The Aerosol Intensive Observational Period (IOP) occurred 5–31 May 2003 at the Department of Energy's (DOE) Cloud and Radiation Testbed (CART) Southern Great Plains (SGP) Central Facility near Lamont, Oklahoma (36.6 N, 97.5 W, 315 m asl). The main purpose of the IOP was to improve understanding and representation of aerosol radiative properties in models. To this end, a variety of platforms and instruments were deployed to measure the physical, chemical and optical properties of aerosol particles at SGP, in addition to the suite of measurements made at the site on an ongoing basis. The campaign and the associated measurements are described by Ferrare et al. . The measurements relevant to the derivation of asymmetry parameter are listed in Table 1 and described in detail below, segregated by measurement type (in situ or remote) and location (surface and airborne). The methods used to derive asymmetry parameter from the measurements are outlined following the instrumentation descriptions. To verify our approach, we compared measured and calculated aerosol light scattering using Mie theory directly or data inversion (which indirectly relies on Mie theory) as appropriate to check the instruments and our calculation techniques. While good agreement between measured and derived scattering does not necessarily imply that we are modeling the aerosol correctly, it does nonetheless give us confidence that the independent data sets are consistent.
2.1. Surface Aerosol Instrumentation
 As part of the long-term aerosol measurements at the SGP CART site (since 1996), NOAA's Climate Monitoring and Diagnostics Laboratory (CMDL) has mentored an “Aerosol Observing System” (AOS) which includes two 3-wavelength integrating nephelometers (Model#3563, TSI Inc., St. Paul, Minnesota) with total and backscatter capabilities for dry and humidified aerosol light scattering measurements (both total scattering σsp, and backscattering σbsp), a particle soot absorption photometer (PSAP, Radiance Research, Seattle, Washington) for light absorption (σap) measurements and a CN counter (Model#3010, TSI Inc., St. Paul, Minnesota). The nephelometers and PSAP are downstream of a 10 μm aerodynamic diameter impactor and every 6 min a 1 μm aerodynamic diameter impactor is switched into or out of the sample flow for 6 min. This results in sub-10 μm and sub-1 μm aerodynamic aerosols being sampled during alternating 6 min periods. The nephelometer measurements are corrected for angular nonidealities using the scheme described by Anderson and Ogren , while the PSAP measurements are corrected using the Bond et al.  algorithm. The AOS system and results from the first 4 years of measurements are described by Sheridan et al. . During the IOP, a mobile aerosol system with an additional nephelometer and PSAP at low-RH conditions was set up in the Guest Instrument Facility (GIF) trailer which was located approximately 150 m from the AOS trailer. This mobile aerosol rack was used for quality control both to check that the same aerosol was being sampled at the AOS and GIF trailers and as a transfer standard to intercompare other nephelometers and PSAPs deployed during the IOP. Additionally the GIF nephelometer and PSAP served as backup for the instruments in the AOS trailer. On the basis of calculations performed for the INDOEX campaign [Clarke et al., 2002], the uncertainty in the nephelometer scattering measurements at the surface are about 10% of the total measured scattering.
 Also in the AOS trailer a passive cavity aerosol spectrometer probe (Model#PCASP-X, Particle Measuring Systems, Boulder, Colorado) measured aerosol number concentrations in 32 size bins between 0.1 and 10 μm (optical diameter). The AOS PCASP is calibrated with polystyrene latex spheres (refractive index, RI = 1.58) as described by Liu et al. , response curves for other values of RI are calculated using Mie theory and a code modeling the PCASP [Hand and Kreidenweis, 1996]. Here we used diameters corresponding to the response curve calculated for RI = 1.55 + 0.015i. Particles in the 0.1–10 μm size range scatter light very effectively; a closure comparison of scattering (Figure 1) measured by the AOS low-RH nephelometer with scattering calculated from the PCASP size distributions using Mie theory shows excellent agreement (within 2% on the basis of the slope of a line forced through the origin, R2 = 0.97) suggesting both instruments are sampling the optically important aerosol. This light scattering comparison is for a wavelength (λ) of 550 nm and assumes homogeneous spheres over the entire PCASP size range. The AOS PCASP instrument was only operational during the middle portion of the IOP, from 12 to 24 May 2003 (Day of year (DOY) 132–144). The light absorption calculated from measured size distributions for the same conditions (λ = 550 nm, RI = 1.55 + 0.015i) also showed good agreement with light absorption measured by the PSAP (within 3% on the basis of the slope of a line forced through the origin, R2 = 0.43). The lower correlation coefficient for absorption shows that calculated absorption is more sensitive to the refractive index (particularly the imaginary part) and that the contribution of absorbing material to the aerosol is variable. Throughout this paper we report calculated optical properties at λ = 550 nm and RI = 1.55 + 0.015i unless otherwise noted.
