0909

pressureCST on i0altitudeMarch, 1965= 9.0-8.5balloon mb.flight, eo = 68.3-66.0 ° ' 94

I_ 46. Photos of model of 0855-0909 CST bidirectional reflectance pattern, e° = 68.3-66.0 °. 95

47. Bidirectional reflectance of snow covered earth and

-t flight,atmospheree i=n 68.3-66.0principal °.plane, i0 March, 1965 balloon 96 O

Iii 48. Bii116directioCST nonal i0reflectanceMarch, 1965 diagramballoon oflight.btained at8 110= 50.5-9- 50.0 °, balloon pressure altitude = 8.5-8.3 m_. 97

I; 49. Photos of model of 1109-1116 CST bidirectional re- I. flectance pattern. 8O = 50.5-50.0 ° • 98

I" iX 1967016633-012

LIST OF ILLUSTRATIONS (Continued)

Figure Page

50. Bidirectional reflectance of snow covered earth and atmosphere In principal plane, i0 March 1965 balloon flight, e = 50.5-50.0 °. 99 O

51. Directional ref.ectance of stratocumulus cloud as a function of sun elevation angle (r is true directional reflectance, r' is r_sult obtained for average of bidirectional reflectance for radiometer nadir angles of O-h5 ° ). 102

52. Reflectance diagram demonstrating spectral dependence of earth reflectance. 105

52. Spectral reflectance curve of earth measured through clear skies from balloon over South Dakota, 26 Junej 1963. 106

5h. Land, ocean, _xnd snow covered areas of the earth, 23 December. 113

55. Mean cloudiness of the earth, 23 December. llh

56. Illustrative example: values of _.. 115 1

57. Average albedo in integration ring k vs ek. 122

58. Images in cat-eye photometer. 128

59. Variation of the brightness of the earthshine. 139

60. Schematic diagram of satellite orbiting the ear.h, lh8

61. Typical black sensor and mlrror temperature observations during a TIROS IV orbit, lh9

62. View of the earth and the precessing TIROS IV orbital plane. 15h

63. Comparison of the meridional variation of albedo for two precessional cycles. 156

6h. Comparison of the meridional varlahion of albedo for March, April, and May with data of London. 157

65. Diagram indicatlng principle of operation of a channel of the TIROS five-channel radiometer. 159 1

66. Effective spectral response of channels 3 and 5 of TIROS flve-channel radiometer. 161 I x 1967016633-013

LIST OF ILLUSTRATIONS (Continued)

,_ Figure , Page

67. The scan patterns of the TIROS medium resolution _ radiometer. 163

_- 68. Optical arrangement of NIMBUS five-channel radiometer (M_IR). 16h 7

i 69. Relative characteristic response, ¢{, of 0.55-0.85- micron channel of F-1 MRIR. 165

i 70. Rel_tive characteristic response, @_, of 0.2-h.O- micron channel of F-I and F-4 MRIR instruments. 166

_" 71. Field of view contours of the 0.2-4.O-micron channel i of the F-_ MRIR. 167

72, TIROS VII: 0.55-0.75-micron channel quasi-global map i averages. 175

73. AugustTIROS VII:1963.0.55-0.75-micron channel albedo, June-July- 177

74. TIROS VII: 0.55-0.75-micron channel albedo, September-

C.-tober-Novembe_ 1963. 178 75. TIROS VII: 0.55-0.75-micron channel albedo, December

196B-January-February 1964. 179 76. TIROS VII: 0.55-0.75-micron channel albedo_ March-April- T May 1964, 180 i 77. TIROS VII: 0.55-0.75-micron channel albedo, June 196B- W May 1964. 181 - 78. Reflectance curves for soils and rocks. 188

r 79. Diffuse reflectance of representative types of desert surfaces. 189

80. Spectral dietribution of reflected energy for minerals and rocks. 190

81. Refl_ctance of NAA standard granite. 191

J A 82. Spectral reflectance coefficients. (i) sand; (2) soil; (3) asphalt; (4) brick; (5) concrete. 192

83. Bidirectional reflectance of sand (@ -- 53 °) and black loam soil (@o = 78'5Q) at different wavelengths.o 194

xi 1967016633-014

LIST OF ILLUSTRATIONS (Continued)

Figure Page

84. Spectral reflectance curves for vegetation. 195

85. Spectral albedo o{ different vegetation: (1) sudan grass; (2) maize; (3) clover; (_) lucerne grass (June), (5) lucerne grass (July). 196

86. Evolution of spectral rmflection of a leaf during the growing season. 198

87. Spectral albedo of a water surface (measured over a la_e with depth of 60 uo 70 cm). 199

88. Spectral albedo of the snow cover in clear weather, 28 March, 1963. The Leningrad Region dry snow. 201

89. Bidirectional reflectance of va;'ious types of soil at different m_gles of incidence. ^ = 0.6h3 micron. 202

90. Bidzrectzonal reflectance of green grass turf at different angles of inczdence. X = 0.6h3 micron. 205

91. Bidirectional luminous reflectance in the principal plane for water of infinite depth. 20B

92. Measured luminance of a snow surface. 210

93. Total reflectance of various types of soil. 211

9h. Dependence of total reflectance of clay soil on its surface condition. 212

95. Total reflectance oz' vegetation. 21h

_,,C r . Total reflectance of water basins. 215

97. Variation of total reflectance of sea surface as a function of sun angle under stratus clouds. 216

98. Change in total reflectance of snow cover with time. 217

99. The spectral albedc for middle layer clouds. 218

100. Intensity functions for water cloud illuminated by 0.h5-micron radiation. 220

lO1. Intensity functions for water cloud illtm_inated by 0.70-micron radiation. 221

102. Total reflectance of coastal stratus cloud as a rune- i} tJon of cloud thickness. 2_2 I I 1967016633-015

I. LIST OF ILLUSTRATIONS (Concluded)

i Figure Page 103. Dependence of cloud total reflectance on cloud thick-

I ness and cloud type. 224 104. ?_stribution of intensity of light emerging from the top

plane. Sun elevation 53° , optical thickness T = 1.O, sur- i of the atmosphere and of the skylight in the principal f'ace albedo A = O, 0.25, and 0.80. 228

|- 105. Surface albedo (Fresnel case) and ratio of upward flux - (Fresnel case) to upward flux (Lambert case) for nonabsorbing, homogeneous, plane parallel atmosphere with _- Rayleigh scattering. 229 I_ 106. Relative intensity o_ outward radiat[on for Rayleigh

atmosphere with red clay surface. 231 107. Relative intensity of outward radiation for Rayleigh atmosphere with white quartz sand surface. 233

108. Sky and earth radiance, for an atmosphere with optical depth 0.4, surface albedo 0.2 (Lambert), and aerosol

scatteringscattering. with five times as much forward as back- 2B6

109. The seasonal distribution of planetary albedo (%). 2_5 [ [ [ [

[

H xiii 1967016688-016

NOMENCLATURE a Radius of the earth a, b - Constants indicating beginning and end of satellite's orbit through earth's shadow

A Anti-source

A Albedo, earth's albedo

A' Apparent earth's albedo for incomplete bidirectional rsflec- tance

A Average earth's albedo

Aa Albedo of atmosphere

Aau _I _lbedo of atmosphere in ultraviolet, visi01e, and infrared, Aav respectively A ! ai _ A Albedo of clouds c

AcuAcv _I Albedospectively of clouds in ultraviolet, visible,and infrared re-

Aci / A Albedo of earth surface e

A Albedo of earth's surface in ultraviolet, visibl_and in- ev frared, respectively

AeiAeu t

AvAu _I Albedospectivelyof earth in ultraviolet, visibl_and infrared, re-

Av_ Spectral distribution of earth's albedo in the visible region of the spectrum ! t l A_ Spectral albedo 1967016633-017

_. NCMENC[ATURE (Continued) i A' Photometric albedo (actually includes ultraviolet) for a o-o.7 clear sky

T Ar Area of radiometer aperture A, B, C Variables used to replace terms in complicated expressions I !. C Brightness of sunlit crescent of moon C % cloud cover. Also weighted % zloud cover i_ C

I" Cm Constants C C

Ct Ch Channel

- Cos*_ Geometrical weighting function for solar radiation incident on an area viewed from a satellite

dm The mass of a scattering element

. ds An element 'iofarea) of a reflecting surface

D DanJon's photometric albedo

i ,_ E East

E Brightues_ of earthlight on moon

f (_) Spectral energy distribution of standard source ,- O

f®(A) Spectral distribution of earth radiation

- fl(_) Empirical solar continuum according to Minnaert

f2(A) l-F, where F is the Fraunhofer line blanketing coefficient

f3(A) Wavelength dependence of over-all reflectiviti of e_rth _, F(n) Lunar phase function

fx(_) Function proportional to earth's phase fianction

1 H Heat capacity of sensor -2 H Irradiance, watts cm |

] I xv 1967016633-018

NOMENCLA'i_/RE(Continued)

HA Solar irradiance absorbed in the atmosphere with normal cloud cover

-2 micron-1 H_ Spectral irrs,diance,watts cm -2 Hs Solar irradiLnce, watts cm -2 -1 Hs_ Solar spectA'alirradiance, watts cm micron

H's Solar irradiance at the earth's surface with a clear sky H" Solar irradiance at the earth's surface with normal cloud cover s h Vertical dist&nce between bottom of balloon and point of its maximum diameter hs Sun's hour angle h(t) Satellite sensor degradation correction factor i Angle of incidence

Idd Radiation transmitted diffusely through the atmosphere, reflected at the earth's surface and transmitted diffusely through the atmosphere

IdD Radiation transmitted diffusely through the atmosphere, reflected at the earth's surface and transmitted directly back through the atmosphere

IDd Radiation transmitted directly through the atmosphere, reflected at the surface, and transmitted diffusely back through the atmosphere

IDD Radiation transmitted directly through the atmosphere, reflected at the surface, and transmitted dizectly through the atmosphere

I Radiation backscattered by the atmosphere, never reaching the s earth's surface

Io Photoelectric current produced by a standard source

I@ Photoelectric current produced by earth radiation

II,12 Photometer images

I1 Intensity of earthshine if 12 Intensity of sunlit portion of the moon I1 1967016633-019

NOMENCLATURE (Continued)

k A constant

kA Coefficient used in Bond's definition of planetary albedo

k_ Mass scattering coefficient

K Conductivity of hemisphere support rod

KI,K2,K 3 Constants

£ Length of load line in balloon train

Mok The magnitude difference of the apparent brightness of the earth at full phase as viewed from ti_e moon and the brightness of the sun at 1 Astronomical Unit

T ME-M c The magnitude difference of the sunlit crescent of the moon and the earthlit portion of the moon

ME-M s The magnitude difference of the apparent b;ightness of the earth as viewed from the moon and the brightness of the sun at i Astronomical Unit

n Index of refraction

n(r) Number of particles with size in range r to r + dr

N Number density

N North

N Radiance, watts cm "2 star -I

N Radiance of diffuse calibration source, watts cm -2 ster -I C

N'c Effective radiance of calibration source, watts cm -2 ster -I -2 N Radiance of surface reflecting solar radiation, watts cm s ster-i

N' Effective radiance of surface reflecting solar radiation, s watts cm -2 ster -I -2 Nc_ Spectral radiance of diffuse calibration source, watts cm ster-i micron -I

_A Spectral radiance, watts cm-2 star -I micron -I

PI,P2 Intensity functions o_ different polarizations

Ps To_al power incident on the ill_inated hemisphere of the earth watts

xvli 1967016633-020

NOMENCLATURE (Continued)

p(cosB) Phase function in scattering theory pA Geometrical albedo q_ Phase _ntegral

Q(_) Function proportional to earth's uhase function r Maximum radius of balloon r Radius of a scattering particle r Specular reflectance calculated with the Fresnel formula r(eO ,@o) Directional reflectance, the fraction of radiation incident from direction (eo,@o) which is reflecte( r (e O ,_o) Spectral directions? reflectance r (eo,$o) Spectral directional reflectance measured under conditions of natural illumination r'(eo,@ o) Apparent directional reflectance when using measurements up to 25 ° r(a,t) Weighted average reflectance of planet for phase angle m and time t

R.A. Right ascension of satellite orbit

Ro_ The magnitude difference of the apparent brightness of the earth at full phase at 1 A.U. and the brightness of the sun at 1 A.U.

-S The mean distance of the earth from the sun

R The mean distance of a planet from the sun p-s

R' The resporsivity of the radiometer detector

R£ Thermal r_diation emitted by the earth and its atmosphere, watts cm---

-2 Rr Radiation reflected from the surfB.cm of the earth, watts cm

R Direct radiation from the sun, watts cm-2 (the solar constant) S

R(R,70) Correction factor, response at 70OF divided by response at TeF

S South

l S Source ', 1967016633-021

[

NOMENCLATUPE (Continued)

S Brightness of sun

SO Brightness of earth as seen from spacecraft, footcandles

S Footcandle output of standard source o

TI,T 2 Two consecutive sensor temperatures, °K [ T Average sensor temperature, °K T Temperature, °K

]i TB Temperature of black sensor, °K

m T TemperatILre of mirror, °K -- oK Tm Average tempe:ature of mirror,

T s Temperature of shielded sensor,

TT Temperature of sensor with Tabor surface, °K

Tw Temperature of white sensor, °K [ Vo Radiometer voltage when viewing calibration source Vs Radiometer voltage when viewing surface reflecting solar radiation

V Volts W West

Ii W Radiant emittance, watts cm -2 -2 -1

. W_Z AltitudeSpectral radiant emittance, watts cm micron

, Z Zenith Size parameter (used in scattering theory)

a Phase angle

m.(_n_t) Coefficients of basic bidirectional reflectances

m_ Absorptivity of spherical shell sensor fo_ thermal radiation

I ms Absorptivity of spherical shell sensor for solar radiatior

i xix ] 9670 ] 6633-022

NOMENCLATURE (Continued)

8 The solid angle subtended by the earth as viewed from • satellite

8 Scattering angle measured from incident ray extended to scattered ray

6 Depolarization factor of air g Declination of satellite

6 Declination of s',n s

A The mean distance of the moon from the earth

_n Magnitude difference

¢6 Emissivity of spher[c_l shell sensor for thermal radiation

Longitude of a point on the surface of a pl_net, as viewed from earth

_' Longitude of a point on the surface of the earth n Colatitude of a polnt on the s_face of a pl_et, as viewed from earth n' Colat_tude of a point on the surface of the earth n Phase angle of the moon as viewed from earth nI Reflectance of earthshine area of moon

_2 Reflectance of sunlit area of moon eo Zenith angle of sun

0 Zenith angle of radiance or reflected ray, and nadir angle of observation

A Wavelength, microns

_, Micron -I v Wave number, cm v_ A constant w 3.1_1596... p Air density pA(_o.¢o.e._._t) Bidirectional reflectance _t a point (_,') on the earth's surface 'i1 1967016633-023

NOmeNCLATURE (Continued)

P(eo,%,e,m) Bidirection_l reflectance, fraction of rad._tion incident from direction (8o,$o) which is reflected in direction (e,_)

pl(eo,$o,8,#) Spectral bidirectional reflectance

pli(6o,¢o,e,¢)_. Basic bidirectional reflectances for use with albedo model , of earth I.

_' Effective a_erage bidirectional reflectance of a surface i as measured by a radiometer

p'' Effective bidirectional reflectance corrected for degradation of satellite sensor

p''' Effective bidirectional reflectance corrected so that i radiation balance is obtained PG Surface albedo

I p Average bidirectional reflectance over bandwidth of _- radiometer channel

_ PJ_'Ps' Effective bidirectional reflectance of r_diometer channel's -_ 3 and 5

_'- e s (min) Mi,_imum zenith argle of sun (at local noon)

a Radius of the earth divided by the distance of the earth _. from the sun

o Stefan-Boltzmann Constant

Optical thickness

Azimuth angle of reflected or scattered ray

_X(_) Phase function at wavelength X

_ Effective spectral response of a channel of a radiometer

' Relative spectral response of a channel of a radiometer

_v Response function of the eye

Ss II Response function of the s II photo emissive surface . multiplied by transmission function of objective lens

I _o Azimuth angle used for integration over sunlit hemisphere of earth measured counterclockwise from north

i xxi 1967016633-024

NOMENCLATURE (Concluded)

¢o Azimuth angle of sun's ray extended, measured counterclockwise from north

= ¢ - ¢o Azimuth angJe of reflected or scattered ray measured counterclockwise from principal plane

Solid angle i, I, I Summation over i, J, k, respectively i J k I Night portion of satellite orbit

II Sunrise and sunset portion of satellite orbit

III Daylight portion of satellite orbit

i xxii ! I 1967016633-025

i i

ABSTRACT

The basic objective of this study is to provide a complete analysis of the physical and observational problems associated with the determination of the earth's albedo. There are two main results of this analysis: One is the conclusion that, insofar as the ,reflectance of solar radiation i. havingis concedifferentrns:d, the diffuse,earth iswavelengtha nonhomogeneousdependentbod_freflectancewith its variousfunctions.regionsThe second is a statement of the geometrical-physical characteristics of a

precise model for the calculation of earth's albedo. The nature of the earth's reflectance is explored by means of precise

resuldefinitions,ts, and newa completeearth reflectancesurvey and datacriticaiobtainedanalysisby radioof e×_stingmeter measure-research ment on three high altitude balloon flights. The precise model is obtained

I by careful detailed application of the precise definitions.

First, the nature of the reflectance of a surface element is consld-

I ered in terms of spectral bidirectional reflectance. Directional reflectance and total reflectance quantitles are defined. The geometrical nature of scattering is reviewed. Then earth albedo is defined precisely

I in terms of the time dependent spectral bidirectional reflectance of all areas of the earth's sunlit hemisphere. The astronomer's definition of planetary albedo, Bond's definition, is consldered. The Bond albedo is

I then expressed as a function of the time dependent spectral bidirectional reflectance. It is concluded that, for a rotating planet such as the earth, the Bond albedo is not the same as the precise albedo, except for

I the case of a homogeneous planet having isotropic (diffuse) reflectance.

Information about the native oi earth's reflectance is presented by f means of summaries of results in several different areas of albedo research:

a. The classical earth albedo experiment of Danjon. - b. Spacecraft and satellite measurements. c. Mcasurements of the reflectance of earth's surface features. d. Theoretical studies of the scattering of solar radiation by - clouds, the clear earth's atmosphere and aerosols. e. Estimates of earth's albedo made in connection with earth's heat balance _tudies.

._ These summaries show that the earth is a nonhomogeneous reflector of solar radiation. Reflectance functions for soil and rock, vegetation, ocean, snow and ice, and scattering functions fcr clouds, clear air and i aerosols are complex, nondlffuse and wavelength dependent. Time varla- XXIIi i 9670 i 6633-026

" i '. m I

ABSTRACT (Contlnued)

tions, diurrml and seasonal, are much in evidence. In spite of this, the model used by experi.Lenters for satellite data interpretation is usually a homogeneous earth _rith diffuse reflectance. Wavelength dependence is also often neglected. The need for a more precise model becomes apparent.

New data obtained with radiometers flown on high altitude balloons are presented and discussed. The balloon flight measurement system is described. The geometry of the measuremePts is shown to be precisely that whicn yieldb bidirectional reflectance or scattering patterns. Calibration curves are shown for the radiometers used. The method of interpretation of data as bidirectional reflectance _s explained. Data from three balloon flights are presented.

Data from a flight on 2 June, 1962 show _ne re_'lectance or scattering of solar radiation from low stratus clouds over farmland. The scattering pa_'Lern obtained is shown to agree qualitatively with theoretical results for single c,:attering from a water cloud with realistic particle size distribution, with large backscBttering, very large forward scat- tcrlz_ _nd indications of a fogbow at about 136 °. Directional reflectances calculated from the scattering pattern for varying solar zenith angle give a maximum total directional reflectance of 85% for zero solar zenith angle, a minimum of 58% at _0 ° solar zenith angle, and 63_ at 89 _ zenith angle, in good agreement with other experimental data. The data also show that cloud reflectance has relatively small spectral variations whereas under broken cloud conditions over South Dakota farmland in June, a ratter Large spectral variation is obtained, with spectral reflectance at 0.55-0.75micron being much less than at 0.2-h.0 i m_crons_

i The spectral variations of earth reflectance noted above are con- _irmed by measurements made with two radiometers on 26 June, 1963. Re- fiect_nce of high cumulus clouds shows a spectral variation similar to Lhat of low stratus.

B_dlrectional reflectance data Cor partially snow covered earth, under clear sky cond_tlons on 20 March, 1965, show large backscatteriDg anG extremely large forward scattering for large solar zenith angles and an almost d_ffuge pattern with an indication of a small specular i component for a smaller zenith angle. Directional reflectance is 3_ ! for 72" solar zenit_ angle, 36% for 67°_ and 30_ for 90 °.

lJsing the above data _t _s shown that errors of I0_ in earth's al-

data obtained with incomplete geometrical sampling, analyzed under the i bedo and 20% in directional reflectance could be produced in satellite a_sumptlon of perfectly diffuse reflectance. Also, it is noted that !

xxiv l 1967016633-027

_. ABSTRACT (Concluded)

. _. narrow band (0.59-0.75 micron) data cannot be used instead of wide band (0.2-4.0 microns) data for earth's albedo without appropriate corrections.

Jl The geometrical-physical nature of the model is indicated using the precise model of earth's albedo with basic time dependent bidirectional

]i reflectanceis indicated functions.and an illustrativeThe procedureexamplefor iscalculationworked out.of Itearth'sis notedalbedo that a much more complete geographical-climatological study is essen-

I tial to complete the model.

xxv 1967016633-028

i- I. INTRODUCTION

It is universally accepted that an understanding of the heat buaget

Ii of the earth is fundamental for a better understanding of the world's weather processes. Thus a very important meteorological parameter is

I.i the earth's heat balance, whlch can be expressed as the difference be- ii tween _he incident solar energy and the outgoing radiant energy which, in turn, is the sum of the reflected solar radiation and emitted ther-

mal radiation. The reflected solar radiation (or albedo) which ib one of three fac-

tots i_,volvedin the earth's heat balance, has been the subject of consider-

able interest, study, and conjecture. It is not only important for local and global, short- and long-term estimates of heat balance, but for the

I study of various problems in bioclimatology, light physiology, visibility, and aerial surveying as well.

The measurement of reflected solar radiation is best done from out-

i side the earth and its atmosphere. Such measurements became feasible with the development of satellite technology, and some have already been

I made.1'2 However, the methodology of these measurements has not yet been perfected_ For example, the analysis of data obtained is usually carried

out using a simple model of the earth based on three assumptions.

a. The reflectance (i.e., albedo) of the earth is isotropic (diffuse) in nature. b. The weflectance of the earth is independent of wavelength. This

ofis reflectedequivalentsolarto theradiationassumptionis equalthat theto thatspectralof thedistributionincident solar radiation.

c. The method of sampling data from the satellite does not produce any error or bias in the result. This assumption would be val_d

only if the earth's surface were perfectly homogeneous. 1967016633-029

It is surprlsing# at first that these assumptions are used. A brief survey of the literature on the reflectance of surface features and scattering by the atmosphere and clouds reveals evidence to the contrary, i.e., earth reflectance and scattering are nonisotropic and wavelength dependent. Also the earth and its atmosphere are obviously not homogeneous. A further search shows_ h_ever, that the precise model, non- " homogeneous with nonlsotropic wavelength dependent reflectance has not i been formulated and studied. Thus the need for using it in applications is not obvious an_ the method of applying it is not available for use.

Indeed, it is appropriate to say that the lack of validity of the above three assumptions is obvious, but ignored, in the interpretation of satellite measurements of reflected solar radiation.

This peper is a limited study leading to the mathematical formulation of a precise model of the earth for albedo purposes_ considering only the first part (a) of the two parts which are necessary for a complete study:

a. The geometrical-physlcal aspects of the reflectance of a surface, scattering by the clear atmosphere and clouds, and the reflectance of the earth as whole.

b. The geographicaL-meteorological aspects as a function of time and location on the earth.

[Vnemain part o£ the study is contained in Sections II-V, each of which treats .:distinct phase of the subject.

In Section II, the nature of the reflectance of a surface element is considered in terms of the spectral bidirectional reflectance. Di- rectional reflectance and total reflectance quantities are then defined.

The geometrical nature of scattering is _ndicated and the definition of scattering angle reviewed. Next earth albedo is defined precisely in

terms of the time dependent spectral bidirectional reflectance of all l i'j i I1 1967016633-030

areas of the earth's sunlit hemisphere. Finally the astronomer's defi-

nition of planetary albedo, Bond's definition, is considered and is

shown to be identical to the precise albedo, for a rotating planet such

as the earth, only when the planet is homogeneous with isotropic reflec-

tance.

Section III contains summaries of results already obtained in sev-

eral areas of albedo research:

a. The classical earth albedo experiment of DanJon.

b. Albedo measurements made from Explorer VII, the TIROS meteorological satellites and the Mariner 2 (Venus) spaceprobe.

c. Experimental data regarding the nature of the reflectance of earth surface features (soil, rock, vegetation, snow, and ocean).

d. Theoretical studies of the scatterin_ of solar radiation by cluuds and the clear _arth's atmosphere.

e. Estimates of earth's albedo which have been made in connection with heat balance studies.

Section III is completed with a discussion of theapproximate nature

of the models of earth's albedo implicitly used by astronomers_ meteoro-

logists, and spacecraft experimenters. The need for a more precise model

is indicated_

? Section IV is devoted to a discussion of new measurements of earth

r_flectance made on high altitude balloon flights with instruments of

the exact same design as those flown on the TIROS and NI3_BUSmeteoro-

logical satellites, instrument calibrations! and the interpretation of results are considered. Possible errors are indicated. Resulting data

' from three balloon flights demonstrating the spectral dependence and non-

isotropic nature of the reflectance of partially snow covered earth and

of the scattering of radiation from clouds are presented. The bidirec-

tional reflectance patterns which were obtained are sho_n to compare 196Y016688-081

favorably with the limited theoretical data whlchare available. The data are then used to indicate the error that might be made in values of earth's albedo obtained by analysis of satellite reflectance data which is assumed to be Isotropic. The unique opportunity of making measurements of reflectance vlth balloon borne instruments gave im- petus to the whole investigation of albedo. Also these measurements have been applied directJ_ to the precise model of albedo described in

Section V.

Section V indicates the nature of a precise model Jf the earth for albedo purposes. The geometrical-physical characteristics of the model are discussed, aud the method of calculating earth's albedo for a given model is outlined. It is suggested that suitable models based on a geographical-meteorological study be made for at least one day in each month of the year and that _tudies of these models be made as outlined above. A sirpie approximate model of the earth, incorporating some nonisotropic features is considered for the purpose of illustrating the technique. Detailed calculations are made and the results are discussed.

It is hoped that the formulation of • precise albedo model may prove to be one of the more significant outcomes of the study.

Conclusions and suggestions for further research are contained in

Section VI. Experimental "_chniquea, methods of data interpretation_ and !imitation8 of the results of each area of research sl_marized in

Section III are given in detail in Appendices A-F. Appendix G contains a sunmary of the four different coordinate systems used in this paper, i 1967016633-032

Ii r II. DEFINITIONS

A. THE GEOMETRY OF SCA_ERING AND REFLECTION

The geometry of scattering and reflection is illustrated by Figure

I i. Q is the point at which reflection or scattering takes place. SO is the ray from the radiation source" in this case, the sun. OR is the

I" reflected or scattered ray. In this example the incident ray is coming from the east at a low elevation angle, the ray OR is going west-north-

west at a high elevation angle. The plane SQZ _s called the principal

plane and the pla,neSQ_ is called the scattering plane. The incident ray is defined by the polar coordinates (Bo,¢o), where % is 'he zenith

I angle and ¢o the azimuth angle measured counterclockwise from the north direction to the extended principal plane. The reflected or scattered

ray is measured by its polar coordinates (B,¢). The an_le _ is equal ! to ¢-¢o" QS is the direction to the source; it has coordinates @o' and @ = 180° . The direction QA to the antisource has coordinates % = 180-BO

_" and _ = O. Where _ = 0 or 180°, for a reflected or scattered ray, the principal plane and scatteri_ plane coincide. B _s the scattering angle. n B. REFLECTANCE

I! Definitions of reflectanc_3'_ that will be used in this study are as follows.

If ds is an element of a reflecting surface at O in Figure i,

(eo,¢o) are the zenith and azimuth angles of the incident radiation and (8,¢) are the zenith and azimuth angles of a reflected ray, then the

_. radiance in the direction (e,¢) is given by: U 1967016633-033

To North I : I I ' l

?igure l. Geometryof reflection and scattering. 1967016633-034

t i 7 I

r N(%_,¢o,8,@ ) = !_P(@o'@o'B'¢)c°s8 H cOS"o o(watLs c_"2 ster-I) (i) t I

i where H is the irradiance from t_e direction (8o,¢o) in watts cm-2 and • p(Bo,_o,8,$) is the bidirectionsl reflectance, i.e., the fraction of rad/a-

i tlon incident from the direction (8o_$o) which is reflected in the dlr_c- tio.(e,_).

