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Keywords:

  • aerosol;
  • retrieval;
  • SAFARI-2000

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[1] Aerosol optical properties that include the extinction coefficient, single scattering albedo, and asymmetry factor are needed to calculate the radiative effects of aerosols. However, measurements of these properties are typically limited to a few wavelengths, and direct measurements of the asymmetry factor are not available. We describe and evaluate a retrieval methodology that uses commonly collected aircraft-based measurements to derive self-consistent aerosol optical properties for the majority of the solar spectrum. Measurements of aerosol scattering and absorption at three wavelengths are required to constrain this retrieval. We apply the retrieval to vertical profiles of biomass burning aerosol data collected by the University of Washington (UW) research aircraft during the Southern African Regional Science Initiative field campaign (SAFARI-2000) and show that the retrieved (or “optically equivalent”) size distributions and wavelength-dependent refractive indices reproduce available aerosol optical measurements within their respective uncertainties. The retrieved optically equivalent size distribution characteristics are consistent with past studies, but the wavelength-dependent refractive indices retrieved using methods presented in this study are ∼14% (∼50%) greater than the real (imaginary) refractive indices retrieved from the Aerosol Robotic Network (AERONET) for three cases that were spatially and temporally colocated with the UW research aircraft. The retrieval presented in this study translates measured aerosol optical properties to parameters used directly as input to models and can be applied to any study that uses similar instrumentation. Provided that uncertainties are properly accounted for, self-consistent aerosol optical properties derived from measurements strengthen the unique contribution of in situ data collection to the modeling community.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[2] Aerosol optical properties are dependent on the aerosol chemical composition [Jacobson, 2001; Chung and Seinfeld, 2005], the chemical mixing state [Ackerman and Toon, 1981; Chylek et al., 1988], and the physical size distribution [Seinfeld and Pandis, 1998]. These fundamental properties are, however, difficult to fully characterize since aerosol lifetimes are short and the sources are heterogeneous [Bond et al., 2004; Reddy et al., 2005]. The uncertainty of radiative forcing due to aerosols is considered to be the largest source of uncertainty when estimating the sensitivity of climate to an increase in carbon dioxide [Anderson et al., 2003; Schwartz, 2004; Delworth et al., 2005; Hansen et al., 2005] and thus aerosols hinder precise predictions of the future climate [Andreae et al., 2005]. A number of field campaigns designed to characterize aerosol properties in different locations around the world have helped address the uncertainties [Reid et al., 1998; Clarke et al., 2002; Russell et al., 2002; Swap et al., 2003; Doherty et al., 2005; Magi et al., 2005; Quinn and Bates, 2005; Redemann et al., 2006; Schmid et al., 2006].

[3] We describe a new methodology to retrieve aerosol optical properties from look-up tables of precalculated aerosol optical properties constructed using Mie theory [Bohren and Huffman, 1983; Seinfeld and Pandis, 1998; Ackerman and Toon, 1981]. Mie look-up tables can be used to determine the optical properties of an aerosol composed of spherical particles given the aerosol size distribution and complex refractive index. This is a “forward” calculation in the sense that the dependent variables, or the aerosol optical properties, are determined from the aerosol physical and chemical properties (or the independent variables).

[4] Alternatively, as discussed by Hartley [2000], Mie look-up tables can also be used to find an aerosol size distribution and complex refractive index that together produce specific aerosol optical properties. This is the “inverse” problem, where we find the independent variables using the dependent variables, and the solution to the inverse problem may not be unique [Redemann et al., 2000]. In this analysis, similar to the work of Redemann et al. [2000] and Hartley and Hobbs [2001], we present a method to solve the inverse problem and find the so-called optically equivalent aerosol size distribution and complex refractive index that together most closely reproduce available optical measurements. In contrast to those studies, however, we solve the inverse problem at multiple wavelengths.

[5] The goal of this study is to use commonly measured aerosol optical properties for a limited wavelength range, including the extinction coefficient and single scattering albedo, to derive self-consistent aerosol optical properties for a broader wavelength range. We apply the methodology to aircraft-based measurements collected during the Southern African Regional Science Initiative in August and September 2000 (SAFARI-2000) by the University of Washington (UW) research aircraft [Annegarn et al., 2002; Swap et al., 2003]. Descriptions and analyses of the UW aircraft data from SAFARI-2000 were discussed by Hobbs et al. [2003], Magi et al. [2003], Magi and Hobbs [2003], and Sinha et al. [2003]. B. I. Magi et al. (Using aircraft measurements to estimate the magnitude and uncertainty of the shortwave direct radiative forcing of southern African biomass burning aerosol, submitted to Journal of Geophysical Research, 2007, hereinafter referred to as Magi et al., submitted manuscript, 2007) present a method to derive measurement-based estimates of southern African biomass burning aerosol radiative forcing using the methods in this study.

2. Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[6] In this section, we describe the technique used to find the best match between measured aerosol optical properties and aerosol optical properties calculated using Mie theory, which assumes that the particles are spherical. We model the aerosol size distribution with a unimodal lognormal function [e.g., Seinfeld and Pandis, 1998] which is a function of the geometric mean diameter (Dg), geometric standard deviation (σg), and the aerosol number concentration (Na) for a specific range of particle diameters. The wavelength-dependent bulk aerosol complex refractive index (mλ = mr,λimi,λ) describes how incident radiation with a wavelength λ interacts with the aerosol described by the unimodal lognormal size distribution.

[7] Extensive aerosol optical properties, or properties that are dependent on Na, are the wavelength-dependent extinction (σext,λ), scattering (σsca,λ), absorption (σabs,λ), and backscattering (σback,λ) coefficients. Values of σext,λ can be determined by adding σsca,λ and σabs,λ and the wavelength-dependent aerosol optical depth (τλ) can be calculated by integrating σext,λ over some vertical limits [e.g., Hartley and Hobbs, 2001; Magi et al., 2003]. Intensive properties, or properties that are not dependent on Na, are the wavelength-dependent single scattering albedo (ωo,λ), backscatter ratio (βλ), and asymmetry parameter (gλ). In all cases, the “λ” subscript notation indicates the dependence of the particular metric on wavelength, λ. The wavelength dependence of σext,λ, σsca,λ, and σabs,λ are often given by the respective Angstrom exponents (αext,λ, αsca,λ, and αabs,λ) which are defined as the slopes of the optical properties with respect to wavelength on logarithmic scale. All aerosol optical properties discussed in this study are defined by Seinfeld and Pandis [1998] and a number of other widely available sources.

2.1. Description of Look-Up Tables

[8] We store aerosol optical properties calculated using Mie theory in multidimensional look-up tables. The input (Minput) to a well-documented, publicly available Mie scattering code [Dave, 1970; Wiscombe, 1980; ftp://climate1.gsfc.nasa.gov/wiscombe/] is defined as

  • equation image

where the terms are discussed in section 2. The basic output of the Mie scattering code gives the extinction, scattering, and backscattering efficiency factors at a wavelength λ (Qext,λ, Qsca,λ, and Qback,λ, respectively) for a single spherical particle of diameter Dp with a particular refractive index. As described by Bohren and Huffman [1983], we can then integrate Qext,λ, Qsca,λ, and Qback,λ over a range of Dp for the lognormal size distribution given by Dg, σg, and Na in Minput to arrive at the size-integrated optical properties in the output matrix (Moutput) defined as

  • equation image

where the elements of Moutput are defined in section 2 and below. We integrate from Dp,min = 0.01 μm to Dp,max = 10 μm to calculate

  • equation image

where the “x” subscript can mean “ext,” “sca,” or “back” such that we can calculate σext,λ, σsca,λ, or σback,λ, respectively, given the appropriate efficiency factor, and n(D) is specified by the lognormal function defined by Dg, σg, and Na in Minput [e.g., Seinfeld and Pandis, 1998]. Using equation (3), we can calculate ωo,λ = σsca,λ/σext,λ and βλ = σback,λ/σsca,λ. We then calculate the asymmetry parameter (gλ) as

  • equation image

where again we integrate the lognormal function from Dp,min = 0.01 μm to Dp,max = 10 μm.