Figure 1. Calculated submicrometer scattering derived from various size distribution instruments (GIF SMPS, AOS PCASP, and GIF TDMA), assuming RI = 1.55 + 0.015i compared with scattering measured by AOS nephelometer for low-RH conditions.
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 A humidity conditioning system and second nephelometer in the AOS trailer are used to measure light scattering and backscattering as a function of relative humidity. Over the course of an hour the humidity conditioning system generates a controlled scan of relative humidity, ideally increasing from approximately 40% up to 90%, although during the IOP the maximum RH achieved was much lower, around 75%. Particles exiting the first nephelometer are exposed to the scanned humidities and enter the second nephelometer. Fits to the data from these humidity scans can be used to predict the value of light scattering at ambient humidity conditions. Here the dry nephelometer measurements were adjusted to ambient RH conditions using the average fit parameters a and b for the “2-parameter” fit [Sheridan et al., 2001] over the course of the IOP:
where σ is either σsp or σbsp and RH% is the measured ambient percent relative humidity from the ARM data archive. Scatterplots of nephelometer measured wet σsp and σbsp versus the wet σsp and σbsp calculated from dry nephelometer measurements and equation (2) showed excellent agreement (slopes = 1.05 and1.00 respectively, R2 = 0.99 for both). This agreement gives us confidence in our adjustment of nephelometer measurements to ambient relative humidity conditions. IOP and long-term values for the fit parameters in equation (2) and for f(RH) are given in Table 2. The median value of f(RH) for the IOP is 1.43 which is lower than the long-term median value of 1.68 at the site (on the basis of continuous humidograph measurements between 2000 and 2004). These f(RH) fall in the middle of values reported for other types of aerosol (some examples include the work of Kotchenruther and Hobbs  which reported a value of 1.16 for biomass burning smoke in Brazil, while Sheridan et al.  reported a values over the Indian Ocean of 2.07 for clean marine aerosol and range of 1.5–1.7 for polluted aerosol).
Table 2. Average Nephelometer Humidity Scan Fit Parameters for Equation (2), Both for IOP and for All 4 Years (2000–2003) of SGP Humidified Nephelometer Data for sub-μm Data for Wavelength = 550 nma
|Scattering (λ = 550 nm)||0.93||0.29||0.84 (0.10)||0.37 (0.15)|
|Backscattering (λ = 550 nm)||1.02||0.10||0.96 (0.16)||0.12 (0.15)|
 During the IOP, an optical particle counter (Climet Cl-550, Redlands, California; diameter range 0.35–11.4 μm), a tandem differential mobility analyzer (TDMA; diameter range 0.01–1.0 μm) and a scanning mobility particle sizer (SMPS; column: TSI#3081, CPC: TSI#3010; diameter range 0.03–0.82 μm) were deployed in the GIF trailer to obtain aerosol size distributions. Hereinafter these instruments will be referred to as GIF Climet, GIF TDMA and GIF SMPS, respectively. For the GIF Climet, the bin diameters are based on the factory calibration using particles with RI = 1.58. For low–relative humidity conditions, comparison of the submicrometer scattering calculated from the measured size distribution from the GIF Climet instrument (assuming RI = 1.55 + 0.015i and λ = 550 nm) showed good correlation (R2 = 0.93) with the AOS nephelometer submicrometer scattering, however the submicrometer scattering calculated from the GIF Climet tended to be about 25% lower than that measured by the AOS nephelometer. This is due to significant scattering contribution from particles in the 0.1–0.35 μm size range not measured by the GIF Climet. The manufacturer reports an uncertainty of 2% for particle diameter and 10% for particle counts.
 For low–relative humidity conditions, comparison of the scattering calculated from the measured size distribution from the GIF TDMA and the GIF SMPS instruments (also assuming RI = 1.55 + 0.015i and λ = 550 nm) showed good agreement (within 11% with R2 = 0.96 for the SMPS, and within 13% with R2 = 0.78 for the GIF TDMA) with the measured submicrometer scattering. From 4 to 19 May the GIF TDMA measured size distributions in the range 0.01–0.75 μm mobility diameter, while from 19 May until the end of study, the GIF TDMA measured diameters up to 1 μm. There is no noticeable change in the scattering comparison after 19 May when the larger particles are included in the GIF TDMA data analysis. More details about the GIF TDMA data during the IOP are presented by Gasparini et al. , while J. Wang et al. (Aerosol size distributions during ARM aerosol IOP, submitted to Journal of Geophysical Research, 2005) present an analysis of the GIF SMPS data. The GIF SMPS was calibrated using polystyrene latex spheres of standard sizes. The uncertainty in size measurement is less than 3%, and the uncertainty in concentration measurement is about 10%. