Light absorption from particulate impurities in snowand ice determined by spectrophotometric
analysis of filters
Thomas C. Grenfell,1,* Sarah J. Doherty,2 Antony D. Clarke,3 and Stephen G. Warren1
1Department of Atmospheric Sciences, Box 351640, University of Washington, Seattle, Washington 98195, USA2Joint Institute for the Study of Atmosphere and Ocean, Box 355762,
University of Washington, Seattle, Washington 98195, USA3School of Ocean and Earth Sciences and Technology, University of Hawaii, Honolulu, Hawaii 96822, USA
At visible and near-ultraviolet wavelengths, ice isso weakly absorbing that small amounts of light-absorbing impurities can dominate the absorptionof sunlight by snow. Submicrometer-sized soot parti-cles, containing a large fraction of black carbon (BC),are produced by incomplete combustion in diesel en-gines, coal burning, forest fires, agricultural fires,and residential wood burning [1,2]. These particlesmay be carried thousands of kilometers in the atmo-sphere before being scavenged by raindrops or snowcrystals or through dry deposition. Soil dust can alsobe transported large distances and can also reduce
the albedo of snow and ice. Typical snow in the north-ern hemisphere measured in 1983–1984 was found tocontain enough soot and dust to reduce its albedo by1%–2% [3]. This small reduction is enough to be im-portant for climate [4–6], but it is not enough to bevisible to the eye or reliably detectable from satelliteimagery.
Determination of the absorptivity and concen-tration of light-absorbing aerosols in snow or ice istherefore most reliably determined by direct sam-pling of the medium. The principal techniques cur-rently available to analyze BC in snow and iceinvolve melting and filtration of the samples to de-posit the aerosol particles onto suitable filters fol-lowed by (a) direct optical analysis of the filters [3]or (b) stepwise combustion of the deposited material,the “thermo-optical” method [7]. A third method is
the single-particle soot photometer (SP2) [8,9]. Thethermo-optical method has been used in several stu-dies on snow (e.g., [10,11]). The SP2 method has beenused on ice cores [12]. Here we describe the char-acteristics and application of a new instrument oftype (a) to carry out optical determination of directabsorption of light, making use of recent advancesin optical instruments including high-resolutioncompact spectrophotometers and stable illuminationsources. We also describe a method for deriving themaximum BC concentration in the snow samples. Anextension of this technique incorporating an esti-mate of the spectral absorption characteristics ofnon-BC material makes it possible to estimate theactual BC concentration and to separate the contri-butions of BC and other constituents to the absorp-tion of solar radiation integrated from 300 to 750nm.
2. Background
When the objective is to determine the effect of soot onthe snow-surface energy budget rather than to quan-tify the carbon mass budget, the optical transmissionmethod has the advantage that it provides ameasureof absorption, which is related to the absorption ofsunlight in the snowpack. Since onemeasures absorp-tion directly instead of measuring particle mass andthen converting it to absorption, this method avoidsthe need to know the mass-absorption cross sectionof the BC. There are additional advantages to thefilter method. The filtering can easily be done in re-mote field camps, so it is not necessary to transportlarge quantities of snow from the field site. Initial es-timates of effective BC loading in the snow can bemade in the field via visual comparison against aset of standard filters to provide insurance againstsample loss and to permit reassessment of the sam-pling strategy while still in the field. The sample fil-ters are then returned to the laboratory for analysisby spectrophotometric techniques.
In prior work begun in 1985 by Clarke and Noone[3], an integrating-plate (IP) photometer [13] wasused to investigate the BC content of snow in the Arc-tic and in the mountains of the Pacific Northwest[3,14–16]. In those studies, snow samples of 100–1000 grams were collected, melted rapidly, andpassed through 0:4 μm Nuclepore filters to collectthe particulate material. The filters were air dried,and transmittance was measured at four wave-lengths to determine the concentration of absorbingaerosol and to provide a spectral signature for thepurpose of separating BC and non-BC components.The calibration was provided by measuring thetransmittance of filters with known (weighed)amounts of BC in the form of Monarch-71 soot, whichhad been prefiltered to produce a size distributionrepresentative of atmospheric BC. A detailed de-scription of the process and the characteristics ofthe standard soot is presented in the 1985 study [3].
Analysis of the IP photometer method [17] showedthat corrections were required due to modification ofthe system reflectance resulting from the interaction
between the particles and the collection filter. Thiseffect can depend on the size distribution and com-position of the particles, and it is particularlypronounced if large aerosol particles with weak ab-sorption are present on the filters. These particlescan produce lensing effects, modifying the absorptionefficiency of the smaller absorptive aerosols behindthem on the filter. If the radiation field interactingwith the particles is not isotropic, they can also actto scatter light out of the field of view of the detectors,producing a spuriously enhanced attenuation thatcould be attributed incorrectly to absorption.