[9] The ranges of the elements of Minput are listed in Table 1. Although Na for real aerosols varies, the elements of Moutput are calculated using Na = 1000 cm−3. Extensive properties can be rescaled to other values of Na as necessary. This saves computation time and significantly reduces the size of Moutput.

Table 1. Ranges of the Input (Minput in Equation (1)) Used to Build the Aerosol Optical Properties Look-Up Tablesa
ParameterRangeStep SizeNumber of Values
  • a

    This includes the individual wavelengths (λ), the real and imaginary parts of the refractive index (mr and mi, respectively), the geometric mean diameter (Dg), geometric standard deviation (σg), and the aerosol number concentration (Na), with units (if applicable) listed in the table. Bold values of λ indicate in situ measurement wavelengths, while the remaining values of λ correspond to the Sun photometer.

λ, nm354, 380, 449, 450, 499, 525, 550, 606, 675, 700, 778, 865, 1019, 1241, 1557variable15
mr1.4–1.950.0512
mi0–0.1, 0.1–0.60.005, 0.126
Dg, μm0.06–0.9850.02538
σg1.1–3.10.0541
Na, cm−31000N/A1

[10] The ranges of the five remaining dimensions of Minput are larger. The wavelength dimension is set to 15 wavelengths between λ = 354 and 1557 nm, for reasons that we discuss in section 3.1. Each wavelength dimension is treated as a separate look-up table in the sense that we specifically calculate optical properties at each of the 15 wavelengths for the same range of sizes.

[11] There are 12 values of mr between 1.4 and 1.95, and 26 values of mi between 0 and 0.6 in Minput. The ranges are based on information published by d'Almeida et al. [1991] and cover complex refractive indices ranging from water with inclusions to pure soot particles. The lower limit of mr is set at 1.4 because the low ambient relative humidity during SAFARI-2000 [Magi et al., 2003] suggests a small contribution of condensed water to the aerosol composition and therefore it is unlikely that the SAFARI-2000 aerosol bulk refractive index would approach that of pure water (mr,water = 1.33). For more general application, values of mr less than 1.4 should be used. The upper limits of mr and mi are those listed by d'Almeida et al. [1991] for a pure soot particle. However, except in areas close to combustion sources (urban highway, near a cookstove), an aerosol is unlikely to be entirely composed of soot particles [Kirchstetter et al., 2004; Bond and Bergstrom, 2006; Roden et al., 2006].

[12] We use 38 evenly spaced values of Dg from 0.06 to 0.985 μm with intervals of 0.025 μm and 41 evenly spaced values of σg from 1.1 to 3.1 with intervals of 0.1 in Minput. Limiting Dg to values less than 1 μm implies that we are assuming the aerosol size distribution is dominated by submicron particles. Since σg determines the width of the size distribution, the range of σg in Minput implies size distributions that extend beyond 1 μm diameter (for example, if Dg = 0.985 μm and σg = 3.1). Magi [2006] used measurements to estimate the aerosol coarse mode volume fraction as the coarse mode (particles with diameters of ∼1–3 μm) particle volume divided by fine mode (particles with diameters of ∼0.1–1 μm) particle volume and found that during SAFARI-2000, the average coarse mode volume fraction was (3 ± 2)%, which is consistent with general biomass burning particle sizes [Reid et al., 2005a, 2005b].

[13] The distribution of the calculated optical properties in Moutput for five of the 15 wavelengths and the full range of the remaining dimensions of Minput (Table 1) are shown in Figure 1. Each element of Moutput (i.e., σext,λ, ωo,λ, βλ, and gλ) will have 12*26*38*41 = 486,096 possible values for each of the 15 wavelengths. The distribution of ωo,λ shown in Figure 1 has a noticeable dip between about 0.45 and 0.6 that arises from the discontinuity in the resolution of the mi dimension of Minput where, for mi > 0.1, we decrease the resolution from 0.005 to 0.1. The decrease in resolution should not affect retrievals of biomass burning aerosol optical properties since biomass burning particles age rapidly away from the source [Magi and Hobbs, 2003] and values of mi > 0.1 are generally thought to only occur close to combustion sources [Bond and Bergstrom, 2006; Roden et al., 2006]. Adjacent values of the individual elements of Moutput are separated by very small numbers relative to the magnitudes of values, which suggests a nearly continuous spectrum of values. For example, 99% of the values of ωo,λ in the look-up tables are separated by less than 0.000027. The look-up tables were designed to be able to resolve optical properties (Moutput) within typical uncertainties that arise from instrument noise, natural variability, and measurement correction factors [Magi et al., 2003] (also section 3.1).

image

Figure 1. Frequency of occurrence (%) in the look-up tables of the wavelength-dependent extinction coefficient (σext,λ) using Na = 1000 cm−3, single scattering albedo (ωo,λ), backscatter ratio (βλ), and asymmetry parameter (gλ) calculated from the input to the Mie calculations listed in Table 1. The total number of possible values for each optical property at each wavelength (λ) is 486,096. Five of the fifteen wavelengths are shown in each of the figures.

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2.2. Retrieval of Optically Equivalent Properties

[14] The first part of the retrieval finds the optically equivalent unimodal lognormal submicron size distribution (described by Dg,oe, σg,oe, and Na,oe) and the optically equivalent refractive indices (moe,λ) at λ = 450, 550, and 700 nm that together most closely reproduce measured values of σext,λ, ωo,λ, and βλ at λ = 450, 550, and 700 nm. The measurement matrix is defined as

  • equation image

where the “λ” and “z” subscripts indicate the dependence of the measurements on wavelength and altitude, respectively. Similarly, the uncertainty matrix is defined as

  • equation image

where each element of δmeas,λ,z is the uncertainty associated with the corresponding element of ψmeas,λ,z and is derived from measurement uncertainty and natural variability (section 3.1). The matrix of calculated values from the look-up tables are defined as

  • equation image

To solve the inverse problem, we calculate

  • equation image

for each wavelength (λ) and at each altitude (z), where equation image = σext,meas,λ,z, equation image = ωo,meas,λ,z, and equation image = βmeas,λ,z, with analogous definitions for equation image and equation image. To reduce computations, we calculate χλ,z2 only when (equation image)2 < (equation image). All values of χλ,z2 are found for each wavelength.

[15] To further reduce computations, we require the number of possible solutions for each wavelength to be between 20 and 100 by allowing δmeas,λ,z to be flexible. If more than 100 solutions are found at a particular wavelength, we reduce δmeas,λ,z by 5% until less than 100 solutions are found. Similarly, we increase δmeas,λ,z by 10–50% if the number of solutions is less than 20.

[16] We now have a set of possible solutions at each wavelength. The optically equivalent size distribution and refractive indices are defined as

  • equation image

and are determined by searching every combination of the solutions at all the wavelengths for a single size distribution that both minimizes the values of χλ,z2 and minimizes the differences in the size distribution parameters across the three wavelengths. Values of the wavelength-dependent optically equivalent asymmetry parameter (goe,λ) are subsequently determined by Mie theory calculations using the parameters in ϕoe,λ,z.

[17] To retrieve ϕoe,λ,z at a particular wavelength and altitude, we constrain the search with the three parameters specified by ψmeas,λ,z and the corresponding uncertainties in δmeas,λ,z. The number of parameters retrieved in ϕoe,λ,z at a particular wavelength and altitude is five. Thus a one wavelength retrieval is an underdetermined problem (three knowns, five unknowns). However, if we run the retrieval for data at three wavelengths, we have nine known values and nine unknown values since we are searching for a single size distribution (described by three parameters) and a wavelength-dependent complex refractive index (two parameters for every wavelength). Therefore we need measured scattering, backscattering, and absorption properties at least at three wavelengths to derive the optically equivalent size distribution defined by Dg,oe, σg,oe, and Na,oe. These parameters, along with the retrieved mr,oe,λ and mi,oe,λ, can be used to derive the values of goe,λ. The retrieved optically equivalent size distribution can then be used to constrain aerosol optical properties at other solar wavelengths.