I The total amount of reflected radiation frca the element of area

i ds is given by the integral over the upper hemisphere, i.e.,

Wds = ¢o,B,¢) sin B d % d ¢ - ds (2)

_; 0=0 _=0

The directional reflectance r(9O ,¢u),_defined as the fraction of incident radiation which is reflected i_

li ( ) = W'ds (3) r-Oo'¢o" H cos a de 0 [ W

r(%,¢,o) = ;- O(eo,¢o,e,¢)cos e sin e d e d ¢ (k) ¢'0 e=O

For perfectly diffuse (Lambert) reflectance, we have:

=(eo,%,e,¢) " p = con.rant (5)

and from (1_)above.

r(eo,%) - _ - r - co.,t,_t (6) n 1967016688-085

Thus for perfectly diffuse reflectance, the directional reflectance is equal to the bidirectional reflectance, and each of these quantities is a constant.

Reflectance is a function of wavelength as well as direction. Spec- tral dependence is indicated by the subscript I, thus:

p1(eo,¢o,e,¢) = spectral bidirectional reflectance.

r_(eo,_o) = spectral directional reflectance. ,

The reflectance without a subscript is the average reflectance over a range of wavelengths. This quantity is al,_ocalled a total reflectance.

Thus, for example the average or "total" directional reflectance over a range of wavelength I1 to 12 is given by:

i2 r1(eo'_o)H1d_ 11 _ (eo,_ o) = 12 (7)

I HI dk 11

-2 micron-1 where HI is the spectral irradiance, _'attscm

Note that average reflectance is a function of the spectral distribution of the incident radiation as well as the nature of the reflecting surface. Thu_ average reflectance quantitie_ measured with one spectral distribution may not necessarily be used as average reflectances for another spectral distribut_on.

Figure 2 shows the distribution of. reflected radiation for a per- I feetly diffuse (Lambert) reflector. The quantity plotted is ! i px(eo,_o,e,_)_ cos e. Note that the distribution of reflected radla- rl tion is the same for all angles of incidence, i.e., D_(eo,$o,e,$) - p - [] 1967016633-036

-_p(eo,_o,e , _ )cose 0

90" 90" 03 02 0.1 0.1 02. 0.3

Figure 2. Distribution of reflected radiation for a perfectly diffuse (Lambert) refJector. constant. For this illustration, 0 = 0.92 and, therefore _ 0 = 0.3.

Figure B shows the d_stribution of reflected radiation for a nondif- i fuse reflector. _ 0_(8o,_o,8,_) cos @ is plotted for three different angles of incidence. In this case the reflector has a fairly large specular component, and is similar to some distributions which have been measured for glazed snow (see Appendix C).

In Figures 2 and 3_ the distribution of reflected radiation has been

shown only for the plane of incidence (in Figure i, the plane SZQ _eter- mined by the normal to the reflective surface and the incident ray).

Complete specification of the distribution requires similar plots for

all vertical planes, i.e., the distribution over the hemisphere. 1967016633-037

d f

Figure 3. Distribution of reflected radiation for imperfectly diffuse reflector. I/r p(eo,_o,e,_) cos e is plotted for three angles of incidence: 0°, 40°, and 60°.

Ideally such a complete hemispherical plot should be obtained for each wavelength in the range of consideration. Then, finally a hemispherical plot of bidirectional refl_ctance should be obtained for each

spectral distribution of interest.

C. SCATTERING ANGLE

In the study of scattering phenomena, it is the scattering angle

B (see Figure i) which is significant.5 The angle _ is related to the

zenith and azimuth angles of the incident ray (eo,_o) and of the scattered ray (0,¢) by the equation

cos B = sin e° sin e cos _ - cos @o cos @ (8)

where _ = _-_o ii il H 1967016633-038

, I

Radiation will be scattered from a scattering center (such as Q in

Figure i) into all directions, into the lower hemisphere as well as the

unper hemisphere. Once the scattering pattern has been determined for

0 _ B _ 180, the radiance in any direction can be specified.

D. EARTH'S ALBEDO

_le geometrical relations that appll to a discussion of earth's

albedo are illustrated by Figures ha and hb. In Figure 4a the earth is

shown with the upper hemisphere illuminated by the sun. The earth's

axis of rotation is the line NS shown in a position corresponding to

summer in the northern hemisphere. The coordinate system (eo,$_) is

fixed by the position of the sun. eo = 0 is a direction pointing at

• the sun and _o'is measured counterclockwise from the north direction

I (as viewed from above) in a plane at right angles to "_hesun's rays.

(Note that $o in Figure 1 was measured in a plane normal to the zenith direction.)

' Note Figure _b shows the aifference between the angles _o and _o'.

! that _o is measured counterclockwise "frc_ north at the subsolar point s,

whereas _o is measured counterclockwise from north at the point of re-

flectance Q. n' is the colatitude of the point Q, 6s is the declina-

tion of the sun, and hs is the sun's hour angle with respect to the point Q.

The solar spectral irradiance at time t on a surface normal to the

sun's rays is:

Hs_(t) watts cm-2 micron"I

The total solar irxadiance is: 1967016633-039

_ S

EARTH

a.I

/___ t6o"180.

Figure _. Oeanetry for calculating earth 's albedo. 1967016633-040

Hs(t) = Hsx(t)dX wattscm (9) 1 0 I. i The numerical value of H (t) varies inversely as the square of the dis-

tance from the sun. Its mean value over a period of a year (the solar

constan_6) is 0.1395 watts cm-2 • During the year values of Hs(t) vary over a range of 0.965 to 1.035 times the solar constant.

The solar radiant power falling on an element of area ds is:

Hs(t) cos eo.dS = HsA(t) cos 0o.dS.d_ (watts) (i0) 0

The element of surface area ds on the surface of the earth is given by:

: 2 ds = a sin 0 d 0 d$" (ii) ._ 0 0 _ 0

and the total power incident on the illuminated hemisphere of the earth

r is:

"_'! Ps(t) = I _ 2 Hs(t) cos 0o a2 sin eo d%o d@_

¢_=0 %=0

Ps(t) = _a2 • t) = wa HsX Hs( 2 S_ (t)d_ (12) 0

_ The rortion of tho earth's surface which lles in the area ds is

continuously changing because the earth is rotating on its axis. Note A ' i.e. also that the azimuth angle of the incident ray varies with eo,_o,

is _o(eo,$_). Thus the spectral reflectance of the area is chan_ing as a function of time; i.e., we have the bidirectional spectral reflectance: 1967016633-041

0x(eo,¢o,e,$,t) (13) and the directional spectral reflectance

W W --

r_(%,_o,t) = _ o_(eo,_o,e,$,t) cos o sin e d e d@ (14) ¢=0 8=0

The power reflected from the earth at the wavelength X is:

(eo,_o,t)Hs,_(t) coo eo.a .sin eo.deo.d_;_ (i5) 4ooe°

The total power reflected from the earth is:

W o

rx(eo,_o,t)Hsx(t)a- cos e Gir,e dOod$od^ (16) X=0 ¢o=0 %=0 o o and the earth's albedo at time t is

] . rx(eo'$o't)Hsx(t) cose o sine o X=O _=0 %=0 A(t) = _ ;"H_(t) dX (17) 0

Usually it is the average value of earth's albedo over a period of time which is of interest, i.e.,

t2 A " t-- t- A(t) dt (18) tI 1967016633-042

I Note that the alb_do represents an integration over many variables, [ i.e., eo,_o,e,¢,_. We can show this explicitly by the equation:

A(t) = o _o

w Hs._(t)d_ t=O

In this equation (Co,@o) are measured in the coordinate system shown

in Figure ha with the direction _o pointing towards the sun, whereas

(e,_) are measured in the coordinate system illustrated in Figure i,

with the direction e = 0 pointing towards the zenith, normal to the element

of area ds.

lJ From the above definitio_ (Equation (19)), we see that a precise

i specizication of earth's a]bedo requires that we know the bldirectlon._l reelectance 0 (eo,@o,e,@,t) at every point eo,@o of the sunlit portion

[! of the earth.

The average albedo of the earth over some time interval is given

by integrating (averaging) over:

i. All directions of reflectance 0 <_e -<2 0_< _ _<2..

! 2. All parts of the sunlit 1_ortionof the earth

<_ O< @o<2_. 0 <%-2 - - 3, The entire range of wavelengths of the solar spectrum I! (_,u,_l.o_.2_<__<__.o_)._ithwei,ht_ctio_i_ H_(t). _. Over the desired period of time t.

__ In practice, a complete knovlodge of 0_(eo.Oo,e,_,t) is not possible.

i As a result, any calcl_lation of earth's albedo is an approximati_ to 1967016633-043

16 the true value obtained by making some assumption about the nature of

0x(eo,,o,e,,,t).

Note: In the above, the azimuth angle _ = _ - _o could have been used

wherever _ has been used, i.e., we could have written

ok(eo,_o 'e'_) instead of 0k(8o,0o,8,_) and could have integrated over _ instead of _. Thus Equation (19) would be

A(t) - .....X e° _o e ,, Hsx(t)dX (iga) k

E. PLANETARY ALBEDO, _N_' S D_'FINITIO]

The work of astronamere on the determination of the albedo of planets has resulted in a definition of planetary albedo 7 which is an

_uproximation to the definition of earth's albedo given in the last sec- tion_ This definition of planetary albedo, Jugseited by Bond and adopted 8 by H. N. Russell, serves for the calculation of a plane,'8 albedo _rca phot_netric obserTations of the planet from another planet.

The geometrical relations that apply to the diacossion are shown in Figures 5a and 5b. Figure 5a shows a planet illuminated by the sun.

S, p, and E represent, respectively, the centers or' the sun, the planet, and the earth, from which measurements of the planet's albedo can be made (a 8imils_ gecmetr_v vould appl_ for mealurenents of earth's albedo fral the moon). The an@_ Q is called the phase ansle.

If the reflectance of the planet In the direction e is given by kk $k(e), whe_:'e el(e), the phale _nction, hal laxiill value $_(0) m 1, i and _f it is alstmed that the reflectance hal the mime vaA_e in all 1967016633-044

' 0.) i

_ _) ! i Pigure _. Planetary albe_cnetrlca/ relatic_s. I • J 1967016633-045

directions on the cone of half angle a formed by rotating PE about PS then the spectral albedo of the planet is given by the definition of Bond:

w f (20) A_ - 2 k_ J ¢_(a) sin a d 0

The intensity of light reflecsed from the planet at the phase angle _ i can be calculated with the help of the geometrical relations shown in Fig- ure 5b. The planet i_ shown as viewed from _ome point in space. The portion PCMD of the he..isphere shown is in shadow. OS is he sun's dJrec- tlon, OEj the direction to the observation point. For any point Q on the planet's surface, @o i'_:the zenith angle of Incidence_ the azimuti_ angle of incidence is '_o" The reflectance angles are 8 and _s a is the phase angle of the observation.

The coordinate sy.tem which will be used for integration over the planetary surface has the equatorial circle CE_C, and the meridian circle

PE_4 as reference circles The meridian circle of the point Q on the surface is PQF. The coordinates of the point Q are the longitude _ and the colatitude n.

The angles of incidence and reflection are related to the angl_s a, _. and _ by:

cos eo = sin n cos(_-a) (21)

cos _ = sin n cos _ (22)

cos_ = cos e cos Co- cosa (23)

sine sin e° il

sin , . sin a cos _ (gh) sin 0 sin 0 ° )!

U 1967016633-046

m J

I We can derive the equation for the Bc .cAplanetszy albedo as follows.

• Assuming:

i. That the surface of the planet is homogeneous and constant

in its character,stics for the time interv_l requires to make

measurements over all phase angles a,

2. The earth is at a constant distance A from tl_eplanet during

this time interval,

3. The planet is at a constant distance Rp-s from the sun durin_ th_s time interval,

the spectral albedo is:

Total reflected solar radiation at wavelenRth A_ = T--otaiincident solar radiation at wavelength

and 2w f_(a) 42 sin a d a T 0S AX = - 2 _-S . • a " HS_ p-s w

where a is the mean radi,_ of the planet b

H is the spectral irradi_ce of the earth by the sun at Rein

• distance RE_S .

fA(a) is the spectral irradiance of the earth due to •olar radiation

reflected fr_ the planet.

Note that the equation _ust written e_es wi_h the Bond definition of

spectral planetary albedo 1967016633-047

A_- 2 k_ ;_ _l(s) sins dr, (26) if _2._ q(_) . -- (27) k_¢_(a)= a2._-s Hsk

The total albedo of the planet can then be obtained from:

I_ A_ Hs_d _ A = (28) I_Hs,d,x

The relation between fA(s) which appears in the expression for the Bond albedo can be related to oA(eo,¢o,e,_,t)on the planet as follows: The 2 spectral solar irradiance of one cm of surface on the planet at a mean distance R from the sur. is: p-s

HsX _ cos 80 p-s

The spectral radiance of this area, due to reflectance uf the solar r,_dia- ticn, is:

1 0_( eo,¢o,0 ,_,t)Hsk _R_-S coseocose p-s

2 The spectral irrauAance of one cm of surface at the earth (no_al to I the earth_plane_ ,_!, +ion) is _ times this last quantity. Thus the spectral _rradiance at the earth due to the portion of sunlit hemisphere of the planet which is viewed from the earth is:

...... II ,, ,r , m ,i i, , ,, r ' " j 1967016633-048

I 21

I cosesinndnd_ = _ P_(eo,Oo'e'O't)c°Seo j f_(_) I A2a2_E-SR--2 Hs_ I_ I 2 I p-s n-o_=_'V (29)

i Substituting for fA(s) in Equation (26), we obtain: w

A_ = _ _ p_(eo,$o,e,_,t)coSeocosesinnsinad_dnd_ (30) s=O n=O _=_._

and finally substituting from (21) and (22):

= -- p1(eo,,o,e,_,t)cos_cos(_-_)sin3nsin_dadnd_

i _=o n=O _=a-_ (31)

Equation (31) indicates that the Bond planetary albedo represents a measurement to which only certain selected values of bidirectional

I reflectance p_(%,_o,e,_,t) contribute. It is obtained b_ integrating over:

Ii i. All phase emgles, u.

I_ 2. That part of the sunlit portion of the planet which can be seen from the observation points at the angles s.

3. period of Ii A time at least as great as the time required to achieve all phase angles 0 <_._ <_.w.

! Finally, we note that the Bond albedo is an approximation in that

I it assumes that the reflectance of the planet in any direction at angle m I to the line OS (see Figure 5b) is the same a_ that measured at the phase

in the may I angle direction OE. This accidentally be so; otherwise this assumption is valid for a rotating planet such as the earth only

I if the surface of the planet is homogeneous _itb perfectly diffuse re-

I flectance, i.e., only if 0A(8o,_o,6,_,t) = p_ , a _onstant. In this

I; ,, , , , ,i ,, T, i,, ,, , 1967016633-049

very special case, the Bond definition (31) and the precise definition of _ibedo (]9,%) wi]] y.ie]d the S_T_e result, A l = 0_, and the phase func-

io_ ,,l(_) becomes:

CA(_) .: sina* (_-_)coma (32)

Ji 1967016633-050

I llI. A REVIEW OF RESEARCH RELATED TO EARTH'S ALBEDO I A. EARTH'S ALBEDO FROM MEASUREMENTS OF EARTHLIGHT ON THE MOON 9-13

i Part of the moon's surface facing the earth, which is not directly { _

illuminated by the sun, is illuminated by light reflected to the moon

by the earth. Although this part of the mcon is only feebly illuminated,

it is visible during most of the month. Measurements of this faint "earthlight" can be used to calculate earth's albedo in the visible

I according to Bond's definition of planetary albedo. Measurements of

this type have been made and reported on by DanJon, 9 Dubois ,l0 BaXos ll

and others.

Details of the experimental technique and the method of data analy-

sis are discussed in Appendix A. The results obtained are summarized

below in Table l, which indicates a long-term average photometric

albedo of 0.h0 and demonstrates _hat the proper model of the earth for

albedo purposes has the following characteristics:

i i. It is nonhomogeneous as indicated by diurnal variations and a reflectance of continental areas greater _han of ocean

8reas. 2. Its albedo is spectrally dependent as demonstrated by the

3 relatively large spectral variation over the smali wavelength

i range already measured. 3. Its reflectance is of a nondlffuse nature. Comparison of the

' ! DanJon phase function with that corresponding to the ideal

diffuse rose (Figuce 6) shows this to be so. f J 1967016633-051

TABLE 1

EAHTH 'S ALBEDO FROM MEASUREMENTS OF EARTHLIGHT ON THE MOOI'.

Photometric Albedo (A = 0.554 micron) lO-Year averagea A_ = 0.40 Yearly averagesb 0.37 < A1 • 0.44

Phase Function (_ = 0.554 micron)a

_ ,2 a 3 - [1.30 _55-.+ 0.19 (_--5-J + 0.48 (i..6.5-)] ,_(=) = 2.-'" Spectral Variationb O.267 0.544 0.606 A_ O.48 C.39 O.215 Seasonal Variationsa'c ,d

Albedo Maxima: Spring and Fall Albedo Minima: Summe..-and Winter

Diurncl and Other Variations i. Diurnal variation with maximum albedo over Asian continent, Probably due to higher average cloud cover over Asia.c 2. Reflee%ance of continental areas muratbe greater than that of ocean areas.C

3. Earthshine approaches maximum as a minimum activity of the solar cycle approaches and the_ decreases rapidly right after the minimum of solar activity._

Limitations of Technique i. Accuracy limited by light scattering in earth's atmosphere and measurement over only a li,,it_drange of phase angles. 2. Measurements made from within 28.5° of the plane of the earth's equator. It would be desirable to measure from other directions in space as well. 3. Measurements made over only a small portion of the spectrum (0.267-0.606 micron) instead of 0.2-4.0 microns. 4. Telescopes used in measurements of DanJon9 and DuboisII were located in France and their data do not necessarily apply to the earth as a whole.12 New measures at other longitudes are necessary.

%anion.9 bAnsstr_,13 from DanJon'a data. cBakos .10 di_._oie'ii

I 1967016633-052

, r ,, /

I 0_- 18o= 1. _in_r @ (_-oricosf •"---= _ (==_=

-[',,o(=,oo--).o• ,oo,._- -=-_.o,oo ,_)'] !/. x, _ (=._= 2.512

Figdiffusuzee 6.homog_ncou_<;o.nparisoenarofth.DanJon's phase function with that of a perfectly

B. EARTH'S ALBEI)O MEASUREMENTS FROM SATELLITES AND [_PACECRAFT ]_'-'_)

I Measu]'ements of earth reflectance (or earth a]bedo) have t)een made

from the Explorer VII satellite, the '|'[ROSand NLMBU',;meteorological 15 satelllte_,1 ' and the Mariner <"' spacecraft ]_'o,_ tht, flight to Venus.

The instruments used were of severa] types, dlfferinE in :_.atL_l

and spmctral resolution, and provlding measurements of .liff_r.-n,.sl@;n:f;-

cance. Details of the experimental technlque_ ar;d .J_t.__nalvsis _ro_lez_."

are discusse_ in Appendix B. The results obtained art. sunm_arlze._ !rl

Table 2. Lon(;-t,erm averse values of" eart_ albe,lo of _,'-_",_are In-

I 1967016633-053

TABLE 2

EARTH'S ALBEDO _ASUREMENTS FROM SATELLITES AND SPACECRAFT

Earth's Albedo

6-Month average a A - 0,35 1-Year average b A -0,322

Phase Function c Some data in reasonable a_reement wi_h DanJon's phase functlon_

Spectral Variation No data

Seasonal Variations

Albedo maxima: S_ring a and/or Fall b

Latitude _ariations a'b

Meridicnal profiles aver_ed over the _lobe show sl_ght maxima at the equator, minima at the subtropical belts and Incre_ing values with latitude up to 60 ° latitude.

Diurnal and Other Varlatlons• . C

1. Diurnal variation with brightspot in _tlsntlc near eastern Sotth America.

2. Semiperlodlc 5-6 d_, variatlon. 3. Reflectance of land areas l.hl times greate_ than reflectance of ocean areas.

Limitations of the Satellite and Spacecraft Experiments

I. Isotropic (diffuse) refl_,.t_nce &ssumed. a,h ?. An earth, homo6eneous, in constant [at_tud_ belts ts iLss_amed,a'['

_. Sampilng errors are i&nore',l,a'k' h. Data 1_mlted t() _/IoN-_,(,_tl.a°_' 5. Al_nu&l al[;e(Ioad.lust_d t_ fl_ _e&t £_l_,_'e est_J%&ted f:'._m _-1;'[..'ua:,n_'l d_ta. |'

a " _) • ;iou_e'

(" 1_. Wi idt.,y

I 1967016633-054

/" 27

dicated. Additional data supporting th_ nonhomo_eneou_ nature of the

e_rtn's reflectance is indicated, although in two uf the experiments 1'2

data is analyzed as though the earth is homogeneous in constant latitude

belts. Earth reflectance is generally assumed to be diffuse in the

ana]ys_s of satellite experiments; _hul, appreciable errors may be in-

troduced into the data.

C. REFLECTANCE OF THE EARTH'S SURFAC_ 30-h6

Although it is possible to define the reflectance of a surface

element quite precisely in terms of the spectral bidirectional reflec-

tLnce 01(6o,0o,e,0), it is an extremely rare ease for which we have

sufficient informs*ion about this quant'ty. In order to calculate the

rwfiectance of a ,lven surface element we lust not only know

0_(eo,)o,e,)}for all values of wavele._th, incident dlrectlon, and

direction of reflection but mu_t also Mnow the spectr_ and directlon_l

1 distribution of the incident radiatior, ea well. Kncwle_e of the latter I is often am difficult to come by aa is _nowledEe of former.

i The earth's surface i_ act hQm,_encous, it is ccalpoled of ma_y

different types of aateri_la which c_n (aft,_r Kon drat' yev jO) be

divided into four general c'Luljel, i.e..

i. 'SOt l_ _)_ roclls

,. , Veg_,.atIon

._. Water bast n_

Appendix C t_ • S_ of _artt_ surface re._ctanc.

o_ spe::tr•l 4ep_nd_c_, _lar d_atribution of _'efi._ctanc_, tot_tl re-

fle,_ttun, depena_r,c, un ,:ond_,tlon# o.f illuml_.at_,)n)_nd __nce on

I ut_._r pe_r_aet_r_, i.e., rouGhne|_) time of d_, ,rowl_ aesop, etc.,

- I 1967016633-055

have been |attested together in this &ppendlx in the form of figures u_.d tables, with Interpretatlon of the data ms necesmary.

A condensed summary cf thl_ data Is eontalned in Table _, leavln_ no doubt that the eLrth'a surface, in itself, Is n_nhomogeneou= wlth nondlffume 8_ectralAy _ependent reflectance.

D. THF. REFleCTANCE OF _LO'_S _7"_2

The reflectance of clouds Is a,n _xtremely important Factor in the eva:uatlo:_ of earth's albedo, 81r.:e as t=uch _ 75_ of the reflex.ted soi_r rsAJiation may be due to cloud reflectance. It is diFFicult to obtain accurate reflect_nces to &pply to a prqctlca] eltu_.i_w,, sin¢_ cloud retfle_teu_ce _tepead| on so Ia41y Factors, i .e., cloud type, cloud thickness, cloud height, the reflectance of the earth beneath the cloud ax.1 solar elevatzon _le.

AlkL_n detailed cloud reFlecte_ce data nu been c_pile_. It. Is contain_d In AppendAx D. Spectra_ reflectance, angula_ diatrlbutioa ot refl,t.'tLnce, an_ total reflectance are Jlscussed. A condensed |va- riety _ conta_ne_ :_,TabLe _. A_ fLr u clouds are concerned, a proper model of _he earth for albedo purposes is nonh_o_eneou_ w_.th noa4tffuae

,pectraIAff dependent reflecte_nce.

_;. FH['. _;('ATTESIN_; ,ft.' S6_AI_ [¢AbIATIO_ B¥ AIR MOLgCULES AND A[]_()SOL,_

Solar ractlatiun f,'um tl_e sun aecreeu=es in intensity U It passes throu4gh the "clear" (hl_=y or aoaclou_) sty, This _ecre_a_ _n tateaelt¥, ca_le_ "ex,,_nct_o_," ks= due to scat_ertn4g _nd tu absorptiJn _y _eroooAs and the nolecui_r i_e4l. 1_e absorb=d ener_ m_¥ a_ar later ae "t*-"_' rad_atAo_ ==_d Is not of co_cer_ u Fiur u e_'th's alL_d_ is concerned, [

S_e oF the scattered enerl_ is returned to apace dArectly e_.er StYliZe )

• I

I 1967016633-056

ii 1967016633-057

_ "tl

._'-4 all m

•_ _ .-4 ( _ .,4 EC_l L, m a_o

_ 0 o O_

_ d

2 I 1967016633-058

scatterln(&, or ultimately after mui:!ple scattering by air molecules

and aerosols and/or reflection from earth sue'face features and scat_:er-

ing from clouds. It is this radiation, scattered sand reflected back

-ut :nto space which constituues the earth's a]be4o.

The ¢3mplete _.cattering problem, which involves multiple scatter-

! ing by alr molecules and aerosoi_ plus refLe_t_oh from ,.az'th surface

features and scatterin_ _'rom cl._ul_, _s not solved _n alk _,: It5 d,:tail { and is even difflcu_t to formulate. H¢weve_, variou_ approximation i to the problem have been considered and a larKe volume cf llt_rature

discussing varlous aspects or" the problem does ?x:ot. 'l_e reoults of

a search of the ]iterature ere aiven tn Appendlx E. _ ,:ond_nsed _ummary,

is _iven in Table 5. AlthouKh it cannot be s_id tb_t solutions for the real atmosphere exist, it is app8,'_,_t that such seatterin_ is wavelen6th

horizons Ii dependent with l_r,e forward scat terin, effects, i.,,, br,g_t

decreasinE in intensity wlth decr.-.asing _olar zen!th an6[e. A clear

I atmosphere itself would contribute approxlmately 't'%to the e-rth's

l albedo. Altn_ugh the maln factor_ det_rmlnin_ th_ nenhomo6enelty of the

eart_ are clouds_ land, and sea areas, _t is po_sit, le that d_'fetences

in aerosoi ,.o_,tent fr,;m one part u!" the atmosuhere to anot_,_[ aie,J

contribute to this cbaracterlst,c.

The nondiffuse nature of reflectance o*' _he _-_rth'_ outface featu;'_-s

a_,d clouds w_ll be so_cwhat, mrd,fi_a by the p_s_,e o! _he reflected

radiation t_rou_h the atmosphere. [n add,tion, the ztmosF.ner _,. ,:¢atter-

_n6 will add to the nondiffuse natu.,'e because of the baste ,'o_=_otrop_c

nature of the scatterln_ _:'_,u=_. 1967016633-060 1967016633-061

The spectral dependenc_ of the reflectance of earth surface features

will be combined with the e_ectral dependence of the scattering processes

to determine the cverai! spe_tral albedo of the earth,

_'. ESTIMATES OF EARTH'S ALBESOTI-8'r

The inforz,lationdiscussed above, the measurements of earthllght re-

flected from the soon, the 8at.1_ite and spacecraft measurements of re-

flected solar radiation, the reflectance of earth's surface feature_, and

the scattering of solar radiation by air molecules, aerosols and cloud|,

all contribute to our knowledgo of the nature of the earth's albedo,

however, they do not serve to precisely define its value.

Attempts to synthesize available information into an average value

of earth's albedo have _een made by meteorologists intereited in the heat

valance of the _arth. Details of some of these are contained in Appendix 71 F. Table 6, taken from Angstrom,13 with London's data added, sun.arises

these attenpts. _ote that modern estimates of earth's albedo (Jinoe

19h8) fall in the range of 0,33-0,38, compared with values eJtim&ted from

satellite and spacecraft measurements of 0,32-0._9.

G. DISCUSSION: MODEI_ OF TH_ EARTH FOR ALBEDO PURPOSZS

It is apparent from the •bo_e sumarM, that lever•l modele oF the

earth are been| used for albedo purposes, Aetrono_erJ uJe • model which

differ_ from that of meteorolo|iltl. Spaeeer•_ experiMnter8 ule & " Ittll different model.

