a. Model forcing parameters

The series of drifting ice stations operated by the former Soviet Union provides a unique and remarkable set of meteorological observations from the interior of the Arctic ice pack. The entire set of surface meteorological data has recently been made available to the west through the cooperation of the Arctic and Antarctic Research Institute (AARI) in Leningrad. The data are available on a CD-ROM from the National Snow and Ice Data Center (NSIDC 1996). The first station in the series was established in 1937 and operated for less than a year. The second was established in 1950 and operatedfor 1 yr. Beginning in 1954, there was continuous coverage by at least one station, usually two, until the end of the program in 1991 with the closing of NP-31. The station with the longest continuous record is NP-22, which remained active for over 8 yr. There are 196321 observations on the CD-ROM providing approximately 73 station years of data.

In addition to the standard meteorological variables, some of the stations also reported various radiative fluxes including downwelling direct, diffuse, and global shortwave radiation, net radiation (long and shortwave), and albedo. Summaries of these observations are available in a recently translated report (Marshunova and Mishin 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 NP drifting ice-station dataset include the air temperature, the mixing ratio, the wind speed, the air pressure, the downwelling short- and longwave radiative fluxes, the snow depth and density, and the surface albedo. Monthly mean forcing parameters are used when missing values are encountered. For convenience, 45 complete calendar years, January–December, were selected for computing the energy balance. This represents 67% of the entire dataset. Figure 1 shows the mean monthly positions of the stations used in this study. The stations are concentrated in the central Arctic basin, with relatively few in the peripheral seas. The stations extend from NP-6 through NP-31 and span the years 1957–90. In some years, as many as three stations reported simultaneously.

The air temperature was measured in standard meteorological observing screens at a height of 2 m. The winds were measured at various heights ranging from 2 to 10 m. All of the wind measurements were corrected to a height of 2 m assuming a logarithmic wind profile and a roughness length of z₀ = 1.3 mm. The mixing ratio was determined from the reported relative humidity (with respect to liquid water) and the reported air temperature.

The albedo of the surface is the monthly averaged albedo for each station and year. These values are reported by Marshunova and Mishin (1994) and represent observations of the nonponded surface near the meteorological observing site. The reported albedo is averaged over the entire month and represents the albedo 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 considerable variability in the monthly albedo values from station to station and from year to year; for example, the values in April range from 0.74 to 0.89 and those in July from 0.45 to 0.80. The high values in July represent years, when not all of the snow melted in the vicinity of the meteorological observing site or when summer snowfalls occurred. The monthly averaged albedo values may significantly smooth abrupt transitions in the spring and fall. The albedo is the mostsignificant and perhaps the least well measured of the forcing parameters. It must be stressed that the values we use do not include ponds, thin ice, or leads, and thus the computed energy balance cannot be generalized to all thick ice or to the ice cover as a whole. Yet, the calculations do represent a significant portion of the ice cover and characterize the energy exchange particularly well when the surface is frozen.

The snow depth and snow density are taken from the values measured at stakes near the weather observing sites. This dataset was also made available through a cooperative agreement with AARI and is on the NSIDC (1996) CD-ROM. The data we used here consist of blended 5-day values of the snow depth and density based on both daily values measured at snow stakes and more sporadic measurements obtained from 1-km-longsnow-measurement lines (I. Rigor 1996, personal communication).

The radiative fluxes for this study are estimated using parameterizations involving the solar zenith angle, reported cloud cover, surface albedo, air temperature, and humidity. We use parameterizations of the radiative fluxes, not the measured values, because the NSIDC CD-ROM includes only the daily average downwelling shortwave flux values (not 3-h observations), and the downwelling longwave radiation is available only in the winter. The parameterized downwelling long- and shortwave fluxes are determined with procedures recommended by Key et al. (1996) who compared several different parameterization schemes with measured fluxes obtained over several weeks in the spring of 1993 at Resolute, Northwest Territories,Canada, and over an annual cycle at Barrow, Alaska. For downwelling shortwave fluxes, they recommend the following parameterization by Shine (1984):

View Expanded

in which F_sw,clr, F_sw,cld, and F_dsw are the downwelling shortwave radiative fluxes for clear skies, cloudy skies, and all skies. Other parameters are the solar zenith angle Z, the solar constant S₀, the near-surface vapor pressure e, the surface albedo α, the cloud optical depth τ, and the cloud fraction c. The albedo in (3) represents effects of multiple cloud-to-ground reflections and should be the average albedo of a wide area around the observation site. For the purposes of the flux parameterization, the albedo in the months of July and August is reduced by 0.05 to account for melt ponds and leads in the vicinity of the station which would reduce the amount of multiple reflections between the clouds and the ice. This value of α used for the reduction is an additional source of uncertainty in the downwelling shortwave flux estimation.

The average daily global shortwave flux measured at stations dating back to NP-17 is used to validate the downwelling fluxes. Based on comparison between the parameterized and observed shortwave fluxes, a cloud optical depth was chosen for each month to minimize the mean monthly difference between them. In the spring and fall it was not possible to find a cloud optical depth that would entirely remove the bias, so a value of 1.0 was assumed. This inability may be due to the difficulties in comparing averaged daily values when the sun is above the horizon for only a small part of the day as well as to possible errors in the parameterization scheme or in the measurements at very low sun angles. The optical depths used for March–September are 1.0, 1.0, 3.5, 5.3, 6.8, 6.2, and 1.0. Figure 2a compares the downwelling shortwave parameterization for daily averaged values with the measured global shortwave radiative flux. For days in which the flux is greater than 10 W m⁻² (N = 6228), the parameterized fluxes average 0.4 W m⁻² less than the measured fluxes, and the rms difference is 31.7 W m⁻². The monthly bias ranges from −7.0 W m⁻² in April to 4.7 W m⁻² in June. If a constant value of 8 is used for the cloud optical depth, as done by Key et al. (1996), the parameterized fluxes average 10.6 W m⁻² less than the measured fluxes.

The errors associated with these parameterized radiative fluxes are comparable to the best estimates of the downwelling surface radiative fluxes made from satellites. Schweiger and Key (1997) used a neural net-based technique to retrieve the surface fluxes from TOVS radiances;they report that in their test cases (79 days from drifting ice stations and 180 days from a coastal station) the daily averaged fluxes show rms errors of 35 W m⁻² for the downwelling shortwave fluxes and 20 W m⁻² for the downwelling longwave fluxes. The mean measurement errors in their study were less than 4 W m⁻².

b. Model description

The time-varying components of the surface energy balance (1) are computed using a thermodynamic ice model. As mentioned previously, the forcing parameters derived from observations include the air temperature, the mixing ratio, the wind speed, the air pressure, the downwelling short- and longwave radiative fluxes, the snow depth and density, and the surface albedo. The important free parameters are the surface (skin) temperature, the ice-temperature profile, and the surface fluxes. The ice thickness is held constant at 3.0 m. The use of a constant ice thickness is justified, because changes in the thickness of multiyear ice during the year do not greatly modify the surface fluxes. The focus of this study is the variability of the surface fluxes for ice of a fixed thickness, and to change the ice thickness with time would add a confusing variable. In addition, the forcing parameters used in the model are not strong functions of the ice thickness if the ice is a multiyear floe and the ice stations were established on floes of different thicknesses. The 3-m ice thickness is near the equilibrium ice thickness of 2.88 m found by MU71.

The model has ten levels, seven within the ice and three within the snow. The levels are quadratically spaced in the ice and snow separately to give thinner layers near the surface. The snow layers are spaced in proportion to the snow depth. When the snow is deep (about 40 cm), the top snow layer is 4 cm thick. The layer thicknesses are consistent with the recommendations of Guest and Davidson (1994) who find that in new snow fluctuations in the surface forcing at a scale of 3 h penetrate about 5 cm deep. The top ice layer is 7 cm thick. The models for the surface energy balance and the subsurface temperature profile have been adapted from portions of the Community Climate Model Version 2 (CCM2) developed by the National Center for Atmospheric Research (Hack et al. 1993). The ice-temperature profile is calculated by solving the thermal diffusivity equation with a fully implicit Crank–Nicholson scheme. The model integrates forward in time with a time step of Δt = 3 h.

An energy balance equation is applied to each layer i; i = 1 at the surface to i = 10 at the bottom. For any layer, the energy balance is

View Expanded

where F_r,i is the radiative flux at the top of the layer,F_s and F_q are the turbulent fluxes (zero except at the surface), F_c,i is the conductive flux at the bottom of the layer, and S_i and M_i are the heat storage and energy available for melting within the layer. We will treat each of the terms in turn.

The net radiation at the surface is

View Expanded

where F_dsw and F_dlw are the downwelling shortwave and longwave fluxes at the surface, α is the albedo of the ice, ε is the surface emissivity, σ is the Boltzman constant,and T_sfc is the surface temperature. The net solar radiative flux is allowed to penetrate the surface and be absorbed within the ice (Grenfell 1979). The amount of penetration depends on the snow cover, the cloud fraction, and the depth in the ice. When snow is present, virtually all of the net solar flux is absorbed within the snow; when it is absent, about 65% passes through the first ice layer and about 50% passes through the top 25 cm of ice. During the summer, the penetrating solar flux causes much of the ice melt to occur below the surface. The snow depth and the snow density are prescribed based on observations from the NP stations.

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

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where ρ is the ice or snow density, c_p the heat capacity, and Δz_i the layer thickness. The total heat storage S in (1) is the sum of the S_i values. The energy available for melting is determined at each time step if a layer temperature exceeds the melting point:

View Expanded

where T_m,i is the salinity-dependent melting point of the layer. The energy available for melting M in (1) is the sum of the M_i values.

The salinity of the ice is modeled with a fixed salinity profile that drops linearly from 3 ppt at the bottom to 0 ppt at the top. This is in rough agreement with the idealized salinity profiles for multiyear ice shown by Maykut (1985). With this salinity profile, the other physical properties of the ice can be computed as follows. The specific heat capacity is from a theoretical expression derived by Ono (1967),

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where c₀ = 2113 J °C⁻¹ kg⁻¹, a = 7.53 J °C⁻² kg⁻¹, and b = 18000 J °C kg⁻¹. The temperature T is in kelvins and salinity S is in parts per thousand. The effective heat capacity is a strong function of the salinity and the temperature near the melting point because of the latent heat of freezing associated with brine pockets within the ice. Until the melting point is reached, the solar heat entering the ice remains as latent heat in the brine pockets. After the melting point is reached in this model, the heat available for melting M is assumed to drain away and need not be removed to begin the cooling of the ice. However, the large heat capacity near the freezing point due to the retention of liquid water in brine pockets requires the removal of a large amount of heat in the fall before substantial cooling begins. The fractional volume of brine is a strong function of temperature and salinity (Maykut 1985), rising to 15% at a temperature of −0.5°C and a salinity of 1.5 ppt (the average salinity of the ice in the model). The total melt, averaging 0.66 m of ice, is about 22% of the imposed 3-m ice thickness. Thus, the water retained within brine pockets is somewhat less than that melted after the freezing point is reached.

The heat conduction at the interface between layers i and i + 1 is proportional to the vertical temperature gradient:

F_c,ik_jT_i+1T_iz_j(15)

where T_i is the layer temperature, Δz_j is the distance between the centers of layers i and i + 1, and k_j is the average thermal conductivity of the two layers. The thermal conductivity of ice is from an expression proposed by Untersteiner (1961):

View Expanded

in which k₀ = 2.2 W m⁻¹ K⁻¹ and β = 0.13 W m⁻¹. The conductivity for snow is from Ebert and Curry (1993) and includes the temperature-dependent effects of vapor diffusion:

k_snow⁻⁶ρ^{2−4(T−233)/5}(17)

where the temperature T of the snow is in kelvins andthe snow density ρ is taken from observations at each ice camp.

The bottom flux F_B in (1) is the conductive flux in the lowest layer. The temperature of the bottom of the ice is assumed to be a constant −1.8°C. Consequently, in the winter, there is a substantial heat flux from the bottom surface. In the model, the thickness of the ice does not change, but this flux could be considered to come both from the ocean and from the latent heat of freezing at the bottom surface. A freezing rate could be determined if a value were assumed for the oceanic heat flux. In the summer, the ice temperature rises to the melting point, which, because of the low salinity of the ice, is warmer than the ocean temperature, so the bottom heat flux reverses sign.

The surface energy balance model and thermodynamic ice model have been checked with eddy-correlation measurements of the sensible heat flux made at the LeadEx ice camp in the Beaufort Sea in the spring of 1992. The surface turbulence measurements are reported by Ruffieux et al. (1995) who estimate an error of ±2 W m⁻² in the measured sensible heat flux. The model was forced with the measured wind speed, air temperature, humidity, and downwelling long- and shortwave radiative fluxes. The measured sensible heat flux had a mean of 2.9 W m⁻² and a standard deviation of 10.5 W m⁻². The mean difference between the sensible heat flux estimated by the model and that measured during LeadEx was −1.8 W m⁻², and the rms difference was 6.2 W m⁻². A full description of the intercomparison is given by Lindsay et al. (1997).

c. One year at one station

We begin our discussion of the results by showing the forcing parameters and resultant fluxes for just one station: NP-30 in 1990. Figure 3 shows the smoothed time-dependent forcing parameters obtained for this station using a 10-day running-mean filter. Because of the filter, the strong diurnal cycle in the downwelling shortwave radiative flux is not apparent. The computed values 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 significant energy is available for melting and the large amount of heat stored in the ice near day 190 (10 July). A time-versus-depth cross section of the ice temperature is shown in Fig. 5. The ice temperature cross section is similar to what MU71 found in their model study using monthly mean values. Note the lag in the cooling of the ice near the bottom until the early winter; this lag is caused by the considerable heat capacity of the ice–brine matrix.

a. Annual cycle of the energy balance

The entire 45 yr are combined to define the seasonal cycle of the energy balance. Box plots are used to showthe median, the quartiles, and the 5th and 95th percentiles of the 3-h values of each parameter by month. Figure 6 shows the annual cycles of the principal forcing parameters and Fig. 7 shows the annual cycles of the terms of the energy balance equation, (1). The variation illustrated by the box plots includes short-term (within the month), interannual, and spatial variability. The seasonal cycles are similar to what has been found by others, but it is noteworthy that there is considerable variation, as indicated by the box plots, in both the forcings and the fluxes.

Table 1 shows the monthly mean values and the standard deviations of the monthly means for each of the principal forcing parameters and the terms of the energy balance equation (1). Here, the standard deviations represent spatial and interannual variability of the monthly mean values and, as a consequence, represent much less variability than exhibited in the 3-h values used to construct the box plots in Figs. 6 and 7. All of the forcing parameters show seasonal cycles consistent with previous climatologies. Note, however, the large variability in most of them. Of particular impact on the energy balance is the variability in the albedo. The albedo is smallest in July, averaging 0.65; at some stations it remains high all summer, never dropping below 0.80. At these stations some snow remained on the ice surface all summer, or there was significant snowfall during the summer.

The monthly mean values of the downwelling radiative fluxes, the albedo, the net radiation, and the turbulent fluxes are compared in Fig. 8 with those used by M82 (for 3-m thick ice) and Ebert and Curry (1993). The Ebert and Curry results for net radiation and turbulent fluxes are area averages (including leads), so they are not comparable to our results for nonponded ice and are not included in the figure. The area-averaged flux values depend critically on the imposed lead concentration. The M82 study used prescribed values for the downwelling radiative fluxes and the turbulent fluxes. The monthly averaged radiative fluxes were from Marshunova (1961) and are based on data from the NP stations, so the good agreement with our values is to be expected. The turbulent fluxes were based on estimates made by Doronin (1963), whereas this study computes the turbulent fluxes based on the measured air temperatures and the modeled ice-surface temperatures. In general, our computed flux values are similar to those used by M82, although the sensible heat fluxes show some significant differences in both the winter and the summer.

