Journal of Geophysical Research: Atmospheres

Optical properties of boreal forest fire smoke derived from Sun photometry

Authors


Abstract

[1] Aerosol optical properties derived from Sun photometry were investigated in terms of climatological trends at two Sun photometer sites significantly affected by western Canadian boreal forest fire smoke and in terms of a 2-week series of smoke events observed at stations near and distant from boreal forest fires. Aerosol optical depth (τa) statistics for Waskesiu, Saskatchewan, and Thompson, Manitoba, were analyzed for summer data acquired between 1994 and 1999. A significant correlation between the geometric mean and the forest fire frequency indices (hot spots) was found; on the average, 80% of summertime optical depth variation in western Canada can be linked to forest fire sources. The average geometric mean and geometric standard deviation at 500 nm was observed to be 0.074 and 1.7 for the clearest, relatively smoke-free summer and 0.23 and 3.0 for the summer most influenced by smoke. A systematic decrease of fine mode Angstrom exponent (αf) was noted (dαf /d log τa ∼ −0.6). This decrease roughly corresponds to an increase in the fine mode effective radius (reff) from 0.09 to 0.15 μm and an abundance (A) to size rate increase near 2.0 (d log A / d log reff). A 1998 series of forest fire events was tracked using TOMS, AVHRR, and GOES imagery, back trajectories, and data from six Sun photometer sites in Canada and eastern United States. The results showed rates of decrease of αf with increasing τa which were similar to the climatological data. An analysis in terms of source to station distance showed a decrease in αf and an increase in reff with increasing distance. This observation was coherent with previous observations on the particle growth effects of aging.

1. Introduction

[2] Smoke particulates associated with biomass burning represent an important aerosol whose global rate of production is comparable to that of sulfate aerosols [Radke, 1989; Houghton et al., 2001]. The influence of smoke in terms of direct and indirect radiative forcing, air pollution, atmospheric chemistry, and visibility reduction is significant both at local and regional scales [Kaufman et al., 1998; Woods et al., 1991; Li, 1998]. Smoke emissions are readily observed by satellite sensors and as such serve as a means of monitoring the long-range transport of smoke aerosols as well as providing remotely sensed indicators of particulate emission rates and the emission rates of associated trace gases [Ward et al., 1991]. Ground-based and airborne observations of smoke are needed to support and validate satellite-monitoring programs and to provide data that cannot be obtained from satellite inversions. The development of databases and climatological parameterizations from all observation techniques is important in order to better understand and model the behavior of these aerosols.

[3] Boreal forest fires within Canada consume an area that is about 40% of the area consumed by all boreal forest fires [Stocks, 1991]. In terms of a global biomass burning budget, boreal forest fires account for less than 10% (even in peak burning season) of worldwide biomass burning activity [Dwyer et al., 1998]. In spite of these modest global contributions the effect of smoke generated by western Canadian forest fires as a nonindustrial source of pollution and in terms of general visibility considerations is significant not only in western Canada [Chung, 1984] and the Canadian Arctic [Hariss et al., 1992] but also in eastern North America [Westphal and Toon, 1991]. Observations in the latter case are not confined to optical smoke monitoring; Wotawa and Trainer [2000] observed that the major source of CO variation over a 2-week period at four eastern U.S. stations was large forest fires in northwestern Canada, while Robock [1988] demonstrated significant short-term reductions in surface temperature over North America induced by an extended smoke plume originating in British Columbia.

[4] A considerable body of research using in situ sampling techniques has been published on the microphysical and optical properties of smoke. This includes the analysis of laboratory burns [Patterson and McMahon, 1984; Hallett et al., 1989], airborne monitoring of prescribed or local forest fires [Radke et al., 1978, 1988; Pueschel et al., 1988; Hallett et al., 1989; Pueschel and Livingston, 1990; Hobbs et al., 1996], and intensive field campaigns involving large-scale forest fires in the Amazon region [Reid and Hobbs, 1998; Reid et al., 1998; Echalar et al., 1998]. Remote sensing techniques have included ground-based Sun photometry [Kaufman et al., 1992], enhanced satellite imagery [Chung, 1984; Li et al., 2001], quantitative inversions of satellite imagery for smoke optical parameters [Ferrare et al., 1990; Hsu et al., 1999; Li and Kou, 1998b; Zhang et al., 2001; Wong and Li, 2002], and ground-based lidar combined with solar occultation satellite instruments [Fromm et al., 2000].

[5] The use of ground-based Sun photometry provides optical indicators of smoke properties which, although crude in the absence of any vertical discrimination capabilities, are robust, nonintrusive, and instantaneous measures of column-integrated aerosol properties. Such measurements are important sources of validation for satellite retrieval algorithms as well as for climatological to meteorological scale aerosol dynamics models. Satellite inversions suffer from signal competition due to surface- reflected photons, while aerosol models require stable benchmark indicators to validate their aerosol transport and chemical algorithms.

[6] Little research on the use of Sun photometry to characterize smoke was published until the deployment of the AERONET network in the early 1990s. Sun photometry work of this nature has, however, been almost exclusively focused on Amazonian tropical forest fires and African savannah fires [Kaufman et al., 1992; Holben et al., 1996; Remer et al., 1998; Dubovik et al., 1998; Eck et al., 1999; Holben et al., 2001; Eck et al., 2001]. A relatively small body of literature exists concerning smoke parameter measurements linked to western or central Canadian forest fire sources. Some in situ airborne measurements have been reported [Pueschel et al., 1988; Radke et al., 1991; Mazurek et al., 1991; Miller and O'Neill, 1997] as well as particulate sampling measurements during smoke events [Chung, 1984]. Significant numbers of observations using satellite data have been reported, usually in the context of tracing smoke plume evolution over the urbanized areas of eastern North America [Chung and Le, 1984; Westphal and Toon, 1991; Ferrare et al., 1990; Hsu et al., 1999; Fromm et al., 2000; Li et al., 2001]. Sun photometry of Canadian or American forest fire smoke is largely limited to short experiments [Pueschel et al., 1988; Pueschel and Livingston, 1990] or generalized studies that were not limited to smoke events and which did not attempt to discriminate smoke effects from other aerosol effects [Markham et al., 1997]. The exception is the multiannual analysis of Thompson, Manitoba, data in the Sun photometer climatological analysis of Holben et al. [2001].

