J ournal oJGlaciology, Vol. 41, No. 137, 1995 Variations of ablation, albedo and energy balance at the tnargin of the Greenland ice sheet, Kronprins Christian Land, eastern north Greenland THOMAS KO NZ ELMAKN Department oJ Geograph)l, Swiss Federal i nstitule of T echnology, CH-8057 Zurich, Switzedand ROGER J. BRAITHWAITE Grrmlancis Geologiske Unciers@gelse, DK-1350 Kf) benhavn K, D enmark ABSTRACT. A meteorological a nd glaciological experiment was carried o ut in July 1993 a t the ma rgin of th e. Greenl and ice sh ee t in KrOl"))Jrins. Christia n L a nd , eas tern north Gree nl a nd. \Vlthm a small area (a bo ut 100 m- ) d ally measurements were made on ten a bl a tion stakes fi xed in " light" a nd " dark " ice and were compa red to eac h oth er. Simulta neo usly, the components of the energy bala n ce, including n et radia tion, se nsibl e-h ea t flu x, la tent-hea t flu x a nd conductive-hea t flu x in the ice were d etermin ed . Gl o b al radiation , lo ngwave in co ming radia tion a nd albedo wer e measured, a nd longwave outgoing radi a tion was calculated by ass uming th a t the glacier surface was melting. Sensible- a nd la tent-h ea t f1u xes were calcula ted from a ir tempera ture, humidity and wind sp eed. Condu c tive-hea t flu x in th e ice was es tim a ted b y tempera ture-profil e meas urem ents in th e upperm os t ice la yer. N e t radia tion is the m aj or source of a bl a tion energy, a nd turbulcnt flu xes are smaller en ergy so urces by a bout three tim es, whil e hea t flu x into the ice is a substanti al hea t sink, redu cing energy ava il a bl e fo r ice melt. Albedo vari es fro m 0 .42 to 0.56 within th e ex perim enta l site a nd ca uses rela ti vel y large differences in a bl a ti o n a t stakes close to each o ther. Sm all-scale albed o variations sh o uld th erefore b e carefull y sampled for large-scale energy-bala n ce calcula tions. INTRODUCTION An a bla tion- clima te stud y was m ad e a t the ma rgin of th e Greenl a nd ice shee t in Kronprins C hristi an La nd , eas tern north Greenl a nd (Fig. I). The stud y was part of a 2 year progra mme on world sea-level ch a nges supported by the European Community. The specific obj ective of th e stud y was to collec t d a ta on clima te, a bl a ti on, radia tion a nd ice tempera ture to estim ate th e so urces and sinks of th e energy bal ance during the period of meas urements (8- 27 J ul y 1993) a nd to com pare condi tions wi th those found in W es t Greenland (Braithwaite a nd Olesen, 1989 , 1990). The fi eldwork was carried o ut a t two study sites. One was located o n the tundra in front of the ice sh ee t (base camp ). Th e o ther was establish ed o n the ice sheet (glacier sta ti on). Th e glacier sta ti on was loca ted a bout 300 m inla nd of th e ice m argin a t a n eleva tion about 50 m a bove th e ground-level a t the edge . Th e si te was well-ex posed with out ma rked slope, i. e. it represents a large a rea close to the ice-shee t margin. Th e surrounding a rea was covered by hummocks about 0. 5 m in height a nd 5 m in wa velength , i. e. th e surface to pogra ph y is rougher th an th e site in W es t Greenland (Camp IV; Fig. I ), wh ere Ambach (196 3) m ade energy-b a la nce studies. Th e glacier sta ti on was a wa lk of only 10 min from th e base camp a nd 174 was vi sited seve ral tim es d a il y during th e experim ent. Th e position of th e glacie r station was d e termined by th e g lo b a l p os iti onin g sys tem (GPS ) to b e la titud e 79°54'43" N and longitud e 24°04'25" W a t an altitud e of 380 m a.s .l. Abla tion was determin ed as the ave rage of readings a t ten sta kes drilled within a n a rea of a bo ut 100 m 2 . T wo th ermi stor strings were also insta ll ed to m eas ure tempera ture g radients in the top 3 m of the glacie r surface. At the sa me tim e as th e a bl a ti on measurements, meteorological d a ta (air temperature, rela tive humidity and wind sp eed ) were obtained once-hourl y a nd r ecord ed by data loggers at base camp and at the glacier sta tion . Radi a ti o n conditions were studied by co ntinuous logging of global radiation a nd all-wa ve (sho rt- a nd longwave ) incoming radi a tion at th e base camp , while albedo was meas ured a t the glacier sta tio n . "Yea ther conditions were ra ther sta ble throughout th e whole field period with nearl y co ntinuous sunshine, liule cl o ud a mount, nearly consta nt tempera tures (daily means of 3- 6°C) and strong wind s from th e ice sheet (d aily mean s of 3-8m s I) . Cloud obse rva tions (amount a nd type ) were mad e six tim es a day using World M eteorologica l Organiza tion cl assification sch emes. The interior of Kronprins Christi a n L a nd is obvio usly drier and has more sunshine tha n the coast in general, e.g. Sta tion ord Downloaded from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X Konzelmann and Braithwaite : Ablation, albedo and energy balance in Kronprins Christian Land climatic data using profile-aerodynamic formul ae (Ambach, 1986 ) , thus saving the weight of heavy instrum ents. By analogy with preliminary geological surveys, such an a pproach m ay be termed a reco nnaissance energybalance stud y and it is hoped th a t the present results legitimate the approach. ABLATION S0NORE OAMANARSSUP SERMIA cf/ • NOROBOGlETSCHER Fig . 