The net radiation is remarkably constant through the winter months, averaging about −27 W m⁻². It changes from negative to positive in May, with the largest positive flux in July, not June when the solstice occurs, because of the lower albedo in July. The net radiation changes to negative again in September. The sensible heat flux is positive in the winter, about 7–10 W m⁻², and is negative only in May, when the increasing solarflux warms the surface above the air temperature. The latent heat is near zero in the winter and averages −10 W m⁻² in June. The bottom flux is near 15 W m⁻² in January and exhibits very little variability from station to station. In the summer, the bottom flux is negative indicating that the ice is warmer than the imposed −1.8°C bottom boundary condition. The rate of heat storage is greatest in July, when the net radiation is most positive. The ice temperature does not increase much at this time, but the specific heat is large owing to the latent heat of melting absorbed in the expanding brinepockets. The energy available for melting is maximum in July, but it has a large range, from less than 10% of the mean to over 200% of the mean. The greatest rate of cooling is in the fall, when the net radiation becomes negative. The heat stored in the ice slows the cooling of the ice substantially. The importance of the release of the stored heat in the fall, which produces a nonlinear temperature profile within the ice, was also pointed out by MU71 and Makshtas (1991).

The annual cycle of the energy balance is illustrated in Fig. 9, in which the monthly mean values of each ofthe terms of (1) are plotted. In the winter, the net radiative loss is balanced mostly by the bottom flux with very little heat storage or loss; however, the sensible heat flux also accounts for about a third of the net radiation. In the spring, the net radiation and the turbulent fluxes become small, and the conductive flux from the ocean begins to warm the ice. In the summer, the strong positive net radiation is largely balanced by storage and melt (in nearly equal parts) and, to a lesser extent, by the surface latent heat flux. Finally, in the fall, the netradiation again becomes negative, and it is balanced mostly by a cooling of the ice (the storage term). The turbulent fluxes and the bottom flux are all small.

Note that the annual average net radiation is just 0.5 W m⁻², which is remarkably close to zero, since there is nothing in the procedures that would force such a close balance. Small changes in the downwelling radiative fluxes or in the surface albedo could change the net radiation significantly. The annual average heat storage is also small, just 0.3 W m⁻², well within the uncertainty of the net radiation. Because we are modeling only one small part of the whole system and do not include lead processes or melt ponds, we need not expect an equilibrium energy balance to ensure a stable ice cover.

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

The scale-dependent variability of the forcings and fluxes on timescales of 3 h to 16 days is analyzed with the formalism of the discrete orthogonal wavelet transform. This method offers a simple and direct determination of the variability associated with each temporal scale and of the times that the variability occurs. It is particularly well suited for analyzing nonstationary time series, such as the annual cycle of the various parameters under study here. There are numerous references in the literature to the use of the wavelet transform in geophysical analysis. The techniques used here are outlined by Lindsay et al. (1996).

The discrete wavelet transform is based on the application of a sequence of high-pass and low-pass filters, in this case a Haar wavelet filter of length 2. The Haar wavelet coefficients are lagged differences of running-mean smooths of the series and are identical to the Allen variance used in many applications. The maximal-overlap algorithm, introduced by Percival and Guttorp (1994), is used to determine the wavelet variance. This algorithm determines the coefficients, one for each scale, for every step in the time series and offers a moreexact estimate of the temporal variability than the orthogonal-pyramid algorithm introduced by Mallet (1989).

Because the transform is orthogonal, the sum of the wavelet variances over all scales is equal to the variance of the observations. In this study, the wavelet coefficients are determined for eight different scales runningfrom 3 h to 16 days. The seasonal wavelet variance is then found by summing the squares of the coefficients for each season. Note that this is a simple procedure with the wavelet decomposition, since the coefficients are localized in time, unlike the coefficients of the Fourier transform. This advantage is one of the principal reasons why the wavelet variance is used here. The plotsshown are log-linear plots of wavelet variance versus temporal scale.

