Angular Radiation Models for Earth-Atmosphere System

NASA Reference Publication 1184 1988

Angular Radiation for Earth-Atmosphere

Volume

ImShortwave

j. T. Suttles, P. Minnis,

and

Research

Hampton,

Hampton,

B. A. Wielicki

Center

Virginia

I. J. Walker Planning

Radiation

R. N. Green, G. L. Smith,

W. F. Staylor, Langley

Models System

and

Research

D. F. Young Corporation

Virginia

V. R. Taylor and L. L. Stowe NOAA National Environmental Satellite, Data,

and Information

Washington,

National Aeronautics and Space Administration Scientific and Technical Information Division

D.C.

Service

i | i

] 1

|

!

J | !

|

! J i =

!

|

Contents Summary

..................................

Introduction Symbols

.................................

Shortwave

and Angular

Directional Satellite

1

Grid

Model Parameters

Bidirectional

GOES

Parameters Parameters

Data

Nimbus

Sets

Data

Bidirectional Directional Overcast Results

3

...........................

3

...........................

4 4

.......................

5

...........................

5

..............................

Models Models

6

............................

6

.............................

7

.............................

8

Cloud Models

...........................

8

...................................

Bidirectional Directional

Models Models

8

.............................

9

.............................

10

Remarks

References

..................................

Appendix A--Application Bidirectional Models B

8

............................

Concluding

Figures

2

..........................

Processing

Processing

Models

Mixed-Scene

.........................

..............................

7 ERB Data

Model Development

Tables

1

...................................

Scene Types

Appendix

1

Equations

10

of Helmholtz ..................... for Mixed-Scene

Reciprocity

Principle

....... Properties

................

....................................

12 13 14

...................................

PRECEDING

to

19

PAGE

BLANK

NOT

III

I_LMED

:1 I!

Summary This document presents the shortwave angular radiation models that are required for analysis of satellite measurements of Earth radiation, such as those from the Earth Radiation Budget Experiment (ERBE). The models consist of both bidirectional and directional parameters. The bidirectional parameters are anisotropic function, standard deviation of mean radiance, and shortwave-longwave radiance correlation coefficient. The directional parameters are mean albedo as a function of Sun zenith angle and mean albedo normalized to overhead Sun. Derivation of these models from the Nimbus 7 ERB (Earth Radiation Budget) and Geostationary Operational Environmental Satellite (GOES) data sets is described. Tabulated values and computer-generated plots are included for the bidirectional and directional models. Introduction Analysis of satellite measurements for determination of the Earth's radiation budget requires information about the angular characteristics of radiation that is reflected (shortwave) 1 and emitted (longwave) 1 from the Earth-atmosphere system (Smith et al. 1986). The angular characteristics can be defined by models which express, for an imaginary surface element at the top of the atmosphere, the exiting radiance for each direction out to space as a function of the total hemispheric flux leaving the element. In principle, a radiance measurement at a single angle can then be converted into an inferred hemispheric flux. For successful application of the angular models, it is necessary to classify the Earth observations into a set of scenes (e.g., ocean, land, snow, and clouds) and to have a complete set of angular models for each scene class. Past investigations of Earth radiation budget from satellite measurements have varied considerably in the approach to angular models for reflected radiation. To analyze the Nimbus 3 measurements, Raschke et al. (1973) used three scenes (ocean, snow, and a cloud-land combination) and "gross-empiriear' models derived from a variety of sources including aircraft, balloons, and early satellite data. The scene identification was a static process, since the scene type for a given measurement location was determined a priori. Because of the lack of well-defined angular models, Gruber (1977) assumed isotropy for all shortwave observations while analyzing the National Oceanic and Atmospheric Adminstration (NOAA) I Reflected spectral marily

region

radiation (0 5#m),

in the longwave

occurs and region

primarily emitted (> 5 #m).

