We will now consider a surface slab of finite thickness consisting of snow during most of the year and ice with melt ponds during the summer, similar to that within view of the ASFG radiometer. The total energy flux, Ftot, into this surface slab is given by
where Q* is the total net radiative flux given by
Note that (4.2) assumes that all radiative flux is absorbed within this surface slab, implying a slab thickness of several centimeters for snow and 1–2 m for ice. Even with this ice thickness, a monthly average of 1–7 W m−2 of solar energy penetrates through the ice into the ocean during July and August (using an ice extinction coefficient of 1.5 m−1 [Maykut and Untersteiner, 1971]), so (4.2) slightly overestimates the energy input from above to this surface slab during these months.
 The conductive flux (C) is estimated from the temperature gradient in the snowpack obtained from the ice/snow interface temperature (Tice), the best radiative estimate of the surface temperature (Ts), manual snow depth measurements (ds) at the ASFG site and the relation
Two values for the thermal conductivity of the snow (ks) are used. The first value (0.14 W m−1 K−1) was obtained with conductivity probe measurements by Sturm et al.  in the vicinity of the SHEBA site in April. This value is a factor of 2–3 lower than that often used for dry snow [e.g., Maykut, 1982], but results because of significant layers of depth hoar in the snowpack. However, Sturm et al.  also show that this direct measurement of ks is inconsistent with the observed wintertime bottom accretion of ice and evolution of the temperature profiles in the ice and snow. They conclude that an effective ks for the SHEBA year would be more similar to previous conductivity studies [e.g., Sturm et al., 1997]. Hence, we also use a value of ks = 0.3 W m−1 K−1 in the surface energy budget calculations to give a range for C. During times with no snow cover, the conductive flux is calculated using the water temperature at the bottom of the ice (Tw = −1.8°C), the approximate ice thickness (di = 2.0 m), the thermal conductivity of the ice (ki = 2.0 W m−1 K−1), and
 The total energy flux at a given time may be positive, negative, or zero. If Ftot is positive, the snow or ice is gaining energy, which can be used to either increase the temperature of the snow or ice (energy storage) or, if the temperature is already at the melting point, to produce melting. If Ftot is negative, energy is lost by the surface slab, and the slab temperature decreases. Note that we are including only the change of phase in this surface slab, not the change of phase at the bottom of the ice. As shown by Perovich et al. , a spatial average of 0.34 m of snow and 0.70 m of ice melted from surface slab during the SHEBA year, while a net of 0.35 m of ice grew on the bottom of the ice. The first two values imply an expected net energy flux excess in the surface slab, and the latter a deficit at the bottom of the ice.
4.1. Annual Cycle
 Each surface energy budget term shows large day-to-day variability (Figure 20). During winter, Ftot varies from −25 W m−2 to +12 W m−2, while in July it varies from +37 to 129 W m−2. This large day-to-day variability in Ftot is due to a large variability in both shortwave and longwave radiative terms, as well as in the turbulent flux terms. The positive values of Ftot in winter occur during cloudy periods, when Ql is near zero [Persson et al., 1999b]. Throughout the year, Ql tends to be either between −30 and −50 W m−2 or near 0 W m−2 (Figure 20b). The minima of −70 to −75 W m−2 occurred in early summer under a clear sky when the surface temperature was high. The slightly positive Ql values occurred during the summer under low-level clouds with above-freezing temperatures when the surface temperature was fixed at 0°C.
Figure 20. Surface energy budget using daily means. The terms are (a) Ftot (solid), the cumulative mean of Ftot beginning on November 1, 1997 (dashed), and Q* (dotted); (b) Qs (light solid), Ql (heavy solid), and α (dotted); and (c) Hs (solid), Hlb (dotted), and C (dashed) using ks = 0.3 W m−1 K−1.
Download figure to PowerPoint
 Variations in the net solar radiation occurred with variations in cloud cover and also with variations in albedo, when for instance, fresh snow had fallen (e.g., JD 535, JD 566) [see also Persson et al., 1999a]. The peak in net solar radiation occurred in early July, after the summer solstice, because rapidly decreasing surface albedo near 1 July reduced the outgoing solar radiation. At other sites with less snow cover, the net solar radiation would likely have peaked earlier.
