Energy exchange at a sea ice boundary

Solar Energy, Vol. 12, pp. 469-490. PergamonPress,1969. Printedin Great Britain

E N E R G Y E X C H A N G E AT A SEA ICE B O U N D A R Y JAMES H. BROWN* (Received 4 March 1969)

Abstract- Energy exchange at the surface of an annual sea ice sheet was computed for five days, during the winter of 1959, from values of the following energy components: radiant flux, conducted flux, sensible flux and latent flux. These were obtained by measurement and by application of the theories of Priestley and Crawford. The latter performed well in adverse changing weather conditions, over the stability range of Richardson's numbers between --0.053 and +0.140. The energy components for a relatively cloudless day were compared with those for an overcast day, demonstrating significant changes in the total net radiation at the ice surface due to cloud cover. It was found that open leads forming in the ice release large amounts of energy from the ocean to the atmosphere. This energy is then transmitted to other areas, modifying the weather in those areas. The energy component with the largest uncertainty is the latent flux. All hourly measured values of latent energy were compared with the flux as determined by the remainder method. This comparison was used as an indication of the total energy balance error. R6sum6-Au cours de I'hiver 1959. l'6change de 1'6nergie 5. la surface d'une couche annuelle de glace 5. 6t6 mesur6 pendant cinq jours cons6cutifs. 5. partir des valeurs des composants de 1'6nergie suivants: flux rayonnant. flux conduit, flux sensible et flux latent. Ceux-ci ont 6t6 obtenus par la mesure et l'application des th6ories de Priestley et Crawford. Cene derni~re m6thode h donne de bons r6sultats dans des conditions atmosph6riques changeantes et d6favorables, dans la gamme de stabilit6 des chiffres de Richardson entre - 0 , 0 5 3 et + 0.140. Les composants de l'6nergie pour une journ6e, pratiquement sans nuages ont 6t6 compar6es avec ceux d'une journ6e couverte, mettant en 6vidence des changements importants dans le total net de radiations 5' la surface de la glace dfl 5' la couche des nuages. On 5. decouvert que des fissures se formant dans la glace lib~rent de l'oc6an vers l'atmosphere de grandes quantit6s d'6nergie. Cette derni~re est alors transmise 5. d'autres zones, modiflant les conditions atmospheriques de celles-ci. Le composant d'6nergie le plus instable et incertain est le flux latent. Toutes les valeurs de mesure horaire de 1'6nergie latente ont 6t6 comparees avec le flux d6termin6 par la m6thode remanente. Cette comparaison a 6t6 utilis6e comme une indication de l'erreur totale de l'6quilibre d'6nergie. R e s u m e n - El intercambio energ6tico en la superficie de una capa anual de hielo de mar fue computado durante cinco dias consecutivos del invierno de 1959 partiendo de los valores correspondientes a las siguientes componentes energ&icas: flujo radiante, flujo conducido, flujo sensible y flujo latente. Estas fueron obtenidas por medici6n y mediante aplicaci6n de las teorias de Priestley y Crawford, las cuales resultaron eficaces, a pesar de los cambios adversos del tiempo, sobre la gama de nfimeros de estabilidad de Richardson entre --0,053 y +0,140. Las componentes energ6ticas aplicables a un dia con cielo relativamente despejado fueron confrontadas con las de un dia nublado, acusando cambios significativos la radiaci6n neta total en la superficie del hielo a consecuencia del cielo cubierto. Se encontr6 que, a trav6s de los conductos abiertos que se forman en el hielo, se liberan a la atm6sfera importantes cantidades de energla oce,Snica, transmiti6ndose 6sta despu6s a otras zonas y afectando alas condiciones meteorol6gicas de las mismas. La componente energ6tica vue resulta mS,s dudosa es el flujo latente. Todas las medidas horarias del flujo latente fueron comparadas con el flujo segfin determinado pot el m6todo de remanente, utiliz~ndose dicha comparaci6n como indicaci6n del error total del balance energ6tico.

INTRODUCTION

THE STUDY of energy exchange o v e r a sea ice sheet has importance in oceanographic and meteorological processes in the Arctic. With the approaching Arctic winter months there is a decrease in solar radiation, which results in cooling of the Arctic atmosphere. In open water regions, energy is given up b y the ocean until the u p p e r sea water layer a p p r o a c h e s an isothermal condition, at which time ice begins to form as further energy *Arctic Sciences Division, Naval Undersea Research and Development Center, San Diego, Calif. 92,132, U.S.A. 469

470

J . H . BROWN

is removed from the ocean's surface. With time, the ice increases in thickness and the ice surface accumulates a snow cover from atmospheric precipitation. In the central Arctic regions, pack ice persists the year-round. With the approach of the Arctic winter months, ice begins to form on the bottom of the pack ice as snow is accumulating from atmospheric precipitation on the top surface. The ice sheet on top of the water is an insulator, slowing the transfer of energy from the ocean to the atmosphere. During the winter months, solar radiation in the Arctic is at a minimum. The high albedo of the snow surface further limits the amount of solar energy which is absorbed by the snow-ice surface. As a result of these processes, the Arctic atmosphere is cooled and large temperature gradients occur in the atmosphere between the high and low latitudes. These gradients intensify the atmospheric circulation. During the summer months, there is increased solar radiation with a corresponding increase in net radiation at the snow-ice surface, which results in melting at the surface. This melting decreases the surface albedo. The decrease in albedo causes an increase in the absorption of solar radiation at the surface, and further increases surface melting. Through these physical processes, sensible and latent energy are transferred from the surface to the atmosphere, and there is a warming of the latter. The warming of the Arctic atmosphere during the summer months decreases the atmospheric temperature gradients between high and low latitudes, with a corresponding decrease in the atmospheric circulation. For a more detailed treatment of the physical processes involved in the Arctic heat budget, the reader is referred to the work of Fletcher[l] and to the Proceedings of the Symposium on the Arctic Heat Budget and Atmospheric Circulation [2]. The present study represents an effort to determine if present instrumentation and theory will give a good balance of the energy flux components by direct measurement over an Arctic ice sheet. It is desired to obtain these balances under 'ideal' and 'adverse' weather conditions. At the present time, there is no known research which gives an accurate balance of all the energy flux components based on measurements taken under the above conditions. If the study has achieved this objective, it will serve as a guide for future experimental work. The measurements were taken on a smooth annual shore-fast, sea ice sheet adjacent to the U.S. Navy Field Station, Wales, Alaska (65 ° 37' N., 168o03 ' W.), during the period F e b r u a r y - M a y 1959. The micrometeorology field site on the ice sheet was 1500 m north of Cape Prince of Wales, 800 m west of the shoreline, with a water depth of 5 m (all figures approximate). The primary purpose of the study was to measure the pertinent energy components, to obtain a balance of the energy equation at the top surface of the ice sheet. THEORY

Over a smooth sea ice sheet with a snow cover, the pertinent energy components at the surface are: net radiant energy flux (Rn), conducted energy flux (Qe), sensible energy flux (H) and latent energy of sublimation or condensation (LE). The relationship of these vector quantities to each other is

R.+Qc+H+LE

= O.