[7] This paper is an attempt to explicitly link Sun photometry measurements with indicators of the influence of forest fire smoke from the Canadian west. It is divided into two major parts; multiyear Sun photometry data from two long-term sites whose aerosol variation is clearly affected by forest fire smoke is presented in section 3, while section 4 is dedicated to the study of a series of forest-fire–induced smoke events which occurred in the first two weeks of August 1998. The attendent objectives are (1) to infer climatological optical statistics of smoke and to analyze the link between optical depth variance and forest fire smoke from western Canada and (2) to record and optically characterize individual cases of large optical depth variations which are known to be induced by western Canadian boreal forest fire smoke and which were measured at various distances from the sources. The latter data are viewed as a means of providing an independent smoke optical depth reference to the optical climatological inferences.

2. Methodological Considerations

2.1. Optical Analysis Techniques

2.1.1. Definition of standard optical parameters

[8] Five standard optical parameters, all extracted from the spectral Sun photometer data, were employed to derive the results presented in this paper. They are the aerosol optical depth (τa), the Angstrom exponent (α), the spectral derivative of the Angstrom exponent (α′ = dα /d ln λ), the fine mode Angstrom exponent (αf), and the ratio (η) of the fine mode optical depth (τf) to τa. These parameters are all evaluated at the reference wavelength of 500 nm after having passed a third-order polynomial of ln τa versus ln λ through each data spectrum [O'Neill et al., 2001b].

[9] The Angstrom exponent is a standard optical analysis parameter which is related to particle size and, to a lesser degree, refractive index. Aerosol optics are largely dominated by a particle size distribution which can be subdivided into a submicron accumulation (fine) mode and a supermicron coarse mode. Given this simple distribution partitioning, one can easily show that α and α′ are expressible in terms of analogous fine and coarse mode exponents weighted by η [ibidem];

equation image
equation image

[10] The derivative α′ indicates spectral curvature of α at λ = 500 nm and is itself sensitive to particle size and refractive index. Eck et al. [2001] demonstrated distinct differences in this parameter for lightly absorbing urban aerosols versus smaller, more highly absorbing biomass burning aerosols. Given certain a priori information concerning the optical behavior of the coarse particle mode and α′f, equations (1a) and (1b) can be inverted to yield αf and the optical fraction η = τfa [O'Neill et al., 2001a].

2.1.2. Dependency of αf on reff and on τa

[11] The fine mode Angstrom exponent can be shown to be a nearly monotonic function of the effective particle radius (reff) (see O'Neill and Royer [1993] and Shifrin [1995], for example, and see the Notation section for a definition of reff). Figure 1a shows a plot of αf versus reff for a Mie simulation of east coast North American aerosols [Remer et al., 1999] and biomass burning aerosols [Reid et al., 1999]. Although there are differences in the fine mode Angstrom exponent between the different aerosol models, significant information about reff can clearly be extracted from a knowledge of αf even in the absence of any a priori information on the type of aerosol being measured.

Figure 1.

(a) Mie simulations of αf versus reff for continental and smoke-like lognormal distributions at a wavelength of 500 nm (μr refers to the geometric standard deviation of the lognormal size distribution). The smoke aerosol was modeled as an inner carbon core of refractive index (m) = 1.8 − 0.6i and an outer shell with m = 1.5 − 0i. The carbon core occupied a volume of 6% of the total [Reid et al., 1999]. A change to 12% volumetric fraction produced curves that were less than 15% below the 6% curves. The continental aerosol was a homogeneous sphere (m = 1.43 − 0.0035i as per Remer et al. [1999]). (b) αf versus τa for the μr = 1.5, smoke case of Figure 1a and different rates of average abundance increase (〈γ〉 = d log A/d log reff; see Appendix B for details).

[12] The dependence of αf on τa can be expressed analytically (compare Appendix B). Figure 1b shows computations applied to a subset of the Mie simulations of Figure 1a for an illustrative example (in this particular example we imagined an influx of particles whose rate of change of effective radius was proportional to the abundance (dreff/dt = KA) and that the abundance was in turn linearly dependent on time (dA/dt = constant); in such a case, γ, the rate of relative increase of abundance to reff, is equal to [dA/dt × reff]/[KA2]). The slopes of these curves are dependent on the mechanism which increases τa; the decrease in αf for the steepest slope of Figure 1b is due to a pure increase in particle size, while the progressively smaller slopes are due to the ever increasing contributions of aerosol particle number. The magnitude of the rates of increase of reff, which were employed to produce this figure, was inspired by typical rates for aged smoke [Reid et al., 1998]. For the three nonzero slope examples, a regression through the curves of Figure 1b from τa = 0.1 to τa = 1.0 yielded values of dαf/d log τa = −0.99, −0.64, and −0.45. These values correspond to (average) abundance to particle size change rates of 0.0, 1.5, and 4.2 (the average of the parameter γ = d log A/d log reff defined in Appendix B). At a more approximate but generalized level, equation (B5) of Appendix B permits an order of magnitude estimate of 〈γ〉 given values of dαf/d log τa.

2.2. Sun Photometer Data

[13] The optical data employed throughout this work were extracted from the automated CIMEL Sun photometer/sky radiometers belonging to the AERONET and/or AEROCAN network (the AEROCAN network is a Canadian subnetwork of AERONET). In solar extinction mode the CIMEL operates in seven spectral bands (340, 380, 440, 500, 675, 870, and 1020 nm plus a 940 nm water vapor band), and in sky radiance mode, it scans off the solar disk to acquire sky radiance data at four wavelengths (440, 500, 675, and 1020 nm). Details concerning the operations and data processing logistics of this network are given by Holben et al. [1998].

[14] In this work we largely limited ourselves to the extinction mode data and excluded the 340 nm band from the seven bands given above since this band is typically more susceptible to errors than the other bands. Formal inversions of extinction and sky radiance were available [Dubovik and King, 2000] but represent a different, much smaller data set. Although some of the inversion data are presented below, we concentrated on the more conventional extinction data given its more robust statistical weight and given that any aerosol content and (average) size trends can be monitored from the purely optical parameters. These parameters also have the added advantage of being more easily comparable with other observations.

[15] The first step in our analysis technique was to visualize the five standard optical parameters as a set of four graphs with τa being the dependent variable for α, α′, αf, and η, respectively (compare Figure 4). This type of representation is an extension of the traditional α versus τa graph wherein particle type and particle number information are presented simultaneously as a two-dimensional histogram in order to facilitate discrimination between different classes of particles [e.g., Kaufman and Fraser, 1983]. An intensive analysis of these quartets of graphs then led to the production of summary trend statistics, which we present in this paper.

