Introduction

There has been a pronounced decrease in the summer Arctic sea-ice cover over the past decade. September ice extent has declined at an average rate of 11% (10 a)^–1 (Reference Serreze, Holland and StroeveSerreze and others, 2007; Reference Comiso, Parkinson, Gersten and StockComiso and others, 2008; Reference StroeveStroeve and others, 2008). Observations from submarines, aircraft and satellites indicate that ice thickness is also decreasing (Reference Giles, Laxon and RidoutGiles and others, 2008; Reference Haas, Pfaffling, Rabenstein, Etienne and RigorHaas and others, 2008; Reference Rothrock, Percival and WensnahanRothrock and others, 2008; Reference Kwok, Cunningham, Wensnahan, Zwally and YiKwok and others, 2009). the ice cover has transitioned to a younger, thinner, more vulnerable state (Reference Maslanik, Fowler, Drobot and ZwallyMaslanik and others, 2007; Reference Nghiem, Rigor, Perovich, Weatherly and NeumannNghiem and others, 2007). There has been considerable research examining the influence of atmospheric and oceanic forcing on the observed decline in sea ice. Contributions to the ice decline include a general overall warming trend (Reference Richter-MengeRichter-Menge, 2009), variations in cloudiness (Reference Francis and HunterFrancis and Hunter, 2006; Reference Kay, Gettelman, Stephens and O’DellKay and others, 2008), shifts in atmospheric circulation patterns (Reference Rigor and WallaceRigor and Wallace, 2004), increased ice export from the Fram Strait (Reference Nghiem, Rigor, Perovich, Weatherly and NeumannNghiem and others, 2007), advected ocean heat from lower latitudes (Reference ShimadaShimada and others, 2006; Reference Woodgate, Aagaard and WeingartnerWoodgate and others, 2006; Reference Polyakov, Walsh, Colony and TimokhovPolyakov and others, 2007), increased solar heating of the upper ocean (Reference Perovich, Light, Jones, Runciman and NghiemPerovich and others, 2007a, Reference Perovich, Jones and Light2008; Reference Steele, Ermold and ZhangSteele and others, 2008) and increases in the length of the melt season (Reference Markus, Stroeve and MillerMarkus and others, 2009).

In this paper, we focus on the impact that increases in melt season length have on ice albedo and solar heat input to the ice (Reference Perovich, Nghiem, Markus and SchweigerPerovich, and others, 2007b). the impact of solar heat on the ice–ocean system is at the core of the ice-albedo feedback. Reference Perovich, Light, Jones, Runciman and NghiemPerovich and others (2007a) examined changes in the solar heating of open water in the Arctic Ocean and adjacent seas. Here we take a similar approach, but with a focus on examining the role of solar heating of the ice. A simple parameterization of ice albedo, based on field observations (Reference Perovich, Grenfell, Light and HobbsPerovich and others, 2002) and triggered by the onset of melt and freeze-up is used (Reference Markus, Stroeve and MillerMarkus and others, 2009). Averages and trends in solar heat input to the ice cover over the period 1979–2007 are computed and compared to values for the solar heat input to the ocean.

Methods

The flux of solar heat input to the ice–ocean system (F _in) is simply the flux of solar heat input to the ice (F _i) and to the ocean (F _o) and can be expressed as

Expanding gives

where F _r is the incident solar irradiance, C is the ice concentration, α _i is the ice albedo, α _o is the ocean albedo and t is time, indicating which variables are a function of time. It is assumed that no sunlight penetrates the ice into the ocean. Reference Perovich, Light, Jones, Runciman and NghiemPerovich and others (2007a) examined the F _o term and here we concentrate on evaluating F _i. Equation (1) was evaluated daily from 1979 to 2007 on a 25 km ×25 km Equal-Area Scalable Earth Grid. Four parameters are needed for this calculation: F _r(t), C(t), α _o and α _i(t).

The mean daily downwelling shortwave fluxes from the US National Centers for Environmental Prediction (NCEP) reanalysis are known to have large biases due to incorrect cloud fractions compared to those of the European Centre for Medium-Range Weather Forecasts reanalysis (ERA-40) (Reference Serreze, Key, Box, Maslanik and SteffenSerreze and others, 1998; Reference Walsh, Chapman and PortisWalsh and others, 2009). Reference Walsh, Chapman and PortisWalsh and others (2009) find that at the Barrow (Alaska) ARM (US Atmospheric Radiation Measurement Program) site, shortwave flux biases averaged over June–August for ERA-40 are 16Wm^–2 too high compared to 143 Wm^–2 too high for the NCEP reanalyses. the NCEP bias results from simulated summertime cloud fractions that are too small. the ERA-40 reanalysis has a more realistic seasonal cycle for clouds, but the data end in 2002. the fluxes in the two reanalyses are well correlated if seasonal and geographic variations are accounted for (Reference Liu, Curry, Rossow, Key and WangLiu and others, 2005), so we can utilize the more accurate ERA-40 values to correct the post-2002 NCEP data by determining seasonal and regional regression equations between the two datasets