(1)

This is the basic formula for all energy exchange or heat budget studies at the Earth's

Energy exchangeat a sea ice boundary

471

surface when there is no melting or freezing taking place. The sign of the energy flux is positive when energy is being added to the surface, and negative when energy is lost from the surface. Radiant energy flux A snow or ice surface is highly reflective to solar radiation in the visible region. Above the near i.r. region, both snow and ice become nearly perfect blackbodies and absorb all radiant energy of wavelength greater than about 1/xm. It is, therefore, valuable for energy balance studies to have information concerning incoming longwave radiation (LWin) from the atmosphere, outgoing long-wave radiation (LWout) from the snow-ice surface, incoming short-wave radiation (SWin) from the Sun and sky and outgoing short-wave radiation (SWout) which is reflected from the surface. From these radiation components, one is able to determine the integral wavelength net radiation (Rn) and the surface albedo, and to observe the effect of various sky conditions on the radiation balance at the surface. C o n d u c t e d energy flux For a uniform homogeneous isotropic floating ice sheet with a snow cover, the conducted energy flux (Qc) in the direction normal to the plane of the ice sheet, for steady-state flow, is given by the relation

Qc =

_k0_r '~z"

(2)

Using finite differences, this equation becomes Qc = - k i T2 - T1 z2 Zl -

(3)

-

where k~ is the thermal conductivity of the snow or ice. T2 and T1 are two temperatures at different levels, and z2 and zl are the heights of these levels. Strictly speaking, the conditions assumed for the use of Eq. (3) are not met for an annual sea ice sheet with a snow cover. However, if the temperatures are averaged over a sufficient period of time to minimize small fluctuations, and temperature measurement is made close to the surface under consideration, at several different places, then the conducted energy flux can be determined with adequate accuracy. In addition, the thermal conductivity of the upper surface layer must be accurately known. Sensible and latent energy fluxes Priestley[3] has derived relationships for both the free and forced convection regimes. The general equation is H = hpcp(g/o)'~loO/Ozl3'2z 2

(4)

where p is the air density, cp is the specific heat of air at constant pressure, g is the acceleration due to gravity, 0 is the absolute .potential temperature of dry air and z is

472

J.H. BROWN

the height above the zero plane. The t e r m / ~ is dimensionless, which for free convection has the form H = h

(5)

where h is a constant to be determined experimentally. F o r forced convection, H has the form H = k21Ri]-'/2

(6)

where k is a constant. Ri is Richardson's number and is given by the equation

~O/Oz

Ri = (g/O) (au/az)2

(7)

where u is the mean horizontal wind velocity. In a similar manner, Crawford[4] derived the following relations for the latent energy flux regimes of free and forced convection:

tf

= tf~p (g/O) 1¢2100/0z11/2(oq/oz) z 2

(8)

where q is the specific humidity and L is the latent heat of sublimation or heat of fusion plus evaporation. F o r free convection, the term E has the form E ----h

(9)

and for forced convection f = k21Ri1-1'2.

(10)

T h e sensible and latent energy fluxes can be determined from Eqs. (4) and (8), provided ~ and E are evaluated, and the temperature and specific humidity gradients are known. In order to evaluate ~ and/~, the sensible and latent fluxes must be measured directly over a large range of stabilities, for both free and forced convection. It has been shown, by Dyer[5], t h a t / 4 and/~ areequal. Values for/-) and/~ are given by Priestley, Crawford and D y e r , loc. cit. T h e E values of Crawford cover the largest range of stabilities. T h e s e were determined from gradients, in conjunction with direct flux measurements at Davis,.California. In the present study, Crawford's values for E will be used both for ~ and H. T h e y are: for free convection, E

for--2.5< Ri < --0.02

(1 1)

E = H = 0.2961 Ri1-°"42, f o r - 0 . 0 2 < Ri < 0

(12)

/~ = / ~ = 0.0941Ril -°'61,

(13)

=

H

=

1.2941Ril -°°4,

and for forced convection,

f o r 0 < Ri < 0.35.

Energy exchangeat a sea ice boundary

473

EXPERIMENTAL MEASUREMENTS All data, except wind speed and wind direction, were logged on MinneapolisHoneywell potentiometric recorders. The recorders were calibrated with a Leeds and Northrup K-3 potentiometer at several points across their span, usually four times daily. The recorders had an accuracy of ---0.1 per cent of full-scale deflection with the potentiometer corrections. A camera was used for recording wind speed; every 4 min, the digits on a set of counters were photographed. These counts were made by cup anemometers chopping a light beam. Wind directions were recorded on an EsterlineAngus recorder, and had an accuracy of about ___5°. One cup anemometer, a dry-bulb thermocouple and a wet-bulb thermocouple were placed at the 25, 50, 100 and 200-cm levels above the snow surface. Each set of four cup anemometers was matched to within +_0.1 per cent of each other, by running the set at the 200-cm level for more than 10,000 rev. The copper-constantan thermocouples used to measure the air, snow and ice temperatures were calibrated prior to installation, and had an accuracy of better than ___0.01°C. All air thermocouples were shielded against solar radiation effects. The dry- and wet-bulb thermocouples were inserted in 0.1-cm dia. tubes. In addition, the wet-bulb thermocouples had a thin cotton wick approximately 3 cm long covering the junction area; the wicks were maintained with a thin ice coat. All thermocouples placed in the snow or ice were in stainless steel tubes 15 cm long with a diameter of 0.16 cm. The lead wires of these thermocouples were brought back horizontally a distance of 50 cm before being brought to the surface. This minimized heat transport by the wires which might adversely effect the readings. All thermocouples were referenced against ice bath thermocouples maintained at a temperature of 0°C, with a stability better than ___0.005°C. The ice baths were housed in insulated boxes which were thermostatically controlled to maintain the temperature at a few degrees above 0°C. In addition to the thermocouples in the ice and snow for measuring the conducted energy flux, heat flow transducers manufactured and calibrated by Beckman and Whitley were placed at different levels to measure the thermal conductivity of the snow and ice. These transducers were thermopiles approximately 0.2 cm thick and 22.5 cm square. Each face of the transducer had a thin, polished stainless steel covering. The transducer had a thermocouple embedded in its center, and all transducer readings were temperature corrected. The incoming and reflected solar radiation intensities were measured by two Eppley concentric ring 10-junction pyranometers, one facing up and the other down. The pyranometer data were corrected for temperature and solar elevation. These pyranometers were calibrated by the manufacturer. The incoming total radiation, composed of the long- and short-wave radiation, was measured with a Beckman and Whitley aspirated fiat-plate total radiometer. The total net radiation, composed of this incoming total radiation minus the outgoing long- and short-wave radiation, was measured with a Beckman and Whitley aspirated flat-plate net radiometer. All data from both of these aspirated radiometers were corrected for temperature. The two aspirated radiometers were calibrated by the manufacturer. The pyranometers and the aspirated radiometers measured both the direct and diffused radiation. These instruments were all mounted at a height of 200 cm above the ice surface. The pyranometers had shields which did not interfere with the radiation being measured. However, the shields minimized errors caused by radiation coming from the direction opposite to the thermopile

474

J.H.

BROWN

face, which is then internally reflected by the pyranometer's glass envelope to the thermopile. On 29 December, 1958, when the ice sheet was 22 cm thick, the 'in ice' sensors were installed. Holes were cut in the sheet and the sensors suspended in the water, to freeze in place. The ice sheet to the north, east and south of the measurement location was smooth. The ice to the west, however, was rafted. DISCUSSION

OF

RESULTS

Data were analyzed for five different d a y s - 2 5 February, 2 March, 14 March, 12 April and 9 May, 1959. There are very few days at Wales that have what might be called 'ideal' weather: that is, clear sky, moderate winds, no precipitation and no blowing snow. Of the days analyzed, ideal periods occurred only on 2 March and during the morning hours of 14 March.

