November 1970 823
UDC 551.521.32(968.2)
RADIATION MEASUREMENTS OVER THE EQUATORIAL CENTRAL PACIFIC
STEPHEN K. COX* and STEFAN L. HASTENRATH
The University of Wisconsin, Madison, Wis.
ABSTRACT
During the Line Islands Experiment in spring 1967, surface shortwave and net radiation was continuously re-
corded a t Palmyra, and Suomi-Kuhn infrared radiationsondes were released daily at the islands of Palmyra, (5’53’
N., 162’05’ W.) and Christmas (1’59’ N., 157’22’ W.) as part of an extensive surface and upper air observation pro-
gram. Data are evaluated in terms of the diurnal march of the surface radiation balance and the radiation budget
characteristics of the troposphere-ocean system. These direct measurements indicate a substantially larger surface
net radiation than is expected from available climatic mean charts based on empirical formulas. Implications for the
tropical heat budget are pointed out.
I. INTRODUCTION
It is generally recognized that the radiation balance of
the Tropics plays a key role in the global heat budget. Net
radiation at the surface enters into considerations of the
sensible and latent heat exchange at the sea-air interface
and the poleward heat transport within the ocean. How-
ever, measurements of the shortwave and longwave radia-
tion fluxes at the surface are extremely scarce, particularly
in lower latitudes. Instead, radiation is usually computed
from available information on cloudiness, applying empir-
ical formulas, the validity of which has been questioned in
recent years (e.g., Ashburn 1963, 1966).
The importance of direct measurements over the tropical
oceans will therefore be appreciated. Just such measure-
ments of the surface radiation budget, along with an
extensive program of surface and upper air observations‘
were performed during the Line Islands Experiment (LIE)
in spring 1967. Results are summarized in the present
paper.
2. INSTRUMENTATION AND OBSERVATION
PROGRAM
A surface radiation instrument site was in operation on
Palmyra Island (5’53’ N., 162’05’ W.) during most of the
daytime and some nighttime hours for the period Mar. 24 to
Apr. 19, 1967. The total downward shortwave irradiance,
SW 1 , was measured with a 50-junction thermopile Eppley
pyranometer.’ The net irradiance, - Ro, mas measured
with a Suomi-Islitzer ventilated net radiometer (Suomi
et al. 1954).
Both radiation instruments were located on a pier piling
approximately 15 m from shore in Palmyra Lagoon. The
Eppley pyranometer was mounted on the top of the piling
and was approximately 3 m above the water surface. The
ventilated radiometer was mounted at the end of a 3-m
catwalk approximately 2j4 m above the lagoon surface.
Geometrical obscuration of the upper hemisphere into
‘Present affiliation, Colorado State University, Fort Collins
1 Mention of commercial products does not constitute an endorsement.
which the sensors looked was less than 0.2 steradian (sr)
out of the total 2 sr and was always lower than 0.17 radians
(rad) above the horizontal plane defined by the sensors’
surf ace.
Data fiom the two sensors, in addition to a zero point,
were recorded on a IO-millivolt (mV) scale sequentially for
intervals of 20 sec each. The normal mode of operation
was to sample the radiometers for a period of 5 min each
half hour. However, there were periods during the experi-
ment where both more and less frequent sampling rates
were maintained. Shortwave and net radiation measure-
ments were not made at exactly the same time, but lag each
other by 20 to 40 sec.
Separation of data into upward and downward short-
wave (SWT and SWl) and infrared longwave (LWT and
LW 1) components was accomplished from the relation
Before solving equation (1) for LWl , we must make
several assumptions involving the SW T and LW 1 terms.
For determining SWT over a plane water surface, the
SWl term must be partitioned into direct and diffuse
components. The ratios as a function of solar height given
in the “Smithsonian Meteorological Tables” (List 1968,
table 155) were used to divide SW 1 into SW 1 (DlR) and
SW 1 (DIF). Values of the surface reflectivity, p, of salt
water as a function of angle of incidence were also adopted
from List’s (1968) table 155. If we assume the SW 1 (DIF)
is is0 tropic, an integrated water reflectivity, p(DIF), over
all angles is approximately 17 percent. The p(D1R) is
directly given in List’s (1968) table 155. Thus we find
With a mean surface temperature of the lagoon of
28.OoC and assuming an emissivity of the water surface
of 1.0, Stefan-Boltzmann’s law yields LW 1 =0.6696 ly
min-’.
824 MONTHLY WEATHER REVIEW vol. 98, No. 11
CT - a ...................
