Temporal Variability of the Energy Balance of Thick …psc.apl.washington.edu/lindsay/pdf_files/varibility_of...positions of the stations used in this study. The stations are concentrated

MARCH 1998 313L I N D S A Y

q 1998 American Meteorological Society

Temporal Variability of the Energy Balance of Thick Arctic Pack Ice

R. W. LINDSAY

Polar Science Center, Applied Physics Laboratory, College of Ocean and Fishery Sciences,University of Washington, Seattle, Washington

(Manuscript received 17 December 1996, in final form 20 June 1997)

ABSTRACT

The temporal variability of the six terms of the energy balance equation for a slab of ice 3 m thick is calculatedbased on 45 yr of surface meteorological observations from the drifting ice stations of the former Soviet Union.The equation includes net radiation, sensible heat flux, latent heat flux, bottom heat flux, heat storage, and energyavailable for melting. The energy balance is determined with a time-dependent 10-layer thermodynamic modelof the ice slab that determines the surface temperature and the ice temperature profile using 3-h forcing values.The observations used for the forcing values are the 2-m air temperature, relative humidity and wind speed, thecloud fraction, the snow depth and density, and the albedo of the nonponded ice. The downwelling radiativefluxes are estimated with parameterizations based on the cloud cover, the air temperature and humidity, and thesolar angle. The linear relationship between the air temperature and both the cloud fraction and the wind speedis also determined for each month of the year.

The annual cycles of the mean values of the terms of the energy balance equation are all nearly equal tothose calculated by others based on mean climatological forcing values. The short-term variability, from 3 h to16 days, of both the forcings and the fluxes, is investigated on a seasonal basis with the discreet wavelettransform. Significant diurnal cycles are found in the net radiation, storage, and melt, but not in the sensible orlatent heat fluxes. The total annual ice-melt averages 0.67 m, ranges between 0.29 and 1.09 m, and exhibitslarge variations from year to year. It is closely correlated with the albedo and, to a lesser extent, with the latitudeand the length of the melt season.

1. Introduction

The surface energy balance is an essential element ofthe climate in any region of the world, but it takes onadded significance in the polar regions, where smallchanges in the surface energy balance can lead to dra-matic changes in the surface itself. The response of theice to climatic-averaged forcing conditions has beenmodeled in the past, but the variability of the forcingparameters and the variability of the ice’s response havenot. The focus of this study is to determine the vari-ability of the forcing parameters and the energy fluxeson temporal scales that include short-term variabilityfrom hours to days, seasonal variability, and interannualvariability. A time-dependent thermodynamic model ofthe ice is used to estimate the energy balance, and sur-face meteorological observations are used to providethe forcings. The observations are from an extensivedataset from the North Pole (NP) drifting ice camps ofthe former Soviet Union. The calculations are based on

Corresponding author address: R. W. Lindsay, Polar Science Cen-ter, Applied Physics Laboratory, 1013 NE 40th Street, Seattle, WA98105.E-mail: [email protected]

45 station-years of 3-h observations beginning in 1957and ending in 1990.

Consider the energy balance of a slab of ice. Thefluxes of energy to the ice are the net radiation Fr ofthe ice slab, the sensible heat flux at the surface Fs, thelatent heat flux at the surface Fq, and the conductiveheat flux at the bottom of the ice Fb. The balance isthen expressed as a sum of the fluxes at the top andbottom surfaces minus the energy stored in the ice Sand the energy available for melting ice M.

Fr 1 Fs 1 Fq 1 Fb 2 S 2 M 5 0. (1)

All fluxes are considered positive if directed toward theice. The six terms of this equation are the principal focusof this study.

The surface energy balance determines the surfacetemperature and the sign and magnitude of the sensibleheat flux to the ice from the atmosphere. The heat fluxin the lower atmosphere (along with the wind stress)helps to establish the depth and the structure of theatmospheric boundary layer and hence the efficiency ofthe coupling between the atmosphere and the ice (Over-land and Davidson 1992). The energy balance at thebottom of the ice helps to fix the freezing rate and thebrine rejection rate and hence the evolution of the oce-anic mixed layer. Thus, the energy balance of the icedetermines the structure and evolution of the ice, the

314 VOLUME 11J O U R N A L O F C L I M A T E

atmosphere, and the ocean and the dynamic couplingbetween the three of them.

The first calculation of the thermal evolution of theice over the entire annual cycle was performed by May-kut and Untersteiner (1971, hereafter MU71). They usedclimatological values for the downwelling radiativefluxes, the sensible and latent heat fluxes, and the albedoand snow depth. They integrated the model over manyannual cycles until an equilibrium ice thickness wasobtained. The study reported here is very much in thetradition of the MU71 study, with the important additionof the use of 3-h observations for forcings and the cal-culation of 45 distinct annual cycles.

An additional study by Maykut (1982, hereafter M82)extended the MU71 study to different ice-thicknessclasses and to a determination of the annual cycle ofthe regional heat balance in the Beaufort Sea. He alsocalculated the annual cycle for 3-m-thick ice, again us-ing climatological forcing values. The current study ob-tains results roughly similar to his for the mean valuesof the terms in (1) and adds information about the tem-poral variability. A somewhat more complex thermo-dynamic model of sea ice is that of Ebert and Curry(1993). They include different ice types, a complex pa-rameterization of the albedo, melt-pond coverage anddrainage, and a prescribed deformation rate. They usethis model to investigate ice/albedo feedback mecha-nisms. An extensive study by Makshtas (1991) of thewinter heat balance of the Arctic ice also uses a ther-modynamic model.

This paper is organized as follows: section 2 de-scribes the drifting ice-station data, the energy bal-ance model, and sample results for a single stationand year. Section 3a summarizes the results for all 45station years and highlights the annual cycle and theseasonal variability of the various terms of the energybalance equation. Section 3b then summarizes thevariability of the terms at temporal scales from 3 hto 16 days for each of the four seasons, and section3c assesses the interannual and spatial variability,again on a seasonal basis. Comments and conclusionsare given in section 4.

2. Surface energy balance model

a. Model forcing parameters

The series of drifting ice stations operated by theformer Soviet Union provides a unique and remarkableset of meteorological observations from the interior ofthe Arctic ice pack. The entire set of surface meteo-rological data has recently been made available to thewest through the cooperation of the Arctic and AntarcticResearch Institute (AARI) in Leningrad. The data areavailable on a CD-ROM from the National Snow andIce Data Center (NSIDC 1996). The first station in theseries was established in 1937 and operated for less thana year. The second was established in 1950 and operated

for 1 yr. Beginning in 1954, there was continuous cov-erage by at least one station, usually two, until the endof the program in 1991 with the closing of NP-31. Thestation with the longest continuous record is NP-22,which remained active for over 8 yr. There are 196 321observations on the CD-ROM providing approximately73 station years of data.

