In this section, we first compare spectral albedo from SNICAR with observations and examine sensitivity of snow albedo and subsurface radiative heating to varying BC concentrations and snow effective radii. Next, we analyze GCM experiments with BC in snow, first comparing predicted BC concentrations in snow with observations, then assessing global forcing, and finally examining climate feedbacks.
3.1. BC Influence on Snow Albedo and Radiative Heating
 We first apply off-line, single-column, 470-band SNICAR to demonstrate model fidelity in reproducing observed snow reflectance. Figure 2 shows measured snow albedo for diffuse incident radiation at the South Pole (Figure 4 of Grenfell et al. , data provided by Steve Warren) and modeled reflectance using SNICAR with a thin (0.25 mm) surface layer composed of 45-μm re snow and a thick underlying layer composed of 100-μm re (snow density = 350 kg m−3). Grenfell et al.  found that a similar two-layer model (with surface re = 30 μm) also matched observed reflectance in both the visible and absorptive NIR. Because they did not measure snow grain size at the very high vertical resolution needed for model testing with fully known snow conditions, Grenfell et al.  pointed out that many arbitrary layer thickness and re model combinations can produce a good fit. Also shown in this figure is modeled albedo of the same snowpack, but with 500 ng g−1 of hydrophilic (coated) BC. The BC strongly reduces visible reflectance, but has negligible influence at wavelengths beyond 1 μm.
Figure 2. Measured diffuse incident radiation snow albedo at the South Pole from Grenfell et al.  and modeled albedo from SNICAR assuming a 0.25 mm thick surface layer composed of 45-μm re snow and a deep underlying layer of 100-μm re snow. The thin surface layer controls reflectance in the highly absorptive NIR portion of the spectrum. Also shown is the modeled snow reflectance with 500 ng g−1 of hydrophilic (coated) BC.
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 Next, we identify how varying concentrations of BC affect spectrally averaged (0.3–5.0 μm) hemispheric snow albedo and subsurface heating with different re. We assume an optically thick, homogeneous snowpack with direct-beam incident flux at a solar zenith angle of 60°. Grenfell et al.  reported that, using the model of Warren and Wiscombe , a uniform distribution of 15 ng g−1 BC reduces albedo by 1% at 500 nm with an effective grain radius of 100 μm. In our model, hydrophobic and hydrophilic BC reduce 500 nm albedo in snow with re = 100 μm by 0.0079 and 0.0108, respectively. The experiments discussed below apply hydrophobic BC optical properties.
 Figure 3 (top) shows spectrally averaged snow albedo for BC concentrations ranging from 0 to 1000 ng g−1 and four different re. Qualitatively, these curves agree well with Figures 1 and 2 of Warren and Wiscombe . As originally noted by Warren and Wiscombe , the presence of absorbing impurities reduces albedo more in snow with larger re. Albedo reduction for 1000 ng g−1 BC is 0.17 and 0.045 for snow with re = 1000 and 50 μm, respectively. Both the absolute perturbation from BC and disparity in perturbation between grain sizes grow as zenith angle decreases.
Figure 3. Top: Spectrally averaged snow albedo as a function of BC mass concentration for various snow effective radii (re). Note that BC perturbs albedo more in larger-grained snow. Bottom: Fraction of total snowpack absorption occurring more than 2 cm beneath the surface as a function of BC concentrations for the same re as the top panel. Absorption occurs deeper in the snow with homogeneously mixed BC because more of the total absorption is from visible radiation, which tends to absorb deeper than NIR, even with large BC concentrations. In both experiments, the snowpack is optically semi-infinite and homogeneous. Incident flux is direct beam from 60° zenith angle. For comparison of these BC concentrations with global observations and model predictions, see Table 2 and Figures 4 and 5.
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 The grain size effect is somewhat counterintuitive, as one naturally expects brighter media to be more susceptible to darkening by impurities. But visible radiation penetrates deeper in snow with larger re because it has a smaller extinction coefficient and, less importantly, scatters more strongly in the forward direction. The snow depth where mean radiative intensity diminishes to 1/e of its surface value is 17 cm for re = 50 μm and 78 cm for re = 1000 μm (λ = 550 nm, snow density = 150 kg m−3, zenith angle = 60°). By traveling through a greater optical depth of impurities, photons thus have a greater probability of absorption by (homogeneously interspersed) impurities in snow with larger re. Sensitivity to grain size highlights the importance of snow aging treatment and realistic re, which can vary significantly on small spatial scales [Painter et al., 2003].