[16] In Appendix A we give details on the weighting scheme used to quantify confidence levels in α, α′, αf, and η. Because most work on the Angstrom exponent is based on a (classical) multiwavelength exponent derived from a spectral regression, we also derive an empirical relation between our monochromatic exponent and the classical exponent.

3. Climatological Optical Data in Western Canada

[17] General Sun photometry measurements without a specific focus on smoke aerosols have been carried out in Canada over a period that extends at least from the initial deployment of the BAPMoN network Sun photometers in the early 1970s [Forgan et al., 1993]. A number of papers whose objective was to characterize the general climatological behavior of the aerosol optical depth and often the Angstrom coefficient were written in subsequent years [Gueymard, 1994; Smirnov et al., 1994, 1996; Markham et al., 1997; Fedosejevs et al., 2000]. Mention should also be made of the much longer climatological records obtained from turbidity (panchromatic) data [Yamashita, 1974; Polavarapu, 1978; Freund, 1983; Uboegbulam and Davies, 1983; Gueymard and Garrison, 1998].

3.1. Links Between Forest Fire Smoke and Aerosol Optical Depths

[18] Holben et al. [2001] reported on the general aerosol optical depth statistics of the AERONET site at Thompson, Manitoba, and qualitatively linked this behavior to forest fire activity. This site is on the northern edge of the boreal forest zone and is regularily affected by smoke plumes of western Canadian forest fires during the fire season. Holben's multiyear statistics showed substantial variation of the aerosol optical depth which they attributed mostly to forest fire smoke. The basis for this observation was the multiyear TOMS estimates of smoke coverage [Hsu et al., 1999] and a general knowledge of the predominant aerosol influences. Li et al. [1997] made a similar observation from qualitative comparisons of Sun photometer data and the known presence of smoke observed in AVHRR imagery.

[19] Figure 2a is a plot of total hot spot counts for all of western Canada as detected using AVHRR thermal imagery [Li et al., 2001]. Hot spot count is closely related to the more relevant parameter of area burned [Fraser et al., 2000]. Figures 2b and 2c are plots of the geometric mean (τa,g) and geometric standard deviation (μτ) [O'Neill et al., 2000] of the aerosol optical depth at 500 nm computed for summer ensembles of data (June, July, and August) at the Thompson, Manitoba, site and a second site at Waskesiu, Saskatchewan, from 1994 to 1999 (details on the lognormal distribution are given by O'Neill et al. [2000]). In spite of the spatial disparity in comparing a regional variable with essentially point variables the level of correlation between hot spot counts and τa,g (or μτ) is significant or close to significant at the 0.05 confidence level. In particular, one can observe the large values of τa,g and μτ in the active fire years of 1994 and 1995 and the correspondingly low values in the relatively fire-free (wet) year of 1997. The corresponding correlation coefficients (R) between τa,g and the hot spot count over all years were 0.69 and 0.85 for Thompson and Waskesiu, respectively, while the analogous coefficients for the geometric standard deviation μτ were 0.91 and 0.65. Such correlations provide independent if circumstantial support of the observations of Holben et al. [2001] concerning the dominance of biomass burning aerosols on the optical depth variation observed at Thompson.

Figure 2.

(a) Hot spot count for western Canada versus year. (b, c) Geometric mean and geometric standard deviation of τa for the Thompson and Waskesiu sites versus year. The averaging period is the summer months of June, July, and August (λ = 500 nm; optical data are cloud screened and error weighted).

[20] The 1997 case serves as benchmark from which one can estimate the background statistics of optical depths for aerosols other than smoke during our nominal 3-month summer period of June, July, and August. The values of τa,g and μτ were 0.08 and 1.6 and 0.07 and 1.8 for Waskesiu and Thompson, respectively. The modal values of 0.055 and 0.056 (peak of a lognormal fit on a linear τa axis) are lower than the value of 0.087 estimated from a lognormal fit to the summer data of Smirnov et al. [1996] for Wynyard, Saskatchewan. If, however, one applies their synoptical air mass theory and their all-season, synoptical air-mass–dependent histograms to estimate a weighted modal average (based on the frequency of occurrence of different synoptical air masses during the summer) then the value obtained is 0.067.

[21] Further to the generic approach represented by Figure 2, a sectorial correlation analysis was performed for each summer period of each year to determine which sector or sectors provided the best correlation coefficient with τa,g. In this case the regression space consisted of the nine temporal bins (of 10-day composite data) stretching across the June, July, and August summer period. R values were computed for all 63 possible hot spot combinations of six individual sectors: Sasketchewan, Manitoba, the Northwest Territories, Alberta, Yukon, and Nunavut (British Columbia was excluded to simplify the computations and because it never contributed more than 3.5% of the total number of hot spots in any given year). Figure 3 shows the six sectors as well as the two key Sun photometer sites of Thompson and Waskesiu. The hot spot distribution for 1998 is overlain on this map to illustrate the type of geographical dispersion one obtains for a given year.

Figure 3.

Map of western Canada showing the six sectors and the Thompson and Waskesiu Sun photomer sites. The hot spots for the 1998 burning season (dark grey points) are overlain to illustrate the appearance of a typical hot spot distribution. The hot spot counts for these six regions were used to generate Table 1.

[22] Table 1 shows the highest R values in any given year along with the combination of sectors which yielded the highest correlation. Often, the difference in R was not very sensitive to the addition or exclusion of source sectors to certain fundamental sectors, and the simplest source combination was chosen when differences were less than 0.01. It can be observed that the R values are all greater than 0.7, with the exception of Waskesiu during the clear 1997 background year. It should be noted that Nunavut sources of 1994 represent a questionable result, given the relatively small number of hot spots and because R was a fairly isolated value (the next highest value of R was 0.601 for 14,906 hot spots associated with Saskatchewan, Manitoba, and Nunavut). On the whole, these systematic results clearly imply a significant association between forest fire sources and variations in τa,g; for both stations and all years, an average of 80% of the 10-day composite variation in τa,g can be linked with hot spot activity.

Table 1. Highest Correlations Between τa,g and Hot Spot Count From the Set of 63 Source Sector Combinations Associated With Six Individual Sectorsa
 WaskesiuThompson
RNhs%Source CombinationRNhs%Source Combination
  • a

    See Figure 3 for a map. The R values are computed for the nine temporal bins (10-day composite data) straddling the June, July, and August period. Sask, Saskatchewan; Alb, Alberta; NWT, Northwest Territories; Yuk, Yukon; Man, Manitoba; Nun, Nunavut; Nhs is number of hot spots associated with the maximum correlation coefficient; % refers to number of hot spots for the most significant combination of the given year relative to the total number of hot spots for that year.