This effect is also important to recognize when con-ducting visual inspection of the sample filters undernonisotropic illumination, since the appearance ofthe filter and the comparison against the calibrationfilters can vary depending on the ambient illumi-nation. Figure 1 shows photographs with a high-magnification optical microscope of the edge of theexposed area of a filter under reflected versus trans-mitted illumination that is essentially collimated.The apparent absorption, indicated by the contrastof the exposed area on the left and the unexposedarea on the right, is seen to be sensitive to the illu-mination conditions. A consequence of this is that thevisual estimates made in the field relative to a set ofstandards are uncertain and require careful controlof the illumination of all filters under comparison. Inaddition to BC, the field filters often contain othermore weakly absorbing particles with higher ratiosof scattering to absorption than the soot on the stan-dard filters. The visual estimates thus give an effec-tive BC value as though all the material on the filteris soot. Our experience has shown that the visualcomparison is best carried out under diffuse reflectedillumination with the filters sitting on a white diffus-ing background. Additional uncertainties includepersonal bias and the difficulty of attempting toignore color when comparing a brown dust-laden fil-ter to a gray calibration filter. As will be shown below,the resulting uncertainty involved is approximatelya factor of 2.
To minimize the influence of the scattering ef-fects, an “integrating-sandwich” (ISW) technique
Fig. 1. Optical microscope photographs of the edge of the exposedzone on a Nuclepore filter showing significant visible differencesbetween illumination with reflected and transmitted light. Thismotivates the integrating-sandwich technique, which removesthe influence of scattering losses by material on the filter.
was developed and tested [18,19] that involves theintroduction of a second highly scattering diffuserto surround the loaded sample filter with a radiationfield that is essentially isotropic. Any light scatteredby the particles is included in the multiply scatteredradiation field surrounding the filter and experiencesvery little loss, and the light passing through thesandwich to the detector is modulated only byabsorption from the material on the filter. The ISWconfiguration also produces an amplification of theabsorption of the light due to multiple passes of theradiation through the material on the filters. Thechallenges with this technique are (a) that the radia-tion transmitted to the detector is faint, requiringeither long integration times or a bright and verystable light source, and (b) that the response of thesystem to BC loading is nonexponential, requiringa set of standards covering the full range of filterloadings and careful calibration.
These considerations, as well as significant ad-vances in the development of improved compact op-tical components, have motivated the construction ofa new spectrophotometer system making use of theintegrating-sandwich technique. The instrument isreferred to here as an ISSW spectrophotometer, asit incorporates an integrating sandwich togetherwith an integrating sphere.
3. ISSW System Characteristics
A schematic diagram of the system optics is shown inFig. 2. A filter is mounted by raising the compressionweight and positioning it with forceps on the bottomwindow. The weight is the only moving part of thesystem, thus avoiding difficulties with optical misa-lignment of the system components. It also ensuresconstant uniform pressure on all filter samples.White light illumination from a Dolan Jenner DC-950H light source using a 150-W quartz-halogenlamp is transmitted into a 50-mm-diameter Spectra-lon integrating sphere via a 6.3-mm-diameter opticalfiber to produce a diffuse radiation field at the outputport of the sphere. The diffuse radiation then passesthrough the sample cell consisting of the sample fil-ter and an upper diffuser consisting of a quartz fiberfilter mounted as shown between 50-mm-diametersapphire windows. The upper diffuser has a reflectiv-ity of about 0.95 and produces diffuse radiation direc-ted from above back at the sample filter, so that thefilter is diffusely illuminated from both sides. Sincethe reflectivity of the integrating sphere is also veryhigh (0.99), the radiation undergoes multiple reflec-tions through the sample filter between the upperdiffuser and the integrating sphere, enhancing theabsorption signal [18].
Fig. 2. (A) Schematic of ISSW spectrophotometer system optics. (B) Expanded view shows the configuration of the integrating sandwichwith the compression weight raised to allow sample filter insertion.
The radiation transmitted upward through the dif-fuser is transmitted to an Ocean Optics Red Tidespectrophotometer, and the resulting spectrum is re-corded on a laptop computer via a USB connection. Acritical feature of the spectrophotometer is the pre-sence of an order-blocking filter, which reduces thesecond-order spectral overlap signal by a factor 104
or better. The second-order spectrum would not besignificant for wavelengths below 700nm in anycase, and for the present application the greatest pri-mary intensity falls in this wavelength range, mini-mizing the potential effect of such light leakage.Dark-level spectral readings are measured for eachsample by inserting an opaque screen into the lightpath and are subtracted from the signal during ourdata reduction procedure. The dark-level spectrashowed no dependence on wavelength, indicatingthat the amount of external stray light entering thesystem was negligible. The spectrophotometer runson 5V DC, rather than using an AC power sup-ply, to minimize system noise and signal drift. Thespectral sensitivity is limited to the range400–750nm. Below 400nm the cutoff is due to thelow sensitivity of the CCD detectors compared withinstrument noise, and a longwave-blocking filtermounted in the illumination unit cuts off the infraredbeyond 750nm. The available wavelength range cov-ers most of the spectral range over which light ab-sorption in snow and ice is predominantly affected
by BC and other light-absorbing aerosols [20]. Thespectral resolution of the system is approximately2nm across the full spectrum, providing the capabil-ity to detect molecular absorption features that maybe present in different types of material collected onthe filters.