* .-
CL
With the above assumptions, only LW 1 in equation (2)
remains unknown. Rearranging equation (1) and sub-
stituting from equation (2), we have
LW 1 = -Bo- p(D1R) X SW 1 (DIR) - p(D IF)
XSW 1 (DIF) +SW 1 +LW T . (3 1
Equation (3) was applied to the average value of each
set of data points grouped around the hour and half hour.
By taking a mean value, the data were smoothed, and the
inconsistencies arising from the fact that the two instru-
ments were not sampled simultaneously were minimized.
When the surface data were first analyzed, LWl de-
duced from the net radiometer appeared consistently
smaller than LWL measured at the surface by the radi-
ationsonde a t the same time. Further investigation showed
that a numerical radiation divergence calculation (Kuhn
1962) for LW1 agreed well with the radiationsonde for
a clear atmosphere, while the surface station tended to
give systematically lower values of LW 1 than theory
predicts for a clear atmosphere. The theoretical compu-
tation for a clear gaseous atmosphere should represent
a minimum value, since the presence of any aerosol
emitters in the atmosphere mould increase LW 1. Based
upon the above evidence, LWl has been adjusted by
adding 4-43 ly day-' to each value, and a corresponding
adjustment was also applied to the net irradiance, -RP.
The 43 ly day-' increment mas derived from four simul-
taneous readings of the ventilated net radiometer and
radiationsondes. All four comparisons yielded an incre-
ment within 5 ly day-' of the 43 ly day-' value.
The pyranorneter data were not always available for
the entire day, and one-half to one-hour periods after
srinrise and before sunset were commonly missing. For
quoting daily values, these data-void periods were filled
in by interpolating between zero, denoting before sun-
rise and after sunset, and the first recorded data points.
The shape of this interpolated curve was modeled from a
cosine curve depicting incident shortwave radiation at
the top of the atmosphere as a function of time.
Suomi-Kuhu balloon-borne radiationsonde (Snomi 1958)
ascents were made nightly from Christmas Island and
Palmyra rawinsonde stations from March 21 to April 20.
These ascents were made a t approximately 2000 LST and
yielded values of LWT and LWj as a function of height.
Preflight baseline or calibration checks of the instruments
were performed in the maimer outlined by Cox et al. (1968)
t o insure maximum confidence in the measurements.
3. SURFACE BUDGET AT PALMYRA
DIURNAL MARCH
The diurnal march of the various radiative fluxes at the
surface, as obtained by averaging over the entire period
(Mar. 24, 25, 30, and Apr. 3 through l S , 1967) is repre-
sentcd in figure 1. Three-hour observations of low, mid-
t ::::::::;::::::::::::::i
r5 LWSwIt -
Wf w, ............
Lw ............
-05 I
-+to
-+05
0.0
1-05
FIGURE 1.-Diurnal march of the surface radiation budget at
Palmyra, all days (Mar. 24, 2Fj, 30 and Apr. 3 through 18, 1967).
Downward-directed shortwavc radiation, SW 1, upward-directed
shortwave radiation, SW , downward-directed longwave radia-
tion, LW 1 , upward-directed longwave radiation, LW 1, net
radiation, SWLW 1 ; in cal cm-2 min-1. CL low clouds, CM
middle clouds, C, high clouds; CT total opaque cloudiness, in
tenths.
dle, and high clouds and hourly observations of total
opaque cloudiness are also reproduced in figure 1.
For comparison, the surface radiation budget during
the days with an average daily opaque cloudiness QT10.4
(April 3, 4, 10 through 14, and 18) and during the days
with an average daily opaque cloudiness CT>0.7 (March
30 and April S and 9) is plotted in figures 2 and 3.
Net radiation -no shows a pronounced dzerence be-
tween clear and cloudy days, its diurnal march being
largely dominated by that of SWJ. The SWT for the
entire period reaches weak maxima after sunrise and be-
fore sunset, as a consequence of the decrease of the effective
albedo with solar height. The diurnal march is least
pronounced on cloudy days, as can be expected from the
smaller contribution of direct solar radiation.
The LWT entered in figures 1 through 3 corresponds to
a constant mater surface temperature of Palmyra Lagoon
of 28.0"C. As explained in sect,ion 2, LWI was obtained
November 1970 Stephen K. Cox and Stefan L. Hastenrath 825
J .._,___. ..
I ! I I :::::!: ::::::: :::: ::I 1 :::::::::::::::::::::::1
l+ 1.5
.....
..............
1-
05
..