in radiation

the

Scanning Radiometer (SR) data. The isotropy assumption obviated the need for scene identification and detailed models; however, accuracy of the results was reduced considerably. For the Nimbus 7 Earth Radiation Budget (ERB) measurements, Jacobowitz et al. (1984) used four scenes (ocean, land, snowice combination, and cloud); a threshold method based on climatological values of reflected and emitted fluxes for cloud identification; and detailed angular models for each scene. The angular models for this analysis were derived by Taylor and Stowe (1984) from the ERB scanner observations. The ERB data processing was the first attempt to use a dynamic cloud-identification procedure for radiation budget analysis. The recent Earth Radiation Budget Experiment (ERBE) described by Barkstrom and Smith (1986) has a complex system of inversion algorithms which include angular radiation models. The ERBE inversion algorithms (Smith et al. 1986) use a set of 12 scenes, a Maximum Likelihood Estimation (MLE) scene identification method, and a comprehensive set of angular models. Because of the special requirements of the MLE method, statistical parameters are required as part of the angular model data set (Smith et al. 1986). The purpose of this report is to describe and present the shortwave angular models and associated statistical quantities that have been developed for the ERBE inversion algorithms. This report is Volume I of a set of two documents; Volume II describes the longwave models developed for the ERBE analysis. The shortwave models include bidirectional and directional parameters and were derived from existing Nimbus 7 ERB and Geostationary Operational Environmental Satellite (GOES) measurements and from theoretical relations. Bidirectional parameters are: anisotropic function, standard deviation of mean radiance, and shortwave-longwave correlation coefficient. Directional parameters are: mean albedo as a function of Sun zenith angle and mean albedo normalized to the overhead Sun value. A brief description of the model characteristics and derivation is presented. Tabulated values and computer-generated plots of the models are also included.

Symbols A

albedo

Ai

average albedo for ith solarzenith-angle bin

a,b

known values used in interpolation

shortwave occurs

pri-

coefficient

Cjk

in normalization

equation for anisotropic factors for angle bin with jth viewingzenith-angle and kth relativeazimuth-angle ranges COVAR(sw,

lw)

covariance and

E0

between

longwave

Earth

GOES

Geostationary Environmental

L

radiance,

L'

normalized

of viewing angle

it0

cosine

of solar

p

correlation

a

Budget Operational Satellite

M

radiation

flux,

Mi

average

radiation

W/m

flux

for ith

bin,

W/m

solar-zenith-angle number

2

2

shortwave anisotropic (defined by eq. (2))

function

average shortwave anisotropic factor for angle bin having ith solar-zenith-angle, jth viewingzenith-angle, and kth relativeazimuth-angle ranges r

Earth-Sun

ro

mean

$C, 0

unknown equation

distance,

Earth-Sun

azimuth

angle,

CR

relative fig. 1)

azimuth

and

Oo

solar

:

angle,

deg

(see

superscripts:

J

index bin

for viewing-zenith-angle

k

index bin

for relative-azimuth-angle

L

land

scene

bin

type

lw

longwave

m

index for a given an angle bin

mix

value for mix and 50-percent

n

index

for colatitude

0

ocean

scene

q

index

for seasons

r

reflected

8w

shortwave

albedo

function

zenith

observation

in

of 50-percent land

ocean

zenith

angle,

deg

deg (see

km

and

includes vegetated snow scene includes scene Data

for

Angular

bin

type

average

value.

Grid

and nonvegetated snow and ice.

types, and the There are twelve

types: nine basic types and three mixed types. for the land-ocean mixed scenes are derived

from values for the basic types as described in the section entitled "Mixed-Scene Models." Four levels

(see

fig.

Types

denotes

angle

The scene types selected for the ERBE data analysis (Smith et al. 1986) are used in this work. These scene types were defined on the basis of broad categories oi%]imat0iogically important surface and cloud features and are given in table 1. The desert scene

bin

angle,

a symbol

1)

of cloud coverage are included: clear sky (0 to 5 percent), partly cloudy (5 to 50 percent), mostly cloudy (50 to 95 percent), and overcast (95 to 100 percent).