2.3. Self-Consistent Aerosol Properties

[18] At other wavelengths where the extinction coefficient and single scattering albedo are available, we can use these information along with the optically equivalent size distribution obtained in section 2.2 to retrieve mr,oe and mi,oe at the other wavelengths. Thus the goal of the second part of the retrieval is to find self-consistent aerosol optical properties such that a size distribution and refractive index at a particular wavelength can be combined to calculate optical properties relevant to radiative transfer calculations. This part of the retrieval accesses the look-up tables differently because we have different inputs to use as constraints. The new measurement matrix is defined as

  • equation image

where σext,meas,λ,z and ωo,meas,λ,z are measurements made at wavelengths where βmeas,λ,z is unavailable, and Dg,oe,z, σg,oe,z, and Na,oe,z are from ϕoe,λ,z in equation (9). The uncertainty matrix is defined as

  • equation image

where δσext,meas,λ,z and δωo,meas,λ,z are the uncertainty associated with σext,meas,λ,z and ωo,meas,λ,z and δDg,oe,z, δσg,oe,z, and δNa,oe,z are determined from the range of values retrieved in ϕoe,λ,z. The matrix of calculated values from the look-up tables is defined as

  • equation image

To find self-consistent aerosol optical properties, we calculate

  • equation image

where we sum the values of Xλ,z2 for the five elements of Ψmeas,λ,z, Ψcalc,λ,z, and Δmeas,λ,z. We retrieve the optically equivalent refractive indices as

  • equation image

by finding the minimum value of Xλ,z2. The crucial part of finding self-consistent aerosol optical properties is the constraint on absorption given by values of ωo,meas,λ,z in equation (10). After evaluating uncertainties associated with the finite dimensions of the look-up tables in section 2.4, we apply the retrieval methodology in sections 2.2 and 2.3 to real data in section 3.

2.4. Structural Uncertainty

[19] The uncertainty that arises from the retrieval itself, or the structural uncertainty, is estimated by calculating aerosol optical properties from a predetermined size distribution and refractive index. However, instead of using one of the discrete values specific to the look-up table used in the retrieval, we calculate the optical properties from a value between the discrete steps used to build the look-up table. For example, referring to Table 1, we could calculate the optical properties at λ = 550 nm using Dg = 0.1475 μm, σg = 1.7, and m550 = 1.60 − 0.02i, noting that the value of Dg falls between the values in Table 1 (i.e., Dg = 0.135 and 0.160 μm) used to build the look-up tables. Thus, although we have an exact solution using Mie theory, this particular exact solution is not explicitly in the look-up tables.

[20] We retrieve ϕoe,λ using a range of predetermined values of Dg, σg, mr, and mi. We independently investigate the uncertainty that arises from each of the input values such that we begin by choosing values of Dg that are not explicitly used in look-up table calculations (per the example above) while simultaneously choosing values of σg, mr, and mi that are used in the look-up table calculations. We then choose values of σg not used in look-up table calculations while using values of Dg, mr, and mi that are used in the look-up table calculations. The same procedure is repeated for mr, followed by mi. The average percent difference between the exact solution and the calculated optical properties for each dimension of Minput is the error associated with that particular dimension of Minput. These average percent differences are propagated together by quadratures for each of the calculated aerosol optical properties. Using this method, we calculate ±4.1% uncertainty in σext,λ, ±1.2% in ωo,λ, and ±3.8% in gλ, keeping in mind that these so-called structural uncertainties are entirely an artifact of the retrieval and apply only to the calculated (or retrieved) aerosol optical properties. It is important to note that these derived structural uncertainties must be propagated together with the measurement uncertainties used in equations (6) and (10) and that we discuss in sections 3.1 and 3.2 and in Figure 5.

[21] Partitioning the structural uncertainty, we find that the smallest contribution to the structural uncertainty in all calculated optical properties arises from the values of Dg used to build the look-up table. The greatest contribution to the structural uncertainty arises from the values of mr for σext,λ and gλ, but from mi for ωo,λ. Thus we can most efficiently reduce the structural uncertainties associated with the look-up tables used in the retrieval by increasing the resolution of the values of mr and mi used to build the look-up tables.

3. Application

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

3.1. Aircraft Data

[22] We apply the retrieval methodology to six vertical profiles of aircraft-based data collected during SAFARI-2000 and described by Magi et al. [2003] and Magi [2006]. The vertical profiles were collected on 22 August over Skukuza, South Africa, 24 August over Inhaca Island, Mozambique, 31 August in southern Mozambique, 3 September over Sua Pan, Botswana, and two profiles were obtained near Mongu, Zambia on 6 September (0917–0929 and 0957–1014 UTC), where all dates refer to the year 2000. The vertical resolution of the profiles was 150 m. The full suite of measurements has been described previously [Magi et al., 2003; Sinha et al., 2003; Magi, 2006], but we summarize the measurements most important to this study.

[23] We measured σsca,λ and βλ at λ = 450, 550, and 700 nm for Dp < 2 μm using a 3λ-nephelometer custom built for the UW and similar in design to the commercially available TSI 3λ-nephelometer [Magi et al., 2003]. All data from the 3λ-nephelometer were corrected according to protocols described by Hartley [2000], which are similar to those described by Anderson et al. [1996] and Anderson and Ogren [1998] for the TSI nephelometer. The values of σsca,λ and βλ are adjusted to ambient relative humidity (RH) based on the work of Magi and Hobbs [2003], although the corrections are small since ambient RH during SAFARI-2000 was usually less than 50% [Magi et al., 2003]. The 3λ-nephelometer was calibrated before and during SAFARI-2000 by standard procedures described by Anderson and Ogren [1998], but Anderson et al. [1996, 2000] show that TSI nephelometer measurements have a ±7% systematic uncertainty that cannot be averaged out. We assume that this systematic uncertainty applies to the 3λ-nephelometer used in SAFARI-2000. All uncertainties (systematic uncertainty, natural variability, instrument noise, and correction factor uncertainty) are propagated using standard quadratures methods [Bevington and Robinson, 1992].

[24] We measured σabs,550 for Dp < 2 μm with a commercially available particle and soot absorption photometer (PSAP) and corrected the PSAP output according to protocols described by Bond et al. [1999], who also show that there is ±20% systematic uncertainty associated with the PSAP measurements. Part of the correction procedure described by Bond et al. [1999] is to verify the flow rates in the PSAP, but because we were unable to quantitatively confirm the flow rates of the specific PSAP used during SAFARI-2000, we assume a slightly higher systematic uncertainty of ±25%. We extrapolate σabs,550 to σabs,450 and σabs,700 using an assumed value of the absorption angstrom exponent (αabs). The value of αabs varies as a function of the aerosol source, composition, and age [Kirchstetter et al., 2004; Ganguly et al., 2005; Bond and Bergstrom, 2006; Roden et al., 2006], but we assume that for the aged biomass burning aerosol in the regional haze of southern Africa, αabs = 1 for August vertical profiles and αabs = 2 for September vertical profiles, based on an analysis of SAFARI-2000 data by Bergstrom et al. [2003]. We propagate an additional ±10% and ±12% systematic uncertainty for values of σabs,450 and σabs,700 due to the uncertainty associated with the assumed value of αabs. The values of ±10% and ±12% arise by assuming that half of the full range of the difference between extrapolating σabs,550 to σabs,450 and σabs,700 using αabs = 1 and αabs = 2 is the uncertainty.

[25] By assuming αabs for visible wavelength, we lose a constraint on the retrieval and are left with eight knowns and nine unknowns. We account for this by using data collected with a TSI, Inc. Condensation Nuclei Counters (CNC) that sampled from the same inlet as the 3λ-nephelometer and the PSAP on the UW research aircraft. The CNC (TSI model 3022) measures Na for Dp = 0.007–1 μm, which is nearly the same as the size range used to compile the look-up tables in the retrieval (Table 1). Thus we use Na as an additional constraint on the retrieval and have nine knowns and eight unknowns.

[26] The second part of the retrieval uses data collected with the NASA Ames Airborne Tracking Sun photometer, which we simply call the Sun photometer [Magi et al., 2003; Schmid et al., 2003, 2006]. Under cloudless conditions, the Sun photometer reported the aerosol optical depth (τλ) above the altitude of the aircraft at 12 wavelengths during SAFARI-2000 [Magi et al., 2003; Schmid et al., 2003]. Values of σext,λ can be derived by differentiating τλ at two vertically separated points, but uncertainties in these derived values are ∼15–20% [Schmid et al. 2003, 2006]. Magi et al. [2003] showed that τ550 derived from the 3λ-nephelometer and the PSAP compared to within 0.04 or 13% (root mean squared difference) with the Sun photometer measurements of τ550, and that the in situ derived τ550 are biased low by 2%, on average, suggesting that the submicron particles dominated the optical properties.

[27] The six vertical profiles of σext,λ,z, ωo,λ,z, and βλ,z at λ = 450, 550, and 700 nm and varying altitude (z) ranges are shown in Figure 2. The values of σext,λ,z are calculated as the sum of σsca,λ,z and σabs,λ,z, but are adjusted to match values of σext,λ,z derived from the Sun photometer. The adjustment for SAFARI-2000 was generally ∼15–30% and is consistent with the thinking that in situ measurements are typically biased low with respect to the Sun photometer [Schmid et al., 2006]. The values of ωo,λ,z are calculated as σsca,λ,z/(σsca,λ,z + σabs,λ,z). More details about the profiles can be found in the works of Magi et al. [2003], Leahy et al. [2007], and Magi [2006].

image

Figure 2. Vertical profiles of the wavelength-dependent (λ) extinction coefficient (σext,λ), single scattering albedo (ωo,λ), and backscatter ratio (βλ) obtained during SAFARI-2000 by the UW research aircraft. The titles of each of the six columns refer to the date (year 2000) and UTC time of the vertical profiles (as listed in Table 2). The solid lines with circles, shaded lines with triangles, and light shaded lines with squares correspond to λ = 450, 550 and 700 nm, respectively. The thick horizontal solid line is the surface, and the altitudes are above mean sea level. The scales on the x axes are the same for ωo,λ and βλ, but more than a factor of two larger for the vertical profiles of σext,λ collected in September 2000.

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3.2. Retrieval Using Aircraft Data

[28] From the available measurements at λ = 450, 550, and 700 nm shown in Figure 2, we specify ψmeas,λ,z (equation (5)), while δmeas,λ,z (equation (6)) is determined by the uncertainties associated with each instrument. Using look-up tables at λ = 450, 550, and 700 nm, we retrieve ϕoe,λ,z in equation (9).

[29] Values of σext,meas,λ,z derived from the Sun photometer at 12 wavelengths between 354 and 1557 nm and the optically equivalent size distribution (ϕoe,λ,z) found by using information at λ = 450, 550, and 700 nm make up part of Ψmeas,λ,z in equation (10). Aside from ωo,550,z, however, direct measurements of ωo,λ,z from SAFARI-2000 do not exist. As explained above, we can justifiably extrapolate σabs,550,z to other visible wavelengths using suggested values for αabs from Bergstrom et al. [2003], but the extrapolation does not necessarily apply to nonvisible wavelengths such as the near infrared (NIR) or ultraviolet (UV) wavelength regions. This deficiency in the understanding of the wavelength dependence of absorption (i.e., αabs) is not unique to SAFARI-2000 [Bond and Bergstrom, 2006].

[30] In lieu of measurements of ωo,λ,z in the NIR and UV, we impose artificial constraints on ωo,λ,z by linearly combining the soot and continental aerosol types in the d'Almeida et al. [1991] aerosol climatology (identical to models given by Hess et al. [1998]) to match the values of ωo,meas,450 and ωo,meas,700 at every altitude for every vertical profile. The linear combination method implies an externally mixed aerosol [Ackerman and Toon, 1981; Chylek et al., 1988; Jacobson, 2001; Chung and Seinfeld, 2005], but the goal in this step is to find a relationship that provides a constraint on the retrieval rather than a specific value. For the six vertical profiles, the average percentage of soot required to match ωo,meas,450 and ωo,meas,700 in the artificial external mixture of soot and continental particles is 18% (standard deviation of 3%). For comparison, Bush and Valero [2002] showed that the polluted aerosol in India could be simulated with an external mixture of 81% sulfate and 19% soot (∼3% uncertainty) from d'Almeida et al. [1991] and if a sulfate and soot combination was used to simulate the SAFARI-2000 aerosol, 22% soot would be required (standard deviation of 3%).

[31] The values of ωo,λ derived from linear combinations of soot with the different aerosol types given by d'Almeida et al. [1991] are shown in Figure 3 along with ωo,λ from a model of Brazilian biomass burning aerosol [Ross et al., 1998] and ωo,λ derived from methods applied to SAFARI-2000 data [Bergstrom et al., 2003]. The black circles are the column-averaged values of ωo,λ at λ = 450, 550, and 700 nm (based on the 3λ-nephelometer and PSAP), while the solid black lines indicate the column-averaged uncertainty in ωo,λ at λ = 450, 550, and 700 nm. The soot contribution for each curve is adjusted to match values of ωo,450 and ωo,700 extrapolated from ωo,550. The potential range of possible values of ωo,λ increases as a function of λ, and the soot and continental aerosol model is qualitatively in the middle of the range. To account for this increasing uncertainty, we apply about ±10% bounds to constrain the retrieval of ωo,calc,λ (equation (12)) for λ < 450 nm and λ > 700 nm. For comparison, the uncertainty in ωo,λ measured at λ = 550 nm or extrapolated to other visible wavelengths is ±3–6%.

image

Figure 3. Different possible constraints on single scattering albedo (ωo) as a function of wavelength (λ) for the six UW research aircraft vertical profiles, noting that the titles refer to the date (year 2000) and UTC times listed in Table 2. Referring to the legend, “in situ” is ωo derived from the nephelometer and particle and soot absorption photometer data at λ = 450, 550, and 700 nm, whereas the “soot” combinations refer to different generic aerosol types given by d'Almeida et al. [1991]. The thick shaded line for “soot + continental” is the aerosol combination that we use to constrain ωo,λ in this study for nonvisible wavelengths. The Brazil model is from Ross et al. [1998], and the SAFARI-2000 curve is from derived values of ωo,λ for a case study described by Bergstrom et al. [2003].

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4. Analysis

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[32] The column-averaged, extinction-weighted mean values of the optically equivalent size distributions from each of the six profiles are listed in Table 2. The lognormal distributions that best reproduce the measured optical properties range from Dg = 0.15–0.22 μm (average of 0.19 ± 0.02 μm), with σg ranging from 1.7 to 1.9 (average of 1.8 ± 0.1). The values of Na for the optically equivalent size distributions range from 1500 to 4600 cm−3 (average of 3600 ± 1300 cm−3) for primarily submicron diameter particles (i.e., Dg < 1 μm). The values retrieved here agree with measurements of biomass burning aerosol size distributions from regions around the world and summarized by Reid et al. [2005a], who show that Dg ranges from 0.12 to 0.23 μm (mean is ∼0.18 μm), while σg ranges from 1.3 to 1.8 (mean is ∼1.6). The larger values of σg retrieved in this study are most likely due to the consideration of very small particles and the assumption of a unimodal lognormal distribution.

Table 2. Information About the Six Vertical Profiles Used in the Retrieval as Well as the Column-Averaged, Extinction-Weighted Mean Values of the Geometric Mean Diameter (Dg), Geometric Standard Deviation (σg), and Submicron Diameter Aerosol Number Concentration (Na) of the Lognormal Optically Equivalent Size Distributiona
IDDate (2000)Latitude, °SLongitude, °EUTC Time, hhmmAltitude, kmSurface Elevation, kmOptically Equivalent Size Distribution Parameters
Dg, μmσgNa, cm−3
  • a

    The vertical profiles can also be cross-referenced with information in Table 3 using the numerical identification (ID).

122 Aug24.98 ± 0.0431.61 ± 0.060816–10060.37–3.820.150.173 ± 0.0071.886 ± 0.0852438 ± 59
224 Aug25.98 ± 0.0332.91 ± 0.020810–08240.21–4.120.070.196 ± 0.0251.923 ± 0.2181508 ± 217
331 Aug21.62 ± 0.1734.27 ± 0.131229–12440.64–3.890.190.152 ± 0.0131.732 ± 0.0624600 ± 48
43 Sep20.59 ± 0.0326.17 ± 0.020831–08501.08–4.580.930.215 ± 0.0111.674 ± 0.0594291 ± 70
56 Sep15.19 ± 0.0523.16 ± 0.030917–09291.37–4.771.030.198 ± 0.0071.799 ± 0.0624430 ± 102
66 Sep15.47 ± 0.2223.46 ± 0.160957–10141.64–5.271.030.189 ± 0.0061.854 ± 0.0584279 ± 117
Average ± standard deviation      0.187 ± 0.0221.811 ± 0.0953591 ± 1292

[33] Haywood et al. [2003a] suggested a trimodal lognormal function to fit data collected during SAFARI-2000, but similar to the assumption in this study, the smallest mode (Dg = 0.24 ± 0.02 μm, σg = 1.3 ± 0.1, and Na = 1400 ± 700 cm−3) dominated the size distribution for transported biomass burning aerosol over Namibia, accounting for greater than 99% of Na. The differences in the width (σg) are most likely due to the choice to model the biomass burning aerosol as a unimodal versus trimodal lognormal function, while the differences in Na and Dg are due to the fact that Na in this study includes smaller particles (Dp = 0.01 μm), whereas Haywood et al. [2003a] consider a size distribution starting at Dp = 0.1 μm. Of interest in this comparison is the fact that particle sizing instruments such as the PCASP-100x used in SAFARI-2000 on the UW research aircraft [Magi, 2006] and by the United Kingdom Met Office [Haywood et al., 2003b; Osborne et al., 2004] report values of extinction calculated from the PCASP measurements that are significantly less than the values of extinction derived from the nephelometer and PSAP.

[34] The ground-based photometers in the Aerosol Robotic Network (AERONET) described by Holben et al. [1998, 2001] retrieved size distributions (Dp = 0.1–30 μm) at a number of locations during SAFARI-2000 [Eck et al., 2003]. All AERONET data used in this study are using Version 2, Level 2.0 (cloud-screened, quality-controlled) data products (see http://aeronet.gsfc.nasa.gov). In a separate SAFARI-2000 study, Leahy et al. [2007] describe five UW vertical profiles that were discussed by Magi et al. [2003] which were within ∼19 km of the AERONET ground sites and obtained within ∼1 to 4 h of the AERONET retrieval times. In this study, we discuss three of the five profiles from Leahy et al. [2007] (labeled as ID = 1, 4, and 5 in Tables 2 and 3); these three profiles were within ∼18 km of the AERONET ground sites and obtained within ∼2 h of the AERONET retrievals. The effective diameters of the fine mode (Dp < 1.2 μm) size distributions from AERONET retrievals ranged from 0.26 to 0.29 μm, which once converted to Dg, are about the same as the values of Dg retrieved in this study.

Table 3. Column-Averaged, Extinction-Weighted Mean Values of the Real (mr) and Imaginary (mi) Parts of the Optically Equivalent Refractive Index (moe) as a Function of Wavelength (λ) for the Six Vertical Profiles That Can Be Cross-Referenced Using the Numerical Identification (ID) in Table 2a
λ, nmmoeCalculated Optical Properties
mrmiσext, Mm−1ωogβ
  • a

    Also listed are the column-averaged extinction coefficient (σext), and the column-averaged, extinction-weighted single scattering albedo (ωo), asymmetry parameter (g), and backscatter ratio (β) calculated using moe and the optically equivalent size distributions in Table 2. The values are listed as mean or weighted mean ± 2 standard deviations. The column-averaged, scattering-weighted g is only a small fraction different than the column-averaged, extinction-weighted g shown in this table.

ID 1: 22 Aug 2000
3541.55 ± 0.010.013 ± 0.002190 ± 1140.930 ± 0.0080.649 ± 0.0070.076 ± 0.002
3801.53 ± 0.010.012 ± 0.002168 ± 980.930 ± 0.0090.648 ± 0.0060.076 ± 0.002
4491.54 ± 0.020.013 ± 0.002133 ± 760.928 ± 0.0100.626 ± 0.0090.084 ± 0.003
4501.52 ± 0.020.012 ± 0.002125 ± 690.928 ± 0.0100.628 ± 0.0070.083 ± 0.002
4991.56 ± 0.020.015 ± 0.002108 ± 580.917 ± 0.0100.598 ± 0.0080.094 ± 0.003
5251.59 ± 0.020.016 ± 0.00298 ± 530.912 ± 0.0110.578 ± 0.0090.101 ± 0.003
5501.59 ± 0.030.016 ± 0.00386 ± 460.910 ± 0.0120.567 ± 0.0100.105 ± 0.003
6061.63 ± 0.040.019 ± 0.00373 ± 380.896 ± 0.0120.537 ± 0.0120.117 ± 0.004
6751.68 ± 0.050.022 ± 0.00357 ± 300.883 ± 0.0140.496 ± 0.0110.134 ± 0.004
7001.74 ± 0.050.024 ± 0.00355 ± 270.877 ± 0.0140.484 ± 0.0110.139 ± 0.004
7781.77 ± 0.070.027 ± 0.00446 ± 280.860 ± 0.0160.451 ± 0.0140.154 ± 0.006
8651.78 ± 0.060.027 ± 0.00438 ± 240.854 ± 0.0170.436 ± 0.0150.161 ± 0.006
10191.76 ± 0.070.029 ± 0.00427 ± 140.828 ± 0.0150.414 ± 0.0140.170 ± 0.006
12411.79 ± 0.060.035 ± 0.00521 ± 120.785 ± 0.0150.388 ± 0.0140.182 ± 0.006
15571.83 ± 0.070.049 ± 0.00814 ± 90.693 ± 0.0140.354 ± 0.0170.198 ± 0.008
 
ID 2: 24 Aug 2000
3541.54 ± 0.020.021 ± 0.002113 ± 1570.890 ± 0.0080.657 ± 0.0170.074 ± 0.005
3801.53 ± 0.020.021 ± 0.002105 ± 1400.891 ± 0.0080.655 ± 0.0170.074 ± 0.005
4491.52 ± 0.020.022 ± 0.00285 ± 1200.881 ± 0.0090.640 ± 0.0220.079 ± 0.007
4501.51 ± 0.020.022 ± 0.00381 ± 1130.880 ± 0.0110.639 ± 0.0210.079 ± 0.006
4991.54 ± 0.020.025 ± 0.00374 ± 1060.869 ± 0.0100.620 ± 0.0210.086 ± 0.007
5251.54 ± 0.020.026 ± 0.00367 ± 970.865 ± 0.0100.606 ± 0.0220.091 ± 0.007
5501.54 ± 0.020.026 ± 0.00361 ± 880.858 ± 0.0100.600 ± 0.0230.093 ± 0.008
6061.56 ± 0.020.029 ± 0.00353 ± 800.845 ± 0.0100.576 ± 0.0250.103 ± 0.009
6751.58 ± 0.030.032 ± 0.00344 ± 690.827 ± 0.0110.552 ± 0.0310.112 ± 0.012
7001.60 ± 0.040.034 ± 0.00443 ± 670.823 ± 0.0110.543 ± 0.0330.117 ± 0.013
7781.64 ± 0.050.040 ± 0.00537 ± 620.800 ± 0.0120.518 ± 0.0370.127 ± 0.015
8651.64 ± 0.040.039 ± 0.00431 ± 530.792 ± 0.0120.506 ± 0.0380.133 ± 0.015
10191.62 ± 0.050.040 ± 0.00526 ± 490.772 ± 0.0110.506 ± 0.0390.133 ± 0.016
12411.65 ± 0.060.050 ± 0.00622 ± 480.729 ± 0.0110.494 ± 0.0390.139 ± 0.016
15571.71 ± 0.060.073 ± 0.01018 ± 440.651 ± 0.0110.469 ± 0.0390.150 ± 0.017
 