1999    0.967372140.0Sask, Man, Alb
19980.716597532.4Sask, Alb0.884253013.7Man
19970.495251.9Sask0.86460645.5Man
19960.803282057.1Sask, NWT0.822344.7Sask, Alb
19950.7432131552.3NWT, Alb0.89440763100.0Sask, NWT, Yuk, Nun
19940.9421352333.5Mani, Yuk, Nun0.7247311.8Nun

3.2. Trends in Angstrom Exponents

[23] Figure 4 shows an example of the standard optical parameter graphs for 1996. The error bars are indicators of weighted data variance (see Appendix A), while the number of samples/bin which contributed to the computation of the weighted means and variances are indicated in the bottom left-hand graph of each quartet. These quartets of graphs were computed for all sites and all years and served as an intermediate analysis tool from which regression statistics versus τa were derived and analyzed. It was found that these results were fairly robust and would survive, for example, a change from third to second order of the polynomial fit, which was applied to all ln τa spectra.

Figure 4.

An illustration of the five standard optical parameters for the case of Thompson 1996. The error bars are estimates of standard deviation for the 10 equimeasurement bins across which the statistics were computed. The dashed lines for α and αf are weighted linear fits, while the dashed line for η is the ratio (α/αf) of these linear fits.

[24] The data of 1996 were unique in that a histogram of α values showed an extreme case of bimodality that was suggestive of a strong influence of thin cloud (one of the α modes was near zero). The cloud-induced mode is the cause of the rapid decrease of α and η with increasing τa as well as the large variances at large τa. It should be emphasized that the cloud-screening algorithm does not guarantee cloud elimination since the criterion employed for optical depth elimination is largely based on temporal excursions in magnitude and not on spectral dependency. Smirnov et al. [2000b] purposely did not include spectral dependency as a cloud flag criterion in order to minimize the possible exclusion of legitimate large-particle optical depths such as those due to dust events. Spatially homogeneous thin cloud events can thus survive the cloud-screening process.

[25] Figure 5, which shows yearly summer averages of αf and α for both Waskesiu and Thompson at large τa (unity), demonstrates the consistency of the αf estimate; the low values of the α averages observable in 1996 and 1997 are most likely the result of (spatially homogeneous) thin cloud contamination, while the relatively stable values of αf suggest that the cloud contamination is largely filtered out.

Figure 5.

Total and fine mode Angstrom exponents, at τa = 1.0, versus year for Thompson and Waskesiu (λ = 500 nm, cloud-screened and error-weighted data). These four curves correspond to the four columns of the regression parameter “b” in Table 2 (under “α” and “αf” for Thompson and Waskesiu, respectively).

[26] Figure 6 illustrates the systematic nature of the decrease in αf with increasing τa which was observed for nearly all years. On average, for both sites, the decrease between τa = 0.1 and τa = 1.0 corresponds to a αf change from about 2.2 to 1.6 (dαf/d log τa ∼ −0.6) or hence a value of 〈γ〉 near 2 (〈d log A/dreff〉 of equation (B5)). From the variation of all the curves of Figure 1a, this change in αf corresponds to a rough increase in reff from about 0.09 to 0.15 μm (where the uncertainty associated with the range of all the curves is about ±0.03 μm). The significant exception to this trend is clearly Thompson 1998, where both α and αf were practically constant and equal across all values of τa (η was always near unity). This trend was found to be very robust (reasonably independent of changes in spectral polynomial order and omitted wavelengths, for example) and thus appears to be significant. It would correspond to conditions dominated by fine mode optics where changes in optical depth are for the most part due to changes in particle number rather than particle size. Table 2 summarizes the trends of both α and αf versus τa in terms of three parameters which result from a linear-log fit to the weighted data (typified by Figure 4). With the notable exception of Thompson 1998, the slope parameter (a = dαf/log τa) is typically more negative for heavy smoke years (1994 and 1995) than for low-turbidity years (1997).

Figure 6.

Fine mode Angstrom exponents (regressed to τa = 0.1 and τa = 1.0) versus year for Thompson and Waskesiu (λ = 500 nm, cloud-screened and error-weighted data). These curves correspond to the regression parameters “c” and “b” under the heading “αf” in Table 2.

Table 2. Yearly Regression Statistics of α and αƒ Versus τa and the Mean and Standard Deviation of η
 Nbinααfη
abcσ(α)abcσ(αƒ)〈η〉σ(η)
  1. a

    (1) Nbin = number of data points per sampling bin. There were 10 sampling bins per α versus τa curve (compare Figure 4). (2) α = a log10a) + b and therefore a = dαf / logτa, b = α(1.0), c = ba = α(0.1) , σ(α) is the standard deviation from the linear regression. The same regression parameter notation is used for αf. (3) 〈η〉 and σ(η) are the mean and standard deviation across the ten τa sampling bins (compare Figure 4).

Thompson
19941210.041.441.390.10−0.61.62.20.060.760.09
199584−0.41.11.50.15−0.441.652.090.100.770.04
1996162−1.80.32.10.17−0.891.822.710.040.610.16
199776−1.10.61.70.18−0.351.812.160.040.850.06
199886−0.21.51.70.04−0.041.511.550.061.020.05
199954−0.21.51.80.17−0.341.922.270.100.800.04
 
Waskesiu
19941390.01.371.370.09−0.91.442.3660.090.690.1
1995124−0.31.321.610.15−0.491.592.080.050.840.06
1996155−10.771.810.2−1.021.652.670.090.630.08
1997153−0.71.121.790.11−0.32.232.5230.060.720.04
1998172−0.51.361.830.04−0.731.702.420.030.80.04

[27] This type of αf decrease is consistent with the findings of Reid et al. [1999] for Brazilian forest fires and those of Eck et al. [2001], who indicated a tendency toward increasing accumulation mode particle size with increasing τa for African biomass burning aerosols. Similar trends have also been observed for more continental accumulation mode aerosols [O'Neill et al., 2001b]. The use of an Angstrom exponent constrained to short wavelengths in the two former papers yields an exponent that is similar to the fine mode Angstrom exponent employed in the present work since the fine mode optical depth increases in relative importance with decreasing wavelength (η → 1).