1. Location of glaciological studies ice sheet referred to in the text. 011 the Greenland is no to ri o us for fog and late-lying snow. The fine weather con ditions durin g th e p eriod of observa ti on were proba bl y not co mpletely typical as there was a stro ng a nticyclo ne over Greenland for most of the field period (Gcb and Naujokat, 1993 ) . Ambac h (1963) showed for the upper a blat ion area (Camp IV ) that the ener gy gain at the s urface in summ er is ca used mainl y by the radiative flu xes as the sensibl eand latent-heat flux es almost cancel each o th er. At ETH Camp (Ohmura a nd others, 1991 , 1992 ; Fig. 1), which is located cl ose to th e m ean equilibrium-lin e altitud e (ELA ) , n et radi a tion provides almost a ll of the abla tio n energy (Ohmura a nd oth ers, in press ) . R adiation was a lso expec ted to be the main so urce of a bla tion energy a t the present stud y site. In th e lower ablation area of a glacier or a n ice sheet, la rge varia tions of th e surface reflectivity (albed o ) can be expec ted. This is du e mainly to different ice conditions, e.g. age, surface undulation , conta mination, slope and orientation. Th ese variations in albedo a ffec t the energy balance and th e a bla tion ra te, and th e relation between sm a ll -scale va ri a ti ons of a bla tion and albedo is treated as thc m a in poi nt of th e prese nt paper. The sma ll er, less importa nt energy-b a la nce compo nents, such as turbulent Duxes a nd condu ctive-heat flux in the ice, were evalu ated b y methods req uiring only lig h tweight eq uipment. Morris (1989) sugges ted tha t acc uracy in es tim a tin g energy-b a lance co mpon ents should be co mmensurate with th eir relative importa nce in the overall energy ba la n ce. W e ex tend this co nce pt b y replaci ng "acc uracy" with " logistic cos t". For example, the turbul ent components were es tim a ted from simple Previous experience has shown that ab latio n measurements in vo lve considerab le error and tha t abla tion itself varies greatly even on a scale of metres (Ol esen and Braithwaite, 1989 ), suggesting that many m eas uremen ts are needed to obtain a representative value for a site. The ten stakes were read daily close to 1900 h local time (about 171 5h solar time ) . As stakes are usua ll y surround ed b y an "ab la ti on hollow" of 0.1 ~ 0.3m di ameter, stake readings wer e made by meas uring fi'om the top of each sta ke to a str aight ed ge laid on the upstream sid e of th e stake which defines an ave rage level of the su rroundin g surface. Differe nces in successive daily readings are conve rted into abla tion valu es ass umin g an ice density of900kgm 3. We find it conven ient to treat ablation as a positive rath er than negative quantity as recomm end ed by Anon. ( 1969 ) to avoid the clumsiness of having to say tha t (negati \"e ) a blation d ecreases with in creasing availa bility of energy. Th e stakes were placed so that fi ve were loca ted in "dark" areas a nd fi ve in " light" areas . Th ese were sec ti ons of the ice surface whi ch had " d ark" a nd " light" co lor, respec ti\'ely, based o n visual inspectio n at the beginning of the fi eld wo rk . The difference between the two kind s of surface a ppea rs to be whether d ebris is spread evenl y over the surface (" d ark " ) or co ncentrated into a few deep cryco nite h oles surround ed by ver y white ice (" light" ) . Abl ation vari ations from d ay-to-d ay and between stakes were a nalysed by the simple linear model of Lliboutry ( 1974): YjI = Qj + (31 + Ejt , (1) where Yjl is the ablation at stake j on da y t, Qj is th e mean ablation at stake j, (31 is the ab lation deviatio n which is the same for a ll stakes on d ay t, a nd Ejt is the error in the model which is ass umed to be random. Measurement errors con tri bu te to th e error term as long as th ey are rand om bu t if they are syste m atic, i.e. sh ared by a ll stakes, th ey contribute to th e abla tion d eviation . Accord ing to Bra ithwaite and O lese n ( 1989), readings at the indi vidua l st a kes should b e a pproxim a t e ly equall y correlated w i th the a bla tion d ev iation (3jl . At ab la ti on stake B, howeve r, the correla tion coeffi cient between th e ablation d evia tion and d ata is onl y 0. 36 while co rrelati ons Unfortunately, for oth er stakes are in the range 0 . 83 ~ 0.95 stake B was loca ted on a steep slope which made it difficul t to use the straigh t -ed ge method. Beca use of inconsisten cy with the other stakes, data from that stake are dropped fi'o m any furth er analysis. Th e ablation va ri a tions a t the remaining nin e stakes a r e shown in T able 1. Th e error in th e lin ea r mod el for th e nin e-sta ke, 20 d matrix is surprisingly low with a sta nd a rd deviation Downloaded from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X 175 Journal of Glaciology Table 1. D aily ablation at nine stakes ( A- J, excluding B ) on the margin of the Greenland ice sheet, Kronprins Christian 2 I Land, J uly 1993. Units are kg 111 cl Date A C D E F G H 1 ] M ean s.d. July 1993 8 9 10 I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 36 58 58 40 45 3I 58 63 58 45 45 58 58 54 45 50 36 31 23 36 40 63 58 31 54 31 40 54 58 31 45 50 58 54 40 54 36 27 31 36 31 54 40 40 27 27 50 50 54 40 45 54 54 50 45 54 31 45 18 31 31 50 45 36 27 31 45 58 40 31 45 50 50 50 36 54 27 27 31 40 31 50 45 27 27 27 31 68 40 31 31 50 54 50 40 50 31 18 18 40 36 50 54 36 31 31 50 63 45 40 45 45 50 45 36 45 31 31 27 31 23 45 45 27 27 27 40 50 36 40 36 50 45 45 40 45 31 31 27 31 31 45 45 27 23 23 40 54 40 27 36 45 50 36 36 50 23 27 18 27 31 58 45 31 36 27 45 63 45 40 50 50 54 54 45 50 36 3I 31 31 32 53 48 33 33 28 44 58 46 36 42 50 53 49 40 50 31 30 25 34 M ea n s. d. 46 12 45 12 42 40 10 38 13 41 10 37 9 35 43 II II 41 10 II of only ± 5 kg m 2 d I which is certainl y small co mpared with the range ± 13 to ± 19 kg m 2 d- I qu oted by Braithwaite (1985, p.21 - 22 ). Thc hypothesis th at the four " d a rk " stakes (A, C, D a nd G ) have the sa me mea n abla tion as the fi ve " lig ht " stakes (E , F, H , I and J ) is tested with the Studcnt t test (Kreyszig, 1968 , p. 219 ) . The mean a nd stand ard deviations for the two data se ts a re 44 ± 9 kg m- 2 d- I a nd 39 ± 10kgm- 2 d- l , respec tively. Th e m ean valu es a re different (a t 5% sig nifi cance leve l) a nd it ca n b e conclud ed that " da rk " stakes have sig nificantl y greater a blatio n than " light" stakes. Th e time series of a bla tion energy for " lig'ht" a nd " dark" sta kes a re presented in Figure 2. Th c glacier surface co nsisted almost always of a 2030 mm thi ck "wea thering crust" (MU ller and K eeler , 1969) with a relatively low density. The effect of this crust on the eva lu a tion of ab lation deserves discussion . The abla ti on in a period is the loss of ma teri al in the surface layer of thickness h relative to a stake fi xed in the ice. Th e total surface-layer thickn ess h consists of a layer of ice of thickn ess hi a nd a layer of crust of thickness he. Th e abla ti o n is given by: 5 6 7 5 10 3 8 7 8 6 6 4 4 6 4 4 4 7 6 5 a blation is evalua ted using only the first term with an ice density of 900 kg m 3 which refers to slightly bubbly glacier ice . Some attempts were mad e in 1986 at Q a ma narssllp sermi a Lo m easure the d en sity of crust with a m iniature co rer (unpublished data from R.J. 250 1--0--- light dark 200 E :;: >- e> 150 Q) cQ) c o 100 ~ :0 « 50 (2) Julian day wherc 11h is the cha nge in surface-layer thickness, 11hc is the ch a nge in crust thickness, and Pc a nd Pi a re th e densities of crust a nd ice, respectively . As the depth of crust is not observed a nd its density is unknown , the Fig . 2. A blation energy for" light" and " claTk" stakes, 827 Ju ly 1993 (Julian days 189- 208), at Kronprills CIzTistian Land. Unit is W 172 2. Downloaded176 from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X I KOllzelmanll and Braithwaite: Ablation, albedo and energy balance in Kronprins Christian Land Bra ithw aite) . Although th ese dat a ca nn ot be very acc ura te, a crust d ensity of 500- 700 kg m 3 was indi cated. Over the whole 20 d period of the fi eld experiment with an average i1h of 0.9m, th e second term , involving cha nge in crust thi ckn ess, is entirely negligible. For th e d a il y a bl ation readings, however, th e second term cou ld be a signifi cant so urce of error althou g h the weathering cru st neve r co mple te ly d isa pp ear ed in th e present ex pcrim ent as obse rved by MUller a nd K eeler ( 1969 ) in their data se ts. It should be noted that a n error of this kind is not detected by the Llibo utry m odel becausc the error is more-or-Icss co mm on to a ll sta kes. RADIATIVE FLUXES Du c to the importa n ce of radiativc Ouxes in th e energy ba lance, priority was given to accuratc radiation measurem ents. At the base camp , glo b a l radi a tion a nd allwave in coming ra diation were m eas ured direc tl y with a Swissteco SS-25 p y ra nometer a nd a Swissteco ST -25 py rradiometer, res pec ti vely. The lo n gwave incoming radi a ti on was then calcula ted as th e difference between th e a ll-wav e in co ming radi a tion an d th e g loba l radi a ti on, a nd compen sa ted for th e emission loss of the instrument (0'T;4) , where 0' is the Stcfan- Bo ltz mann con sta nt ( = 5.67 x 10 8 Wm 2 K .,) a nd 1i th e tempe rature of the p yrradiometer in kelvin. Th e cosine error of th e u pfacing p yranomete rs was co rrected for ze nith a ngle > 70 ° using a pol y n o mi a l function, whereby onl y the part of direc t sola r radia tion was taken into acco unt. Based on meas ure m ents made und e r simil a r meteoro logical cond-itions a t ETH Camp in June 1990, it was ass um ed th a t 70% o f g loba l radi a tion is ca used by direct sola r radiation (K o nzel ma nn , 1994) . Du e to a poss ibl e und erestim a tion of th e a ll-w ave in co ming radiation du e to thermal co nv ec tion as proposed by Ohmura and Gilge n ( 1993 ), the longwave in co ming radiation was correc ted accordingl y. Shortwave radi a tivc Ouxes at th e g lacier sta tion were m eas ured with a Swissteco S'vV-2 two- co mpon e nt p yra nom e te r (a lb e dom e ter ). Th e in str ument \ov a mounted on a tripod a t a height of abo ut I m a nd was reloca ted every seco nd d ay to sampl e as many ty pes of surface as possible. In genera l, g lo b a l radi a tion a t th e g lac ie r sta ti o n and a t base camp ag reed closely. Howe\'Cr, to avoid poss ible sys tem a tic errors due to a n y tilt o[ th e r a diometer a t th e glacier sta tion , g loba l radia tion meas ured at base ca mp w as used to calculate a lbed o toge ther with shortw ave refl ec tcd radiation at th e glacier stati o n. A ss uming melting co nditi ons a ll da y a t th e glacier station , longwa\'e o utgoing radiation was se t a t 3 16 \V m 2 according to th e Ste[an Boltz mann law. Th e response tim e of the radi om eters is abo ut 5 sa nd th e sig na ls of the instruments were co ntinu ously recorded every 15 s. Every 30 min th e average was computed and stored. The opera tion of the instrumen ts a nd da ta loggers was checked sever al tim es a da y. Th e un ce rta inty in the longwave in co ming radiati on was se t at ±IO W m 2 acco rd i ng to th e correc tion meth od m en tioned above a nd a n in str um e nt intercomp a ri so n perform ed b y D eLuisi a nd oth ers ( 1993 ). TURBULENT FLUXES Th e sensible-heat flux (SHF ) is estimated by th e method o[ Amb ac h (1986 ) from m eas ured wind speed and temperature: (3) where K s is the exchange coeffi cient for turbulent-h eat flux , P is the atmosph eric press ure, U2 is the wind speed at 2 m above the glacier surface and T2 is th e a ir temperat ure a t 2 m a bove the glacier surface. Th e glacier surface is ass umed to be a t the melting point. For a Prandtl-ty pe neutral boundary layer with loga rithmic profi le for wind speed , temperature a nd vapour press ure, the exch a nge coeffi cient is given by: where cp is th e specific heat of air with co nsta nt pressure (1005Jkg 'K ' ), kisvo nK a rma n'sco nsta nt (0.41 ), po is the densit y of air in the sta ndard conditi on ( 1.29 kg m \ bo is the stand a rd atmosph eric pressure ( 1.01 3 x 105 Pa ), Z is th e in strum ent heig h t (2 m ) and ZOw a nd ZOT are th e roughn ess lengths [or loga ri thmi c profi les o[ wind and temperature, respectively. Th e la tent-h eat flux (LHF ) is similarly es tim a ted from meas ured d a ta [or wind speed a nd vapo ur press ure: (5) wh ere KL is th e exc hange coe fIi c.ien t for late nt-h ea t flux a nd i1e2 is th e difference be tween \'apo ur pressure at 2 m a bove th e g lac ier surface a nd that at th e melting glacier surface. For th e same assumpti ons as befo re, th e exchange coeffi cie n t is given by: where L is th e latent hea t o[ evapo ra tion o r sublimation as app rop ri a te (( 2.514 o r 2.849 ) x 106J kg ' ) and ZOe is th e ro ug hn ess length [o r th e logarithmi c profil e o[ water vapour. Followi ng Ambach ( 1986 ), th e roug hn ess length [or \\'ind ove r an ice surface is ass um ed to be 2.0 x 10 3 m while the ro ughn ess len g th s fo r temperature a nd water va pour a r e both assumed to be 6.0 x 10 b m . As formu la ted by Ambach ( 1986 ), th e exchange coefficients K s and KL are valid for a neutral boundary layer while th e air just over a glacier surface m ay be ra th er sta ble. Th e tu rbu lent-heat 0 uxes were calcu lated ever y hour according to Equ a tion s (4) and (6 ) using th e air temper a ture, relative hum idity a nd wind sp eed measured a t 2 m. Some r a di a tion hea tin g of th e tempera ture/humid ity screen was noted whereby temperatures sud-d en ly rose when wind speeds were low, and th e d a ta we re co rrected by h a nd. Hourl y values of th e calcu lated turbu lent Duxes and ha l[-hourl y values of th e radiative flux es were then summ ed up to daily values e nding a t 1900 h loca l time, so th ey co uld be co m pared direc tly wi th a b lation meas u re m en ts mad e a t th a t tim e. Downloaded from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X 177 Journal of Glaciology ICE TEMPERATURES AND CONDUCTIVE-HEAT FLUX IN THE ICE 4 It was exp ected tha t the co ndu ctive-h eat flu x in the ice wo uld b e a significant en ergy sink in contras t to the icesheet m a rgin in Wes t Gree nl and where it was ass umed by Braithwaite a nd Olesen ( 1990) to be n egligibly small. Englacial tempera tures were therefore m eas ured ever y day to calculate the conductive-h eat flu x in the ice. The measurements were mad e a t two strings with thermi stors which were drilled a t 0. 5 m intervals dow n to a maximum of 3 m d ep th. M eas ured tempera tures were even lower than expected with the ooe isotherm only 0.2- 0 .3 m below the surface (even with the possible help of radia ti on warming of th e thermistor cables) . This probably accounts for th e ra ther difficult drilling conditions en countered when placing th e stakes, i.e. a wet drill b a rrel penetra ting very co ld ice and frequently j amming . During the period of m easurements, the ice tempera tures a t th e various depths rose by 0.2- 0.3 K d- I. The ra te of change of ice tempera ture with time is aT I at given by: 3 aT l at = - (11pic) dH (z)/ dz, (7) where Pi is density of ice (900 kg m-3) , C is specific heat of ice (2009J kg- I K - I), H (z) is the englacial-h eat flu x and z is the d epth below the surface . Ass uming that aT I at equ als a consta nt C du ring the period of m easurements, then H (z) is a linear fun ction of depth: H(z) = Ho - CPiCZ, (8) wh ere Ho is the heat flu x through the glacier surface a t Ho can be calcula ted as the intercept in a regression equ a tion of h eat flu x versus depth where th e hea t flu x H(z) is calcula ted from englacial-temperature d a ta according to the equ a tion z = 0 m. Equa tion (8) suggests tha t H (z) = - KaTl az, (9) where K is the th ermal conductivity of ice, 2.1 W m- I K - I according to Paterson ( 198 1, p. 186 ). The heat flu xes for each d ay a re strongly co rrela ted with d epth with gen era lly similar equ a ti ons and , assuming that an y differen ces are du e to sta tistical flu ctu a tions, the mean hea t flu x Ho for the whole period was calcula ted by combining all the availa ble da ta in to a single regression equ a tion (Fig. 3). The intercept is 17.6Wm 2 and th e slope of the regression lin e correspond s to a constant temperature change of 0.21 K d- I during th e field period . Extrapola tion of the regression line (Fig. 3) to greater depth sugges ts that the h ea t flu x becomes zero at a bout 4 m d epth bu t it is more likely tha t th e a pproach to zero flu x is asymptotic at greater depths tha n 4 m . ENERGY BALANCE Th e en ergy used for a blation ABL is given by: o o +-.~ o 20 15 5 10 2 Conductive heat flu x in the ice W m - Fig. 3. Ca lculated conductive heat flux in the ice versus depth below the glacier surface, 8- 27 July 1993 . ABL + CHF = SWR + LWR + SHF + LHF + ERR, (10) where ABL is calcula ted from measured a bla tion using the la tent h eat of fu sion (3.34 x 105Jkg I), CHF is conductive-heat flu x in the ice, SWR is sh o rtwave net radia tion , LWR is longwave net radia tio n , SHF is sensible-heat flu x, LHF is la tent-heat flu x, a nd ERR is th e total error du e to measurement erro rs, simplifying assumptions a nd disregard ed t erms in the ene rgy-balance equation . D efin ed as above, ERR can be regarded as an unknown , extra source of en ergy which is es tim a ted from the residu al of th e oth er terms in Equ a tion ( 10 ). The magnitud e of ERR is a usefu l ch eck on th e accuracy of the other terms. F or calcul a tion of SWR an albed o of 0. 