DEPART" OF COMMERCE
SINCLAIR WEEKS, Secretary
WEATHER BUREAU
F. W. F@ZCHELDERFER, Chief
MONTHLY WEATHER REVIEW
Editor, JAMES E. CASKEY, JR.
Volume 82 HIlmber 2 FEBRUARY 1954 Closed April 15, 1954 Issued May 15, 1954
METHODS OF CALCULATING SOLAR RADIATION VALUES
AT BLUE HILLOBSERVATORY,MILTON, MASSACHUSETTS
I. F. HAND
U. S. Weather Bureau, Blue Hill Observatory, Milton, M a d
Nonuscript received June 10, 1953; revlsion received October 5, 19531
ABSTRACT
Methods of calculating direct solar radiation received at normal incidence and the total solar and sky radiation
received on a horizontal surface, applicable with accuracies within *2.5 percent at Blue Hill Observatory, are pre-
sented. As many workers in radiation are content with accuracies within 10 or 15 percent, the same methods might
be used with a lesser degree of accuracy in many other areas where atmospheric conditions approximate those at Blue
Hill. With data of total solar and sky radiation received on a horizontal surface now available from more than 80
stations in continental United States, Canada, Alaska, and outlying islands, but with few values of normal incidence
radiation in the same solar network, it is suggested that these methods can be used to estimate normal incidence for
many new regions.
INTRODUCTION
The primary purpose of this paper is to show methods of
wing the numerous available values of total solar and sky
radiation received on a horizontal surface to calculate the
amount of solar radiation received at normal incidence.
A method also is shown whereby normal incidence data
may be used to calculate the total solar radiation received
on a horizontal surface; calculated values of diffuse radia-
tionon a horizontal surface may be obtained as a by-
product. These methods are developed from radiation
records at Blue Hill Observatory for January 1950 through
April 1952. A briefreview of instrumental equipment
furnishing radiation records is made before developing the
me~ods to give the reader an indication of the type and
accuracy of available data.
INSTRUMENTALEQUIPMENT
Records of total solar and sky radiation received on a
horizontal surface at numerous stations in the United
States, Canada, Alaska, and outlying islands are furnished
by the e. m. f. generated by Eppley 180° pyrheliometers
[1,2] and suitable potentiometers. At all the normal inci-
Bmeau in Beptamber 1953.
IPreSent address: Box 115, Afton, N. Y. Mr. Hand retired from the Weather
dence stations in this network, with the exception of Table
Mountain, Calif,, values are obtained by means of Eppley
normal incidence pyrheliometers [3,4] and suitable record-
ing potentiometers. At Table Mountain, the Smithsonian
Institution uses silver-disk pyrheliometers to measure the
solar constant, while at Blue Hill this type of instrument
is used for standardization purposes. Although recording
instruments suffice for most climatological purposes, this
method of obtaining normal incidence values with a sec-
ondary instrument lacks sufficient accuracy to warrant its
use in this study. It was necessary to use the recordings
of total solar and sky radiation obtained instrumentally,
but values of normal incidence radiation measured with
the eye-read silver-disk pyrheliometer at Blue Hill were
usedexclusively in these calculations. Experienced ob-
servers can and do read these instruments with an accuracy
within one-fourth of one percent [5 ]. Obvious errors occur
in recorded values unless the instrumental equipment is
maintained in almost perfect condition, that is, the pyr-
heliometer compared frequently with a standard and the
potentiometer calibrated so that it reads correctly at all
points. At Blue Hill, the 180' pyrheliometer is compared
periodically with a standard and the potentiometer is
checked frequently. That this apparatus is in good condi-
tion seems apparent from the results presented in this
43
44 MONTHLY J’VEATHER REVIEW FEBRUARY 1954
paper. Diffuse radiation on a horizontal surface is meas-
ured by means of an occ.ult8ing ring which continuously
shades the diffuse pyrheliometer from the dire.ct rays of
the sun, but permits the diffuse or sky radiation to impinge
upon the receiving surface at all times [6]. Some of t,he
instrumental sources of errors are listed in the terminal
sect8ion of t,he present st>udy.
