4.1. Annual Means and Annual Cycle
 Table 1 gives annual averages and monthly means of the basic atmospheric budget terms [equation (1)] for the polar cap (the region north of 70°N) in W m−2. Monthly atmospheric transports and tendencies of atmospheric energy are given for both ERA-40 and NRA. The tendencies for both reanalyses are calculated following the study by Trenberth et al. . The energy content at the beginning of a month (BEG) was obtained by averaging the energy content at 18Z of the last day of the previous month and 00Z of the first day of the given month. The energy content at the end of the month (END) was obtained from averaging 18Z of the last day of the given month and 00Z of the first day of the next month. The monthly tendency is then (END − BEG) / (N * 86,400), where N is the number of days in the month and 86,400 is the number of seconds in a day. Along with Rtop from ERA-40, the ERA-40 minus ERBE difference is provided over the common period of coverage (February 1985 to April 1989). Planetary albedo from the APP-x data set is listed for months with a significant solar flux. Also given is the residual in the ERA-40 energy budget. This indicates the degree of closure (or lack thereof) in the budget averaged over 1979–2001. With perfect closure, the residual would be zero.
Table 1. Monthly and Annual Mean Components of the Atmospheric Energy Budget of the North Polar Cap From ERA-40 and Other Sources
|Month||Fluxes and Storage Changes, W m−2|
|∂AE/∂ta||Rtopb||−∇ • FAc||Fsfc||Plan. Albedod||Res.e|
|January||−2 (−1)||−175 [−11]||108 (117)||56||–||−9|
|February||5 (5)||−171 [−10]||112 (128)||51||–||−13|
|March||12 (12)||−143 [−1]||110 (121)||40||0.71||−5|
|April||25 (25)||−88 ||92 (102)||17||0.66||−4|
|May||21 (21)||−27 ||66 (77)||−18||0.64||0|
|June||18 (18)||23 ||89 (78)||−70||0.54||24|
|July||1 (−1)||11 ||94 (81)||−85||0.45||19|
|August||−17 (−16)||−66 ||98 (91)||−39||0.48||10|
|September||−27 (−26)||−145 [−5]||106 (104)||17||0.55||5|
|October||−22 (−22)||−183 [−9]||114 (108)||53||–||6|
|November||−11 (−12)||−184 [−12]||105 (114)||55||–||−13|
|December||−3 (−4)||−178 [−12]||111 (115)||58||–||−6|
|Mean||0 (0)||−110 ||100 (103)||11||–||−1|
 Looking first at the annual means of atmospheric transport, it is encouraging that the mass-adjusted value of 100 W m−2 from ERA-40 is quite close to the value of 103 W m−2 from NRA. On the basis of simulations with REMO 5.1 over nearly the same period 1979–2000, Semmler et al.  report 99 W m−2. Their simulation was driven at the lateral boundaries using data from ERA-15 and (for 1994 onward) operational fields from ECMWF. The annual transport from the work of Nakamura and Oort , based on a 10-year data set (November 1963–1973) compiled by the Geophysical Fluid Dynamics Laboratory (GFDL), is 98 W m−2. From an expanded GFDL data set (November 1964–1989), Overland and Turet  also report 103 W m−2. With recognition that these estimates are based on different periods and data sources, the annual value in −∇ • FA seems well constrained. The annual TOA radiation deficit in ERA-40 is −110 W m−2 compared to −104 W m−2 from the REMO 5.1 simulations. Over their common time period, annual means from ERA-40 and ERBE are nearly identical.