The me&euremente of the utrononere are interpre_e4 in tense of 3ond'e

definition of plaaetsz7 &lbedo. Phot_etrio (Viliblt) &lbedo on_ _l

dilouned. Tail definltlon•u_ee that the en_'th hal & honojeneoue err-

F&oevlthperfeetlWdlfFueerefleo_eaoehe_ vever,_he phasefUaetloaoh- 1967016633-062

TABLE 6

SUMMARY OF EARTH ALBEDO _STIM_TES

Author Year Clouds Oround + Platletary Photometric Atmosphere A [bedo Albedo

Abbot & Fowle7_ 1908 LI.65 O,37 Aldrich50 1919 0,78 O.17 O.h3 Simpson73 1928 0,Th O.17 O,h3 B&ur _ Phi].ip_7h 193h 0,72 0,085 O,h15

Fritz75 19h@ 0.h7-0,52 O,17 O,3h7 0,39&

Houghton76 195h 0.55 O,135 0.3h

London71 1957 0.50 O,13h-0.173 0,35

AngI%t_m 113 1962 0.16 O,195 0,33 O,39&

An6s_r_ I113 1962 0,5_ 0.195 0,38 0.h3 aDinjon1&re,'ohtmled %hilv&lue_o 0,_0. 1967016633-063

! rained and th? diurnal and mes_ona] variations noted are not conmiet.nt

Ii with thi. ansumptJon, Tl_e model of the e&rth con.id_red by meteorologi.te conei_er5 o_iy

I meridlon.] varlatJons, Equator_a_ symmetry Is assumed on a yearly average

basin, 3eanonal variation, are considered but diurnal and y_arly variations are not,

Ii The satellite meuurementn of House2 and BandeenI uned the meteor- ologlete model having meridlonal vsriation_ only, with the additional

Msumptlon of diffuse reflectance, Seasonal variations were noted,

It seems to bu quite obviou0 that a more precise model of the earth should be uned for albedo purposes, Thin model should allcw fnr diu_al i seaional and annual variationo,&nd should _oneider the apeotrally dependent nondittune nature of the reflect&nee and mcatterins of solar i radiation by the earth and its atmonphere,

I Additional new d_ta, obtained on high altitude balloon fli|hte, daonu sir&ring the noniaotro_io nature of the earth's reflectance will be pre-

eent_, i,_the next nction. Pinally the nature of a preceDe model of the earth for &ibe4o purpoeei will be indicated, n

] -] 1967016633-064

IV. BALLO,''T:FLIGH_ MEASt_EMENTS OF EARTH REFLECTANCE

A , T.hTRObUtT)BY" ' "'_ NOTES

Radiometers of th_ .ame type as the five channel radiometers flown on the TIROS anl NTMBUZ sate_l_tes hav_ been flown on a series of high altltud_ balloon flights by members of The Unlv-rnlty of Mlch_an'_

High Altltude Englneerln_ Lmboratory, as a part of a research and ( development program in support of the NASA Goddard Space Flight Center's

(GSFC) M_teorologlcal Satellite Program.

The philosophy of this b•llon flight test program is the following.

PerhapJ the most important factor in the interpret•tlon of the data measured by • radiometer (actually any instrument used for aclentific data gathering) is an intimate detailed knowledge o" its operatlon_l characteristics, a thorough understanding of which is best obtained by frequent, careful calibrations. Ide&lly, the calibrations would be made under the sue environmental condltionl as experienced by the instrument when it il used for dats taking, i.e., for these radiometers, under near space conditions. Also, it is desirable to make callbrationl both before and after flilht data are obtained, and indeed, if possible, during ,: the flight. This was not _ossible for the satellite-borne radiometers du, ing the early phase_ of the meteorologic_l satellite pl'o_r_ and &ccordln|ly, the ba41oon fli|ht pro|ru was initiated "or j 1 thls purpose.

The TIROS five-channel radi_eter 10_ and the NIMBUS M_ih F-1 and il F-h radiometers have been flovn a ntmber of times on high altitude bal- t_ loon flight _ests. The result| of an exten|ive |eriel of cslibrstion_ [!

Of _he vi|Ible channels of then Inetruaenti are dil@us|ed in teshnlei£ |] II repor j.7,88 1967016633-065

I 37

, Additional benefits have been obtain,,don those occasions when i measurements were made simultaneously by instruments on the balloon and by similar measurements on _ satellite orbiting overhead, since a compari_

son can help i o_'balloon and sa_ellite measurements in the interpretation of the satellite measurements. Some of these results have also been ! i, reported.22,89

Finally. the radiation =euurements made by these instruments art

of great interest in themselves for what _hey tell us about atmospheric

I radiation processes. Of particular interest for this paper are the meas-

urements of scattered _nd reflected solar radiation which help to show

the nonhomogeneous natur_ of the earth as a reflector of solar radiation

_T And also show the nonilotropic wavelength dependent nt,tureof the reflec-

tance of the earth's atmosphere and surface. "7 The data that will be _resented was o_tained o- throe balloon flights. The dates of these flights and the radiometers uee_ for the measurenents

on these flights are:

2 June 1962 TIROS #103A Five-Channel Radiometer I TIROS #I03A FivelChannel Radiometer -- 26 June 1963 NIMBUS F-I MRIR

I0 March 1965 NIMBUS F-_ MRIR

B. THE BALLOON FLIGHT MEASUREMENT SYSTEM

A typical balloon _iight configuration for the radic_:e_ertest flights

is shown in FIKure 7. The gondola which _arrles the radiation measuring

instruments hangs at the end of a long load llne, the length, _, of whioh

is determined by the requirement that the sun shine direotly on the ion-

; doll at all time| Of the fliBht. ThUl the length used is slightly &rearer

than the value of _ siren by! 1967016633-066

r _+h • tanss (sin) where 8s(min) is the zenith an_l of th, _un at _oca] noon. Typical values of r, h and £ which have been used are ]00, 92, and 250 feet, respectively. In addition to the payload recovery parachute and flashing red light shown in the figure, other b_lloon control eouipment may be hung or.the load line. The radiometers, power supplies, control devices, a,_iliary measuring sensors, and telemetry equipment are c_rried in the gondola.

Figure 8 is a photograph of the balloon gondola used on the 2 June

1962 bal!oon flight, shown suspended from the back of the launching truck.

The TIROS five-channel rad_.ometerprojects from the balloon gondola on the left and a 70 _ aerial cwnera, boresighted wlth the rad_ometer, is or the right. Another 70 mm camera, looking vertically downward, is in the front of the gondola.

The TIROS radiometer and its associated camera _ere mounted on the ends of a horizontal shaft. When the shaft was rotated, the field of view of the radiometer and caners moved in a conical scan (60° cone h_it _gle) across the surface of the earth from horizon to horizon.

At the top of the gondola was a circular ring with a set of photo- cells for the measurement of the azimuth of the shaft with respect to th_ sun. The eu_'e azimuth and elevatienOare known accurately &e a I

_nction of time.

The geometr_ of the r_iation me,_ureaente is exactly that shown !1

:n Figure l, io tha_ when mea|urement_ ar_ made, info,_ation abou_ hi- l i / I directional reflectance patterns, or scattering patternz, is obtained.

t_ 1967016633-067

Ii J - Load Line f. - Flolh0n0 Rid L_Oht

_- -f-- Porachute Ii _°-'° Figure 7 B_]ioon flight configuration.

...,.. .v

i ! "

' . . ',.;, : .

_irll _"* -- _v ! I . • t ,I,/o "

j °-

i't • FigurrJ 8. Balloon gondola uJed on 2 June, 1962 balloon flight.

! II" 196701663g-068

The ]n_ arrangements for the other balloon flights was ,nt

s_milar to that shown in Figure 8. Worn the NIMBUS MRIR was used, t

was mount_,Jon the gondol8 in such a fashion that, wit}]a motlonless

gondola, it would scan the earth from horizon to horizon, in a verc_c&i

plane. When the gondola rotates, its a71muth data mu_t be consldered

in the calculation of reflectance and scattering patterns.

The balloon gondola does not hang vertically beneath the balloon

du,ing the ascent portion of the flight. However as it approaches its

float altitude and begins t9 move with che wind, i% assumes a position

vertically beneath the balloon and provldec its suspension system has

been alJusted properly, a well defined coordinate system is obtained.

An FM-FM telemetry sy3tem was used to transmit data %o a mobile

telemetrf ground station. The airborne portion of the system consists

of up t¢ about 12 voltage controlled oscillators, a mixlng amplifier,

a two watt transmitter and a crossed dipole antenna system. The

telemetry ground station is built into a bus. Antennas and a pre-

amplifier are located on the roof _f the bus, and receivers, FM dis-

I criminators_ direct wrlting recorders, tape recorders, A-D converslon

equipment with paper tape punch and flexowri_er print out, WWV recelver,

and standard time code generator are located inside of the bus. The

airborne unit and ground station are shown in Figures 9 and i0 re-

spectively.

The airborne antenna is mounted in a horizont_l plane, beneath a

horizontal reflector, under the ha)loon _nndo_a and radiates _uite uni- !

formly in all dlrection_ below and to the side of the balloon gondola.

The maximum range of _he telemetry is determined by the horizon as J'_ viewe_ from the gondola. When the balloon is at 115000 feet altitude, I 1967016633-069

Figure 9. Photograph of airborne te]emetr_ unit and equipment pro_:am- mlng unit.

the horlzon is about h25 miles away. Wlth the ground station built into

a bus, the length of a flight, for which data can be received, is in-

creased by moving the bus along the road _n the same direction :_ the

balloon is traveling. Data c_n be received and recorded without dif-

ficulty as the bus moves over modern roads at speeds up to _0 mph, When

the bud Ic moving, a eorner reflector, steerable in azimuth from inside

the bus, is used. ghen the bus is standing still, a bifilar helical

antennae can be ased on top of the bus.

The accuuacy of the telemetry system is about 0.5% of full scale

for low frrquency signals of the radiometer type This accuracy is

checked And maintained by two independent 5-polnt calibration units with which che telemetry system is calibrated at 5-mlnute intervals before,

after, and throughout the flight. This 0.5% accuracy in the telemet_, _2

1967016633-070 1967016633-071

.- L i

is better than the accuracy of calibration of the radiometer and thus

_ does not significantly limit the data accuracy.

An electrical control system for equipment on the balloon gondola,

deriving a program of electrical signals for operation '_fall equipment

on the gondola from a basic timing unit, i8 also carried on the gondola.

One of these systems is also shown in Figure 9. A typical flight program

is outlined schematically in Figure ii. The time sharing of signals on

each telemetry channel is indicated. Housekeeping functions which are

monitored are indicated in the lower portion of the figure.

The basic power supply for the balloon gondola is a number of sets

of Yardney silver cell batteries, with solid state voltage regulators

where necessary. The mobile telemetry ground station has two 5 kw, gas-

oline motor driven 60-_ycle generators. Commercial power can be used

when the bus is standing still.

C. RADIOMETER __J_SUREMENTS: CALIBRATION AND INTERPRETATION

i. Calibration of the Radiometers

The method of calibrating the TIROS and NIMBUS medium resolution

radiometers is d_scussed in Appendix B. A calibration curve is made from

pairs of values of radiometer output voltage, Vc, and values of the N' where: effective radiance of the calibration source, c'

• Nc- I_ Nc_,_d_

I Usually, the interpretation of radio_aetervoltage readings _s made in

terms of % reflectance T 1967016633-072

t 1967016633-073

i 1967016633-074

Nc, I_Ic_X d_ • = -- (33) o,

Thus it is _vessary to know accurately the value of Nab of the source over the spectral range of the channels (C_.2-4.0microns). In addition, e the _.urce should have uniform radiance Nch cver the entire area within the radiometer field of view. The intensity of the source should be vari- able in magnitude, so that values of N'c covering the neces_laryrange can be obtained. At any intensity setting, the source should be stable

ror a length of time suitable for the ca]ibration.

The sources for the calibratiozzof the visible channels of tks_ threu radiometers used for the balloon flight measurements are described in detail in technical reports.27'88'90 The sources (a,b,c,d,e) are shown schemati_ally in Figure 12.

Source a was developed at NASA GSFC for TIROS radiometer calibration. Source b is used at the Santa Barbara Research Center (SBRC) for NIMBUS MEIR calibrations. Sources c, d, and • have been used for calibrations at The University of Michigan, and represent a development sequence to arrive at the most suitable source e. The character-

Istics, advantages, and disadvantages of each source ar_ given in the technical reports noted above.

Calibrations of el_chradiometer were carried out several times over a long interval of time during which the bal_oon flights were made. This calibration data is given in Figures 13 to 18.

Calibration curves for the TIROS radiometer #I03A are shown in

Figures 13 and lb. The data was taken at GSFC in 1961 and 1962 with source a, and at The University of Michigan in 1964 with source e. 1967016633-075

Radiometer

a.) GSFC CALIBRATION SOURCE.

Plastic Filter II| I llEll Plastic Fiiter .,x

---- Condenser Lens

-- Diffuser GE. Photo- Enlarger Lamp Nc 212 I- ra b.) SBRC CALIBRATION SOURCE

Figure 12. Calibration sources. 1967016633-076 1967016633-077

46 1967016633-078

J f

4£ 1967016633-079

, !

5O 1967016633-080

51 \ \ l

\ \ _,.z..d ,_=_w_ 8 _ °°" " 'i i ,?

* !i

z t

t L___._A_

$170A '39VITOA U3131,_lOlOV_l 1 1967016633-081

All sets of data for the 0.55-O.75-micron channel (Figure 13) _ree reason- ably well. The calibration curve is extrapo]ated line_ri'-above 46% reflectance. The 1964 University of Michigan data for the 0.2-5,5-micron channel (Figure 14) disagree with the data taken at GSFC in 1961 and 1962.

The University of Michigan 1964 data are thought to be more reliable and have been used as for analyses of the 0.2-5.5-micron data. The reason for the discrepancy in the two sets of c_libraticns may be due to un- certainties in the ref]-_ct_mceof the Kodak Jhite paper in the GSFC calibration source.90

Calibration curves of the F-I MRIR radiometer are sho'_,in Figures 15 and 16. Calibratiuns were made over the time bet'weenNovember, 1962 throush June, 19615. For the 0.55-0.85-micron cha_mel no two calibrations agree. Inspection of the optics of the radiometer in June, 1964, showed n1 that the filter for this channel bad deteriorated badly. The November

1962 calibration data was used for the analyses of data from this channel of this radiometer. It is rea_;onablyclose to average • " all sets of calibration data. However, it should be kept in mind that the data fr • tL_s channel of the F-I radiometer may be in error because of the deterioration of the filter. Calibration curves for the 0.2-h.O-micron channel of this r_.diometershow excellent agreement. An average calibration curve was used.

Calibration curves for the O.2-h,O-micron channel of the F-h HRIR radiometer are shown in Figures 17 and 18. The SERC data shown i**Figure

17 are in agreement within the accuracy e_ected_ The average o:'the h SBRC calibrations cannot be distinguished fr_ hhe averse of the three

University of Michigan _aliDrations. 1967016633-082

° 1967016633-083

I L I I I I I o m I I ' I I I

39VI70A 1NdlOO i 1967016633-084

55 1967016633-085

: I

0 in _u ._.0 -- U) • • O) I _ <_ _I 0

W _AJ

n-U) LUU z_ -2 _ zo o_ <1:_ ._._ (.,) I-- z _ubJ _, w N

-_, _

\ "' e

_\ : o

__0 _

_e \ _o _

I t I I I I I "_ _ _ _ _°" o._ o I _ I I I I 3 9VJ.'IOA IndJ.rlO i 9670 i 6633-086

...... t I

I_ A discussion of the e._perimentalerrors which are possible in mak- i ing the calibrations is contained in Reference 27. Although the precision should be 2_ or better, possible systematic errors as

Io large as 8% may exist because of inaccuracies in the secondary standard thermopiles used in the calibratio1_s. In addition significant errors

may arise i_ the interpretation of the radiometer data. This topic will

I be discussed next. 2. Interpretation of the Radiometer Data

The values of reflectance measured by the visible channels of the li medium resolution radiometers differ from the _ctual earth reflectanees which we desire tu measure, as follows_ assuming normal incidence, we

Ii want to measure:

p ffi _ 0 PlHsA dA (3h) i dX

We actually measure: i.

PX Hsx¢_dl NcX@X d_ li p : o : o (35) j! Ti I o® HsXSXdA i I_HosI_AdA

E i In addition to calibration errors, which relate to the substitution of

I® d_, I j 0 Ncx_x I!

I'i 1967016633-087

We have the error in inLerDretation due to the fact chat we have measured a we:gbted avela_e reflectance using the wei._hting function Hsk¢ i instead of }I sA

Weighting functions for the visible channe].z of the TIROS #]O_A five

ch_nne] yadiometer and the F-I and F-h M_IR radiometers are shown in Figures

19 to 22.

The weighting functions of the na' ow band channels emphasize the

z_ectra] ranye of 0.55 to 0.75 micro, J,see Figures 19 and 2], ,%nd e.qDec_a]ly

the _.ar£ow bsl}d channel of the TIROS radiometer which D]aces particularly

great emphasis on the 0.58-0.60-micron region. I_ is apparen_ that the

reflecc_,ces measared with these narrow band channels cannot be inter-

p_.L: d as total reflectances (i.e., over the 0.2-1_.O-micron ran_e), nz '4 1 was done by Bamdeen. Also it is apparent that different results m&v

be obtained with the narrow band channels of the two types of radiom-

eters b_:cause of the emphasis of the 0.58-0.60-micron region and the

additional spectral region of response (1.2-2.8 microns) of the TIROS

#I03A radiomtt_r _

The welghting functions for the w._de band channels, which are shown

in Figures 20 and 22, are similar to the function h sA.. The weightin_

function of' the NIMBUS F-h MRIR places relatively greater emphasis on

the _ _ micron region.

Finally, in regards to the interpretation of the radiometer d_ _a,

it is impol-teu_t to keep in mind that _he _uantity measured is a bldir-

ectiona] reflectance. The assumption that the surface ts .% diffuse re-

flector wi]] often lead to error. It %s absolutely necessary to make

measurements at all an_]es o£ incldenee a_,d reflectance to correct]v

evaluate earth reflectance data. 1967016633-088

I N. 0

d 0 i.i (NO_I311Na_I ::)/S.L.LV"_MON)VlOVUU"lIVU.L3:3,=IS

f-', 1967016633-089

, t

6o I i _

. . io II _o , _. _

, , _, // Q_ , \,,- :/

\. /I _°

o '_ _o 8 oci ct d (NOU311q/_IM_/SI.I.VM) ":I3NVIOV_II qvkI.L33dS 1967016633-090

I" 51

I! "_ I /° N ,I

.{ I ' _

-? uJ _

_i "!

i i • i i O

c_ ci

(N01:I311_N!3/S.I.,I.VM)33NVIQVI:II:II"IVI:IJ.33dS

I 1967016633-091

., o. I "

8 o

( NO_1311_/al_13/$.I..I.V_33} NVI(i_I_I "1V_.33¢15 1967016633-092

These two important factors connected with the interpretation of

radiometer reflectance data will be discussed more completely in regard

to the radiometer data taken on the high altitude balloon flights.

D. DATA OBTAINED ON THREE mLIGHTS

1. The 2 June, 1962 Balloon Flight

The 2 June, 1962 balloon flight was launched through a layer of low

altitude cloud_ at 1034 GMT (OhSh CST), from Sioux Falls, S. D. (43.4°N-

96.70W). It floated at an average altitude of ll3000 feet (34 km) for

about 13 hours above various types of cloud cover. The altitude vs.

" time curve and a trace of the balloon trajectory are shown in _igures 23

and 24. The flight was terminated at 0120 GMT, B June 1966; parachute

recovery of the balloon gondola was successful.

The v_rious types of cloud cover viewed by the radiometer on this

flight are ._hovn in the four pictures of Figure 25. A summary of the

_ types of clouds viewed by the radiometer is given in Table 7. The re-

flectance data obtained is difficult to analyse when the clouds viewed

are ncnhomogeneoms as in the last three cases of Table 7. It is only

I TABLE 7

I CLOUD COVER VIEWED BY RADIOMETER, 2 JUm_ 1962 BALLOON FLIGHT

Sun's Ele,:ation Time, GMT Cloud Type Degree

1034-1300 Stratocumulous, 2000 ft thick 0-22 tops at about 6000 ft 1300-1745 Cirrus above stratocumulous 22-68

17_5-2000 Broken -.tmulus 68-56 2000-0100 Cirru_ above scattered cumulus 56-10 1967016633 1967016633-094

.l : _ ,',M i lh 4! (;)_I I

Figure25. Photographsof cloud cover for 2 June,1962 balloon flight. 1967016633-095

when the cloud surface is quite uniform and homogeneous, as it was up

to 1300 GMT; so that the radiometer fie]d of view Js completely filled

by the same type of cloud surface, that the data is well enough defined

to plot a scattering pattern. At the same time, the gondola motion in

azimuth combined with the conical scan of the radiometer must be such

that data covering a wide range of scattering angles is obtained. Such

data was obtained in four h0-sec intervals at ]157, 1215, 1233, and 1251

GMT. Even then, it was necessary to eliminate portions of the data ob-

tained when wispy cirrus or shadows of wispy cirrus came into the field

of view. This data, plotted as a function of the scattering angle _,

is shown in Figures 26 and 27 for the C.55-0.75-micron and 0.2-5.5-micron

channels of the radiometer, respectively.

Stratocumulus Cloud Reflectance

Data _s obtained for scattering angles_ 8, of 50-145 ° . The curves

are similar in shape to the scattering patterns derived by Deirmendjian

for single scattering from a water cloud with realistic size distribution

(see Figures 100 and 101, Appendix D). There are maxima of scattering

at low scattering angles and at high scattering an_les, with a minimum

at 8 equal to ll0-120 °. There are indications cf a f_gbow at about ]35 ° .

There is a certain amount of scatter in the data, which is probably due

to nonuniformities in the cloud structure (i.e., composition and thick-

BESS).

There is an indication of a slight increase in forward scattering

& and a slight decrease in backscattering with increasing time (i.e • , in-

_ creasing sun elevation angle). However, because of insufficient knowledge i about the exact cloud thickness and physical characteristics durin_ this

time interval, it is premature to s_v that the increase in forward 1967016633-096

! 1967016633-097

-Ill i t I I I I I I I i__

-:331WJ,_3%-1:31_V1lOli::)l_lle-le ',7 1967016633-098

scattering and decrease in backscattering is caused by the increase in li sun elevation angle. Average curves for each of the channels are shown in Figure 28.

the within I They are essentially same the accuracy of the radiometer measurements, so that it is reasonable to take an average as representative i of t_e scattering pattern of stratocumulus clouds, over farmland, lOO0 to

2000 feet thick with top at about 6000 feet. _lis average of the radiom- i eter data for stratocumulus clouds is shown in Figure 29, with Deirmend-

Jian's calculation for single scattering in a ,_. com- I ---+o_cloud model for parison. While the single scattering model does not produce the inten-

I sity of the actual cloud scattering, the qualitative agreement of the

I functional relationship should be noted_ even to the existance of the

maximum of the curve at B = 1B6° (i.e., the fogbow). This angle is

less than the theoretical angle of iI_3° for _ = 0.70. °_incedata was obtained only for 50° • B < 145° the curve has been

!_ extrapolated from 50° to 0° and from 125° to 180° using the theoretical

curve as a guide. This final curve, also shown in Figure 29 is a final estimate of the scattering pattern of a stratoculumulus could for high

solar zenith angles (70-80°). A three-dlmensional model of this scattering pattern is shown in Figure 30. In this figure, the flat circular

disk represents the top of a flat cloud. Solar radiation is incident from

_i the right at an elevation angle of 20@ . The spike in the scattering pattern pointing to the right is backscattering. The fogbow is the next

"scallop" in the pattern. The large amount of forward scattering is shown at the left. The truncation of this forward scattering is merely due to

the limit in the size of the model. The small bow in the center of the

pattern may possibly be due to noise. DeirmendJian's calculations show 1967016633-099

WW c_ ZZ -_ Z_

ZZ -_ O0 -- _0

O_ I I n-_lll n;, x_ - ,--Ii • " _ O

O0 "_ m"

o _ _o°__ m_

, I'- _ ,', w

or't | _ °_

• 0 CO

I I I I I I l I I I

30NV.l_3"l.'13bl"NNOIJ.33_II0-;8' _d 1967016633-100

I" TI

(/ I

I I03 :... I "'. • • o e , | . ! .! ....,v...... _CONJECTURE ___ , @ i ioz .!.. ,,, . . • o oo o ,o o I

i0 ! pAIv, TFORIROSSTRATOCUMULOUSi03A RADIOMETER

I; g ,.,. I

_N lO0 ,.\.\ PI+I_ , DEIRMENDJIAN CLOUD 2 MODEL

[ "\\.\/ X=0.70 MICRONS5 iI [ ,o-' ,. I i' ...."" [ [ io-2 ,,

, fl I°-_ 30 60 90 120 150 180

I SCATTERINGANGLE,.8 Figure 29, Comparison of experimental measureme_ts of bidirectional j ringeflepatternctance of waterstratocloudcumulusmodel.cloud with theoretical single scatter-

I 1967016633-101

72 1967016633-102

that the bow exists at 9.3 microns but not at lower wavelengths.

Note that the complete scattering pattern is a figure of revolution

having the ray of incident solar radiation as axis, and that the bireflec- i tance pattern oi'the cloud is obtained by merely cutting the scattering

pattern with a plane, as in Fig-,re30, so that the correct angle of in-

cidence is obtained. Thus it is obvious, tna_ the total directional re-

i flectance of such a cloud is _.function of the elevation angle of the 1 sun, and can be calculated by integrating over the hemisphere above the

I plane. This has been done for the scattering model shown in Figure 30 with

li the result shown in Figure 31, which shows total directional cloud re-

flectance as a function of the solar angle of elevation. The total directional reflectance has a minimum value of 58% at a solar elevation

angle & angle. of 40° , and maximum of 85% at 0° elevation These results are in good agreement with those of other experimenters (see Section

Ill-D) ; i.e., Neiburger obtained total reflectances of 70-8C% for a

I_. 1800 feet thick stratocumulus cloud (solar elevation angle not noted). L: Reflectance Scatter Diagrams

Although the data for much of this balloon flight caz_ot be used to plot bidirectional reflectance or scattering diagrams, it does pro-

I vide some information about the spectral dependence of reflectances

I measured. Values of the radiometer measurements taken simultaneously by the two channels of the radiometer are plotted in a modified scatter

J diagram in Figure 32, i.e. the ratio of the bidirectional reflectance

of the wide ban4 channel, P3'' divided by the bidirectional reflectance

I of the narrow band channel, n!,), . is plotted vs * p;.

i. 1967016633-103

...... ; i

lO0[- Z x

..1_ 60 - x'X"x--x-x-x---x'_x-'*-x-×-'_ - Z 0 t--. _ 40-- W a ..J 2o-

L._ i I I I I I I I I I0 20 30 40 50 coo 70 80 90 SOLAR ELEVATION ANGLE = (9o- e,)

Figure 31. Total directional reflectance of & stratocumulus cloud as a function of solar angle of elevation. 1967016633-104

[

X [

I ::)0- x x

X X I X X X X X x _x x I x )_ xX XXx_ X X

1.0- _, _( X X

t i 1 i t _ I { 0 I0 20 30 40 50 60 70

1 ! ! i _'igure32. Reflectsmce diagram, ratio O_/P_ vs. O_ for 2 June,I_2 i balloon flight. All data taken above compl_te overcast or broken '_o scattered cloud conditions.

I 1967016633-105

The data samD]es were taken Pt _.5.-mznute znterva]s throughout the day, so that the diagram shows samp]es of data taken at different scatt_ - ing angles and for different cloud conditions. The di_;r_un shows that for the most _art channe] ! (0.2-_.5 m_crons) reflectances are =reater than channel 5 (0.55-0.75 micron) reflectances, with the ratio being approximately equa] to ] at high _ef!ectsmces __nd as high _s 2 for low values of reflectance. This diagram provides additional evidence that the narrow band chennel data cannot be used for earth albedo calculations, and that if it is so us6d a value of earth's albedo which s too small

_ill be ¢0tained (as was obtained by Bandeenl). Given Bandeen's data a correction factor for his earth's albedo could h_ calculated fren a curve such as shown in Figure B2.

In Figure 33 the reflectance ratio is plotted as a f_._ctlon of time during the balloon flight. A general description of the scene yielded is given along tl_e bottom of the figure for correlation with the reflectance raxio. _rhen the radiometer v_ews the stratocumulus cloud, the reflectance ra_io is very close to ]. However, early in the morning when the sun is at aver} low elevation ang]e (< 80), the ratio is considerably less than i: and ].ate in the day_ when the radlom- e_er is looking through scattered clouds at th( ear_h, the ratio is much greater the, i. This change of the ratio during the d_¥ is consistant

%'ith a spectral distribution containi**g primarily short wavelength scattered radiation in the mornins, roughly equal intensities at all wavelengths when looking at stratocumulus with the sun above 8 e, and increased refleetaunc¢ at wavelenKths above 0.75 micron when l_oking at the earth through scattered clouds in the afternoon. 1967016633-106

T 1967016633-107

2. The 26 June, 1963 Balloon Flight

The 26 June, 1963 balloon flight was launched at 1057 GMT from Sioux

Falls, South Dakota. It flew over cloudless skies at a height of 112000

feet until 1730, apnroximately. The sky th( . gradually became cloudy

and at 1950 GMT the balloon flew over a large storm system with very high

clouds. The flight was terminated at 0015 GMT, 27 June; oarachute re-

covery wg_ successful. The altitude vs. time data and a trace of the

balloon trajectory are shown in Figure 3h. The data has not yet been

analyzed for geometrical dependence of reflectance. However, this will

be done in the near future. A reflectance ratio study has been made.