[28] The result is also supported indirectly by Westphal and Toon [1991] who pieced together a graph of (classical) Angstrom exponent versus smoke age to demonstrate a decreasing tendency. The equivalence between a trend versus smoke age and a trend versus optical depth is justifiable if one presumes that a significant proportion of τa changes are due to the increasing size of aging particles (as opposed to an influx of similarly sized particles). Figure 1b shows how variations in slope can occur; the slope dαf/log10τa changes from a minimum of ∼−1 for pure particle growth (case of 〈γ〉 = 0) to values that progressively approach zero as the effects of particle influx become more important than particle growth. The three examples are governed by realistic rates of particle growth, abundance to particle growth rate (γ), and by the assumption that the particle growth rate varies as the number density or abundance [Reid et al., 1998, 1999]). The values of the slope obtained encompass the slope values (relative to αf) in Table 2 and as such lend illustrative support to a general trend involving fine particle growth in the presence of differing degrees of abundance increase.

4. Focus on Smoke Events During the First Two Weeks of August 1998

[29] Figure 7 shows the six Sun photometer stations whose data were employed in this portion of the study as well as important forest fire sources that were active during the first two weeks of August 1998. The location and qualitative strength of these sources were identified from AVHRR imagery using algorithms for detecting fire hot spots [Li et al., 2000] and smoke plumes [Li et al., 2001]. A local fire which does not appear on this map but which probably had local effects on the Sun photometry of the Waskesiu station and which could be seen in the AVHRR imagery occurred near Crean Lake about 30 km north of the Waskesiu site (P. Pacholek, personal communication, 2000).

Figure 7.

Major forest fire sources during the 2-week smoke events of 1998 (circles) and Sun photometer stations where smoke data were acquired. The codes for the major forest fire sources are given in Table 3.

[30] Table 3 is a compilation of smoke events seen by the Sun photometers at the different stations and referenced to the probable source of the smoke. The source column is a three-digit code for the fire source whose geographic location can be seen in Figure 7. Column 4 (D) is an estimate of the distance between a source fire and the Sun photometer station. Column 5 (Δt) is the approximate temporal range of the smoke event at a given station, while the following columns give the optical statistics (means and standard deviations). Columns 17 (reff) and 18 (ω0) (single-scattering albedo) are averages of inversion data. Generally, only one to a few values of reff and ω0were available during the time period Δt (in particular for ω0, which requires rather large optical depths to achieve reasonable error levels [Dubovik et al., 2000]).

Table 3. Parameters and Statistics for 1998 Smoke Events
Aug.StationSourceD, kmδt, UTNτa,gμτασ(α)α′σ(α′)αfσ(αfησ(η)reff, fωoImagery Supporta
  • a

    A, AVHRR; T, TOMS; G, GOES 10.

  • b

    Salmon Arm and August 9 Waskesiu cases (in italic type) could not be satisfactorily linked to the Sun photometry on the basis of the smoke assessment criteria (these cases were not used in the statistical computations in the main text).

Nearby Sources: Crean Lake (Cobra)
7WaskCRL327.50–7.60100.421.151.890.011.330.171.810.071.040.030.1360.99A
11WaskCRL3211.84–12.02160.331.161.950.040.930.161.990.070.980.020.1380.97A
 
Lower Lake Athabasca Fires
9Waskb 3449.509.62110.191.121.50.041.450.271.430.131.050.060.117 A, T
10WaskCLS30610.55–11.00400.231.181.830.080.680.381.970.120.940.070.137 A, T
12ThomCLS51612.81–12.91100.951.31.20.120.860.331.40.090.890.1 0.85T
 
Slave Lake Fires
11WaskSLL60611.55–11.64120.31.231.650.021.080.11.680.040.980.020.140.98A, T
12WaskSLL60612.91–13.05130.61.281.70.11.480.181.590.141.070.040.170.99T
 
Distant Source: Great Bear Lake Fires
4ThomGBL18804.60–4.80180.841.291.480.081.820.081.280.11.140.020.129N/AT
4ThomGBL18804.9–5.05140.431.161.620.091.90.11.320.071.140.030.1560.92T
8HowlGBL40878.55–8.91340.231.121.520.080.880.251.640.050.930.060.148 T
 
Lower Lake Athabasca Fires
11BondCLS224911.59–11.72130.561.131.320.161.250.251.310.0710.080.1510.89G
11BondCLS224911.77–11.9131.061.061.31.011.940.031.060.011.200.1360.93G
12EgbeCLS229912.46–12.60200.261.481.30.152.010.471.250.251.070.10.180.73T
13SherCLS266413.56–3.75190.321.481.680.031.510.091.560.051.070.020.1590.98T
13SherCLS266413.75–13.96250.381.261.390.212.170.341.410.181.090.050.1640.96T
 
Salmon Arm, B.C.
7Thomb 17977.51–7.74140.291.11.590.071.270.091.560.091.020.04N/A T
7Thomb 17977.74–8.01140.662.011.470.191.590.731.510.171.010.161.430.9T

[31] In order that a particular sequence of Sun photometer measurements be declared a smoke event, a number of criteria had to be satisfied. The back trajectory analyses had to indicate that the trajectory path at one or more of four pressure levels passed over the smoke sources indicated in Figure 7 and that the source was active at the corresponding time. All sequences declared to be smoke events were normally supported by TOMS imagery. AVHRR imagery and Meteosat imagery were used to support TOMS imagery and, on certain occasions (Bondville, Illinois, and Crean Lake, Saskatchewan), were the only imagery available for a smoke event. The smoke discrimination criteria defined in Appendix C were used to check that the (noncloud screened) data defined as smoke was contained within certain bounded regions of α versus τa and dα/dτa versus τa.

[32] Figure 8 shows the temporal variation of the hot spot count as well as τa,g and μτ for the summer of 1998 (the sampling in this case is over 10-day composites). The sectorial sources for the hot spot numbers (Manitoba for Thompson and Saskatchewan and Alberta for Waskesiu) were deduced from the best correlation coefficients (compare Table 1). The 2-week period that we employed to focus on smoke events at our six stations is shown between the dotted lines.

Figure 8.

(a) Hot spot count for Manitoba sources (Thompson) and Saskatchewan and Alberta sources (Waskesiu) as a function of 10-day composite bin intervals over the summer months of June, July, and August 1998. (b, c) Geometric mean and geometric standard deviation for the Thompson and Waskesiu sites (λ = 500 nm; optical data are cloud screened and error weighted).

