Atmospheric Environment 36 (2002) 2545–2551

Monte Carlo modeling and measurements of actinic flux levelsin Summit, Greenland snowpack

Matthew Petersona,*, Douglas Barbera, Sarah Greenb

aDepartment of Civil and Environmental Engineering, Michigan Technological University,

1400 Townsend Dr. Houghton, MI 49931, USAb Department of Chemistry, Michigan Technological University, Houghton, MI 49931, USA

Received 4 June 2001; received in revised form 7 September 2001; accepted 11 January 2002

Abstract

Knowledge of actinic flux levels in snowpack is needed to find the influence of snowpack photochemical processes on

atmospheric composition. Measurements show that while o0.2% of direct UV and visible light is transmitted through

0.7 cm of snowpack, downwelling actinic flux levels are at least 10% of incident levels at a depth of 10 cm within the

snowpack. This results from the highly forward-scattering nature of the snowgrains within the snowpack. A 1-D Monte

Carlo model of photon scattering from, and absorption in, snowgrains accurately simulates relative actinic flux levels in

a horizontally homogeneous, vertically layered representation of the upper meter of Summit, Greenland snowpack. The

resulting relative actinic flux levels may be used with other measurements, or with other radiative transfer models, to

estimate absolute actinic flux levels within the snowpack at Summit. Results from the 1-D Monte Carlo model also

demonstrate that buried radiometers which completely block upward scattered light from lower layers observe e-folding

depths that may be more than an order of magnitude lower than actual values. Additional simulations with a 2- or 3-D

Monte Carlo model are needed to quantify the magnitude of this effect for partial blocking of scattered light. r 2002

Elsevier Science Ltd. All rights reserved.

Keywords: Snow; Photochemistry; Radiative transfer; Radiometer; Ice

1. Introduction

Quantifying the relative decrease of actinic flux levels

within snowpack is important for at least four reasons.

First, because short-wavelength radiation shining on

relatively large particles ðdblÞ is highly forward

scattered (Henyey and Greenstein, 1941) UV and visible

light penetrates snowpack (snowgrains are B0.1–1 mm).

As a result, the high albedo (the ratio of upwelling and

downwelling actinic flux under diffuse lighting) of the

earth’s snow covered regions depends on snowpack

morphology and composition as these determine

the amount of absorption within snowpack during

multiple scattering (Warren and Wiscombe, 1981).

Second, the shortwave energy absorbed in the snow-

grains is the biggest single term in the snowpack energy

balance (Loth et al., 1993). Third, the ability of algae to

grow and thrive within ice floes beneath snowpacks in

the Arctic and Antarctic is regulated by the availability

of actinic (photosynthetic) flux within snow and ice

(Arrigo et al., 1991). Actinic flux is directly proportional

to the number of photons arriving at a unit plane from

all solid angles; multiple scattering enhances actinic flux

by factors of 2–4 within and above clouds (Madronich,

1987) and snowpack (Simpson et al., 2002). Due to the

large variation in measurements of snow transmissivities

(reported as e-folding depths, see King and Simpson,

2001 and references therein) and lack of information

regarding actinic flux in snowpack, the modeling

described here may be used to improve radiative

transfer parameterizations in models of snow cover

and of photosynthetic flux levels beneath snow and ice.

Finally, very recent measurements demonstrate that*Corresponding author. Fax: +1-906-487-2943.

E-mail address: mpeters@mtu.edu (M. Peterson).

1352-2310/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 1 3 5 2 - 2 3 1 0 ( 0 2 ) 0 0 1 3 3 - 4

photochemical reactions within snowpacks produce

nitrogen oxides and organic compounds and destroy

ozone (Honrath et al., 1999; Sumner and Shepson, 1999;

Peterson and Honrath, 2001). These light-initiated

reactions depend on the actinic flux and on the

probability that a specific molecule will absorb photons

and dissociate. The convolution of the actinic flux and

these probabilities over the relevant wavelength range is

the molecular photolysis frequency (Madronich, 1987).

Knowledge of photolysis frequencies and actinic flux

levels in snowpack is needed to quantify the influence of

snowpack photochemical reactions on the composition

of the atmosphere (Honrath et al., 2002).