 Nearly all albedo reduction from BC is due to increased absorption in the visible spectrum. NIR albedo decreases by only 0.02–0.06 with 1000 ng g−1 BC, whereas visible albedo is reduced by 0.07–0.28 (not shown). This produces another surprising result: With homogeneously mixed BC, the fraction of total absorption occurring more than 2 cm beneath the snow surface increases with increasing BC amount, up to a limit. Figure 3 (bottom) shows this fraction increasing by up to 0.11 with re = 1000 μm. While BC shifts the visible absorption to nearer the surface, a much greater portion of total absorption is in the visible spectrum. Even with large BC concentrations, visible absorption tends to occur deeper than NIR absorption. Most NIR absorption occurs in the top 1 mm of snow [Brandt and Warren, 1993; Flanner and Zender, 2005]. With sufficiently high BC concentrations, however, absorption shifts to higher in the snowpack, as can be seen by the slight downward trend in sub-2 cm absorption for re = 50 μm and BC concentrations greater than 400 ng g−1. The BC concentration of maximum sub-2 cm absorption depends on re because of the visible depth-penetration dependence on re. If aerosol is more concentrated at the snow surface, however, because of dry deposition or accumulation of impurities near the snow surface during melt, total absorption shifts toward the surface. By influencing subsurface melt [Koh and Jordan, 1995], changes to the vertical distribution of heating can have important influence on snow climatology [Flanner and Zender, 2005].
3.2. GCM Experiments
 We conducted six GCM experiments with BC in snow, using configurations presented in Table 1, designated from here on as YYYY low, central, or high experiment, where YYYY is 1998 or 2001. To assess climate response and efficacy, we also completed paired control simulations for the central and high experiments (YYYY central and high control), identical to the experiments except without BC in snow. Forcing in the low experiments was insufficient to perturb climate. To help constrain efficacy, we also conducted experiment and control simulations with 10× 1998 BC and OC emission inventories (1998 10× experiment and control), with otherwise central model configurations (Table 1). Finally, to help discern the relative forcing contributions from FF, BF, and BB sources, we conducted experiments emitting only FF + BF and FF central estimate sources (FF + BF and FF experiments). All runs apply annually repeating emissions.
 The wide range of climate perturbation in these experiments required different spin-up periods for equilibrium. In the discussion that follows, we report results from the final 15 years of 16-year simulations (1998 and 2001 low, FF + BF, and FF experiment), 25-year simulations (1998 and 2001 central experiments and controls), and 35-year simulations (1998 and 2001 high experiments and controls). For the 1998 10× experiment and control, we analyze the final 20 years of 50-year simulations. The 95% confidence interval of linear trend in global mean 2-meter air temperature (T2m) of these 15- and 20-year time series included zero for all experiments and controls except 2001 central and high experiments, which both had trends of +0.01°C yr−1. Because the corresponding controls had no trend, it is possible we underestimated the climate response for these scenarios. Global mean top-of-model (TOM, about 3 mb pressure) radiative energy flux, averaged over the analysis periods, was within 1 W m−2 of equilibrium for all model runs.
3.3. Measured and Modeled BC Concentrations in Snow
 Table 2 summarizes measurements of present-day BC in snowpack from all studies known to the authors. When mean values are not reported in the original literature, we report means of all published measurements from each location. Measurement techniques and uncertainties vary considerably between studies and are discussed to varying degrees in each reference. Most studies utilize optical or thermal/optical techniques, although Slater et al.  applied an acid-base/thermal method. Table 2 also shows CAM/SNICAR predictions of BC concentrations in the surface snow layer. Data in the lower portion of the table show BC concentrations in precipitation, with model estimates derived from wet deposition and precipitation rates. When the measurements correspond to a particular time of year, we report model predictions from the same months. Otherwise, model results are annual mean estimates. Central estimates for 1998 and 2001 are reported with low-high range in parentheses. A log-log whisker plot of these data is shown in Figure 4. The center model point on this plot is the mean of 1998 and 2001 central experiments, and vertical error bar represents the greatest minimum-maximum range from both 1998 and 2001 low and high experiments. Global distributions of model annual mean BC concentrations in surface snow, averaged only when snow is present, are shown in Figure 5 for FF + BF and 1998 (FF + BF + BB) central estimates, plotted on a log scale.
Figure 4. Model versus observed BC concentrations in near-surface snow for data from Table 2, grouped by region (precipitation measurements excluded). Model data are from the top 2 cm of snowpack. The center model point on this plot is the mean of 1998 and 2001 central experiments. The upper extent of the model error bar represents the maximum of 1998 and 2001 high experiments, whereas the lower extent is the minimum of both low experiments. The correlation coefficient of the log of these data is 0.78.
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Figure 5. Annual mean predicted BC concentrations in snow (ng BC per g of ice) using central estimate (top) fossil fuel and biofuel sources only, and (bottom) fossil fuel, biofuel, and 1998 biomass burning emission sources.