4. Calibrations
Calibration of the system is based on a set ofseven standard filters with a series of loadingsðL; μg cm−2Þ of Monarch 71, a commercially producedsoot. These were prepared through sequential dilu-tions and gravimetric confirmation of a standard sootsuspension obtained after previous filtration through2:0 μm and 0:8 μm pore Nuclepore filters in order toremove larger particles not representative of ambientsamples. Preparation of these reference filters isdescribed in [3]. The filter loadings span a range suf-ficient to define the instrument sensitivity curves forfield samples over the full visible spectral band of in-terest. Observations of the transmitted light sensedby the system for a sample, SðλÞ, are compared withthe signal detected for a blank filter, S0ðλÞ, and therelative attenuation is expressed as
χλ ≡ ln½S0ðλÞ=SðλÞ�: ð1Þ
Specification of these and other symbols used in thetext is given in Table 1. An integration time of 5:8 s
Table 1. Symbols Used in Text
Symbol Description of Subscripts
est Estimated; e.g., best estimate of BC levelequiv Equivalent; based on ascribing all absorption on filter to an equivalent loading of BCMAX Maximum; based on assuming that all absorption from 650 to 700nm is due to BCNBC Non-black-carbon component of absorptiontot Wavelength integrated from 300 to 750nm
Symbol Description of Variables
Åi Absorption Ångstrom exponent describing the wavelength dependence of absorption by a particular type ofabsorber in a specified spectral range via τðλÞ ∝ λ−Å. Index i denotes tot, BC, or NBC as required.
βðλÞ Mass-absorption efficiency, m2=g. For our standard M71 soot samples βð525nmÞ ¼ 6m2=g.τki Absorption optical depth (dimensionless) of the material deposited onto the filter. Equal to filter loading
multiplied by β, and in general depends on wavelength. Index i denotes tot, BC, or NBC as required. The index kdenotes MAX or estimated (est); it is absent if i ¼ tot.
LkBC BC loading of filter. Index k denotes MAX, est, or equiv.
CkBC Concentration of BC in snow. Index k denotes MAX, est, or equiv.rj The ratio τjðλ0Þ=τtotðλ0Þ, where j denotes BC or NBC as indicated. Here λ0 ¼ 525nm.f kBC The ratio of BC absorption to total absorption from 300 to 750nm. Index k denotes MAX or est.f kNBC ½1 − f kBC�. Index k denotes MIN or est.Ek
BC Maximum wavelength-integrated absorption of solar energy by BC from 300 to 750nm. Dimensionless.Index k denotes MAX or est.
ETOT Wavelength-integrated absorption of solar energy from 300 to 750nm by all material on filter. Dimensionless.S0ðλÞ Detected signal for an unloaded filter, relative voltageSðλÞ Detected signal for a loaded filter, relative voltageχλ Relative spectral attenuation, ln½S0ðλÞ=SðλÞ�. Dimensionless.Fnet Net spectral irradiance in the vicinity of the filter and integrating sandwich, W=m2
Fs Scalar irradiance in the vicinity of the filter and integrating sandwich, W=m2
κabs Volume absorption coefficient of the material deposited onto the filter for single transit of a plane wave, m−1
R1 Reflectivity of the integrating sphere-filter combinationR2 Reflectivity of the integrating sandwichA/M Ratio of exposed area on filter (A, m2) to the total mass of snow filtered (M, g).
has been used for both the calibration tests and pro-cessing of field samples. A representative calibrationcurve for 600nm is shown in Fig. 3. Multiple filterswithdifferent loadingsareneededbecause the systemresponsedeviates fromaBeer’s lawexponential beha-vior as shown. This is a consequence of the multiplereflections produced by the integrating sandwich[18] and will be described in more detail below. Athird-order polynomial fit to the calibration curve re-produces the observations to within the accuracy ofthe measurement, allowing us to convert measuredvalues of χλ to L. Absorption optical depth is then cal-culated from τλ ¼ Lβλ, where βλ is the mass-absorp-tion efficiency for which we use 6m2=g at 525nm,the value for the Monarch 71 BC on the standard fil-ters. This ensures that the radiation absorption by thesample at 525nm is consistent with the radiationabsorbed by the standard filters. The calibrationsequence is repeated regularly to monitor for unex-pected changes in systemcharacteristics. For samplesof pure soot, we would in principle need measure-ments only at a single wavelength, but since naturalsamples often contain other material besides BC, wecan exploit spectral observations to investigate theamount of BC versus non-BC material. In this case,L is the equivalent BC mass loading that producesthe correct total radiation absorption. The treatmentof BC versus non-BCmaterial is discussed in detail inSection 7.
5. Precision and Uncertainties
After a warm-up time of about 1 h, the stability of thesystem is approximately 0.4% over several hours ofoperation. A series of 28 calibrations spanning sev-eral weeks gave a standard deviation of 2.5% or less,demonstrating the long-term system stability. Repre-sentative results at 600nm are shown in Fig. 4. Theshort-term stability of the calibration over individualtests lasting several hours was 0.2%.