In this paper, we present measurements constraining

the relative decrease of actinic flux levels within

snowpack, which are used to validate a 1-D Monte

Carlo model. This model predicts the relative decrease in

actinic flux as a function of depth in horizontally

homogeneous snowpacks in which grain size and density

are either constant, or vary according to the snowpack

stratigraphy. A 1-D Monte Carlo approach, in which

the probability of upward or downward scattering is

computed from the snowgrain scattering phase function,

is used as Monte Carlo modeling is a reliable and

accurate method of computing light levels in multiple

scattering media (Groenhuis et al., 1983; Katsev et al.,

1997). Although this appears to be the first attempt to

simulate snowpack radiative transfer using Monte Carlo

modeling, this method has been used previously to study

light transmission through terrestrial and jovian clouds

(Min and Harrison, 1999; Dyudina and Ingersoll, 2000),

the ocean (Tynes et al., 2001), sea ice (Trodahl and

Buckley, 1990), and glacial ice (Askebjer et al., 1997).

The only other attempt to simulate actinic flux levels in

snowpack is presented in Simpson et al. (2002).

2. Methods

2.1. Experimental

2.1.1. Measurement site

All experiments were conducted at Summit, Green-

land during summers in 1999 and 2000. Summit is

located at the site of the GISP2 ice core drill site at an

elevation of 3.2 km on the peak of the Greenland Ice

Sheet (72.331N, 38.751W).

2.1.2. Penetration of direct insolation

The penetration of direct insolation into snowpack

was determined by measuring solar radiance through a

variable-thickness snow slab using four narrow (2.51)

field of view UV-visible sunphotometers (SPUV-6,

Yankee Environmental) fixed to a telescope mount

equipped with a clock-drive. These sunphotometers were

housed together in a tube sealed with a quartz window

and measured the solar radiance centered at 325 nm

(bandwidth 2 nm), 415, 500, and 615 nm (bandwidth

10 nm). A 12 cm thick snow slab was cut from the

surface of the snowpack and placed in front of the

sunphotometers in order to completely block their field

of view. With the clock-drive activated and continuous

manual corrections to maintain proper alignment, the

sunphotometers pointed directly at the sun through the

snow slab, and thus measured the amount of direct

insolation penetrating the slab. Calibrations to deter-

mine the instrument sensitivities were not performed or

required for this study as the sunphotometers responses

are stable over periods of months, and the ratios of the

background-corrected unobstructed and obstructed

signals measured over a period of about 1 h were used

to compute the fractional transmittance of solar

radiance. During the experiment, the face of the snow

slab was shaved off in increments between 0.3 and

1.8 cm, ultimately resulting in a thickness of not more

than 0.7 cm.

2.1.3. In situ actinic flux levels

Relative downwelling actinic flux levels within the

snowpack were measured using a rugged, cylindrical

spectroradiometer (23 cm diameter� 20 cm long) fitted

with an integral dome-shaped sensor (2.9 cm diameter

� 3.8 cm high) designed to accept light without angular

dependence at wavelengths of 290–730 nm with a

bandwidth of B1 nm (Meteorologie Consult, Germany).

This instrument consists of a diffusing, hemispheric

quartz collector coupled to a monochromator via a

short fiber-optic junction. Data is transmitted to a

computer via a 20m cable. In each in situ experiment

described here, the incident downwelling actinic flux was

measured and then the entire spectroradiometer and

quartz dome assembly was placed in the snowpack such

that the base of the quartz sensor was between 10 and

70 cm beneath the snow surface with the sensor facing

up. In some cases the spectroradiometer was placed at

the bottom of a hole and buried, and in others the

spectroradiometer was placed under undisturbed snow

using an access trench which was shoveled full of snow

prior to obtaining measurements. The downwelling

actinic flux above the snow and within the snow were

typically both measured in a span of less than about

30 min in order to constrain the relative decrease in light

levels within the snow in the absence of insolation

variations. Since only the background-corrected ratios

of these measurements were used, sensitivities were not

applied to the raw data.