Radiant energy flux The measured radiation components are summarized in Tables 1-5. These data are tabulations from a computer after the analog information had been scaled and punched on IBM cards. Some care must be exercised in their use in regard to weather conditions and solar elevation. Figures 1 and 2 demonstrate some of the limitations of this

T a b l e 1. S u m m a r y o f r a d i a t i o n c o m p o n e n t s at W a l e s , A l a s k a , 25 F e b r u a r y 1959 Time (BST*)

T o t a l in (Ly/mint)

T o t a l net (Ly/min)

SWirI

SWoul

LWin

(Ly/min)

(Ly/min)

(Ly/min)

LWout (Ly/min)

0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

+0.340 + .344 + .352 + .343 + .342 + .349 + .328 + .365 + -422 + -494 + .613 + .621 + -591 + .543 + .469 + .398 + -285 + -230 + .244 + -206 + -179 + .179 + '192 +0'338

+0-011 + -008 + -016 + .006 + .011 + .012 + -002 + .017 + -026 + -041 + .075 + .048 + .043 + .034 + .013 -- .009 -- -046 -- .075 -- .060 -- -084 -- .100 -- -093 -- "082 +0"013

--0.002 -- -002 -000 + .001 + .001 .000 + .001 + .017 + .073 + .137 + .252 + -275 + -246 + .206 + .156 + .094 + .018 + .001 + .002 + .002 .000 + .003 + -003 0-000

--0-001 - .001 + .001 + .002 + ,003 + ,001 + .002 -- .014 -- .058 -- .111 -- .200 -- .223 -- .209 -- .170 -- -128 -- -075 -- .011 + -003 + -004 + .004 + .003 + .005 + -006 +0-001

+0.338 + .342 + .352 + .342 + .341 + -349 + .327 + .348 + .349 + -453 + .361 + .346 + .345 + -337 + .313 + -304 + .267 + .229 + -242 + .204 + .179 + -176 + "189 +0'338

--0.328 -- .335 -- .335 -- .335 -- .328 -- .336 -- .324 -- .334 -- .338 -- -342 -- .338 -- .350 -- .339 -- .339 -- -328 -- .314 -- .228 -- -152 -- -180 -- • 118 -- .076 -- .081 -- -104 --0"324

+0.365

--0-007

+0-061

--0-050

+0.307

--0.275

Mean

*BST = Bering Standard Time, t L y ( L a n g l e y ) / m i n = c a l / c m 2 min.

Albedo

0.82 .80 -81 -79 -81 .85 .83 .82 0.80

0.81

Energy exchange

T a b l e 2. S u m m a r y

475

at a sea ice boundary

of radiation components

at Wales, Alaska, 2 March

Time (BST)

Total in (Ly/min)

Total net (Ly/min)

SWtn

SWo~t

(Ly/min)

(Ly/min)

(Ly/min)

LWout (Ly/min)

0100 0200 0300 0400 0500 O60O 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

+0.057

--0.119

+0-006

+0.015

+0.051

--0.047

+ .082 + • 133 + .269 + .475 + .506 + .624 + "620 + "527 + -414 + .266 + "170 + "132 + "136 + "139 + .140 + "130 + "126 +0-085

- - • 112 - - - 109 - - -120 -- .084 - - -036 -- .046 -- .050 - - -071 - - "092 - - .117 - - -120 - - .115 - - "116 - - "118 - - "117 -- '112 - - -105 --0"123

+ + + + + + + + + + +

-009 .064 '185 '327 '308 .432 .406 "315 .210 .083 -022 -000 - - -008 - - "008 - - -008 - - "008 - - "0(O +0"006

------------

.009 -033 .133 "247 .248 .352 .341 -304 .241 .130 .038 .000 - - -004 - - .003 - - .004 --.003 - - "004 -t-0"014

+ .073 + .069 + -084 + '148 + .192 + .192 + '214 + "212 + -204 + "183 + .148 + "132 + "128 + "131 -I- " i 3 2 + "122 + "I18 +0"079

- - .021 -- .009 - - "016 -- .144 - - -216 - "226 - - "229 - - .152 - - -081 - - .019 - - .012 - - .017 - - "016 - - "018 - - "019 - - "015 - - "017 --0"024

+0.265

--0.099

+0.098

--0.086

+0.137

--0.068

Mean

LWi,

1959

Albedo

0"72 .76 -81 .81 0-84

0.79

THE SUN'S ANGLE OF ELEVATION FOR DATES iNOICATED

10/27 10/20 10/29 i= E

i

2"70

2,60

.e 2.50 2'40 E -z

~

21"8 °

31-6 °

39.3 °

43.7 °

43.0 °

39.8 °

32.4 °

22-7 °

11.7 °

_.3 o

-1"5 °

10"4 °

21-6 °

31.4 °

39.0 °

43.4 °

43.6 °

39.5 °

32-1 °

22.5 °

11,4 °

-.4 o

-1"6 °

102 °

21"3 °

31.1 °

3,6.7 °

43.1 °

43.3 °

30.2 °

31.8 °

22.2 °

11.2 °

-.6 o

iOCT,

20,11065

OCT. 27.

1965

/

I /,

e

2'10

z .1(

16'6 °

2"30

2.20 c,

-1"3 °

2'00 I

"90

,,c

1"90

r

:' ,"

SKY CONOITION:

0700

0000

/

~_.,.

oct 29.1lg05

J

V

i

CLEAR, HAZE BELOW 10 DEGREES 6900

1000

1100

1200

1300

1400

1500

1600

1700

TIME - PDST

F i g . 1. C a l i b r a t i o n

of a concentric ring Eppley pyranometer, at San Diego. California. PDST = Pacific Daylight Standard Time.

1800

476

J. H . B R O W N T a b l e 3. S u m m a r y

of radiation components

1959

SWin

SWout

LWm

(Ly/min)

(Ly/min)

(Ly/min)

LWout (Ly/min)

+ "258 + .242 + .266 + 0 " 154

--0-097 -- '072 -- "087 -- .099 -- '102 -- .102 -- -100 -- .105 -- -059 -- -028 + .002 + .004 -- .003 -- "008 -- .038 -- .084 -- "089 -- .063 -- "054 -- "060 -- .045 -- '048 -- .037 --0"095

--0-002 -- .001 -- .002 -- -002 .000 .000 + .035 + .167 + -312 + .430 + -489 + .527 + '507 + .413 + "331 + .197 + -071 + "015 + -001 + -001 + .002 + .001 +0.001

+0.002 + .003 + "002 + "002 + .003 + .002 -- "019 -- "122 - .241 -- '353 -- "418 -- "467 -- -461 - -385 -- '327 -- "213 -- .066 -- .007 + .004 + .004 + -004 + .004 +0-004

+0.140 + "190 + '168 + .146 + "137 + "134 + "132 + "114 + .096 + "117 + '156 + "155 + "174 + .192 + .186 + "208 + .190 + .244 + .261 + '254 + '256 + "241 +0"265

--0.043 -- -116 -- .081 -- .047 -- .032 -- .030 -- .048 -- -054 -- -108 -- .166 -- "225 -- .211 -- .217 -- "212 -- .152 -- .108 -- .106 -- -189 -- .204 -- "191 -- '209 -- .190 --0.225

+0.326

-0.061

+0.146

--0.128

+0-181

--0-138

Time (BST)

T o t a l in (Ly/min)

Total net (Ly/min)

0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900

+0"142 + '191 + .170 + . 148 + -137 + .134 + "167 + "281 + .408 + .547 + .645 + -682 + "681 + "605 + "517 + -405 + -261 + "259 + .262

2000

+ "255

2100 2200 2300 2400 Mean

at W a l e s , A l a s k a , 14 M a r c h

Albedo

0"73 "77 "82 "86 0"89

0-81

'290 --

e

"200 '270

E

"250

~'E

25o 240 230 "220

OCTI 1965

~,~

\

"210

sE,,T 30, ,005

"200 "190 SKY CONDITION: CLEAR, HAt[ 6[LOW ,10 OEGR[[S '180 0700 0800 0900 lO00 I100 1200

1300

1400

1500

1600

1700

1800

TIME - PDST

F i g . 2. C o m p a r i s o n o f a B e c k m a n a n d W h i t l e y a s p i r a t e d f l a t - p l a t e t o t a l r a d i o m e t e r w i t h a b a n k o f t h r e e E p p l e y p r e c i s i o n p y r a n o m e t e r s , at S a n D i e g o , C a l i f o r n i a .

