Black carbon (BC) in snow lowers its albedo, increasing the absorption of sunlight, leading to positive radiative forcing, climate warming and earlier snowmelt. A series of recent studies have used prescribed-aerosol deposition flux fields in climate model runs to assess the forcing by black carbon in snow. In these studies, the prescribed mass deposition flux of BC to surface snow is decoupled from the mass deposition flux of snow water to the surface. Here we compare prognostic- and prescribed-aerosol runs and use a series of offline calculations to show that the prescribed-aerosol approach results, on average, in a factor of about 1.5–2.5 high bias in annual-mean surface snow BC mixing ratios in three key regions for snow albedo forcing by BC: Greenland, Eurasia and North America. These biases will propagate directly to positive biases in snow and surface albedo reduction by BC. The bias is shown be due to coupling snowfall that varies on meteorological timescales (daily or shorter) with prescribed BC mass deposition fluxes that are more temporally and spatially smooth. The result is physically non-realistic mixing ratios of BC in surface snow. We suggest that an alternative approach would be to prescribe BC mass mixing ratios in snowfall, rather than BC mass fluxes, and we show that this produces more physically realistic BC mixing ratios in snowfall and in the surface snow layer.

Model studies indicate that black carbon (BC) deposited on snow and sea ice
produces climatically significant radiative forcing at both global and
regional scales by reducing surface albedo (“BC albedo forcing”) (e.g., Warren and Wiscombe, 1980; Hansen and Nazarenko, 2004; Jacobson et al.,
2004; Flanner et al., 2007). Global, annual average radiative forcing by BC
in snow has been assessed as

A critical difference between forcing by BC in the atmosphere and BC in snow
is that forcing by BC in the atmosphere scales with the vertically resolved

To date, the Community Earth System Model version 1 (CESM1) is the only global climate model that accounts for all of these processes, through the SNow, ICe, and Aerosol Radiative model (SNICAR; Flanner et al., 2007) in the land component (known as the Community Land Model version 4, CLM4; Lawrence et al., 2012), which accounts for snow on land, among other things. A more simplified treatment of BC in snow that is on sea ice and in the sea ice itself is also included in the most recent version of the CESM1 sea ice model component, CICE4 (Holland et al., 2012). In addition to treating processes that determine snow BC mixing ratios, SNICAR captures both fast and slow feedbacks that amplify the radiative forcing by BC in snow: surface snow warmed by BC absorption generally transforms to larger snow grain sizes, which further reduces snow albedo. In addition, the reduction in albedo for a given mixing ratio of BC is greater for larger-grained snow (Fig. 3 of Flanner et al., 2007). These feedbacks further accelerate warming and lead to earlier snowmelt, which in turn leads to higher BC mixing ratios in surface snow as described above. Eventually this also leads to earlier exposure of the underlying surface, further reducing surface albedo (i.e., the classic “snow albedo feedback”) (Flanner et al., 2007, 2009; Fig. 29 of Bond et al., 2013).

This comprehensive treatment in CESM1 made possible the recent Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP) studies where BC albedo forcing was estimated for surface deposition fields derived from a suite of climate models (Lee et al., 2013). This forcing was included in an overall assessment of modeled radiative forcing under ACCMIP (Shindell et al., 2013). In the Lee et al. (2013) study, each participating ACCMIP model calculated BC atmospheric abundances and deposition rates using a common set of emissions. The resulting deposition fields (e.g., grams of BC deposited per square meter per second in each grid box/day) were then used in CESM1 to calculate snowpack BC mixing ratios. Estimated BC albedo forcing for the different models' aerosol fields covered a wide range, reflective of differences in BC transport and deposition rates. Comparisons of the modeled snow BC mixing ratios with observed mixing ratios across the Arctic and Canadian sub-Arctic showed significant positive model biases for Greenland (a factor of 4–8), a factor of 2–5 low biases over the Arctic Ocean, and agreement to within a factor of 2–3 elsewhere, though, with the exception of one model (CESM1-CAM5, which has version 5 of the Community Atmosphere Model), the BC mixing ratio biases in the remaining regions were more often positive than negative (see Lee et al., 2013; Table 6).