 ERA-40 depicts a mean annual upward net surface flux (a heat transfer from the subsurface column to the atmospheric column) of 11 W m−2. Nakamura and Oort  estimated a much smaller value of 2.4 W m−2. Theirs was calculated as a residual from the atmospheric transport based on the GFDL data set and Rtop based on data from Earth-orbiting satellites between the years 1966 and 1977. The REMO 5.1 annual value of 6 W m−2 falls roughly in the middle. These differences can be important. For example, a net surface flux of 1 W m−2 over a year is equivalent to melting approximately 0.1 m of sea ice at its melting point. The difference in the net surface flux between ERA-40 and REMO 5.1, taken over a year, hence represents roughly half a meter of ice. In a steady state climate, the positive net surface flux in the long-term annual mean would have to be balanced by oceanic sensible heat and sea ice transports [equation (5)]. While global warming invalidates the assumption of steady state, results for the Arctic Ocean domain (discussed later) argue that the ERA-40 annual net surface flux is too large.
 The range between estimates of the terms can be larger for individual months or seasons. For example, differences in atmospheric transport between ERA-40 and NRA are 16 W m−2 in February, whereas the May minimum of 66 W m−2 in ERA-40 is 11 W m−2 short of the corresponding NRA value. Monthly atmospheric energy tendencies from the two reanalyses are within 1–2 W m−2 of each other. Our winter and summer averages of 55 and −65 W m−2 for the net surface flux compare well to corresponding values from REMO 5.1 [Semmler et al., 2005] of 52 and −67 W m−2. On the other hand, there can be large differences in the monthly Rtop from ERA-40 and ERBE over their common period of record. In autumn and winter, Rtop in ERA-40 is too negative compared to ERBE, whereas for spring and summer, the opposite holds. In May, the two estimates differ by 26 W m−2.
 This brings us to the energy budget residuals in ERA-40. In the annual mean, the ERA-40 atmospheric energy budget, after applying mass corrections to the atmospheric transports, is almost closed. However, this is the result of compensating positive and negative residuals for individual months. Spatial fields of residuals for January and July down to 60°N are shown in Figure 2. Following the work of Trenberth and Solomon , these fields were truncated from T159 resolution to T42 using a tapered weighting function to remove excessive (and extraneous) noise that exists at higher wave numbers. The basic conclusions are that the residuals may be very large depending on location, and their spatial structure varies seasonally. Negative residuals dominate the Barents, Kara, and Laptev seas in all months. The extent of negative residuals (energy deficits) is large in January, covering much of the Arctic Ocean and land areas. Consistent with Table 1, July shows a majority of positive residuals (energy surpluses) over the polar cap region. Given that the atmospheric transports have been mass corrected, one is led to conclude that the imbalances arise largely from the ERA-40 TOA radiation and net surface fluxes.
Figure 2. Maps of the energy budget residual from ERA-40 for January and July extending down to 60°N. The 70°N latitude circle is indicated in bold. Contours for −100 and 100 W m−2 are shown as dashed lines.
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 For most of the year, the Arctic land is largely covered by high albedo snow (>0.70), and the albedo of sea ice is high even in summer (0.50–0.60). Snow and ice albedo are difficult to parameterize, and even small errors could substantially impact the TOA radiation budget, as well as the net surface flux. Furthermore, the Arctic is cloudy throughout the year, but especially in summer over the ocean when there is extensive low level stratus [Herman and Goody, 1976; Beesley and Moritz, 1999], for which both shortwave and longwave radiative properties are still not well understood. There may also be competing effects between temporal changes in surface albedo and in clouds [Kato et al., 2006].
 Yang et al.  and Allan et al.  documented problems in Rtop for both NRA and ERA-40. Allan et al.  compared the ERA-40 TOA radiation budget with ERBE data along with information from the ScaRaB instrument (1994–1995) and CERES product (January-August 1998). Evaluated over common periods of record, the TOA radiation budget in ERA-40 was found to be inferior to NCEP. Allan et al.  emphasized inaccurate radiative properties of clouds (rather than problems in cloud fraction) and (for high latitude lands) underestimation of surface albedo in ERA-40. The latter is associated with overestimates of both absorbed solar radiation (ASR) and outgoing longwave radiation (OLR). Their high-latitude comparisons, however, are primarily limited to results from the short ScaRab record: The ERBE comparisons use only data from the Earth Radiation Budget Satellite for 60°N to 60°S, whereas the CERES data only span 40°N to 40°S. They did not address seasonality.