ID 3: 31 Aug 2000
3541.59 ± 0.030.022 ± 0.003148 ± 1010.891 ± 0.0110.589 ± 0.0040.096 ± 0.002
3801.57 ± 0.030.022 ± 0.003136 ± 920.889 ± 0.0130.587 ± 0.0070.097 ± 0.003
4491.58 ± 0.040.021 ± 0.00397 ± 660.885 ± 0.0140.553 ± 0.0080.110 ± 0.003
4501.59 ± 0.040.021 ± 0.00397 ± 660.885 ± 0.0130.552 ± 0.0050.110 ± 0.002
4991.63 ± 0.040.025 ± 0.00380 ± 510.865 ± 0.0150.511 ± 0.0100.127 ± 0.004
5251.65 ± 0.040.026 ± 0.00374 ± 510.858 ± 0.0140.496 ± 0.0100.133 ± 0.004
5501.70 ± 0.050.030 ± 0.00467 ± 430.848 ± 0.0150.481 ± 0.0100.140 ± 0.004
6061.70 ± 0.050.030 ± 0.00457 ± 380.836 ± 0.0190.454 ± 0.0120.152 ± 0.005
6751.78 ± 0.080.035 ± 0.00545 ± 320.812 ± 0.0180.414 ± 0.0090.169 ± 0.004
7001.82 ± 0.060.038 ± 0.00542 ± 280.808 ± 0.0180.406 ± 0.0090.173 ± 0.004
7781.84 ± 0.080.039 ± 0.00530 ± 230.775 ± 0.0210.358 ± 0.0130.195 ± 0.006
8651.82 ± 0.060.037 ± 0.00525 ± 180.769 ± 0.0210.353 ± 0.0100.198 ± 0.005
10191.86 ± 0.080.038 ± 0.00519 ± 130.744 ± 0.0190.328 ± 0.0140.209 ± 0.006
12411.86 ± 0.050.037 ± 0.00414 ± 90.703 ± 0.0200.295 ± 0.0080.225 ± 0.004
15571.90 ± 0.060.042 ± 0.00510 ± 70.620 ± 0.0190.256 ± 0.0140.244 ± 0.007
 
ID 4: 3 Sep 2000
3541.60 ± 0.020.035 ± 0.002385 ± 3020.848 ± 0.0060.623 ± 0.0040.084 ± 0.001
3801.60 ± 0.020.035 ± 0.002361 ± 3180.847 ± 0.0060.618 ± 0.0030.086 ± 0.001
4491.59 ± 0.020.036 ± 0.003267 ± 2010.836 ± 0.0080.593 ± 0.0040.094 ± 0.001
4501.58 ± 0.020.035 ± 0.003265 ± 2060.836 ± 0.0080.593 ± 0.0040.094 ± 0.001
4991.62 ± 0.020.037 ± 0.003231 ± 1900.834 ± 0.0090.560 ± 0.0050.106 ± 0.001
5251.64 ± 0.030.037 ± 0.003212 ± 1620.834 ± 0.0080.542 ± 0.0040.113 ± 0.002
5501.68 ± 0.030.038 ± 0.003190 ± 1410.831 ± 0.0070.528 ± 0.0040.120 ± 0.001
6061.69 ± 0.040.038 ± 0.004160 ± 1270.826 ± 0.0070.497 ± 0.0050.132 ± 0.002
6751.73 ± 0.050.038 ± 0.004126 ± 1100.823 ± 0.0090.457 ± 0.0070.149 ± 0.003
7001.79 ± 0.060.041 ± 0.005117 ± 950.820 ± 0.0080.443 ± 0.0060.156 ± 0.002
7781.80 ± 0.060.044 ± 0.00588 ± 780.792 ± 0.0090.399 ± 0.0080.175 ± 0.003
8651.79 ± 0.050.042 ± 0.00570 ± 630.784 ± 0.0080.386 ± 0.0100.182 ± 0.004
10191.76 ± 0.070.040 ± 0.00650 ± 530.760 ± 0.0070.369 ± 0.0100.190 ± 0.004
12411.77 ± 0.070.043 ± 0.00733 ± 430.719 ± 0.0100.338 ± 0.0090.205 ± 0.004
15571.81 ± 0.060.051 ± 0.00722 ± 340.636 ± 0.0080.295 ± 0.0080.225 ± 0.004
 
ID 5: 6 Sep 2000
3541.59 ± 0.010.033 ± 0.002458 ± 1710.850 ± 0.0060.643 ± 0.0070.079 ± 0.002
3801.58 ± 0.010.033 ± 0.002428 ± 1840.848 ± 0.0070.639 ± 0.0070.080 ± 0.002
4491.58 ± 0.020.036 ± 0.002342 ± 1380.835 ± 0.0070.620 ± 0.0080.086 ± 0.002
4501.58 ± 0.020.036 ± 0.002337 ± 1460.834 ± 0.0080.620 ± 0.0080.086 ± 0.003
4991.61 ± 0.020.037 ± 0.002299 ± 1480.835 ± 0.0060.595 ± 0.0110.095 ± 0.004
5251.62 ± 0.030.037 ± 0.002267 ± 1110.833 ± 0.0060.582 ± 0.0130.100 ± 0.005
5501.61 ± 0.030.036 ± 0.002240 ± 960.832 ± 0.0070.572 ± 0.0130.103 ± 0.005
6061.65 ± 0.030.037 ± 0.003212 ± 1030.832 ± 0.0080.546 ± 0.0140.114 ± 0.005
6751.70 ± 0.040.038 ± 0.003167 ± 710.830 ± 0.0080.505 ± 0.0170.130 ± 0.007
7001.76 ± 0.060.041 ± 0.004154 ± 660.824 ± 0.0080.495 ± 0.0160.135 ± 0.007
7781.77 ± 0.060.045 ± 0.005122 ± 600.801 ± 0.0100.457 ± 0.0180.150 ± 0.008
8651.76 ± 0.060.043 ± 0.00599 ± 500.794 ± 0.0090.444 ± 0.0190.156 ± 0.008
10191.70 ± 0.060.038 ± 0.00664 ± 290.776 ± 0.0100.424 ± 0.0180.165 ± 0.008
12411.68 ± 0.080.039 ± 0.00743 ± 170.730 ± 0.0090.400 ± 0.0210.177 ± 0.010
15571.68 ± 0.080.046 ± 0.00829 ± 240.646 ± 0.0090.361 ± 0.0180.195 ± 0.008
 