In addition to the standard meteorological variables,some of the stations also reported various radiative flux-es including downwelling direct, diffuse, and globalshortwave radiation, net radiation (long and shortwave),and albedo. Summaries of these observations are avail-able in a recently translated report (Marshunova andMishin 1994). The average daily values for stations NP-17–NP-31 are also available on the NSIDC CD-ROM.

The model-forcing parameters derived from the NPdrifting ice-station dataset include the air temperature,the mixing ratio, the wind speed, the air pressure, thedownwelling short- and longwave radiative fluxes, thesnow depth and density, and the surface albedo.Monthly mean forcing parameters are used when miss-ing values are encountered. For convenience, 45 com-plete calendar years, January–December, were selectedfor computing the energy balance. This represents 67%of the entire dataset. Figure 1 shows the mean monthlypositions of the stations used in this study. The stationsare concentrated in the central Arctic basin, with rel-atively few in the peripheral seas. The stations extendfrom NP-6 through NP-31 and span the years 1957–90. In some years, as many as three stations reportedsimultaneously.

The air temperature was measured in standard me-teorological observing screens at a height of 2 m. Thewinds were measured at various heights ranging from2 to 10 m. All of the wind measurements were correctedto a height of 2 m assuming a logarithmic wind profileand a roughness length of z0 5 1.3 mm. The mixingratio was determined from the reported relative humidity(with respect to liquid water) and the reported air tem-perature.

The albedo of the surface is the monthly averagedalbedo for each station and year. These values are re-ported by Marshunova and Mishin (1994) and repre-sent observations of the nonponded surface near themeteorological observing site. The reported albedo isaveraged over the entire month and represents the al-bedo for the average cloud cover for the month. Hence,no additional adjustment is made to the albedo for day-to-day changes in the cloud cover. There is consider-able variability in the monthly albedo values from sta-tion to station and from year to year ; for example, thevalues in April range from 0.74 to 0.89 and those inJuly from 0.45 to 0.80. The high values in July rep-resent years, when not all of the snow melted in thevicinity of the meteorological observing site or whensummer snowfalls occurred. The monthly averaged al-bedo values may significantly smooth abrupt transi-tions in the spring and fall. The albedo is the most


FIG. 1. Map of the mean monthly positions of the NP drifting ice stations used in this study. The locations of the stationsduring each of the 45 annual cycles are connected by separate lines, with January enclosed in a box.

significant and perhaps the least well measured of theforcing parameters. It must be stressed that the valueswe use do not include ponds, thin ice, or leads, andthus the computed energy balance cannot be general-ized to all thick ice or to the ice cover as a whole. Yet,the calculations do represent a significant portion ofthe ice cover and characterize the energy exchangeparticularly well when the surface is frozen.

The snow depth and snow density are taken from thevalues measured at stakes near the weather observingsites. This dataset was also made available through acooperative agreement with AARI and is on the NSIDC(1996) CD-ROM. The data we used here consist ofblended 5-day values of the snow depth and densitybased on both daily values measured at snow stakes andmore sporadic measurements obtained from 1-km-long

snow-measurement lines (I. Rigor 1996, personal com-munication).

The radiative fluxes for this study are estimated us-ing parameterizations involving the solar zenith angle,reported cloud cover, surface albedo, air temperature,and humidity. We use parameterizations of the radia-tive fluxes, not the measured values, because theNSIDC CD-ROM includes only the daily averagedownwelling shortwave flux values (not 3-h observa-tions), and the downwelling longwave radiation isavailable only in the winter. The parameterized down-welling long- and shortwave fluxes are determined withprocedures recommended by Key et al. (1996) whocompared several different parameterization schemeswith measured fluxes obtained over several weeks inthe spring of 1993 at Resolute, Northwest Territories,


Canada, and over an annual cycle at Barrow, Alaska.For downwelling shortwave fluxes, they recommendthe following parameterization by Shine (1984):

2S cos Z0F 5 (2)sw,clr 1.2 cosZ 1 0.001(1 1 cosZ )e 1 0.04550.5(53.5 1 1274.5 cosZ ) cos Z

F 5 (3)sw,cld 1 1 0.139(1 2 0.9345a)t

F 5 (1 2 c)F 1 cF , (4)dsw sw,clr sw,cld

in which Fsw,clr , Fsw,cld, and Fdsw are the downwellingshortwave radiative fluxes for clear skies, cloudy skies,and all skies. Other parameters are the solar zenith angleZ, the solar constant S0, the near-surface vapor pressuree, the surface albedo a, the cloud optical depth t , andthe cloud fraction c. The albedo in (3) represents effectsof multiple cloud-to-ground reflections and should bethe average albedo of a wide area around the observationsite. For the purposes of the flux parameterization, thealbedo in the months of July and August is reduced by0.05 to account for melt ponds and leads in the vicinityof the station which would reduce the amount of mul-tiple reflections between the clouds and the ice. Thisvalue of a used for the reduction is an additional sourceof uncertainty in the downwelling shortwave flux esti-mation.

The average daily global shortwave flux measured atstations dating back to NP-17 is used to validate thedownwelling fluxes. Based on comparison between theparameterized and observed shortwave fluxes, a cloudoptical depth was chosen for each month to minimizethe mean monthly difference between them. In thespring and fall it was not possible to find a cloud opticaldepth that would entirely remove the bias, so a valueof 1.0 was assumed. This inability may be due to thedifficulties in comparing averaged daily values whenthe sun is above the horizon for only a small part ofthe day as well as to possible errors in the parameter-ization scheme or in the measurements at very low sunangles. The optical depths used for March–Septemberare 1.0, 1.0, 3.5, 5.3, 6.8, 6.2, and 1.0. Figure 2a com-pares the downwelling shortwave parameterization fordaily averaged values with the measured global short-wave radiative flux. For days in which the flux is greaterthan 10 W m22 (N 5 6228), the parameterized fluxesaverage 0.4 W m22 less than the measured fluxes, andthe rms difference is 31.7 W m22. The monthly biasranges from 27.0 W m22 in April to 4.7 W m22 in June.If a constant value of 8 is used for the cloud opticaldepth, as done by Key et al. (1996), the parameterizedfluxes average 10.6 W m22 less than the measured flux-es.

For downwelling longwave fluxes Fdlw, Key et al.(1996) recommend the Efimova (1961) parameterizationof the clear-sky flux used in the Jacobs (1978) param-eterization for all skies:

Fdlw 5 sT 4(0.746 1 0.0066e)(1 1 0.26c), (5)

where s is the Boltzman constant and T is the near-surface air temperature. Figure 2b compares the dailyaveraged values during winter. Measured longwave flux-es at the NP stations are unavailable once the sun comesup. During the dark time of the year, the parameterizedfluxes average 1.5 W m22 less than the measured fluxes,with an rms difference of 11.9 W m22 (N 5 4403).