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Table 2. Comparison of Modeled and Measured BC in Snow, Sea-Ice, and Precipitation
|Site||Reference||Measurement Period||Measured BCa, ng g−1||1998 Model BC central (low-high)||2001 Model BC central (low-high)|
|Summit, Greenland (72.6°N, 38.5°W)||Slater et al. ||1994–1996||14.6 (4.2–30.1)||5.2 (1.7–64.1)||3.5 (1.5–34.5)|
| ||Cachier ||1991–1995||2.0–19.0b|| || |
| ||Chylek et al. ||1989–1990||2.0 (1.5–2.7)|| || |
| ||Cachier and Pertuisol ||1988–1989||1.0–4.0b|| || |
|Camp Century, Gr. (77.2°N, 61.1°W)||Chylek et al. ||∼1985||2.4 (2.1–2.6)||13.3 (1.2–26.9)||6.2 (0.9–19.6)|
|Dye 3, Greenland (65.2°N, 43.8°W)||Clarke and Noone ||May 1983||6.4 (4.3–8.5)||11.8 (3.6–131)||8.2 (3.0–29.1)|
|Alert, N. Canada 83.5°N, 62.5°W)||Clarke and Noone ||Nov.-Dec. 1983||56.9 (0–127)||2.2 (0.9–5.9)||2.5 (1.0–6.0)|
|Greenland Sea (79.8°N, 4.2°W)||Clarke and Noone ||Jul. 1983||38.7 (5.4–75.5)||23.9 (3.0–104)||20.4 (3.5–93.9)|
|Spitzbergen (79°N, 12°E)||Clarke and Noone ||May 1983||30.9 (6.7–52)||12.7 (3.7–37.0)||7.2 (4.6–34.4)|
|Barrow (71.3°N, 156.6°W)||Clarke and Noone ||Apr. 1983, Mar. 1984||22.9 (7.3–60.4)||9.7 (4.1–26.4)||8.4 (3.2–25.4)|
|Abisko (68.3°N, 18.5°E)||Clarke and Noone ||Mar.-Apr. 1984||33.0 (8.8–77)||80.7 (15.3–332)||96.4 (19.4–279)|
|Hurricane Hill (48.0°N, 123.5°W)||Clarke and Noone ||Mar. 1984||14.7 (10.1–18.5)||29.5 (7.1–101)||35.2 (7.1–125)|
|Arctic Ocean (76°N, 165°E)||Grenfell et al. ||Mar.-Apr. 1998||4.4 (1–9)||8.4 (4.2–21.8)||5.8 (2.4–16.7)|
|Cascades, Wash (∼47°N, 121°W)||Grenfell et al. ||Mar. 1980||22–59||36.8 (6.3–86.3)||35.1 (6.7–85.9)|
|Halifax, Nova Scotia (45°N, 64°W)||Chylek et al. ||Nov. 1995–Mar. 1996||11 (4.3–32)||84.0 (22.0–244)||84.9 (18.9–270)|
|French Alps (45.4°N, 5.3°E)||Sergent et al. ||winters 1989–1991||161 (80–280)||165 (50.5–226)||136 (37.7–287)|
| ||Sergent et al. ||winters ∼1992–1997||123 (34–247)|| || |
| ||Fily et al. ||Apr. 1992||482 (235–826)||394 (92.2–)c||69.4 (32.7–498)c|
| ||Fily et al. ||Dec. 1992||115 (22–302)||29.0 (37.4–349)||43.5 (17.6–51.5)|
|West Texas/New Mexico (32°N, 106°W)||Chylek et al. ||1982–1985||10.6 (2.2–25.4)||31.6 (8.4–89.6)||15.5 (6.4–73.0)|
|Vostok (78.5°S, 106.9°E)||Grenfell et al. ||Dec. 1990–Feb. 1991||0.6||1.08 (0.07–2.1)||0.50 (0.07–1.8)|
|Siple Dome, Ant. (81.7°S, 148.8°W)||Chylek et al. ||1982–1985(?)||2.5 (2.3–2.9)||0.08 (0.04–0.68)||0.09 (0.04–0.51)|
|South Pole (90°S)||Warren and Clarke ||Jan.-Feb. 1986||0.23 (0.10–0.34)||0.20 (0.07–1.23)||0.21 (0.06–1.2)|
|BC in Precipitation|
|Rural Michigan (45.5°, 84.7°W)||Cadle and Dasch d||Dec.-Apr 1984–1985||72 (28–210)||50 (22–108)||46 (21–98)|
|Urban Michigan (42.5°N, 83°W)||Dasch and Cadle d||Jan.-Apr 1984–1985||160 (17–5700)||57 (26–132)||53 (23–113)|
|Lithuania (55.5°N, 21°E)||Armalis e||Dec. 1986–Jun. 1990||100 (8–530)||61 (22–177)||56 (20–179)|
 Figure 4 shows that central estimate BC/snow predictions capture the nearly 4 orders of magnitude range in observations with no apparent systematic bias. The correlation coefficient of the log of central model estimates and mean observations is 0.78. Furthermore, in nearly all cases, there is some overlap between the range of measurements and low-high model predictions.
 Central model predictions are within the range of observations on Greenland and Antarctica, indicating reasonable model long-range BC transport. An exception is Siple Dome, where Chylek et al.  reported measurements an order of magnitude greater than more recent Antarctic observations [Warren and Clarke, 1990; Grenfell et al., 1994]. Measurements in Table 2 are not time resolved, except for Slater et al. , who reported elemental carbon (EC, often considered synonymous with BC) concentrations with quarter-annual resolution, varying from 4 to 30 ng g−1 over the course of two years. EC concentration spiked in the fall of 1994, although 14C analysis shows a predominantly fossil fuel-derived source. At Summit, monthly mean BC concentrations vary from 2 to 10 and from 7 to 330 ng g−1 in our 1998 central and high estimate experiments, respectively, peaking in August and July.