0 2 4 6 8 IO 12 14 16 18 20 22 24
LST
I
,,,,, I ,I ,,,,,,,,,,,,,,,,,
-05
FIGURE 2.-Diurnal march of the surface radiation budget a t
Palmyra during clear days, C ~5 0 .4 (April 3, 4, 10 through 14,
and 18). Symbols used as in figure 1.
as a residual from equation (1). Figures 1 through 3 in-
dicate a pronounced diurnal march, with lowest values of
LW] during the midday hours. The net-radiometer used
is not a precision instrument, and the possibility that the
measurement error might have a diurnal march cannot
be completely ruled out. However, in qualitative terms,
the diurnal march of LW 1 , dispIayed by figures 1 through
3, seems consistent with the cloudiness conditions. Low
and middle clouds show a tendency to a decrease during
the midday hours. This could indeed account for a de-
crease in LW l. The marked effect of cloudiness on LW T
is further illustrated by a comparison of figures 2 and 3,
which indicate on clear days substantially smaller LWl
than on cloudy days.
MEAN RADIATIVE FLUXES
Values of radiation as averaged over the entire period
are listed in table 1. Components of the radiation budget
of the atmosphere, to be discussed in section 4, are also
included in table 1. For consistency, measurements by
radiationsondes only were used for longwave radiation.
The LW T s,c computed from Stefan-Boltzmann's law
corresponds t o a temperature of 27.5"C for Palmyra and
253°C for Christmas. From the available. airborne radio-
L W l t c
_-----_ __ ..............
- fl.0
-+05
-- 00
1-05
I I I I I I I I I I I I 4 I 1 1 1 ~1 1 1 1 1 1 1
0 2 4 6 8 10 12 14 16 18 20 22 24
LST
FIGURE 3.-Diurnal march of the surface radiation budget a t
Palmyra during cloudy days, CT>0.7 (March 30 and April 8
and 9). Symbols used as in figure 1.
TABLE 1.-Longwave (LW) and shortwave (SW) radiation budget of
ocean surface and atmosphere during the LIE, upward- and down-
ward-directed radiation at 100 mb, rad and rad 1 loo; infrared
radiative jlux divergence and solar radiation absorbed in the layer
1000 to 100 mb, respectively, [rad] ,$$; upward- and downward-direc-
led radiation at the surface, rad T rad 1 *fc; units, cal cm-2
min-1
Palmyra Christmas
LW sw LW sw
rad T IW 0.3126 0.1928 0.3653 0.1354
rad 1 IW .0490 ,6090 .0361 .6om
.2327 .09% ,2859 .m 7
.6647 .0324 ,6501 ,0261
,6338 .a90 .6068 .4100
metric measurements during the LIE, these sea-surface
temperatures are considered representative for the open
ocean in the two areas. It 1 d 1 be noticed that the assumed
effective radiation temperature at Palmyra differs from
that used in section 2. Assessment of the radiative flux
components for the surface measuring site a t Palmyra
Lagoon required the local surface temperature of the
lagoon, whereas we are here concerned with a radiation
budget representative of a larger area.
826 MONTHLY WEATHER REVIEW Vol. 98, No. 11
LWiT at the surface should be compared to the general
magnitude of values measured by Charnel1 (1967) near
the Hawaiian Islands (0.04 to 0.12 ly min-l) and values
obtained from Budyko’s (1963) charts (0.064 ly min-l).
Wyrtki (1965, 1966) computed the net longwave radiation
at the surface, I=LWlT, from the following empirical
formula presented by Budyko :
where u is the Stefan-Boltzmann constant, e emissivity,
T, and T, water surface temperature and air tempera-
ture, respectively, in degrees Kelvin, CT the fraction of
total cloudiness, and e water vapor pressure in millibars.
The values of the coefficients adopted by Wyrtki are
a1=0.39, a2=0.05, and U3=0.5. After using temperature,
humidity, and cloudiness values for Pdmyra during the
LIE, equation (4) yields a value for the net longwave
radiation a t the surface of about 0.074 cal cm-2min-l.
Table 1 shows for Palmyra a value of 0.0309 from the
evening radiationsondes only. Accohnting for the daily
march of LW 1 as obtained from the surface installation
yields a value of 0.0875 cal cm-2min-l for the averageof
all days and values of 0.0902 and 0.0778 for clear and
cloudy days, respectively (figs. 1 to 3).