 The monthly ERA-40 minus ERBE differences shown in Table 1 are computed using the revised ERBE record which combines information from three satellites. Trenberth and Solomon  estimated a root mean square error of the ERBE fluxes of 7.8 W m−2 for the three-satellite combination. There is similarity between the seasonal structure of these differences and the ERA-40 energy budget residuals (last column of Table 1). This also holds when the ERA-40 residuals are calculated for the ERBE period.
 To the extent that the revised ERBE record can be used to validate ERA-40, the negative differences between ERA-40 and ERBE in winter point to excessive OLR (solar radiation is small or absent in winter). While deferring additional evaluation to a future study, it is likely relevant with respect to OLR that the vertically integrated sensible heat storage in ERA-40 is high relative to NRA for all months (see section 4.4). Positive ERA-40 minus ERBE differences for spring and summer suggest a contribution from overly low albedo (as suggested by the study of Allan et al.). The differences in Table 1 are largest for May, when high albedo is coupled with a fairly large solar flux. However, the study of Kato et al.  points to shortcomings in ERBE. Their study focused on CERES depictions of TOA fluxes and planetary albedo for the region 60–90°N. As part of the effort, comparisons were made with an ERBE-like product that applies the ERBE algorithms to CERES radiances. Errors in TOA radiances from the CERES instruments are smaller than those in ERBE largely because of better scene identification and better angular distribution models. As averaged for the period March 2000 through February 2004, the CERES albedo of 0.469 is somewhat lower that the ERBE-like value of 0.487. The annual net allwave TOA flux from the ERBE-like product is about 5 W m−2 more negative than the CERES value, which seems to be largely determined by the albedo difference. The CERES data suggest that the spring and summer TOA budget in ERA-40 may not be as bad as indicated in Table 1.
 With these caveats in mind, we step through the annual cycle of the atmospheric energy budget from ERA-40. To complement Table 1, Figure 3 gives graphical representations from ERA-40 of (1) the four primary atmospheric terms, (2) TOA radiation budget components, (3) atmospheric transport and its latent heat and dry static energy components, and (4) terms of the surface budget.
Figure 3. Annual cycles from ERA-40 of terms of: (a) the atmospheric energy budget; (b) the TOA radiation budget (Rtop) with SWtop and LWtop being shortwave and longwave components, respectively; (c) atmospheric transport, with DSE and LE being dry static energy and latent heat energy, respectively (the small kinetic energy term is not shown); (d) the surface energy budget, with SWsfc and LWsfc being shortwave and longwave radiation components, and QH and QE being the turbulent sensible and latent heat fluxes, respectively.
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 According to ERA-40, there is a net loss of energy from the atmospheric column in August of −17 W m−2. The net loss is largest in September (−27 W m−2) and becomes less negative through the winter (Figure 3a). The atmosphere begins to gain energy in February. The net energy gain increases during spring to a maximum of +25 W m−2 in April. Essentially, steady state conditions characterize July. This annual cycle, which is similar to that computed by Nakamura and Oort , will be reflected in the changing magnitude and sign of the vertical and horizontal fluxes.
 During autumn, there is a growing TOA net radiation deficit as net solar radiation declines while net longwave losses remain large (Figure 3b). The autumn decline in the solar flux and hence its contribution to cooling of the atmospheric column is greater in high as compared to middle latitudes. While this fosters an increase in the atmospheric transport, the increase with respect to summer is modest. This can be understood from the net surface flux, which turns positive, also adding energy to the atmospheric column. Hence although the atmosphere is losing energy strongly in autumn, fundamentally because of the declining solar flux, attendant increases in both Fsfc and the atmospheric transport act as “brakes” on the system. Put differently, the atmosphere loses energy at a slower rate than one would expect simply from the declining solar flux.