 None of the measurements overlap our two years of emission scenarios. Because of interannual variability in biomass burning and trends in regional fossil fuel use, validity of this model-measurement comparison is therefore reduced. For example, our predictions are lower than four arctic measurements [Clarke and Noone, 1985] made in the early 1980s, when BC emissions from the former Soviet Union were much greater than today [Novakov et al., 2003].
 Conversely, predictions exceed measurements at Abisko (Sweden), Hurricane Hill (Washington) [Clarke and Noone, 1985], and Halifax [Chylek et al., 1999]. While Hurricane Hill may be representative of long-range transport because of prevailing westerlies, it is in the same model grid cell as Seattle and has a large local source. Measurements east of Seattle by Grenfell et al.  show double the concentrations from Hurricane Hill, in accord with central model predictions. Halifax has a smaller, but still significant, local source. Chylek et al.  specifically measured urban areas, however, so our model may have a high bias in this region. Low predictions are in range of measurements at Halifax and Abisko. In the French Alps near Grenoble, central model estimates agree well with those of Sergent et al. , but are lower than those of Fily et al. . Central estimates of BC concentrations in precipitation are within range of measurements in rural Michigan [Cadle and Dasch, 1988] and Lithuania [Armalis, 1999], although they are lower than measurements made near Detroit [Dasch and Cadle, 1989].
 The largest predicted BC concentrations in snow are in northeast China (Figure 5), near strong industrial sources. There, concentrations in excess of 1000 ng g−1 can lower snow albedo by more than 0.13. Annual mean concentrations in the eastern USA and Europe exceed 100 ng g−1, enough to lower snow albedo by >0.03, depending on re. While fossil fuel-derived BC is the dominant source of midlatitude BC in snow, the effect of strong 1998 wildfires can be seen across the Arctic and Greenland (Figure 5). Annual mean BC concentrations in snow averaged over Greenland are 44% greater in 1998 than 2001. Comparing with the FF + BF simulation, we estimate that 43% and 24% of the annual mean BC in arctic snow (66.5–90°N) is from biomass sources in 1998 and 2001, respectively. During summer (June, July, and August), these BB source fractions rise to 60% and 36%.
 Summer atmospheric conditions favor enhanced wet and dry arctic BC deposition rates [Stohl, 2006], implying greater summer BC concentrations in snow regardless of temporal variability in emissions. Koch and Hansen  predict that South Asia is the largest source of tropospheric arctic BC, but Stohl  contests this and predicts that biomass sources dominate summer arctic BC using a mean 1980s burning inventory [Lavoue et al., 2000]. Stohl  also suggests that Siberian fires, and northern Eurasia sources in general, can reach the Arctic more easily than emissions from other regions of similar latitude. Future studies should use reanalysis winds to study the impact of individual fire events.
3.4. Global Mean Forcing and Response
 Table 3 lists for all experiments (from left to right) the global annual mean surface forcing from BC in snow (Fs,snow), the fraction of Fs,snow acting over land (where the remaining fraction operates over sea-ice), Fs,snow averaged temporally and spatially only over snow-covered land surface, Fs,snow averaged only over sea-ice, the change in global annual mean T2m (ΔT2m) relative to control simulations without BC in snow, forcing “efficacy,” and finally TOM forcings from atmospheric BC + OC (Ft,atm). Efficacy is defined as [Hansen et al., 2005]:
where Fa is the forcing at the tropopause after stratospheric adjustment [e.g., Hansen et al., 1997] and ΔTs is the change in global mean surface air temperature. The denominator is the response-to-forcing ratio from CO2. Hansen et al.  used forcing and temperature response from 1.5× preindustrial CO2 levels. We apply CAM3 slab ocean model results from Kiehl et al. , who report Fa(CO2) = 3.58 W m−2 and equilibrium ΔTs(CO2) = 2.47°C from a doubling of CO2 (355–710 ppm). In deriving Fa from Fs,snow, we assume that instantaneous forcing at the tropopause (Fi) is 0.91Fs,snow, and that Fa is equal to Fi (i.e., there is negligible immediate stratospheric radiative adjustment to the surface forcing). The first assumption is derived from numerous off-line experiments with SWNB [Zender et al., 1997]. We examined the change in net solar energy at 132 mb relative to that at the surface (Fi/Fs) for slight reductions in visible surface albedo of a typical snow surface (initial visible and NIR albedos of 0.97 and 0.60). With zenith angle varying from 20° to 70°, cloud extinction optical depth τcld varying from 0 to 50, and visible albedo reduction varying from 0 to 0.10, the ratio Fi/Fs varies only from 0.94 to 0.96. While Fs is substantially reduced under cloudy skies, Fi/Fs remains large and constant. However, absorbing aerosol significantly reduces Fi/Fs, particularly when it resides beneath a cloud, as multiple scattering between snow and cloud enhances absorption by the aerosol. Absorption optical depth τa = 0.05 (λ = 550 nm) can reduce Fi/Fs to 0.44. But assuming global mean τa = 0.0096 inferred from AERONET scaling of aerosol climatologies [Sato et al., 2003; Koch, 2001], τcld = 5, and zenith angle of 60°, we estimate Fi/Fs = 0.91, which we apply to derive efficacy. The ranges reported in Table 3 represent standard deviation in the annual mean time series. The reported range of ΔT2m assumes unpaired pools (of global mean temperature from each year of equilibrium simulation) with equal variance. Efficacy standard error combines, in quadrature, standard deviations of Fs,snow and ΔT2m. Support for our second assumption (that Fa equals Fi) comes from Hansen et al. , who report Fa for BC/snow forcing within 2% of Fi.