The errors associated with these parameterized radiativefluxes are comparable to the best estimates of the down-welling surface radiative fluxes made from satellites.Schweiger and Key (1997) used a neural net-based tech-nique to retrieve the surface fluxes from TOVS radiances;they report that in their test cases (79 days from driftingice stations and 180 days from a coastal station) the dailyaveraged fluxes show rms errors of 35 W m22 for thedownwelling shortwave fluxes and 20 W m22 for thedownwelling longwave fluxes. The mean measurement er-rors in their study were less than 4 W m22.

b. Model description

The time-varying components of the surface energybalance (1) are computed using a thermodynamic icemodel. As mentioned previously, the forcing parametersderived from observations include the air temperature,the mixing ratio, the wind speed, the air pressure, thedownwelling short- and longwave radiative fluxes, thesnow depth and density, and the surface albedo. Theimportant free parameters are the surface (skin) tem-perature, the ice-temperature profile, and the surfacefluxes. The ice thickness is held constant at 3.0 m. Theuse of a constant ice thickness is justified, becausechanges in the thickness of multiyear ice during the yeardo not greatly modify the surface fluxes. The focus ofthis study is the variability of the surface fluxes for iceof a fixed thickness, and to change the ice thicknesswith time would add a confusing variable. In addition,the forcing parameters used in the model are not strongfunctions of the ice thickness if the ice is a multiyearfloe and the ice stations were established on floes ofdifferent thicknesses. The 3-m ice thickness is near theequilibrium ice thickness of 2.88 m found by MU71.

The model has ten levels, seven within the ice andthree within the snow. The levels are quadraticallyspaced in the ice and snow separately to give thinnerlayers near the surface. The snow layers are spaced inproportion to the snow depth. When the snow is deep(about 40 cm), the top snow layer is 4 cm thick. Thelayer thicknesses are consistent with the recommenda-tions of Guest and Davidson (1994) who find that innew snow fluctuations in the surface forcing at a scaleof 3 h penetrate about 5 cm deep. The top ice layer is7 cm thick. The models for the surface energy balanceand the subsurface temperature profile have been adapt-ed from portions of the Community Climate Model Ver-sion 2 (CCM2) developed by the National Center forAtmospheric Research (Hack et al. 1993). The ice-tem-perature profile is calculated by solving the thermal dif-


FIG. 2. Comparison of parameterized and measured daily average downwelling radiative fluxes: (a) shortwave (6228days), and (b) longwave, during the winter only (4403 days).

fusivity equation with a fully implicit Crank–Nicholsonscheme. The model integrates forward in time with atime step of Dt 5 3 h.

An energy balance equation is applied to each layeri; i 5 1 at the surface to i 5 10 at the bottom. For anylayer, the energy balance is

(F 2 F ) 1 F 1 Fr,i r,i11 s q

1 (F 2 F ) 2 S 2 M 5 0, (6)c,i c,i11 i i

where Fr,i is the radiative flux at the top of the layer,

Fs and Fq are the turbulent fluxes (zero except at thesurface), Fc,i is the conductive flux at the bottom of thelayer, and Si and Mi are the heat storage and energyavailable for melting within the layer. We will treat eachof the terms in turn.

The net radiation at the surface is4F 5 F 5 (1 2 a)F 1 « (F 2 sT ), (7)r r,1 dsw dlw sfc

where Fdsw and Fdlw are the downwelling shortwave andlongwave fluxes at the surface, a is the albedo of the ice,« is the surface emissivity, s is the Boltzman constant,


and Tsfc is the surface temperature. The net solar radiativeflux is allowed to penetrate the surface and be absorbedwithin the ice (Grenfell 1979). The amount of penetrationdepends on the snow cover, the cloud fraction, and thedepth in the ice. When snow is present, virtually all ofthe net solar flux is absorbed within the snow; when it isabsent, about 65% passes through the first ice layer andabout 50% passes through the top 25 cm of ice. Duringthe summer, the penetrating solar flux causes much of theice melt to occur below the surface. The snow depth andthe snow density are prescribed based on observationsfrom the NP stations.

The sensible heat flux is determined by the differencebetween the model-calculated surface temperature andthe measured 2-m air temperature using a stability-de-pendent exchange coefficient (Hack et al. 1993):

Fs 5 rcpCsU2m(T2m 2 Tsfc), (8)

where r and cp are the air density and heat capacity,U2m is the wind speed at a height of 2 m, and T2m isthe air temperature at a height of 2 m; Cs is the heattransfer coefficient and is a function of the bulk Rich-ardson Number of the surface layer. A value of Cs 50.0023 is used for neutral stratification. The latent heatis determined with the model-calculated surface mixingratio qsfc and the mixing ratio determined from the mea-surements of relative humidity at a height of 2 m q2m:

Fq 5 rLCqU2m(q2m 2 qsfc). (9)

In computing the latent heat flux, the latent heat ofevaporation of the surface L includes the latent heat ofmelting if the surface temperature is below freezing. Asin the CCM2 model, the transfer coefficients for heatand moisture are the same, Cq 5 Cs.

The heat storage is determined from the time rate ofchange in the layer temperature:

]TiS 5 Dz rc , (10)i i p ]t

where r is the ice or snow density, cp the heat capacity,and Dzi the layer thickness. The total heat storage S in(1) is the sum of the Si values. The energy available formelting is determined at each time step if a layer tem-perature exceeds the melting point:

(T 2 T )m,i iM 5 Dz rc , (11)i i p Dt

where Tm,i is the salinity-dependent melting point of thelayer. The energy available for melting M in (1) is thesum of the Mi values.

The salinity of the ice is modeled with a fixed salinityprofile that drops linearly from 3 ppt at the bottom to0 ppt at the top. This is in rough agreement with theidealized salinity profiles for multiyear ice shown byMaykut (1985). With this salinity profile, the other phys-ical properties of the ice can be computed as follows.The specific heat capacity is from a theoretical expres-sion derived by Ono (1967),

bSc 5 c 1 a(T 2 273.16) 1 , (12)p, ice 0 2(T 2 273.16)

where c0 5 2113 J 8C21 kg21, a 5 7.53 J 8C22 kg21,and b 5 18 000 J 8C kg21. The temperature T is inkelvins and salinity S is in parts per thousand. The ef-fective heat capacity is a strong function of the salinityand the temperature near the melting point because ofthe latent heat of freezing associated with brine pocketswithin the ice. Until the melting point is reached, thesolar heat entering the ice remains as latent heat in thebrine pockets. After the melting point is reached in thismodel, the heat available for melting M is assumed todrain away and need not be removed to begin the cool-ing of the ice. However, the large heat capacity near thefreezing point due to the retention of liquid water inbrine pockets requires the removal of a large amount ofheat in the fall before substantial cooling begins. Thefractional volume of brine is a strong function of tem-perature and salinity (Maykut 1985), rising to 15% ata temperature of 20.58C and a salinity of 1.5 ppt (theaverage salinity of the ice in the model). The total melt,averaging 0.66 m of ice, is about 22% of the imposed3-m ice thickness. Thus, the water retained within brinepockets is somewhat less than that melted after the freez-ing point is reached.

The melting temperature is determined from the fol-lowing expression by Ono (1967):

Tm 5 273.16 2 0.05411S, (13)

where T is again in kelvins. The specific heat in snowis taken from Anderson (1976). It is similar to that ofpure ice, which also exhibits a strong dependence ontemperature due to its crystalline structure:

cp,snow 5 92.88 1 7.364T. (14)

The heat conduction at the interface between layersi and i 1 1 is proportional to the vertical temperaturegradient:

Fc,i 5 kj(Ti11 2 Ti)/Dzj, (15)

where Ti is the layer temperature, Dzj is the distancebetween the centers of layers i and i 1 1, and kj is theaverage thermal conductivity of the two layers. The ther-mal conductivity of ice is from an expression proposedby Untersteiner (1961):

bSk 5 k 1 (16)ice 0 (T 2 273.16)

in which k0 5 2.2 W m21 K21 and b 5 0.13 W m21.The conductivity for snow is from Ebert and Curry(1993) and includes the temperature-dependent effectsof vapor diffusion:

ksnow 5 2.845 3 1026r2 1 2.7 3 1024 2.0(T2233)/5,(17)

where the temperature T of the snow is in kelvins and


the snow density r is taken from observations at eachice camp.

The bottom flux FB in (1) is the conductive flux inthe lowest layer. The temperature of the bottom of theice is assumed to be a constant 21.88C. Consequently,in the winter, there is a substantial heat flux from thebottom surface. In the model, the thickness of the icedoes not change, but this flux could be considered tocome both from the ocean and from the latent heat offreezing at the bottom surface. A freezing rate could bedetermined if a value were assumed for the oceanic heatflux. In the summer, the ice temperature rises to themelting point, which, because of the low salinity of theice, is warmer than the ocean temperature, so the bottomheat flux reverses sign.

The surface energy balance model and thermodynam-ic ice model have been checked with eddy-correlationmeasurements of the sensible heat flux made at theLeadEx ice camp in the Beaufort Sea in the spring of1992. The surface turbulence measurements are reportedby Ruffieux et al. (1995) who estimate an error of 62W m22 in the measured sensible heat flux. The modelwas forced with the measured wind speed, air temper-ature, humidity, and downwelling long- and shortwaveradiative fluxes. The measured sensible heat flux had amean of 2.9 W m22 and a standard deviation of 10.5 Wm22. The mean difference between the sensible heat fluxestimated by the model and that measured duringLeadEx was 21.8 W m22, and the rms difference was6.2 W m22. A full description of the intercomparisonis given by Lindsay et al. (1997).

c. One year at one station

We begin our discussion of the results by showingthe forcing parameters and resultant fluxes for just onestation: NP-30 in 1990. Figure 3 shows the smoothedtime-dependent forcing parameters obtained for this sta-tion using a 10-day running-mean filter. Because of thefilter, the strong diurnal cycle in the downwelling short-wave radiative flux is not apparent. The computed val-ues of the six terms of the energy balance equation, (1),also smoothed with a 10-day filter, are shown in Fig. 4.Note the relatively short time period in which significantenergy is available for melting and the large amount ofheat stored in the ice near day 190 (10 July). A time-versus-depth cross section of the ice temperature isshown in Fig. 5. The ice temperature cross section issimilar to what MU71 found in their model study usingmonthly mean values. Note the lag in the cooling of theice near the bottom until the early winter; this lag iscaused by the considerable heat capacity of the ice–brine matrix.

3. Temporal variabilitya. Annual cycle of the energy balance

The entire 45 yr are combined to define the seasonalcycle of the energy balance. Box plots are used to show

the median, the quartiles, and the 5th and 95th percen-tiles of the 3-h values of each parameter by month.Figure 6 shows the annual cycles of the principal forcingparameters and Fig. 7 shows the annual cycles of theterms of the energy balance equation, (1). The variationillustrated by the box plots includes short-term (withinthe month), interannual, and spatial variability. The sea-sonal cycles are similar to what has been found by oth-ers, but it is noteworthy that there is considerable vari-ation, as indicated by the box plots, in both the forcingsand the fluxes.

Table 1 shows the monthly mean values and the stan-dard deviations of the monthly means for each of theprincipal forcing parameters and the terms of the energybalance equation (1). Here, the standard deviations rep-resent spatial and interannual variability of the monthlymean values and, as a consequence, represent much lessvariability than exhibited in the 3-h values used to con-struct the box plots in Figs. 6 and 7. All of the forcingparameters show seasonal cycles consistent with pre-vious climatologies. Note, however, the large variabilityin most of them. Of particular impact on the energybalance is the variability in the albedo. The albedo issmallest in July, averaging 0.65; at some stations it re-mains high all summer, never dropping below 0.80. Atthese stations some snow remained on the ice surfaceall summer, or there was significant snowfall during thesummer.

The monthly mean values of the downwelling radi-ative fluxes, the albedo, the net radiation, and the tur-bulent fluxes are compared in Fig. 8 with those used byM82 (for 3-m thick ice) and Ebert and Curry (1993).The Ebert and Curry results for net radiation and tur-bulent fluxes are area averages (including leads), so theyare not comparable to our results for nonponded ice andare not included in the figure. The area-averaged fluxvalues depend critically on the imposed lead concen-tration. The M82 study used prescribed values for thedownwelling radiative fluxes and the turbulent fluxes.The monthly averaged radiative fluxes were from Mar-shunova (1961) and are based on data from the NPstations, so the good agreement with our values is to beexpected. The turbulent fluxes were based on estimatesmade by Doronin (1963), whereas this study computesthe turbulent fluxes based on the measured air temper-atures and the modeled ice-surface temperatures. In gen-eral, our computed flux values are similar to those usedby M82, although the sensible heat fluxes show somesignificant differences in both the winter and the sum-mer.

The net radiation is remarkably constant through thewinter months, averaging about 227 W m22. It changesfrom negative to positive in May, with the largest pos-itive flux in July, not June when the solstice occurs,because of the lower albedo in July. The net radiationchanges to negative again in September. The sensibleheat flux is positive in the winter, about 7–10 W m22,and is negative only in May, when the increasing solar


FIG. 3. Forcing parameters for NP-30 (1990) smoothed with a 10-day running-mean filter.

flux warms the surface above the air temperature. Thelatent heat is near zero in the winter and averages 210W m22 in June. The bottom flux is near 15 W m22 inJanuary and exhibits very little variability from stationto station. In the summer, the bottom flux is negativeindicating that the ice is warmer than the imposed21.88C bottom boundary condition. The rate of heatstorage is greatest in July, when the net radiation is mostpositive. The ice temperature does not increase much atthis time, but the specific heat is large owing to thelatent heat of melting absorbed in the expanding brine

pockets. The energy available for melting is maximumin July, but it has a large range, from less than 10% ofthe mean to over 200% of the mean. The greatest rateof cooling is in the fall, when the net radiation becomesnegative. The heat stored in the ice slows the coolingof the ice substantially. The importance of the releaseof the stored heat in the fall, which produces a nonlineartemperature profile within the ice, was also pointed outby MU71 and Makshtas (1991).

The annual cycle of the energy balance is illustratedin Fig. 9, in which the monthly mean values of each of


FIG. 4. The six terms of the energy balance equation computed for NP-30 (1990) and smoothed with a 10-day running-mean filter.

the terms of (1) are plotted. In the winter, the net ra-diative loss is balanced mostly by the bottom flux withvery little heat storage or loss; however, the sensibleheat flux also accounts for about a third of the net ra-diation. In the spring, the net radiation and the turbulentfluxes become small, and the conductive flux from theocean begins to warm the ice. In the summer, the strongpositive net radiation is largely balanced by storage andmelt (in nearly equal parts) and, to a lesser extent, bythe surface latent heat flux. Finally, in the fall, the net

radiation again becomes negative, and it is balancedmostly by a cooling of the ice (the storage term). Theturbulent fluxes and the bottom flux are all small.

Note that the annual average net radiation is just 0.5W m22, which is remarkably close to zero, since thereis nothing in the procedures that would force such aclose balance. Small changes in the downwelling ra-diative fluxes or in the surface albedo could change thenet radiation significantly. The annual average heat stor-age is also small, just 0.3 W m22, well within the un-


FIG. 5. Cross section of the ice temperature versus time and depth for NP-30 (1990) in degrees Celsius. The dotted linesshow the top of the snow and the top of the ice. The field has been smoothed with a 10-day running-mean filter.

certainty of the net radiation. Because we are modelingonly one small part of the whole system and do notinclude lead processes or melt ponds, we need not expectan equilibrium energy balance to ensure a stable icecover.

This dataset offers an opportunity to quantify thewell-known dependence of the air temperature on thewind speed and cloud cover. Table 2 shows the monthlymean air temperatures, the standard deviations of the 3-h observations, and the squared correlation coefficientsR2 for total cloud amount and wind speed. The wind orclouds during the winter individually account for 20%–30% of the within-month variance. A linear model forthe air temperature that includes both the cloud fractionand the wind speed is

T2m 5 a0 1 acc 1 awU2m 1 «, (18)

where a0 is the intercept, ac and aw are the coefficientsfor cloud fraction and wind speed, and « is the error.As shown in Table 2, this model accounts for about 40%of the winter within-month air temperature variance.The difference between cloud-free and cloud-coveredconditions is greatest in October, when overcast skiesare accompanied by temperatures 10.48C warmer thanfound with clear skies. The difference between windyand calm conditions is greatest in December, when awind of 10 m s21 is accompanied by temperatures av-eraging 11.18C warmer than those found under calmconditions. In the summer, there is no significant rela-tionship between the air temperature and the cloud cover

or the wind speed. This linear model might offer a sim-ple correction for estimating the surface temperaturesunder clouds based on satellite observations of the near-by clear-sky surface temperatures.

b. Short-term variability of forcings and fluxes:3 h to 16 days

The scale-dependent variability of the forcings andfluxes on timescales of 3 h to 16 days is analyzed withthe formalism of the discrete orthogonal wavelet trans-form. This method offers a simple and direct determi-nation of the variability associated with each temporalscale and of the times that the variability occurs. It isparticularly well suited for analyzing nonstationary timeseries, such as the annual cycle of the various parametersunder study here. There are numerous references in theliterature to the use of the wavelet transform in geo-physical analysis. The techniques used here are outlinedby Lindsay et al. (1996).

The discrete wavelet transform is based on the ap-plication of a sequence of high-pass and low-pass filters,in this case a Haar wavelet filter of length 2. The Haarwavelet coefficients are lagged differences of running-mean smooths of the series and are identical to the Allenvariance used in many applications. The maximal-over-lap algorithm, introduced by Percival and Guttorp(1994), is used to determine the wavelet variance. Thisalgorithm determines the coefficients, one for eachscale, for every step in the time series and offers a more


FIG. 6. Monthly box plots of the forcing parameters for the 45 station years. Each box plot shows the 5th, 25th, 50th, 75th,and 95th percentile values. Thus, half of the observations fall within the range indicated by the box, 90% fall within the rangeindicated by the vertical lines, and the median value is the horizontal line near the middle of each box. The distributions arebased on 3-h values.

exact estimate of the temporal variability than the or-thogonal-pyramid algorithm introduced by Mallet(1989).

Because the transform is orthogonal, the sum of thewavelet variances over all scales is equal to the varianceof the observations. In this study, the wavelet coeffi-cients are determined for eight different scales running

from 3 h to 16 days. The seasonal wavelet variance isthen found by summing the squares of the coefficientsfor each season. Note that this is a simple procedurewith the wavelet decomposition, since the coefficientsare localized in time, unlike the coefficients of the Fou-rier transform. This advantage is one of the principalreasons why the wavelet variance is used here. The plots


FIG. 7. Monthly box plots of the terms of the energy balance equation (1), for 45 yr of NP drifting ice-station data. Thedistributions are based on the 3-h calculated flux values.

shown are log-linear plots of wavelet variance versustemporal scale.

In a Fourier-centric view of the world, the Haar filtersare the worst approximation of ideal high- and low-passfilters, since they are subject to severe leakage effectscompared with higher-order (longer) wavelet filters(Daubechies 1992; Lindsay et al. 1996b). The lack ofcorrespondence with a Fourier analysis is, however, bal-anced by an easy and direct interpretation of the wavelet

variance that is calculated: it is simply the variance ofthe difference between adjacent nonoverlapping sam-ples averaged over a period corresponding to the time-scale.

Figure 10 shows the wavelet variance of the six forc-ing parameters with significant small-scale temporalvariability for each of the four seasons. The down-welling shortwave flux shows the greatest variability atdiurnal timescales, 6 and 12 h. The strength of the di-


TABLE 1. Monthly mean values of principal forcing parameters and energy fluxes in (1) and the standard deviations of the monthlymeans.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Forcing parametersDownwelling shortwave flux (W m22)

Mean:Std dev:

0.00.0

1.21.9

31.514.0

146.09.7

263.36.8

307.911.4

230.613.7

134.78.2

44.214.7

2.64.3

0.00.0

0.00.0

Downwelling longwave flux (W m22)Mean:Std dev:

164.013.1

160.513.0

164.19.6

188.112.1

245.211.2

291.26.2

303.93.9

297.05.7

263.811.9

210.912.4

177.013.6

166.09.4

2-m air temperature (C)Mean:Std dev:

231.43.6

232.83.6

231.62.6

224.12.7

211.02.1

21.80.9

20.10.3

21.40.7

28.02.4

219.52.7

227.63.4

231.12.3

Relative humidity (%)Mean:Std dev:

78.74.6

78.44.7

79.64.7

82.14.8

86.53.6

91.71.9

95.11.5

94.31.8

90.72.2

83.83.5

80.15.3

78.76.0

2-m wind speed (m s21)Mean:Std dev:

4.40.9

4.00.8

4.00.7

3.90.8

3.90.6

4.20.7

4.10.6

4.20.8

4.50.8

4.20.9

3.90.8

4.00.9

Total cloud fractionMean:Std dev:

0.470.13

0.490.14

0.500.13

0.530.11

0.760.09

0.850.09

0.890.07

0.910.07

0.880.05

0.750.10

0.540.12

0.510.12

AlbedoMean:Std dev:

0.830.04

0.820.03

0.830.02

0.770.06

0.650.08

0.700.08

0.800.05

0.830.02

Snow depth (m)Mean:Std dev:

0.270.06

0.290.08

0.310.08

0.330.09

0.340.09

0.290.11

0.090.09

0.030.04

0.110.06

0.190.07

0.240.07

0.260.08

Snow density (kg m23)Mean:Std dev:

304.121.4

313.520.8

320.324.3

322.226.9

327.022.9

349.712.2

379.32.5

223.91.2

236.314.5

272.630.2

287.833.8

295.731.6

Energy fluxesNet radiation (W m22)

Mean:Std dev:

227.43.4

226.33.7

221.93.3

24.14.4

20.15.0

54.715.1

68.716.2

28.910.5

28.16.1

223.73.7

227.93.4

227.13.1

Sensible heat flux (W m22)Mean:Std dev:

9.93.6

8.43.6

6.63.3

0.13.3

25.83.0

21.62.6

2.22.6

1.21.7

0.52.1

2.03.2

5.63.8

7.03.1

Latent heat flux (W m22)Mean:Std dev:

1.30.8

1.10.6

1.10.5

20.00.9

25.91.7

210.32.7

26.53.5

26.72.6

23.92.1

20.10.9

1.00.9

1.10.8

Bottom flux (W m22)Mean:Std dev:

15.40.7

14.21.4

13.91.9

11.61.8

6.41.2

2.30.5

0.40.4

20.90.5

21.50.4

21.50.5

0.42.4

7.43.8

Heat storage (W m22)Mean:Std dev:

20.82.0

22.62.5

20.31.8

7.52.2

12.21.8

17.97.8

30.89.7

8.64.7

213.54.1

223.33.8

220.93.9

211.74.5

Energy available for melting (W m22)Mean:Std dev:

0.00.0

0.00.0

0.00.0

0.00.0

2.62.0

27.29.0

33.910.5

13.88.4

0.51.7

0.00.0

0.00.0

0.00.0

urnal cycle is a strong function of latitude. The varianceat a scale of 12 h drops from about 2500 (W m22)2 at758 to nearly zero at the pole. The downwelling long-wave radiative flux shows the greatest variability atscales of about 2 days, but there is little variability in

the summer owing to the constant cloud cover and con-stant temperatures. The variability increases at a scaleof 16 days, because the variability associated with theannual cycle begins to be included. The air temperatureshows the greatest variability in the winter at timescales


FIG. 8. Comparison of the fluxes calculated in this study with those used by Maykut (1982) for 3-m thick ice and withthe downwelling radiative fluxes used by Ebert and Curry (1993).

of 8 days and little variability in the summer. The spe-cific humidity shows the greatest variability at time-scales greater than 1 day. In both the air temperatureand the specific humidity, there is no clear gap betweenthe synoptic-scale variability of several days and theannual-cycle variability that begins to be seen at a scaleof 16 days. The downwelling shortwave flux and thecloud fraction exhibit such a gap. The wind speed showspeak variability at timescales of 2 days and more vari-

ability in the fall and winter than in the spring andsummer. Finally, the cloud fraction, which modulatesthe downwelling radiation, shows the greatest variabilityin the winter and spring at timescales of about 1 day.

Figure 11 shows the wavelet variance of the sixterms of the energy balance equation (1). The netradiation shows a strong diurnal cycle in the springand summer, but the variability is relatively smallerin the spring because the surface albedo is high. The


FIG. 9. Annual cycle of the energy balance. Plotted are the monthly mean values of each of the terms of (1). Theirsum is zero.

TABLE 2. Air temperature related to 3-h clouds and wind speed. For definitions of a0, ac, and aw see (18).

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Mean T2m (8C)Std dev

231.47.9

232.87.1

231.66.1

224.16.6

211.05.0

21.82.6

20.10.9

21.41.9

28.05.5

219.57.0

227.67.0

231.17.1

R2, cloudsR2, wind

0.280.23

0.250.20

0.170.20

0.160.14

0.210.05

0.000.02

0.010.00

0.030.00

0.180.07

0.320.13

0.300.19

0.300.24

a0 (8C)ac (8C)aw (8C m21 s)Rms error (8C)R2, both

239.98.01.086.10.40

240.87.31.095.60.37

238.25.11.035.10.30

230.35.20.905.80.24

216.95.80.394.40.23

22.80.40.162.50.02

0.220.4

0.030.90.02

23.01.60.011.90.03

217.68.70.434.90.22

230.410.40.765.50.39

236.28.31.035.40.42

239.37.51.115.40.42

sensible heat flux is most variable at the shortesttimescales. The latent heat flux shows significant vari-ability only at small scales in the summer and exhibitsa weak diurnal cycle. The bottom flux shows no short-term variability and only a small amount at scalesnear 10 days, and mostly in the winter. Again, thisvariability is related to the annual cycle. The vari-ability in heat storage is greatest in the spring andsummer and also shows a diurnal cycle. Finally, theenergy available for melting shows variability onlyin the summer and exhibits a strong diurnal cycle.Note that there is no pronounced diurnal cycle in theair temperature (Fig. 10) or the sensible heat flux (Fig.11) in any season. The large diurnal cycle in net ra-diation is largely balanced by diurnal cycles in thestorage and melt terms.

c. Interannual variability

There is considerable variability in the forcing pa-rameters from year to year and from station to station,and this is reflected in the energy available for meltingFm. In Fig. 12, the total annual energy available formelting (the time integral of Fm), expressed as metersof ice, is shown for each of the 45 station years. Thelatent heat of freezing of pure ice is used as a conversionfactor. The total annual melt averages 0.67 m of ice,ranges between 0.29 and 1.09 m, and exhibits largevariations from year to year.