DEFINITIONS O F SYMBOLS
The following synlbols will be used:
is the nleasured total solar and sky radiation received
Dhm is t,he measured diffuse radiation on a horizontal
Z is the solar zenith distance expressed in degrees.
I,, is the calculated direct solar radiation received on
surface, expressed in langleys/nlinute 161.
surface normal to the sun and expressed iu langleys/
minute.
Ihc is the calculated t,otal solar and diffuse radiation
received on a horizontal surface espressed in langleys/
minute.
D,, is the calculated diffuse radiation on tt horizontal
surface expressed in langleys/minute.
on a horizontal surface, espressed in langleys/minute
[I, 21. I n order to avoid such a cumbersomeex-
pression,hereaft.er i t millbe ternled “t,ot,alllorizont,nl The calculabion methods are t’o bedeveloped through
radiation”. use of the rat,io
is the measured direct normal incidence radiation, Inn cos z
expressed in langleys/minut8e 13, 41. (1)
CALCULATION METHODS
F=
I h m
E
H
0
L
li=
.87
.8 6
.8 5
.84
.8 3
.82
.8 I
.80
.79
.f 8
.7 7
.7 6
.7 5
.74
.7 3
c
0
0 0
0
0
0 0 0
0 O 0
/:
0
0
0
0
0
0 ,I .2 .3 .4 .5 .6 -7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
I hm
FIGWEE I.-Plot of the ratio (1“. cos a /I h m nraiust L . The straight line, fltted by eyc, gfves equntlon (0.
&BBUAlZY 1954 MONTHLY WEATHER REVIEW 45
Kimball [7] has evaluated this ratio as a function of solar
altitude, but for the present purposes we shall first desig-
nate it as Fh and empirically evaluate it as a linear func-
tion of I h m to be used in computing Inc. Next, we shall
designate the ratio as F, and evaluate it as a linear func-
tion of I ,, to be used in computing I h c . Thus, the
factors Fh and F, are the critical quantities for the cal-
dation methods. In terms of Fh and F,, the calculated
vdues I ,, and I h c are given respectively by
lnc= IhmFh/COS (2)
and
Ihnc= (Inn& cos z> /F n (3)
To obtain Fh for use in (2) we plot the ratio
(Inrn cos z )/I h m against the measured total horizontal radi-
ation I h m (see fig. 1). Drawing a line of best fit as deter-
mined visually we obtain a linear equation,
Fh=O.1I*m+O.713 (4)
having substituted Fh for (Inm cos z >/I h m in accordance
with (1).
In a similar manner we obtain F, for use in (3) by
plotting the same ratio against measured normal incidence
radiation I,, (fig. 2 ). Drawing a line of best fit as deter-
mined by eye, we find
Fn=O.275Inm+O.4475 (5 )
h d y , by definition of terms, Dhc may be calculated from
Dhc=Ihnr-Inm COS z (6)
RESULTS
The Blue Hill data from whichfigures 1 and 2 and
equations (4) and (5) were derived are presented in table
1, The resdts of computations of I,,, I h c , and Dhc are
also given in table 1 and are compared with the measured
values Inm, I,,, and Dhm, respectively. As an example to
illustrate the methods described in the preceding section,
the computations for January 17, 1950 are given step by
step at the foot of table 1.
While the percentage differences between the measured
snd calculated diffuse radiation are rather large, the aver-
crge difTerence in langleys/minute is relatively small,
being of the order of 0.07 ly./min. In every case, the
calculated value is larger than the measured.