 The turbulent heat flux has even greater day-to-day variability than do the radiative fluxes. Typically, each of the large peaks (in magnitude) of Hs and Hl corresponds to a synoptic event that has increased the wind speed. Most of the peaks are negative, showing downward heat transport and reflecting the stable stratification of the Arctic planetary boundary layer. Events with upward heat transport occur principally in May, June, and August, though some periods of upward heat transport occurred in conjunction with the wintertime near-neutral stratification events mentioned in section 3.2 and discussed by Persson et al. [1999b]. The large positive Hs on 27 January (JD 392) appears to be a plume from a lead that opened upwind of the ASFG tower in the vicinity of the SHEBA ice station.
 The variability of the conductive flux is less than for the other terms, reflecting the damping effect of the deep snow-layer for which C was calculated. The large variability of the various energy budget terms shows that long-term sampling and high data recovery are needed to obtain reliable flux estimates.
 Most studies of the climate over Arctic pack ice use monthly mean values of the terms in the surface energy budget [e.g., Sverdrup, 1933; Maykut, 1982]. Hence, monthly mean values for the ASFG site are presented here and are compared to the earlier studies. The monthly means show a net flux energy deficit of 10–20 W m−2 from September through March and an energy surplus from April to August (Figure 21a), with a peak of about 85 W m−2 in July. (The October 1998 values are interpolated from September 1998 and November 1997 values.) Clearly, the radiative terms are dominant. The net shortwave has a positive impact from March to September, and the net longwave radiation is negative throughout the year (Figure 21b), resulting in a positive net radiation balance from May through August and a negative balance during September through March. Though a factor 5–10 smaller in magnitude, the average turbulent heat flux (Hs + Hlb) opposes the effect of the net radiation, except during July. That is, it warms the surface during the winter and July while cooling it slightly during May, June, and August. The July downward Hs results from warmer air aloft being present over a surface with a fixed temperature of 0°C. Both of our estimates of the conductive flux have magnitudes comparable to the turbulent heat flux. It warms the surface during the winter and has a weak cooling effect during the summer as one would expect.
Figure 21. As for Figure 20, but using monthly means. In panels (a) and (c), values of Ftot, Ftot-run_mean, and C using the conductivity fluxes with ks = 0.14 W m−1 K−1 are also shown with a light line.
Download figure to PowerPoint
 Figure 21a shows the running mean of the net flux from November 1997 to October 1998. By October 1998, an annual average energy excess of 7.0–9.5 W m−2 exists, with the smaller and larger values corresponding to the use of the smaller and larger values of the thermal conductivity, respectively. This annual excess corresponds to a net melt of 0.84–1.14 m of ice. Interestingly, about 0.70 m of ice melted from the top of the undeformed multiyear ice pack during the year [Perovich et al., 1999] along with about 0.5 m of snow estimated for the radiometer site (equivalent to about 0.18 m of ice). Hence, the estimated excess energy in the surface slab and the observed surface melt of 0.88 m of ice agree well. Accretion and melting on the bottom of the ice also occurred, but these are irrelevant to the energy budget of the surface slab considered here.
4.2. Comparisons to Previous Studies
 Previous studies of the annual surface energy budget over the Arctic pack ice have relied on incoming radiative fluxes determined from sparse climatological estimates [Marshunova, 1961; Untersteiner, 1961; Doronin, 1963; Badgley, 1966; Maykut and Untersteiner, 1971; Maykut, 1982], derived from regressions using observed environmental conditions and estimates of cloud cover, albedo, and cloud optical depth [Sverdrup, 1933; Lindsay, 1998] or determined from models [Ebert and Curry, 1993]. Even the relatively rich data set from the North Pole drifting ice camps established by the former Soviet Union contain only limited downward longwave radiation measurements of questionable accuracy [Marushunova and Mishin, 1994; Lindsay, 1998; Jordan et al., 1999]. The other fluxes, such as Qso, Qlo, Hs, and Hl, have been determined through parameterizations using state parameters and assumed parameters, such as albedo and turbulent transfer coefficients. The SHEBA field program is unique in that direct measurements of all of the fluxes but one (C) in (4.1) and (4.2) are available at 1-h resolution throughout the year. All state parameters are measured, and no assumption of albedo is needed. However, we are using specified values for the εs and ks, and we are also calculating a transfer coefficient for the latent heat flux to gain temporal coverage.
 Because the SHEBA estimate of the annual cycle of the surface energy budget is based entirely on flux measurements, comparisons with budgets from other studies using climatological data, models, and parameterizations could provide insights into the representativeness of the SHEBA year, reveal differences leading to new interpretations of the energy budget over the Arctic pack ice, and spark insights into possible model shortcomings. The studies of Badgley  (B66), Maykut and Untersteiner  (MU71), Maykut  (M82), Ebert and Curry  (EC93), and Lindsay  (L98) are used here. Because Untersteiner  (U61) did not provide monthly means, his SEB estimates will only be compared when examining the annual mean budget.