477

E n e r g y e x c h a n g e at a s e a ice b o u n d a r y T a b l e 4. S u m m a r y o f r a d i a t i o n c o m p o n e n t s at W a l e s , A l a s k a , 12 A p r i l 1959

SWin

Time (BST)

T o t a l in (Ly/min)

Total net (Ly/min)

(Ly/min)

SWout (Ly/min)

0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

+0.184 + • 189 + -231 + -251 + .269 + .379 + .516 + .620 + -778 +1.011 +1.120 +1.238 +1-137 + .932 + .835 + .785 + .610 + .442 + -259 + -176

+0.194

--0-089 -- .095 -- .059 -- .041 -- -037 -- .020 + -021 + .029 + .038 + .093 + -089 + .121 + .098 + .089 + .070 + .051 + .007 -- .040 -- .079 -- .040 -- .107 -- .099 -- -093 --0.087

+0.004 + .003 + -004 + .004 + .019 + .135 + .220 + .322 + -509 + .678 + .784 + .852 + .775 + .593 + .495 + .463 + .317 + -196 + .065 + .012 + -007 + .007 + .006 +0.003

+0.574

--0.180

+0.268

Mean

LW,~ (Ly/min)

LWout (Ly/min)

+0-007 + .008 + .008 + .008 -- .006 -- .093 -- .171 -- -261 -- .411 -- .552 -- .650 -- .722 -- -653 -- .488 -- -413 -- -251 -- .260 -- .159 -- -004 + .004 + -008 + .009 + .006 +0.007

+0.180 + • 186 + .227 + .247 + .250 + .244 + .296 + .298 + -269 + .333 + .336 + .386 + .362 + .339 + .340 + .322 + .293 + -246 + • 194 + .164

--0-088 -- .086 -- .164 -- .202 -- .226 -- .266 -- .324 -- .330 -- .329 -- .366 -- .381 -- .395 -- .386 -- .355 -- .352 -- .483 -- .343 -- .243 -- • 176 -- .132

+0.191

--0.100

--0.212

+0.272

--0-273

Albedo

0-77 -81 .80 .81 .83 .83 .84 .82 .84 .83 0.82

0.82

model of the Eppley pyranometer and of the Beckman and Whitley total radiometer, especially at low sun elevations. From the radiation measurements, the incoming and outgoing long-wave radiations were determined by the following relationships:

LWln = TOtin- SWln

(14)

and LWout =

Tohn

-

TOtnet -- S Wout.

(15)

The albedo values in this study agree closely with those reported by Gavrilova[6] for latitudes 650-70 °. During the afternoons of 2 and 14 March, unusually high values of albedos were m e a s u r e d - even exceeding unity, or total reflection. These values were not included in the albedo averages since they were probably caused by frost forming on the pyranometer envelopes during those periods. The frost formation was observed to be greater on the cover of the incoming pyranometer in both cases. While both the incoming and outgoing short-wave radiation would be reduced by the frost formation, reduction in the former component would be the greater. Hence, the albedo values recorded would be too high. Since the incoming and outgoing long-wave radiation was determined from Eqs. (14) and (15), as a function of the measured incoming and outgoing short-wave radiation, the long-wave radiations for these two periods are in error and require correction.

478

J. H . B R O W N T a b l e 5. S u m m a r y o f r a d i a t i o n c o m p o n e n t s at W a l e s , A l a s k a , 9 M a y 1959 Time (BST)

T o t a l in (Ly/min)

T o t a l net (Ly/min)

SWin

SWout

LWln

(Ly/min)

(Ly/min)

(Ly/min)

LWout (Ly/min)

0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

+0.353 + -352 + .357 + -378 + .420 + -511 + .616 + .719 + -855 + -951 +1.198 +1.124 +1.107 + -980 +1-000 + .903 + "741 + "568 + "446 + "411 + '362 + '347 + "343 +0"353

-0-014 - .018 -- .025 - .0•6 - -017 + .007 + .028 + .055 + -075 + .091 + .143 + .129 + .128 + .107 + -108 + .091 + '060 -- "026 -- '003 -- .008 -- .019 -- .027 -- .038 --0.016

+0.005 + .005 + -008 + -026 + .024 + -149 + -248 + .357 + .490 + .574 + .787 + -741 + -723 + .600 + .616 + .514 + .367 + '108 + '095 + .059 + .014 + .004 + .004 +0.004

+0.005 + .005 + .002 -- .012 - -038 - .107 - .187 - -280 - .381 - .453 - .628 - .587 -- .546 -- "459 -- '468 -- "388 -- -275 -- "151 -- "067 -- '039 -- "003 -- .004 -- .004 +0.004

+0.348 + .347 + .349 + -352 + .396 + .362 + .368 + .362 + .365 + -377 + -411 + .383 + .384 + -380 + .384 + -389 + -374 + "460 + "351 + '252 + "348 + "343 + "339 +0"349

--0.334 -- .329 - -330 -- .350 - .365 - .397 -- .401 -- .384 - .399 -- .407 - .427 -- .408 -- .432 -- .414 - -423 -- .424 -- .406 -- -391 -- '376 -- '364 -- .340 -- .316 -- .301 --0-333

+0.641

+0-033

+0.271

-0.211

+0.370

-0.377

Mean

Albedo

0.72 .76 .79 .78 .79 .79 .76 .77 -76 .76 .75 .74 .74 0.70

0.77

On 14 March and 9 May there was a considerable amount of blowing snow. However, it did not appear to change the albedo by any significant amount; this lack of change agrees with Liljequist's [7] work in the Antarctic. The snow cover on 9 May had a gray appearance, indicating a lower albedo unaffected by the blowing snow (also in agreement with the studies of Liljequist). During the morning hours of 25 February, the sky was overcast and there was light to very light snow. During this period, the total net radiation was positive and the total incoming radiation appears to be considerably higher than usual, as is shown in Table 1. At first glance, it might seem that the snow precipitation caused the higher incoming total radiation and the positive total net radiation. However, viewing the total energy balance of all energy components in Fig. 3, this looks correct and would indicate that the base of the clouds was radiating at a higher temperature than that of the surface. The recorded incoming long-wave radiation appears to be in general agreement with the results of Liljequist [8]. Average values for the radiation components are given in the relevant tables, The total net radiation for 2 March (Table 2) shows a surface loss of radiant energy during each hourly period. However, for 25 February, 16 of the hourly periods (Table 1) show a gain of radiant energy, although the daily average shows a loss of surface energy. This clearly demonstrates the effect of cloud cover in such instances. The (negative) net radiation at the surface, during relatively cloudless conditions, is about 15 times greater than when clouds are present.