[33] Figure 9 shows an interesting example of the data sources brought to bear to identify a smoke event. In this particular case, smoke plumes from forest fires near Slave Lake, Alberta, traveled south on August 10 and then, according to the back trajectories, were transported west toward Waskesiu on August 11. Figure 10 shows the back trajectories referenced to the Waskesiu site along with TOMS imagery and AVHRR smoke-enhanced imagery. The plume effect is evident in both sets of imagery and is suggested in the peaking of the Sun photometer data around 11.7 UT. The fact that the more local sources of smoke are not seen in the TOMS imagery is consistent with the reported low-altititude aerosol insensitivity of this sensor. One can observe that the optical depths remain relatively large in the afternoon; this suggests, given the back trajectory analysis (not shown) and the AVHRR imagery, that the Crean Lake local source is the cause of the afternoon smoke event. The value of the α, which is systematically larger in the afternoon than in the morning, indicates the presence of smaller aerosol particles in the afternoon and, from a pure standpoint of the distance dependence discussed below, that the afternoon aerosol is of a local nature.

Figure 9.

AVHRR smoke-enhanced data for the day preceding a smoke event at Waskesiu (10 August 1998). Bands of smoke from Slave Lake can be seen to be drifting south.

Figure 10.

TOMS, AVHRR, back trajectory data, and Sun photometer data on 11 August 1998. The time unit is the day in August plus fractions of the day in UT. The TOMS equatorial crossing time is 1140 CST (1172 UT), while the AVHRR equatorial crossing time is 1430 CST (1185 UT).

[34] Table 4 lists the α versus τa statitistics for all Sun photometer smoke events clumped indiscriminantly together. In spite of the geographic disparity of the sites relative to the sources, some resemblance between these latter graphs and the summer statistics of Thompson and Waskesiu is evident. A trend of decreasing αf with τa similar to the trends typified by Figure 4 and the results of Table 2 yielded a value of dαf/log10τa ≅ −0.5 and a value of 〈γ〉 near 3 (〈d log A/dreff〉 of equation (B5). In this case, however, η was close to unity across the range of τa since the points had been carefully selected to represent fine particle smoke optical depths (in Table 4, the average across the 10 τa bins was 〈η〉 = 0.99). An estimate of the corresponding change in reff, assuming an average of the smoke curves in Figure 1a, is roughly 0.10 to 0.15 μm (where the uncertainty associated with the range of all the smoke curves is about ±0.01 μm).

Table 4. Regression Statistics of α and αf Versus τa and the Mean and Standard Deviation of η During the 2-week Period in August 1998a
All Stations
Nbinα7alpha;fη
abcσ(α)abcσ(αf)〈η〉σ(η)
  • a

    All smoke points from all stations are treated as one ensemble population. See footnotes of Table 2 for details.

15−0.381.451.830.12−0.481.451.930.080.990.08

[35] Figure 11a shows plots of the decrease in average fine mode Angstrom exponent versus distance from the forest fire source and Figure 11b the increase in reff versus distance. The latter parameter was derived from radius averages applied to the fine mode component of the size distributions retrieved from solar and sky radiance inversions [Dubovik and King, 2000]. For Figure 11a we note a decrease in the dashed regression line from about 1.9 at 30 km to 1.4 at 2000 km. The regression line through the inversion results yields an increase in reff from about 0.13 to 0.15 μm between 30 and 2000 km. The associated estimates using averages of the smoke curves in Figure 1a are again roughly 0.10 to 0.15; the differences are in part due to the more comprehensive computations involved in the inversion procedure but are also very likely related to the relatively small number of points involved in the inversions).

Figure 11.

(a) αf versus distance and (b) reff versus distance for the data of Table 3.

[36] An analysis of mechanisms which might induce the trend toward larger particle size with increasing distance requires caution, given the disparity of sources and the complexity of smoke dispersion over thousands of kilometers. However, the trend is systematic and has similarities with the observations made above concerning the decreasing trends in αf. In particular, the results are coherent with the observations of Westphal and Toon [1991], Kaufman et al. [1998], and Liousse et al. [1995] concerning the decrease of the Angstrom exponent with smoke aging and those of Reid et al. [1998] who demonstrated an increase of smoke particle size with aging for Brazilian forest fire smoke.

[37] The back trajectories for the smoke events defined in Table 3 indicated that the travel times would vary from less than a day for the near-source cases to 4–5 days before the Great Bear Lake and Lower Lake, Athabasca, smoke plumes arrived at the eastern Sun photometer sites. In their analysis of Brazilian forest fire smoke, Reid et al. (ibidem) suggested that the principal mechanisms for the growth of regional smoke particles (1–4 days old) was condensation as well as particle coagulation and that after about 3 days of aging, coagulation would probably become the dominant mechanism. They also pointed out that condensation was more likely associated with high volatility organic species than water vapor since the influence of the latter was demonstrated to be weak [Kotchenruther and Hobbs, 1998]. A significant proportion of the condensation-induced particle growth was ascribed to cloud processing. Kaufman et al. [1998] pointed out that the size distribution of Brazilian smoke particles was fairly stable after about 3 days of aging; Remer et al. [1998] exploited this fact by employing optical depth measurements as a means of estimating cloud condensation nuclei (i.e., by assuming that changes in optical depths were mostly due to changes in number of smoke particles rather than size).

5. Conclusions

[38] Aerosol optical statistics for two western Canadian Sun photometer stations were analyzed for summertime data acquired between 1994 and 1999. It was demonstrated that a significant correlation exists with forest fire frequency indices (hot spots). This correlation indicates that on average, 80% of summertime optical depth variation in western Canada can be linked to forest fire sources.

[39] The average values of the geometric mean and standard deviation of τa(500 nm) was found to be 0.074 and 1.7, respectively, for the clearest, relatively smoke free year of 1997, while the values for the heaviest smoke year of 1995 were 0.23 and 3.0, respectively. The average (linear scale) modal value for the clearest year of 1997 was near 0.06.

[40] A new spectral technique for estimating the fine-particle Angstrom exponent (αf) and the optical fraction of fine mode aerosols (η) was employed to extract the contributions of fine mode aerosols from the generic Angstrom exponent (α) and its spectral derivative (α′). This technique is particularily relevant to the isolation of fine mode smoke properties at small to moderate optical depths (at large distances from the forest fire source, for example) and in cases where homogeneous thin clouds contaminate the smoke optical depths. It could well be applied to the analysis of thin optical depth smoke in other regions such as South America and Africa where (as in the current study) spectral Sun photometry data are much more abundant than the combined Sun photometry and sky-scanning data employed to invert for particle size information.

[41] Systematic observations of decreasing αf with increasing τa were noted; the average slope (dαf/d log τa) being of the order of −0.6. This rate of decrease corresponds roughly to an abundance to particle size rate increase (〈γ〉 = d log A/d log reff) of ∼2 and, in the absence of any a priori particle-type information, an increase in effective particle radius (reff) from about 0.09 to 0.15 μm.