Table 3. Summary of Model Experiment Results
|Model Scenario||Fs,snowa, W m−2||Land frac.b of Fs,snow||Fs,snow LANDc, W m−2||Fs,snow ICEd, W m−2||ΔT2me, °C||Efficacyf||Ft,atmg, W m−2|
|1998 low||+0.007 ± 8%||0.73||+0.08||+0.04||–||–||+0.07 ± 14%|
|1998 central||+0.054 ± 7%||0.82||+0.60||+0.23||+0.15 ± 0.03||4.52−0.97+0.98||+0.37 ± 2%|
|1998 high||+0.131 ± 6%||0.83||+1.56||+0.79||+0.23 ± 0.02||2.83−0.34+0.35||+1.31 ± 1%|
|2001 low||+0.007 ± 9%||0.74||+0.07||+0.04||–||–||+0.05 ± 11%|
|2001 central||+0.049 ± 7%||0.83||+0.55||+0.20||+0.10 ± 0.03||3.29−1.11+1.12||+0.28 ± 2%|
|2001 high||+0.122 ± 6%||0.83||+1.42||+0.75||+0.16 ± 0.03||2.11−0.37+0.37||+1.09 ± 1%|
|FF + BF||+0.043 ± 5%||0.85||+0.48||+0.15||–||–||+0.19 ± 5%|
|FF||+0.033 ± 6%||0.85||+0.26||+0.12||–||–||+0.10 ± 4%|
|1998 10×||+0.277 ± 3%||0.77||+2.90||+1.11||+0.54 ± 0.02||3.11−0.14+0.15||+4.96 ± 1%|
 Table 3 shows that global BC/snow forcing is small relative to forcing from atmospheric BC + OC (columns 2 and 8 in Table 3). When Fs,snow is averaged spatially and temporally only over snow, however, central estimates suggest that 0.55–0.60 additional W m−2 are absorbed by snowpack on land and 0.20–0.23 W m−2 by sea-ice because of the immediate presence of BC in snowpack. Our central estimates of Fs,snow = +0.054 and +0.049 W m−2 predict ∼10% greater forcing in 1998 than 2001. Comparison with the FF + BF run suggests that about 20% of the total forcing can be attributed to biomass burning in 1998 and 12% in 2001. Estimates from the study by Hansen and Nazarenko  of Fa = +0.16 W m−2 were downgraded to +0.05 W m2 [Hansen et al., 2005] (corrected result published in Appendix A.5 of Hansen et al. ). The latter estimate is derived from spatially varying BC deposition, but without a detailed radiative transfer solution for snow with BC.
 An estimate of Fa from FF + BF BC in snow and ice from Jacobson [2004b] is +0.06 W m−2 (M. Jacobson, personal communication, 2006), greater than our estimate of +0.039 W m−2 (0.91 × 0.043 W m−2). Jacobson [2004b] treats BC in snow with a radiative transfer approximation, but prescribes spatially and temporally uniform snow grain size and an empirical fall speed for BC removal from snowpack. Atmospheric aerosol and cloud physical processes are highly sophisticated in Jacobson [2004b], however. Size-resolved BC and hydrometeors (including graupel) interact in clouds and precipitation through nucleation and coagulation, and both first and second aerosol/cloud indirect effects are treated. These processes enable prediction of more realistic size distribution and mixing state of BC deposited on snow. Because BC ages rapidly in our model relative to the transport time from source to remote snow surface, 87% of the BC deposited on snow is via wet deposition (providing a minimum estimate of the hydrophilic BC fraction in snow). This is less than the 98% BC wet deposition fraction on snow reported by Jacobson [2004b], but likely greater than Koch and Hansen , who reported that dry deposition is responsible for the majority of BC landing on Greenland. Model differences could be due to several reasons, including more explicit treatment of size-resolved in-cloud scavenging processes by Jacobson [2004b], different dry deposition velocities, and different spatial pattern of emissions relative to model snow cover.
 While Fs,snow is small globally, its efficacy is very large. Mean efficacy from the five experiment/control pairs in Table 3 is 3.17 (2.1–4.5). Because the temperature signal/noise ratio is small for realistic (central estimate) BC/snow forcing, the 1998 10× experiment and control provide a more constrained efficacy estimate. (More years of analysis also improve statistical constraint of the temperature response.) Tight agreement between 1998 10× efficacy and the mean of the other experiments is also encouraging. We caution, however, that efficacy does not necessarily scale linearly with forcing magnitude for a given agent (Figure 25 of Hansen et al. ). Global mean T2m cooled several degrees before achieving steady state in both 1998 10× experiment and control runs because of extreme atmospheric aerosol optical depth, in spite of a positive TOM aerosol forcing.