The resd ts for InC and I h c show promise as evidenced by
&e 8mall probable errors of the values of calculated from
-
bo (1." co8 m /I b m , are not strictly compatible. This Inconsistency may be avoided
IEDITOEIAL NOTE: It is apparent that equations (4) and (5), with F b and F. replaced
bymnntructing a single scatter diagram on which values of I h m are plotted against the
wduata values 1." and cos Z. Equally-spsoed straight isopleths can then be fitted
tothe fleldof Ir., and the multlng chart used to determine either I b . or I.. with an
Mamy on tbe Blue Hill developmental data comparable to that obtained by Hand.
measured which average less than f2.5 percent based
on the formula
p.e.=0.6745 J""- n- 1
Obviously the chief cause of the close relationship between
the ratios of the two types of radiation values is the
secant-effect. Nevertheless, when used with caution we
believe this method should prove useful for rough deter-'
minations. However, discretion should be exercised in'
applying these methods to other areas for unless at-
.85 -
.84 -
.83 -
.02 -
N
v)
.81 - S E
E E Hi
H .80 -
L
0
.79 -
.78 -
.77 -
.76 -
.75 -
O 0
0
0 O
fOO
0
O0
.74r/0
.73 1.0 1.1 1.2 1.3 1.4 1.5 1.6
46 MONTHLY WEATHER REVIEW mRUABY 1854
mospheric conditions approximate those a t Blue Hill,
serious errors will result. In particular, no attempt should
be made to use these methods over large industrial areas
t~ the diffuse radiation then is too large a percentage of
the total radiation [SI.
SOURCES OF ERROR
In the interpretation of the results for Blue Hill or in
the application of the methods to data from other stations:
the following sources of instrumental and observational
errors should be kept in mind in addition to errors resulting
from changes in atmospheric conditions that the methods
(1) The occulting ring cuts off approximately 5 percent
of the sky radiation in addition to shading the
instrument from the direct rays of the sun [6].
(2) The area adjacent to the sun is the brightest portion
of the sky 191.
(3) Errors of Eppley pyrheliometers, while not of great
magnitude, include internal reflections from the inner
portion of the hemispherical bulb, caustics and
striae caused by the glass cover, and variations in
efficiency of the thermopile with fluctuations in
temperature [lo]. And obviously the shaded diffuse
pyrheliometer remains cooler than a freely exposed
d o account: instrument when the sun is shining.
TABLB l.-Obsetved and computed solar radiation values at Blue Hill Observatory, Milton, Mass.
- -
10
B X
=
16
$" 2
f/: .=
+2 +2 -6 -1
t; -3