Energy exchange at a sea ice boundary

479

0"25

0'20 0.10 0-10 z

i

,.~

I /

0"05

. ~

°

/%.

\ "'~

/": ~

"-'"'",

t,,-.a---'r'.',.

---"-..~-.-"--~,,

-0-05

"%/" -0-10 -0.15

-0'20

. . . . ...... m ........

-0"25 0000

LATENTENERGY FLUX BY REMAINDER MEASUREDLATEHT EHERGY FLUX RADIANT NET ENERGYFLUX CONDUCTEDENERGY FLUX SENSIBLE ENERGYFLUX

1

0000

0000

0900

1200

I

1

1500

I

I

t

1800

I

2100

l

2400

TIME • BST

Fig. 3. Summary of energy components over sea ice at Wales, Alaska, on 25 February 1959 (Ly/min = cal cm-2min-l). Note: BST = Bering Standard Time.

Conducted energy flux T h e c o n d u c t e d e n e r g y flux at t h e s n o w - a i r s u r f a c e is d e t e r m i n e d b y u s e o f Eq. (3). T h e m e a s u r e d t h e r m a l c o n d u c t i v i t i e s o f s n o w a r e g i v e n in T a b l e 6 for different d e p t h s . T h e s e t h e r m a l c o n d u c t i v i t i e s w e r e d e t e r m i n e d f r o m t e m p e r a t u r e profiles a n d f r o m t h e c o n d u c t e d e n e r g y flux as m e a s u r e d b y h e a t flow t r a n s d u c e r s . T h e d a t a w e r e t a k e n o n l y after the Sun was below the horizon and steady-state conditions were apparent. The t h e r m a l c o n d u c t i v i t i e s o f s n o w , c o m p u t e d for s u c h c o n d i t i o n s , w e r e t h e n u s e d f o r t h e entire day. Table 6. Summary of thermal conductivities of snow cover at Wales, Alaska

1959 2 March 14 March 12 April 9 May

At 0-cm snow level above ice (cal/cm sec °C)

At 5-cm snow level above ice (cal/cm sec °C)

At 10-cm snow level above ice (cal/cm sec °C)

Total snow depth (cm)

0.00190

0.000364

0.000727 0.000808 0.000625

0-00142

0.000114

19 22 17 11

P o r t m a n [9] a n d P h i l i p [ 10] h a v e s h o w n t h a t large e r r o r s o f m e a s u r e m e n t c a n r e s u l t w h e n t h e r e is a d i f f e r e n c e b e t w e e n t h e t h e r m a l c o n d u c t i v i t y o f t h e h e a t flow t r a n s d u c e r a n d t h e m e d i u m . T h e s e e r r o r s h a v e n o t b e e n a n a l y z e d in the p r e s e n t w o r k b e c a u s e t h e e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f t h e t r a n s d u c e r is n o t a c c u r a t e l y k n o w n . T h e s n o w t h e r m a l c o n d u c t i v i t i e s g i v e n in T a b l e 6 a p p e a r to b e r e a s o n a b l e . T h e v a l u e s o b t a i n e d at t h e 10-cm s n o w level a b o v e t h e i c e - s n o w i n t e r f a c e for 2 M a r c h , 14 M a r c h

480

J . H . BROWN

and 12 April (Table 6) were used to compute the conducted energy flux. No determination of the snow's thermal conductivity was made for 25 February, so the 2 March value was used to compute the conducted energy flux for that date. The value obtained at the 5-cm snow level above the ice-snow interface was used to compute the conducted energy flux for 9 May. By this date, the snow cover had become flaky, with a high air content, and the thermal conductivity appears to be significantly lower than the other values recorded. This was the result of the air temperature approaching and, on occasion, exceeding the melting value of the snow cover. For all days, the distance from the top snow surface to the heat flow transducers varied from 6 to 12 cm. The temperature gradient, determined from a number of fixed thermocouples embedded in the snow, was taken within (approx.) the upper 10 cm of the snow. The distance between the snow surface and the upper snow thermocouple varied between 1 and 3 cm. It is of interest to compare the, ice growth with the conducted energy flux in the ice for the five daily periods. The thermal conductivity was computed from the measured conducted energy flux and temperature gradients, as previously described for the snow cover. The measured thermal conductivities of sea ice are shown in Table 7. These measured values appear to be generally higher than the theoretical values of Anderson I11] and Schwerdtfeger[12]. They may be higher for two reasons: incorrect heat flow transducer calibrations, and differences between the thermal conductivities of the transducer and sea ice. The conducted energy flux is computed by use of Eq. (3). Table 7. Summary of thermal conductivities of sea ice at Wales, Alaska

1959

At 25-cm level below top of ice (cal/cm sec °C)

At 50-cm level below top of ice (cal/cm sec °C)

Total ice thickness (cm)

2March 14March 12April 9May

0.00605 0.00389 0.00617 0.00634

0.00594 0.00464 0.00516 0.00389

79.1 88.9 110.5 124.5

The total measured conducted energy flux with its equivalent ice growth is shown and compared with the measured ice growth, in Table 8, for the five days. Since measured temperature, salinity and density profiles of the sea ice were made, it is possible to compute the thermal conductivity of the sea ice from these profiles from relations developed by Schwerdtfeger loc cit. Then, from these computed thermal conductivities, the conducted energy flux at the sea-ice boundary is determined (Table 8). The equivalent sea ice growth for each day is computed from the conducted energy. In both cases, the appropriate latent heat of formation was also taken from Schwerdtfeger. Because of instrument failures, the measured thermal conductivities were at the 50-cm level, and the temperature gradients were taken at the 45-cm level on 4 days and at the 75-cm level on one day. The measured ice growth for each day was taken from the tangent to the ice growth curve for the particular day; the ice growth curve was a smooth curve of the ice thicknesses measured in the vicinity of the instrument site at numerous times. The equivalent sea ice growth, calculated both from the measured and computed thermal conductivities, agrees quite well with the measured ice growth.

Ice depth (cm)

45 45 45 45 75

( 1959)

25 February 2 March 14 March 12 April 9 May 48.96 82.94 53.44 41.01 3"24

Conducted energy flux (using measured thermal conductivities) (Ly/day) 0"73 1-25 0'80 0"67 0"05

Equivalent sea ice growth (cm/day) 35.20 59.62 51.82 37"19 3.49

Conducted energy flux (using Schwerdtfeger's thermal conductivities) (Ly/day)

0-53 0"90 0-78 0"61 0"05

Equivalent sea ice growth (cm/day)

0"80 0"79 0.77 0.68 0.04

Measured sea ice growth (cm/day)

Table 8. Comparison of the measured sea ice growth with the sea ice growth computed from the conducted energy flux

t~ O"

go

~r

,.<

482

J . H . BROWN

Since the conducted energy flux in the sea ice was not measured at the exact sea-ice boundary layer, but rather in the ice at a distance from the layer, a time error occurs. This results from the thermal inertia of sea ice, which delays the heat of formation from being detected at the measuring instruments for a period of time. In addition, it has been assumed in this discussion that the sea water under the ice sheet was isothermal, and that all heat of formation was conducted toward the atmosphere. The results agree favorably with a recent study on the melting of sea ice by Langleben [ ! 3]. The conducted energy flux at the snow-atmosphere boundary is less than at the seaice boundary. This decrease appears to be caused by the aeration of the snow surface, as described by Vinje[14]. In addition, the temperature gradient starts to decrease in the snow between 14 and 17 cm below the air-snow surface, except for 9 May when the decrease occurred at 3 cm. This decrease in the gradient was not caused by an increase in the thermal conductivity since the snow density was decreasing from a snow depth of 15 cm to the air-snow surface. It appears the aeration process transforms the conducted energy flux to sensible energy flux within the upper snow cover. In this study, the amount of conducted flux converted to sensible flux was generally small; however, on 2 March 1959, it attained a significant value of 0.02 Ly/min. It is important to recognize that the conducted energy flux measurements taken in the upper aerated snow layer should not be used to compute ice growth.