Reflectance Scatter Diagrams

Curves of the reflectance ratio o½/0% vs. D_ for this balloon

flight, were plotted for both the TIROS #103A and MRIR #F-I _adiometers.

They are shown in Figures 35 and 36, respectively. They show a functional

relationship similar to that shown by the TIROS #IOBA radiometer on the

June 2, 1962 balloon flight, with p_ > O_ for low values of O_ and

_ % _ for high values of 01.P The TIROS radiometer data show

p35'/O ' = 1.0 at 05' = 90, whereas the NIMBUS radiometer data show the

ratio = 0.8 at this value of _. The difference may be due to calibration errors (recall that the calibration of the narrow band channel of

the F-I radiometer is uncertain because of filter deterioration). At

any rate the data bear out the conclusion that the narrow band channel

data cannot be used to infe_ earth albedo values without the use of a

correction factor derived from curves such as Figures 35 and 36.

Reflectance ratios have been plotted as a function of time fo_ this

balloon flight in Figureb 37 and 38. A_ain the _eneral nature of the

terrain viewed is indicated at the bottom of the f_ure. When _he radiom-

% 1967016633-108 1967016633-109

4.0

x 3.0 - x

X XX xxx "_' X

I P3 x I X X Ps _ 2.0 - _

X X_X X _ X X x_xx_ _

1.0-- _ x xx x_ X X i_ X X X X X X X X

0 .....I0I EOI 30I 40I 50I 60I 70I 80I 90i I00 # 05

! - i balloonFigure 35.flight,ReflTZR_ectance#103diagraA radi_etev.m, ratio p3/_5 vs. p_ for 26 June,1963

[

| 1967016633-110

i _ 81

I !

I•

I O O O

I. 3.0 - 8° 0

I 0 _ o_

{ ,o_ t

: 2.o- _t_ o

1,0- eo°c_°o =o o 0 0 o0 Oo 0 0o oO_oo%o_o ! I 0 I I I, I I I I I I i _o zo _o 40 so eo 70 80 so ioo

Figure 36. Reflectsm.cediagram ratio p3/p5 vs P5 I balloon flight. NIMBUS _R F-1. ' ' • ' for 26 June,1963 I

] 1967016633-111

4.0

X _k x_ x x 3.0 - x xx xx x x X x

X X X X pi " x x X X x X 11( x x:_xx :_ x x

2.0-" : "" x xx xx x X 1( _1( 1( '_X x_j___ X X X Xx t( X XL_ XquK x X x • x ,_x I( X _ X X K 1( X X _. Mx X X x xx _1( x

X x X -"_Xx_ xt( _'t _x xx , _xN xx _x_ _ xxx_x_

x x x

,- HIGN ATTERED ; - cL..sK,Es - SCACLOUDS_.So--CUMNIMBUS UqLO--c_s q I . I 1 I A _1 I l I I I 1200 1400 1600 1800 2000 2200 2400 TiME _M,T,

Figure 37. Reflectance ratio vs. time for 26 Jun_ 1963 balloon flight, TIROS #I03A radiometer. 1967016633-112

11 1967016633-113

8_ eters view the high clouds at the end of the flight the reflectance ratio is close to i. Ho,_ever,for clear sky conditions earlier in the flight, the ratio is as high as 3.5, due to the fact that the reflectance of the earth is greater in the long wavelength regioy_. The ratio for clear skies decreases with increasing sun angle as we should expect, because of a decrease in scattered short wavelength rsSiation.

3. The i0 March,1965 Balloon Flight

The i0 March,1965 balloon flight was launched at 1210 GMT (0610 CST) from Sioux Falls, S. D., and floated at an altitude of i07000 feet for about 7 hours above terrain which was 25-90% covered wlth wind blown fmow.

The altitude vs. time curve and a trace of the balloon trajectory are shown in Figures 39 and hO.

The MRIR F-h radiometer which was flown on this _,_llonflight had only one channel (0.2-h.O microns) for measurement of reflected _la scattered solar radiation. Thus reflectance ratio was not studied_ However, bidirectional reflectance patterns for this type of terrain and atmosphere were obtained at three different sun zenith angles, 72°_ 58° , and 50°, at 083_, 0900, and iii0 CST, respectively. When the sun was at zenith angles greater than 72° , the balloon was not yet at altitude and so data was not obtained. During the rest of the flight, except at those times noted, data for reflectance patterns was not obtained because of insufficient gondola rotation or nonhomogeneous fields of view (i.e., scattered clouds in the field of view).

The reflectance patterns obtained show the sum of reflected radiance from the snow covered terrain plus the scattered radiance from the atmosphere. The data is di_pla_ed in several wa_.sfor better und_.-_anding of its characteristics. 1967016633-114

Figure 39. Altitude vs. time curve for 10 _re] 1967016633-115

Terminotion by .... _,,_-x..._. _ _.._._ Rodio Commond

-----___1536 C..S. r.

i t• _d i 7' [' - I-I/2 Miles

I' -I. . 30 14@0 IlO0 ILK)@

_ 1965 balloon flLght.

! 1967016633-116 1967016633-117

lit 1967016633-118

Figure 41 shows the coordinate system used for display of th_ entire bimirectional r_flectance pattern in one diagram. T_e geometry is that of Figure l, as viewed from the zenith. Th_ angle _3 meazured from the principal plane runs frcm 0 to 360 ° counterc!o_kwise around the outside of the polar diagram. The concentric circles are curves of constant zenith angle, r_ining from 0 ° at the center to iOO° at the outside of the diagram. Solar radiation is incident f]'om the azimuth direction _ = 180 °.

The orientation of the diagram on the earth's surface will depend on the sun's azimuth, i.e., tbe time of day; for example sometime in ,,,i4morning with the sun shining from the southeast, the direction E would lie at

= 22_ ° on the diagram 3 with N at 31_ (i.e., _o = 4_°)" Note that the horizon will lie at a zenith angle of 9_.9 ° (i.e., the earth-atmosphere interf_e as viewed from the ba%loon at llO000 feet.

The bidirectional reflectance diagram is shown on this coordinate system by a set of contours of constant reflectance.

Figure h2 is a bidirectional reflectance pattern that "as obtained et 0B32- 836 CST, with the sun at a zenith ar_le of 72.2-71.5 °. The b_oon was still ri_ing, and the pressur_ altitude _aried from 20-16._ mb during the data taking time interval. Not_ tha_ the sun's position iz not shown along the _ = 180 ° line. _lthough calculations were made so that the diagram would have the sun at this value of _, the symmetry of the results obtained indicates t_et the sun's position should be along the _ = 188 ° line, inside of the 70% reflectanc_ contour (which represents the peak of the atmospheric backscattering). Large forward scattering is show_ by the contours on the r_ght hand side of the diagram. The maximum contour shown is 99_, the maximum value allo_ed in the data processing. A second pass through the data will yield higher values of 1967016633-119

Figure 21. Polar coordinate system for bidirectional reflectance dlagcams. 1967016633-120

i . 200 340 I \ \ 3zo i 25O 27U

Figure 42. B_directional reflectance diagram obtained at 0832-0836 CST on i0 March, 1965 talloon flight. 0o = 72.2-71.5°, pressure altitude _ 20.0-16.5 mb. 1967016633-121

9O reflectance in this region and thus would show more detail on the peak of the forward scattering pattern. The reflectance pattern decreases sym- metrically fr_m the forward and backscatterin_ peaks maintaining higher values near the horizon at all azimuths with the minimum value of reflectance of slightly less than 25% at the zenith. For geographical orientation note the E, S, W, and N direction_ of the figure.

Photographs of a three-dimensional model of this reflectance pattern are shown in Figures 43a and b. In Figure 43a, the view is from

N.E., showing the backscattering peak. The arrow indicates the direction of the imcident radiation. In Figure 43b the _attern is viewed from the S. W., showing that the forward scattering is a maximum very close to the horizon. The photographs show the generally diffuse but slightly nonhomogeneous nature of the reflectance in directions approach- ing the zenith.

A third method of data display for the bidirectional reflectance pattern is to select a vertical slice of the Dattern at some azimuth and

*toplot the resulting d_ta as a function o£ zenith an_le. Such a plot of the 0834 CST data in the principal plane is shown in Figure hi_, showing the forward and backscatterin_ with a rather unlform diffuse scattering toward the zenith.

The total directional reflectance for th_s pattern has been calculated by numerical inter_ration. A value of 35.0% was obtained. 1967016633-122

4 i i "- 91

I 1967016633-123

o o o o - Z 0 -D- . __ o _"_ o o _,_ 0 o_-

,_ o

% .r..I

_Oo -_ _m o -o_ _

°°ooo _ _ V N ,--I oo -_ _;

0 0 "_=_

0 0 _o_ .,-_

o _ 0 • _, o --_ O0 _ _ 0 0 _ _ o _o

13NVJ._}l'ld311 ' ,# 1967016633-124

I 93

The three different displays of the bidirectional reflecte_ce pattern

|- obtained at 0855-0909 CSA on this balloon flight are shm_n in Figures I_ hS-h7. The sun was approximately 5° higher, i.e., 68.3-66.0° zenith angle.

I Inspection of the figures shows a psi.tern similar to that obtained at the earlier time. However, now the L%c,suatterlng Is less intense, but

I covers a slightly broader range of angle_. The forward s('atter_n_ is

i less intense and not :_ broad in angular range. In F_gu:'e 4'7 it can be seen that the forward scattering has dropped to 73_ at 8 = ,90° whereas

j at the earlier time, with the sun 5° lower in the sky, the ref] trance '_s still saturated at 8 - 90 ° . The directional reflectance, obtained t-

with the earlier value within the egperiment&l error of measurements.

Figures 48-50 show the bidirectional reflectance pattern with %

[ much higher sun, i.e., a zenith angle of 50 ° . The pattern i_ significantly different from that c,btainad earlier in the day. The high In-

I tensity forward and backscattering is not a feature at tb_s high sun

angle. There is a stall1 pea_ _t the proper angle for b_cksc'attering Lnd a general maximum at almost all azimuths nee, the hort'zon. 'l_2ere is

another pe_k at _ zenith Lngle about _l° greater than at.at for specuAar refl_ction. 'I'his_s conaimtent with uurface m_asuremcnt_ of the mirror

component of reflection from snow. The directional r_flectaace, ut,tair_e_d

by numerical integration of this reflectance patterr,, w_ f,,,_ndto be i _,.i_, about 5_ l_wer t,_, the value:_ ,,btalned earl,or _r. tr.e d_.y.

J E. DASVUSSI_,N OF DATA OBTAXNMD

From th= above data, tt i,_ a_|_rent that tt_ M_umFt:_h _,:' _,tr_Ac-

wavel_ngth Ind_pen_ient reflect_uAce usu&_ly employed A_ ,,_A_.j,rat_

of the e_Artn's albedo obvlo_sly lea_s to a very poor approatmat.i_)_, to 1967016633-125

I00 SIC) 80

J 120

140 t- 40 1967016633-126

! 1967016633-127

0 _8 0 0

0 I

o °o _ i. O0 _ o

o Oo° _ '_.: oo _ _.,_

I0_ o_

0 0 _J 0 N °o _ _ z O0 I_ ,-_ o° _ _,_ °o o_ "L, i _ .,.4

°f.4

• _

O 0 _ oo_ _ ___.T,

O, _ t-

]I/NVJ,_]'IJ]U '.d 1967016633-128

Figure _. Bidirectional reflectance di_rwm cbtained at 1109-1116 (:ST on 10 March, l_65 balloon flight, e - 50.5-50.u a bLlloon pressure IltItude • 8,5-H._ mb. o ' 1967016633-129

98 1967016633-130

• 0 0 o ° oo o

! 0000o °° -- o i ___...• %ooo __o,, °_°° _i [ +2 !

- _ ._

, 1...... _..._, ,*, + .___i_.,,-+

]Of_VJ.O3"ld3W',_ 1967016633-131

lO0

the haracterlstics of the solar radiation reflected and scattered back out

into space by the eart_l.

i. Nonisctroplc Earth Reflectance

The balloon fl_ght r_easurementsof the bidirectional reflectance

pattern_ of the low altitude stratocumulus cloud and the partially snow-

covered earth under clear sky conditions are t_o examples of the extre-

mely nonisoiropic nature of the earth'_ reflectance. The departure from

isotropy is greatest at low Bun angles, when t]_every larg_ forward and

backscattering peaks put most of the reflected radiation into near-horl-

zontal directior.s. With increasing sun elevation the departure from

isotropy becomes s'naller. Although the reflectance patterns for con-

dltions of clear _kies and water basins, or clear skics and bare soil a or vegetation covezed earth have not been measured from balloon flights,

the reflectance patterns for these casez should show the same type of t nonisotropy because _f the large forward scatterin_ o£ aerosol containing atmosphere and th_ forward and backscatterlng of soils and vegetation b

noted in Section IIi-L. The reflectance patterns may be nonisotroplc

to a sm_ller deg.'eeth_ noted above, but qualitatively they should be

the same with greatest nonisotropy.,_orgreatest solar zenith angles.

The magnitude of error which might be obtained in the interpretation

of satellite radiation measurements can be demonstrated by application

of the calculation technique of BandeenI to the balloon flight measured

reflectance patterns. Recall that in Bandeen's work the maximum solar

I zenith angle was 70" and the maximum nadir angle of the radiometer optical

axis was 45' for the data used in tee study.

If we apply these conditions to the reflectance pattern for strato-

cumulus clouds, that is assuming th&t the directional reflectance can be 1967016633-132

i01

obtained a, the average bidirectional reflectance for nadir angles from

0 to 25° , we will obtain the results indicated in Figure 51. For sun

_levation angles , h5°, the apparent directional reflectance r' is greater

I than r, for sun elevation angles _ h_° , r ' < r. The average, A' , of r' i for sun zenith angles of 0-70° is 5h.9_ whereas the true average A of r over all zenith angles is 6].h_. Thus the ass_nption of isotropic te- l flectance combined with Ba,deen's limitations for radiometer sampling would produce an earth albedo 89.h% of the true value.

I. Application of Bandeen's conditions to the three reflectance patterns

measured for clear sky, partial snow cover gave the following results.

0o m 72.2-71.5_ 35.8 _9.3 1.22

I 68.3-66.0° 36.2 30.8 i.17 50.5-50.0° 30.1 26.7 i.13 [ Thus in this case a lower dir_ctlonal reflectance would be obtained for

I all three _un zenith angles. These results are es_ecially significant in the light of the fact

that Bandeen's albedo was low by perhaps as much as 60S.

E _. The WavelenEth Depend_nce of Earth Reflectance The balloon flight measurements made with the TIROS and NIMBUS radima-

etern also demonltrste the w_velength dependence of earth reA'lectanoe.

_I Figure _2 show, three mooth curves obtained from Figure, 32, 35, and 36 which eh_ plnte of the ratio D /P _ re. PS'' These demon,trate that

II the reflectance in the 0.5_-0.7_-micron region ot the bpectmm can be _ifz'erent fro_ the average reflectance over the entire -an|e of _he lole_ 1967016633-133

102 1967016633-134

I i 1o5 i rq_ectrum0.2-II.0microns. j The experimental data has been s,tpplementedwith theoret_cally calculated data points obtained from selected spectral reflectance curves

of various types by calculating the true average reflectance and predicted

instrument measured reflectances for the spectral response regions of

_he two channels ol the F-I MRIR radiometers. The results pre shown in

Table 8, and the ratio of the predicted measured reflectances are plotted in Figure 52. The calculated data are in agreement with the curves

I measured by the radiometers. It is quite clear _hat the spectr&l dependence of the reflected

I'; solar radiation varies considerably with the scene viewed, sad that meas-

urements with the ,'adiometernarrow band channel (0.55-0.86 micron) cannot be used for earth albedo without the application of a correction factor.

a The correction factor however cannot be calculated without detailed knowledge of the narrow band readings so used. g_ I[ , In addition an inspection of Table 8 shows that for .pectral di,-

tributions typical of vegetation, the narrow band channel does not measure the true average reflectance over the 0.55-O.?5-micron range. n 1967016633-135

LO_

TABLE 8

THEORETICAL F-I MRIR REFI,ECT;,NCE MEASUREMENTS

r).5-n.R_ Mic_.c,n r_.;'-5.n Mieronn

! !

.;|,eurrllt, r<_:f'l(._,l,:Cipeh1_r'.V...... , I O,_/P_ l_r I' I_., 0 I _', -- _° . :',

Middle layer clouds (FIR. 99) 7J.O 71.)_ 65.n 6J_.5 .90

Green leaf (Like Fig. 8h curve h) 26.] ]5.6 ,?6.1j 2.7.3 ].7_

Dry sand a (Like Fig. 82) 13.5 ]_.h ]] ._ ]2.2 .91

Pinus strobus a (Like Fi_. 86) 18.0 10.9 18.1 19.6 1.80

Clear sky a'b (Fi_. _.,,) R.6 6.q ]11.0 16.0 2.32

aReflectance curves modified by H?O absorut_on bands. bspectral reflectance curve measured over South D,_kotn on 26 J_ne, ]963 with clear sky. 1967016633-136

lO5

4.0

o IO3A RADIO;dETER.,JUNE 2, 1962 , x 103A ., ,, 26, !963

I 5.0 o_ CF-A-ILCULATED. DATA, TABL. 26,1963E 20

2.0 _ I l _ i \\ a

I. Y_Ix_ \ x

i 0_A _ -"'" "-A."..-- "- ' ' X' i I cLp.,sc..._,,..o_.

CUMULO- N IMBU8

' I , l I ' I I i I! 0_ I0 o20v_50;_,4.'0--;L,,60_,,6o-c0 10o._O0__904 I00 I P5

I!- eFiargureth re52.flectanReflectance. ae diq_'_ demonstr&ting epeotr&l dependenoe of

f 1967016633-137

I06

I, I,, I I I o _ _ ". - 30NV.LO37_3EI 7VNOI.I.C)3EIIO-18 ] 9670q6633-q 38

t ,

?. A MODIL OF THE F.J_THFOR ALBEDO PIr;.DOSE8

A model of the earth for albedo purposes must 5_ ba_ed on the precise

definit!on of earth's albedo which is contained in Equation (19a) i.e..

_ (19a) i'

The co.ordinatesystem (0o.0_) which Is used for integration _ver the earth's

[i surface is that shown in Figure ha, i.e., one determined by the pos!tion of the I

sun. Now the portion of the earth's surface which lies at any positioz_of this i coordinate system continuously changes because of the changing sun's declination

' I! and the earth's rotation on its axt,° Even though this information is implicitly specified by t, for practical purposes ve wtll indicate that we must know

0_(eo,_o,e,O,_:n:t) where _' is long_tude west of the Greenwich mer.'diaz_ a_d

is the angula_ distance south of the north pole (colatttude). The relations between t and (_' ,n') can be calculated with the hel_ of

I[ ,,.gure_b. From the lay of sines ors ,,hericLl triangle, ve have

_[ __ocos _ • isiinnheo . -sinsin,rI'_ (36) l! From the law of cosines:

a ,) cos .' - cos (90-6,1 cos e° + sin 190-_ s) sin eo ooe ,_ 1371

I:| 107 1967016633-139

1C8

If we specify the bidir,__ctional reflec*ance 0_(eo,¢o,e,@,_;'n't) for every point on the earth's surface, we _an perform _he integration for earth's albedo indicated b:/ Equation (19a) usisg the following procedure.

i. Specify t (day of year e.;.4GMT'_.

2. F_nd 6s and GKA (of Bun). iT_bles from the Aiz Al_nac are quite suitable. )

3. For a given (Oo'¢_)u calculate n', ha, _'_ and ¢o' in that order from:

cos n' " cos (90-6 s ) cos B° + sin (_0-6)s s_n eo cos ¢o' (37)

-sin 8 sin _' sin h = o -o (38) s sin h'

_, - G_A - h (39) s sin h cos 6

sln q s s (_o) "o sin e o

• ¢ ! b Integrate pA(eo,¢o,e,_,_,n,t)over e,@.

! 5. Repeat the process for all eo,¢o to obtain the intergral for A(t).

B. FHVB[CAL CHARACTERTSTICS

The physical characteristics of this model of earth's albedo aye specLfied by _A(_o,¢o,e,@,_n_t). Although it is not possible _t the present tlm_ to specify 01 in fin_ detail for all of the earth's surface it appears that an initial rather precise model could be set up am follows.

Divide the wavelength range into four interval_: 0.2-0.,-0.7-2.0-5.0 microns, containing 9, h0, _5, and 6% of the _olar energy, respectively.

Bidirectional reflectance functions Oki(@o,$o,@,, ) would be e.tlmsted for ea@hwavelength interval for at least eight basic .a.th features: 1967016633-140

I09

i. Sandy and/or rocky areas - clear sky.

2. Soil and/or vegetation - clear sky.

3. Ocean - clear sky.

4. Snow -- clear sky.

5. Low clouds over ocean.

6. Low clouds ovec land.

7. Low clouds over snow.

8. High clouds.

With the aid of a careful geographical-climatological study a resultant

bidizeztion I reflectance model:

o_(eo,_o,e_,c;o_t) _ vL a i ; _n_t)o_i(5o,¢o ,6,_) (hl) i

where

! ! ! ' [ a.(<'1 n,t) = 1 for any (_,n,t) (h2) i

would be set u_ for each of approximate]v i00 areas on each hemisphere of the

earth. The (_ n') areas might be arranged as follows in each hemisphere:

Latitude Aq___L A____L

0 .I0° 20 ° i0 i0 o 200

20 150 200

35 150 200 50 -17.5 ° 30 ° : 67.5 22.5 ° h5 ° 9O 1967016633-141

]i0

For a conlplete study models should be made for one day in each month of the year although four days, _! M_rch, 21 June, 20 September, tO Decem- ber could be studied first. With each model, diurnal variations of albedo could be revealed by making calculations at 4-5 evenly spaced wiues of time o,,each day. The directional characteristics of the reflectance of radiation out :nto space could be calculated to help in the interpretation of satellite experiments and earth based experiments such as those of Dan-

ion.

C. ILLUSTRATIVE EXAb_LE

The following simplified example is provided to illustrate, in part but not in comprehensive detail, the type of calculation which can be made with the model proposed. Both the model and calculation have been greatly simplified in this example, as follows:

I. The value of albedo, but not the directional characteristics

of radiation reflected back out into space, is calculated for

23 December at 0000 GMT and 1200 GMT.

2. Diffuse reflectance is assumed for all earth features except

the ocean and clouds. For these two features directional

reflectance data is used.

3. The basic reflectance values are assumed to be averages over

the entire solar spectrum.

We can write the precise definition of earth's a!bedo, Equ&tion

(19a), as:

A(t) .! . I I r(8°'¢°'_n_t)sine o cose o d8 o d¢_ (43) ! 8o ¢o 1967016633-142

iii

where the directional reflectance _s glven by:

i i I I_A( _ ,e,_,_n_t)HsA(t)sinecoseded_dA r(eo,,o,Clnlt)= _ e _ e°'*°

JI Hsg(t)dX (4h)

substituting from (hl), we have:

[ai(_,n,t) I I I 0ki(eo,¢o,e,_)Hsk(t)sinecoseded_dA r(eo,¢o,_,n,t ) --

" i Hs_ (t)d_

= [ ai(_n_t) • ri(ed¢o) (h5)

and thus we have

A(t) --_i JFeoi,o"_c_i(_;n_t)ri(e°'¢°)sinelo cOSeo deo d¢o (_6)

The baszc reflectance models used for this simple calcu]ation

1. Sandy and/or rocky area - clear sky, rl, = 35

2. Soil and/or vegetation - clear sky, r2 = 15

3. Ocean - clear sky, r3(eo) (see Figure 96, curve 2)

h. Snow - northern hemisphere, rh = 80 (new snow)

5. Snow - antarctic region, r5 = 83

6. Cloud cover, r6(8o) (see Figure 51, curve r)

7. Cloud cover over snow, r7(eo) - r6(eo) + lO

Note that none of these reflectance models are a function of ¢o" The integration over So,Co was obtained by numerical summation over areas with 1967016633-143

112

_o " 20o • 9 radians

w _eo " i0° " i_ radians • p

Thus :

A(t) - ; J-I k-i [i "iC_'_k'njk't)ri(ek) 'inek c°SekAekAeJ (_T)

This can be written differently to indicate the order in which the sum-

mations were carried out: i

_Jk' jk sin2e (b8) k=l J 1 j

The earth was then divided into (I) la,,d,(2) ocean, or (3) snow-covere6

areas as shown in Figure 5h. The global cloud cover assumed was based

on a map of mean cloudiness for the month of November92 and is shown

in Figure 55. In Figure 5h, where a given (_In) area contains more than

one type of earth surface feature (i,2) or (2,3) they were assumed to

be equal in area. Values of the ai for each (E_n')area are shown in Figure 56. t

Values of 6Z • -23.h366° and GHA of 180.3° (at 0000 GMT) and 0.23° (at 1200 GMT) were obtained from the Air Almanac.

/ Then calculations proceeded as follows:

!. For each ¢'J'Bk area,njk' and _Jk' were calculated from.

cos_k • cOS(90-6s)cOS8k )sinek eos¢0_ (h9)

[,ineksln_ _ sin hs(J,k) - (_0) sin n',Ik 1967016633-144

113 1967016633-145

ii_

1967016633-148

116

_Jk = GHA - hs(J,k) (51)

2. The values of _Jk and n_k thus obtained made it possible to calculate the sum over i:

i mi(_k,n_k,t)ri(e k)

3. and the sum over J:

1- jl -

_. Finally A(t) was obtained by summing over k.

Values njk,' _Jk" and the sum over i are showr,in Tables 9 through 13. The result obtained showed no diurnal effect, values of A(t) of

_i.04 at 0000 GMT and 41.26 at 1200 GMT were obtained. The values of

the sum over J are plotted as a function of ek in Figure 57, In this i figure the increase of reflectance at high solar zenith angles is ob-

vious. Recall that direction_l effects were included only for ocean

and cloud, but since the earth is nearly 80% ocean and average cloud

cover is better than 55%, the directional effect is seen in the final

results.

Diurnal effects were minimized by the fact that mhe calculation

was made for a day on which the sun vas fartS:st south, thus emphasiz-

ing the large ocean areas of the southern hemisphere. It is expected

that a diurnal effect would be noticeable when the sun was farther

north, and a diurnal change from mainly ocean area to mainly land area

would occur.

An additional factor w_ich would serve to minimize diurnal varia-

tions, is the smoothing effect contained in the cloud cover distribution 1967016633-149 1967016633-150

zz8 1967016633-151

I i iz9

I! 1967016633-152 1967016633-153

121

-_ ,_o o ,--o _-o o,_,_o o _-_ _-o o_ t'--0 kC) OqO O'_kC) 0 _'-D--0 kC) C"_O C,n_ 0

I -','_ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PI ,-I PI PI PI 04 OJ 04 OJ 04 mo,%m

_-i04 m.-._ U'x_D I--_00xO _ OJ re-.l" b'xXD D-_ l 1967016633-154

122

I00 -

90-

80-

70-- x

_. Gi ((;jK,'r/jK, t)ri (OK,_) / 60- ,, //,°

50 - / 40 ox_--,__-._.__.__,,_,._. ;o%(- 1 i x 0000 G.MT. 30 - o 1200G.M.T. _"

20-

I0- i

I I I I I I I I I , 0 20 40 60 80 eK

Figure 57. Average albedo in integration ring k vs. ek. 1967016633-155

chosen, i.e., an average over a month. Thus most (_n0 areas contained about 50% cloud cover, with a few showing as low as 15% and a few as high as 85%. Actually on a given d_, some areas would have 0% and other8

100% cloud cover and diurnal variations would be much more noticeable. 1967016633-156

VI. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH

A. CONCLUSIONS

The above study has been carried out with the ultimate objective

of creating a precise model of the earth for albedo purposes, to replace,

on a practical basis the isotropic, wavelength independent homogeneous

earth model which is usually employed in the analysis of satellite measured relectance data. To this end the following results have been obtained.

1. A precise definition of earth's albedo has been formulated

in terms of the distribution of bidirectional reflectance

over the surface of th_ earth (including clouds and the at-

mosphere).

2. This definition was compared with the Bond definition of

planetary albedo which has been employed by astronomers in

the interpretation of measurements of photometric earth

albedo. The Bond definition was shown to represent earth's

albedo only if the earth is homogeneous with perfectly dif-

fuse reflectance.