 Hansen et al.  reported similarly large BC/snow efficacy of 2.7 (corrected result in Appendix A.5 of Hansen et al. ), the largest efficacy of all forcings studied. Conversely, mean efficacy of atmospheric BC (∼0.69) is less than CO2 [Hansen et al., 2005]. Possible reasons for even greater BC/snow efficacy in our study include (1) greater albedo change sensitivity to temperature change in the Intergovernmental Panel on Climate Change (IPCC) AR4 NCAR model relative to the GISS model [Qu and Hall, 2006], (2) representation in our model of impurity accumulation near the surface during spring melt, which enhances the forcing precisely when it can have the largest impact on snowmelt and thus snow-albedo feedback, and (3) representation in our model of dynamic snow grain growth, which is enhanced by excess snowpack heating from BC. Better constraint on efficacy will require larger ensembles of GCM simulations with varying initial conditions and is beyond the scope of this study.
 Forcing from atmospheric BC + OC (Ft,atm) is about 5–6× greater than BC in snow (Table 3). However, if forcings are scaled by their respective efficacies, as Hansen et al.  suggest, the resulting atmospheric BC + OC and BC/snow “effective” forcings are of similar magnitude. Much of the forcing from atmospheric BC is offset by OC, which is emitted simultaneously as BC in greater proportion, and which strongly scatters solar radiation. The net effect of atmospheric BC + OC forcing depends on aerosol optical properties, relative aerosol quantities, and reflectance of the underlying surface [e.g., Ramanathan et al., 2001]. The OC/BC emission ratio is smaller in FF combustion than BB [e.g., Bond et al., 2004]. Hence net radiative forcing from FF BC + OC is positive [e.g., Jacobson, 2001], whereas the sign of net forcing from BB BC + OC could be positive [e.g., Hansen et al., 2005] or negative [e.g., Myhre et al., 2003], depending especially on whether aerosol is lofted above clouds, where it is much more likely to have positive forcing. However, many other scattering aerosols are emitted in significant quantity from biomass burning, leading Jacobson [2004a] to suggest a global net surface cooling effect from all biomass burning aerosols. In our study, biomass burning contributes a much greater portion to Ft,atm (49% and 32% in 1998 and 2001 central estimates, respectively) than to Fs,snow (Table 3). Atmospheric aerosol forcing is not the focus of this study though, so we refrain from a detailed analysis.
3.5. Spatial/Temporal Climate Response Patterns
 The primary reason why BC/snow forcing is so efficacious is its ability to trigger snow-albedo feedback. Here we look at spatial and temporal distributions of forcing, snowmelt, albedo change, and temperature response to assess this feedback.
 Figure 6 depicts the Northern Hemisphere distribution of annual mean surface forcing from BC in snow for 1998. The top panel shows mean grid cell forcing, which depends on snow cover fraction. The bottom panel shows forcing averaged only over snow-covered surface within each grid cell, irrespective of SCF, and averaged only when snow is present. This metric describes the quantity of energy added specifically to snowpack, providing some insight into how local snowpack evolution may be affected. However, because model snow depth is very low in regions of low snow spatial coverage, and because forcing is reduced with shallow snowpack because of the radiative influence of the underlying ground, the snow-only forcing is significantly underestimated in unresolved mountainous terrain that should have deep snowpack. This deficiency can also be gleaned by noting very low snow-only forcing in the southernmost regions of model snow cover, where Figure 5 depicts large annual mean BC concentrations. The largest forcing is over the Tibetan Plateau (30–40°N, 80–100°E), averaging 1.5 W m−2 over all land. Forcing over northeastern China and much of Eurasia becomes larger when considering snow-only forcing, as expected from large BC/snow concentrations (Figure 5) but modest snow cover fraction. During some spring months, snow-only forcing exceeds 10 and 20 W m−2 over parts of eastern China and the Tibetan Plateau, respectively. Although BC mixing ratios and albedo reductions are greater in northeastern China, forcing is greater over the Tibetan Plateau because of greater ground-incident solar flux (because of closer proximity to the equator and less vegetation cover). More than 98% of the global forcing operates in the Northern Hemisphere.
Figure 6. Central estimates of 1998 surface forcing (W m−2) from BC in snow; (top) annual mean grid cell forcing, representing the true climate forcing; (bottom) forcing averaged spatially and temporally over only snow-covered surface, representing the mean increase in energy absorption by snowpack.