The interannual variability was investigated by firstconsidering each parameter in the dataset as the sum oftwo elements: a high-frequency ‘‘detail’’ signal (a high-pass filtered version of the time series) and a low-fre-


FIG. 10. Average wavelet variance of the forcing parameters with significant small-scale temporal variability. These areseasonal averages for 45 station years: winter (December–February), spring (March–May), summer (June–August), and fall(September–November). For this analysis, the Haar wavelet filter is used in the discrete wavelet transform, so that thevariance at a given scale is the variance of the difference between adjacent nonoverlapping averages taken over a timeperiod indicated by the scale. At a scale of 1 day, the downwelling shortwave flux variance is 0, 65, 113, and 3 (W m22)2

for winter, spring, summer, and fall.

quency 16-day smooth (a low-pass filtered version)(Lindsay et al. 1996b). The variability of the detail sig-nal is analyzed in the previous section; here only theseasonal, spatial, and interannual variability of thesmooth is considered. The smooth used here is simplythe 16-day running mean.

For station k at time i, the smooth Ci,k of a parameteris modeled as the sum of a time-dependent mean sea-sonal cycle over all of the stations S i, plus a spatialcomponent Xi,k, and a residual ri,k:

Ci,k 5 Si 1 Xi,k 1 ri,k. (19)


FIG. 11. Average wavelet variance of the terms of the energy balance equation for each season. At a scale of 1 day, thenet radiation variance is 22, 20, 9, and 22 (W m22)2 for winter, spring, summer, and fall.

The spatial component Xi,k is modeled with a simpleleast squares fit to the latitude f :

Xi,k 5 a0 1 a1f i,k, (20)

where the fit is made to the difference Ci,k 2 S i, andthe residual of the fit is ri,k. The limited spatial coverageof our dataset precludes more complex spatial modeling.The number of degrees of freedom is reduced in eachfit because of the serial correlation of the smoothed

signals (Wilks 1995). As a result, only a few of thespatial fits are significant at the 95% probability level.Increasing the complexity of the spatial fit to include,for example, a two-parameter plane component reducesthe significance levels of the fits. Assuming the threecontributions to the variance of C are independent, thevariance of the smooth can be expressed as

5 1 12 2 2 2s s s s ,C S X r (21)


FIG. 12. Total energy available for melting expressed in terms ofmeters of ice that would have been ablated versus year.

TABLE 3. Partition of variance for 16-day smoothed signals.

Standard deviation

Total Seasonal Spatial Residual

Fraction of total variance

Seasonal Spatial Residual

Net radiationWinterSpringSummerFall

14.415.120.110.7

13.714.413.49.3

0.91.36.61.8*

4.24.4

13.64.9

0.920.910.450.75

0.000.010.110.03

0.080.090.460.21

Sensible heat fluxWinterSpringSummerFall

6.25.93.83.8

4.84.62.31.9

0.31.10.80.6

3.93.62.93.2

0.600.620.390.25

0.000.030.050.03

0.400.360.580.73

Latent heat fluxWinterSpringSummerFall

1.62.24.12.8

1.21.92.12.2

0.10.30.70.6

1.11.13.51.6

0.550.730.260.63

0.010.020.030.04

0.450.260.730.33

Bottom fluxWinterSpringSummerFall

4.23.11.41.1

3.62.61.30.4

0.8*0.6*0.20.6

2.01.60.41.0

0.740.680.890.16

0.040.040.020.26

0.220.280.100.75

Heat storageWinterSpringSummerFall

8.66.0

12.37.1

7.75.58.35.4

0.80.6*2.90.5

3.82.48.84.5

0.800.830.450.59

0.010.010.050.00

0.200.160.510.41

Energy available for meltingWinterSpringSummerFall

0.00.4

12.31.5

0.00.26.80.4

0.00.34.20.3*

0.00.49.51.4

0.060.210.310.07

0.000.750.120.05

0.920.790.600.88

* Indicates significant spatial fit at the 95% confidence level.

in which is the variance of the mean seasonal cycle,2s S

is the spatial variance, and is the residual inter-2 2s sX r

annual and unmodeled spatial variance. The variabilityand spatial structure of the parameters may change withthe seasons, so a separate analysis is performed for eachof the four seasons independently. In each season, fivesamples from each station were taken 16 days apart togive 225 points for each fit.

The results of this analysis for the energy fluxes arepresented in Table 3, which shows the standard devia-tions of the total variance of the low-pass smooths alongwith the standard deviations of the mean seasonal cyclewithin the season, the mean spatial component, and theresidual. Also shown are the fractions of the total low-pass variance accounted for by the mean seasonal cycle,the spatial fit, and the residual. By and large, there islittle dependence on latitude in the 16-day smoothedsignals. The interannual and unmodeled spatial varianceaccounts for over 10 W m22 of the net radiation onlyin the summer.

4. Comments and conclusions

The air temperature is closely coupled to the surfacetemperature through the sensible heat flux. The air–sur-face temperature difference, DT 5 T2m 2 Tsfc, deter-mines that flux as shown in (8). The magnitude of thisdifference is important in estimating the near-surface airtemperature from satellite measurements of the surfacetemperature (Yu et al. 1995). The snow-surface tem-perature is determined as a free parameter in the model,


FIG. 13. Monthly box plots of the 3-h modeled air–surface tem-perature difference DT 5 T2m 2 Tsfc, where T2m is the air temperatureat a height of 2 m and Tsfc is the surface temperature.