Sensible and latent energy fluxes The theory and method for determining the sensible and latent energy components are similar. The sensible energy flux is computed from Eq. (4) and the latent energy flux from" Eq. (8). However, before these two equations can be used, ~ and/~, which appear to be equal, must be determined from any one of Eqs. (11), (12) or (13). The choice of which equation to be used depends upon the value of the Richardson nmaber. in using them, the air density, specific heat of the air and the acceleration due to gravity were obtained from the Smithsonian Meteorological Tables[15]. The temperatures, temperature gradients, specific humidity gradients and wind speed gradients were computed from recorded data which were averaged over hourly periods. On 12 April a shutter microswitch failed on the camera of the wind speed recorder, and no wind speed data were recorded. These values for this day were taken from a micrometeorological mast on shore, approximately 1250 m to the east of the mast on the ice sheet. A comparison between data taken at the two masts, during periods when the wind was from approximately the same direction, indicated that the wind speed at the mast on the ice was l 0 per cent lower than that at the shore station. Since this difference appeared to be reasonably constant, the 9 April wind speed data from the shore mast was multiplied by 0.90 and used for the ice station. Other missing hourly data were salvaged, by interpolation, using standard procedures (Brooks and Jones [16]). The dry-bulb temperatures were converted to virtual temperatures to correct the air density for water-vapor content, and then to potential temperatures to correct for temperature changes caused b.y adiabatic heating and cooling. The specific humidities were computed from the dry- and wet-bulb temperatures, by standard thermodynamic relations. A discussion of these procedures has been given by Sutton [ 17]. All horizontal wind velocity and temperature profiles were smoothed on the computer by a least squares method. The sensible and latent energy fluxes were computed from tempera-

Energyexchangeat a sea ice boundary

483

tures and specific humidities at the 50- and 100-cm levels by finite differences. Since the profiles are generally logarithmic in the lower boundary layer, the height of the logarithmic mean of the two levels was adopted for these computations. At times, the temperature gradients have a persistent zig-zag profile which appears to be real. At first, it was believed that these profiles might occur as a result of incomplete shielding of the thermocouples from incident solar radiation or from recording errors. However, these two possibilities were eliminated: the first, by standing downwind and to the side of the wind flow a distance of about 5 m from the mast, and shadowing the measuring thermocouples with a mask for several periods each of 15 to 30 min. No effect on the shaded thermocouples could be detected in the recorded data. The second possibility (viz. recording errors) was eliminated by checking the recorder with the potentiometer, and by the growth or decay of zig-zag profiles from or to smooth profiles. These zig-zag profiles appear to develop with increasing solar radiation and disappear with decreasing solar radiation. Vinje has also observed similar profiles at Norway Station, Antarctica. He gives a theoretical interpretation of the zig-zag profiles which, based upon his observations, appears to be correct. Since these profiles persist for long periods, their regularity indicates that a systematic physical process is the cause. He demonstrates that the upper (approximately 12 cm) snow layer is permeable, and small pressure fluctuations at the snow surface cause an aeration of the upper snow layer. This aeration produces an exchange of energy in the form of sensible heat from within the snow to the air. The snow permeability regulates the interaction of air fluctuations with the snow. This regulation is shown to produce vortices which have preferred dimensions; vortices with fixed dimensions would cause an overturn of the stable air near the snow surface to a higher level. Accordingly, the parcel of air, at the higher level, would be brought to a lower level. As this is a continual process, and the two levels are at different temperatures, there is an overturn in temperatures between the levels. The number of vortices with different dimensions will determine the amount of zig-zag in the normally well-mixed smooth profile. Calculation of the latent and sensible energy components is the largest source of error in the energy balance equation because of the difficulty of measurement. The wetdry bulb method for determining the specific humidity is subject to large errors, especically below 0°C. Spencer-Gregory and Rourke[18] discuss some of the errors associated with this method. From wind tunnel tests, they show that the wet-bulb depression below an air velocity of 4-5 m sec -1 can vary by a factor greater than two. The latent energy flux calculated by two methods is shown in Figs. 3-7. The first method used was to compute the latent energy flux, LE, by use of Eq. (8), with specific humidity gradients determined from wet-bulb depressions. The second method was to compute the latent energy flux, LE(Rn + Qc + H), by 'the remainder method'. In the latter, the net radiant energy, the conducted energy and the sensible energy fluxes are determined. Then, with the aid of Eq. (1), the latent energy flux is computed as a remainder. A comparison of the values obtained by the two methods gives some measure of confidence in the energy balance.

Energy balance On 25 February all energy components appear to be relatively small. The sky was overcast the entire day. Wind velocity, wind direction and air temperatures showed

484

J.H.

BROWN

0"25 0-20

I

MEASUREDLATENT i ENERGY FLUX i RADIANT NET ENERGY FLUXi i CONDUCTEDENERGYFLUX SENSIOLE ENERGY FLUX ?I .,

..... 0"15 i

0,10

m

\

! o

LATENT ENERGYFLUX BY REMAINOEli

\

'l

"~ 6"65 •

|

'"

-:..~.

o

~

'

-0"05

! \//~--\

.,,""~/I

!/"

-e-10 -0-15 -0"20 -0"25 0000

0300

0600

0900

1200

1500

1800

2100

2400

TIME-BST

Fig. 4. S u m m a r y of energy c o m p o n e n t s over sea ice at Wales, Alaska, on 2 M a r c h 1959.

0"25 0-20 0"15

/

0.10

"\

0-05

\

I

~

,, \ ~ , "

_.~

,/

'-~

~:~

0 -0"05 w.

/

\

y"

\-.7

-0-1( . . . . -0.1! -0-21

. . . . - .........

LATENT ENERGYFLUX BY REMAINOER MEASURED LATENT ENERGY FLUX NADIANTNET ENERGYFLUX CONDUCTEDENERGYFLUX SENSIBLEENERGYFLUX

I

I

I

0300

0600

0900

11 0000

1200

1500

1000

Jl 2100

2400

TIMEJIST

Fig. 5. S u m m a r y o f energy c o m p o n e n t s over sea ice at Wales, Alaska, on 14 M a r c h 1959.

Energy e x c h a n g e at a s e a ice b o u n d a r y 0.25,

. . . . . ....... 0.20 ~ ........

0"15

.=_ z

LATENT ENERGY FLUX BY REMAINDER MEASURED LATENT ENERGY FLUX UAOIANT NET ENERGY FLUX CONDUCTEDENERGY FLUX SENSIBLE ENERGY FLUX

"

0.10

/ ~"~,."*

O,05

485

i

~"

"~,\

od J

/

)t - - "

/'i

,...,...--\--'%L

i

\

'/

sic

r.o

L,

-.. I

7 N ¢"2"

°

",~.

"1

-0.05

~.1

-0'10

"",..

:'~" •,.