-4 -3
-4 0 0 0
"1
-3
-2
0
+:
+: +: +:
"1
+2 +1 +3
+2
-1
-1 -i
0 0
-
16
23
I-@
28
+. 011
+. 012
-. 041
+. 008 -. 008
-. 025
-. 016
-. 058 -. 023
-. 055
+. 005 -.007
+. 004
-. 020
-. 041
+. rn -. 020
+. 011
+. 005
+. 030
+. 012
+. 042
+. 051
-. 002
+. 043 +. 022
+. 008 +. 035
-. 004
-. 009
-. 010 -. 007
-. 001 -004
+. 006
+. 008 -. 004
+. 005 -. 007
-. 016 -. 026
-. 004
-. 018 -. 009
+. 033
+. 026
+. 026 +.a19
+. 040
+. 053 0
+. 048
+. 041
+. lloR
+. 015 -.014
+. 019 -. 008
+. 011
+. 004
+. 021
-. 00s +. 004
+. 003
+. 001
-. 017
0
+. a9
1 12
3
4s EB
14
- 0
g2
:2 +G
0.537
.815 .728
.718 .466 .a15 .616 .so5 1.408 1.436 1.401 1.315 1.464
1.231 1.494
1.374 1.284 1.483 1.507 1.515 1.642 .996 1. m 1.603 1.202 1.234 1.471 1.046 1.265 1.316
1.263
1.070 1.019
.951 .866 .794 .626
.524 .676
.663
.473
.963
.774
.SI4 1.324
1.457 1.092
1.382 1.394 1.255 1.494 1.245
1.266 .8R2
1.614 1.440 1.321
.896 .937
.674 .864
.828
.753 .632
.e11 .6ei
.689
. 71s
Date
70. 1 61.1 61.4 64.6
60.6 73.0
60.7 67.8
34.8 35.1 28.6 40.0 32.4 29.4 42.3 36.3 39.8 27.6 23.2
24.7 27.9
52.3 28.0
37.0 19.8
40.2 25.6 48.8 38.4 39.7 41.7
49.7 51.7
53.7 57.3 60.3 65.4 63.1
69.2
1.249 1.150 1.432 1.381 1.272 1.368 1.324
1.451 1.345
1.518 1.272 1.454 1. K 3 1.462 1.374 1.437 1.355 1 .8 7
1.337
1.424 1.451
1.321 1.427 1.434 1.150
1.324 1.301
1.262 1.299 1.446 1.416
1.358 1.343
1.288 1.284 1.283 1. I48
1.112 1.1R5
1.284 1.142 1.408 1.494 1.334 1.475 1.393 1.455 1.462 1.452 1.376 1.421 1.332 1.266 1.324 1.400 1.373 1.421
1.38: 1. 27l 1.316 1.377 1.35c 1.372 1.346
1.286 1.183
1.35E
I. 27a
0.526 .716 .856 .724
,840 .458
.632
.828
1.466 1.491 1.408
1.460 1.310
1.272 1.514
1.368 1.304 1.472 1. 502
1. m2 1.532
.984 1.458 1.552
1.212 1.428 1.040 1.230 1.320 1.272 1.026 1.080 .952 .870 .794 .620
.518 .680
1.204
.670 .468 .8M) .9m .SIR 1.333 1.110 1.490 1.356 1.368 1.236 1.4.54 1. I92
1.218
.a62
1.476 1.399 1.316 .sa1 .951
.856 .SI7 .714 .732
.Ma .Ma .@a
.a70
. ma
0.426 .556
.592 .685
.672 .372
,600 ,658 1.191 1.242 1.117 1.114 1.252
1.016 1.265
1.158 1.064 1.229 1.229
1.294 1.282
.808 1.260 1.349 .918 .994 1.194 .831 1.018 1. I12 1.057
.878 .832
.763 .694 .636 .478 .ti14 .395
.530 .360 .646
.827 .663 1.130 .go7 1.235 1.174 1.181 1.037 1.252 1.013
1.027 .686
1.260 1.188 1.107 .714 .778
.646
.689
.588 .w
.517 .621
.46Q .513
.666
0.808
.800
,776
.818
.so0
.812
.791
.SI2 .795
.a 3 ,793 ,850 ,858 ,836 .799 ,846 .SI6 .835
.818
.856 ,837
.a21 .864 .869 .762
.836 .820
.799
.a28 .842 .831 .SI1 .813 .a01 .798 .so1 .771
.766 .756
.791 .769
.844 .so7
.a10
.848
.SI7 .829
.863
.E66
.839 .861
. R50
.796 .843