The percentage uncertainty in derived loading at awavelength of 600nm is shown in Fig. 5(a) as a func-tion of loading. The noise-to-signal ratio for filterloading is optimal near 2 μg=cm2 with a range of goodperformance of better than ∼7% from about 0.2 to6 μg=cm2. For L values outside this range the signallevels decrease significantly relative to system noise.For L values near the optimum value, the accuracyfor an individual sample is about 2%. The corre-sponding uncertainty versus wavelength for a repre-sentative value of L ¼ 2 μg=cm2 is shown in Fig. 5(b).The uncertainty is ∼2% from 490 to 730nm and isless than 5% between 420 and 740nm. In practice,we exclude wavelengths longer than 750nm to con-form to the band over which background levels oflight-absorbing aerosol absorption are significantfor snow. These results show that the optimal volumeof snow for a sample is that which gives a filter load-ing of 1–3 μg=cm2. It is not possible to know the pre-cise volume needed a priori at a new site since therequired volume increases for cleaner snow; butnear-optimal results can be obtained iteratively byvisually examining the darkness of the initial filtersand resampling with an adjusted volume of snow.
Uncertainty in ISSW measurements arises notonly from instrumental uncertainties but also fromnonuniformities in the aerosol deposition on the fil-ter. In addition, filters occasionally shifted partiallyout of the fiber-optic field of view when lowering thecompression weight. For this reason, we made twomeasurements for each sample filter, repositioningit in the sample cell between the two measurements.Generally the difference between the two measure-ments was in the range 0%–4%, and the averagevalue is recorded. Where the difference was 10% ormore, subsequent repeat measurements were made.If agreement to better than 10% between multipleadditional measurements was obtained, the resultwas included in the data set; otherwise the samplewas excluded. Less than 1% of field samples were ex-cluded, and in each of these cases the filter exposurewas nonuniform. This type of error does not depend
Fig. 3. Calibration curve for 600nm wavelength relative toMonarch-71 standards. Individual points are the values fromISSW scans. The solid curve is a best-fit to the loading, L, usinga third-order polynomial of the form L ¼ Aχ þBχ3. A ¼ 8:689and B ¼ 1:862
Fig. 4. Uncertainty in filter loading. Standard deviation, σχ , ver-sus χ ¼ lnðSo=SÞ at 600nm for a series of 28 calibration runs on aset of reference filters.
on the performance characteristics of the ISSWsystem.
6. Theory
Because of the highly diffuse radiation field in thesample cavity, the integrating-sandwich methodlends itself to analysis using a straightforward trans-formation of the flux integral {Eq. (56) in [21]}, alter-natively known as Gershun’s law ([22], p. 423). Thisis a rigorous result based on the equation of radiativetransfer for an arbitrary plane parallel scatteringand absorbing medium that isolates the absorptioncoefficient:
dFnet
dz¼ −κabsFs; ð2Þ
where Fnet is the net irradiance and κabs is the vol-ume absorption coefficient. Fs is the scalar irradiance[23,24], 4π times the mean radiance. Since the radia-tion field interacting with the sample filter in thecavity between the integrating sphere and the diffus-ing sandwich is diffuse, we assume that the radiationfield is isotropic in both the forward and backwardhemispheres at the location of the filter. With thisassumption, the solution of the flux integral can bederived by the same method used for the discrete or-dinates method. The derivation is given in theAppendix. The ratio of detected signal intensity, S,at a particular wavelength for a loaded filter com-pared with that of a reference blank is shown to be
SS0
¼ expð−2τÞ 1 − R1R2
1 − R1R2 expð−4τÞ; ð3Þ
where R1 and R2 are the reflectivities of the integrat-ing-sphere/filter combination and the integrating-sandwich diffuser, respectively, and τ is the total ab-sorption optical depth for the material on the filter.Rather than using the thickness of the collected
material, we measure LBC for each sample by com-parison with the standard filters, and the absorptionoptical depth is given by the more convenient quan-tity τ ¼ L · βλ, which is equal to
Rκabsdz.
Equation (3) is essentially an exact solution for theinstrument, subject only to the assumption of hemi-spherical isotropy and the approximation of plane-parallel geometry at the filter location. Invertingand taking the logarithm, we obtain
χλ ¼ 2τ þ ln½1 − R1R2 expð−4τÞ�
½1 − R1R2�: ð4Þ
The first factor in Eq. (4) shows that there is an en-hancement of absorption by a factor of 2 over a beamtransmission measurement (2 is the mean secantof a diffuse radiation field). The second factor de-scribes the additional absorption produced by multi-ple passes of the radiation through the filter due toreflections in the integrating chamber.
The system response is independent of scatteringby the material on the filter. Although scatteringlosses by BC are expected to be small compared withabsorption, non-BC material can contribute signifi-cant scattering losses when using an apparatus thatdoes not have a truly isotropic radiation field. TheISSW instrument essentially removes the influenceof all scattering losses from the system. The denomi-nator of the second term in Eq. (3) indicates that theresponse of the system is nonexponential as seen inFig. 3. The system sensitivity is related to the slope ofthis curve and is greatest for very small values ofloading, reaching an asymptotic value for large τ.