The ratio of the daily sums of reflected to incoming
shortwave radiation corresponds to an effective albedo of
the sea surface of 6.5 percent, which agrees with earlier
estimates and values commonly used (Anderson 1952,
Houghton 1954, Hutchinson 1957, Bernhardt and Philipps
195S, and C016n 1963). Downward-directed shortwave
radia tion measured a t Palmyra is considerably larger than
expected from available climatic mean maps (Black 1956,
Beriihardt and Fhilipps 1958, and Budyko 1963), based
on empirical relationships, but seems compatible with the
findings of Quinn and Burt (1967). Wyrtki (1965, 1966)
computed the downward shortwave radiation at the sur-
face, I=SW 1, from the following empirical formula
I=& (I -a,C, --a2 x (7%) (5)
where the downward-directed shortwave radiation for
clear-sky conditions, Io, is taken from Budyko’s (1958)
table, and QT is total cloudiness. Wyrtki used a1=a2=0.3S.
After using the observed cloudiness (CT=0.49) at Palmyra
during the LIE, equation (5) yields a value of I=504 cal
ern-+ day-’, which is practically identical to the observed
value.
The net (shortwave plus longwave) radiation, -Bo,
turns out to be larger than available climatic mean esti-
mates (Budyko 1963 and Wyrtki 1965, 1966). In this
connection, it should be recalled that cloudiness during
the LIE seems to have been less than the average value
for this season of the year. Some implications of this result
will be discussed further below.
STATISTICAL RELATIONSHIPS
In view of the paucity of direct measurements, empirical
formulas have been widely used in the computation of
shortwave and longwave radiation fluxes a t the surface.
Direct measurements during the LIE invited an attempt
to test these statistical rels tionships.
A least-squares fit was performed on the following
expressions for longwave radiation:
I=alaT:, (6)
(7)
(8)
(9)
(10)
(11)
I= &(al + a&, (12)
I=uTt(ai+az&) (I f a s Q ~), (13)
I= alu Ta (1 + a2 6,) ,
I =a ~u T:(1+ azC,+a,Ciw+ a4C!) ,
I= UT: (al + azl O-”J e),
I= u T:(al +~4 0 -~3 ~) (1 +a4CT),
I= u T4,(al + a ~0 -~3 ~) (1 + u4CL+ a,CM+ a&,),
I= uT:(al + a2&) (1 +a3CL+ a4CM+a5QL), (14)
I= (a1 + aZCT)’ (16)
(16)
and
I= (a1 +azC,+ a3Ca.f+ a4Cd
where C,, CM, and C, denote fractions of low, middle, and
high cloudiness, respectively, and the other symbols are
used as previously. Expressions (6) through (16) were
fitted for I=LW 1 and I=LW M . For I=LWiT, equation
(4) and the following two equations were applied
additionally :
and
I= cuTk(a1 +az&) (1 -u,C‘~) (17)
I= mPW (al +a2&>, (W
assuming an emissivity of 1 .O.
Equation (9) for I=LWl? was proposed by hgstrom
(1916), and equation (12) is due to Brunt (1932). Bolz
and Falckenberg (1949) and Bolz and Fritz (1954))
applied equation (9) for I=’LW 1. Attempts at accounting
for the effect of cloudiness through expressions in the form
of equations (7), (lo), (11)’ (13)’ and (14) have been
reviewed by Budyko (1958).
Regarding I=SW 1, a least-squares fit was applied on
equation (5) and the following expressions
I=Io(al+uz~T+asC;) (19 1
I= Io( 1 - a1 6%). (20)
and
A clear-sky value 1,=0.482 ly min-’ for Palmyra in
March-April was adopted from Budyko’s (1958) table.
November 1970 Stephen K. Cox and Stefan L. Hastenrath 021
TABLE 2.-Least-squares $1 to daily means of downward-directed
shortwave radiation, SW 1, (cal cm-2 min-1); ai=coeficients in
equations (6), (19), and (90) with 96-percent conjidence limits in
parentheses; VR= variance of residuals after regression; df =degrees
of freedom.
Eq. no. a1 a2 a3 ar ar a6 VR df
5 0.240 0.516
(f. 318) (f. 456)
19 .am -.453 1.069
(f. 406) (fl. 511) (fl. 258)
20 .584
(*. 111)
0.003446 18
.a 7 0 17
.wm 19
Least-squares fitting for LWTJ and LWTJ was per-
formed on the daily totals (20 data points) and separately
on the individual half-hourly mean radiation fluxes
(66 data points). The number of half-hourly data points
available is limited by the 3-hr cloud observations.
Computations for SW 1 were performed on the daily data
only. Results are summarized in tables 2 through 6.