Relative in situ actinic flux levels were also determined

from nitrate photolysis frequencies measured using

chemical actinometers placed in the snowpack. A

complete description of these measurements is given in

a companion paper (Qiu et al., 2002). Briefly, these

actinometers consist of transparent tubes (5mm OD,

M. Peterson et al. / Atmospheric Environment 36 (2002) 2545–25512546

250mm long) filled with a solution containing nitrate

and radical trap compounds which react with hydroxyl

radical (OH). When exposed to UV light with wave-

lengths o320 nm, some of the nitrate photolizes,

releasing OH which reacts with the radical traps to

form stable products. The amount of stable product

formed is proportional to the actinic flux within the

snowpack during the measurement (Qiu et al., 2002).

After exposure, the actinometry tubes were sealed in

light-proof boxes and returned to Michigan Technolo-

gical University for analysis.

2.2. Model

The snowpack radiative transfer model consists of a

1-D Monte Carlo scattering module and an absorption

module. The Monte Carlo scattering module computes

photon histories based on the 6.6% probability that

isotropic photons will backscatter, and on the 93.4%

probability that they will forward scatter, from snow-

grains. The scattering probabilities are computed using

the measured scattering phase function of broken and

irregular snow particles (Wetzel, 1981) (representing

snowpack snowgrains) weighted by the fraction of

photons scattered into solid angles corresponding to

equal zenith angle increments. The range of the back-

scattering probability is 6.5–6.9% based on experimental

uncertainty (Wetzel, 1981), which does not affect the

results presented here. A somewhat more complicated

approach is needed to correctly account for scattering by

non-isotropic radiation (i.e., direct insolation). How-

ever, this is not attempted here in order to simplify this

first Monte Carlo modeling attempt, and because

cloudy, diffuse lighting conditions are dominate in the

Arctic during summer when mean monthly cloud

amounts exceed 80% north of 801N (Schweiger et al.,

1999). Photon histories are determined by a random

walk, which continues until the simulated photon passes

out of the top of, or through, the model snowpack. The

absorption module uses Beers Law to compute the

fractional decrease in light intensity resulting from

transmission through each 1-D snowgrain, assuming

snowgrains absorb light like pure ice (Grenfell and

Perovich, 1981; Perovich and Govoni, 1991).

Random walk histories of 100,000 photons are

accumulated at wavelengths of 290, 350, 390, 470, 590,

and 650 nm in order to reduce the median statistical

uncertainty in each wavelength to less than about 1% at

snowpack depths shallower than 30 cm. Reducing the

number of histories by a factor of ten increases this

uncertainty to B10%. The six wavelengths chosen span

the UV and include the minimum ice absorption

wavelength (470 nm), an inflection point in the ice

absorption (590 nm), and a representative longer wave-

length (650 nm). Thus, interpolation to find relative

actinic flux levels at other wavelengths is reasonable with

this choice of wavelengths.

Simulations of in situ actinic flux levels are computed

using both a homogeneous and vertically layered

snowpack morphology; the model snowpack is 1-D

and includes alternating snowgrain and air layers.

Model snowgrains consist of pure ice without additional

absorbing impurities. A total snowpack depth of 1m is

used, as simulations indicate downwelling actinic flux

levels are at least three orders of magnitude lower than

incident levels below this depth. Measurements of snow

physical parameters made at Summit in the summer of

2000 (Albert and Shultz, 2002) indicate a median density

of 0.34 gm/cm3 in the upper meter of snowpack, and a

typical snowgrain thickness of 0.25 mm. These measure-

ments also indicate that the upper meter of snowpack

may be approximated using seven stratigraphic layers

divided at 3, 6, 9, 12, 45, and 57 cm having densities of

0.26, 0.30, 0.35, 0.30, 0.34, 0.39, and 0.34 gm/cm3,

respectively. Based on digital images of snowpack

sections preserved in frozen dimethyl phthalate (Albert

and Shultz, 2002) the snowgrain thickness is estimated

to be 0.15 mm in the first three layers, 0.3 mm in the next

layer, and 0.25 mm in the remaining three layers. These

snowgrain size and snowpack density measurements are

used to establish the spacing of snowgrain layers in

the 1-D snowpack model.

3. Results and discussion

Less than 0.2% of the direct insolation at the UV and

visible wavelengths measured by the sunphotometers

(see Section 2.1.2) penetrated a snow slab 0.7 cm thick.

This is not surprising considering that at the median

snowgrain thickness of 0.025 cm, as many as 28 forward

scattering events may be required to traverse a snow slab

0.7 cm thick. Based on the scattering phase function of

broken and irregular snow (Wetzel, 1981), a maximum

of B50% of incident light is forward scattered into the

2.51 FOV of the sunphotometers. With these con-

straints, just nine scattering events will result in a

decrease in the direct beam radiance of 99.8%

(0.59=0.002). Thus, UV and visible light are completely

diffuse in the snowpack at Summit at depths well less

than 0.7 cm.

In contrast, in situ downwelling actinic flux levels at

470 nm measured with a spectroradiometer buried

beneath 10 cm of undisturbed snowpack (see Section

2.1.3) are at least 10% of incident downwelling actinic

flux levels, and are at least 5% and 4% of the incident

level at snowpack depths of 20 and 30 cm, respectively

(Fig. 1). Corresponding relative downwelling actinic flux

levels measured from the bottom of snow pits filled with

shoveled snow at depths of 10 and 20 cm are similar;

those at a depth of 30 cm are smaller than levels under

M. Peterson et al. / Atmospheric Environment 36 (2002) 2545–2551 2547

undisturbed snow by about 50% (Fig. 1). While these

relative downwelling actinic flux levels are high when

compared with the o0.2% penetration of direct

insolation, they represent lower limits as the large size

of the spectroradiometer (see Section 2.1.3) blocked

some of the adjacent upwelling light within the

snowpack.

In order to compare the results of the 1-D Monte

Carlo model with the in situ downwelling actinic flux

measurements made with the buried spectroradiometer,

two situations are simulated. In one, the in situ light field

is preserved, and relative downwelling actinic flux levels

are the same as in the undisturbed snowpack. This

situation corresponds to observations made with a

transparent radiometer with uniform response to radia-

tion from the downwelling hemisphere. In the other, the

in situ light field is highly perturbed such that the

downwelling actinic flux at a particular depth does not

include contributions from upward scattering from

lower in the snowpack. This situation corresponds to

observations made at various depths in the snowpack

with a radiometer with uniform response to radiation

from the downwelling hemisphere placed just above an

infinite black sheet. A homogeneous snowpack

(r ¼ 0:34 gm/cm3, snowgrain thickness=0.25 mm, see

Section 2.2) is used in these simulations as some

spectroradiometric observations of relative downwelling

actinic flux levels were made in different years (1999 and

2000) with different snowpack stratigraphy. As shown in

Fig. 1, the relative downwelling actinic flux levels

observed with the buried spectroradiometer are near

those predicted for an instrument measuring just above

an infinite horizontal black sheet. This result is

consistent with the large size of the spectroradiometer

body (see Section 2.1.3), and suggests that the 1-D

Monte Carlo simulations are accurate.

Finding the e-folding depth at specific wavelengths is

often the goal of measurements of light transmission

through snow. This parameter is important as it is used

to compute photosynthetic flux levels beneath snowpack

(Arrigo et al., 1991), and to estimate energy deposition

within snow cover (Loth et al., 1993). King and Simpson

(2001) provide an overview and summary of the few

available observations, and show that there is consider-

able variability in normalized e-folding depth measure-

ments.

The 1-D Monte Carlo simulations of the two

situations described above demonstrate that instruments

which block scattering from lower layers will observe

smaller downwelling actinic flux levels and e-folding

depths than those observed by perfectly transparent

instruments within the same snowpack (Fig. 1). Com-

plete blocking of scattering from lower layers results in

reduction of the 470 nm e-folding depth from a true

value of 20.7 cm to one of 1.7 cm for a clean,

homogeneous snowpack with a density of 0.34 gm/cm3

and a snowgrain thickness of 0.25 mm under diffuse

lighting conditions (Fig. 1). When adjusted to this

snowpack density (see King and Simpson, 2001 for

method and initial liquid equivalent e-folding depths),

previous observations of 470 nm e-folding depths made

using small fiber-optic sensors placed within different

snowpacks are all less than predicted for a clean,

homogeneous snowpack and disagree with each other

0.01

0.1

1

0 100 200 300 400

Depth in Snowpack (mm)

Do

wn

wel

ling

470

nm

Act

inic

Flu

x (F

ract

ion

)

Model: Transparent InstrumentsModel: Opaque InstrumentObservations: Undisturbed SnowObservations: Shoveled Snowe-folding depth