The NCEP predictor variables are the downwelling solar flux, F _{swd, ncep}, and the sea-level pressure, P _ncep. These are the two variables we found that significantly improved the NCEP estimates. the ERA-40 downwelling solar flux was interpolated to the NCEP grid using five years of data, evenly spaced from 1979 to 1999. Separate regression equations were determined every 5 days of the seasonal cycle for every second gridpoint of the NCEP data. This is justified because the regression coefficients do not change rapidly with the seasonal cycle or location. All pairs (NCEP and ERA-40) of daily average values were included for each fit within 5 days of the designated time of year from all five years and within 750 km of the grid location. For location, x, and time of season, s, the least-squares estimates of the coefficients were determined for

The mean root-mean-square error of the regression is 29Wm^–2. Biases in the ERA-40 downwelling shortwave flux remain in the adjusted data. Finally, corrected estimates of the daily mean solar flux were computed for all locations and times on the NCEP grid by interpolating the three coefficients to each time and location and using the NCEP values for the downwelling solar flux and the sea-level pressure in the regression equation.

Passive microwave observations were used to determine the ice concentration, C(t), from the NASA Team algorithm (J. Maslanik and J. Stroeve, http://nsidc.org/data/docs/daac/nsidc0081_ssmi_nrt_seaice.gd.html; D. Cavalieri and others, http://nsidc.org/data/nsidc-0051.html). Summer melt ponds may lead to underestimates of ice concentration, due to the difficulty in distinguishing between ponds and leads. We do not expect there to be any temporal trend in this uncertainty. Based on the field observations of Reference Pegau and PaulsonPegau and Paulson (2001) the albedo of the open ocean was set to a constant 0.07, with no time dependence.

The most difficult time series to estimate was the ice albedo. Due to persistent summer clouds, there is a not a comprehensive dataset of remotely sensed sea-ice albedos. the evolution of sea-ice albedo was approximated from the field observations of Reference Perovich, Grenfell, Light and HobbsPerovich and others (2002). They determined that the seasonal evolution of albedo for multi-year ice has five distinct stages, namely, dry snow, melting snow, melt pond formation, melt pond evolution, and fall freeze-up, and that the evolutionary sequence is determined in large part by the onset dates of melt and freeze-up. This albedo sequence is applied everywhere in our region of interest, but the daily values of albedo depend on the local onset dates of melt and freeze-up. the albedo sequence includes melt ponds, assuming they follow an evolution similar to that observed by Reference Perovich, Grenfell, Light and HobbsPerovich and others (2002). Using the method of Reference Markus, Stroeve and MillerMarkus and others (2009), daily-averaged satellite passive microwave temperatures are used to map four onset dates for each gridcell for each year: early melt, full melt, early freeze-up and full freeze-up. Briefly, the melt season is determined using temporal changes in brightness temperatures at 37 GHz and temporal changes in the gradient ratio between 19 and 37 GHz. the melt indicator of Reference SmithSmith (1998) is also applied. the strength of all three indicators determines the beginning and end of the period of continuous melt. the first and last days of melt are identified by secondary peaks in the weight of the three indicators before and after the melt starts and ends. Finally, sea-ice concentration provides additional information on ice disintegration and formation. Using the four melt/freeze-up dates the following sequence in albedo evolution is applied at all gridcells for all years:

1. 1. Before melt onset the snow albedo is 0.85.

2. 2. At early melt the albedo decreases to 0.81.

3. 3. Starting with full melt, there is a linear decrease to 0.71 in 15 days.

4. 4. For the next 6 days, decrease from 0.70 to 0.50.

5. 5. Albedo decreases by 0.0029 d^–1 (but to no less than 0.2).

6. 6. At early freeze-up set albedo to 0.46, representing some ponds freezing.

7. 7. At full freeze-up, albedo increases by 0.026 d^–1 to 0.85.

Applying this algorithm, with the satellite-derived onset dates, we were able to evaluate Equation (1) at all grid locations every day from 1979 to 2007. the resulting solar flux was then integrated over time to compute the total annual solar heat input to the ice. This is done by calculating the solar heat input to the ice per unit area for the entire gridcell,

where Δt is 1 day (86 400 s) and the summation is over all days of the year. If no ice is present in a gridcell (C=0), then there is no contribution to Q _i for that day. Similarly the solar heat input directly to the ocean, Q _o, per unit area for the entire gridcell is

The mean annual values of Q _o and Q _i are computed for the period 1979–2007, and year-to-year trends over that period are calculated. the relative contributions of solar heat deposited in the ice and in the ocean are explored.

Results

The mean annual solar heat input to the ice for 1979–2007 is mapped in Figure 1. Mean values range from 100 to 1000 MJm^–2. the minimum solar heat input to the ice occurs at the edge of the marginal ice zone in the Greenland Sea, where ocean heat drives the spring ice retreat, before much solar heat is absorbed in the ice. In contrast, peak solar heating occurs in the eastern Beaufort Sea where incident solar radiation is large, surface melting starts early and the albedo is small. In the Arctic basin, solar heating of the ice decreases northward from about 700 to 500 MJm^–2 due to reduced incident solar irradiance and a shorter melt season.

Fig. 1. Mean value of total annual solar heat input to the ice within a gridcell, Q _i. the units are MJm^–2.

To put these numbers in perspective, it takes ~300 MJm^–2 to thin the ice by 1 m. of course all the solar heat deposited does not contribute to surface melting; some is absorbed in the interior of the ice and some is transmitted to the ocean. Also, there are other major components to the surface heat budget (e.g. longwave radiative losses) that temper the impact of solar heating.

The 1979–2007 trend in solar heat input to the ice is mapped in Figure 2. This was calculated by performing a linear least-squares fit to the time series of annual Q _i for each gridcell. Trends are generally modest and are a mix of positive and negative values. This mix is a result of the two distinct parameters that contribute to Q _i: the ice concentration and the ice albedo. the negative trends around the periphery of the Arctic are due to reductions in ice concentration. the strongest negative trends are mainly near Greenland and the Fram Strait and result from ice completely melting earlier in the season, so that solar heat goes into the ocean rather than the ice. Areas of positive trend in Q _i are regions where ice concentration has not changed appreciably over the years, but the melt seasons have lengthened, resulting in an overall decrease in albedo.

Fig. 2. The trend in total annual solar heat input to the ice within a gridcell, Q _i. the units are %a^–1.

Figure 3 explores trends in the relative contribution of solar heat input to open water compared to the entire gridcell, by plotting the trend of the ratio Q _o /(Q _o +Q _i). Roughly 90% of the study area shows an increasing relative contribution from solar heat absorbed in open water, averaging 1%a^–1, with a peak of 4%a^–1. the growth in the open-water solar heat contribution is primarily due to a trend of increasing open water.

Fig. 3. The trend of the relative contribution of solar heat deposited in open water to the total solar heat deposited in the ice–ocean system, Q _o/(Q _o +Q _i). the units are %a^–1.

Longer melt seasons have resulted in modest increases in solar heating of the ice. This results in some increases in surface melting, but the impact is likely moderated by other components of the surface heat budget (Reference PerovichPerovich and others, 2010). However, in interpreting Figure 2, it needs to be kept in mind that our simplified approach does not account for the replacement of multi-year ice by first-year ice with lower summer albedos (Reference Perovich, Grenfell, Light and HobbsPerovich and others, 2002). the contribution of solar heat to the ocean is increasing faster than the contribution to the ice due to the loss of sea ice. This impacts the sea-ice mass balance through a trend of increasing bottom melt (Reference Maykut and McPheeMaykut and McPhee, 1995; Reference Perovich, Jones and LightPerovich and others, 2008) or reduced ice formation in the fall and winter. Extra heat deposited in leads also increases lateral melting of floes. Lateral melt is a major mechanism for the ice-albedo feedback because as the area of open water is increased the mean albedo is reduced. Determining the degree of this enhancement requires further research.

Discussion

The analysis in this paper is a first step in assessing changes in solar heat input to the ice as a result of changes in the melt season. the impact of increasing seasonal ice replacing multi-year ice should be considered next. This entails distinguishing between multi-year and first-year ice, using both passive and active microwave sensors, and then applying an appropriate albedo evolution algorithm to each type. an algorithm for the albedo evolution of first-year ice needs to be developed to complement the multi-year ice algorithm that was applied here. Field observations indicate that first-year ice has a somewhat similar, but amplified, albedo evolution compared to multi-year ice. There are significant differences as well. First-year ice typically has a thinner snow cover than multi-year ice, so the melt of the snow cover is faster and pond formation occurs earlier. Due to its flat topography, pond fractions early in the pond formation stage can be as large as 90%, much greater than multi-year ice. After drainage occurs in the pond evolution stage, first-year pond fractions are closer to multi-year ice values (Reference Hanesiak, Barber and YackelHanesiak and others, 2001; Reference Grenfell and PerovichGrenfell and Perovich, 2004). There is a rapid decrease in bare ice albedo if the ice thickness drops below ~0.5–0.7 m. Should the first-year ice completely melt in summer, the fall freeze-up of open water will take much longer than it does in an area with multi-year ice. Taken together this implies that albedos for first-year ice are less than those for multi-year ice over the course of the melt season, and the solar heat input to the ice is significantly greater. Our analysis applying a multi-year ice albedo evolution algorithm to seasonal ice overestimates the albedo and thus underestimates the solar heat input. As the multi-year ice pack declines and more of the Arctic has a seasonal ice cover, more solar heat will be input to the ice–ocean system, resulting in an enhanced ice-albedo feedback.