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 Maximum BC/snow forcing occurs with the combination of high BC concentrations in snow, surface-incident solar flux, and snow cover. This pattern is manifested in Figure 7, which shows Northern Hemisphere zonal, monthly mean surface forcing from BC in snow for 1998 and 2001 central estimates and derived estimates of the 1998 biomass burning contribution. The latitude of maximum forcing moves north as the spring progresses, following regions with large amounts of snow and incident sunlight. While BC emissions are consistent or stronger in fall than spring (1998 boreal fire intensity peaked in August and September), seasonal snowpack does not generally form before incident sunlight significantly diminishes, thus greatly reducing forcing during the accumulation phase. The 1998 arctic BC concentrations in snow peak in August, as opposed to July in 2001, attributable to boreal fires. But 80–90°N surface-incident solar flux drops to only 96 and 26 W m−2 in August and September, reducing the radiative forcing potential. Thus April–June boreal fires have the greatest potential for strong BC/snow forcing. A second reason for greater forcing during the snowmelt phase is accumulation of impurities near the surface. This effect is controlled by the scavenging ratio (Table 1), which is largely unconstrained.
Figure 7. Zonal mean surface forcing from BC in snow as a function of month and latitude for (top) 1998 and (middle) 2001 central estimates, and (bottom) 1998 biomass burning only. The biomass burning forcing contribution is estimated as the difference between 1998 central (FF + BF + BB) and FF + BF only forcing.
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 The forcing space-time pattern in Figure 7 coincides closely with that of snowmelt onset. Thus BC/snow forcing, while generally small, is maximum precisely when it can have the greatest influence on snowmelt rate. Zonal-mean forcing is large at high latitudes, although BC concentrations are lower, because a greater portion of the surface is snow covered. Arctic forcing is 17% greater in 1998 than in 2001, and we attribute 35% of the total arctic forcing to biomass burning in 1998.
 Strong evidence for BC influence on snowmelt timing is seen in Figure 8, which shows change in zonal mean snowmelt rate (averaged over land only), resulting from inclusion of BC in snow. Hatching shows statistically significant change at the 0.01 level. High-latitude melt rate clearly increases during the early snowmelt phase and decreases during the late melt phase, as there is less snow available. Quantified one way, zonal mean melt rate increases in the experiments by 8–54% in the month prior to maximum melt of the controls at latitudes north of 50°N. Area-weighted, this increase is 28% and 19% for 1998 and 2001, respectively. Figure 8 shows that statistically significant melt changes are more widespread in 1998 than 2001.
Figure 8. Difference in zonal monthly mean land snowmelt rate between central experiments and their respective controls. Experiment and control are identical except that BC only affects snow reflectance and heating in the experiment. Hatching shows statistically significant change at the 0.01 level.
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 Surface snowmelt on Greenland has been shown to increase the rate of ice sheet flow [Zwally et al., 2002]. Summer mean melt rate averaged over Greenland is 3% and 13% greater in 1998 and 2001 central experiments than their respective controls, but these changes are not significant at the 0.05 level. Summer T2m warming over Greenland is 0.44°C in both central experiments. Corresponding warming in both 1998 and 2001 high experiments is 1.15°C, and melt rate changes are both significant at the 0.05 level. Central and high estimates of BC in Antarctic snow are too low to have significant influence on snow albedo, but we wonder if strong Australian wildfires could have a noticeable effect.
 Along with snowmelt changes are highly significant reductions in zonal mean surface albedo. Figure 9 shows these changes, averaged over land and ocean, with hatching again at 0.01 significance. Annual mean albedo (weighted by surface insolation) of all arctic surface is reduced by 0.047 and 0.017 in 1998 and 2001 central experiments, respectively. The late-summer (August-September) 0.10–0.18 reduction in 80–90°N 1998 albedo happens because summer snow depth on sea-ice is reduced by 72%, exposing the darker bare sea-ice. This large reduction follows the 1.5 W m−2 June-July BC/snow forcing (Figure 7).
Figure 9. Difference in zonal monthly mean surface albedo between central BC/snow experiments and their respective controls. Hatching shows statistically significant change at the 0.01 level.
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 Observations spanning 1954–1991 from Soviet drifting stations indicate that snow on top of perennial sea-ice is generally nearly gone by July or August [Warren et al., 1999]. Surface Heat Budget of the Arctic (SHEBA) observations from 1998 show snow ablation by early July [Perovich et al., 2002], whereas model snow depth reaches August minimums of 29 and 13 cm in 1998 and 2001 central control simulations, and 5 and 11 cm in 1998 and 2001 central experiments, respectively. These observations indicate a model tendency of excessive snow cover on late-summer sea-ice. Perhaps encouragingly, the inclusion of BC in snow reduces model snow depth.
 Excess snowpack heating and climate feedback in the model also appear to accelerate snow grain growth, which darkens the snow itself and enhances the perturbation from BC (Figure 3). The increase in 80–90°N June and July re relative to 1998 central control is 289 μm. The forcing responsible for this feedback is largely from biomass burning and is clearly damped in the 2001 central experiment (Figure 7), where 80–90°N June and July re is only 52 μm greater than 2001 central control, summer snow depth on sea-ice reduced by only 13%, and late-summer albedo reduced by 0.05. Note that these results are sensitive to the CSIM snow height/SCF relationship [Briegleb et al., 2004], which determines the proportion of exposed bare sea-ice. Slight changes to snow depths less than 10 cm have large impact on SCF and therefore albedo. In spite of large albedo reduction, sea-ice area changes are small. July–September mean arctic (66.5–90°N) sea-ice coverage is reduced by 3% and 1% in these two experiments relative to their respective control simulations.