 The atmosphere continues to lose energy through January, but at a slower rate than for autumn. The net solar flux is essentially zero. In January, the TOA longwave loss is almost balanced by the combination of atmospheric transport and Fsfc.
 Spring approaches and the atmosphere begins to gain energy. The positive tendency in atmospheric energy storage is largest in April and May due primarily to the large input of solar radiation which strongly reduces the TOA net radiative loss (Rtop). However, atmospheric energy gain is modulated by the high planetary albedo associated with sea ice, snow cover, and cloud cover. In addition, the sign of the net surface flux changes from positive to negative. Atmospheric transport declines sharply to a minimum in May. The continued positive change in atmospheric energy content during June would be much larger than indicated in Table 1 if not for the strong losses associated with the net surface flux (a transfer of heat from the atmospheric into the subsurface column).
 According to ERA-40, the net surface flux during June and July is almost as large as the atmospheric transport. As cloud cover over the Arctic Ocean is at its maximum in summer, mostly extensive low-level stratus, the low planetary albedo in July is primarily due to extensive open water and snow-free land. By August, TOA net solar radiation has declined from its June peak, and TOA net radiation has turned negative. The net surface flux for August is also still negative. Both processes contribute to a loss of atmospheric energy, with the atmospheric transport acting to decrease the rate of loss.
 Atmospheric transport is dominated by dry static energy (sensible heat plus geopotential). The annual cycle in the much smaller latent heat term (Figure 3c) is, by contrast, characterized by a late summer to early autumn peak, as it follows the higher temperatures and increased water holding capacity of the atmosphere. The seasonality in the vapor flux convergence implied by Figure 3c is broadly in accord with the observed late summer/early autumn maximum in precipitation over the polar cap and Arctic Ocean [Serreze et al., 2007]. For long-term annual averages, the vapor flux convergence equates to net precipitation (precipitation minus evaporation, or P − E). Several studies have examined P − E for the polar cap domain using NRA and ERA-15 vapor transports. Long-term annual means range from 182 to 207 mm [Genthon, 1998; Cullather et al., 2000] compared to the ERA-40 value of 193 mm for the period 1979–2001.
 Recall that the net surface flux is the sum of the surface radiation and turbulent heat flux terms. As seen in Figure 3d, the vertical sensible and latent heat flux terms are small through the year. In winter, the small sensible heat flux tends to be directed toward the surface (i.e., negative, hence an atmospheric energy sink) in association with temperature inversion conditions. The small latent heat flux is, by contrast, always upward (an atmospheric heat source). The net longwave flux is considerably larger but, compared to the net shortwave flux, is rather steady through the year. The annual cycle of the net surface flux consequently mirrors the annual cycle in the surface net shortwave flux.
4.2. Spatial Patterns of the Net Surface Flux
 Maps of the net surface flux for the four midseason months from ERA-40 demonstrate the importance of the ocean (Figure 4). The salient features in January are intense upward fluxes over open ocean areas including the Norwegian and Greenland seas where there are very strong air-sea temperature gradients, smaller upward fluxes over the ice-covered ocean, and even smaller upward fluxes over land regions. For April, fluxes are still upward over ocean areas but of smaller magnitude and are downward over land. For July, fluxes are everywhere downward. They are largest over ocean areas south of the 80°N where strong ice melt can be expected and (further south) where low albedo open water areas promote strong solar heating, replenishing the oceanic sensible heat store. Note the sharp coastal contrasts in July. Warming of the atmosphere is strongly inhibited over the ocean compared to land. This sets up a summer Arctic frontal zone, providing favorable conditions for summer cyclogenesis, especially near the shores of eastern Eurasia and Alaska [Serreze et al., 2001]. October depicts the transition back toward winter conditions, with large upward fluxes over open water areas and the coastal Arctic seas where thin ice is growing, compared to smaller fluxes over the central Arctic Ocean where sea ice is thicker. The study by Trenberth and Stepaniak  provides a complementary analysis of seasonal changes in the net surface flux over ocean regions for 60°N to 60°S.