GMKS01 KS78

KS01 - King and Simpson, 2001

- Grenfell and Maykut, 1977

- Kuhn and Siogas, 1978

GMll

KS78 -

Fig. 1. Observations of average relative downwelling 470 nm actinic flux levels in snowpack (squares) and two 1-D Monte Carlo model

simulations (solid lines) spanning the range expected for the undisturbed in situ light field (transparent instrument) and for the light

field resulting from elimination of scattering from lower layers (opaque instrument). Error bars span the observed range. Uncertainty

in observation depths is estimated to be o740mm. The range of possible e-folding depth observations in this model snowpack with

diffuse lighting is plotted at an y-axis value of 0.37. Previous observations of 470 nm e-folding depths made with fiber-optic probes,

normalized to the model snowpack density of 0.34 gm/cm3 (see King and Simpson, 2001 for method and initial liquid equivalent e-

folding depths), are also shown.

M. Peterson et al. / Atmospheric Environment 36 (2002) 2545–25512548

by as much as 300% (Fig. 1 and King and Simpson,

2001). These differences may be due to variations in

snowpack composition (King and Simpson, 2001).

However, some of the difference may also be due to

partial blocking of upward scattered light by the opaque

sensors. The magnitude of the effect will depend on the

size, shape, orientation, and spectral signature (i.e., the

amount of forward and backward scattering and

absorption) of the sensor. Additional simulations with

a 2- or 3-D Monte Carlo model are needed to study this

issue further.

Although measurements of relative actinic flux levels

made using the buried spectroradiometer are near

modeled lower limits, this is not the case with measure-

ments made using transparent chemical actinometry

tubes (Qiu et al., 2002), or with simulations of the light

field in the undisturbed snowpack. The relative change

in photolysis frequencies with depth in the snowpack

measured with this technique equals the corresponding

change in actinic flux during relatively short periods

when temperatures are approximately isothermal and

reaction probabilities and quantum yields are nearly

constant (Qiu et al., 2002). Thus, only those chemical

actinometry observations integrated over a period of

about 2 h near midday are used for comparison with the

1-D Monte Carlo simulations. Although refraction at

the air-actinometer interface may influence measure-

ments of absolute actinic flux levels, it is not expected to

cause substantial error in the relative actinic fluxes

reported here as this effect is proportional to the

incident light levels (and will thus divide out). A

complete listing of the modeled relative in situ actinic

fluxes are shown in Table 1, and the actinometry data

are compared to the modeled 290 nm relative actinic flux

levels in the upper 250mm of the snowpack in Fig. 2.

While simulations of relative actinic flux levels in a

homogenous snowpack are somewhat higher than

observed levels (Fig. 2), simulations of these levels in a

seven layer snowpack with variable density and snow-

grain size derived from measurements (see Section 2.2)

are in excellent agreement with observed levels (Fig. 2),

confirming the accuracy of the 1-D Monte Carlo model.

Thus, the relative actinic flux levels in snowpack listed in

Table 1 may be used in conjunction with incident

downwelling actinic flux levels (from spectroradiometric

measurements or an atmospheric radiative transfer

model) to find absolute actinic flux levels in the Summit

snowpack under diffuse lighting conditions.

While the results presented here demonstrate that a

1-D Monte Carlo modeling approach is sufficient to

simulate actinic flux levels in a clean, horizontally

stratified snowpack, a 2- or 3-D model is required to

predict light levels inside experimental chambers used to

study snowpack photochemical processes (Honrath

et al., 2000; Dibb et al., 2002). Such a model is also

needed to find the influence of small opaque objects

(such as radiometers, see above) on light levels within

the snowpack, and to study light penetration through

tilted, irregular snowpack surfaces, common over sea ice

(Worby et al., 1996), or in areas where drifting occurs.

Table 1

Relative actinic flux levels in Summit snowpack from modeling

Depth (mm) Wavelength (nm)

290a 350a 390a 470a 590a 650a 290b 350b 390b 470b 590b 650b

0c 1.90 1.92 1.93 1.93 1.93 1.92 1.92 1.93 1.93 1.94 1.93 1.93

0d 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

5 0.94 0.95 0.96 0.96 0.96 0.95 0.94 0.95 0.95 0.96 0.95 0.95

10 0.91 0.92 0.93 0.94 0.93 0.92 0.91 0.92 0.93 0.93 0.93 0.92

20 0.85 0.92 0.93 0.94 0.93 0.92 0.85 0.92 0.93 0.93 0.93 0.92

40 0.74 0.79 0.82 0.83 0.82 0.78 0.72 0.76 0.79 0.80 0.79 0.76

60 0.65 0.71 0.75 0.77 0.75 0.70 0.60 0.65 0.69 0.71 0.69 0.65

80 0.57 0.63 0.68 0.70 0.68 0.63 0.48 0.54 0.59 0.60 0.59 0.53

100 0.50 0.58 0.64 0.66 0.64 0.57 0.41 0.47 0.52 0.54 0.52 0.47

150 0.36 0.44 0.50 0.52 0.50 0.43 0.30 0.37 0.42 0.44 0.42 0.36

200 0.25 0.32 0.37 0.40 0.37 0.31 0.21 0.26 0.31 0.33 0.31 0.26

250 0.17 0.22 0.27 0.29 0.27 0.22 0.14 0.18 0.22 0.24 0.22 0.18

300 0.11 0.16 0.19 0.21 0.19 0.15 0.09 0.13 0.16 0.17 0.16 0.13

400 0.05 0.07 0.10 0.11 0.10 0.07 0.04 0.06 0.08 0.09 0.08 0.06

500 0.02 0.03 0.04 0.04 0.04 0.03 0.01 0.02 0.03 0.03 0.03 0.02

600 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

aHomogeneous snowpack (r ¼ 0:34 gm/cm3, snowgrain thickness = 0.25mm).bStratified snowpack (see text).cRelative to the actinic flux downwelling from the sky under diffuse lighting conditions.dRelative to the actinic flux at the snowpack surface (i.e., first row in this table).

M. Peterson et al. / Atmospheric Environment 36 (2002) 2545–2551 2549

Based on the 1-D Monte Carlo simulations, we have

begun making in situ downwelling actinic flux measure-

ments just above the center of large black sheets at

different depths in snowpacks. With this procedure,

scattering from lower layers is eliminated, producing a

limiting case in the possible range of snowpack down-

welling actinic flux observations. Differences between

the resulting measurements and corresponding simula-

tions of relative downwelling actinic flux levels using

pure ice absorption coefficients provide the data

required to estimate the absorption coefficients of

snowpack contaminants (not required here, and beyond

the scope of this paper), and thus model wavelength-

dependent e-folding depths in dirty snow. While we

expect this technique to be sufficient in some cases, it is

difficult to implement, especially with respect to

undisturbed snowpacks, and additional work is needed

to fully understand the influence of contaminants and

opaque sensors on in situ light levels in snowpacks.

4. Conclusions

(1) UV and visible radiation is completely diffuse in the

Summit snowpack at depths o0.7 cm.

(2) Opaque instruments buried in snowpack partially

block upward scattering from lower layers which

results in reductions in observed downwelling

actinic flux levels and e-folding depths.Simulations

of limiting cases indicate that complete blocking of

light scattered upward from lower layers reduces the

observed e-folding depth from 20.7 to 1.7 cm at a

wavelength of 470 nm in a homogeneous snowpack.

Additional simulations are needed to quantify the

magnitude of this effect for partial blocking

situations.

(3) A 1-D Monte Carlo modeling approach yields

accurate relative actinic flux levels for a stratified,

horizontally homogeneous snowpack representing

the upper 1m of snowpack at Summit, Greenland.

These results can be combined with available

spectroradiometric measurements or atmospheric

radiative transfer simulations to compute absolute

actinic flux level in the Summit snowpack.

Acknowledgements

We thank Michael Dziobak, who provided essential

logistical support and helped design and implement

methods for placing the spectroradiometer under

undisturbed snow. The permissions to work in

Greenland are greatly appreciated. We thank the 109th

NY ANG for airlift support under adverse conditions.

This material is based upon work supported by the

National Science Foundation under Grant No. OPP-

9907197. The SPUV-6 sunphotometer and associated

data acquisition system was provided by funding from

NASA.

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0

0.2

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0.8

1

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0 20 40 60 80 100 120 140 160 180 200 220 240Depth in Snowpack (mm)

<320

nm

Act

inic

Flu

x (F

ract

ion

)

Model: Homogeneous Snow pack

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