Table 2 for SWl shows equations (5) and (19), where
the square of total cloudiness is used, to be superior to
the more simple equation (20), which requires the same
basic information. This would support suggestions by
Budyko (1956) and Wyrtki (1965, 1966).
Table 3 for the daily values of LWl illustrates that,
for the uniform moisture conditions in the environment of
Palmyra, vapor pressure offers little information. Brunt’s
equation (12) and the extended versions (13) and (14)
are clearly to be preferred to Angstrom’s exponential
expression (9) and the corresponding equations (10) and
(1 1). This seems to be partly due to the small variation in
vapor pressure. I t is noticed that equations (9) through
(11) are not better than the simple equation (6). The most
critical information is cloudiness. Thus equation (7)
yields a drastic improvement upon (6). I n fact, the best
fit is provided by the simple equations (15) and (16)’
using cloudiness only.
Table 4 presents computations for the daily values of
LW T i . Vapor pressure seems to have little information
value. Angstrom’s expression (9) and equations (10) and
(11) are even less satisfactory than Brunt’s equation (12)
and its versions (13) and (14). Contrary to LWI (table 3),
air temperature rather than cloudiness is the critical
information. Thus equations (7) and (8) yield no improve-
ment upon (6). Similarly, (10) and (11) and (13) and (14)
give a poorer fit than (9) and (12)’ respectively. The least-
squares fit is poorest for equation (4)’ with somewhat
better results for the simpler versions (17) and (18).
Equations (15) and (16) based on cloudiness only are
comparatively less successful than for LWI, and by far
the best fit for LW is provided by the simple expression
(6), using air temperature only.
The relative merit of the various formulas in the least-
squares fit for half-hourly values of LW J and LWTJ
differs somewhat from the daily values as a consequence
of the greatly increased number of degrees of freedom.
Results for the half-hourly values of LWl are sum-
marized in table 5. The variance of residuals obtained for
equations (6), (9)’ and (12) suggests that vapor pressure
is of subordinate importance. Brunt’s equation (12) and
equations (13) and (14) are preferable to hgstrom’s
equation (9) and the corresponding expressions (10) and
(11). With a relatively large number of degrees of freedom
available, the added cloud information in equations (lo),
(11), (13), and (14) provides an improvement upon equa-
TABLE 3.-Least-squares Jit to daily means of downward-directed longwave radiation, LW , (cal cm--2 min-l); ai=coeficients in equations (6)
through (16) with 96-percent conjidence limits in parentheses; VR=variance of residuals after regression; df = degrees of freedom.
Ea. no. a1 a2 aa ar as a1 VR df
6
7
8
9
10
11
12
13
14
16
16
0.879
(*. 134)
.a1
(*. 331)
.869
(*. 048)
.298
(f77. Mlo)
.138
e437 1
.176
(f4M2 1
.3!m
(f. 726)
.577
(*. 899)
.760
(fl. 320)
.677
(It. 021)
.690
(*. 030)
-0.029
(f. 079)
.026
(A 146)
.364
(*70.860)
.600
(3431 )
.644
(*4026 )
.117
(f. 153)
.060
(*. 196)
.m (*. 286)
.017
(*. 040)
.Oll
(*. 077)
0. w 1
(*. 140)
-. 009
(ztl. 140)
-. 004
(*Z w -. 001
(2%. 988)
-. 044
(*. loo)
-. 014
(zt. 202)
.M6
(*. 082)
-0.066
(*. 127)
-. 045
(*. 106)
-. 015
(f. 233)
-. 076
(f. 163)
-. 042
(*. 070)
-0.076 -0.060
(*. 180) (*. 120)
.059
(zt. 152)
0. a00400
.000321
.000360
.Ooo398
. ooo4w
. a00411
.000374
.OW78
.M)(y(84
.000321
.000319
19
18
16
17
16
14
18
17
15
18
16
,
406-039 0 - 70 - 5
828 MONTHLY WE ATH E R REV1 E W vel. 98, No. 11
TABLE 4.-Least-squares fit to daily means of net longwave radiation, LW#, (cal cmWs min-l); ai=coeficients in equations (6) through (If,), (4, (17), and (18) with 95-percent confidence limits in parentheses; VR=variance of residuals after regression; df =degrees of freedom.