2

_--

deg

for solar-zenith-angle

Scene

in interpolation

solar-zenith-angle

viewing fig. 1)

of radiance,

index

A bar over

km

distance,

values

normalized ith

deviation

radiance

of observations

number of observations for angle bin having ith solar-zenith-angle, jth viewing-zenith-angle, and kth relative-azimuth-angle ranges R

between

i

W/(m2-sr)

average radiance for angle bin having ith solar-zenith-angle, jth viewing-zenith-angle, and kth relative-azimuth-angle ranges, W/(m2-sr)

angle

longwave

¢

eq. (13)) Lijk

and

standard

Subscripts

(see

zenith

satellite)

W/(m2-sr)

W/m 2 (value distance)

radiance

(e.g.,

coefficient

shortwave

radiance

Radiation

cosine zenith

shortwave

solar constant, 1376 for mean Earth-Sun

ERB

#

=

11

The surface type at a given location on the Earth can be determined a priori by reference to a geographic map or atlas. The presence of a cloudy scene must be determined as part of the data processing using a scene identification technique. Note that a scene identification procedure must be applied during both the development and application stages for the angular models. Because of differences in measurements available in the two stages, the scene identification methods for development and application, in general, are not the same. The shortwave models in this report are defined according to the angular coordinate system shown in figure 1. The principal plane is the plane containing the ray from the Sun to the target area and the zenith ray that is normal to the target area. For an exiting ray (e.g., to a satellite), the relative azimuth angle CR is measured from the principal plane on the side away from the Sun. Thus, forward reflecting corresponds to CR = 0°, and backward reflecting corresponds to CR = 180°. To describe the angular variation of radiance, the angular coordinates are divided into ranges called "bins," and the model is represented by mean values for each bin. Table 2 gives the angular bin definitions for the solar zenith angle, viewing zenith angle, and relative azimuth angle. Symmetry about the principal plane is assumed for the azimuth angle. The illustration accompanying table 2 shows no bins for the first viewing-zenith-angle bin because, in fact, little variation exists. To derive a value for this socalled "cap bin," data for all azimuths are included in determining the average. However, as a practical matter for computer application, azimuthal bins are also provided for the first zenith bin to avoid indexing problems. This is accomplished by replicating the cap-bin value for all azimuths. The data presented in this report include this replication. Shortwave

Model

Parameters

Bidirectional

Parameters -a7

,76 2.6 -.34b

(!0) (10) (I0)

.76 Z.5 -.638

(I0) (10) (lb)

,73 2._ -,411

(i01 (I0) (10)

.b7 _o7 -.369

(i0) (I0} (IC)

,6E 2._ -,305

liD) liD) (iC)

,68 _,9 -,356

(I0) (I0) (i0]

,70 Z,_ -.600

410} (I0] (I0)

,72 _o_ -.458

(101 (I01 (10)

_7-39

.85 2.7 -,239

(_) (q) ( 9)

.e2 3.0 -.337

[Ib) (_u) [i0)

.76 _.9 -,668

(I0) (Iu) (101

.72 2,5 -._lZ

(i0) (i01 (10}

.7_ a.E -._7_

(iO) (iO) (10)

,74 Z,8 -.368

(IO) (lO) (lO)

,76 1,3 -,_T6

(I0) (lO) (lO)

.83 _.7 -,331

( 9) ( _) ( q)

_9-5_

*.12 3.6 -,26b

(I0) (/0) (i0)

l. U5 3.0 -,231

(_u) (ib) (lu)

• 91 3.1

5

_l-b3

1,61 5.9 -.17_

(i0) i/U} [iO)

1.42 5.0 -,036

(i_) (I0) {iu)

o

_J-75

3.i0 ZC,2 -,05v

(i01 (I0) (I0)

2.3E 11.6 -.013

7

f_-90

3.07 _7.8

3

5._0 29.8 -.028

2.00

(g) { q) (

9]