.a54 .849
* 842
.a10
.SI6 .792 .833 .837 .823 .848 .so8
.m
.777
.a21
0.7656
.7986 .7846
.7854 .7588 .7970 .7762 .7968 .8596 .8621 .8538
.8440 .85W .8644
.8402 ,8498 .8434
. 8m2 ,8632 .8662
,8642 ,8114 .8588
,8682 .8334 .8342 .8558 .8170 .a360 .8450 .8402
.a210
.8156
.8082
.m .m 4
.77.50
.7646 .7810
.7 m .7598
.SI10 .7930
.7948
.8463 .8240 .a620
.8486
.8498 .8366 .8584
. e322 .7992 .8348 .8605 .85%
.8445 .so11 .SO81
.7786 .m
.7947 .7844 .7862
.7770
.7738 . 7790
.7818
1.183
1.428 1.162
1.326 1.189 1.364 1.298
1.535 1.346
1.571 1.369 1.443 1.485
1.445 1.502
1.442 1.432 1.429 1.411
1.438
1.502
1.306 1.418 1.432 1.256
1.355 1.324
1.290 1.312 1.450 1.431 1.350 1.371 1.300 1.288 1.270 1.164
1.111 1.174
1.265 1.127 1.383 1.436 1.308 1.473 1.405 1.512 1.433 1.430 1.454 1.416 1.305 1.272 1.310 1.410 1.379 1.425
1.371 1.256
1.230 1.285
1.307 1.287 1.272 1.297
1.235 1.186
1.292
-0. OM +. 012
-. 004
-. 056
-. OR3 -. 004
-. 027
+. 001
+. 084
+. 053
+. 097
+. 002 --.on
+. 071 +. o c a
+. 005
+. 047
+. 042
+. 074
+. 014 +. 051
--.a15
-. 009
+. 106 -. 002
+. 031 +. 023
+. 028
+. 013
+. 005
+. 015
+-. 007
+. 013
+. 012
+. 004
+-. 009 -. 013
-t-. 039
-. 001
-. nrcl -. 015
-. 025
-. 058
-. 026
-. 002
+. 012
+. 057
-. 029
-.on +. 078
-. 005
-.on +. 006
+. 010 -. 014
+. 006
+. 0 0 4
-. 014 -. 014
+. 013
-. 086
-. 071
-. 063
-. 100
-. 048
+. 003
-. 050
-. 088
+:
-5
-4 -7
-2
0
+6
0
+3 +8 -1
0
"3
+3
+4
-1 0
+9
+2
+2 +2
+I
+I
+x
+:
2:
+:
+;
+:
+I
-1
--I
-1 -2 -4 -2
0
+I
2;
7;
--I
E -1
+t
+;
C
-1 -1
-€
-e "5
-4
0 -4
"6
0.101
.171 .I60
.os6
.132
.168 .I32
.275 .170
,249 .291 .I96 .208 .249 .256
.210 .a0
.243
.273
.218 .260
.I76 .198 ,203 .286 .218 .234 .209 .212 .208 .215
.202 .I94
.189 .I76 .158 .I42
.121 .166
.140 .lo8 .154
.I53 .155
. a03 .255
.187 .182
.IS .a1 .I79 .17E .I91 .216 .211
.20E .1 R i .I76
.lo6 .I81
.133 .I% .I 1 1
.I23
.118 .I47
.I23
.m3
0.064
.I12 .lo8
.I04 .OM .I45 .112
.210 .lo7
.210
,2 0 0
.OS5 .I04 .115 .116 .I04
.I23 .115 .I78
.loo
.098
.IO0 .lo5
.I13 .232
.I16 .118
.I16 .I14 .078 .OS7
.om .I27 138
.IO2 102
M
M M
0.7910
.8413 .7638
.7973
.8273
.8237 .8ll6 .SI74 .8465
.8650
.7973 .8474 .a553
.8254 .8468
.a127 .884 .8289 .81,52 .8465 .8391 .8108 .8399 .8419 .7638 .SO52 .8116 .7946 .8047 .8449 .8369
.8210 .SI68
.SO17 .SO06 .m 3 .7632
.7533 ,7596
.SO06 .7616
.8584 .8347
.SI44 .8531
.8306 .a 7 6
.&I496 .8468 .8259 ,8383 .SI38 .7956
.a25
.a116
.a251
.8383 .7968 .82M
. m 4 .7973
.8%2 .a188
.8248
.SI74
.so09
.7728
.E210
b p t . 7 ."""""".
Sept. 17 ____________. Sept. 17 ____________. &pt. 17 ____________. I
Oct. 5 """"""". Oct. 5 """"""".