For the present configuration, the lowest usefulvalues of L are approximately 0:2 μg=cm2. For val-ues of L above about 6 μg=cm2, the transmitted radia-tion will be attenuated below levels where systemnoise again begins to dominate. As mentioned above,
Fig. 5. Percent uncertainty in loading, 100L
∂L∂χ σχ , for an ensemble of 28 calibration runs versus (A) filter loading at 600nm and (B) wave-
length for a loading of 2 μgC=cm2. The optimal spectral range is from 420 to 740nm.
exceeding these limits can be avoided by resamplingthe snow to adjust the volumes of meltwater filtered.
7. Separation of the Contributions to Absorption byBlack Carbon and non-Black-Carbon Absorbers
In addition to BC, snow often contains other light-absorbing aerosols such as soil dust and organic car-bon. These are often brown or reddish-brown. Anoptical-microscope photograph of an example fromsnow in Canada is shown in Fig. 6 in which many co-lored dust particles are visible. To understand thespectral absorption of light in a snowpack it is impor-tant to distinguish between particles consisting ofpure BC and other colored particulates that we referto here collectively as non-BC particles. The effect ofthe latter on the ISSW scans is to alter the spec-tral shape of the absorption curves and the resultingtotal absorption. This effect has been describedpreviously [3,25,26].
Because the ISSW instrument provides 2nm spec-tral resolution, it offers the potential to determineseparately the contributions of BC and non-BCaerosols to the total absorption. The dependence ofabsorption optical depth on wavelength is often char-acterized by a power law, τðλÞ ∝ λ−Å, over a particularwavelength range of interest, where Å is called theÅngstrom exponent. For BC, the value of Å is veryclose to 1 for visible wavelengths, and the values fornon-BC aerosols are significantly larger [27–29]. Wetake advantage of these differences in spectral shapeas described below. Non-BC light-absorbing compo-nents have been identified and characterized asbrown carbon [30,31], organic carbon [32], and soildust [33]. Brown sediments have also been foundin samples of sea ice and its snow cover [16].
A. Upper Limit to Black Carbon
As an initial limiting approximation, we determinean estimated upper bound to the contribution of
BC to absorption of solar radiation by assuming thatall absorption from 650 to 700nm is due to BC, withan absorption optical depth τMAX
BC . The filter loading,LMAXBC , is derived from the calibration against the
standard samples over the 650–700nm interval.The corresponding BC concentration in the snow isgiven by
CMAXBC ¼ LMAX
BC · ðA=MÞ; ð5Þ
where M is the mass of meltwater filtered and A isthe exposed area on the filter. This gives a value ofnanograms of BC per gram of snow meltwater or,equivalently, ppb. To determine τMAX
BC we multiplyLMAXBC by a mass-absorption efficiency, βðλÞ, obtained
by scaling the value of 6m2=g at 525nm and extra-polating to 675nm, using an Ångstrom exponent of1.0 as specified above. Values of βðλÞ for a set of cali-bration filters using a different type of soot may dif-fer from this, in which case βðλÞ should reflect theoptical properties of the chosen calibration material.
Using the spectral dependence of the measuredlight absorption offers the potential to obtain addi-tional information about other material that maybe present in the snow. A representative case isshown in Fig. 7. After specifying τMAX
BC , the BC spec-tral curve (dashed line) is calculated by extrapolatingfrom the 650–700nm band over the range 300 to750nm again using an Ångstrom exponent of 1. Thiswavelength interval has been chosen because solarradiation at the surface is negligible below 300nm,and impurities have little effect on snow albedo forλ > 750nm. We use the measured absorption overthe 420–700nm interval where the signal-to-noiseratio is optimized. The total absorption curve is ex-tended over the full spectral range by linear extrapo-lation from 420 to 300nm and from 700 to 750nm.The extrapolations are carried out using the mean
Fig. 7. Absorption optical depth versus wavelength for a samplefilter containing BC and non-BC components from a snow samplefrom the Canadian Arctic in spring 2009. The solid line showstotal absorption optical depth, and the dashed curve gives themaximum BC contribution assuming that all absorption at650–700nm is due to BC and that ÅBC ¼ 1:0. The dotted curvegives the estimated BC absorption using Eqs. (9) and (10) assum-ing ÅNBC ¼ 5.
Fig. 6. (Color online) Optical microscope image of filter samplefrom snow in northern Canada, May 2009, showing black soot con-glomerates and red-brown dust particles. Smallest visible detail is∼0:2 μm. Courtesy of Professor Don Brownlee (University ofWashington, Department of Astronomy).
slope of the absorption curve in the range 420 to450nm for the ultraviolet wavelengths, and themean slope in the range 630–700nm is used for thenear infrared. To obtain the relative contributions ofthe estimates of BC and non-BC material to the ab-sorption of solar energy over the entire solar spec-trum, the total and extrapolated absorption curvesare weighted by the incident spectral irradiance,FoðλÞ.