 Badgley  used intermittent measurements made on drifting ice stations during and after the International Geophysical Year, supplemented by reports from Yakovlev . The solar fluxes were computed from the solar constant, the annual position of the sun, estimates of atmospheric transmissivity and surface albedo. Their results are valid between 70 and 90°N. The turbulent fluxes are computed from bulk methods. The calculations by B66 combine the surface melt and the conductive flux, thereby eliminating the determination of C and Ftot as defined in our study. MU71 performed a 1-D modeling study over a uniform multiyear ice pack using climatological forcing parameters representative of the central Arctic. Atmospheric humidity, temperature, and Hs and Hl were derived from Doronin  and climatological Qsi and Qli and α were obtained from Marshunova . The monthly means were interpolated in time, and a constant oceanic heat flux was assumed. L98 used Soviet drifting ice station data from 1957 to 1990 in the Beaufort and Chukchi Seas from 73 to 90°N to derive estimates of forcing parameters, then used parameterizations to compute surface fluxes. The forcing parameters derived from the data include air temperature, mixing ratio, wind speed, air pressure, Qsi and Qli, snow depth and density, and α. Because these stations were located on multiyear ice floes, this study probably did not include substantial effects of leads. In contrast, the modeling study by M82 partitioned the central Arctic pack ice into thickness categories, including leads, to obtain integrated surface fluxes. The model calculations for ice thickness categories greater than 0.8 m were similar to those by MU71, except that bulk estimates of Hs and Hl were computed in the model using a constant wind speed of 5 ms−1. The M82 3-m ice category probably represents conditions most similar to the ASFG site, though their 0.8–∞ m category is also compared (see Table 6). The 1-D model of EC93 was forced by radiative fluxes and cloudiness computed from the model of Curry and Ebert , climatologies of atmospheric temperature, humidity, winds and precipitation [Vowinckel and Orvig, 1970; Oort, 1983], and oceanic heat flux estimates [McPhee and Untersteiner, 1982]. The forcing parameters were representative of approximately 80°N. The EC93 model included the effects of melt ponds and leads as well as sophisticated parameterizations of some parameters such as albedo. The SHEBA ASFG site was on a 1.9-m-thick multiyear floe and leads were generally not directly sampled by the observations. Hence, we expect that the surface energy budget at the ASFG site is more similar to the conditions in the studies of MU71, L98, and the 3-m ice category of M82 than to EC93 and those in the other categories of M82. However, some effects from the nearby melt pond at the ASFG site make comparisons to the latter two useful as well.
Table 6. Comparison of Annual Energy Budget Components From the SHEBA Observations With Badgley  (B66), Maykut and Untersteiner  (MU71), Maykut  (M82), Ebert and Curry  (EC93), and Lindsay  (L98)a
|Parameter||SHEBA||SHEBA (αJuly = 0.64)||B66||MU71||M82 3m||M82 0.8–∞ m||EC93||L98|
|Qs + Ql − Hs − Hlb||3.18 [4.17]||1.59 [2.29]||−0.5||−0.92||2.56||1.79||1.33||1.18|
|C||2.45 (5.04)||2.45 (5.04)||N/A||7.96||6.31||5.82||8.12||5.68|
|Ftot [Ftot]||5.63 (8.22) [6.57 (9.12)]||4.04 (6.63) [4.69 (7.24)]||N/A||7.04||8.87||7.60||9.45||6.86|
 Comparisons of net radiation throughout the annual cycle (Figure 22a222222) show that the SHEBA Q* was generally comparable to the climatological (M82) and parameterized (B66, L98) fluxes, though there are differences of up to 29 W m−2 for some individual months (e.g., July compared to B66 and August compared to M82). However, despite the agreement in Q*, some notable differences exist in individual radiative components. Despite the SHEBA July Q* being very similar to M82, the albedo for July at the SHEBA ASFG site is lower by 0.08. This is reconciled by the observation that the July SHEBA Qsi is 10–26 W m−2 lower than the other studies (Figure 22b). Recall that the July ASFG albedo of 0.56 includes the effect of a melt pond during July. However, the July albedo of just the pure white ice along the IPG albedo line is 0.64 [Perovich et al., 2002], in excellent agreement with M82 and L98. With a Qsi of about 205 W m−2 at SHEBA, Q* over white ice for July would have been about 16 W m−2 lower than that at the ASFG site, 5–15 W m−2 less than M82 and L98, and 13 W m−2 greater than B66, but still well within the ±1 standard deviation given by L98. However, note that the Qsi at SHEBA are close to being significantly lower (by 2 standard deviations) than those given by L98 for June, July, and August. Note also that the large standard deviation given by L98 for the July albedo suggests that some of the stations used in that study may have been at least partially viewing meltponds similar to the ASFG site.
Figure 22. Comparisons of selected SHEBA monthly mean surface energy budget components with previous studies. Shown are (a) net radiation (Q*; heavy lines) and albedo (thin lines), (b) incoming shortwave radiation (Qsi), (c) incoming longwave radiation (Qli), (d) sensible heat flux (Hs), (e) latent heat flux (Hlb), (f) conductive flux (C), and (g) the residual or net surface flux (Ftot). The previous studies used in the comparisons are Badgley  (B66), Maykut  (M82) and Lindsay  (L98). In (f) and (g), SHEBA curves are shown using C determined from ks = 0.14 W m−1 K−1 (squares) and ks = 0.3 W m−1 K−1(dots). The error bars show ±one standard deviation of the monthly means from L98. The 3-m ice category from M82 is used in (a), (d), (e), (f), and (g).
Download figure to PowerPoint
 During September, October, November, March and April, the Qli at SHEBA was 20–45 W m−2 greater than most of the other studies (Figure 22c), which is clearly significant based on the standard deviations provided by L98. This difference possibly indicates the occurrence of more fall and springtime clouds at SHEBA and/or warmer air at radiatively important altitudes. Whether the SHEBA floe's spring location in the Chukchi Sea just north of the Bering Strait favored clouds or warmer air compared to other regions in the Arctic Basin is unknown at this time but could be assessed with other data collected at SHEBA. Interestingly, the incoming shortwave radiation at SHEBA isn't lower during September, March, and April (Figure 22b), and the difference in the net radiation is much smaller than that for Qli though still significant for March (Figure 22a). As seen in Figure 9a, the surface temperature was abnormally high at SHEBA during these five months, so the Qlo was unusually large, resulting in a Ql comparable to the other studies.
 The observed SHEBA turbulent heat fluxes have an annual cycle similar to the previous studies (Figures 22d and 22e). However, the magnitudes of Hs are much smaller than for M82 for the entire year and smaller than for B66 during the summer. The May–September Hl are 4–10 W m−2 lower than M82 and L98. There is slightly better agreement with L98 than with M82, especially for Hs and since L98 shows a tendency for Hs to warm the surface in July. Note that the smaller summer SHEBA values imply that the atmosphere doesn't cool the surface as much, permitting more surface heating and melting. Our crude estimates of the SHEBA winter conductive flux using ks = 0.3 W m−1 K−1 are similar to the M82 estimates for 3 m ice except in May and September; our estimates using ks = 0.14 W m−1 K−1 are 5–10 W m−2 less (Figure 22f). The negative C in May for M82 implies that heat flows from the surface into the ice, a phenomenon not indicated by the SHEBA data. The L98 values represent conduction at the bottom of the ice, so direct comparisons to the SHEBA values aren't useful.
 For the total annual budget, the SHEBA-ASFG data show 5–10% less incoming solar radiation than the other studies (Table 6). However, because of the lower albedo, the net solar radiation is similar to B66, MU71, M82 and L98 but still lower than EC93. If the July white ice albedo of 0.64 is used, the annual average ASFG Qsi is lower by 1.6 W m−2 or 7–11% lower than B66, MU71, M82, and L98. The ASFG data show 10–19 W m−2 more incoming longwave radiation and a longwave radiative loss that is similar to M82, 1.4–3.1 W m−2 less than B66, MU71 and L98, and 7.1 W m−2 less than EC93 which includes effects of leads and meltponds. The observed sensible heat flux is similar to estimates by EC93 and L98, but the observed latent heat flux is substantially less than all but B66 and EC93. When comparing the sums of the atmospheric surface fluxes (Qs + Ql − Hs − Hlb), the ASFG data produce a larger excess than that seen in the other studies (B66 and MU71 have small deficits). However, if the July albedo of white ice is used, the ASFG atmospheric flux excess is very similar to the other studies. The estimates by Untersteiner  indicate an annual average deficit in the atmospheric surface flux of about 6 W m−2, implying that the Arctic atmosphere is a heat sink. Except for B66 and MU71, the other studies, including the SHEBA data, imply that it is a heat source.