Goldenson et al. (2012) also used CESM1 with prescribed atmospheric aerosol concentrations and deposition fluxes to compute the climate impacts of BC in snow on both land and sea ice and BC in sea ice. They found significant impacts on surface warming and snowmelt timing due to changes in BC deposition in year 2000 versus year 1850. They also found that forcing by BC in snow on land surrounding the Arctic had a larger impact on Arctic surface temperatures and sea ice loss than did BC deposited on sea ice within the Arctic. On sea ice, Goldenson et al. (2012) found poor spatial correlation between modeled and observationally estimated BC concentrations (see their Fig. 3), though the range of concentration is similar; on land, the two are better correlated but the model concentrations tend to be higher, by roughly a factor of 2 (Goldenson et al., 2012; Fig. 4).

Jiao et al. (2014) applied CESM1 to simulate BC in snow on land and sea ice using deposition fields from the Aerosol Comparisons between Observations and Models (AeroCom) suite of global simulations. In comparison with measurements of BC in Arctic snow and sea ice (Doherty et al., 2011), they found that models generally simulate too little BC in northern Russia and Norway, while simulating too much BC in snow elsewhere in the Arctic. As with Goldenson et al. (2012), they found poor spatial correlation between modeled and measured BC-in-snow concentrations, though the multimodel means, subsampled over the measurement domain, were within 25 % of the observational mean.

Here we test whether the use of prescribed BC mass deposition rates in CESM1, as was done in the Goldenson et al. (2012), Holland et al. (2012), Lawrence et al. (2012), Lee et al. (2013) and Jiao et al. (2014) studies, produces a bias in surface snow BC mixing ratios, and therefore a bias in snow albedo. The bias being investigated would result from the fact that BC deposition fluxes in CESM1 prescribed-aerosol runs are decoupled from snow deposition rates, combined with the fact that the model's top snow layer has a fixed maximum thickness and is divided when it exceeds this thickness. Note that the bias being tested for here is independent of any biases due to errors in input emissions or in modeled transport and scavenging rates; it is purely a result of the mathematical approach taken in the model to estimate surface snow BC mixing ratios.

Prescribed-aerosol fields are derived from prognostic-aerosol model runs, where the resulting atmospheric concentrations and dry and wet mass deposition fluxes are saved as model output. This is used as input to the prescribed runs. In prognostic model runs, aerosols are emitted directly or formed from aerosol precursors in the atmosphere. Aerosols and their precursors are transported, dry-deposited to the surface, and scavenged in rain and snowfall according to the modeled meteorology. In prognostic-aerosol models, wet deposition of BC occurs only when there is rain or snowfall. The mass of wet-deposited BC depends on the amount of precipitation, the ambient BC concentration, and the hygroscopicity of the BC, with these dependencies varying from model to model.

When prescribed, atmospheric aerosol concentrations and deposition fluxes
are typically independent of the meteorological fields in the model, as is
the case in CESM1; the meteorological fields themselves in these runs may be
either prescribed or prognostic. Furthermore, the input aerosol fields are often
interpolated in time from monthly means. Therefore the episodic nature of
aerosol deposition in reality (owing to wet deposition) is generally absent
in prescribed-aerosol fields. This was the case for the prescribed-aerosol
studies of Goldenson et al. (2012), Lawrence et al. (2012), and Holland et al. (2012), and for all integrations of CCSM4 (i.e., CESM1-CAM4) that were
submitted to CMIP5 (Climate Model Intercomparison Project Project Phase 5) and used in the Lee et al. (2013) and Jiao et al. (2014)
studies. In the Lee et al. (2013) and Jiao et al. (2014) studies, these BC
deposition fields were then coupled with prescribed meteorology from the
Climatic Research Unit (CRU)/National Center for Environmental Prediction
(NCEP) reanalysis data for the 1996–2000 (Lee et al., 2013) or 2004–2009 period (Jiao
et al., 2014) to calculate surface snow mixing ratios of BC. The CRU/NCEP
data set is described at