The solar spectrum used here and shown in Fig. 8is an example from summer in the Arctic Basin [34]extended to 300nm using the SBDART model [35]using the subarctic summer atmospheric profile.The weighted curves (Fig. 9) are then integrated overwavelength as follows to give the wavelength-integrated relative absorption by all the materialon the filter (ETOT) and by BC (EMAX
BC ):
ETOT ¼R750300 FoðλÞτTOTðλÞdλR
750300 FoðλÞdλ
;
EMAXBC ¼
R750300 FoðλÞτMAX
BC ðλÞdλR750300 FoðλÞdλ
:
ð6Þ
The estimated upper bound of fractional absorptionfor BC and the corresponding minimum for non-BCare given by the ratios
fMAXBC ¼ EMAX
BC =Etot; fMINNBC ¼ 1 − fMAX
BC : ð7Þ
An advantage of this technique is that no assumptionis necessary concerning the Ångstrom exponent forthe non-BC material; however, this technique pro-vides only a lower limit to the absorption by non-BC because non-BC absorption is not negligible at650–700nm in general.
B. Estimated Black Carbon
Our best estimate of the actual amount of BC andnon-BC material on the filter is obtained by exploit-ing differences in the Ångstrom exponents for BCand non-BC components. From the measured ab-sorption spectrum using τtotðλÞ specified as describedabove, we compute the Ångstrom exponent, Åtot, thatdescribes the wavelength dependence of the absorp-tion optical depth for all the material deposited on aparticular filter in the neighborhood of a referencewavelength λ0. The exponent is calculated from theshape of the total absorption curve (e.g., solid curvein Fig. 7) using the logarithmic formula
Åtotðλ0Þ ¼ln½τtotðλ1Þ=τtotðλ2Þ�
ln½λ2=λ1�; ð8Þ
where we have used values of 525, 450, and 600nmfor λ0, λ1, and λ2, respectively We can express Åtotðλ0Þin terms of the BC and non-BC components asfollows:
τtotðλ0Þ ·� λλ0
�−Åtot ¼ τBCðλ0Þ ·
� λλ0
�−ÅBC þ τNBCðλ0Þ
·� λλ0
�−ÅNBC
; ð9Þ
where ÅBC and ÅNBC are the Ångstrom exponentsfor BC and non-BC specified at λ0. If we define rBCand rNBC to be the ratios τBCðλ0Þ=τtotðλ0Þ andτNBCðλ0Þ=τtotðλ0Þ, respectively, then in a neighborhoodaround λ0 we can show via Taylor series expansion,for example, that
Åtot ¼ ÅBCrBCðλ0Þ þ ÅNBCð1 − rBCðλ0ÞÞ; ð10Þ
where rNBC ¼ 1 − rBC. So Åtot is a linear combinationof the exponents for BC and non-BC weighted by theabsorption fraction of each type of absorber, and it
Fig. 8. Incident solar irradiance, FoðλÞ, from the Arctic summer(2005) in the northern Beaufort Sea for a relatively clear day withsome light clouds and fog [34]. The wavelength range is limitedto the 300–750nm band used for the absorption calculations.The spectrum has been extended from 350 to 300nm using theSBDART model [35] using the subarctic summer atmosphericprofile.
Fig. 9. Spectral absorption, FoðλÞτðλÞ, for a site in the CanadianArctic in 2009 for all constituents (solid line), maximum BC(dashed line), and estimated BC (solid line) using the same Å val-ues as for Fig. 8.
can be determined directly from an observed spectralabsorption curve using Eq. (8). Thus, if we have in-dependent knowledge of ÅBC and ÅNBC over a wave-length interval of 100–150nm about λ0, for example,then rBCðλ0Þ is given by Eq. (10). For our analysis weassume that ÅBC ¼ 1:0. A value of 5 was chosen forÅNBC, consistent with Ångstrom coefficients reportedin the range 4 to 6 for the “brown carbon” componentof biomass-burning aerosol [31] and with valuesinferred from spectral absorption measurements oforganic-carbon aerosols (Table 4 of [32]). For ÅNBClower than about 4.5 nonphysical values (estimatedBC concentrations of less than 0) resulted for somesamples. Values of Åtot fall between ÅBC and ÅNBC[36] as per Eq. (10).
as shown by the dotted line in Fig. 7, and the esti-mated BC loading is given by
LestBC ¼ ½LMAX
BC · hτestBCi650–700=hτMAXBC i650–700�: ð13Þ
The spectrally integrated fractions of absorption byBC, f estBC, and by non-BC constituents, f estNBC ¼½1 − f estBC�, are obtained from Eqs. (6) and (7) substitut-ing τestBCðλÞ for τMAX
BC ðλÞ. The estimated concentration ofBC in snow, Cest
BC, is derived from the loading on thefilter, Lest
BC, as in Eq. (5).The main limitation of this method is the accuracy
to which we know the value of ÅNBC in the vicinity ofλ0; however, even if ÅNBC is not well known, Åtot,which is measured directly, is important per se tohelp provide a general characterization of the sam-ples. Results are included in Figs. 7 and 9 assumingthat ÅNBC at that site is 5.0. In the Arctic, the absorp-tion by the non-BC component is highly correlatedwith the biomass-burning source factors [37], whichindicates a preponderance of brown carbon as op-posed to dust. A chemical analysis profile is clearlydesirable in conjunction with the ISSW observationsto help specify the nature of the non-BC fraction. IfÅNBC is less than (greater than) 5, our derived BCamounts would be biased high (low).