6
7
8
9
10
11
12
13
14
15
16
4
17
18
0.126
(zt. 013)
.137
(*. 032)
.117
(f. 046)
.E 6
(*. 013)
.137
(*. 034)
.117
(f. 059)
.405
(3 ~. 665)
.352
(*. 851)
.I53
(f l . 061)
.093
(f. 021)
. as0
(*. 030)
.450
(*. 910)
.330
(*. 831)
.436
(f. 665)
-0.157
(*. 406)
.190
(*l. 051)
97.570
(13.717XIOs)
103.3
(f3.779XlOs)
(f3.802X109
8.831
-. 059
(*. 141)
-. 047
(i. 185)
-. 008
(f. 230)
-. 017
(f .4 0
.O l l
(*. on)
-. 068
(+. 195)
-. 042
(*. 178)
.066
(+. 140)
-0.439
(el. 092)
4.181
(f3.717X108)
4.773
(f3.779XlOS)
.782
(13. os2xl@3)
.083
(*. 581)
.n1
(fl. 468)
-. 035
(fO. 81)
.327
(f. 465)
(f. 462)
.131
0.545
(fl. 055)
-. 157
(*. 432)
.190
(i l . 124)
-. 451
(*l. 251)
.042
(It 071)
-0.439
(fl. 167)
.529
(ztl. 183)
5.545
(*l. 128)
0. oo0309
,000317
.000316
.oo0345
.000367
.ow361
.000314
.m1
.m 7
.ow321
. 000319
,000372
.ooo331
. ow318
19
18
18
17
16
14
18
17
15
18
16
17
17
18
TABLE 5.-Least-squares f i t to half-hourly means of downward-directed longwave radiation, LW 1, (cal em-2min-1); ai= coeficients i n equations
(6) through (16) with 96-percent confidence limits in parentheses; \‘R=variance of residuals after regression; df= degrees of freedom.
Eq. no. a1 a2 a: a4 as ak VR df
6
7
8
9
10
11
12
la
14
15
16
0.863
(f. 020)
.824
(*. 046)
.834
(*.
.417
(3~7.242)
.470
(*4.632)
.323
(f5.735)
1.167
(*. 021)
1.271
(*. w
(f. 817)
.w2
(*. 028)
.w 7
(*. W)
1.740
0.063
(*. 095)
.063
(*. 112)
.614
(f6.778)
.658
(f3.221)
(f2.163)
-. 066
(*. 150)
-. 063
(*. 147)
-. 190
(*. 171)
.019
(*. 047)
.017
(*. 056)
1.245
0.051
(*. 124)
.007
(*. 113)
.012
(f. 167)
.017
(f. 185)
.079
(k. loo)
.w (*. 111)
.025
(*. w
-0. w3
(*.
.079
(*. 102)
.a 5
(*. 111)
. 054
(*. 120)
-. 019
(*. 049)
0.054
(*. 122)
-. 082
kt. 097)
-0. a32
(*. loo)
0.003002
.002962
.002967
.@I3059
.m 7 9
.oo2832
.m o l 2
.m1
.002784
. OM548
.002553
66
64
62
63
62
GO
64
63
61
64
62
November 1970 Stephen K. Cox and Stefan L. Hastenrath 829
TABLE 6.-Least squares fit to half-hourly means of net longwave radiation, LW#, (ea1 cm-2 min-1); ai=coeficients in equations (6)
through (16), (4 ), (17), and (18) with 95-percent confidence limits in parentheses; VR=variance of residuals after regression; df=de-
grees of yreedom.
Eq. no. a1 a2 a3 ac as a6 VR df
6
7
8
9
10
11
12
13
14
15
16
4
17
18
0.146
(*. 018)
.I60
(*. 042)
.153
(*. 049)
-. 023
(f5.199)
-. 041
(f5.058)
-. 044
(fl. 255)
-. 191
(zt. 643)
-. 296
(*. 743)
-. 708
(fl. 603)
.lo8
(*. 030)
.1w (*. 003)
-. 334
(*. 138)
-. 277
(.t. 711)
-. 191
(*. 654)
-0.159
(=I=. 397)
(+. 510)
.os
(f3.642)
,064
(*3.436)
-. 140
.010
(*. 415)
(*. 136)
.098
(*. 159)
.181
(*. 153)
-. 019
(i. 295)
.071
-. 017
(.t. 405)
.lo6
(*. 171)
.092
(+. 151)
.071
(*. 138)
-0.246
(=%. 576)
-. 021
(*. 629)
-. 023.