FIG. 14. Dates of the onset of melting and freezing as a functionof latitude.

so the statistics of the difference are easily determined.Figure 13 shows monthly box plots of the modeled DTvalues. The air is commonly stable in the winter andnearly neutral in the early spring, summer, and fall, justas we saw for the sensible heat flux. Only in May, whenthe rate of surface warming is greatest, is DT signifi-cantly negative, and there is an upward sensible heatflux as seen in Fig. 7. During the summer, the surfaceis melting and the surface temperature is maintainedclose to the freezing point (08C) so that the temperaturedifference is largely established by the measured airtemperature. In all months, the mean value is closelyrelated to the wind speed. In January, for example, themean value of DT is 2.0 K for winds less than 2 m s21

but only 0.4 K for winds greater than 10 m s21. Ingeneral, the absolute value of DT approaches zero withhigh winds, but in the summer, when near-neutral strat-ification is common (DT ø 0.0 K), the air becomes morestable with high winds, perhaps because warm air aloftis mixed down to near the surface, while the ice remainsnear the freezing point.

The snow-surface temperature was measured rou-tinely at the NP drifting stations from September toApril with an alcohol-in-glass thermometer placed ontop of the snow. The temperature was recorded to thenearest 8C. The air–surface temperature difference DTis found by subtracting the surface temperature from theair temperature which was measured in a Stevenson-type screen at a height of 2 m. The monthly mean valuesshow rough agreement; however, the monthly squaredcorrelation coefficients for the 3-h observations do notrise above 0.15. The poor correlation could be due toinaccuracies in the model-forcing parameters (in partic-ular, the temporal variation in the downwelling radiativefluxes) to inaccuracies in the model’s physics (in par-ticular, the thermal conductivity of the snow or the tur-bulent fluxes) or, finally, to inaccuracies in the mea-surements (in particular, the coarse resolution of therecorded snow-surface temperature). It is not possibleto sort out the exact cause of the poor correlation fromthis dataset alone, but accurate measurements of thesurface temperature without the use of a radiometer arenotoriously difficult.

The date of the onset of the melt season and its length

are often thought of as sensitive indicators of the totalamount of melting to expect. The dates of the onset ofmelting and freezing are determined by a procedure sug-gested by R. Colony (1994, personal communication).The 2-m air temperature is filtered with a 2-week run-ning-median filter, and the first and last day that thefiltered temperature is above a threshold of 20.58C aredetermined. For this threshold, the average date of meltonset is 19 June (day 170), with a range from 2 Juneto 11 July (days 153 to 192). The average date of freezeonset is 13 August (day 225), with a range from 18 Julyto 9 September (days 199 to 252). The average lengthof the melt season is 55 days, with a range from 20 to83 days. There is a weak dependence of these dates onlatitude, as shown in Fig. 14, with less than 5% of thevariance in either of the dates being explained by lati-tude.

The total melt (Fig. 12) is most closely correlatedwith the albedo in July, June, and August (correlationcoefficient R 5 20.86, 20.73, and 20.64), the lengthof the melt season (R 5 0.60), the latitude (R 5 20.54),and the air temperature in July (R 5 0.51). The highcorrelation with albedo is, of course, a manifestation ofthe well-known ice/albedo feedback. Note that thelength of the melt season is more important in explainingthe total ice melt (R 5 0.64) than when the melt seasonbegins (R 5 20.32) or ends (R 5 0.49). Our use ofalbedo values appropriate for nonponded ice means thatover entire floes, which have a lower average albedo inthe summer, there would be more total melt. In thisdataset there is about 0.21 m more melt for each 0.10decrease in the July albedo.

The freezing rate can be determined from the con-ductive flux at the bottom of the ice if an oceanic heat


flux is assumed. This heat flux is assumed to be zero,and the monthly freezing rate is determined by con-verting the average monthly bottom flux to the equiv-alent change in ice thickness; this conversion is doneusing the latent heat of freezing for freshwater, as wasdone for the total melt. The result is an average totalaccretion of 0.58 m. This is a close match to the averagetotal melt of 0.67 m, considering that there is a widerange in the ablation and accretion values found fordifferent stations and different years. The oceanic heatflux is more likely to be slightly positive; for every wattper meter squared of annual average oceanic heat flux,the annual average bottom accretion would be reducedby 0.10 m. The freezing rate is most closely correlatedwith the surface temperature, because the temperaturegradient through the ice determines the conductive fluxat the bottom and hence the freezing rate.

There is no doubt that there are large uncertainties insome aspects of the model-forcing parameters and inthe simplifications inherent in the model. Yet, the NPdataset offers a valuable opportunity to make estimatesof the energy balance over many years that is not easilysurpassed. The downwelling radiative fluxes are perhapsthe most serious approximation in the forcing param-eters, since they determine the net radiation, the largestterm in the energy balance equation. Although there maybe considerable error in the day-to-day values, the meanvalues should be much better and have been verifiedwith the measured daily-averaged flux values from theNP stations. Little information is available with whichto make better estimates of the downwelling radiativefluxes, even from satellites. Adding to the uncertaintyin the downwelling radiative fluxes is the uncertaintyin the albedo measurements. We have used monthly-averaged albedo values as measured at the ice camps.These measurements are for the area immediately sur-rounding the meteorological station and do not representthe average over the thick ice of the region, includingmelt ponds. If melt ponds had been included, the sum-mer albedo would have been much lower with a con-sequent increase in the energy absorbed and the energyavailable for melting. No doubt, including melt pondswould have also considerably increased the interannualvariability in the modeled total ice melt.

The treatment of meltwater and melt ponds is, per-haps, the most serious approximation in the model. Wedo not include the formation of melt ponds, their influ-ence on the albedo, and the storage of latent heat thatthey represent. In addition, a single ice class of fixedthickness is enforced. Future work could include usingthe NP drifting ice-station data to determine the energybalance for different ice classes, including ponded iceas well as thin ice. These energy balance calculations,with the addition of ice-thickness distribution estimatesand pond-fraction estimates, would allow a more com-plete determination of the regional energy balance ofthe ice.

The energy balance of thick ice has been computed

in the past, but usually using climatological-mean forc-ing values. Here, the energy balance is computed using3-h measured values of the air temperature, wind speed,humidity, cloud cover, and albedo for 45 annual cyclestaken at 21 different drifting ice stations of the formerSoviet Union. The mean annual cycle of the forcingsand the fluxes, their short-term variability, monthly vari-ability, and interannual variability have all been deter-mined. The determination of the variability in the forc-ings and the fluxes over thick ice will help in the designof observational programs that seek to monitor the stateand evolution of the Arctic ice pack.

Acknowledgments. I would like to acknowledge fruit-ful discussions with G. Maykut and R. Colony and thehelpful comments of the reviewers. This work was gen-erously supported by Office of Naval Research GrantN000-14-96-10070 and National Aeronautics and SpaceAdministration Grant NAGW 4950.

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Documents

Temporal Variability of the Energy Balance of Thick …psc.apl.washington.edu/lindsay/pdf_files/varibility_of...positions of the stations used in this study. The stations are concentrated