C. Equivalent Black Carbon
Models that do not distinguish the various impuri-ties in snow may represent the effect of all absorbersby the amount of BC needed to explain the total ab-sorption. We therefore also report this quantity forour analyses of filter loading, which we call “equiva-lent BC.” It is determined by the ratio of the integralsof the total and estimated spectral absorption curves
(Fig. 9):
LequivBC ¼ Lest
BC
R750300 FoðλÞ τTOTðλÞdλR750300 FoðλÞ τestBCðλÞdλ
¼ LestBC
f estBC; ð14Þ
CequivBC ¼ Cest
BC=festBC: ð15Þ
8. Comparison of ISSW Results with VisualAbsorption Estimates
Since some published results were obtained using vi-sual comparison against our set of standard filters[15,16], it is important to know how well these esti-mates compare with spectrophotometer results. Thevisual comparison gives an estimate of the equiva-lent BC concentration ðCequiv
BC Þ, which is the amountof BC that would be needed to explain the totalfilter darkening including both BC and non-BC com-ponents. The visual comparisons are made by com-paring the filter loading contrast relative to thestandards between the exposed area of each filterand its unexposed outer edge and then applyingEq. (5) with superscript MAX replaced by equiv.
Figure 10 shows a comparison of equivalent BCconcentration with visual estimates spanning arange of about 200 for snow samples from one expe-dition. Departures from the ISSW values lie withinbounds of uncertainty that span a factor of 2. The lin-ear regression curve in logðCvisÞ − logðCISSWÞ spaceis shown. The coefficient of correlation is 0.973with a standard error of 0.300, which is less thanlnð ffiffiffi
2p Þ ¼ 0:346. There is good agreement to within
a factor of approximatelyffiffiffi2
p. There is a slight low
bias particularly evident for low concentrationslikely due to personal bias of the observer. The error
Fig. 10. Comparison of equivalent concentration, CequivBC deter-
mined by the ISSW spectrophotometer fromEqs. (14) and (15), ver-sus the values from visual estimates for samples of snow from theRussian Arctic in 2007, for which the non-BC levels were low. Theupper and lower lines show the limits of a factor of 2 variationabout the line of perfect agreement. Linear regression in ln-lnspace, the dashed curve, gives ln½CðVisualÞ� ¼ f1:038 �ln½CðISSWÞ� − 0:2432g with a correlation coefficient of 0.973 anda standard error of 0.300.
in the visual comparisons is small compared withnaturally occurring temporal [12] and spatial [3] var-iations of BC, so the visual estimates provide usefulinformation; however, the ISSW instrument im-proves the precision by a factor of ∼70.
9. Conclusions
A new spectrophotometric instrument for measuringthe absorption properties of light-absorbing aerosolspresent in ice and snow based on the integrating-sandwich principle has been constructed, taking ad-vantage of recent developments in optical componenttechnology. The short-term stability is ∼0:4%, andthe long-term stability for a series of 28 measure-ments spanning several weeks is better than 2.5%.Calibrations against a set of filters of known BC load-ing have shown that the relative accuracy in loadingranges from 2% to 5% over the spectral range420–740nm for loading near 1 μgC=cm2. Theoreticalanalysis based on the flux integral of radiative trans-fer provides a quantitative measure of the sensitivityenhancement over the integrating-plate photom-eter technique. It demonstrates the capability of theintegrating-sandwich configuration to isolate the ab-sorption properties of material deposited on polycar-bonate Nuclepore filters, essentially eliminating theeffect of losses due to volume-scattering by absorbingand nonabsorbing particulate material in or on thefilter. This advantage far outweighs the disadvan-tage of the strong light attenuation introduced bythe integrating-sandwich configuration. Using theassumption that all 650–700nm light absorption isdue to BC, we derive the maximum concentration ofBC in the snow and the minimum contribution to ab-sorption by other aerosol by comparing wavelengthintegrals of total and BC absorption of solar radia-tion. We also determine an Ångstrom exponent forall light-absorbing aerosol in the sample to furthercharacterize each sample. By combining Åtot withan estimate for the absorption Ångstrom exponentfor BC and non-BC aerosols, the method is extendedto give values of the actual BC concentrations andfractional absorption of visible and near-UV solarradiation due to the non-BC aerosol.
We have used the ISSW instrument specificallyto quantify BC and non-BC contributions to lightabsorption in snow; however, the instrument and theanalysis described here can be used for identificationof other types of light-absorbing aerosol. This wouldrequire recalibration using a set of standards for thematerials of interest in conjunction with the use ofthe appropriate spectral signatures to separate thecontributions from the different absorbers.