3. A review of research related to earth's albedo was used to

demonstrate that,,insofar as albedo is concerned, the earth

is obviously nonhomogeneous with wavelength dependent, non-

isotropic reflectance. However, in the application of Bond's

definition, in the analysis of satellite radiation data, and

in general heat balance considerations, these characteristics

are usually ignored. 1967016633-157

_. New data obtained from outside the earth's atmosphere on

three high altitude balloon flights was shown to confirm

both the spectral dependence and nonisotropic nature of earth

reflectance as follows.

a. Curves of the ratio of wide band (0.2-4.0 microns) reflec-

tance to narrow band (0._}-0.75micron) reflectance were

sho_u_to be a function of narrow band reflectance. Thus

the narrow band channel data cannot be used for earth al-

bedo data over the 0.2-5.0-micron range, as it was by Ban- deenj et al., without the application of an appropriate cor-

rection factor. Correction factors, obtained from the bal-

loon flight data, were verified by theoretical calculations.

b. Bidirectional reflectance data for a stratocumulus cloud

was shown to verify that cloud reflectance is a scattering

process, consistent with theoretical results of Deirmend-

Jian for an approximate cloud model. Using this data the

total directional reflectance was calculated for all solar

zenith angles and the results were shown to be Consistent

with measurements by Nelburger. These results were then

used to demonstrate the kind of error which could result

in the analysis of satellite radiation data based on the

assumption of isotropic earth reflectance combined witr.

satellite radi_eter data omnpling for a limited range

c_ solar zenith angles and radiometer nadir angles.

c. Bidirectional reflectance data for partially snow covered

earth at several solar zenith an_les showed pronounced

forward scattbring for low sun angles and less forward 1967016633-158

...... i I

126

scattering with a specular reflectance component for a

higher sun angle. The reflectance patterns obtained

agree qualitatively with surface measurements of snow

reflectance.

5. The characteristics of a more precise model of the earth for al-

bedo purposes were discussed. The model would have nonisotropic

wavelength dependent reflectance an.ia nonhomogeneous earth;

and would be based on the exact definition of earth albedo

formulated in Section II of this paper. The procedure for

setting up a first approximation to this model and for cal-

culating earth's albedo from this model was outlined.

6. An illustrative example was carried out with a simplified

model of earth reflectance. The example did not have the

characteristics of the precise model of the earth. It served

only to illustrate the calculation procedure and not the

comprehensive detail that can be obtained from the precise

model.

B. FURTHER RESFARCH

The precise model of the earth for albedo purposes should be studied more completely.

A geographical climatological study o: the earth should be made to determine the number of characteristics of basic bidirectional reflectance patterns CAi and the coefficients aif_,n,t• ! ! ) that are needed for the model.

Additional measurementi'of bidirectional reflectance patterns should be made of Various earth surface f_atures from outside of the earth, and these meuurementa should be supported by theoretical caleulatione 1967016633-159

l i of scattering in a real atmosphere including the effects due to multiple-

scattering processes, absorption and nonisotropic reflectance at the

I earth' s surface.

I The results of the study of the more preciee model of the earth. should be applied to the planning and analysis of satellite measure-

f ments of earth's albedo, to all other albedo experiments, and to

theoretical calculations of earth's albedo, J ]

p 1987018833-180

APPENDIX A

EARTH'S ALBEDO FROM MEASUREMENTS OF EARTHLIGHT ON THE MO0_

1. THE WORK OF DANJON9

The messurements of DsnJon9 were msde with s double Imsge photometer.

Using this photometer, two imsges of moon sre observed as shown in Figure

98. The two imsges sre 8rrsnged so that region B of the sunlit crescent

of one imsge is adjacent to region A of the esrthllght of the other image.

I t I

t Fig,_re98. Images in eat-eye photometer.

Image I1 passes directly through the photometer, but i-,-ge I2 passes

through the photometer after two reflections from prisms between which

is located and adjustable disphra_n. The intensity of B is reduced to

that of A by the disphra_n which is calibrated to give the ratio of

intensity of the two Images. In this fsshion_ many measurements of the

ratio E/C of earthlight to the sunlit crescent were rode for phase a_lea

of the moon (q) from about _0 to 165 ° . This ratio is _uolly expressed

28 1967016633-161

iz9

C. The brightness of the in stellar magnitudes, i.e., ME-MC = 2.5 log

sunlit crescent is also measured relative to the brightness of the sun,

i.e., the r_tio C/S is measured. The ratio E/S is then calculated from

the data and expressed in stellar mag:'._tudesq-M S = 2.9 log ES. The data

ME-MS are plotted vs. c_,the phase angle of the earth, where:

--18o- n

DsnJon found that the function: i _%-Ms --9.99+1.3o +o.19 +o._S (52) } j was a good fit for data obtained in the photometric region of the spectrum

(A = 0.55_ micron) during the years 1926-1935. The constant term is i Mo_ = 9.99, equal to the magnitude difference of the apparent brightness

I of earth at full phase as viewed from the moon and the brightness of the

sun st i AU (astronomical unit).

If we change the constant term to RoAt the magnitude difference of

the apparent brightness of earth at 1 AU and the brightness of the sun

a_ 1 AU we have RoA = 22.9_ (magnitude).

The Bond albedo is then 81_ven by:

where o = a/R = radius of serf.h/distanceof earth from sun. 1967016633-162

13o

Thus we have:

R°---__ = 22.94 - 21.89 = 1.09 (magnitude) G2

_nd

P_ : aT_o_, : (2.512).1.o9 : 0.366

qA = 2 j l8O2.512 -[l.30(a/100+ )O.19(:/l_)2 + 0._(_/1_)s]sin o (9_) : 1.o99

-_x = _'q_ : 0.366. z.o95 = o._o

Note that AA : _0_ is the mesn slbedo, 19_6-1935, in the visible region of the spectrum (i.e., A = 0.99_ micron, approximately).

The accuracy of the method is limited by several factors. Soma of the light from the sunlit crescent is scattered by the atmosphere and therefore interferes with the measurement of the ratio C/E. This scat- taring has greatest effect Just before or after full moon, when the esrthlight results from a very narrow earth crescent, while the scattered and reflected light is very strong. DanJon sta+_s that the double image photometer measurement, with regions A and B on the same diame_erp elim- inates the offset of scattered light. Howe_er, Bakoe 11 notes (after

Whipple) that the sk_ backgro_d still affects t_ measurement, because altbot_b tha backgroun_ is _he same for both regions A and B, it suds the same amount tc both numerator and denoBinator of the ratio and there- fox. cha_es the ratio. 1967016633-163

131

Jelt._er ratio C/E or C/S can be measured for ell of the necessary

phase angles. In the work of DonJo _, C/_.was measured _or _0° < q < 165",

end C/S for 11" < _ < 196". The date is extrrpolsted to O" and 1CC',

respectively.

Irltz12 notes that, since the measurements of Denton and Dubols were

made from western Europe, they do not necessarily apply to the esrth 8s

e vhole.

DanJon notes that his meesm'ements end those of Dubols ez: not suf- i flcient to establish vsrletlons of the p_ _ function (i.e., diu_nsl_

seasons1, etc.). If the phase f1"_ctlonis assumed to be con-tent then

J each observation yields 8 value of mgnitude st full phlse. With thls

assumotlou, the observstlo_s show seasonal verletlons from the mean value 9.99, with slbedo mxiBtur in spring end fall and ,Ltnlmumin summer and

winter'.

j Angstroml3 has derived values of photoa_tric 81bedo from Don_on'a data for the years 1926-_4. as follows:

Year 1926 19"27 1928 1929 1930 1931 1932 1953 193_

Photometric i Albedo O._l 0._ 0._0 0.39 0._9 0._0 0._8 0.37 0._8

2. T_ WORK OF BAK08Lx

During the Internst&onal Geoph_sic81 Year an 8tteapt wee made to cor-

relate fluctuations in the ear_h_hine _ith cloud condition8 on the ¢_u_-

f_ee of _he earth. 81x Denton-type _ters were Instslleh at the

utellite traekins stations of the 8a!theonian Asts_physie&l _oelety (see 1967016633-164

132

Table 14). Measurements were made fron_ 1957 until 1960 and have been reported on by Bakos.ll

TABLE 14

EARTHSINE PHOTOMETER STATIONS

Station Longitude Lat[tude Arequipa, Peru 4h 46.1 m -16.4 °

Yerkes Observatory Williams Bay, Wis. 5h 54.2 m +42_6 °

Organ Pass, N.M. 7h 06.2 m +52.4 °

Haleakala, Hawaii I0 h 25.1 m +90.7 °

Woomer8, Australia lhh 12.8 m -51 .I°

Shiraz, Iran 20 h 29.8 m +29.6 °

Measurements of the ratio C/E, as de'scribed above, were made with red, green, and blue filters, as well as without any filter. Systematic differences between data taken st each station were found by plotting the earthshine observations as a function of phase angle. When these plots were compared to that for Yer_es (Williams Bay, Wis. ) a vertical shift was found. These vertical shifts were eliminated, thus making all observations conslstant with those of _rkes. Also morning observations were found to be brighter than those made in the evening, because of different reflectivlties of the two parts of the lunar surface. Observa- tions made with the green and blue filter were reduced to cle@r observations by the same technique of eliminating systematic differences. The 1967016633-165

155

"red" observations were excluded.

Statistical errors were evaluated by comparison of "filtez" and "no

filte{' observations after they were reduced to a common base, i.e., to

Yerkes magnitudes. Also comparison of readings made by different ob-

servers on the same instrument checked the consistancy of the data. It

was concluded that the mean error of a single observstion wss ±0.20 mag-

nitude.

The data obtained was prepared for analysis as follows:

a. A curve _ mean values (uncorrected for systematic or other er-

rors] vs. phase angle was prepared.

b. A carve of best values (the mean of observations reduced to "no

filter" and Yerke_ magnitudes) vs. phase angle was prepared.

c. The difference between best and mean values was computed. This

is called the O-C reading and contains errors as well aS fluc-

tuations of eart_hshine due to varying conditions on earth.

d. Cloud cover information for a time close to the time of an ob-

servation was plotted on a globe and the area of the earth which

would reflect light to the moon was photographed. Of 196 such

weather maps, only 17 contained cloud cover distribution for

more than 70% of the are, of interest.

e. Estimates of snow cover were added to each of the maps.

Following are some results obtained from analysis of the data:

a. O-C readings showed no obvious correlation with cloud cover. 1967016633-166

134

b. The earthshine shows a slow and continuous fluctuation with a

period of one day, resulting from the earth's rotation. The

author attributes this fluctuation to a "bright spot" on the

earth in the Asian hemisphere. Average mean cloud cover for

five longitudinal areas oi the earth are compared with mean

values of O-C in Table 15. For Asia the cloud cover is about

i0_ higher than for the other longitudes _nd the earthshine

brighter by about 0. 9 magnitude.

c. Changes of the earthshine during the year are shown by the

laonthly means of the O-C date taken in 1957, 1958, and 1959

(see Table 16). These data show that the earthshine is the

brightest in March through June. Bakos reasons t_mt because, _'_

statistically, the cloud cover does not change substantiall

during the course of a year, thi_ phenomenom must be due to the

difference in reflectance of continents and oceans. During

March through June, the earthshine is primarily from the northern

hemisphere and.thus reflectance of the continents would be dom-

inant. The reflectlvlty of contlnents must therefore, in gen-

eral be greater than the reflectivity of the oceans.

d. Finally the dzta was used to calculate the average albedo of

the earth for 1998 and 1999. The equatioD used for earth's

albedo was that due to Kazachevsky:

A = am • 2/180 Q(e)s±n (99) o 1967016633-167

135

TABLE19

LONGITUDINAL VARIATION OF CLOUD COVER (After Bakosll) Longitude Area O-C Cloud Cover O°W Africa O.14 mag. 30_

90° America O.04 ---

150° E. Pacific 0.i0 29_

180° W. Pacific 0.09 51_

24o° Asla -o.72 41_

TABLE 16

Month O-C |_ 19,7 19,8 19,9 ti January -0.03

[! February -0.i0 Msrch -0.16 +O.14

[i April +0.02 -0.36

I May +0.03 +0.07 June -0.13 -0.49 [ ! July +0.Ol -0.Ol

Augus_ +0.12 +0.05

September +0.ii +0.21

October +0.i0 +0.08

November +0.50 +0.17 +0.16

Dscember -0.02 +0.0_ l,i 1967016633-168

136

where :

A = earth's albedo

d = the mean distance of the moon from the earth

s = the radius of the earth

The function Q(G) is of the form:

Q(a)= h F(n) = K.f(a) I2 ql where

11/12 = intensit_ of esrthshine intensity of sunlit portion of moon reflectance of sunlit ares qe/_1 = reflectance of earthshine srea

F(q) = lunar phase function

= 180 - a

f(a) = proportional to the earth's phase function

Using DanJon's phase function, Bakos found:

A = 0.368K = 0 •368 f(a)Q(_) "

Next, Bakos applied the idea of a "norma_' brightness of the earthshine. This is the value of earthshine at G = ll9@ or 2_ @, used because other writers have found, that for different phase functions con-

Sidered all had essentially the same value at these values of G. At a = 119° and 249°, F(_) = 0.192, and f(_) = 0.345 . Therefore, the albedo is given by: 1967016633-169

157

A --o.. 8

la _i

where II '3Eis the normal brightness of earthshine, i.e.3 st G = 119°

I or 249°.

li Each value of earthshine measured by Bakos, et al., was converted to a normal bx ightness using a correction factor obtained from a plot of all

observstions vs. phase angle. A mean value was then obtained after ad-

justments for systematic errors were made. The yearly mean values of earth's albedo obtained in this way are: H No. of Year Albedo

1998 o.41 Obser21vati9 ons

19_9 0.42 I_8 These values agree nicely with DanJon's average albedo of 0.4 for 1926-

1935.

3. THE WORK OF DUBOISI0

Dubois has made measurements similar to those of DsnJon, using blue, green, yellow, and red filters. He notes that the brightness of the

' earthshine varies with phase, color, and also the hour of the observa-

I tion, because a diurnal variation is caused by the dissimilarity of the albedos of oceans and continents. He has reported on data taken between

[ 1940 and March, 1942. " 1967016633-170

138

He has studied the seasonal variation of the earthlight, using the green-filter observations near 0.53 micron, for phase angle (_= 115°, taken around 1900 G_r. These brightness curves are shown in F_.gures

59a and 39b for the years 19_6-1948 and 19_9-19_4, respectively. Max- ima of brightness (minima of Am) occur in April-May-June, and October-

November-December.

In addition, the yearly variations were studied. Relative luminances for 30 June of each year 1940-1954 are shown in Figure 59c. Th_ figAre shows that the esrthshine approaches a maximum as the minimum activity of the solar cycl_,approaches and then decreases rapidly right after the minimum of the solar activity. 1967016633-171

139

,o--d _.'! II

8 j F. Aj. J J A s o I N Om MONTH

O.)1946-1948 MONTHLY VARIATIONS

o h_ ...d , J , . A .IJIJ • s o . = 8 | I MONTH ; b.) 1949-1954 MONTHLY VARIATIONS

40 41 42 43 44 M 45 47 48 41) 80 81 52 l_l 84 YEARS ' ,',O.)YEARLY VARIATIONS

] Figure 59. Yarlatloa of the brlghtnes8 of the earthshlne (after Dubol8I0). ! 1967016633-172

APPENDIX B

EARTH'S ALBEDO MEASUREMEB_fSFROM SATELLITES AND SPACECRAFT

The instruments used for these measurements are of two basic types;

the low resolution instr,.eat with broad field of view and wide spectral

response and the medium resolution instrument "'iths narrower field of

view and wide (sometimes not wide enough) spectral response. The meas-

urements with the low resolution instruments will be discussed first,

those with the medium resolution instrument next. The Mmrlner 2 measure-

ments which are different from the satellite measurements in that they

were made from a deep space probe (and. indeed, are most llke %he meas-

urements made by DanJon) will be discussed last.

I. THE LOW RESOLUTION MEASUREMENTS

The low resolution measurements are made with instrum_:ntswhich are

an extension of the design of the Suomi-Kuhn "economical" net radiometer.

In the idealized instrument, a small spherical shell sensor of low heat

capacity, exposed to radiation from the earth and the s_, shielded from

satellite radiated energy and isolated from the satellite by insulators

of very low heat conductivity, will ass_,nea temperature determined by

its radiative heat balance. For the ideal experiment, the radiative heat

balance equation is usually written in a form similar to:

C%...as + O%._.Rr + SiS.R, = _.c_.o.T" (58) i

i_0 1967016633-173

• i

lhl

I ' . where:

Rs = Direct radiation from the sun, watts/era2.

I Rr = Radiation reflected from the surface of the earth, wstts/cm2.

i RI = wThermalatts/c_rad.iation emitted by the earth and its atmosphere,

i 0% = The absorptivity of the shell for solar radiation. 5! = The absorptivity of the shell for thermal radiation.

¢! = The emissivity of the shell for thermal radiation.

= The solid angle subtended by the earth as viewed from the satellite.

j s = The Stefan-Boltzeman constant. T = The sensor's temlm.rature,*K.

Different forms of the experiment have been discussed, by:

a. V. Suo_i, R. J. Parent, and co-workers st %he University of Wisconsin.14 I b. R. A. Honel, F. Bartko, end co-workers at Goddsrd Space Flight

i Center 17,18 c. F. B. House at the University of Wisconsin.2

Two excellent papers which discuss theoretical and practical aspects of

I the experiment are those by K. J. Dignel119 and M. S. Msl}_vich, et 81.20 In the form of the experiment originally proposes by Suomi, several

I sensors with different costings, providing wavelength discrimination,

_ were used and some were shielded from the direct radiation of the sun.

In this case each of the sources of revSiation can be determined from the "i

temperature_ of the several seniors. For exlmple, if the values of

£n could write the fol£c_l_ absorptivity were as Kiven Table 17, ve 1967016633-174

equations.

TABLE 17

VALUES OF ABSORPTIVITY FOR VARIOUS COatINGS

Coating u. ul Black paint 0.99 0.99

White paint 0.05 0.99

Tabor coatin_ . 0._O 0.i0

For the dark side of the earth (for any sensor):

Ut_R ! = 4_Eto.T4 _. F.!

If 8, El, and 5! are k_own R! can be calculated from measured values of T.

On the sunlit side of the earth:

BIae__s_!_: 0.99,r% _ _a, = _,.o.99._ o.9_ o.9_

o.o9,_ _ _R, = _,.o.9_._ o.o9 o._ T,bo.__..Z.s_=.._.:

0.90.1_ + 0.90 19Rr + O.IO DRa = _x.O.lO.o_

Shielded Tabor Sphere:

0.9o _r _aa - _..o.lo._ o.lo 1967016633-175

Combining_the equatiors for the Tabor and shielded spheres: (

u° (T_-T_) ,-_" r_ -- _.J . ,.,:,. 1 i

From the equations for the black and white spheres:

9 - , thus

Rr --38-_(T_-T_)_ °_(T_-T_) (60)

also

2 o_(17N'r_) ¢61)

? ! J Now Rs is the solar constant. It is probable that its value is " _o_n

more accurately than ¢sn be obtained from _.quetion(99). The accepted J value can be used instead of the.data obtained from the Tabor and shielded

] sensors. I. this case

J 'I Sensors of this type were constructed bH the University of W-_econsln

group under Suomi for one of t_ Vanguard satellites which was not

orbited successfully. Other sensors of s different design we._ flown on

Explorer VII, TIPO8 Ill, TIlq06 IV, sn_ TIROS VII. In the _ew design

hemispherical sensors were used. They were thermally isolated from the

satellite _y being mo_nte.d on insulatinK rods above a hl6hly reflective

mirror au_s_.-e. Thermal isolation _a not complete, however, and so it

t we_ necessary to add terns to the radiation balance equation to account 1967016633-176

: i

for heat conducted from the sstelllte to the hemisphere slang the in-

sulatlng rod. Data snalysis also required consideration of the heat

capacity of the sensor. Thus the heat balance equation for a sensor is

changed to:

as_Rs + asGRr + aLBRl = 4_elaT4- H _T . K(Tm-T) (63 )

where the factors involved are:

H = Heat capacity of the sensor. _T _t Time derivative of the sensor's temperature.

K = Conductivity of the hemisphere support rod.

Tm = The mirror temperature.

Papers written by Suomi indicate that it is not possible to calculate

daily heat balance from the satellite because of restrictions imposed on

data sampling by the satellite orbit. Results from Explorer VII data

were a series of long-wave radi3tlon loss maps derived from data taken

b# the white hemispherical sensor at night. Daytime measurements of i

T earth reflectance were not obtained (not published).

R. Hansl and F. Bartko have discussed low-resolution sensors of a

different design, i.e., thermister detectors mounted on an insulating

base st the bottom of a highly reflecting truncated cone. The detectors

were assembled in pairs with one white thermister and one black thermister

for wsvelengt, discrimination. This design was flown on TIROS II, TIROS

Ill, and TIROS IV. Some data have been published, however, Bartko, et 1967016633-177

149

81o ,18 indicate that the value of this instrument for heat balance and

earth albedo measurements is limited because of the data acquisition

limitations of TIROS.

£n_ only s_udy of albedo and long-wave radiation based on measure-

ments with the icw resolution instrument is tnat of F. B. House, using

data from TIROS IV. This study is unique in that data from only t.he

black sensc was u_ed, and that constants in the equation were determined

from in-flight data, i.e., in part, in-flight calibrations were made.

] The sensors on TIROS IV were hemispheres mounted above mirrors which

prevent the hemisphere from "seeing' the satellite. Two systems of sen-

J sors and mirrors were mounted on opposite sides of the satellite, each

system having one black and one anodized sensor. When the satel_ite;

rotates on its axis, at some point of the rotation a part or all of one

sensor may be eclipsed from d_rect view of the earth. However, at this

i time, the matched sensor on the opposite side of the satellite starts viewing the earth_ The sensors are connected in series, so that the sver- i age temperature of the two sen_ors is measured. When the satellite spin

period is short compared to the sensor's time constant, the measured

average temperature can be taken as the temperature of a severed sphere

which views the earth.

The raJiatlon balance of this spinning sensor is written as:

Ct_7_s'_Rsd(_ _s _: + _Rl " 4_'_oT_- Cm'_ 4) Cc'(T-Tm) _7

1 1967016633-178

where the terms on the right hand side of the equation represent:

a. The energy emitted by the sensor to the mirror and to space.

b. The energy radiated to the sensor by the mirror.

c. The energy conducted to the sensor along the mounting post. !

d. A thermal lag term involving the heat capacity of the sensor.

Sensor temperature measurements were taken on the satellite every 1 29.16 seconds. If TI and Te are two consecutive sensor temperature ob- [ !

serwtions and T and _m ere average sensor and mirror temperatures, then

the radiation balance for the sensor can be written as:

....as _Rs + _Rr + eR! 4_ -- _4 CmV_m4 + Cc(T-Tm) + Ct(cTe4-sT14) a! a! _! (65)

The constants Cm, Cc, and Ct were evaluated from in-flight data and lab-

oratory tests, as follows. Laboratory measurements by Sparkman on in- J struments similar to the ones flown on the TIROS IV satellite yielded

the relation : fi

Cm = 300c •

A study of sensor and mirror temperature changes (390 cases) in the 3-

min. period after the satellite entered the earth's shadow (see Figures

60 and 61) with the assumption of constant thermal radiation _R! during

this time gave the result:

Ct = KsCc + Ks . 1967016633-179

127

Finally a study of sensor and mirror temperature changes over a 25-min

interval while the satellite was in the earth's shadow, for many orbits

over a precessional period of the satellite, resulted in a value of Cc.

The radiation balance equation could be written as:

8R_ = 4_ ¢__I0_4 + Cc[(___m ) . KIc_4 + KaCc_-oT_)] al *K3(oT2-4 oT4i) (66)

i.eo_

_R! = A + Cc'B + C

In each orbit the equation is evaluated at position s at the beginning

of the 2_-min. interval and position b near the end of the interval (see

Figure 61). Summing over nll orbits considered we have: 1

2(_Rz)a 2(A)a* Cc2(B)a*_(C)a

(GRI)b = >i(A)b * Cc r (B)b + 7(C)b

assuming

_(_R,)a " Z(,aR,)b we find

cc . Z(_,7.(_)_..- Z'o,.-Z(o,_ (67)

ZCB)b- ZCB). 1967016633-180

148 1967016633-181

! I

I; ! _ _o

q_ o II _ill ,.' /4 _- I] _. / j4_.;_:o.

(! i' -T:'J" /---14

I,l _.--..--Lfi I 1JO

I: g _ o '!_ 8! "!' I", IC]VMOI.I.N310 811_1_1¢]

I1 1967016633-182

150

Values of the constants obtained were:

C c = 0.010 -+ 0.0009

Cm = 0.300 -+ 0.019

Ct -- 43 _+ 2.19

Thus, the radiation balance equation becomes

4 4 as as ct_" - o _m + O.OlO(_-_m)+_3.o(_r2-_) a_'--_R!+ _ _R r + BR t = 4_ at_ (68)

The data from the black seusor was then analyzed _ _.llows. At night, we have

(BRt)I-- [__ a-7ct _ + correctlons_ I (69)

At the time of transition to earth sh&dow,

On the sunlit .Ide of the earth,

_Tt _Rs + a-7 _Rr + _Rt_iiI " a t III

Then also, asaumlng

(_R,)x - (aRt)if

t ._.)II . [\a_.R.! . _,)II -(_R,)I (72) "19670"16633-'183

I 151 i Assuming

(o,,III> (o._ o_ 8Rsr + ,)III - (o_R/IIs (73) . _. BRr + _R = .R s + 15R i The mean thermal radiation loss at an latitude over a precessional period

is: _ (_Rt)i I, BR( ----_')I= (74) n

Ji ,, The mean daytime radiation loss (reflected solar plus emitted thermal

radiation) at a given latitude over a precessional perlcd is: n

as _.,(_ _Rr+_R!)III (7_) (Yl_Rr+ _)zll "

The mean of the reflected solar radiation is taken to be: I ------" (0% 0% _R! (BRI)I (76) J_ (z!_Rr)III 1 (_! 15Rr + )III " The incident solar r_dis%lon is Rs cos*_, where cos*_ geometricelly

I weights the solar radiation which is incident to the |tea viewed by the

1 satellite. Assuming perfec_ly diffuse reflectionp the men albedo at a

given latitude over e precessional cycle is:

i00.f___s " (__,,.oo..w_- (_'_

II 1967016633-184

L52

_s where _.Rs cos*_ is a term which represents the mean reflected sol=r

radiation which would be received by the sensor if the earth's re_'lect-

ance were iO0_ and perfectly diffuse. This term can be calculated from: n

--ms Rscos*= (aT s)incos- (78) al _ n

Results were obtained by House for four months of TIROS IV data, 8

February, 1962 to ii June, 1962. The method of sampling over the earth's

surf&ce, and limitations in cove,age in time and geographical area should

be noted. Factors which result in sampllng limitations are: the in-

clination of the satellite orbit and the precession of the orbit with re-

spect to the sun, data storage capability, and the location of data read-

out ground stations. House has discussed the problem briefly, more com- 21 plate discuscions of the problem are those of Widger and Wood, and in

the TIROS IV Radiation Data Catalogue and Users Manual.22 These dis-

cussions can be summarized as follows:

The geographical area of sampling by TIROS IV wao limited 0y the in-

cllnetion of the orbit to the earth's surface area between _8"N and _8eS.

Further limitation in the latitude of data coverlq;eIs imposed by the

i planeened fhorad so• laprer cilluaieaalon•l natlmonotioonf thofe e-_.4_•rth°/d'_ay. surface.As a Thresulte TIROSof thIVia orbpreita- l

cession of the orbital plane end the movement of the earth in it• orbit,

• complete cycle of the precession of the plane of the aetellite orbit

occuzred in •bout 66 deya. The TYROS IV launch we8 mJde on 8 Februsry, 1967016633-185

with the northern part of the orbit over the sunlit portion of the earth

(see Figure 62). On 23 February, the orbital plane was located in such

position tbac TIROS IV viewed sunlit earth in both northern and southern

hemispheres, with _ampling at the equator at about high noon. On II

March, the southern hemisphere portion of the orbit was sunlit with noon

sampling corresponding to the southernmost portion of the orbit. Since

the albedo varies as a function of solar elevation angle; it is necessary

that samples be obtained at ell solar elevation angles if a proper albedo

value is to be obtained. For any geographical area it is necessary to i sample over the entire precessional cycle to obtain samples at eli times

of the day.