-.173

(10) (10)

.79 2.5

(10) (10)

-.28o

(lO)

-.323

(1C)

-._05

(10)

-,196

(lO)

-.38Z

(lO)

-.225

(lO)

l.i_ 3.b 1,058

(I0) (10) (10)

.82 _.7 1.1Z5

(I0} (10} (10]

,8! Z._ m'_04

(I0) (10) (1O)

._ 3.Z --'333

(tO) (10) (10)

1.01 2.6 --'368

(lOl (10) (10)

.qq 2.5 --.Zk8

(I0) (101 (101

(i_) (11} (i_)

1.o6 6.1 -.17_

(iO) (10) (10)

.Qb 3.7 -,227

(i0} (10) (10)

.q_ 3.C -.kl_

(iO) (10) (lO)

l.lb 3.5 -._0_

(I0) (lO) (lO)

1.28 3,Z -,314

(II) (11) (11)

l,ZP 3.7 -.18_

(i01 (10) (lOI

(10) (lu)

Z.3Z 8.8 -.ZZ9

(10) (10) (10)

1.50 5,4 -.19_

(5) ( 5] ( 5)

1.35 6,3 -.Z6_

(5) ( 5) ( 5)

1.48 4.1 -.015

(q) ( q) ( _)

1.Sq 3,4 -.Z85

(10) (10) (lO)

1.b7 3,1 -,_23

(9) ( 9) ( q)

(lul

-

/

,77 2.5

2.00

(lO) (101

,T8 3.1

(lO) (1O)

.83 2.3

(10) (lOI

.86 z.q

(lO) (1CI

--

1.75

1.75

1.50 1.50

0 0 ,( 1.25 U.

_b1.25

/1t

1.00

0

.75

I

0 1.00 0 C_ .75

AZIMUTH

AZIMUTH

BIN 1 2 3 4

.50

.2

I I 1 I I I I I I 0

10

20

30

40

VIEWING ZENITH

50

80

ANOLE(

(j)

70

80

.SO

.25

--

I I I I I I I I 1 0

10

20

30

40

VIEWING ZENITH

DEO )

Solar-zenith-angle Figure

5 6 7 8

--

0

90

BIN

Z

50

60

ANGLE(

70

80

gO

DEG )

bin 10, 84.26 ° to 90.00 °. 9.

Concluded.

51

SCENE DATA

SUN MEAN NORMALIZED

TYPE 1 Z 3 ( )

ZENITH ALBEDO ALBEDO

RELATIVE I C-q

BIN NO, ANGLe(DE6,) VI_wIN_ ZEhLT_ bin NO, ANbLE(bE_,) 1 0-15

Z q-30

1.o7 23,_ -.lOJ

(1l) (111 (11)

Z

1_-27

1._b 23.8 -.DZo

(i0) (1_) (10)

3

17-30

.q_ 23.8 -.Oeb

(101 (10) (10)

_9-_1

1.07 23.0 -.lu_

3 30-60

: : s

,C .2369 1.0C00

25.8 ( 14 ( 16

SW RADEANCES(WINee21SR) SW RADIANCES

) )

AZIMUTH

4 60-_C

5 QC-120

6 120-150

7 150-171

B 171-180

(11) (111 (11)

1.07 23.0 -.10G

(11) (11) (11)

1.07 23.0 -.100

(111 (11) (111

1.07 23.C -.10C

(11) (111 ill)

1.07 13.0 -.I00

(11} (11) (111

1.07 23.0 -.100

(11) (11) (11)

1.07 23.0 -.100

(111 (11) (11)

._g 24.1 .004

(11) ill) (lid

1.03 14._ -.OlO

ill) (lid (11)

1.04 24.0 -.081

(11) (11) (11)

1.0_ 23.C -.09_

(11) (11) (11)

1.08 22.7 -.194

(11) (lid (11)

1.09 21.6 -.227

(11) (Ill (11)

1.12 22.0 -.252

(11) (11) (11)

.98 2_.2 -.Oe?