Examples of prescribed wet (left axis) and dry (right axis) BC mass
deposition fluxes in CAM4 for year 2000 for

To test the effect of using decoupled BC mass and snow mass deposition rates
on surface snow BC mixing ratios, we first compare ensembles of
prescribed-aerosol and prognostic-aerosol runs of CESM1/CAM4. The
prescribed-aerosol runs use the same monthly-resolved, year 2000 BC aerosol
mass deposition rates that were used in the 20th century integrations
of CCSM4 that were submitted to CMIP5. These deposition fluxes themselves
come from a separate prognostic model simulation (Lamarque et al., 2010) and
are interpolated from monthly-input fields (as shown in Fig. 1 for two
model grid boxes in Greenland corresponding to research camps where BC in
snow has been measured in snow pits and ice cores). CESM1/CAM4/CLM4
prescribed-aerosol runs were done for 10 years at 2

Below we compare surface snow BC mixing ratios from CESM1 prescribed-aerosol
and prognostic-aerosol runs to see if there is a systematic difference
between the two, despite the fact that the aerosols are derived from the same emissions year
and nearly the same emissions database. In the model, the mixing ratio of BC
in the surface snow layer (

In addition to differences deriving from coupled versus uncoupled

Overview of the model runs and offline calculations compared herein. All are based on the same year 2000 aerosol and aerosol precursor emissions data set (Lamarque et al., 2010).

In CESM1, at each time step,

While Eqs. (1) and (4) allow for wet deposition of BC even in the
absence of snowfall, a more physically realistic calculation of surface snow
BC mixing ratios (minus the influence of in-snow processes) is given by

[

[

These smoothed snowfall BC mixing ratios are compared to those given by using the prescribed-aerosol model values directly.

[

The wet and dry BC mass deposition rates used to calculate all values of

Surface snow BC mixing ratios [

We conduct two full sets of offline calculations of
[

Note that while averaged values of

We compare the results of the prognostic-aerosol runs versus the
prescribed-aerosol runs and across our six sets of offline calculations
(Table 1) for three geographic regions where forcing by BC in snow on land
is climatically important: Greenland (60—85

Annual means, medians and standard deviations (SDs) of
monthly-average BC mass deposition (ng m

Differences in the meteorology and in aerosol transport and scavenging rates
between the prognostic-aerosol and prescribed-aerosol runs lead to
differences in the average mass of deposited BC
(

A similar comparison between paired prescribed-aerosol and prognostic-aerosol CESM1 runs was described briefly by Jiao et al. (2014), and our analysis of their runs provides additional confirmation of a systematic difference between prescribed- and prognostic-aerosol runs. One simulation involved CAM4 and CLM4 coupled with prognostic-aerosol deposition, i.e., with self-consistent meteorology and deposition. The other simulation was conducted with CLM in stand-alone mode, driven with 6-hourly CRU/NCEP meteorology and with monthly-averaged, prescribed-BC deposition fluxes from the first run. We analyzed the Jiao et al. runs and found that the annual Northern Hemisphere average concentration of BC in the surface snow layer was larger by a factor of 2.0 in the prescribed-aerosol simulation, weighted by snow-covered area in each month and averaged over the same domains, despite the fact that time-averaged BC deposition fluxes were identical in both simulations. Our analysis of the Jiao et al. runs therefore supports the main conclusions drawn earlier from comparing prescribed- and prognostic-aerosol runs above. Our offline calculations provide further support to our hypothesis that the prescribed-aerosol runs will have a high bias in surface snow BC mixing ratios due to the fact that BC and snow-water deposition to the surface are decoupled in the prescribed runs.