(A 546)
-. 044
(*. 282)
-. 219
(*. 377)
-. 270
(*. 475)
-. 025
(+. 410
.363
(*. 341)
.203
(+. 352)
0.178
(+. 514)
-. 218
(*. 404)
-. 265
(*. 485)
-. 212
(*. 549)
. 019
(** 658)
-0.202 0.550
(*. 664) (*. 705)
0.002471
.002488
.m94
.002500
.om499
.m 5 9
.IN2467
.@E465
.m 4
.002548
.002653
.003001
.002527
.002532
65
64
62
63
62
60
64
83
61
64
62
63
63
64
tions (9) and (12), respectively. As in the case of the
daily values of LW (table 3), the simple equations (15)
and (16) using cloud information only yield the most
satisfactory fit.
Table 6 presents the results for the half-hourly values
of LW TJ . As seen from a comparison of equations (6),
(9), and (12), vapor pressure offers comparatively little
information. Brunt’s equation (12) and versions (13) and
(14) are again found superior to Angstrom’s expression
(9) and the corresponding equations (10) and (11). Equa-
tions (4), (17), and (18) again yield the poorest fit, along
with (15) and (16) based on cloud information only. Con-
trary to the daily values with few degrees of freedom, the
added cloud information in equations (lo), (l l ), (13), and
(14) yields some improvement upon (9) and (12) and make
(14) clearly preferable to the simple expression (6), which
in table 4 was found to be the best predictor for the daily
values of LW TJ .
Conceivably, coefficients may vary depending on
whether half-hourly, daily, or monthly means are used in
the various formulas. Application to other areas may not
always be feasible, since, for example, moisture variations
may play a more prominent role. Tables 2 through 6 are
meant to provide general background information on the
dependence of radiative fluxes on temperature, humidity,
and cloudiness conditions at Palmyra.
4. RADIATION BUDGET OF THE TROPOSPHERE
Longwave radiation has been measured directly by
radiationsondes during the LIE. Profiles of infrared radi-
ative cooling over Palmyra and Christmas are plotted in
figure 4. Longwave fluxes in the vicinity of the tropopause
are included in table 1. I n contrast to computed profiles
available in the literature (Yamamoto and Onishi 1953,
London 1957, and Rodgws and Walshaw 1966), measure-
ments bear out a more pronounced infrared cooling in the
lower layers and much smaller values in the upper tropo-
sphere. This is in qualitative agreement with Riehl’s (1962)
findings for the Caribbean. Cox (1969) has shown results
of computing infrared cooling for a clear tropical atmos-
phere and compared these with actual observations. Even
for the clear case, the measurements show more radiative
cooling near the surface and less cooling in the upper
troposphere than the computations. Clouds may act to
enhance this discrepancy even more. Cox attributes the
disagreement t o the presence of aerosols, even in a “clear”
atmosphere, and t o the change in the area viewed by the
instrument as it passes from a cool island to a warm mater
underlying surface.
Absorption of solar radiation was computed from con-
ventional radiosondes and surface observations of -cloudi-
ness during the LIE, following the procedure of Mugge
830
200
300
400
w
67 cn w
5 500
600
700
800
900
MONTHLY WEATHER REVIEW Vol. 98, No. 11
-
-
-
-
-
-
-
-
100 1
IOOOl I I I I I I
-4.0 -3.0 -2.0 -1.0 0 I .o
I R TEMPERATURE CHANGE “C DAY-’
FIGURE 4.-Vertical profiles of infrared radiative cooling over
Palmyra and Christmas Islands.
and Moller (1932) for clear sky and using the values of
reflectivity, absorptivity, and transmissivity presented by
Korb et d. (1956) for different cloud types. Computations
were performed for 100-mb-thick layers between 1000 and
300 mb separately for clear sky, an overcast of low clouds
(900-800 mb3, and an overcast of middle clouds (650-600
mb). Results were then weighted for every 100-mb-thick
layer, according to the 3-hr surface observations of cloudi-
ness at Palmyra, Fanning, and Christmas, assuming no
overlap of areas with low clouds and middle clouds, re-
spectively. For the layer 300 to 100 mb, Yamamoto’s
(1962) vdues for April and the latitude belt 0’-loo N.
were adopted. Results of these calculations are included
in table 1.
From the surf ace radiation measurements, the radiation
soundings, and the computed absorption of solar radiation
in the troposphere, the net shortwave, SW J. mb, and the
net shortwave plus longwave radiation in the vicinity of
the tropopause, Roar over Palmyra is obtained (table 1).
Longwave radiation fluxes at 100 mb listed in table 1 were
adjusted slightly, so as to match exactly the longwave
fluxes at the surface and the infrared radiative flux
divergence in the layer 1000 to 100 mb. The amount of
adjustment is within the accuracy of measurements
(Euhn and Johnson 1966).