{11) (1_) (i_]

1.01 Z4.2 -.0_5

(11) (11) (111

1.01 2_.1 -.130

(11) (11) (111

1.O_ 23.4 -.176

(11) (11) (11)

1.05 22.4 -.229

(11) (111 (Ii}

1.09 22.3 -.229

ill) (11) i11)

1.08 21.6 -.292

(10) (101 (101

._2

(1C)

(111

.q_

(11)

1.00

(11)

1.0_

(111

1.02

(11)

1.05

(11)

1.03

(11)

2_.t .04_

(101 (101

24.e -.103

(11) (111

24.7 .01_

(11) (11)

24.0 -.O4Q

(11) (11)

23._ -.151

(11) (11}

22.3 -,214

(11) (111

22.8 -.188

(111 (11)

22.4 -.136

(11) (11)

_1-b3

._1 23.u -.o_e

(10) (13) (10)

._3 24._ -.O_

(111 (1.) (11)

.ql _.o .031

(lid (111 (11)

.qB 24.0 -.064

(10) (10) (10)

.94 22.E -.14_

(lid (I1) (11)

1.01 22.1 -.149

(lid (111 (111

1.02 22.4 -.190

(Ill (11) (111

1.01 22.3 -.153

(11) (11) (11)

b

0_-7_

._ Z_._ -.0_2

(10) (iu) (101

.93 2_.1 -.142

(111 (11) (111

.91 23.5 -.Oq_

(11) 411) (11)

.94 2_.4 -,161

(11) (11) (11)

.97 22._ -.2_(

(11) (11) (111

1.00 20.9 -.148

(11) (111 (11)

.98 21.5 -.110

(11) (111 (11)

.99 21,3 -.1_9

(11) (111 (11)

7

75-_

._ _.7 -.153

(lO) (10) (10)

.q_

._3 21.9 -.13_

(10) (1_) (101

.go 21._ -.0_7

(11)

,@7

(Ill (11)

(10)

18.8 -.093

2.00

1.75

--

1.75

l

1.25

(lO) (10)

.98 18.b -.214

(101 (10) (10)

.96 18.2 -.094

(11)

.98

(10)

(11) (11)

20.0 -.242

(10) (10)

"50

--

1.25 I

--

IJ.

L_

0 _. 1.00 0 Q::

r..) _. 1,00 0 n,_)

.75

AZIMUTH

(,rl

z

AZIMUTH

_m

BIN I

50

.7S

l

50

"

I

n," 0 I-C)

(101

lq.C -.27_

l

--

F-0

.9E

(lO) (10)

2.00

1

s CLEJR DESERT - SW JNISOTROPIC FACTOR - STANDARD DEVIATION Of - CORRELATION OF LW AND - DATJ SOURCE

_

BIN 5 6 7 8

.SO

.25

25

I I I I I I I I I 0

I0 20 :30 40 VIEWING ZENITH

50 60 ANGLE(

70 DEO

80 )

gO

(a) Solar-zenith-angle Figure

10. Bidirectional

model

for clear over desert.

0 I I I I I I I I I 0

10 20 30 40 VIEWING ZENITH

50 60 ANGLE(

70 DEO

ISO )

bin 1, 0° to 25.84 °. (See table 5 for explanation

52

i

of data

sources.)

9O

ORIGINAL OF

PAGE

POOR

SCEHE DATA

IS

TYPE 1 2 3 ( )

QUALITY SU_

ZENITH

!

2_,E

ALBEDO ALBEO0

! ;

,2388 1.0080

VLtWLN_

3 30-60

q-3C

0-q

CLEAR DESERT Sw $NISOTRDPZC FACTOR STANDARD DEVIATIDN OF CORFELATIDN OF LW AND OATA SOUPCE

MEAN NUE_ALIZED

RELATIVE

ANGLf(DEG.)