I It is obvious that the weather (and even the _ea_on) is different J for days early in the cycle when morning samples are being obtained in

the n_rthe,n hemisphere, as compared to days later in the cycle when the

afternoon hours are being sampled. The distribution of samples oh-

is=ned 9hould be studied carefully to see that a bias is not introduced

into the data. House did not consider this problem except to say that

it could be expected that samples are obtained with equal frequency in

clear an_ clo_dy situations and therefore wei6hting aT the result due to

storm systems would not occur.

Avera_inl_ periods were selected fo. tvo almost complete precessional

cycles, 8 February to 10 April, end 11 AL,ril to 10 June. Marldionel pro-

_1lea of out6oln_ thermal radiation, albedo, and net radiation were pre- 1967016633-186

15h

• FIB. SUN I--18.O 2S F[I. SUN 6--10.O IIMAR. SUN l •-&I (181t8_14.:7) IdlA,311.7 (05 It UT) R£, 338.0 (23 h UT) IqA,B_d.7 INJECTION aifx IllO* ._,_IZ?O* b# =iO0.? * (a) (b.) (c.)

ItAi2S.ll

Ill MAR. SUN.$s*3.0 14 APR. llUN&stll.4 I MAY SUN$:*tS.0 (11)k t_T) RA:?.O |18 k UT) RJ.a2SL8 (*ollltUT) RAa3ll.I 4_ i O* 6f" SO* _" leO*

(d.) (e.) (f.)

_e-lll Ji _6"')0.4 _ ....I =*142 ..s .... IOMAY |UN $,*19.4 S dUNE llUN l,,Ir, lt.| Io 4iJiW llUN 1 "*I_A (OOit UT) }_A, ll4.1 (ll k UT) RAw?I.O (00 k u'r) RAaIILO 64"I?0" 611O"" 611"II0"

19.) (h) (i)

ALL CALENDAR DATES ARE IN 196Z.

FtEure _2. Yiev of _..mLi and the prccessiul TZlt06 IV orbital pl_t (_r%er StsTr )4embers"). 1967016633-187

sented. Limitations in the date due to sampling techniques were zot fur-

ther discussed.

The merldional profiles of albedo obtained by House are shown in

Figures 63 end 64. In Figure 63 the results for the two precessional

periods ere compared. Both periods show slight maxima in the tropical

regions, minima in the subtropics, and increasing values towards the

pnles. The albedos in the subtropical regions are i-_ higher for the

second period. In Figure 64, the data for March, April, and May are c_.-

pared with estimates, by London23 (see Appendix F), of albedo for spring

" and fall seasons. House's data indicate a lower slbedo in tropical

latitudes of 4-6_ and higher values of 3-5_ in midd Le latitudes. A global

slbedo of 3_% was obtained after extrapolating t_ profile i_nearly to

61_ at the pole.

', In summary, the only albedo aeasurements obtained wit_ the low

resolution instrument are those of House. Assumptions mad _ in the anal-

ysis were: i a. The earth's reflectance i_ assumed to be Isotropic.

b. The term which represents thermal radiation received by the

sensor is the ._emein the trl.nsitlonregion as it is on the

dark aide of the earth, i.u.,

(eel)I o (eel)H

c. The tera which represdnte the direct solar radiation received

by t_: ,_nsor is the seas in the tra_ltion r_gioa as it :s on

the s,_,A It side of the earth, i.e., 1967016633-188

156

0 _0_ z

0 tO i ...... i 1967016633-189

157 1967016633-190

198

I o_s ':(°./III

d. The mean value of the thermal radiation on the dark side of the

earth is equal to the L_ean value of the thermal radiation on

the sunlit side of the eslth, i.e.,

(BR_)I = (8Rl)iiI

e. Averaging the samples at s meridian which are available over a

precessional cycle produces the average daily meridionel value

of albedo, i.e., there is no sampling error.

2. THE MEDIUM RESOIDTION MEASUREMENTS

Two types of medium resolution instrument have been used for satel-

lite measurement of earth reflectance or albedo to date. The TIROS 5-

channel radiometer24 was flown on TIROS II, III, IV, and VII. The 25 NIMBUS Medium Resolution Infrared Rsdlometer (MRIR), also s 9-channel

instrument but of a different design, has been flown on the NIMBUS II

satellii3

The principle of the TIROS 5-channel radiometer is illustrated

schematically in Figure 65, shoving the basic components of s single ehan- i nel of the radiometer. The field of view of each channel is about 9°

wide at the half power-point (the field of view down to 5_ of maximum {

response is 8 to 9@). The chopper disk-prism arrangement causes the | radiometer to look alternately in opposite directions. During flight and 159 1967016633-192

160

during calibration, a reference target is viewed in one direction, and the earth or calibration target in the opposite direction. The reference target for the visible channels is outer space during flight and is a dark cavity during calibrat'_on. As the half mirror-half black shopper disk rotates, the radiation reaches the detector alternately from opposite directions. The resulting chopped signal is smpllfled and rectified to produce s d-c signal, which in the ideal instrument is proportional to the difference in energy flux received from the two directions. The two viewing directions are called "wall" and "floor" side of the radiometer according to their location in the TIROS satellite, i.e., one view is through the wall side, the other through the floor side of the satellite.

The nominal characteristics of the two visible channels, channels

3 end 9, with which we are concerned, are given in Table 18. The effective spectral response of each of the channels is given in Figure 66.

TABLE 18

NOMINAL CHARACTERISTICS OF TIROS RADIOMETER CHANNELS 5 AND 9

Channel number: 5

Purpose of "Reflected" solar Compmrlaon measurement: radiation with TV photos

Wavelength (nominal ): 2-6 micron •_9-.79 micron

Optics (lenses): A/205 AI20_ BoF2 SiO 2

Filters : Interference end chance gleam 1967016633-193

161

0.8 - CHANNEL _x

i ,,,II: o.4- L. " ,4 0

[. ,I.o zoI _I 4I o 5! .0 6• .o ,.t o 1i >..wAv,,.z,,O,,T..c,,o,s

'")_ | o.s ii c,A,,,L5 10.4 I' io.' .4 -! 1 ._ , _ 1.0 |.0 IO eO &O &O 1'0 , WAV[L[N6TH, MICRONt

I 1967016633-194

162

The raolometer i_ mounted in the satellite with Its optical Bxis at

_5 ° from the satellite spin axis. It revolves around the spin axis in a double cone with 43 ° half angle. T Se scan over the earth varies from a circle to two alternating quasi-hyperbolic branches, as shown in Fig-

_re £7.

Tne NIMBUS VaRIR is a five-channel scannin_ radiometer designed to measure the flux of thermal radiation and the reflected and scattered solar radiation from the earth and it_ atmosphere.

The _pticai design cf the radiometer is illustrated s_.hematlcaily in Figure 68. Incoming radlati_n is reflected by the scennir.g mlrr_r int_ the five Cassegranian telescopes and tr_n passes tnro_h the chopper into the c3].lecting ".ptlcs, filter, and botherer detecter.

Tn_ sss_clatea electronics consists of preampllfler_, mixer ::;r- cults, po_._r amp, tfle:'_, synehuno_s detectors, output f_iters_ lln_ p:._w,:z s uppl 2 •

Tr,_ reLIt, /e -r_arlcter_._ :," re_t',,r,_e _+ 9f t_';e tw, v:alt .e _'r,annv.4

_Y the }-I f!'._rr,', _,_e. , :'_ .meter are _n.gwn l,_ F:_.._e_, , , e_,_l .'..

of vL_w c*.:ntJurs_f ti_e 0.2-4.0 lllel_onchllnr_eJ. Of tl%_ F-* l_ik llr: irlowr_ 1967016633-195

163

It 1967016633-196

,161, 1967016633-197

165

I00 -

90-

I 1967016633-198 1967016633-199

167

02.- 0.4 i_ICRON CHANNEL DATA 7- :51-63. -- VERTICAL FIELD OF VIEW

.... HOPlZONTAL, FIELD OF VIEW

Figure ?1. Field of view contours of the b.2-k.O-ateron eh_nel of the

i; 1967016633-201

168

TABLE 19 I NOMINAL C}L_RACTERISTICS O_ F-4 _RIR (O. 2-4.0-M_ cron Channel )

Spectral region (9_ points) 0.2-4.8 microns

: Id of view (-6 db points) 2.8 °

Optical entrance aperture 1.72 in. dis

Effective system f/no. 0.93

System input noise 0.99 A,volts rms

System gain 3.9.103 (rms to de)

Responsivity 1.6.109 volts/watt/cm 2

NEPD 1.92.10 .8 watts/cm 2

Time constant 0.02 sec

Tercet range 0-80_ albedo

Output impedance 9.8°K

_ut voltage range 0 to -6._ volts

The MRIR is installed on the NIMBU8 satellite so that its rotation

mirror scans at right angles to the plane of the satellite orbit. The

field of view gives each channel a resolution of about 29 miles on the

earth's surface. When the orbit Is at the proper altitude, allghtly over-

lapping scans of the earth, extending to the horiaon on _ach side of the

orbital path, are obtained°

The visible channels of the medium resolution radiometers are de-

ai6ned to obtain a measurement of the fraction of incident solLr radi_-

ti,m which la reflected or sea, tared back out into space fro,,, the sur- 1967016633-202

169

face of the _arth, the clouds and the atmosphere. Thus the attempt is

made to interpret the radiometer readings in terms of an equivalent aver-

age "reflect_vit_' or "albedn" of that portion cf the earth and its

atmosphere lyi_ within the radiometer field of'view.

The interpretation is madc as follows.27 Recall that the solar con-

st_nt is defined to be the amount of solar radiation received at normll

incidence (i.e., on a plane surface normal to the sun's rays) outaid2 of

the atmosphere at the mean earth-sun distance. The value used is 2.0

langleys min"I (2 cal cm"2 min"I or 0.1599 watt cm"2). Recall that the

aol_ constant sen be expressed as:

Hs = Hskdk (9) l

where

! Ha is the solar constant (irradlance). i HsA is the solar spectral irradiance in wa_ts cm-2 micron-I.

If one solar constant of radiation at normal incidence is reflected

: from a perfectly diffuse reflecting surface with spectral bidirectional

I reflectance OA, the radiance of the reflecting surface will be:

I, N, . i _®p_Hs_d _

and the bidirectional reflectance of the surface, averaged over all wave-

lanstha will be:

I .I

U 1967016633-203

170

_" ,., PAtlsAd_ o

axd_, 0

This average bidirectional reflectance is s weighted average with weighting function taken to b_ the spectral distribution of the solar redistion.

When the _urface is viewed by the visible channel of the radiometer, the radiometer voltage will be:28

v, = s'ArnN_ (80) where

R' is the responsity of the detector

Ar is the area of thv radiometer aperture

is the solid angle viewed by the radiometer {

N_ is the effective radiance of the reflected solar constant, i.e.,

Ns .- O_HsAxd_ (81) 0

For Ph " 1 (i.e., 100% reflectance), we would have:

N&(1oo1&)- _, _ 0

For 0h _ i, we may calculate an "effective" average bidirectional r,_- flectance of the surface 1967016633-204

i71

C. " ® (83)

The average reflectance O' _hus obtained is _ welgbted average with

weightin_ function +aken to be the product of _pectrsl dist_'_butionof

the solar radiation multiplied by _,heinstru:=nt response eunc%lon.

']'heinstrument readings ca;,_utactually oe _nterpreted st all unless

suitable callbr_tlons have been made. Problems typically encountered in i making such calibrations are discussed in detail in Reference 27. Briefly,

1" the method used for the calibration is referred to in the literature28

as the "near extended source method." A diffuse source larger than the

; radiometer aperture, which will completely fill the radiometer, so thct

the transmiJsivity of the medium between t:_e,sourceand the instrument

is essentially unity. The calibration procedure consists of the follow-

i ing four steps:

a. Vary Nc, the radiance of the diffuse calibration source for

which the distribution of spectral radiance NcX is known, over

the desirod range of amplitudes.

J b. Recor_ corresponding values of r&diomter output voltage Vc

and source radiance Nc.

c. For each value of Nc, calculate the corresponding value of N_ i by the equation f- 0 i i lit 1967016633-205

17C

d. Flot the ct-llbrmtloncurves of Vc vs. N_.

This cslibrstlon procedure must be carried out for sll instrwrLenttem- peratures _t which the instrument will be operated.

The c_llbretlon curve of the visible channel of the radiometer may be given in terms of percent reflectance by tsklng that value of N_ equal to _i_(!OO$) ss representing iO0_ reflectsnce, for rsdlstion norr.,slly incident upon the surfmce viewed. Further a radiometer voltage reading

Vc corresponding to a value of N_ = 0.5 N_ (IOC_) represents a reflectance of 50_ for normally incident rmdlktion. Similcrly, in general, we define the percent reflectance of solar rsdistlon_ ss measured by the visible channel of the radiometer by:

'_NcA_kdk

1 ®

Finslly, to correct for sngles of incidence other than 90°, it is necessary to divide the value of reflectance obtained by cos 8, where 8 is the zenith angle of the incident radiation.

To s_amsrize then, the interpretation of re_iome_er resdinp u percent reflectance is made by changing the radiometer calibration curves

! ! to the form of Nc/Ns (i00_) vs. Vc. For normal incidence, s given radiometer reading corresponds to a reflectance equal to the v(lue of

t ! Nc/Ns (i00_) obtained from this curve. For other shales of incidence of the solar rays it is necessary to divide by cos 8, where Z Is the solar 1967016633-206

173

zenith angle, Thus:

pt N (IOO cos).e

, ,, 4 Ncx...... x, x (851 sos 8' . Hs,_Oxdk

Ii One finml correction to be made is a correction for variation in

values of HeR. Values of HsA used in drawing calibration curves are

values for the sun at its mean distance from the earth. Variationo of

values of HsA during a year are ss great as ±3.3_ and should be cot- 0 rected for.

i The only study of earth's sibedo based on medlum resolution measure° J 1 ments from a satellite is that of Bandeen, e_}tel., using data obtained

I with the TIROS VII _-ehannel radiometer. The albedo study was only e

part of a general radiation balance study using the TIROS Vll data. Re-

su!ts have been obtained for a two-year interval, June 1963 through May

196_. The firs_ years results were published in Reference 1 and the

second year's data were included in a paper presented at the 4/_Ann_s_

Meetin_of _he AmeTican 0eophyaicld Union.29 Only the first year's te- l cults &re discussed herein.

II Although ideally a study of heat balanct an_ mlbedo would be made

with da%a obtained by the "%o%a_' thermal und solar radiation channels, l ' 8-_0 microns and O.2.6microns, %heJe channels were not used by Bandeen,

Ij e_tsiT.,because of en_ineerln8 problems. Instead data from the 8-12-

_t 1967016633-207

micron and 0.55-O.#5-micron channels were used.

The elbedo results were obtained as followo. Values of reflectance calculated by Equetion (65) were used, assuming isotropic, i.e., per. fectly diffuse reflection. The reflectance was also assumed to b_ independent of wavelength. The maximum allowable solar zenith angle allowed was 70° and the maximum nadir angle of the radiometer optical axis was

_9° for the data used in the study. With the satellite orbital inclina tion of 58._°, this resulted in coverage between 63.5"N and S. This area was called the "quasi-globe." A square mesh grid having 2376 ele- ments was superimposed on a Mercator map of the "quasi-globe," and averages were made of measurements accumulated in each grid square over a period of about seven days. Averages of all individu_l measurements for the week were al_o _alculated. Seventeen of these averages were plotted vs. time for the first years data (see Figure 72). A least squares linear curve fitted to these data wera taken to represent an apparent degradation of the instrumental response aa e function of time.

The individual reflectance raadinga were then corrected for the degrade- tion by the factor h(t), i.e., a corrected reflect6nce value becomes,

p" . h(t).p' (86)

The weekly grid averages were then recomputed using the correction factor for degradation. Orid averages of four weekly maps, each separated by approxiutely 19 daya_ were evera6ed to give e grid average for a season. 1967016633-208

IT5

!1 1967016633-209

]'76

Meridionsl averages were then computed for each season, as shown in l_lg-

urea 73 through 76. The merid_onel averages for the season were ex-

tended beyond 65.9 u, up to 90 ° by reference to the work of London, 23

i.e., the curve was extended in a direction parallel to the data of

London.

Meridians] integrations were then made u_ing a planimeter to inte-

grate over the curve, thus weighting th,_.fllbedocontributions according

to l_:'.darea of the various latitude zom..s. The annual albedo of the earth was then found by averaging the results for the fovr seasons.

When th_s was done, it wa_ found that the annual planetary albedo required to balance thL annual long wave flux deuermined from the 8-12 micron channel was 32.2_, whereas the value obtained from the cslcula-

_ion was 20.I_. Assuming that radiation balance exists on the average over the year, there is a glaring inconsistency between the two types of data. Since it was felt that the long wave meuuremnt¢ were more

precis,_than the solar radiation reflectances, all reflectances were i multiplied by a factor of 2_20.1 . 1.6. Thus finally we have for TIROS

VII reflectances:

I I I Pc - 1.6'h(t)'O' (87)

The final values obtained are given in T&ble _'<). The annu_l meridional values of a]bedo are shown in Figure 77. Data from London |re shown for

comparison.

1967016633-211

178 1967016633-212

i"[9 1967016633-213

18o 1967016633-214

181

"\ 1967016633-215

z_ 1967016633-216

183

The author ass,_aesthat the additional unexplained factor of 1.6 for reflectances, which is necessary to provide radiation balance over the year, may be explained by some combination of the following factors.

a. Error in the original calibration.

b. Error due to the assumption of isotropic reflectance. (In this

regard, recall that reflectance samples used were :_stricted to

solar menith angles of less than ?0@ and radiometer nadir angles

of less than 42°.)

c. Error due to unobserved deterioration before the first orbit on

19 June, 1963.

d. Error due to the assumption of reflectance independent of wave-

length. (Related to this is use of the 0._-0.7_micron chan-

nel reflectanccs for total solar albedo.)

Examination of the method of data analysis indicates two other possible sources of error.

a. A bias due to the geographical sampling technique.

b. Error in the method used to obtain planetary albedo from the

meridional albedo curves.

_. THE MARINER 2 _ASUREMENTS

Some information on brightness variations of the earth as viewed from relatively large distances was obtained from measurements made with the earth tracking system on board the Mariner 2 spacecraft on its flight to the planet Venus.16 1967016633-217

184

The measurements were obtained by the photometer which was one pert

of the 5ong Range Earth Sensor (LRES) on th_ spacecraft. In addition

to signals which provided information for altitude correction of the

spacecraft, the instrument output included a signal which indicated the

amount of light being sensed, This signal was calibrated _hoto_etrically before the flight, however no in-flight calibration was made.

The brightness of the earth as seen fro_ the spacecraft was com-

puted from the photometer signals by means of the following equation:

fe(k)'_v(k)'dk' fo(A)_sii(A)dk 18 s, = r,® . So'R(T,70) (66)

_o fe(h)'_sII(h)dk'_ f°(A)'_v(k)dk where

Cv = the response function of the eye.

_sll = the response function of the SII photo emissive surface multiplied by the transmission function of the objective lens.

fo(k) = spectral energy distribution of the standard source.

fe(k) = spectral _istribution of the earth radiation.

Io - photoelectric current produced by the standard source.

Ie = photoelectric current produced by the earth radiation.

R(T,70) = response at 70°F. response at T°F So - footcandle output cf the standard source.

Se = the earth brightness in footcandles. 1967016633-218

189

The spectral distribution of earth radiation was assumed to be con-

stant and equal to

fe(k) = f1(A)'fe(k)•fs(k) (89)

where

f1(k) = the empirical solar continuum according to Minneert.

f2(x) - I-F.

F = the Fraunhofer line bl_nketing coefficient according to Michard.

fs(_) = an assumed wavelength dependence of the overall refle_- tivity of the earth, based on three color observations of DanJon. The assumed curve is linear with a value of 1.47 at 4330_ and 1 at 9940_.

Data were obtained for a 92-day period, from 29 September to 22

November, 1962. Th_ space probe distance from the earth varied from

8.6'106 km to 33.4.106 km during this time. During this time, the earth's

phase angle as viewed from the apace probe varied from 490 down to 11.3°

and then back to 24.4°. After this time, the temperature, which had been

rising rapidly, was too high for temperature corrections.

It was found that the data obtained did not agree with absolute

values obtained by DanJon. The following conclusions were drawn:

a. The part of the data obtained for increasing phase did not qree

with the data for decreasing phase angles. It was assumed that

the temperature corrections were incorrect for high temperatures.

b. DanJon's phale curve, normalized to fit the Mariner 2 data at

minimum phase angle, was found to agree well with data taken

,J for decreaalng phase angle. 1967016633-219

c. Diurnal brightness variation_ and a semi periodic variation of

5-6 d_ys was observed. d. Since the latitude variation of the Mariner 2 suborbital point

did not very greatly, being spproxirastelyst the earth's equa-

tor, variation with latitude was not measured. e. The diurnal varlatAons indicated m.ostpronounced relative maxima

corresponding to a point in the Atlantic above the eastern ex-

trem of South America, and most pronounced relative minima

corresponding to the center of the Pacific Ocean. A calcula.-

tion, considering the percent land/ocean area in each case, in-

dicated a reflectance of land form 1.41 time as great Is that

of ocean area. f. A possible explanation of the greater reflectivity of land rela-

tive to ocean is that clouds may tend to concentrate over land

rather than _ater. 1967016633-220

APPENDXX C

REFLECTANCE OF THE EARTH'S SURFACE

1. SPECTRAL REFLECTANCE

a. Soils and Rocks

The spectral reflectance of soils and rocks is illustrated by

Figures 76 tc 83, taken from References 31 to 36. Although all of these figures yield information concerning the spectral dependence of reflectance, care mu_t be taken in using the d&ta, because dif-

fezent quantities have been :,easured.

In Figures 78, the quantity measured is the bidirectional reflectance: ¢_(_'3°,O, O, 0), i.e., the incident r_diat!.onhas zenith

angle _5 ° and the reflected radiation is meuured normal to the reflecting surface (at zero degrees zenith angle)_

Figures 80, 81, and 82 are measurements of the directional reflectance:

r;_(eo,¢o) -_'II 0x(eo,%,e,,)cosesine dedl (90) _=0 e=O

The zenith angle of incidence eo viii not necessarily be the same for all three cases, since it has not been noted in the papers, however, it is probably close to zero degrees.

The quantity indicated in Figure 79 wu measured under conditions of natural illumination, so that the scurce is direct sunlight plus the dtff,_se sk_'light. We can indicate this meuurement by the following defiaition:

187 1967016633-221

i , 1967016633-222

189

0"8 lr 1 ' l

0o..6 7' SALT B_D

04 NON-SALINIE DRY PLAYA bJ

J, _ 0.5 GRANITE PEDIMENT-_ BRUSH& WINDBLOWN SAND--_.,_ ._ ,_,_ _ _ , 0.2 .._ .--_LA6 eURF,r,EOF _ "'_ "- RED sCORIA ON SAND_

0.0 ALFALI' FA ! I 40CC) 4500 5000 5500 6000 6500

_' WAVELENGTH , A

! Figure 79. Diflhase reflectance of representative types of aesez_c sur- tsces (a_,'ter Aehburn, e__.sl.t 32), i

] 1967016633-223

190

I00 ------_ ------I. t. MgO F- z _o 2. MONAZlTE

_0 - :3. WILLt-MITE 6o 4. QUARTZ I.=J _ 0.. 40 - _ -_ / \_,, f ,-.,,"_

o.s o,e LO _.a L4 L¢ _.8 2.o a.z 2.4 MICRONS

I. AMAZONSTONE (K-FELDSPAR) 2. CLEAVELANDITE FELDSPAR 3. BERYL (QUARTZ) =oo- 4. ZINNWALDITE

w6o-'/ o -----, ... _..

=°1,:'__ _- 4-- _I_" | [ i I I I I I 1 ! 1: ! I I I ,,I,, I I I -II 0.6 0,0 1,0 1.2 1.4 1.6 I.O 2.0 2,2 2.4 MICRONS

Figure 80, Spectral distribution of reflected energy for minerals and rocks (after Gerharz_ _t _1,33), 1967016633-224

I 191

/!/!J

.¢ _I i =

I_ _'-- °°V ° " _t5 _ I I d

_.--.'.->. "",'k / ...... ""...... __.._,_.,Q t. -J _ • <." _ s'-'-- ,-'"7 :'_:'/ _> t ...... _':'4_._ '..... -_lli.'*lit.. ,,,4ill.._t-

...... \_._. --_, •-...... _.,._ _,,_,,,... I oI oL oI _I $I _] oi oI o

, (,LN3OU_Id) 3 0 NV,I,_)':l"l,-I 3t:l 1967016633-225

192 1967016633-226

i93

W 2_ _ 2_

I I I I _'(eo'_o'_")'_: _sinO'_o)oCded_eod'o°sesinec°ose o _=0 e=0 $o=0 eo=O rx(eo,eo) = r [ l j J Hx(eo'_o)C°Seo'sineodeod_o (91) _o=0 90=0

It is a weighted average: directional reflectance, with the weighted aver-

age taken over all dir_ctions of incidence. The zenith angle of the

sun was not specified for this figure and so the amount of diffuse in-

cident (for it I radiation is not Known low sun angles, may be as much

as 10% of the direct sunlight). This quantity is called the albedo of

the surface element by the author.

The data of Figures 83a and 83b, show the bidirectional reflectances ¢_(53 °, 0, %,$)for desert sand and 0_(78.5 °, 0,e,$) for black loam soil. l; The measurements are taken in the principal plane so that ¢ has the values o, 180 ° as shown. i! All of the above measurements show an increase of reflectance wlth

I_ increasingwavelength up to at least i micron, and a decrease of re- lJ flectance with increasing wavelength beyond 2 microns.

_ The data of Figure 78 indicate that wetting a crust clay surface decreases its reflectivity, and Figure 81 indicates that powdering a i rock material may increase its reflectivity.

b. Vegetation

The speatral reflectance of various types of vegetation is il- l lustrated by Figures 8_ to 86 taken from References 31, 37, and 38.

I Again the figures represent different quantities. Figure 8h shows the bidirectional reflectance 0_(_5 _, O, 0, 0), Figure 85 represents meas-

[i _ urements made under conditions of natural illumination, i.e., the

|_ 1967016633-227

19h

80 .... i ! , | I I I I' u

o 60 _,_ - z ,02=)Ay, _ 50 % _ ..._ -

" 40 _ 'm A "'b. _ _ "qk. 4 "4t4.6430.4-.li,e.-..e.e" •4_'1 _. -

r,. 30 - '_"_..,_.._.4ttO A ._.....,=..,.A - 20- "_"_'_ -

,o-0 1 I n I L I , _ t 806040200 20406080 $.o- ,_-_8o" NADIR ANGLE, (°)

o.) DESERT SAND.

' , , I , ' , , |

8 0 0o=uoJ, 70 gO- /

k zo o_

,o0 I , I i I i i i ,i i 80 60 40 20 0 20 40 60 80 $.o- _,-,8o" NADIRANGLE.(')

b.) BLACK LOAM SOIL.

Figure 83. Bidirectional reflectance of sand (e^ = 53 °) a_d black loam soil (e° = 78.5 °) at different wavelengths (afte_ Coulson36). 1967016633-228

195 i

I1 1967016633-229

196

50- d t I

_--Z ;ti ,.,..°°_"°_ _° d.._..s..S4 IAI 40- e f"" (._ ,t n,' '1 I,LI ;/ __.,_x-. ,_ 2

4b oW l ;7

'_ ZO-

W MO H/

0 t I i I I i 400 500 G00 7GO 1100 900 I000

WAVELENGTH, MILLIMICRONS

Figure 85. Spectral albedo of different vegetation: t,.., _, sudan grass; (2) maize; (3) clover; (4) lucerne grass (June), (5) lucerne grass (July) (afte'_-Kondratier,et ai.37). 1967016633-230

I 197

quantity r_(eo,¢o) defined above (sun's zenith angle not given), and

I Figure 86 shows measurements of directional reflectance r_(6°,0). The data show low reflectance starting at 0.4 micron with a small

I maximum in the region 0.5-0.55 micron, followed by a minimum in the i chlorophyll absorption band at 0.68 micron. There is a sudden increase I in reflectance at 0.7 micron to a higher value which is maintained up

I to a wavelength greater than i micron; the reflectance then decreases in the infrared.