48 was used . The condutive-h ea t flu x in the ice was taken as 17.6 W m- 2 . The time series of all compon en ts of th e energy b ala n ce is presented in Figure 4. The calcula ted energy b ala n ce for the 20 d is shown in T able 2 a nd summ a rised in T a b le 3. As disc ussed below, the main error is probably du e to the turbulent flu xes so tha t they p ro b ably constitute more tha n th e 26% of abla tion en ergy shown in the ta ble. ERROR IN THE CALCULATED ENERGY BALANCE On average, the error term ERR represents n ea rl y I1 % of th e total en ergy balance. I n view of the uncerta in ty of the various ass umptions, it is good tha t the mean er ro r is not even larger. For example, Braithwaite and O lesen (1990) found errors of -40 to + 29 % of monthly a bla tion at Nordbogle tsch er and Q a m a n a rssup sermia . In terms of variance, th e error corresponds to about on e- third of the ablation varia nce. There is therefore a substa nti a l source of both sys tem a tic and ra ndo m error in th e energybalance calculation . The error ERR has almost no correla tion with the radi ation terms SWR and L WR. On the other h a nd , the error has mod era te correla tion with the turbulent flu xes, i.e. r = + 0 .63 for SHF a nd r = - 0.53 fo r LHF , whi ch Downloaded178 from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X Konz elmann and Braithwaite : Ablation, albedo and energy balance in III Wm- 2 i'R 11 SH' 0 OF IIIlI! LHF ~ ABL • Ern I suggests that they maybe the main sources of systemati c error in the calculated energy balance. For example, if both SHF and LHF are multiplied by a factor of 1.5 before calculating the energy balance, the mean error is essentially reduced to zero (th e error standard deviation is littl e changed ). In order to assess the plausibility ofa 50% error in the turbulent fluxes it is necessary to examine in more detail how they are calcu lated, i.e. with regard to sta bility and to the assumed surface roughness. The exchang e coeffici ent [or sensible-h ea t nu x (Ambach , 1986 ) given by Equation (4) does not take account of the stability of the boundary laye r over the m elting glacier. Price and Dunne ( 1976) propose stabili ty corrections in terms of the bulk Richardson numb er, and application of this r ed uces the sensible-heat flux in the present stud y by 5- 18 %, thus increasing the error in th e calc ulated energy balance rath er th a n reducing it. The Ambach ( 1986 ) formulation uses different rough n ess lengths for wind , temperature and water vapour (over ice) while Price and Dunne (1976) a nd Moore ( 1983 ) assume the same roughness lengths (over snow). Pu tting ZOw = Z OT = Z Oe = 10- 3 m in Equations (4 ) and (6) would exactly account for the mean error in the calculated energy balance. Such a roughness length falls well within the wide range of values quoted in the literature [or ice, e_g. by Grainger and Lister ( 1966), Streten and Wendler (1968), W endler and Weller ( 1974), Poggi (1977 ) and Hay and Fitzharris (1988 ), although Morris (1989 ) suggests that some o[ the larger roughness 300 c '(ij 200 Cl >, Cl Q; c 100 w 0 (/) (/) .Q -100 >, ~ Q) c w -200 -300 o ill Ol Ol (\j Ol Ol l() o(\j o (\j ~ co o (\j Fig . 4. Energ)1balance 8-27 July 1993 (Julian days 189208) at Kronprins Christian Land with net radiation (NR ) , sensible-heat flux ( SHF) , latent-heat Jlux ( LHF), conductive-heat flux in the ice ( CHF), ablation energy ( ABL) and error ( ERR ) . AB L conesjlonds to stake measurements. ERR appears either on the top or on th.e bottom depending on whether there is a surplus or dificit oJenergy. Unit is Wm 2 . Table 2. Daily energyl balance 011 the margin oJ the Greenland ice sheet, Kronprins Christian Land, Ju0' 1993. Units are W m- 2 + LWR + Date Jul y 199 3 SWR SHF 8 9 lO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 186.0 182.9 168 .9 178.8 149.2 145.6 175 .7 174.6 174.1 159.1 168.9 170.5 162.7 159.6 159.6 156.5 158. 1 159.6 158. 1 155.5 - 58.0 - 54.0 - 5 1.0 - 55.0 --43.0 - 35.0 --48 .0 --46.0 --46.0 - 38.0 --4 1.0 - 49.0 - 52.0 --44.0 - 50.0 - 51.0 - 56.0 - 60 .0 - 63.0 - 58.0 59.9 79.7 78.4 43.8 45.6 3 1.2 65.1 88.2 90.5 59.5 49_8 82.7 87.5 75.6 67.5 82.2 57.3 33 .8 33. 1 38.8 Mean s.d. 165.2 11.0 --49.9 7.4 62.5 20 .1 + LHF + + ERR ABL - 25.4 - 26.6 - 14.6 - 14.0 - 18. 5 - 9.1 - 18.4 - 23.9 - 33.3 - 18.6 - 12.4 - 31.9 - 33 .2 - 21.8 - 25.0 - 34.8 - 28 .6 - 15 .9 - 19 .2 - 17 .5 - 20.1 39.4 23.3 - 8.9 12. 3 - 5.2 15. 