Relative frequency distributions of daily mixing ratios
of BC in snowfall calculated using three different pairings of BC mass
deposition fluxes and snowfall rates, as described in the text:

Our offline-calculated snowfall BC mixing ratio,
[

Surface snow BC mixing ratios (

As noted above, our offline calculations of [

Means, medians and standard deviations of BC mixing ratios
in snowfall (

Surface snow BC mixing ratios become smaller as the wet deposition flux of
BC varies in a more physically consistent way with snowfall, i.e., going from
[

Histograms of the ratios
[

Medians of the ratios, [

Figures 4 and 5 show histograms of the ratio
[

As in Fig. 4, but for offline calculations using the
CRU/NCEP reanalysis

As noted earlier, prescribed-aerosol wet deposition fluxes are based on
prognostic model runs and so are influenced by the prognostic model's
precipitation rates. Biases in the prognostic model's precipitation rates at
a given location will therefore translate directly to biases in the aerosol
mass deposition rates. Coupling these model-derived BC mass deposition rates
with observed precipitation rates can therefore produce unrealistic values
of

Our offline values of [

Since the prescribed BC mass deposition fluxes used in the model runs are
spatially smoothed climatologies, we consider coupling these deposition
fluxes with climatological snowfall rates to provide a more realistic
estimate of how BC wet deposition affects time-averaged surface snow BC
mixing ratios. Furthermore, we have shown that doing so yields lower surface
snow BC mixing ratios, and therefore assert that prescribed-aerosol runs of CESM1
include a high bias. The ratios [

We argue that prescribing temporally and geographically smoothed surface BC deposition fluxes in a model where snowfall varies on typical meteorological timescales (i.e., daily or faster) will produce high biases in time-averaged surface snow BC mixing ratios. Using comparisons of prescribed-aerosol and prognostic-aerosol model runs and offline calculations, we have demonstrated that (a) prescribed-aerosol runs have higher surface snow BC mixing ratios than prognostic-aerosol runs, by a factor of about 1.6–3.0, despite being based on the same BC emissions and accounting to first order for differences in total BC and snow deposited to the surface; and that (b) decoupling of BC wet deposition fluxes and snowfall rates leads to surface snow BC mixing ratios of a factor of about 1.5–2.5 higher than if the same mass of BC was wet-deposited in proportion to the snowfall snow mass. Both of these biases are significant at daily, seasonal and annual timescales.

Black carbon mass deposition fluxes in snowfall depend on ambient BC
concentrations, the scavenging efficiency of BC in snow, and snowfall rates.
Thus, while BC deposition fluxes do not depend solely on precipitation
rates, removing any dependence on snowfall leads to biases in the mixing
ratio of BC in snowfall,

We estimate that prescribed-aerosol model runs of CESM1 have approximately a
high-bias factor of 1.5–2.5 in surface snow BC mixing ratios due to the use
of climatological/smoothed BC mass deposition fluxes coupled with modeled,
daily-varying snowfall. In CESM1 (i.e., in the SNICAR component of CLM) the
surface snow layer is 1–3 cm deep. Sunlight usually can penetrate
> 10 cm into the snowpack, depending on snow density (Warren and
Wiscombe, 1980), so mixing ratios over this full depth are relevant for
albedo reduction and BC albedo forcing. SNICAR accounts for this, with
albedo being determined by

Using climatological, prescribed mass deposition fluxes coupled with
daily-precipitation rates produces a large positive bias in surface snow

Existing studies using CESM1 and prescribed aerosols to study BC albedo forcing (e.g., Goldenson et al., 2012; Holland et al., 2012; Lawrence et al., 2012; Lee et al., 2013; and Jiao et al., 2014; and all CMIP5 integrations with CCSM4) are biased by this effect.

An alternate approach should be used in CESM to calculate surface snow mixing ratios of BC and other particulate absorbers. This also applies to any other model using or planning to use prescribed wet deposition fluxes to study the climate impact of albedo forcing.

We suggest that, for wet deposition, one option is that instead of
prescribing mass deposition fluxes (e.g., kg m

This study was supported by the National Science Foundation grant ARC-1049002. We thank C. Jiao for helpful analysis of model simulations. We also thank two reviewers for suggestions that lead to a significant improvement of the paper. Edited by: M. C. Facchini