In a Fourier-centric view of the world, the Haar filters are the worst approximation of ideal high- and low-pass filters, since they are subject to severe leakage effects compared with higher-order (longer) wavelet filters (Daubechies 1992; Lindsay et al. 1996b). The lack of correspondence with a Fourier analysis is, however, balanced by an easy and direct interpretation of the waveletvariance that is calculated: it is simply the variance of the difference between adjacent nonoverlapping samples averaged over a period corresponding to the timescale.

Figure 10 shows the wavelet variance of the six forcing parameters with significant small-scale temporal variability for each of the four seasons. The downwelling shortwave flux shows the greatest variability at diurnal timescales, 6 and 12 h. The strength of the diurnal cycle is a strong function of latitude. The variance at a scale of 12 h drops from about 2500 (W m⁻²)² at 75° to nearly zero at the pole. The downwelling longwave radiative flux shows the greatest variability at scales of about 2 days, but there is little variability inthe summer owing to the constant cloud cover and constant temperatures. The variability increases at a scale of 16 days, because the variability associated with the annual cycle begins to be included. The air temperature shows the greatest variability in the winter at timescalesof 8 days and little variability in the summer. The specific humidity shows the greatest variability at timescales greater than 1 day. In both the air temperature and the specific humidity, there is no clear gap between the synoptic-scale variability of several days and the annual-cycle variability that begins to be seen at a scale of 16 days. The downwelling shortwave flux and the cloud fraction exhibit such a gap. The wind speed shows peak variability at timescales of 2 days and more variability in the fall and winter than in the spring and summer. Finally, the cloud fraction, which modulates the downwelling radiation, shows the greatest variability in the winter and spring at timescales of about 1 day.

Figure 11 shows the wavelet variance of the six terms of the energy balance equation (1). The net radiation shows a strong diurnal cycle in the spring and summer, but the variability is relatively smaller in the spring because the surface albedo is high. Thesensible heat flux is most variable at the shortest timescales. The latent heat flux shows significant variability only at small scales in the summer and exhibits a weak diurnal cycle. The bottom flux shows no short-term variability and only a small amount at scales near 10 days, and mostly in the winter. Again, this variability is related to the annual cycle. The variability in heat storage is greatest in the spring and summer and also shows a diurnal cycle. Finally, the energy available for melting shows variability only in the summer and exhibits a strong diurnal cycle. Note that there is no pronounced diurnal cycle in the air temperature (Fig. 10) or the sensible heat flux (Fig. 11) in any season. The large diurnal cycle in net radiation is largely balanced by diurnal cycles in the storage and melt terms.

c. Interannual variability

There is considerable variability in the forcing parameters from year to year and from station to station, and this is reflected in the energy available for melting F_m. In Fig. 12, the total annual energy available for melting (the time integral of F_m), expressed as meters of ice, is shown for each of the 45 station years. The latent heat of freezing of pure ice is used as a conversion factor. The total annual melt averages 0.67 m of ice, ranges between 0.29 and 1.09 m, and exhibits large variations from year to year.

The interannual variability was investigated by first considering each parameter in the dataset as the sum of two elements: a high-frequency “detail” signal (a high-pass filtered version of the time series) and a low-frequency 16-day smooth (a low-pass filtered version) (Lindsay et al. 1996b). The variability of the detail signal is analyzed in the previous section; here only the seasonal, spatial, and interannual variability of the smooth is considered. The smooth used here is simply the 16-day running mean.

The results of this analysis for the energy fluxes are presented in Table 3, which shows the standard deviations of the total variance of the low-pass smooths along with the standard deviations of the mean seasonal cycle within the season, the mean spatial component, and the residual. 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 is little dependence on latitude in the 16-day smoothed signals. The interannual and unmodeled spatial variance accounts for over 10 W m⁻² of the net radiation only in the summer.