I_ The change in reflectance with growing season is shown by curves

li 4 and 5 in Figure 85 and by Figure 86; the chloryphyll absorption at 0.68 micron is most noticeable when the leaf is green, the reflection

above i micron is a maximum for young planets,decreases as the plant matures, and increases again as the plant looses its green color.

c. Water Basins

I The spectral reflectance of a smooth water surface is illustrated

by Figure 87 (from Reference 37), which shows the quantity rk(e0,¢o_ I measured under natural illumination (sun's zenith angle not given).

i These measurements agree quantitatively with calculatlons based on the Fresnel formula for spectral reflection from a smooth surface, i.e.,

1 a decrease of reflectance of water depends on the backscattering (f

radiation in the water as well as by reflection at the surface, and thus

depends on the water turbidity. In addition the surface reflectance

depends on the surface roughness and conditions of i!l_ainationo De-

tails of the spectral reflectance of water for various t,Arbiditiesan_

surface conditions are not presently available in the literature. I 1967016633-231

198 1967016633-232

199

ji 400 500 600 700, 8

! WAVELENGTH, MILLIMICRONS i Figure 87. Spectral albedo of a water surface (measured over a lake with depth of 60 to 70 cm) (after Kondratlev, e_tai.37), 1967016633-233

200

(I. SlJow and ice

The spectral reflectance oi'snow is illustrated by the data of

Figure 88. The quantity measured is r_(eo,¢o), under conditions of natural illumination. Data have been taken at different times _uring the day. The spePtral reflectance is a maximum in the 0.7 to 0.8 micron region and slightly less at lower and hi_her wavelengths. Tne reflectance of snow shows great variability, deDendence on dryness, purity, surface roughness and conditions of illumination.

2. ANGULAR DISTRIBUTION OF REFLECTANCE a. Soll and Rocks

The angular distribution of spect_.a] ref]ectance for various soils is illustrated by the curves of FiAnlre 89, taken from references 36 and

B9. As the data shows, the reflectance is not perfectly diffuse, although for small zenith angles it approximates this ideal case. Each set of data shews backscattering of an amount which increases with increasing zenith angle of incidence. In addition, as the zenith angle of incidence increases, forward scattering develops. For large zenith angles of incidence the forward scattering becomes greater than the backscattering for both types of sand, whereas for red clay and olack lo_m the backscattering is greater than the forward scattering. For h,ack loam the forward scatte,.ing is almost nonexistant. The back-scattering property is referred to as "black gloss" by those interested in visibility problems.

Additional data on bidirectional reflectance characteristics are contained in Table 21, taken from Reference 40. The data in t.his table, taken under conditions of natural illumination, show forward and back- scatte;in_ for both hard packed dirt and sand dunes, the data for podsol, I! 1967016633-234

_01

l i rime OF DAY: _____...... I000 ...... 1400

: - - I100 ---*-- 1500 ...... 12C0 ...... 1600

...... :300 ...... WOO

400 500 600 700 800 900 I000 I albedo of "_hesnow cover in clear weather, 28 Narch_ FiEure1963. T88.he LeSpectr_lningrad Region. Dr_ snow (after Koneratlev, --,'-_a!-37)" 1967016633-235

202

I I ! | I | | ! s ..... ,201- ,,ol-"_\,, _ /_,.-J,- _,ooI-',,,\ I . ,oo "_" " i-.

" 50 / 2_P"-L'_---*'_J_=''_'-'_ 23" - F_" I 20_'- - 0 1 , I, I ' I , , , :1 806040200 20 40 60 80 I0 - _)--0" '_=lSO" I I , I , NADIR ANGLE (*) 0 20 0 20 40 60 80 ¢,=o" _-ieo- NADIR ANGLE OF OBSERVATION,*

0.) WHITE QUARTZ SAND. b.) DESERT SAND.

/ ' ' ' ' I ' ' ' 1"_'8 "°l Jt 1" i ....

UP I ,,, Ir _!:_1:oO\2F,%,_'- ' _/L_/''" "°"_40,.o-oI e, =78.

1 '-'0 78" ,.0 f2t oIoI_- , ,_ , i , , , l , eo so_:o40"20 o zo_4o6o-mo"so 80 ,:_040 20 0 2040 60 8'O _): O* _=180" NADIR ANGLE 101 NADIR ANGLL":OF OBSERVATION,

C.) RED CLAY SOIL. d.) BLACK LOAM SOIL.

Figure 89. Bidirectional eeflectance of various t_e_6of soil at different _ngles of incidence. X = 0.6k3 micron (after Cou.lson _ ). 1967016633-236

" " ..OF. THE OR1GI P ._! '. ,'(" REP" R-"o• D.._.U':e'i,.- BiLi ...... " ' ...... -_...: : .i...... o:...... o'R.''"

203

TABLE 21 Y i BIDIRECTIONAL LUMINOUS REFLECTANCE OF TERRAIN BACKGROU_DS FOR MODERATELY HIGH SUN 40_ (After Duntley, et a±.

._i,,,,ud_ d the i_tb Sun of sight Zenith sagle oi psth ol sight maith relative to D_ angle the sun 180 156 150 13,$ 120 10ft 100 96 I. PimDt_mmdl, ttailo_mly_ 41.5 0 0.G_']3 00241 00214 0.1Y._I4 0.026) 00379 0.0463 0.0859 D•ta aJrefo' _ tin,rain 45 0.0222 0.0202 0 6194 0 _-10 0 (k'.'.'.'.'0.'..0387'.'._3 0.0549 ovw which &tmc_b_ric data 90 0.0315 00311 0 0317 00317 00337 0.0387 0.04e3 giv_iaSee. Vl were collected. 135 0.0335 0 0382 0 0392 0.0387 0.0438 0.0463 0.0672 180 0.0402 00444 /}.0578 0.0640 007it 00758 0.0825 2. GrL_thick, rstherlo_,lmJegrven, 41.5 0 0.088 0.081 0.076 {, 977 0 088 0 09_ 0.096 0.094 I 6orr_d_%dryil_, little ground 180 0.098 0.119 0 146 0.160 0 153 0.153 0 160 I ,ho,_.o 8. Asphalt, o;ly, with dust film blown 42.0 0 0.06s 0.057 0 038 0 060 0 06_ 0/_JO 0.104 O. 12_ oato o_1." 1_0 0 067 0.080 0 i01 0.090 0.086 0.086 0 0_

• 180 0 289 0.313 0.343 0 367 0 350 0.343 0.320 I 4. "White" conc_te, Np_d." 42.2 0 0.265 0.2/53 0.254 0 254 0.266 0.298 "0.320 0.374 6. Cldmwste_,ininiteopticslde_th.' 41.b 0 0.0222 0.0"234 0.0297 00509 0.139 0.267 0.461 45 0.0230 0.0"240 0.0"272 0.0357 0.107 0.199 0.325 90 0.0"221 00'._22 0.0"_,_14 0.0293 0.0711 0.121 0.214

180 0.0"214 0.0"212 00"216 0.0.2d7 0.0718 0.125 0.254 i 135 0.0213 U.0"212 0.0"220 0.0"270 0.06_ 0.113 0.203 6, Gram, Ioah lmea, closely mowe_ _0 4 0 0.100 0 096 0.098 0 108 0.120 0.140 0.168 thick I-wn.• 39.6 90 0.103 0.110 0.121 0.138 0.159 0.168

39.9 180 0.109 0.109 0.119 0.I22 0.125 0.125 J 7. Ms_adam, wuhedoffsndmbbed." 39.48.6$ I3_0 0,113 0 115107 0.1250.119 0.1480 128 0.140.1668 00.178.194 0.0.217829 50._ 90 0.110 0 1(19 0 i16 0.122 0.139 0.147 46.0 180 0.129 0.141 0.156 0.156 0.17"2 0.176

56.5 d0 0.243 0.25_ 0 _ 0.276 0300 0.304 t 8, Dirts hard packed, yeUowi_., 51.1fi3.2 ,800 0.243 0.2720 _30 0 312239 0.370_A0 0.4.0.252_2 0.4320.300 0.4340.330 9. Mim_lllr_formt, deciduom(osk) 39. r 0 0.(]_0 0.032.,_ 0.0"291 00"205 0.0203 00312 I made_'lp'_(pine)._ 37.0 180 00410 0.0403 0.04'.i3 0.0820 0.263

11.10. Glqnef_m,oredry_, dmeadow, dm_b mid- 4533.5 00 0.0003_8J555 0.03850.0897 0.090.03_00_ 0..0.01_7A6 0.070.108A6 0.1290.0.200 atmunor., 45 _,) 0.0778 0.0890 0 101 0.111 0.130 45 180 0.116 0.131 0.143 0.153 0.170 45 '1_0 0. 107 0.121 0. I_I 0.137 0.132 12. llyu, sporm sml dry, ydlowi_ 40 0 0.231 0.829 0.342 0 356 Iprsmoa ram/&t md o_ _zam_., 40 90 0.1&3 0.176 0.198 40 180 0.295 0.35_ 0.359 40 M0 0.292 0.237 O.220 18. 8tuddunm, dmqdYUll_miem- 40 0 0.288 0.183 0.337 0 3_3 ndi_, dry., 4_ 90 0.284 0.329 0.306 _' 40 180 O.240 O.gS@ O.276 40 270 0.278 0.410 0._81 14. Podml, plo_ moist.' 50 0 0.50/_ 0.0_0 0.06_ 0.0_5 50 90 C.Oa_ 0.01153 0,0715 0.0614 0 o761 50 270 0,149 (o, 180)/ 0. IM 0.168 (o. 180_ H,,, , i i ,i iii ,.i, • 'r'.motm_swwemeuumtoetbsffoundt_meugdl_r, b_u_,.,hmiddurin8theeoUeetd_ the_ts in

t Oomputed from _quatiom by DuntJey 119521 fo_ ti_ lightia9 oooaitloa pmvailinli for items 1 aad 2 in this fe_e. t Bm.•LYI._t6 _dtm ruth_ 8_, I00el_ 1_. • Dsta takes with • I_ t_ from • h_leeptor •t 300 ft (91.4-m) sltitud_, mountain Io_mted m_m_ Julimk 13d_o_ maqmmb_tem.

/3.1.E. IUmnimmt B. Diq_tty bstw_t dsts for ui_uth_ 90" had 270" "b uplaim_l sp_tly by the dimetitm ol dMdlow furrows l In*reluLumimli,m _to,, thedl_ueuutioR]", (Kr_ lnov-Bdkovfor, tl_I_13, pII. ?_). 14 w_m eomlmted _rom ap_ttOlplmtm_,mt_rtedata by I_lnov (1947) tmlall t Pamatlm_ indicat__mmt_ _ ea iaeom_ _ d_t_,

[ " 1967016633-237

204

ploughed, moist, shows only backscattering. J

b. Vegetation

The angular distribution of reflectance of vege_aion of various

types is illustrated by th_ curves in Figuze 90 for green grass turf

and in Table 21 for several kinds of grassy and forested areas. The

data all show pronounced backscattering (black gloss) and a small amount

of forward scattering for very high angles of incidence.

c. Water Basins

Table 21 has angular reflectance data for calm water calculated

according to Duntley, for a moderately high sun angle. Similar cal-

culated data for calm water and low sun angle, and measured data for

ocean water, under wind speed of 5 m/sec and high sun angle, are given f

in Table 22 (Reference 41). Calculated data for calm water and over-

cast conditions are given in Table 23 (Reference 42). The data for

these four cases have been plotted for the principal plane in Figure

91. The sun's angle is shown for each figure. The calculations in- 1967016633-238

eo5

I00 ......

0 80 60 40 20 0 20 40 60 80 ,_=o" ,_=,80" NADIR ANGLE (o)

Figure 90. Bidirectionalreflectanceof green grass t__f at different angles of incidence, k = 0.643 micron (afterCoulson_ ). 1967016633-239

_*i "REPRODU...... CIBILITY OF TH'E.....ORIGINAL PAGE IS ...... •POO.__. R."...... , i

206

TABLE 22

BIDIRECTIONAL LUMINOUS REFLECTANCE OF TERRAIN FOR LOW SUN ANGLES (After Boileau and Gordon41)

A_,imuth

lath 8*m of sight Direct;onal reflectance for se.ith *ng J mmith relltive Dmcription angle to mm # - IS0 165 J.rd) 135 120 105 !(10 115 I. Ocean water, infinite optic4d depth, 77.3 0 0.0230 0 G?_q 0 0369 0 0,55 0 132 ' 0 3_4 0.3&q windspeed.qm/aee _ 45 00246 t).032_ 00417 0065 0(tq7 0.104 0.1._q 90 0 0242 0.026(, 0.0297 0.:_373 0,061 0.076 0 093 13,5 0.0264 0.0280 0.0309 O.OP_I O.(ri2 0.096 0.110 180 0.0268 0.02_8 0.0325 0.0440 0,072 0.099 0,125

2. Calm ocean watm', infinite optical 77.3 0 0.0152 0 0177 0.ffJlO 0 04(18 0.140 A 1.03 1.03 depth" 45 00188 00'200 00181 0.0371 0.107 0.190 0.34S 90 0.013_ 0.0139 0.0156 0.0388 0.132 0.154 0.243 135 00133 00141 0.01fl0 0.0267 0.Gq23 0.140 0.345 IRO 00158 00206 0.0425 0.108 0._ 0.823 1.03

3. 8n,w, with s,rfsce hoar" 74.0 0 0.09 0.09 0 73t 0 78s 0.89 1.20 1.39 1.73 90 0 64 065 0.69 0.73 0.73 0.73

4. P;now, with rain crust (_ crttst farmed 74.0 0 0.73 0.73 0.74t 0.79! 0.91 1.47 1.81 2.44 by falling rain which dora not freeze 45 0 71 0 71 0 09 0.67 0.02 0.60 0.58 ulmn falling)• 90 0.73 0.73 0.71 0.72 0.71 0.69 135 0 71 0.74 0.77 0.82 0.89 0.90

8. 8n,w, with glazed rag, crust (rain crust 74.0 0 0.80 0 80 0 88! I. 13! 1.90 5.0 8.4 10.9 cemp[etely covered by _ slightly un- 45 0.75 0.77 0,72 0 68 0.65 0.61 0 56 &dating _heet of ice formed by frees- 90 0.75 0 7_ 0.75 0.74 0.72 0.70 0.65 ins rainfall followed by warm rain, 135 0.76 (I 77 0 80 0.81 0.85 0.64 s.bseq_lent free•ins temperat.m but .. f.rther precipitation) •

ft, Dirt, fiat desert road, freshly bulidosed 77,8 90 0.230 0,24,3 0264 0,275 0.314 0.380 0.4_16 0.4_ to remove encroschi,g • Data are from Flight _.0,5. • Value n.t &v&ilable,near to direct reflectance from am, • Comp, ted from equations by I),ntley* for the lighting condition prev&il_ngfor Item I in this table. d Vahie hot eomptlted since _ky himinanc_ ncm*sun m poorly defined. • J)lt• tiken with • idephotometer Api_l 1960 of mmulMed snow laving reflectamceehar_,terittim reported by Mkldleton mid Mun- gMl.* The photometry wm_done in the n•tund lighting slmulator, using the *ky lumimmee disi_'ibutlon from ltlillht, 106. t l)*t8 intmlX_tecl graphie_ly. • Data t-ken with • llonioplmtometa¢ at N•vM Onlmmus Tat BbLtlon,Chi.• lake, California, in July m_.dAulu_ 1962. _ qx_ trld mllectanceof • mmtlded the dirt was mmaumd with S Hardy qpeetrophotometm'. Udnll Clle inumimmt B, ehromMiei W enordi- nstmwemz - 0.b70, Ir - 0.NI, s - 0.N; domimmt wsv_ml[th m M0m_; recitation puTity. 10%. 1967016633-240

fi ' I::ZEPRODUCIBI TY OF THE ORIGINAL PAGE IS POOR

i 2O7

1 TABLE 25 L BIDIRECTIONAL LUMINOUS REFLECTANCE OF TERRAIN BACKGROUNDS UNDER OVERCAST i (After Gordon and Church42) l I " Omitted (se_ _ordon and

lO1 j _urch 42)

Asimuth of_th gun of mght Zmdth magicof path of dght _tb rdstive Dmcription _e toeun 180 106 150 135 120 105 100 05 . i

!1. C_mwJ_. b_ni_opU ,-n 5_ 0 0.0206 0 0314 0 0336 0 0287 0._53 0.197 0._56 0.57

_1 90 _ 0 0305 0 0272 0 0294 0 064 0.229 0.340 0.51 j dep_' 5151 13545 _-- 0.0.02(_73 00.0313(r_9 0 02640287 0 03(k578 0 183229 00.260376 0.55425 51 180 _ 0 0273 0 0254 0 0238 0 0421 0.145 0 234 0.450 12. 8oow. with suHsee hoard 51 0 0 60 0 68 0 66 0 66 0.57 0 67 0 70 --

51 90 _ 0.66 0 65 0.66 0.67 0.68 0.69 -- " 5151 13545 d_ 0.670.66 0.0.6565 0.650.66 _0.6766 0.0 6697 0.68-- 51 180 _ 0 68 0.64 0.65 0.66 0.68 0.60 --

formed by faHi,g rain which 51 45 -- 0.67 0.Tq 0.66 0.67 0.67 0.67 0.68 - 13. hdow.ec; nowtithfve"rsinseuponcrustfed(a Jing)cruetd 5151 O00 0.67-- 0.0.676 0.6767 0.0.6677 0.670 68 0.6687 0.678 0.67 51 135 -- 0.&5 0.66 0.67 0.68 0.68 0.67 060 61 180 -- 067 0.64 0.65 0.67 0.68 0.68 0.60

(rain croat com_et_y covered 51 45 -- 0.76 0.76 0.76 0 76 0.77 0.78 -- i 14. 8now.by a sligwithhtlygleundulatingsed r-_n cruesheett 5611 900 0.7--4 0070.74 00..76 0076.76 0.7776 00.78.77 0.77 -- of ice formed by freesing rain, 51 13,5 -- 0 74 0.76 O.77 0 77 0.70 0.78 -- subeequcot freezing tempers- 61 180 _ 0.74 0.74 0.75 0 75 0.76 0.77 --

i 15. Calmtur_ butwaterno, infinitefurther optieslpreeJpJ- 52 0 0.023_ 0.0278 0.0350 0.(t393 0.()95 0.287 0.438 0.69 depth' 52 45 _ 0.0240 0.0240 0.0262 0 069 0.247 0 405 0.68 52 ._9 _ 0.0239 0.0220 0.0239 0.061 0.212 0.343 0.58

52 180 _ 0.0216 0.0214 0.0_3 0 057 0.201 0.331 0.414 52 !._ -- 0 0216 0 0210 0 0218 0.(_54 0 194 0.314 0.462 16. 8now, with surfMe honrl 52 0 0.65 0.52 0.03 0.67 0.05 0.70 0.71 -- 53 45 -- 0.65 0._ 0.67 0 68 0.70 0.70 -- 52 90 -- 0.65 0.65 0.65 O.M 0.68 0.68 --

I 53 136180 -- 0,0.6564 0.030.04 0.0364 0,670.03 O.Oi0.(i6 _ 0.M-- -- 52 0 0 65 0 62 0 &l 0 6.1 0.68 0 67 0.67 0 68 17. 8now, with rldn ¢rpet (It 52 45 -- 0.66 0.66 0 67 5 66 0.68 0.68 0 OR cr,_t f,rw._ by falling 52 tiC} -- 0 tiff 0 66 0.66 0.67 0 67 O.M 0 f17 ! r_i, which d_ not fr_e 5_ 135 -- 0 66 0 68 0 67 0 69 0 70 0.70 0 73 ul_m fslli,gl 52 180 -- 0.65 0 65 0.67 0 67 0.68 0.67 O.IMl

,52 0 0.7.5 0.77 0 72 0 74 O.77 0 R! O.6t -- IR. S,,w, with glazed rain cruet .52 45 -- 0.75 0 76 0.77 0.70 0.70 0.80 --

i (rabyins ,clightruet.yCompletelyundulatincoverg _heedvt 52 19035 .---- 0'4 7745 0 77.51 0.7475 00.7775 0 7786 0 77A6 -- of ire formedby h'e"singrsin, 52 IRO -- 0 74 0.74 0 73 0.74 0 76 0.16 -- ettl,eequentrinsing tempers- turembut nofurther preeipi. ! ration)! • lYir_t rm-_lluminoue r_l_t_ncm of terrains I thruqgh IOwereeomp_ted fr.m epectrophotemetrie dItta taken by Krincv u_inl C.I.E. llh,minant B. *The zenith angle of the psth of sight ;e i15% ' Computed from equmtiomiby Duntley for the luh_inance distriblstion metsitred by Hood on 21 May 107. ' DItts take. with • teiephotometer (April 1950) of simulated mow having rd_t_nee churacterietim reported by Middleton •nd Munl_ll. The photometry win done in the natural lighting simulator, ueing the sky h,minsnee dlntribution menenred by Hood on 31 May 1957. • Computedfrom _¢ltmtioMby Duntley for the luminancedistributionme,,red by hood on 34 Ms}' 1057.

Munlpdl. The photomet_ wu done in the n•tund lightinl simulstor, ueing the aky luminance dietrih_ltionmenmtredby Hood on 34 [ May' D195st_7te. k. with. ---- (April 1.) of dmul.ted -- having rd_.-- ehsrsct_sristimreported by Mkldleten .nd I] 1967016633-241

208

i 1967016633-242

2O9

clude scattering in the tarbld sea as well as reflection at the surface.

All of these data show a very 19_rge amount of scattering at low angles,

in both forward and backward directions. The experimental data for low

sun angles also a large I shows amount of scattering in the forward direction with a rather sm_ll amount of backscatter. The possibility of a

mirror component of reflection is also indicated by the experimental

I data. l d. Snow and Ice [- The =_ured luminance of snow cover indic;_ted in Figure 92 (Ref-

I} erence h3)shows a diffuse reflectance compone'at plus a specular component which becomes larger for large angles of incidence. The five types of li snow may be listed in order of increasingly large specular component

as follows, surface hoar, settling snow, new snow, rain crust, wind

packed snow, and glazed rain crust. These results have been ccnfirme_

for low sun angles by th_ res, lts of Kondratyev and Manolova. 44

i 3. TOTAL DIRECTIONAL REFLECTANCE

a. Soils and Rocks

I The total reflectance of various types of soil, shown in Figure 93

I (Reference 30), range from 5-43%. From this data we see that the total reflectance of soil is decreased by 5-20% by the additfon of moisture.

The dependence of surface by I conditions is illustrated the data of

Figure 9h. In general, the smoother the surface, the higher the total

I reflectance.

I If we refer back to Figure 89, we note the increase in bidirectional reflectance for large angles of Incidence. This effect appears for all I |l 1967016633-243

210

0 0

200 I00 I00 200 200 moo 0 I00 200 LUMINANCE LUMINANCE

Q.) WIND PACKED SNOW. d.) SETTLING SNOW.

@ @

200 I00 0 tO0 2OO LUMINANCE LUMINANCE

b.) NEW FALLEN SNOW S.) SURFACE HOAR. IN CALM.

i @ •

-,-v -- - -- r ...... r ..... i " - • .... j - • ZOO IOO IOO _r_ IOOO IOO lO I00 IOOO LUMINANCE LUMINANCE

C) RAIN CRUST. f.) GLAZED RAIN CRUST•

Figure 92. Measured luminance of a snow surface (after Middleton, et ai.43). 1967016633-244

211

--- River Sand

40 - - White Sand .... Yellow__ . Sand J

' ¢J 30-- Surface of Clay Desert- 4-I : Z j Gray Soil- Dry J _J -- Blue Clay-Dr

w_ 20 Y_ _-__GroySand .j -- Blue Cloy- Moist " _. -- Ploughed Field - Moist F-- I0 Follow Field- Dry ii"l o L- °,°, - ' ...... ______. _ _ _Follow Field - Moist

Figure 93. Total reflectance of various types of soil.

I 1967016633-245

212

30 Graded --- Dust Covered (.) z --- Small Lumps

U .uJJ 20 Large Lumps " Newly Ploughed Field :t 01:::

' I.<-1: I0- 0 I,--

O m

Figure 94. Dependence of total reflectance of clay soil on its surface condition. 1967016633-246

213

wavelengths and thus implies a diurnsl effect in the total reflectance

of soil, with maximum value for low ._an angles.

b. Vegetatzon

Figure 95 shows the range of typical values of _ota_ reflectance

of d_fferpnt types of vegetation. _:o_e that the rm_ge of values zs

not as great as for soils. The maximum value or' total tel ±ect_nce of

vegetation appears to be about 25%. Again there zs a dlurnal variation

(as can be inferred from the curves of Figure 90) w±tn maxzmum value

for low sun angles.

c. Water Begins

The reflect_ nce of a smooth surface of pure water can be calcul_.ted

from the Fresnel formula.

r -- --12 sin2sin2(i+r)(i-r)" tan2(i-r)tanR(i+r) (92)

sin i i where sin r = n = 1.33 z = %he angle of incidence

r = toe angle of reflectanae

n = the index of refraction.

Figure 96 (Reference 30) compares experimental data wzth data calculated

according to the Fresnel formula. The decrease in _otal reflectance

for small solar angles is due to the increase of scattered radiation

relative to the direct sunlight. In part, the dzsagreement between

experimental and caiculated data is due to the znlluerce of waves, wmter

turbidity, and experlmen%al error. 1967016633-247

I i

u) 3: .PoI

bO o ._c a. 0 O. _ o

o o o

C_. 0°.)

I j ..Z ._ J I cu g

I I "_ 4,

oe i.__ ._1 O.m n--t- o ,1 I I I iI tOI I ,I iI I _ I l , i,, _,,,, I o o o o o _ _0 N -- .. (%, '30NV10.-77.-13_ 7_I01 1967016633-248

215

6o _.v_ _'l. _ ,. o.t-o._CLOUOCOVER A % 50 ,!. :.__'_.: \ 32. . F_CLOESNELUDLESSFORSKIESMULA i 40 ?;/_'i]!'_

30 __.__!_ 2o... 'ii__@ ,: "."._[!,< IO- Ct_'_..:,_.,_.:..:_.._..,,_.. -,....

Imlml i IIIID e u o lllllll l 41_m I I I I I I I 0 I0 20 30 40 50 60 70 h.

Figure 96. Total reflectan_.*of water basins (after Kondratiev30). 1967016633-249

216

_0 ---

p W c.) Z 15 -- I-

_ !0 --

0 5 -- I----

I I I I 0 0 2 0 40 60 80 ELEVATION ANGLE OF SUN

Figure 97. Variation of total reflectance of sea surface _s a function of sun angle under stratus clouds (after Neiburger_ et al. 5). 1967016633-250

217

The total reflectance of water basilm is dependent on cloud cover

conditions. Neiburger45 has studied the .-eflectionof the sea surface

under overcast conditions. He observed total reflection of the sea

surface for radiation transmitted below stratus clouds to be 10.5%.

The observed variation of total reflectance under stratus clouds

reproduced in Fi_ire 97, indicates that the radiation under stratus

clouds is not perfactly diffuse.

d. Snow and ice

The total reflectance of snow varies over wide limits, depending

on purity and surface conditions. Figure 98 (from Reference 30) shows

this variability very clearly, with a range of values of 25-80% at one

location. The mean value of total reflectance in the antarctic30 is

about 8h%. Data by A. F. Spanoh6 show 83% total reflectance for the

antarctic polar plateau and 7h% for the Ross Sea area for winter ice.

Measurements by Kuz'min30 indicated a total reflectance of 30-h0% fog

sea ice in the White Sea area.

,oop

6O 4O

25 4 14 22 26 30 4 _ 12 16 23 4 9 16 22 II IIi IV V DAYS, MONTHS Figure 98. Change in total reflectance of snow cover with time (after Kondratyev30).

J 1967016633-251

: I

APPENDIX D

Th/ REFLECTANCE OF CLOTDS

i. SPECTRAL REFLECTANCE

Perhaps the earliest comprehensive study of cloud reflectance is that of Hewson, h7 who studied fogs of particles of fixed diameter and density. According to Hewson's data, the spectral reflectance is constant up to about 1.3 microns; in the longer wavelength regions there is a decrease of spectral reflectance with dips due to absorption by water vapor. A calculation by Novoseltsev h8 yielded similar results, see Figure 99. The spectral reflectance is constant to about 0.3 micron, with dips mainly due ta, water vapor absorption bands. Note that this curve is only a very approximate result for cloud spectral reflectance, since it has fixed size fiameter and considers only water particles and not ice particles.

O,O-

O.a

O OA

O.Z

O i,l.i,l,l,l,i,l 02 G6 LO L4 I_ U 2B 3.0 ,microns Figure 99..The spectral albedo for middle layer clouds (after Novoseltsev46).

2. ANGULAR DISTRIBUTION OF REFLECTANCE

The angular distribution of scattering from a water cloud with

218 1967016633-252

219

_9 realistic particle size distribution has been calculated by DeirmendJiau.

Results for _ = 0.45 and 0.70 micron are shown in Figures 100 and lO1

respectively. The figures show the intensity functions for parallel

and perpendicular polarization as a function of scatterin_ angle, i.e.,

the intensity of scattering of both polarizations for a small volume

element of the cloud. The curves show a pronounced peak for scattering

I angle 8 < 5° , much brighter in the blue than in the red. As 6 inczeases,

intensities fall, reach a minimum at 80 < 8 < lO1°. The intensity then

I increases as B increases, showing a fog how at 143° (with a hin_ of a smaller fog bow at 122° for _ = 0.7 micron). Finally the intensity has

I! a secondary bright sp_ for _ = 180° (backscattering). Although this

li calculation does not represen_ cloud reflectanc_ for a specific real type of cloud, we might expect to observe the salient features of this

Ii scattering pattern in cloud reflectance measurements.