ID 6: 6 Sep 2000
3541.57 ± 0.010.032 ± 0.002421 ± 1240.850 ± 0.0070.653 ± 0.0040.076 ± 0.001
3801.57 ± 0.010.031 ± 0.002399 ± 1140.849 ± 0.0070.649 ± 0.0050.077 ± 0.001
4491.57 ± 0.020.035 ± 0.002317 ± 1020.837 ± 0.0080.629 ± 0.0060.083 ± 0.002
4501.57 ± 0.020.034 ± 0.002309 ± 990.837 ± 0.0080.631 ± 0.0050.082 ± 0.001
4991.59 ± 0.020.035 ± 0.002272 ± 880.835 ± 0.0080.610 ± 0.0090.090 ± 0.003
5251.59 ± 0.020.035 ± 0.002245 ± 720.836 ± 0.0080.598 ± 0.0090.094 ± 0.003
5501.59 ± 0.030.034 ± 0.002222 ± 740.836 ± 0.0090.590 ± 0.0090.097 ± 0.003
6061.62 ± 0.030.035 ± 0.003198 ± 710.836 ± 0.0090.567 ± 0.0110.106 ± 0.004
6751.65 ± 0.040.035 ± 0.003156 ± 630.832 ± 0.0090.532 ± 0.0110.120 ± 0.004
7001.70 ± 0.040.037 ± 0.004142 ± 500.831 ± 0.0100.519 ± 0.0110.125 ± 0.005
7781.72 ± 0.050.041 ± 0.004114 ± 420.807 ± 0.0100.483 ± 0.0130.140 ± 0.005
8651.69 ± 0.050.038 ± 0.00591 ± 370.801 ± 0.0100.475 ± 0.0130.143 ± 0.006
10191.64 ± 0.060.035 ± 0.00562 ± 210.782 ± 0.0100.457 ± 0.0140.151 ± 0.006
12411.61 ± 0.060.034 ± 0.00640 ± 130.742 ± 0.0090.427 ± 0.0140.165 ± 0.006
15571.60 ± 0.070.040 ± 0.00826 ± 90.656 ± 0.0100.390 ± 0.0160.182 ± 0.007

[35] The column-averaged, extinction-weighted mean values of the wavelength-dependent, optically equivalent refractive indices for the UW vertical profiles are listed in Table 3. Haywood et al. [2003a, 2003b] suggested m550 = 1.54 − 0.018i for biomass burning aerosol transported from east to west across southern Africa while the average (±standard deviation) in Table 3 is m550 = (1.60 ± 0.06)–(0.029 ± 0.007)i for biomass burning aerosol closer to the sources. The higher values of mi,λ from the retrieval here compared to those for a more aged aerosol described by Haywood et al. [2003a, 2003b] are consistent with the thinking that aging processes result in a more scattering aerosol [Reid et al., 2005a].

[36] Values of retrieved mi,λ are higher for the September profiles than for the August profiles. When heavy tropical African biomass burning smoke was transported over the SAFARI-2000 sample region during a period from about 2 to 10 September 2000 called the “River of Smoke” [Annegarn et al., 2002; Swap et al., 2003], this resulted in higher values of mi,λ than when the SAFARI-2000 sample region was dominated by smoke from local sources [Stein et al., 2003]. Gao et al. [2003] and Kirchstetter et al. [2003] showed that the carbonaceous aerosol contribution to the overall aerosol composition increased during the River of Smoke. Referring to in situ measurements, this change during the River of Smoke corresponded to a decrease in ωo,λ, while an increase in Na [Magi, 2006] resulted in an increase in τλ [Magi et al., 2003]. Thus the higher retrieved values of mi,λ during the River of Smoke profiles (September) is expected considering the strong contribution of absorption to the magnitude of mi,λ [Bond and Bergstrom, 2006].

[37] AERONET retrieved complex refractive index at λ = 438, 669, 871, and 1022 nm based on sky radiance measurements [Dubovik et al., 2000]. In Figure 4, we show the comparison of mλ retrieved using the methodology in this study and those reported by AERONET [Eck et al., 2003], showing only the three vertical profiles (discussed above) when the UW aircraft was colocated spatially and temporally with AERONET [Leahy et al., 2007]. There is no clear systematic bias in the overall wavelength dependence, but on average, mr,λ from AERONET during SAFARI-2000 is ∼14% less than mr,λ in Table 3, while mi,λ from AERONET is ∼50% less than mi,λ in Table 3. The differences in the wavelength dependence shown in Figure 4 are most likely due to the particle sizes considered in the individual retrievals; mλ from AERONET is for particles with Dp = 0.1–30 μm, while mλ in this study is for Dp ∼ 0.01–1 μm (Dg = 0.06–0.985 μm in Table 1, but this refers to the mean diameter). Under high aerosol loading (τ440 > 0.5), the estimated uncertainties in the absorption products from AERONET retrievals are low [Dubovik et al., 2002], but this study supports the ideas presented by Ackerman et al. [2004] and Kahn et al. [2004] that specific campaigns to characterize aerosol properties above AERONET sites [Haywood et al., 2003a; Magi et al., 2005; Leahy et al., 2007; Schmid et al., 2006] are needed to properly validate AERONET retrieved products. This is especially important since AERONET retrieved products are subsequently used to evaluate satellite products and model output [Reddy et al., 2005; Zhou et al., 2005; Kinne et al., 2006; Ginoux et al., 2006].

image

Figure 4. Comparison of the real and imaginary refractive indices (mr and mi, respectively) as functions of wavelength (λ) derived from the retrieval in this study (line with squares) and reported by AERONET (dashed line with circles). The titles list the dates (year 2000) and UTC times of the three UW research aircraft vertical profiles (corresponding to ID = 1, 4, and 5 in Table 2) which were obtained within ∼18 km of AERONET stations and within ∼2 h of the AERONET retrievals. The squares and circles denote the specific wavelengths of the individual retrievals. The confidence limits in mr and mi from the retrieval in this study (solid thin shaded lines) are determined from variability within a vertical profile (listed in Table 3) and uncertainty in retrieval itself (±0.05 for mr and ±0.005 for mi, per Table 1). The confidence limits in the AERONET retrieved values (dashed thin shaded lines) are ±0.04 for mr and ±40% for mi [Dubovik et al., 2002].

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[38] The wavelength-dependent optical properties calculated from the optically equivalent size distributions and refractive indices are also listed in Table 3. After we apply the retrieval methodology to the data in Figure 2, we compare ψmeas,λ,z to ψcalc,λ,z (which are determined by ϕoe,λ,z) to assess the quality of the retrieval with respect to the original data at λ = 450, 550, and 700 nm. In Figure 5, we show the histogram distributions of the percent difference of the elements of ψmeas,λ,z from the elements of ψcalc,λ,z, calculated as 100*(ψcalc,λ,zψmeas,λ,z)/ψmeas,λ,z and sorted into evenly spaced bins. Data from λ = 450, 550, and 700 nm and all altitudes are considered together in the histograms for a total of 417 points of comparison. A value of 1% in Figure 5 means that, for example, ωo,calc,λ,z calculated from the optically equivalent size distribution and refractive index (at λ) was 1% different from ωo,meas,λ,z.

image

Figure 5. Histograms showing the average percent differences between measured optical properties and those calculated from the retrieved optically equivalent size distribution and refractive indices. Uncertainties in the measured optical properties are ±10–20% for σext,meas,λ,z, ±3–6% for ωo,meas,λ,z, and ±6–10% for βmeas,λ,z. The dashed curves are the Gaussian distribution functions given by the mean (±2 standard deviations) in each figure. The solid curves connect the points that denote the center of the various bins. The number of points used to compile each of the histograms is 417.

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[39] In general, the elements of ψcalc,λ,z vary by less than the typical uncertainties in the measured elements specified as δmeas,λ,z (±10–20% for σext,meas,λ,z, ±3–6% for ωo,meas,λ,z, and ±6–10% for βmeas,λ,z), which implies that the measured aerosol optical properties can be represented by the retrieved optically equivalent size distribution and refractive indices to within measurement uncertainties. This agreement exists in part because the biomass burning aerosol in southern Africa is composed primarily of submicron diameter particles [Haywood et al., 2003a; Eck et al., 2003] that evolve to nearly spherical shapes [Posfai et al., 2003] within hours after emission from the fires [Li et al., 2003; Magi and Hobbs, 2003]. The bimodal percent difference distribution in Figure 5 for σext,λ,z arises from the generally larger percentage uncertainties associated with σext,meas,λ,z (δσext,meas,λ,z) which weights the retrieval more heavily to values of ωo,meas,λ,z and βmeas,λ,z by equation (9).