1 50.0 11.5 - 4.4 15.1 40.0 56.4 36.9 21.9 59.4 8 .3 15.6 5.1 29.3 124.9 203.8 187.4 127.1 128.0 109.9 171.9 225 .3 179.2 140.0 162.8 194.7 203.8 188.7 156.4 194.7 121.5 115.5 96 .5 130.5 17.6 17 .6 17.6 17.6 17.6 17.6 17.6 17 .6 17.6 17.6 17.6 17 .6 17.6 17 .6 17.6 17 .6 17.6 17.6 17.6 17.6 - 22 .1 7.6 20.1 22.0 158.2 37.8 17.6 0.0 CHF Downloaded from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X 179 Journal oJ Cla ciology values may be ca used by slope errors . It appears, therefore, th a t the calcula tion of the energy b a lance is ex tremely sensitive to th e ass umptions a bout s urface roughn ess in agr eement with Munro (1989 ) . This is an importa nt point for future attempts to co upl e ice-shee t models to ge neral circula tion mod els (GCMs) . EFFECT OF ALBEDO ON ABLATION 190 ~ A 180 E • . c ;= 170 >- CJ) • D. ID cQ) 160 c 0 fij 150 G • • :0 « H • E • F 140 M eas urem ents of a lbedo are norm a ll y mad e a t one point a nd therefore d epend strong ly o n th e local s urface conditions. For a n area of 50 m x 100 m in th e upper a blation zone (Camp IV ) , Ambach ( 1963 ) gives a variation of the a lbedo from 0.34 to 0.58 for a particular d ay . Preliminary res ults from a n a ltitudinal profile of a lbedo on bare ice close to the prese nt study site show a lbedo variations of between 0. 30 and 0.62 (p ersonal co mmuni ca tion from H. O erter) . On a total of 16 d, a lbed o was meas ured a t different places insid e the area of ablation m easurements. Parts with " d ark" surface (8 d ) and " light" surface (8d ) were selected subjec tively. For the " dark " surface a mean albedo of 0.43 was fo und and the " light" surface showed a mea n value of 0.53, while the m ean albed o of all sites was 0 .48. The a lbedo difference between " light" a nd " dark" surfaces is here 0.10 . For a d ail y mean glob al radia tion of320 W m 2, this gives a d iffer ence in calc ulated melt of 8.3 kg m - 2 d I which is about 20% of the mean a bla tion over the whole d ata set (T able I ). Th e difIc rence in mean a blation between the four " dark" and th e fi ve " li ght" stakes is 5 kg m 2 d I while the greatest inter-sta ke difference is I1 kg m 2 d I between stakes A and I (Table I ) . The above disc ussion refers to separate a blation a nd a lbedo variatio ns within a n area, a nd it would be interesting to extend th e disc ussion to th e relation between a bl ation a nd a lb edo for indi\'idual stakes. H owever, it is impossible to measure albed o exactly a t a stake because th e stake a nd the albedometer interfere with eac h other , a nd a mo re subjective procedure [or estimating albedo a t each stake is used . In thi s method, the su rface co nditions under the albedom eter were co mpa red on eac h day to the situations at n earby stakes, and the measured a lb edo va lu e was assign ed to one or more stakes that appea red to have a simil a r surface. The a lbedo for each stake was then d etermined as the average of the assigned albed o values. The estima ted a lbedos o[ the four " dark " stakes (A, C, D and G ) agree close ly but there is quite a large r a nge [or th e fiv e " light" stakes . Average albedos for the gro ups are higher than previously stated , but this simply refl ects the different sampling. Th e relation between mean daily a blation a nd th e estim ated a lbed o for the individual stakes is illustr ated by Figure 5. The correlation sh ows a \'alue of r = - 0.82, whi ch aga in suggests that a lbedo is a main factor 111 ablation varia ti o ns within a small area. The above indi cates that a point meas urem ent of a lbed o is no t sufficient for acc urate energ y- balance calc ula tions in a blation areas. Therefore, a n albedo value for a larger area should be determined , either by m easurements from high towers (L a ngleben, 1968) or by enough point m eas urements at gro und level to sa mpl e small-scale a lb edo variations as attempted here. 180 • 130 0.4 0.45 0.5 0.55 0.6 Albedo Fig. 5. Ablation energy in IV 171 2 as a function of albedo based on mean daily values on the margin oJ the Greenland ice sheet in July 1993, Kronprins Christian Land. COMPARISON WITH WEST GREENLAND I n ,1\1 es t Greenland , energy-bala nce studies were carried o ut b y Braithwaite an d Olesen ( 1990 ) at Nordbogletscher (NBG ) and Q a ma n a rssup sermi a (QAM ), a nd by Van de Wal a nd O erleman s ( 1994 ) near S0ndre Stmmfjord in en vironments similar to those found a t th e present stud y site (KCL). At all of these stations the net radiation was meas ured at one poin t and no albedo variation was taken into acco unt . Ambach (1963 ) performed a more sophistica ted energy-ba la nce stu d y at Camp IV , but the sta ti o n was located in the upper a blation a rea, a nd the a lb edo variations and their efIect on abla ti on were unfortunately not a na lysed in detail. The energy balance from different experiments is summ a ri zed in Table 3. Net radiation is th e main so urce of ablation energy at a ll locatio ns. Turbulent flu