Figure 4. Maps of the net surface heat flux from ERA-40 for January, April, July, and October extending down to 60°N. The 70°N latitude circle is indicated in bold. The −100, 0, and 100 W m−2 contours are shown as dashed lines. Areas in white are ±10 W m−2.
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 The field of the annual mean net surface flux follows in Figure 5. Over the ocean, it is of the expected positive sign, with the largest values over the northern North Atlantic and Atlantic subpolar seas. As discussed with reference to Table 1, the values are likely too large. Assuming a steady state climate, the flux should be close to zero over land. However, according to ERA-40, the annual average flux over much of the land is between −5 and −10 W m−2 and locally greater. While these also seem much too large, the sign is likely correct as available observations point to subsurface warming. Recent positive trends in surface air temperature over Arctic lands encompass all seasons [Serreze and Francis, 2006], and warming of near surface permafrost has been documented for Alaska, especially on the North Slope [Osterkamp, 2005], Canada [Smith et al., 2005], and Russia [Pavlov and Moskalenko, 2002]. An increase in active layer thickness over permafrost (the maximum depth of seasonal thaw) could be allied with a prominent downward flux as it involves phase change in the surface layer which is often ice rich. At least for Russia, there is strong evidence for increasing active layer depth [Zhang et al., 2005].
Figure 5. Map of the annual mean net surface heat flux from ERA-40 extending down to 60°N. The 70°N latitude circle is indicated in bold. The 0 W m−2 contour is shown as dashed lines. Areas in white are ±2 W m−2.
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4.3. Zonal Asymmetry of Atmospheric Energy Flow
 Figure 6 shows longitudinal variations by month of the vertically integrated meridional flow of total atmospheric energy and the latent heat component across 70°N in units of gigawatts per meter (GW m−1 = 109 W m−1) based on ERA-40. Results from NRA are, in general, very similar and are not shown.
Figure 6. Annual cycle of the vertically integrated flow of: (a) total atmospheric energy; (b) latent heat from ERA-40 across 70°N by longitude.
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 Looking first at total energy (Figure 6a), there is a prominent region of poleward (positive) flow centered at about 50°W. This is just east of the axis of the mean 500-hPa eastern North American trough, pointing to contributions from the time mean flow and eddy transports associated with the North Atlantic storm track. These are strongest in winter and weakest in summer. A strong region of equatorward (negative) flow lies to the west, centered at about 110°W, associated with the descending leg of the 500-hPa western North American ridge. These are again strongest in winter. Over Eurasia, centered at about 150°E, is a region of inflow during the cold season and weak outflow in summer. In winter, this longitude is just downstream of the East Asian trough. The trough weakens and shifts east in summer, helping to account for the outflows in this season. Finally, outflow dominates a broad region from about 30°E to 90°E, with the longitude of the maximum varying by season. This shows a broad correspondence with mean equatorward winds on the western limb of the Urals trough.
 The only notable difference between ERA-40 latent heat transport (Figure 6b) and that of NCEP is that the peaks are somewhat stronger in ERA-40, perhaps because of this model's higher resolution. Recall from Figure 3c that the zonally averaged meridional latent heat transport exhibits a summer/early autumn peak. It is evident that this is largely the result of strong moisture inflows in four regions. These more than compensate for the strong outflows centered at about 110°W. The area of inflow at around 90°E is slightly east of the Urals trough (during summer, the trough axis at 500 hPa is at about 80°E). In turn, the area of summer inflow at about 165°W is just east of the East Asian trough. Prominent inflows at about 50°W and near the prime meridian are separated by a region of equatorward flow in summer and weak poleward flow in the other seasons. This separation manifests blocking by the Greenland ice sheet. Most of the moisture flow occurs below 700 hPa (roughly 3000 m). At 70°N, the highest ice sheet elevations of about 2900 m are found at about 35°W longitude.