~ ~.,,~

/

%

-0-15

,,!"

i

,

-0"20

/

'-,.I ,

-0'25 OOO0

0600

O30O

0900

1200

1500

1600

2100

24D0

TIME - OST

Fig. 6. S u m m a r y of energy c o m p o n e n t s over s e a ice at Wales, Alaska, on 12 April 1959.

0"25 0.20 0'15

.~

O.lO'

/

0.05

i//

\-

,.,

\

/

,

\/..,,....~

/ --

I*" /--~-"~ ~

l -0"05 •~,

-0"10 -0"15

-0"20

.#

~', . . ~ ° , s •

. . . . . LATENT ENEUSY FLUX BY REMAINDER ....... MEASUREDLATENT ENERGY FLUX ~NAUIANT NET ENERGY FLUX ,, CONDUCTEDENERGY FLUX ......... SENSIBLE ENEOGY FLUX

I --0"25 OOOO

I I

) 0300

I 1

I

I OlOO

I

] OlD0

I

1

I

1200

I

I

1500

I

I

1800

I

I

2100

t

2400

TIME - BST

Fig. 7. S u m m a r y of energy c o m p o n e n t s over s e a ice at Wales, Alaska, on 9 M a y 1959.

486

J.H.

BROWN

only gradual changes. In Fig. 3 the energy components correlate quite well and the agreement of LE and LE(Rn + Qc + H) is good. On 2 March the components are much larger than on 25 February. T h e sky was relatively clear throughout the entire day. Wind velocity, wind direction and air temperatures showed only gradual changes. In Fig. 4 the energy components agree quite well, and the coincidence between LE and LE(Rn+ Qc+H) is good. During the mid-day hours, the surface gain of sensible flux is very large, almost a step function, while the surface loss of latent energy also appears to be great. A reasonable explanation for this result may be that a large lead opened up in a colder area north of the measuring site. This could cause a considerable amount of energy to be transferred from the ocean to the atmosphere by vaporizing of the water. Badgley[19] has shown that an open lead can have a significant effect on energy components. The water vapor coming into contact with the cold air condenses or freezes, releasing large amounts of latent energy. As this air mass is moved by winds from a colder to a warmer region, the released latent energy in the atmosphere is transformed primarily into sensible form to maintain the total balance. As this warm air mass moves across an ice sheet into a warmer area, the advected sensible energy flux will be large and of positive sign. H o w e v e r , the latent flux will also be large but of negative sign. In the present work, the edge of the shore-fast ice was approximately 2500 m north of the measuring site, and the wind direction was from the n o r t h - e a s t for the whole day. Sea smoke was visible to the west, indicating open leads in the Bering Straits. On 14 March the sky was clear until the afternoon, then by evening it was overcast. The winds were from the south with speeds of about 6 m sec -1 during the early hours, increasing to 16 m sec -1 during the late hours of the day. Air temperatures were relatively constant over this period, By mid-morning, there was heavy blowing snow, and sea smoke was visible to the west throughout the day. In Fig. 5, the differences between LE and LE(Rn+ Qc+H) are large during the daylight hours but in close agreement during the night hours. The general shapes of the two curves are very similar. Both curves are positive in sign, indicating the precipitation of water vapor in the form of frost which was observed to be forming on a number of the instruments. It is difficult to ascertain the reason why greater differences occurred between LE and LE(R~, + Qc + H) on this day. If Eqs. (4) and (8) are compared, using the appropriate stability Eqs. (12) or (13), it can be seen that large errors could be introduced in H and LE through measuring errors of the temperature, the specific humidity and the wind velocity gradients. Errors in the temperature gradient could occur from frost forming on the dry-bulb thermocouples. The heat of formation would be greater on the lower thermocouples, resulting in an incorrect decrease in the temperature gradient which would have very little effect on LE but would cause a significantly incorrect decrease in the computed magnitude of H. The errors, causing a decrease in magnitude of H , would cause LE(R,, + Qc + H) to be of smaller magnitude. Specific humidity gradient errors could be caused by differences in ventilation of the ice-bulb thermocouples at the different levels of measurement. This could result in the gradient being erroneously increased, yielding too high computed values of LE. The horizontal wind velocity gradient could be in error because of the heavy blowing snow. During such conditions, the lower a n e m o m e t e r cups tend to collect more snow and rotate at a slower rate than is the case with the higher cups. This would cause the wind gradient to be erroneously increased, and result in the magnitude of the computed values of

E n e r g y e x c h a n g e a t a s e a ice b o u n d a r y

487

H and L E being too high. Hence, the errors in LE and LE(Rn + Qc + H) would be of equal magnitude and sign. On this day, it would appear that water vapor was being advected from leads to the south, where air temperatures were usually higher than those at the measuring site. In this situation, the latent energy flux at the measuring site would be of positive sign while the sensible energy flux would have a negative sign. After a few hours of high winds, most of the loose surface snow would be stripped from the surface. The leads, several thousand meters to the south, would be expected to close because of ice pressuring. As this occurs, even though high winds persist, the positive latent energy should decrease and finally become negative. The negative sensible energy would then increase and become positive. At the same time, the accuracy of the total energy balance should improve. A comparison of the measured latent energy flux with the value calculated by the remainder method (Fig. 5) indicates that these physical processes appear to be occurring. On 12 April the sky was overcast the entire day. The wind direction was from the east-north-east, the wind velocity was moderate and steady, and the temperature changes were gradual and moderate. There was very light snow around noon. Ice fog was reported most of the day and sea smoke was observed to the west in the morning. In Fig. 6, the energy components are large for this day. The latent flux is high with a positive sign, indicating that warm moist air is being advected. This is rather surprising since the wind was from offshore. However, in the region of Cape Prince of Wales, the wind patterns can be highly irregular. In Fig. 6, the agreement between LE and LE(Rn + Qc + H) is very good. On 9 May the sky was overcast. The wind direction was constant from the northnorth-east, the air temperatures changed little and the wind velocity was strong. Wind velocities of 11 m sec -1 were measured at the 2-m height during the day. It snowed and there was blowing snow throughout the day. In Fig, 7 the energy components balance quite well. The agreement between LE and LE(Rn + Qc + H ) is good considering the unstable weather conditions of the day. The sensible and latent energy flux were negative most of the time. There did not appear to be any large amount of advected energy flux for this day. It is of some interest to have an estimate of the total energy flux errors. The absolute sum of the individual components, using the latent flux value calculated by the remainder method, gives the total energy plus the resultant errors. If the total energy is large compared to the resultant errors, then a relative flux error (RFE) may be defined as

RFE =

LEmeas.-- LErem.

IR.I + loci + Inl + ILgrem.l"

(16)

This relation should give an indication of relative errors when the total energy is large compared to the resultant errors. When the total energy is relatively small compared to the resultant errors, the relative flux error will be large. The relative flux error will always exaggerate the true error except when the resultant error is zero in the divisor of Eq. (16). In Fig. 8, the frequency distribution of the hourly relative flux errors is given for the 5 days; they seem to be randomly distributed. Figure 9 illustrates the hourly relative flux errors in terms of the atmospheric stability for the 5 days. Again,

S. E. VoL 12:4 ~ E

488

J.H.

BROWN

20

24

2~

m

-1'0

-0'6

-06

-0-4

-0-2

0-2

0-4

0-0

0"6

I"0

I ' ~ F 2 : ~ 1"505--1"$

RELATIVE FLUX ERRORS

Fig. 8. T h e frequency distribution of the hourly relative flux errors over sea ice for 5 days.