An attempt was made to arrive also at an estimate of
Bo and Roa over Christmas Island during the LIE. At
Christmas only, longwave radiation has been measured
by radiationsondes. However, some inference on the
shortwave budget is possible, using the Palmyra measure-
ments.
Solar radiation at the top of the atmosphere according
to latitude and season can be taken from the “Smith-
sonian Meteorological Tables” (List 1968). Subtracting
Rodgers’ (1967) value for the solar radiation absorbed in
the layer 7 to 100 mb yields an estimate of the downward-
directed shortwave radiation at the tropopause, SW J, mb,
over Palmyra and Christmas, respectively. Values thus
obtained are listed in table 1. For Palmyra, the net short-
wave radiation at the tropopause, SWJT mb, has been
determined additionally, as described above. From this,
an estimate of the planetary (shortwave) albedo at
Palmyra during Mar. 24-Apr. 19, 1967, is readily ob-
tained. The estimated value of 32 percent is larger than
values read from Raschke’s (1968) albedo maps for various
fortnightly periods in May-June 1966. This may seem
compatible with the characteristic seasonal variation of
cloudiness in the Line Islands region. However, unpub-
lished precipitation records (courtesy of the British Mete-
orological Office, London) for Christmas and Fanning
Islands indicate larger rainfall in May-July 1966 than in
March-April 1967. It must also be recalled that Raschke’s
maps are based on noontime observations. The consis-
tency of planetary albedo estimates for the LIE with
Raschke’s (1968) maps can thus not be clearly assessed.
Surface albedo at Palmyra was found to be about 6.5
percent for clear sky. Total cloudiness is available from
surface observations during the LIE (CT=0.49 for Pal-
myra). From this information and weighting albedo ac-
cording to the proportion of clear and cloudy areas, a
representative average cloud albedo over Palmyra can be
derived (55 percent).
Now assume that the Palmyra estimates of surface and
cloud albedo are approximately valid for Christmas, and
use the surface observations of total cloudiness over
Christmas during Mar. 24-Apr. 19, 1969 (CT=Q.32).
Then a value of the planetary albedo representative of the
Christmas region can be derived (22 percent,). From the
planetary albedo and the downward-directed shortwave
radiation at the tropopause, as assessed further above, an
estimate of the net shortwave radiation at the tropopause
is obtained. Subtracting the solar radiation absorbed
between 100 and 1000 mb then yields the net shortwave
radiation at the surface. A surface albedo of 6.5 percent
then leads to the estimates of downward and reflected
shortwave radiation at the surface, as listed in table 1.
It is noted that the downward-directed shortwave
radiation thus obtained agrees closely with the value
computed from equation (5), using the observed total
cloudiness at Christmas.
November 1970 Stephen K. Cox and Stefan L. Hastenrath 831
Combining these computed shortwave radiation values
with the directly measured longwave radiation finally
leads to an estimate of R, and Ro, for Christmas (table 1).
5. CONCLUDING REMARKS
Measurements of the surface radiation budget a t
Palmyra during the LIE were limited t o a period of only
about 3 weeks. However, the program is considered
particularly valuable, in view of the chronic scarcity of
direct measurements in lower latitudes. Results indicate
a larger surface net radiation than seems to be generally
accepted for climatic mean conditions. It is noticed,
however, that cloudiness during the LIE was below
average.
Absorption of solar radiation and infrared radiative loss,
arrived at in the present study for the tropospheric
column as a whole, do not essentially differ from the general
magnitude of estimates obtained in earlier studies (e.g.,
London 1957). Taken in conjunction with the surface
radiation measurements, this would agree with an upward
adjustment of the net radiative flux at the tropopause
compared to estimates of the presatellite era, as has been
suggested by House (1965) and Vonder Haar and Hanson
(1969).
The ratio of surface net radiation to the net radiative
gain of the earth-troposphere column has a bearing on the
relative importance of ocean and atmosphere in the heat
export to higher latitudes. Increased net radiation at the
sea surface implies a larger lateral export of heat by ocean
currents, unless there is reason for an upward adjustment
of the present estimates of sensible and latent heat transfer
at the sea-air interface. In this connection, more direct
measurements of the surface net radiation over the
tropical oceans appear desirable.
ACKNOWLEDGMENTS
This study was supported by the National Science Foundation
through Grant GA-1010 and the Environmental Science Services
Administration through Grant E22-113- 68( G) . P. Guetter assis-
ted inthe programming for the CDC 3600 and Univac 1108
computers.
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[Received December 19, 1969; revised May fl, 19701