4.4. Time Series of Atmospheric Transport and Storage
 Monthly time series of the energy transport and its components from ERA-40 and NRA are plotted in Figure 7. The ERA-40 results extend from 1979 to 2001. Those for NRA are for the longer record 1979–2005. Units are in petawatts (PW = 1015 W). Division by the area of the polar cap would yield W m−2.
Figure 7. Monthly time series of the components of atmospheric transport from ERA-40 (1979–2001) and NRA (1979–2005) across 70°N. Mean differences (ERA-40 minus NRA) are shown for each component and at 3 orders-of-magnitude less than the y axis scales.
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 The two reanalyses are remarkably close in the transports of sensible heat. They are also close in their depiction of the kinetic energy and latent heat transports, but with a tendency for NRA to yield slightly larger peak summer values in the latter as well as slightly larger winter values. Compared even to the latent heat transport, the kinetic energy term is quite small. There is less agreement in the geopotential transport, particularly in the early part of the record, when ERA-40 is lower than NRA. We calculated the ERA-40 geopotential transports both from the archived fields of this term and by subtracting the sensible, kinetic, and latent heat transports from the total transports. The time series do not match, but should. The cause of this discrepancy is not clear. The geopotential transport shown in Figure 7 is based on the latter (residual) calculation, which compares better with NRA. Assuming that this is the correct representation of the ERA-40 transport, the remaining departures from NRA may involve several issues, such as assimilation of satellite data and the higher vertical resolution of ERA-40 in the upper troposphere and stratosphere. Since geopotential is very large at high atmospheric levels, and noting that the geopotential transport tends to peak in the upper troposphere, even small percentage differences in geopotential between the two reanalysis could yield a significant difference. There are also potential issues with NRA. Trenberth and Stepaniak  documented a “pathological problem” with NRA in the stratosphere, most pronounced where topographic gradients are steep and the magnitude of the wind increases with height in the stratosphere. This appears to be related to use of the terrain-following (sigma) coordinate system and the upper boundary condition in the assimilating model.
 Departures between the two reanalyses in total energy transport hence primarily result from departures in the geopotential and latent heat terms. In particular, compared to NRA, ERA-40 depicts smaller total transports for about the first 5 years of the record. In the later part of the common period of record, there is more agreement.
 Figure 8 compares monthly time series of the stores of sensible heat and latent heat. The annual cycle is of course very prominent. Sensible heat storage always tends to be somewhat higher in ERA-40. While reasons for this are not clear, it may contribute to problems in the TOA radiation budget in ERA-40 discussed earlier. Warm biases relative to NRA are readily evident in ERA-40 surface air temperatures over the Arctic (I. Rigor, personal communication, 2006).
Figure 8. Monthly time series of sensible and latent heat storage for the polar cap from ERA-40 (1979–2001) and NRA (1979–2005).
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 The Arctic is known to be in the midst of pronounced change, characterized by increases in surface air temperature (SAT) in recent decades [Serreze and Francis, 2006] and strong reductions in sea ice extent, especially in September (http://www.nsidc.org [Stroeve et al., 2005]). As discussed earlier, there are indications of subsurface warming over land and rising active layer thickness over permafrost. Other studies demonstrate increases in oceanic heat transport into the Arctic Ocean through Bering Strait and Fram Strait [Woodgate et al., 2006; Schauer et al., 2004].
 Graversen  argued that rises in Arctic SAT as depicted in ERA-40 over the period 1979–2001 can be partly explained by a weak positive trend in poleward atmospheric energy transport. Our investigations of the longer NRA record point to pronounced surface and lower troposphere warming in recent years (2000–2005), as well as a small but significant positive trend in annual mean latent heat storage (1979–2005). However, at least for the polar cap, there is little evidence from either reanalysis for increases in vertically integrated sensible heat storage. These findings must acknowledge that trend assessments from reanalysis are fraught with uncertainty (see the study by Trenberth et al.  regarding trends in column water vapor and the work of Trenberth and Smith  for spurious temperature trends in ERA-40).