1'60 1.40 1'20 1'00 'ao "UO •40

""

• 20

I

•

i

% •

0

" - 2 - •- - -

20

I- . . . ' ; ~ . . I,

",'+ ;"

." "~.. ,,,

.

.

.

.

.

g .

.

.

.

oO

.

.

-'40 --60

" ~

- "80 -1'00 -1"20 -1-40

-,uo

~

~_~-~2

~1 ~ o', ~ ~3 ~, o'+ o' ', o' o'R I'O ~1 ,'2 ~3 I, ,Is R I C H A N D S O N ' $ NUMBER -

Hi

Fig. 9. C o m p a r i s o n of average hourly values of the relative error with a t m o s p h e r i c stability over sea ice for 5 days.

Energy exchange at a sea ice boundary

489

t h e e r r o r s a p p e a r to b e r a n d o m l y d i s t r i b u t e d . H o w e v e r (Fig. 9), it c a n b e s e e n t h a t t h e e r r o r s a r e v e r y large w h e n R i c h a r d s o n ' s n u m b e r a p p r o a c h e s z e r o . T h e r e a s o n is t h a t t h e s e n s i b l e a n d l a t e n t e n e r g y fluxes a r e a p p r o a c h i n g z e r o . W h e n this c o n d i t i o n p r e v a i l s , t h e s e t w o e n e r g y c o m p o n e n t s a r e s e n s i t i v e to the e r r o r s in t h e t e m p e r a t u r e a n d specific h u m i d i t y g r a d i e n t s . H e n c e , t h e r e l a t i v e flux e r r o r is u n d u l y large. F r o m F i g s . 8 a n d 9, it a p p e a r s t h e e r r o r s a r e o f a r a n d o m n a t u r e , p r o v i d i n g s u p p o r t to t h e c o n t e n tion t h a t t h e m e t h o d s f o r d e t e r m i n i n g t h e e n e r g y c o m p o n e n t s a r e valid. CONCLUSIONS T h i s s t u d y h a s d e m o n s t r a t e d t h a t e x i s t i n g i n s t r u m e n t a t i o n a n d t h e o r y will give a g o o d b a l a n c e o f t h e e n e r g y flux c o m p o n e n t s o v e r a n A r c t i c ice s h e e t b y d i r e c t m e a s u r e m e n t . I t is p o s s i b l e to o b t a i n s u c h e n e r g y b a l a n c e b o t h u n d e r ideal a n d a d v e r s e w e a t h e r c o n d i t i o n s . T h e t h e o r i e s o f P r i e s t l e y a n d C r a w f o r d a p p e a r to give r e a s o n a b l e v a l u e s f o r t h e s e n s i b l e a n d l a t e n t e n e r g y fluxes. T h e t h e o r i e s p e r f o r m e d w e l l in adverse, changing weather conditions, over the stability range of Richardson's numbers b e t w e e n --0-053 a n d + 0 . 1 4 0 . T h e g r e a t e s t u n c e r t a i n t y f o r a n e n e r g y c o m p o n e n t w a s for t h e l a t e n t flux. T h e difficulty a p p e a r s to b e in t h e m e t h o d o f m e a s u r e m e n t a n d n o t in t h e t h e o r y . I n a r e a s w h e r e l e a d s c a n f o r m , large a m o u n t s o f e n e r g y c a n b e t r a n s m i t t e d f r o m t h e o c e a n to the a t m o s p h e r e . T h i s e n e r g y is t h e n t r a n s m i t t e d to o t h e r a r e a s , modifying the weather there. Cloud cover can significantly change the total net radiat i o n at t h e s u r f a c e , w h i c h , in t u r n , will c a u s e c h a n g e s in t h e o t h e r e n e r g y c o m p o n e n t s . T h e a g r e e m e n t b e t w e e n e x p e r i m e n t a l a n d t h e o r e t i c a l p r o c e d u r e s u s e d in this s t u d y should, hopefully, provide guidance for such future Arctic energy balance studies. A c k n o w l e d g e m e n t s - T h e author wishes to acknowledge the many rewarding hours spent with the late

Professor F. A. Brooks in discussion of energy exchange processes. In addition, he acknowledges the support discussions and encouragement of Drs. Waldo K. Lyon and M. Allan Beal. Others who gave considerable assistance are Gene L. Bloom, Edward E. Howick and William C. Lockett. The research was supported by NAVSH1PS. This paper does not necessarily represent the official views of the U.S. Navy. REFERENCES [1] J. O. Fletcher, The heat budget of the Arctic Basin and its relation to climate. The Rand Corp., Rep. No. R-444-PR (1965). [2] Proc. Syrup. Arctic Heat Budget and Atmospheric Circulation (Edited by J. O. Fletcher). The Rand Corp., Rep. No. RM-5233-NSF (1966). [3] C. H. B. Priestley, Turbulent Transfer in the Lower Atmosphere. The "University of Chicago Press, Chicago ( 1959). [4] T. V. Crawford, Moisture transfer in free and forced convection. Q. Jl R. met. Soc. 91, 18 (1965). [5] A. J. Dyer, The turbulent transport of heat and water vapour in an unstable atmosphere. Q. Jl R. met. Soc. 93,501 0967). [6] M. K. Gavfilova, Radiation Climate o f the Arctic. GIMIZ, Gidrometeorologicheskoe lzdatel'stvo, Leningrad (1963); Translated from Russian by the Israel Program for Scientific Translations, Jerusalem ( ! 966). [7] G. H. Liljequist, Energy Exchange o f an Antarctic Snow-Field, Vol. 2, Part 1A. Norwegian-BritishSwedish Antarctic Expedition Scientific Results, ! 949-52, Norsk Polarinstitutt, Oslo (1956). [8] G. H. Liljequist, Energy Exchange o f an Antarctic Snow-Field, Vol. 2, Part lB. Norwegian-BritishSwedish Antarctic Expedition Scientific Results, 1949-52, Norsk Polarinstitutt, Oslo (1956). [91 D.J. Portman, Conductivity and length relationships in heat-flow transducer performance. Trans. Am. Geophys. Union 39, 1089 (1958). [10] J. R. Philip, The theory of heat flux meters.J. Geophys. Res. 66,571 (1961). [11 ] D.L. Anderson, The physical constants of sea ice. Research 13, 3 I0 (1960). [12] P. Schwerdtfeger, The thermal properties of sea ice. J. Glaciol. 4,789 (1963). [ 13] M. P. Langleben, The heat budget of a melting cover of sea ice. To be published,

490

J . H . BROWN

[14] T. E. Vinje, Some results of micrometeorological measurements in Antarctica. Arch. Met. Geophys. Bioklim. Set. A 16, 31 (1966). [15] Smithsonian Meteorological Tables (Edited by R. J. List). The Smithsonian Institution, Washington (1951). [16] F. A. Brooks and F. V. Jones, Data processing and computer programming. Investigation of Energy and Mass Transfers Near the Ground Including the Soil-Plant-Atmosphere System, Chap. IX. University of California, Davis (1963). [ 17] O. G. Sutton, Mierometeorology. McGraw-Hill, New York (1953). [ 18] H. Spencer-Gregory and E. Rourke, Hygrometry. Crosby Lockwood and Son, London (1957). [19] F. I. Badgley, Heat budget at the surface of the Arctic Ocean. Proc. Symp. Arctic Heat Budget and Atmospheric Circulation (Edited by J. O. Fletcher). The Rand Corp., Rep. No. RM-5233-NSF (1966).