 Finally, Figure 10 shows significant surface air warming from BC in snow, especially from 60 to 90°N during June-November, 1998. Annual mean T2m warming averaged over the arctic is +1.61 and +0.50°C for 1998 and 2001. The late-summer polar warming pattern in 1998 is logically coupled with the forcing and albedo change patterns described above. The 1998 winter and spring warming may be a consequence of thermal inertia from fall warming or could be dynamical in nature. We note that our 1998 central experiment showed the highest efficacy of all experiments, so we urge caution in assuming that the large responses discussed are due entirely to biomass burning emissions, which cause only a modest increase in forcing (Figure 7c).
Figure 10. Difference in zonal monthly mean 2-meter air temperature between central BC/snow experiments and their respective controls. Hatching shows statistically significant change at the 0.01 level.
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 These changes provide evidence that significant snow-albedo feedback occurs from BC in snow, despite its small forcing. Reasons why BC and other aerosols can provoke disproportionately large responses include their ability to warm snow, either directly melting it or priming it for earlier melt, enhanced snow grain metamorphism, which darkens the snow itself and increases the radiative perturbation by impurities, and amassing of impurities at the surface during melt. Changes in the timing of snow ablation, however, have the greatest influence on the surface energy balance because of the huge contrast in surface reflectance between snow and most other surfaces. Hence the subtler effects of snow impurities come into play when they combine to influence snowmelt timing, as they apparently do in both 1998 and 2001 central experiments.
3.6. Individual Uncertainties
 Finally, we examine the influence, to first order, that each of the five uncertainties discussed in section 2 have individually on global BC/snow forcing. This offers insight into the relative importance of constraining uncertainty in each factor.
 To derive estimates of variability in global annual mean Fs,snow, we performed the following experiments: For the role of BC emission scenarios, we conducted two 6-year simulations using 1998 central configuration (Table 1), but with low and high emissions estimates. For optical properties, we conducted off-line 470-band SNICAR experiments, estimating hypothetical forcing assuming less absorptive and more absorptive BC, given annual mean BC concentration and re at each grid cell of the 1998 central experiment. For snow aging, we also used off-line SNICAR to estimate forcing at each grid cell, assuming annual mean BC concentration from the 1998 central experiment, but using the corresponding annual mean re from the 1998 low and high experiments, representing slow and rapid aging. (If a grid cell contained snow in the central experiment, but not in the high or low, we assumed the global mean high or low re). For the role of meltwater scavenging, we conducted another pair of 6-year CAM3 experiments with 1998 central configuration, but with meltwater scavenging factor ranging by 2 orders of magnitude (Table 1). Finally, we assess the role of SCF by scaling the BC/snow forcing at each grid cell of monthly output according to hypothetical SCF (calculated from snow depth), using the high and low representations discussed in section 2. Note that it would be more appropriate to estimate optical property and aging uncertainty at monthly resolution, as with SCF, but this would require an excessive number of off-line SNICAR runs.
 The range in mean Fs,snow estimated with these approaches is shown in Table 4. Uncertainty in emissions has the largest bearing on BC/snow forcing, closely followed by snow aging. The low-high range of FF + BF emissions from Bond et al.  is greater than the range we derived for BB emissions (Table 1). Some of this difference is because we derive uncertainty using an observational inversion constraint, whereas uncertainty from Bond et al.  is derived from compounding forward uncertainties. Global mean snow re varied from 91 to 812 μm between 1998 low and high experiments. While our choice of scaling snow aging by a factor of 2 was purely subjective, there are no observations of all relevant parameters required to constrain aging processes [Flanner and Zender, 2006]. Uncertainty in scavenging factor can significantly decrease the global forcing estimate, but can raise it only slightly. This happens because scavenging, even for hydrophilic impurities, is relatively inefficient in the central estimates. Thus decreasing the scavenging ratio increases the forcing only minimally in the high experiment, as impurities tend to reside near the surface during melt in the central experiment. Increasing the scavenging efficiency, however, significantly lowers the global forcing estimates, as impurities efficiently flush through the snowpack during the melt phase. Grenfell et al.  reported relatively uniform vertical profiles of BC in the snow on sea-ice during the SHEBA campaign in late March and April 1998. More observations of BC profiles during the melt phase will help constrain scavenging ratios. Additional off-line SNICAR experiments showed that the range of effect of varying BC optical properties was relatively insensitive to snow grain size, in spite of the sensitivity of forcing to grain size (Figure 3), but the range narrowed slightly with increasing BC concentrations. Finally, the range of effect of SCF representation is small but slightly asymmetrical. This can be explained by the probability density function of snow depth where and when BC forcing operates. Snow depths greater than 20 predict SCF close to 1 with both central and high estimates, but much lower SCF with low estimates.
Table 4. Estimated Range of Change in Global Mean BC/Snow Radiative Forcing (Fs,snow), Represented as a Scalar, Resulting From Variation of Individual Factorsa
|Snow Cover Fraction||0.83||1.08|