[42] A 1998 series of forest fire events were tracked using TOMS, AVHRR, and GOES imagery, back trajectories, and the optical depth data measured at six Sun photometer sites across Canada and the eastern United States. This data set provided a reference in terms of known smoke optical depths for the climatological statistics deduced for Thompson and Waskesiu. The results show similar rates of decrease of αf with increasing τa: an average slope ∼−0.5, an abundance to particle size rate increase ∼3, and a corresponding reff increase from approximately 0.10 to 0.15 μm). An analysis in terms of source to observation distance showed a decrease in αf and an increase in reff with increasing source distance. This observation was coherent with previous studies on the particle growth effects of aging.

Appendix A: Data Processing Issues

A1. Data-Weighting Considerations

[43] In all averaging schemes involving the standard optical parameters (α, α′, αf, and η), weights were assigned to a given parameter “x” according to the expression

equation image

where εc is a threshold error and εx is the error in the parameter “x” associated with the quadrature sum of the estimated instrumental error in τa plus the residual error between the third-order spectral polynomial in τa and the measured value of τa at 500 nm. One can appreciate the necessity for both terms of quadrature sum given that a perfect polynomial fit is no guarantee that the data are error free. The threshold error εc is needed to exclude inordinately large weights being assigned to τa spectra associated with spuriously small errors. The magnitude of εα and εα′ were estimated using the expressions in the work of O'Neill et al. [2001b, equation (10)], while εαf and εη were derived from differential relations related to εα and εα′. It is noted also that in the case of αf a damping weight was activated when the value of αf exceeded the physical limits permitted for this parameter [O'Neill et al., 2001a]. This situation often occurred when a particular band was known to be suspect.

A2. Relationship Between the Classical Angstrom Exponent and the Monochromatic Angstrom Exponent at 500 nm

[44] The classical Angstrom exponent (wavelengths 440, 500, 675, and 870 nm) is a standard of AERONET publications [e.g., Holben et al., 2001], and thus it follows that the interrelationship with the mononchromatic (500 nm) α defined above must be established. It is noted that the AERONET Angstrom exponent is itself not a universal standard and that there are a variety of multiwavelength exponent regressions reported in the literature.

[45] The multiwavelength formulation of the AERONET exponent (αclassical) suggests that it should be proportional to α and, in a second-order sense, to α′. Table A1 shows some regression results between αclassical and α for (1) Mie simulations over a variety of lognormal fine mode particle size distributions and a variety of refractive indices and (2) the Waskesiu and Thompson data ensemble defined in section 3 below. The exponent αclassical in the case of the fine mode Mie simulations is always greater than α since the Angstrom exponent typically increases with wavelength [Eck et al., 1999], and thus a positive bias is necessary in the case of the zeroth-order expression of Table A1. In the case of the real Sun photometer data, one expects a variety of curvatures (a variety of α′ values), and no strong bias exists or is expected if no discrimination in optical depth magnitude is made. If such regressions were tied to classes of optical depth magnitude there would be more of a tendency for a positive bias at large τa since an increase in this parameter often coincides with an influx of fine mode particles.

Table A1. Expressions for αclassical and Associated RMS Errorsa
 0th Order in α′RMS Error1st Order in α′RMS Error
  • a

    αclassical = α + k0 + k1 α′ where α and α′ are evaluated at 500 nm.

  • b

    Twenty-nine different lognormal size distributions of varying size parameters, real and complex refractive index [O'Neill et al., 2001a].

  • c

    Average of (weighted) yearly regressions for all the multiyear data of section 3.

Mie calculationsbα + 0.2750.081α + 0.209 α′0.038
Thompson and Waskesiuα0.23α + 0.15 α′0.17
data ensemblec    

Appendix B: Theoretical Expression for dαf/d log τa

[46] In the case of a pure fine mode aerosol component, one can express the aerosol optical variation in terms of the differential

equation image

where A is the abundance (aerosol particle number per cm2 or μm2 of atmospheric column), Cext is the average extinction cross section in cm2 or μm2 of the total size distribution over altitude, and τa = ACext. If we suppose that the rate of increase of reff is some function of A (linked by time in the case of diurnal events) then the differential dαf can be normalized by the differential of d log τa to yield the general derivative

equation image

relationship, where the logarithm is to the base 10 and where τ*a = A0Cext is the increase in optical depth due to an increase in particle size only (due to an increase in Cext only, with A fixed to some initial value A0). Given that Cext is positively correlated with reff, equation (B2) shows explicitly that for an increase in reff and a positive correlation between reff and A, the slope dαf/d log τa* is the maximum magnitude of dαf/d log τa. Equation (B2) can be further recast into a form that is more directly linked to variations in reff and A;

equation image

where

equation image

and where we have used the approximation

equation image

The parameter γ is a unitless variable representing the relative variation of the abundance A with respect to reff. The constant “k,” which describes the relative variation of Cext with respect to reff, is a typical empirical result for fits to Mie-scattering computations applied to lognormal size distributions. It is moderately dependent on the refractive index and the size distribution width of the aerosol which induces changes in the local optical depth. The form of the numerator in equation (B3) was inspired by previous studies, which indicated that αf was approximately linear with log reff [e.g., O'Neill and Royer, 1993]. It is also moderately dependent on the refractive index and the size distribution width. It is noted that (as equation (B3) implies) the time element is not fundamental to the production of the curves in Figure 1b; what is important is how reff varies with A. An approximation that is commensurate with regressions through the αf versus log10τa curves is to work with averages (across τa) in equation (B3);

equation image

so an estimate of the average rate of change of αf versus log τa can be used to infer the relative rate of change of abundance versus reff;

equation image

where dαf/d log reff and k have been replaced by their nominal values for the smoke (μτ = 1.5) case of Figure 1a but where the deviations from dαf/d log reff and k are less than 15% and 25%, respectively, for all the cases shown in that figure.

[47] One final note is needed in order to apply these results to measured data. The equations above were developed for a single fine mode aerosol and so one should strictly plot αf versus τf to analyze the interplay of fine mode number density and size effects. However, to miminimize potential artifacts due to overprocessing and to maintain a standard τa axis (comparable to other work), we selected τa as the abscissa rather than τf. This is actually not a critical issue since the slope of αf versus τf is close to the slope of αf versus τf in the absence of large changes in η. Given that all variables are uniquely related as a function of time (that they are functions of each other), one can express the relationship between the two slopes, as below;

equation image

which shows explicitly that the two slopes are indentical if η = constant. A survey of our results indicated that changes in η (for τa between 0.1 and 1.0) rarely exceed the limits of 0.5 and 1.0 and were limited to a standard deviation range confined to values between 0.7 and 1.0. This yields equivalent logarithmic ranges of ± log (1.4) and ± log (1.2) and d log(η)/d log τa values of 30% and 16%, respectively.