Nov. 6 _____________. OCt. 31 ____
~
4-1
0
-1
+a
--I
2; -2
-1
0
-a "2 +2 +2
+a +3
+4 +3
+2 -1
+2
-1
+I +I
+:
+:
2:
+: 0
Nov. 6 Nov. 13 Nov. 13
65.6 71.6 62.7 56.4 60.2 40.0 49. 4 31.9 36.6 35. 6 41.1 28.2 40.5 67.2 39.1 25.8 30.1 38.8 65.8 55.9 57.2 66.5 Bo. 2
64.2 63.1 67.4 64.3 67. 8 66.4
.120 .098 .IO1
. lo6 .I13 .I05
. I07 .I62
.I10 .118 .I30 .133 .111 .143 .I52
.1m
M152 M .128
.OB5
.112
.OS7 .os1 .OS5
.080 .IO2 .077
.n o
IFEBBUABY 1954 MONTHLY WEA4THER REVIEW
TABLE 1.-Observed and computed solar radiation values at Blue Hill Observatory, Milton, Mass.”Continued
5 1 6 /7
9 13
6
d
48
1.112
1.275 1.136
1.393 1.352 1.310 1.409 1.449 1.428 1.346 1.309 1.215 1.380 1.310 1.340 1.358 1.181 1.277 1.450 1.428 1.460 1.482 1.501 1.408 1.477
.w4
,582 ,534 ,730 ,722 ,616
,824 ,970 .894 .668
1.142 .812
1.130 1.058 1.238 1.380 1.064
1.372 1.200
1.199 1.328 1.480 1.532 1.441) 1.360
.7634 .7712 .7764
.78m .7852 .7746 .7954 .8100 .SO24 .7798 .7942 .8272 .8260 .8188
.8368
.a 9 4 .8510
.8330 .a502
.I3828
.a58
.8662 .8610
.8579 .8490
+o”
-5 -3 -2 -4
-2 -3
0 -3 -1
2;
2:
+3
-1
+5
+8
-4 -1 0
0
+4 -1
.1n .I34 .lo2 .139 .144 .117 .147 .170 .174 .129 .159 .242 .191 .181 .a 4 .xi4 .257 .229 .197 .161 .195 .207 .205 .259 .I91
.7533 .7599 .7981
.8193
. as0
.So78
.am .a 0 2
.So76 .8177
.7816
. So78
.8160 .8210
.7723 .m 7 .8463 .8405 .8490 .8551 .m 3 .8347 .E637
. am
. 8270
.m .689 .541
.705 .618 .810 .945
.659 .867
1.152 .m
1.136
1.230 1.085
1.045 1.360
1.216 1.388 1.235 1.336 1.489 1.542 1.426 1.369
. nl
-. 004
+. 007
+. 007
-. 019
-. 017
+. 002
-. 014
-. 025
-. 037
-. 004 -. 009
+. 006 +. 010
+. 027
-. oil8
-.019 -.om
+. 016
+. 016
+. 036
+. 007
+. 009
+. 010
+. 009 -. 023
-1
+1 +1 -3 -2
0 -2 -3 -4
-1
+1
0
+1 +3 -1
-a -2
+1 +1
+1 +1
+1
+a
2;
.377
.448 .432 .591 .578 ,499 ,677
I720
,800
,539
.653
.m .939 .877 1.004 1.116 .807 .971 1.175 1.038 1.133 1.273 1.327 1.190 1.169
.748 .770
.Bo9 .m .800 .810 .821 .824 .SO6
.m4 .m7
.788 ,831 ,828 .811 .809 .758
.E56 . m9
.866 .853
.866 ,860
.E21 .859
+. 024
+. 003
-. 067
-. 040
-. 025
-. 058
-. 044
-. 006 -. 026
-. 046
-. 016
+. 060
-. 009
+. 043 -. 015
+. 070
+. 095
+. 038
-. 010
-. 055
+. 002 -. 013
+. 001
+. 063
-. 018
.m .113 .073 .OB7
.os3 .079 .OB7
.091 .091
.OB7 .112 .172
.om .179 .124
.121 .154
.124 .1n ,106 .112 .la .096
.094 .090
1.136 1.139 1.208 1.353 1.327 1.252 1.366
1.422 1.423
1.301 1.284 1.275 1.371 1.295 1.383 1.428 1.276 1.315 1.440 1.374 1.447 1.484 1.502 1.471 1.459
Jan. 11 ____._________
Feb. 12 __....________
64.7
60.1 Feb. 13 ______________
66.4 Feb. 12 ______________
59.7 Feb. 12 ._____________
56.5 Feb. 12 ._____._______
61.3 Feb. 12 ___. ~
_________
67.6
Am. 4 ______._______.I 42.2 Apr. Apr. Apr.