[40] Values of gλ,z are not measured and are strictly a product of the retrieval, but we compare the results of the retrieval in this study with AERONET retrieved gλ for the three cases discussed above. Values of gλ retrieved by AERONET (for fine mode aerosol, Dp < 1.2 μm) are greater than gλ retrieved in this study for λ = 438 nm and 669 nm but less than gλ retrieved in this study for λ = 871 nm and 1022 nm. On average, gλ retrieved by AERONET are (3 ± 11)% less than gλ retrieved in this study and the difference ranges from −25% to +7%. Thus the bias between the two retrievals is not systematic.

5. Summary

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[41] We designed an original and straightforward retrieval algorithm that searches look-up tables constructed using Mie theory to find a size distribution and refractive indices that most closely reproduce in situ and remote sensing measurements of aerosol optical properties. The optically equivalent size distribution and refractive indices are not necessarily representative of the real aerosol size distribution and refractive indices, especially if the aerosol is not composed of spherical particles, but they offer some insight into what properties are needed to reproduce available optical measurements.

[42] To properly constrain the retrieval, information about σext,λ, ωo,λ, and βλ are needed at least at three wavelengths. This is widely available for σsca,λ and βλ from nephelometry [Anderson et al., 1996; Anderson and Ogren, 1998], and multiwavelength measurements of σabs,λ are becoming more common [Ganguly et al., 2005; Sheridan et al., 2005; Virkkula et al., 2005; Roden et al., 2006; Schmid et al., 2006]. The result is that σext,λ and ωo,λ at three wavelength can be readily derived. For SAFARI-2000, σabs,λ was only measured at one wavelength [Magi et al., 2003] and we extrapolated this to two other wavelengths using other data collected during SAFARI-2000 and described by Bergstrom et al. [2003]. This reduces the number of constraints on the retrieval from nine to eight, such that we have eight knowns and nine unknowns. To account for this underdetermined problem, we use SAFARI-2000 measurements of Na as an additional constraint on the retrieval. The resolution of the look-up tables used in the retrieval is adequate to resolve the optical properties to within typical uncertainties (section 3.1), while the so-called structural uncertainties in calculated optical properties that arise from the discrete input used to build the look-up tables (Table 1) are ±4.1% for σext,λ, ±1.2% for ωo,λ, and ±3.8% for gλ (section 2.4).

[43] From the more detailed and readily available measurements at three visible wavelengths, we retrieve the optically equivalent size distribution and refractive index and use this information with derived values of σext,λ at λ = 354–1557 nm from the NASA Ames Airborne Tracking Sun photometer on the UW research aircraft [Schmid et al., 2003] as the basis for a simple search algorithm to obtain self-consistent aerosol optical properties. However, with no data available about ωo,λ beyond λ = 550 nm during SAFARI-2000, we combine an assumption of αabs for visible wavelengths based on two case studies from SAFARI-2000 [Bergstrom et al., 2003; Pilewskie et al., 2003] with the assumption of a continental and soot aerosol combination [d'Almeida et al., 1991] to serve as a constraint on ωo,λ. If in future studies, a better understanding of the regional dependence of αabs developed from, say, more detailed measurements [Ganguly et al., 2005; Sheridan et al., 2005; Virkkula et al., 2005; Bond and Bergstrom, 2006; Roden et al., 2006], this retrieval could easily be modified to utilize the information.

[44] Although the optically equivalent size distribution and bulk refractive index from the retrieval are not necessarily representative of the true size distribution and refractive index, we showed that the optically equivalent size distributions in Table 2 are similar to the submicron modes of the size distributions in the works of Haywood et al. [2003a, 2003b] and retrieved from AERONET [Eck et al., 2003] during SAFARI-2000. The retrieval in this study reports higher values of Na than Haywood et al. [2003a], but as discussed in section 4, we include smaller diameter particles. However, the optically equivalent real and imaginary refractive indices derived in this study (Table 3) are, respectively, ∼14% and ∼50% greater than those derived from AERONET retrievals for three cases when comparisons can be made, and in some cases show a very different wavelength dependence.

[45] In southern Africa, fluctuations in the aerosol properties of the regional haze during the biomass burning season are primarily due to fluctuations in the number of biomass fires [Eck et al., 2003; Magi et al., 2003], and the biomass burning aerosol is dominated by submicron diameter [Haywood et al., 2003a; Eck et al., 2003], nearly spherical [Posfai et al., 2003] particles that age rapidly away from the fire source [Li et al., 2003; Magi and Hobbs, 2003]. The retrieval presented here is thus particularly well suited for SAFARI-2000 data since supermicron diameter, nonspherical particles play a minimal role in southern African aerosol optical properties. For locations where supermicron diameter particles, like mineral dust, play a more significant role, the retrieval methodology in this study would require information specific to the supermicron mode of the aerosol size distribution [e.g., Clarke et al., 2002; Doherty et al., 2005] to properly constrain the larger solution space. The retrieval would also require a different approach if the aerosol is composed of particles that cannot be represented with spheres.

[46] The results of the retrieval offer a method to find self-consistent aerosol properties such that closure between independent measurements can be obtained or, conversely, that potential discrepancies between in situ instruments [Haywood et al., 2003b; Osborne et al., 2004] are highlighted. Combining the retrieval methodology with the methodology presented by Magi et al. (submitted manuscript, 2007) provides a method to transition from field measurements to model input, assuming the measurements themselves properly characterize the regional aerosol. The retrieval methodology is constrained by data that has been routinely collected in other aerosol measurement campaigns [Reid et al., 1998; Clarke et al., 2002; Russell et al., 2002; Doherty et al., 2005; Magi et al., 2005; Redemann et al., 2006; Schmid et al., 2006]. We urge the measurement community to apply the retrieval methodology described in this study whenever the required constraints are available. This would provide a good point for comparison with model input or with available climatologies of aerosol properties [d'Almeida et al., 1991; Hess et al., 1998]. If this retrieval is modified, data about supermicron diameter particles could be used and provide even more information.

[47] Most of the measurements made from the University of Washington (UW) research aircraft during SAFARI-2000 have not been incorporated into any model of southern African biomass burning [e.g., Abel et al., 2005; Kinne et al., 2006]. Magi et al. (submitted manuscript, 2007) describe a methodology to derive aerosol radiative forcing from in situ measurements by combining the retrieval methodology in this study with a radiative transfer model, while in future work, we discuss the broader implications of the measurement-based estimates of biomass burning aerosol radiative forcing using multiyear satellite data. In the end, combining the various methodologies with the data collected on the UW research aircraft during SAFARI-2000 can offer important comparisons with model input at a regional level as well as with ground-based and satellite-derived aerosol products.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

[48] We thank the late Peter Hobbs for his support during the research phase of this project. We want to acknowledge the work of the science and the flight crews for the University of Washington research aircraft during the SAFARI-2000 field campaign. Valuable discussions with Dean Hegg, Tad Anderson, and Tom Ackerman, as well as comments by three anonymous reviewers, helped improve this research. We thank Brent Holben and Stuart Piketh for their efforts in establishing and maintaining the Mongu, Sua Pan, and Skukuza AERONET sites in southern Africa. B.M. is supported in part by NSF grant 0314453 and by NASA grant NNG04GM23G. Q.F. is in part supported by NASA grant NNG04GM23G.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methods
  5. 3. Application
  6. 4. Analysis
  7. 5. Summary
  8. Acknowledgments
  9. References
  10. Supporting Information
FilenameFormatSizeDescription
jgrd13724-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
jgrd13724-sup-0002-t02.txtplain text document1KTab-delimited Table 2.
jgrd13724-sup-0003-t03.txtplain text document9KTab-delimited Table 3.

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