I -

-

SW RAOIANCES(WIHee21SR) SW RADIANCES

3b.% [ (

1_ 1_

) )

AZIMUTH

_ 60-%0

5 9C-120

6 120-1_0

T 150-171

e 1Tl-180

_LNITH _-15

.gV 24,4 •ogG

(11) (11) (11)

,g9 2_.& .U9¢

(11) (1_) (11)

,Qg 2_._ ,09G

(11) (11) (11)

,g9 2..4 ,090

(11) (11) (11)

,9; Zk.; ,OgC

Z

i_-Z7

.9_ ZS.O -.Or7

(iv) (10) (i_)

.$g 24,o ,155

(lu) (LO) (L0)

,99 29,6 ,008

(11) (11) (11)

,97 2;,3 -,003

(11) (11) (11)

1,01 (11) 25,((11) ,01; (11)

3

_1-3_

.99 26._ -.OZ_

(10) (10) (I0)

.Q5 26.9 -.0;4

(1v) (LO) (1_)

.q2 2_.7 -.037

(10) (10) (10)

,_5 22.3 ,102

(10) (10) (10)

,gE 22,2 -,06_

39-_1

.8_ _._ ,0_

(IO) (lOJ (10)

._9 27.1 -.01_

(11) (_1) (11)

.87 24._ .0_

(10) (10) (10)

,_7 25,0 -,C89

(10) (10) (10)

1,01 2_,_ -,11¢

_1-o3

._ l_._ • O1_

(10) (I_) (iv)

._C 26.7 -.0_6

(_0) (10) (_O)

,go 25,7 -.037

(1C) (1C)

1.O1 27.2

(10) (10)

,g_ Z3,2

(1C) (10)

1,10 26.0

(10) (10)

(10)

,01]

(10)

,058

(10)

-,022

(10) (10) (10)

1,03 2_,_ -,103

(10) (10) (10)

(5) (5) (_)

1,05 23.7 -,0_

(6) (6) (6)

(10}

-.102

6

o5-7)

1,00 Z7._ -.1_

(iO) (10) (10)

._2 24.2 -,I2_

(11) (1_) (11)

,8_ 23.8 -.023

(11) (11) (11)

,_3 26._ .Z_3

(10) (10) (10)

.q_ 21._ -.00_

7

7_-90

1.11 lo,_ -,13_

( ( (

1.C2 2_.9 -.2_1

(lu) (i0) (10)

.9_ 2_.2 -,Obb

(10) (10) (10)

._9 Z5.6 .132

(8) (B) (B)

,_ 22,£ .034

9) 9) 9)

2.00

2.00

1.75

1.75

rv" 1.50 O Ft.) -90

2,Ol _3,_ .oco

(12) (13) (O)

1,99 t2,9 .000

(12) (13} (_)

1,71 10,0 .OoC

(123 (13) (D)

1,41 9,5 .000

(123 (13) O)

1.4_ 8,_ • OOf

(1E} 413) (C)

1.79 I0.0 .000

(12} (13) (O)

2,10 10.6 .000

(123 (13) O)

2.1q IO,0 .000

(12} (13) O)

7

.q_

//

2.00

2.00 1.75

--

1.25

/f

1.75

r_ 1.50 O I--

S!J

--

) (2)

1,63 q.7

(2) (2)

1,42 7.2

(2) (2)

1.65 6.3

(2) (2)

-,DOg

(2)

.065

(

( 2} (2)

1.0_ 8.1

,6d 4,6 -.041

(2) ( 2}

,84 6,8

2)

-,Iii l.

2,58 I_.8

(2) (2)

(2) (2) (2)

-,OBg

(2)

,.oo_ ///

-.03!

2}

1,94 8.2

(2) ( 2}

2._3 12.e

(2) t 2)

.005

(2)

,192

(

i 2"00

F

1.75

F

2!

•

1.75

(Z: 1.50

//

-

--

/

//

C)

/ 1 25

0

/_//i/

II

///

¢D

./Y 1#// /

_O100

_.._ _ J

(/I "