Apr. Apr.
Am. Apr.
47.1 48.0 41.5 34. 7 46.9 40.5 35.9
Sample computation for Jan. 17,1950
Glvm: Z=7O.l0, cos 2=0.34038 Z.,=1.249ly/min In--0.526 ly/mln Dnm=0.064 ly/min Step 1’ From equation (4) ~~~=0.1(0.526)+0.713=17666
Step 2: From equation (2) Z..=(0.526)(.7~6)/0.3~8=l.ls3 Step 3: Dlfference=Z..-Z.~=l.I~~- .1.249= -0.066
step 4: Percent ~e r e n c e =+~~~~~=-~
(4) Errors arising from instrumental recording. In this
particular case, the recording pyrheliometer used
for diffuse radiation lacks the accuracy of t’he re-
corder for measuring total horizontal radiation.
Differences in the same direction and of approximately
the same magnitude were found by Dr. C. F. Brooks
and Miss S. H. Wollaston in an unpublished study.
(5) The human error ordinarily is an important factor,
but in this case we have attempted to minimize this
effect by double-checking int,egration of records and
the various calculations.
REFERENCES
1. I. F. Hand, Pyrheliometers and PyrheliometricMeus-
urements, U. S. Weather Bureau, Washington, D. C.,
1946, 55 pp.
2. H. H. Kimball and H. E. Hobbs, “A New Form of
Thermoelectric Recording Pyrheliometer,” Monthly
WeatherReview, vol.51, No. 5, May 1923, pp.
3. H. H. Kimball, “Turbidity and Water Vapor Deter-
minations from Solar Radiation Measurements at
Blue Hill and Relations to Air-Mass Types,”
Monthly Weather Review, vol. 62, No. 9, Sept. 1934,
239-242.
pp. 330-333.
4. I. F. Hand, “Review of United States Weather
Bureau Solar Radiation Investigations,” Monthly
WeatherReview, vol.65,No.12,Dec.1937,pp.
415441.
5 . Charles G. Abbot, Annals of the Astrophysical Obsem
d o r y of the Smithsonian Institution, vol. 5, Wash-
ington 1932, p. 136.
6. I. F. Hand and F. A. Wollaston, “Measurements of
Diffuse Solar Radiation a t Blue Hill Observatory,”
U. S. Weather Bureau, Technical Paper No.18,
Washington, D. C., May 1952, 19 pp.
7. H. H. Kimball, “Variations in the Total and Luminous
Solar Radiations with Geographical Position in the
United States,” MonthlyWeatherReview, vol. 47,
No. 11, Nov. 1919,p.777.
8. I. F. Hand, “Atmospheric Contamination over Boston,
Massachusetts,” Bulletin of the A m d n Meteor-
ological Society, vol.30, No. 7,Sept.1949, pp.
9. H. H. Kimball and I. F. Hand, “Daylight Illumina-
tion on Horizontal, Vertical, and Sloping Surfaces,”
MonthlyWeatherRewiew, vol. 50, NO. 12, Dec.
1922, pp. 615-628.
10. T. H. MacDonald, “Some Characteristics of t,he
Eppley Pyrheliometer,” Monthly Weather Review,
V O ~. 79, NO. 8, Aug. 1951, pp. 153-159.
252-254.