I 3. TOTAL DIRECTIONAL REFLECTANCE The classical measurement of cloud total reflectance is that of

Aldrich.50 I He measured the total reflectance of a stratus cloud over land from a captlve balloon. The cloud base varied from 1000-2000 feet

I during the measurements and the cloud top remained at 2600 feet. Aldrich i, reported a measured total reflectance of 0.78 independent of cloud thick- hess.

I. Measurements by Luckiesh5! from an airplane indicated that the total reflectance varied from 0.36 for thin clouds to 0.78 for dense c!ou_s

I of extensive area and great depth.

i Neibur_er52 made measurements from a blimp over coastal stratus and rbtained the results shown in Figure 102, showing the variation of

I total reflectance with cloud thickness. The maximum value of about 0.80 |I 1967016633-253

220

"_ I ! I t i I ! |

102 -

CLOUD MODEL re=4_ x-o.45_. A= a i0 t

4w"

I00 _---t ......

Figure i00. Intensity functipns for water cloud illuminated by O.h_-micron radiation (after DeirmendJian_Y). 1967016633-254

I 221

i I I i I I02 - ' CLOUD MODEL - i rc=4 F J i i I _=o.7o/A_=i I ,o, i - " I " I. i i , i

I; 4_- - ,i _ i li , iO-t = O. 79

ii - _ '_\ " "

0 20 40 _0 SO I00 120 140 !60 180 _. p (DEGREES)

ixI Figradureiationi01.(aftIentr ensDeityirm_.fundJr,ictian_Y).pns for water cloud illuminated by O.70-r_leron

j ,

I J U 1967016633-255

222

2000 -- l--l--I l-- uJ I---@--I iiuJ 1500--

WZ ' ""- I L)"_ 1000- T I --,. I I-- C3 I _. I 0 500 -- _I I "" ', 0 "

?" L I I I , I ,, J 0 20 40 60 80 I00 TOTAL REFLECTANCE

Figure 102. Total ref]eetance of coastal stratus cloud as _ function of cloud thickness (after Neibu_-ger52). 1967016633-256

223 i for very thick clouds agrees well with previous estimates, the variation

I of total reflectance with thickness is greatest for thin clouds.

Observations of N. I. Cheltsov 30 also show the dependence of cloud

I total reflectance with cloud thickness (see Figure 103). His data show

reasonable agreement with that of Neiburger, and also show that cloud I , form has an influence on the total reflectance of clouds of a given

, thickness. Again, maximum values of about 0.80 were measur£d. J

The dependence of total reflectance of clouds on the nature (re-

flectance) of the underlying surface is illus_rated by the data in Table

2h. 30

TABLE 2h

DEPEFDENCE OF CLOUD TOTAL REFLECTANCE ON UNDERLYING SURFACE

Reflectance _i i0/I0 (st, sc. ns) Total

I' Over ice clearimgs 0.70

I Over water openings 0.32

U 1967016633-257

224

+ .... SC,WITH CLEARINGS " ..... SCt CU. A ...... SC, I0/10 • ------AC, IO/tO (/) n- 700 w / . I- .+/, / b,,! SOO _' : •= / / O_ 500- , , /' (n i bJ /;/ .."- =,oo :// ,:/-, o_ ,,,-/:, .i, _oo ,,,./i,,,+..,/ _.00 ,/.1 _'i 1.1

/ # i/ i// d'- IO0 I/1 ." .."

I I ,1 I ,1 o IO 20 3o 40 so so i'o 8o 9o "_ TOTAL REFLECTANCE

Figure 103. Dependence of cloud total reflectance on cloud thickness and cloud type (after Cheltser, see Ref. 30). 1967016633-258

APPENDIX E

THE SCATYERING OF SOLAR RADIATION BY AIR MOLECLr_ES AND AEROSOLS

i. MOLECULAR SCATT_ING

Scattering by air molecules has been called Rayleigh scattering, 53 after Lord Rayleigh who was firs_ to successfully consider its theory.

More specifically Rayleigh scs tt_::ing is the case of single, independent

scattering by _l agent satisfying the conoition that the size parameter:

2wr = ---< 0.i (93) A

radius of the and the i where r = the scattering particle wavelength of the radiation. The angular distribution of radiation scattered fmom !

an incident beam of radiance N_ is described by a phase function p(cosS),

I where 8 is the sca,.tering angle. The radiance of the scattered en,_rgy ! in the direction 8 is given byS3: I ' _x'_) = - K p(cos_)4_ Nl dm watts cm -2 ster -I micrcn -i ('4)

where: k_ = the mass scattering coefficient i dm = the mass of a scattering element i For R_yleigh scattering in the atmosphere55:

8 .3(n2-1)2 6+36

kx = 3 xh N • p + 7---36 (95)

p(c_s8) = _ (i + cos2_) (96) I I where n = the index of refraction of aic i N = the molecular number density t 0 = the air density

I 6 = is tY: _-, -larizatton factor of air 225 [ , 1967016633-259

226

The total loss of radiance is _iven by integrating dN z (6) over

the 4_ solid angle, i.e.,

aNA = _ dNx(6)dn 4_

- klNldm (97)

since f J (1 + _os2B)d_= i (98) 4_

Thzs theory provides a quzlitative description of the brightness of the

sky. Since the scattering coefficient is inversely proportional to the

fourth power of the waveleng+h, the sky is blue. The an_ular distribu-

tion of scattered liKht is symmetric and for 6 = 90 °, the scattered

light amounts to one half of that scattered forwar_ or backward. The

brightness of the sky is determined by the anMular distribution and the

increase i_ scatte_u£ &if m_Sb near the horizon as compared to the

vertlcal H. ver, for an accurate description of sky brightness,

multiple scattering, and &_rosol scattering must be conszdered.

A quantztative explanation of some of the observed features of the

sky brightness was made possible Dy _he development of the e_act solu-

tion of the equation of radiative transfer_ In a mediw_ scatterln_ de- 54 cordinl to Rayleigh's law, by CSandresekhar. The extensive aeries

57,58 of computations by Chandrusekhar and ElbJrt, 56 Zekera and co-workers w

and Coulson 59'60 explained the maln features of the radzation transmitted

and ref'_ct_d by a nonabsorbing, homogeneous, plane parallel atmosphere

_f moderate optical thlcKnes_ :, w:th Ravle_gh scatterinK, and diffuse

(Lambezt) reflectJon at the surface. C_lculations were made for the

J 1967016633-260

227

entire upward and downward hemispheres for

= 0.002, 0.05_ 0.i0, 0.15, 0.25, 0.50, 1.0

cose o = 0.i0, 0.20, 0.40, 0.60, 0.80, 0.92, 1.0

A = 0.00. 0.25, 1.00

where _ = optical thickness = JI kA(z).o(z)dz (99) z o

k I = mass scattering coefficient

n(z) _ atmosrh_ric density

8o = r_n's zenith angle

= total reflectance (albedo) of surface

z = altitude

_ese calculations clearly show the horizon brightening in the outgoing

radiation (see Figure 104) and the dark part of the sky at about 90 °

from the sun. An integration of the upward flux over the entire hemisphere

for incident radiation having the spectral distribution of the sun's

radiation, for radiation wavelengths 0.32 < _ • 0.8 m_cron, corrected

by estimates of scattered radiation for A < 0.32 micron and _ > 0.8 micron, yields a value of 7.6% for the earth's planetary albedo due to

scattering by the clear atmosphere, decreased to 6.9% when corrected

for ozone absorption.

Further studies of this same molecular scattering problem include

those of Sekera 61 and Fraser 62 with Fresnel (specular) reflection at 63 the surface and the work of Coulson, e_}.ta_l., using experimenta1_y

determined reflectance characteristics of red clay soil and white

quartz sand for surface reflectance. Fraser's results _nciude curves

of surface total reflectance (albedo) vs. optical thickness (Figure 1967016633-261

0 0

Figure 104. Distribution of intensity of light emerging from the top of the atmosphere and of the skylight in the principal plane, sun elevation 53 °, optlcal thickness r = 1.0, surface albedo A = 0,0.25 and 0.80 (_fter Coulson59).

105a) and the ratio of upward flux (Fresnel case) to upward flux

(Lambert case) vs. optical thich_ess I_Igure ]05b). The figures show that, for solar :'enith angles < 65 ° , the surface albedo _s < O.1, and the ratio is essentially unity. For largez zenith angles and for optical thickness < 0.5, the surface a]bedo increases and the ratio decreaf3es. From Table 25 (after Coulson 60 ), we see that normal oDtical thickness of the earth's molecular atmosphere < 0.5 corresponds to wavelengths > 0.61_i_m_cron. Thus the decrease of the ratio noted above applies only for wavelengths > O.L4h _cron. 1967016633-262

229

" I I I I '

m < 0,2- w u "< eS.4" n_ 0.1 = 60. gl I 0.0 I I J ' OJO2 006 010 O,ZO 0.80 1.00 2.00 OPTICAL THICKNESS

0.) SURFACE ALBEDO (_:RESNEL CASE)

, i ' d=_,1.01,_o T T t w 0=@!

o _ oo7 r i 0.95 F 0,94/ I ,I...__._._.-L_

I 0.02 0.05 0.10 O.20 0.50 1.00 2.00 OPTICAL THICKNESS

I b.) FLUX RATIO, J

I FiEure 105. Surface albedn and ratio of upward flux (Fresnel case) • t_ upward flux (Lambert case) for nonabsorbing, homogeneous, plane parallel atmosphere with Rayleigh scattering (,z:'terFraser6_). L

|_ 1967016633-263

23O

TABLE 25

WAVELENGTH DEPENDENCE OF NORMAL OPTICAL THICKNESS

OF EARTH'S MOLECULAR ATMOSPHERE ABOVE SEA LEVEL

(After Coulson 60) imml T 1.00 0.50 0.25 0.15 0.i0 0.05 0.02

l, microns 0.312 o.37I._c 0.h365 0.h95 0.5h6 0.6hh O 809

63 Coulson, et al., uses the surface reflectance data for white quartz

Band and red clay soll (Figures 89a and 89c) In similar calculations.

The 7esults for red clay soil are shown in Figures 106a and 106b. The

figures show relative intensities of five components and their sum, as

a function of nadir angle in the principle plane. The components are:

Is - radiation backscattered by the atmosphere, never reaching

the earth's surface

IDD - radiation transmitted directly through the atmosphere, re-

fleeted at the surface, and transmitted directly back

through the atmosphere P

m F IDd radiation transmitted directly through the atmosphere,

reflected at ths surface, and transmitted diffusely back

through the atmosphere

IdD - ra41ation transmitted diffusely through the atmosphere,

reflected at the surface, and transmitted dizectly back

through the atmosphere

Idd - radiation transmitted diffusely through the atmosphere,

reflected at the surface and transmitted diffusely back

through the atmosphere 1967016633-264

231 ,o_ /,, ibt\= /i "._ki\ / ! I=7\i lt't,,_-_j .Or,,, __,, _=..,-.--,.:,',,\.--

o80_ 60 40 20 0 20 -10 60 80 O, O" O" !110* NADIR ANGI.lr OF OBSlrRVATION

a.) _'=0.49I! MICRONS ('L"iO.ISe), eeiS3.1".

.40

.30 !iz ! 10,°Ik I_

O,Oe O, 18." NADIR AN3LIr OF OBSirRVATION

I' t).) 4( ,0.i48 MICRON8 (*l'i,O.08*), e,,88.1". '

I Figurephere with106. redRelativeclay surfaceIntensity(ai_erof Coulson63).outward.radiation for Rayleigh at,nos- [ I 1967016633-265

232

At 0.h92 micron, the limb brightening of Is dominates at large nadir angles, but for e < 62°, IDD is > Is. At 0.693 micron, the limb brightening of Is still is evident, but IDD is > Is for e < 80° . In both cases the integrated upward flux is dominated by IDD. Figures 107a, b show results for the white quartz and case. At

0.h92 micron, limb brlshtening is still evident, at 0.6h3 micron the limb brightening on]._occurs in the forward direction ($ = 0), the domin- ance of IDD is complete for 8 • 60° . The maximum at 8 = 85 would be less pronounced in a spherical atmosphere. For eo = O, the nadir is brightest, with a gradual decrease of intensity with increasing nadir angle.

The program of calculations of this type is a continuing one, results for other types of surface reflectance are promised by the author. Results published so far indicate a pronounced dependence of outgoing radiation intensity on surface reflectance characteristics with a dominant role played by the IDD component.

2. AEROSOl,SCATTERING

The solutions for molecular scattering problems do not completely describe scattering in the real atmosDhere. For example, the bright region immediately surrounding the sun, which is always observed in the clear sky, is not accounted for by molecular scatterlng theories and although the polarization of skylight i_ accounted for mainly by m,_cular scattering, details of polarization patterns indicate that real atmospheric scattering is governed by a law more comDlex than that of molecular scattering. In extremely clear atmospheres, at high altitudes, measured scattering patterns agree better with the molecular 1967016633-266

233

[ 1967016633-267

23h

scatterin_ pattezns, than they do in the case of haze atmospheres near to

the ground.

T_e deviations from molecular scattering are caused by aerosol scat-

tering; for example, the bright "aureole" surrounding the sun is due to

the very stron_ forward scatterin_ ,'f aerosol particles. Characteristics

of the aerosol in the atmosphere, which must be known, are the size

distribution, their distribution in snace and the nature of the particles.

The scattering process, i.e., an_ular dependence of scattered light must

then be calculated.

The theory of scattering by spherical dielectric or absorbing par- 6h ticl_s has been developed by Mie. The nature of the scattering process

depends on the ratio of particle radius, r to radiation wavelenKth i.e.,

for a = _2wr < 0.i, we have R_vleigh scattering: for 0.i < a < h0, the

Mie theory indicates sharp forward s_,attering. As _ increases the in-

finite series which describe the scatter_n_ function converKe more slowlM,

and only the advent of high speed computers has made solutions feasible.

A large number of scattering functions for specific particle sizes and

index of refraction now exists,5

The aerosol is composed of a mixture of particles Junge 65 found,

by direct measurements of the number and size of particles, that a

continuous size distribution, from ions to giant nuclei up to I0 mierors,

exists. He de,erlbed such a d[strlbution with hhe form_l relation:

-_J -3 dn(r) = N(r) • dr = c.r d)lo_ r) em

dn(r) = 0.h3h.e.r-(V_+l)d_ (i00)

! 1967016633-268

235

_,hele the constant c depends on the number of particles per cc, and

values of _* are usually in the range 2.5 < _* < h. Symbols in this

equation are:

n(r) = number of particles with size in range r to r + dr

N(r) dr(r) -h = dr , cm u _ : a constant.

Also, Volz 66 has &..own by measurements of sky radzation, that the

index of refraction for atmospheric aerosol was 1.5 instead of 1.33,

I the index of refraction of water, which had been used previously In the I

early computations.

I The angular distribution of scattering of aerosol particles of a

I given size distribution must be found by integratzon over particle size. Rayleigh scattering is then added to the result. Many such scattering

I. patterns have been computed (see Bullrich67). Strong forward scatter-

ing is due to many large particles, whereas small particles cause in-

I creased scattering at right angle_.

I For an explanation of sky brightness, a1_ integration over wavelength must also be made. In addition multiple scattering and reflsc-

must the I tion from the earth's surface be included in calculatlons. Bullrzch 6T considered single scattering with the change of scatterlng 68,69 I pattern with wavelength. Fiege]son, et a__l. considered multiple

i scatterln_, but at fixed wavelength only. The work of Bullrlch is summarized in an extensive three volume set of tables published by the

Air Force Cambridge Research Laboratories 70 Results of Fiegelsou's

work are illustrated by Figures 108a and b. Figure 108a shows the

I brightness around the sun and the dark zone stretching from the anti-

i solar uky to the part of t,_e sky below the sun. Figure 108b shows a

I 1967016633-269

236 1967016633-270

237

bright horizon in the forward direction, with a dark area in the region

where a specular reflection could occur.

3. S_/MMARY

The problem of scattering of solar radiation in the real atmosphere

is not yet solved in all of its aspects. A complete solution must con-

sider molecular and aerosol multiple Jcautering processes, aerosol par-

ticle size di3tribution as a function of altitude, selective absorption

by all molecules, and the na%ure of reflectance at the earth's surface

for all wavelengths of the incident solar radiation. Some solutions

for problems considering a few cf the above parsx.e_ers have been made

as described above.

I I I 1967016633-272

APPENDIX F

F. ESTIMATES OF EA_PH'S ALBEDO

Fritz_- has attempted to evaluate the mean albedo of the entire earth,

aM we]] tt_est.b]Ish how it is derived from various reflecting and scat-

tering sources. The incoming solar radiation is divided up into three

spectral r_nges; ultraviolet (0.2 < k < 0.4 micron), visible _O.4 < h < 0,79

,,ic..on),infrared (0.79< _ < 4.0 micron,), containing 9_, 49_, and 46%

of the incoming energy, respectively. The reflectance of the earth's

surface, the atmosphere and clouds, in each of _hese three spectral re-

gions is then calculated, so that, finally, values for a table such as

Table 26a are obtained. The subscripts e, a, and c stand for earth sur-

face, atmosphere, and clouds, respectively, and u, v, and i stand for

ultraviolet, visible and infrared, respectively. The results were ob-

tained in five steps, as follows:

i. Estimate R% of solar radiation absorbed by ozone, in the ultra-

violet. Therefore solar radis _ion reaching below the ozone I

layer arrives in the ratio 7:49:46 for the three spectral

regions.

2. Use Abbot and Fowle's estimate of 2.3_ of total radiation re-

flected back into space by ear_ surface features, i.e.,

_'_ Ae = e._. Divide Ae in the ratio 7:4_I_6, i.e., Aeu -

.: 0.i, Aev _ i.I, Aei = i.i.

2)8 1967016633-273

I 2_9 1 f 3. _ssume lh_ of incoming solar radiation scattered back into space I by cloud free stmosphere_ and 9_ by atmosphere above clouds_

thus

As : i4(l-c)_ 5"c "

where c is the _ cloud cover of the earth. Assuming c = 0.94_

we have Am = 9.1_. Divide this up in the ratio 2:4:1. Thus i Aau = 2.6, Aav = 5.2, and Aai = 1.3, h. Assume Danjon's value of 39_ for photometric aibedo. Then

Av = 0.45'39 = 17.6 and

I Acv = Av - Aev - Aav = 11,3

Ii On the basis of cloud spectral reflectance t AcI = 0,9 Acv = 10,2

1.8 I Acu = 714bAcv =

I_ 9. Thus w, obtain the data of Table R6b. The earth's llbedo is

I ' 35_, with an ultraviol_t reflectance of 50_, visible reflect- I ante of 39% (DanJon'a photometric albedo) and infrared re-

I, flectance of 27_.

. It is interesting to summarize this work in aMmbolic form_ see Table 26o. Eieh of the nine basic quantities is given in terms of Ae, Ae or

._ Aov. Ae ia eetime%ed %0 by E._ end Aa Ind Acv ire given by,

i Aa - 14 (l-c)+_o - Z_- 9c ( _ Acv - Av- _}/98Ae - _/TAi I 1967016633-274

TABLE 26

REFLECTION OF SOLAR RADIATION_ (After Frltz791 Ultraviolet Visible Infrared Total ..p , Earth's Surface Aeu Aev Aei Ae

Atmosphere Aau Asv Ami As

(s) Clouds Acu ACV Acl Ac } Total Au Av Ai A !

Solar Energy _ 2_. 26 I00 - -- i

Earth's Surface 0,i i,I i,i 2,

Atmos phere 2,6 9,2 i, _ 9+1

Clouds i, 8 11, _ i0,2 2}, ) (b) Total 2.9 17.6 12.6 ._2,7

Sola:.' Energy 9 29 46 I00

. .Ref!ect, ance ...... _0 3_ .... 27 ..... 3_5 _

Esrth's Surface 7/90Ae 25/98Ae 26/98Ae Ae

.. C.lou.ds..... 7/25__cv: Acv Q,._.A.. 2,O_v_ !!

i 1967016633-275

241 f

where e Is _ cloud cover (In decimal form) and Av = O.h5 D; where D ±_

I Danjon's photometric albedo. Thus A = Aetna+2,056 A_ .ubatituting

from above A -- ,096Ae - O.17_:Ae + 0.929D i or A _ .056Ae + 0.925D + *.979c - 2.4> (IOI)

I In the final snalysis_ Fritz's estimate _f mean ecrth'_ ,ibedo can be written as a function cf Ae, D, and c. With Ae _.2._ D = 39 (Danjon)

I and c = O._4j we obtain

i His estimate thus is determined primarily by the Denton value_ with minor

i corrections due to the other factors. With DanJon's new estimate of

D = 40_, we have for Fritz's A = 3_,_%'

Houghton's76 estimate of earth's albedo was obtained as a part of

a calculation of the annual heat balance of the northern hemisphere.

The com_utations were based on the followin_ data'

I i, Annual means_ for North America s of total solar and sky radia-

tion received at the surface (pyrheliomete'_data),

. 2. 8mithaonian Aatrophyaie|l Obaervatorys77 atmospheric transmis-

sion ourveb for clear sky scattering and absorption.

_. Cloud cover data by C.E.P. Brookss 78 and C, F. Brooks, TMHaur-

wits and Auatin_80 and the _reliminary Climatic Atlas Of the

World. 81

|] 1967016633-276

2_2

h. Surface reflectance deto from Buttner,82 Richs_dson,8_ Bertels,84

Angstroms89 end mBny others.

9° Cloud ebsorptlon data by Fritz,86 Nelbeugerj_2 Hewson,47 end

Heurwitz._7

For eBch i0° latitude :Ircle_ 81bedo was calculated by s procedure which

_Bn be _prese_f' b7 the following equation',

A _...... }ls Hs-H}_-H_R(c')(1-_o) a = - ..... (Io2) HS +,

where

H8 = incident solar radiation outside of the atmosphere,

HA = radiation absorbed in the atmosphere with normal cloud cover.

_ = solar radiation at the surface with normal cloud cover.

I{_ - sol_r radiation at the surface with clear sky.

R(c) - _/H_, s function of cloud cover, c (derived from data for

North America, applied world wide).

e - weighted cloud cover.

PO " _u_'fecealbedo.

Houghton's data is summarized in Tables 27a and 27b. His average albedo

for the northern hemisphere shows remarkable a_reemen_ with Frltz'a _,_,

> London's71 estimate of eerth'_ albedo was obtainwd ea a part of l

+ study of atmospheric heat balance baaed on a rather detailed "reellatio

% : phyaical model" of t_ _tmoaphere, Vertical an_ l&titudinel diatribu- J .i 1967016633-277

24_ I TASL_;27

" DATA USED TO OBTAIN ALB_'DO OF NORTH]_RN HEMISPXF_E

(Aff,_r Houghton 76) (a) Computed values (ly/day) of disposition of solar Ii radiation incident on a clear atmosphere

i4muw(_. N)

_nol _"""lD_r!lecll'Ullhimlst iurhiltlur_tacl _9o3 '_,....,,'L,T|_-'",__!!i'-"i Abeorbedby itmoJphere 198 Ig0 169 14_ 12J 99 I| 41

lummermiitia, Atlim4wdDDJiim:tVumbeamIt bJuty i_t(ice.l_urhice.nhe_l. . _ _ Ill2 49SJ9|9_ 94_910tS 988l:I 19_i I_ I_ 191It0

' ^nnull _f_' _Mm I|.urflc_ 0| II metn ADlblm4Jld_uw it byJutlitrnospheri/ice 19933 I|f I_ llt I_ 114 91 J| II II -- . i i i i ...... i ii i i i l III II mill -- I I (b) Disposition of solsr rsdlatlon (ly/day) with normal cloud cover.

...... I J...... - I II Eli I

j: II/ j i1[ I 471II I _ O,l| -- NIII III i I i i I i laD 44f , _miimm_

i1 1967016633-278

244

tio,,_of telnpereture#pressure and relative humidity v._reprepared for each of the four seasons, as were latitudinal distributions of :loud cover of'each of six types and of total cloud cover. The slbedo calculations included consideration of ground reflectance, cloud/_catter-

ing and absorption; the depletion of radiation due to scattering by air molecules, water vapor and dust particles; the abso2ption of the

! direct solar beam by ozone# water vapor, and dust; and the sbsorptic_n T of,scattered radiation by water vapor and dust, Dust scattering and 1 ground reflection data were based on Houghton's work ell other calcula- J tions were new estimates by London and co-workers. The results, the distribution with latitude and season of planetary albedo in the northern hemisphere, is shown in Figure 109. The figure shows a minimum albedo of 27% in the sub_ropics in winter shifting poleward about I0" and increasing _o 2_ in summer. The higher albedos at high latitudes are due to increasing cloudiness and higher reflectivities in polar regions. The ! total planetary albedo averaged overall latitudes and seasons was about

_%, only a small variation with season was shown (35,6% in winter and

36.3% in au.,ner). The contributions to the average total albedo were I earth 4%j atmosphere 7%, and clouds 2_%. With a mean cloudiness over the northern hemisphere of _1%, the mean albedo of clouds waa _7%, and albedo [ of clear sky conditions (ground reflectance plus atmospheric Jcattering) !i was as sho_ i n Table 28. 1967016633-279

24_

0 i .... t I.... I t WINTER 8P._O. SUMMER FALL WINTER

Figure i09. The season_l distribution of the planetary slbedo (%) (after London71).

TABLE 28

SEASONAL DISTRIBUTION OF PLANETARY ALBEDO COMPONENTS DUE TO ATMOSPHERYC SCATTERING AND GROUND REYLECTANCE (After London71) Wlnter ..... _Spring Summer Fall I- Ground 9.0 7._ 9.O 6.0 At,.,. Scattering 8.3 _/_ 8_ __ Total 17.3 19.0 i_.9 i_._

I _ ..,. _ i i i il ]i I

I Angstrom'sl_ determinations of albedo are based on aeasure,,entsby Drus.aondof the nature1 illumination of the sun and sky in South Africa. 1967016633-280

246

After derivlng e forl_luls,from these date, to express the Elobsl illt_nina- tlon st sea level es s function of air mess end turbidity, he proceeded as follows:

I. He derive.| 8 photometric loss factor E, fo_. the effect of the

atmosphere on the incident solar flux, end then obtained average

values E, which were equal to 0.52 st the equator" and 30 ° istl- 1

tude, with e slight increase to 0.54 at higher latitudes.

2. A correction, for 8bsorption, of 0.07 was applied, and an esti-

mated factor of 0.039 was added for reflected energy reaching

outer space. Thus the slbedo in the photometric band, for clear

sky, of 0.52-0.07+0.32 - 0.28_ was found.

3. Another correction, adjusting for the difference in land and

ocean reflectance, brought the photometric albedo to 0.29_.

This clear sky slbedo i_ assuz_d to apply for the whole earth

at 0.955 micron, t

4. Using DanJon'a photometric albedo of 0.39 _or the earth and

%eking c = 0.52 in the relation

0.39 • (1-c)O._ + c.Acv !

gave Acv • 048. Applying Hewson'a spectral dependence of cloud

elbedos gave Ac - 0.46 for the total spectral range. 1 5. From DanJon'a photomLtric albedo measurements at three waw_.- I lengths, i.e., [ 1967016633-281

21+7

k = 0.46/ 0.543 0.606

AvX = 0.48 0.39 0.315

the relation A?.= I.O3-i.19k wBs found, end the photometric

elbedo for the range O to 0.7 micron wa_;found to be

,O. 7A>_t!st_dk = 0 41 Ao-o.7 = 0._

O.5 / O.7Hs_d_.

The value of photometric albedo for clear sky A_.O.7 was found

from I

I (l-c)A"o,7 + cAc = 0. i

with c = 0.52 and Ac = 0._6. Thus:

Ab.o.7 ,. o.}_5 .

6. An estimate of 15_ more scattered energy for the evltlrespectraA

range was made, a:,dthe total clear sky albedo was found to be

A - _'3_5 • 0.gUO • _,:1_

I 1.98 where 0.9&O is the incident Joler energy in the range 0-0.7

I micron at 1.98 is the solar constant.

average 7. The planetary albedo under conditions of cloudiness wee

i then A - (1-0._2)0.19_ * o._2 • o.u6 . o.333 I 1967016633-282

2_8

The second calculation made by Angstrom was a modification of Hot,gh-

%on's wcrk. If we ta_e 0.19_ (instead of 0.135) as the albedo of the cloud free atmosphere, and use Houghton's cloud Blbedo of 0.55, we obtain s planetary albedo of 0.38. This implies that Danjon's photometric albedo should be 0.4} instead of 0.39. This second result _s favored by Angstrom. 'I 1967016633-284

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