Appendix A: Derivation of Eq. (4)
Considering the radiation field in the vicinity of thesample filter (Fig. 2), we assume that a plane-parallel representation provides an accurate descrip-tion near the filters, since the radiation field is highlyhomogeneous there. We define three regions to beconsidered where we specify the boundary conditions
for the problem. Region 1 is the cavity volume belowthe material on the filter. Region 2 is the cavity vo-lume above the filter and below the integrating sand-wich, including the material deposited on the filter.Region 3 is the volume above the integrating sand-wich from which the radiation is transmitted tothe detector by the optical fiber. We divide the inte-grals for irradiance in Gershun’s law into separatecomponents for the upward and downward hemi-spheres:
Fnet ¼Z
2π
0
Z1
0μIðμ;ϕÞdμdϕþ
Z2π
0
Z0
−1μIðμ;ϕÞdμdϕ;
ðA1Þ
Fs ¼Z
2π
0
Z1
0Iðμ;ϕÞdμdϕþ
Z2π
0
Z0
−1Iðμ;ϕÞdμdϕ;
ðA2Þ
where Iðμ;ϕÞ is the radiance, μ is the cosine of thepolar angle, and ϕ is the azimuth angle, standard de-finitions in radiative transfer theory [21]. The radi-ance in the vicinity of the filter is highly diffuse andassumed to be separately isotropic in both hemi-spheres. In this case, the radiance can be expressedas Ið�Þ ¼ Fþ=π or F−=π in the upward and downwardhemispheres, respectively. Then we obtain
Fnet ¼ Fþ − F−; ðA3Þ
Fs ¼ 2ðFþ þ F−Þ: ðA4Þ
Gershun’s law [Eq. (2)] can then be expressed as
dðFþ − F−Þdτ ¼ −2ðFþ þ F−Þ; ðA5Þ
where dτ ¼ κabs · dz is the formal definition of differ-ential absorption optical depth, and the total absorp-tion optical depth of material on the filter isτ ¼ R
κabs · dz. We have the following boundary condi-tions: in region 1
Fþð1Þ ¼ F0 þ R1 · F−ð1Þ; ðA6Þ
in region 2
F−ð2Þ ¼ R2 · Fþð2Þ; ðA7Þ
and in region 3
Fþð3Þ ¼ ð1 − R2Þ · Fþð2Þ: ðA8Þ
Fo denotes the direct contribution to Fþð1Þ from thelight source. Its value is not needed because it can-cels out of the final solution needed here. If the fieldof view of the optical fiber detector is Ωd, then thedetected signal, S, is proportional to ΩdFþð3Þ.
Following the techniques of Chandrasekhar [21],we seek solutions of (A5) of the form
Fl ¼ gl · expðkl · τÞ; ðA9Þ
where l denotes þ or −; kl are coefficients related tothe absorption properties of the aerosol on the filterand are specified by the form of (A5); and gl are in-tegration constants for (A5) to be specified by theboundary conditions (A6) through (A8). Substitutinginto (A5) and collecting terms, we obtain the charac-teristic equation for (A5):
For (A10) to hold for an arbitrary value of τ, the coef-ficients of each exponential term must separately bezero giving
kþ ¼ −2; k− ¼ 2; ðA11Þ
so
Fþ ¼ gþ expð−2τÞ; F− ¼ g− expð2τÞ: ðA12Þ
Substituting these into the boundary conditions (A6)and (A7) noting that τð1Þ ¼ 0 and τð2Þ ¼ τ, the ab-sorption optical depth of material on a filter, we have
gþ ¼ F0 þ R1g−; ðA13Þ
g− expð2τÞ ¼ R2gþ expð−2τÞ: ðA14Þ
These give
gþ ¼ F0
1 − R1R2 expð−4τÞ; g− ¼ R2 expð−4τÞF0
1 − R1R2 expð−4τÞ:
ðA15ÞSo
Fþ ¼ F0
1 −R1R2 expð−4τÞexpð−2τÞ;
F− ¼ R2 expð−2τÞF0
1 −R1R2 expð−4τÞ: ðA16Þ
We assume that absorption by the optical compo-nents of the system is negligible, although the finalresults are still rigorous even if a small constantamount of absorption is present. Then from (A8)the detected signal, S, for a loaded filter is
S ¼ ΩdFþð3Þ ¼ΩdF0ð1 − R2Þ
1 − R1R2 expð−4τÞexpð−2τÞ: ðA17aÞ
For a blank filter the signal, S0, is
S0 ¼ ΩdF0ð1 − R2Þ1 − R1R2
: ðA17bÞ
The ratio then gives the required result
SS0
¼ expð−2τÞ 1 − R1R2
1 − R1R2 expð−4τÞ: ðA18Þ
We thank Richard Brandt for useful suggestionsand help with the photometer design and Tom Acker-man for discussions on the separation of BC and non-BC contributions. Angel Adames and Hugo Froylandprovided helpful suggestions based on their use ofthe photometer to process filters. We thank DonBrownlee for optical microscopy of the filters (Figs. 1and 6). Two reviewers provided helpful suggestionsto clarify the presentation. The research was sup-ported by the National Science Foundation (NSF)grant ARC-06-12636.
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