xes are a n important energy so urce in the ablation zo ne co mpa red to the situ a tio n close to th e ELA (Am bach, 1963; Ohmura and others, in press) , corresponding to an ab lation rate of about 10- Table 3. Energy balance in July 1993 in Kronprins Christian Land ( KCL ) compared with July values at Qamanarssllp sermia ( QA M ) Jor 1980- 86 and ./I"ordbogletscher (NBC) for 1979- 83 }i"om Braithwaite and Olesen ( 1990) . Signs correspond to the difinition given in Equation (10) . Small letter ( a) indicates a value assumed to be 0 Wm 2 Elevation D ays Net radiation Turbulent flu xes H ea t cond uction Error Melting energy m Wm Wm Wm vV m Wm 2 2 2 2 2 KCL Q;1M N BC 380 20 11 5 40 18 20 157 790 185 123 79 a -4 198 890 155 89 44 a 2 135 Downloaded from https://www.cambridge.org/core. IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X Konzelmann and Eraithwaite: Ablalion, albedo and eneTgy balance in Kronprins Chrislian Land ') 1 20kgm - d . In contrast to West Green land where heat conduction into the ice is assumed to be sma ll , it is an important heat sink in the present stud y. The possible ab lation is red uced by about 4.5 kg m 2 d I. Ablation rates a nd degree-da y factors for KCL , QAM and NBG are summarized in Tab le 4. Despite the low elevation of the statio n compared with the two West Greenland sites, the ab lation rate is quite low. This is partly du e to lower air temperature , but that is offset by a high er degree-day factor. At KCL a value of 9.8 mm d 1 cC 1 was found compared with 7.2- 8.1 mm d 1 QC 1 at the West Green land sites (Braithwa ite, 1992 ), which may be th e res ult of higher wind speeds . Boggild and others ( 1994) a lso got a higher degree-day factor (9.6 mm d 1 QC I) at Storstr0mmen in north eas t Green la nd (Fig. I ). Table 4. Ablation rate and degree-da)1 faclor ill July 1993 in Kronpl'ins Christian Lalld ( K CL ) comjJared with Ju£y values at QJlfnanarssu/J sel'mia ( QlIM ) for 1980- 86 and ~ V ordbgletsc h er (}vBG ) for 1979 83 from Braitlzwaite (1992) m E levation Da ys mmd- I Ab lation ra te QC Air temperature Degree-d ay mmd 1 QC factor ms Wind speed NEG KCL (LAM 380 20 40 4.2 9.8 790 185 53 6.3 8.1 890 155 35 4.6 7.2 6.2 4.8 3.2 CONCLUSIONS Net radiation is th e major so urce of a bla tion energy at the margin of th e Green land ice shee t in Kronprins Ch ristian L a nd as in other parts of Green la nd. Albedo varies greatly within a sma ll area and, because of the high in co me of g loba l radiation , causes relati\'ely large differences in a blation at stakes close to eac h other. Sma ll-sca le a lbedo variations mu st therefore be ca refu ll y sa m pled to 0 btai n represen ta ti ve a l bcdo val ues for largescale energy- balance calculation. Th e ca lculated energy balance in the pre ent study a lso has a substantial error w hich may be caused by und erestimation of the turbu le nt flux es using the aerodynamic formu lae of Ambach ( 1986 ). The reaso n is probably that the glacier surface is rougher than assumed. Th e co nducti\'e-h ea t flux in the ice is a substantial hea t sink and reduces th e energy available for ablation. The average ab lation rate in Kronprins Christian Land in J uly is low co mpared wi th values in West Greenland, re flecting lower temperature a lth o ugh this is panly ofIset by a higher d egree-day factor due to high wind speed. The degree-day factor is significantly higher in north Greenland than th e ones found in West Greenland. ACKNOWLEDGEMENTS This paper is published by permission of The Geologica l Survey of Greenland (GGU ). K. SchroIT (Department of Geogra phy, Swiss Federal Institute of Technology) and O. O lcsen (GGU ) prepared instruments. Logistic support was supplied by GGU' s camp at Centrum So, Kronprin s Christian Land, led by GGU Stat. geolog N. Henriksen. The research is supported by th e European Community und er co ntra ct numb er EV5V-CT91-0051 which is coordina ted by the C limate R esearc h Unit, U niversi ty of East Anglia. Th e first draft of this paper was prepared in November 1993 when R.J. Braithwaite was a guest of Professor A. Ohmura, D epa rtm ent of Geography, Swiss Federal I nstitute of T ec hnology (grant No. 0-04-509-93 ) . Professor Ohmura a lso made useful comments on the m an uscri pt. REFERENCES t\ mbach, \\'. 1963. UnLersuchungen ZU1l1 Energieumsatz in der Ablationszone des gronhindisc hen Inland eises (Camp J\' EGIG, 69 40'05":-.1, 49 ~ 37'58" \\' . . I/ etlt!. Grolll" 174 (4 ). 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IP address: 168.151.137.40, on 23 Sep 2017 at 20:48:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S002214300001786X