 Note that when the ASFG atmospheric flux is calculated from only those hours for which data from all terms are available (given in brackets in Table 1) rather than summing the mean components, the annual atmospheric flux excess for the ASFG data is larger by 0.7–1.0 W m−2. Hence, the presence of data gaps makes a nontrivial difference in these calculations. This difference represents an estimate of the accuracy of the SHEBA mean annual fluxes. Because a change in one SEB term generally implies a compensating response in another term [e.g., Persson et al., 1999b], the bracketed values may be the better estimates. For the ASFG data, the annual average conductive flux is significantly smaller for ks = 0.14 W m−1 K−1 and only slightly so for ks = 0.30 W m−1 K−1 compared to the other studies. With the uncertainties due to the value of ks and the data gaps, along with the possible unrepresentativeness of the ASFG July albedo, the observed annual excess net flux ranges from 4.0 to 9.1 W m−2. Probably the best ASFG estimate to use in comparisons to the other studies is 7.2 W m−2, which represents the data using a July white ice albedo, a ks = 0.30 W m−1 K−1, and the times with only the concurrent surface energy budget terms.
 Other biases in the ASFG data set may also have an impact on these estimates. The possible “cold” bias of the Eppley pyranometers (see section 2.2.2) may add as much as 2–4 W m−2 to Qsi and 1–3 W m−2 to Qs for the annual average, though quantifying the effects of the cold bias is difficult because of the unknown nature of this error [Dutton et al., 2001]. The overestimation in Qs due to solar transmission through the ice could reduce Qs by about 1 W m−2 for the annual average. The bulk latent heat flux may be underestimated during April and May because of the underestimation of the surface temperature, so the annual average Hlb may increase by up to 1 W m−2. The range of the conductive flux shown in Table 1 (2–5 W m−2) is estimated to be representative, providing an uncertainty of up to 3 W m−2. Therefore, with the possible net bias of 0–2 W m−2, an adjusted Ftot would be in the 4–11 W m−2 range and our best estimate is 8.2 W m−2. The best estimate is obtained by assuming a 2 W m−2 cold bias, a 0.5 W m−2 bias due to summertime transmission through the ice, and a 0.5 W m−2 bias in Hlb, producing a net bias of +1 W m−2 added to our best estimate of 7.2 W m−2 from Table 6. This range encompasses the mean excess fluxes from all of the other studies, and our best estimate is greater than MU71, L98 and between the two values from M82 (Table 6). The observed ice/snowmelt of 0.88 m ice equivalent at SHEBA implies an annual average surface energy flux excess of 8.4 W m−2. This value falls within the range from the observations presented here and is surprisingly close to our best estimate.
 An estimate of the annual average surface flux excess for multiyear ice in equilibrium could be obtained by assuming that the SHEBA floe would have been in equilibrium if the surface melt had equaled the observed bottom accretion of 0.53 m of ice. This balance would imply a surface mean annual flux excess of +5.1 W m−2. Alternatively, the annual average Ftot values of 6.86–7.04 W m−2 from MU71 and L98 may be representative of equilibrium conditions, since the model in MU71 was run until equilibrium conditions were established and L98 used observations from 1957 to 1990. For either equilibrium estimate, the larger annual average energy flux excess of 8.4 W m−2 estimated from the observed melt agrees qualitatively with the net loss of 0.35 m of ice (surface ablation minus bottom accretion) observed at SHEBA [Perovich et al., 1999]. Since the 4–11 W m−2 range of the observed SHEBA annual surface energy flux excess encompasses the equilibrium estimates and the value from the observed nonequilibrium conditions, differentiating between equilibrium conditions and ice-loss conditions such as observed at SHEBA will require an even better data set than was collected at SHEBA. This data set will need to have fewer data gaps, less uncertainty in the radiative fluxes, and a significant reduction in the uncertainty of the conductive flux estimates.
 If the effective ks truly is 0.3 W m−1 K−1, as the results of Sturm et al.  suggest is possible, and our estimates of the biases are accurate, our best estimate of the observed annual average flux excess of 8.2 W m−2 would be in remarkable agreement with the flux excess of 8.4 W m−2 expected from the observed surface melt. We could then conclude that the SHEBA year produced a net melt because of the unusually large surface melt due to 1) greater incoming longwave radiation during the fall and spring and 2) weaker cooling by the latent heat flux. Weaker warming by the sensible heat and conductive fluxes was inadequate to completely compensate. These conclusions are dependent on the above caveats and hence tentative.