Appendix C: Issues Related to Cloud Screening Versus Smoke Discrimination

[48] The transformation from α to αf represents a form of cloud filtering in its own right. However, to address the issue of cloud screening versus smoke discrimination in the analysis of the August 1998 smoke events, we chose to work directly with α and in so doing to reduce the processing chain involved in cloud-screening/smoke-discriminating algorithm to a minimum. The results in this appendix represent a developmental effort at finding a smoke-discriminating algorithm based on simple physical concepts and built on the independently assessed 1998 smoke data.

[49] Note that smoke discrimination is somewhat of a misnomer in that the real objective was to discriminate “noncloud” τa in order not to eliminate potential smoke data in any study of smoke statistics. The discrimination criteria, which are presented below, are confined to an appendix because they were not used in the climatological study of section 3 and because they were only used to check the veracity of the smoke label in section 4; they amount to a necessary condition for smoke but not a definition of smoke.

[50] Differentiating equation (1a) with respect to τa yields

equation image

where

equation image

In the presence of thin temporally variable cloud, τc is variable and τf is constant. Expressions (C1) and (C2) accordingly reduce to

equation image

where the partial derivative notation has been dropped for the sake of simplicity. Equation (1a) can be rewritten in a similar manner by eliminating τc;

equation image

These expressions show analytically that we expect α to always decrease in the presence of a cloud-induced increase in τa. A range of values can be associated with the numerators of equations (C3) and (C4) and accordingly bounding expressions to identify thin cloud events can be defined. In addition to this essentially temporal criterion, one can impose a nontemporal criterion on α; based on Mie computations such as those of Figure 1, we set this to be α < 1 for cloud-contaminated optical depths.

[51] Figure A1 shows an example of these bounding expressions in α and dα/dτa applied to all the data acquired at Sherbrooke, Quebec, in the first two weeks of August 1998. The left-hand graphs show α versus τa, while the right-hand graphs show dα/dτa versus τa. The upper pair of graphs are data which have not been cloud screened according to the standard procedure defined by Smirnov et al. [2000b], while the bottom pair is cloud screened. The upper bound in α (which is beyond the scale of the graph) and the lower bound in dα/dτa are rather loosely defined according to whatever value of τf one chooses to define as a maximum.

Figure A1.

Sample of cloud discrimination criteria applied to data that have not been cloud screened according to the standard prodedure (top pair of graphs) and which have been cloud screened using the standard procedure (bottom pair of graphs). The bounding conditions (solid lines) which define thin cloud conditions are given by 0.07 < τa α < 4.2 on the α versus τa graphs and −0.07 / τa2 > dα/dτa + Δ(dα/dτa) and dα/dτa − Δ(dα/dτa) > − 4.2 / τa2 on the dα/dτa versus τa graphs. The derivative dα/dτa is computed from the ratio [dα/dt]/[dτa/dt].

[52] The circles represent data without restrictions, while the crosses represent values (including error bars) which fit into the cloud-bounding expression for dα/dτa. The solid grey circles represent data which were defined as a smoke event according to independent information (TOMs, back trajectories, etc.). One can note that the smoke event points are not defined as cloud (neithor in terms of the α or the dα/dτa criteria) and that a significant number of generic points are allowed into the dα/dτa cloud zone because their error bars extend outside of the cloud boundaries. The standard cloud-screening algorithm does a good job of removing the cross-marked points and points for which α < 1 but also removes points that have not been labeled as cloud for α > 1.

[53] For the 2-week period of August 1998 and all six stations, standard cloud screening eliminated an average of about 48% of data for which α > 1. An average of about 10% of unscreened data points with α > 1 are actually eliminated by the derivative criterion on dα/dτa. If we accept the derivative criterion as a valid indicator of the noncloud label then about 38% of the points eliminated by the standard cloud-screening algorithm for α > 1 should not have been eliminated since they may represent smoke.

[54] Thus the standard cloud-screening algorithm, which includes no spectral filtering criteria, largely succeeds in eliminating thin cloud based on temporal criteria only. It does, however, tend to overeliminate temporally variable data whose spectral behavior suggests that fine mode aerosols (and not coarse mode clouds) are the cause of the variation.

A

abundance (number of particles in an atmospheric column per unit area with typical units of cm−2 or μm−2).

Cext

average extinction cross section of a single aerosol particle (typical units of cm2 or μm2).

αf

instantaneous slope of − ln τf versus ln λ.

αc

instantaneous slope of − ln τc versus ln λ.

α

instantaneous slope of − ln τa versus ln λ; α = αf η + (1 - η)αc.

α′f

instantaneous slope of ln αf versus ln λ.

α′c

instantaneous slope of ln αc versus ln λ.

α′

instantaneous slope of ln α versus ln λ.

η

optical mixing ratio τfa.

γ

relative rate of increase of abundance with respect to reff (equation (B3)).

log

log10.

μ, μr, μτ

μ is the geometric standard deviation associated with a lognormal frequency distribution. If σ(log x) represents the standard deviation of a distribution of parameter x on a log scale then μ = 10σ(log • x); μr and μτ are the explicit representations of this parameter for a lognormal particle size distribution and a lognormal optical depth frequency distribution, respectively (x = r and x = τa); note that μr = exp(σg) of Hansen and Travis [1974].

ωo

Single-scattering albedo.

R

correlation coefficient for a linear regression.

reff

optically effective radius of a size distribution in μm (= rg exp (2.5 ln2μr) for a lognormal size distribution, ibidem); in this paper, reff refers specifically to the fine mode (subscript “f” suppressed for simplicity).

rg

geometric radius of a lognormal particle size distribution in μm (ibidem).

τa,g

geometric mean of a frequency distribution of τa values.

τc

coarse mode optical depth.

τf

fine mode optical depth.

τa

total aerosol optical depth; τa = τf + τc.fs

Acknowledgments

[56] The authors would like to thank the National Research Council, NASA, the National Sciences and Engineering Research Council of Canada, and the Canadian Institute for Climate Studies for their financial support. Valuable in-kind support was obtained from the Canada Center for Remote Sensing (CCRS) and the Meteorological Services of Canada. The contributions of Ilya Slutsker of the AERONET group and Jin Ji-zhong of CCRS are particularly acknowledged.

Ancillary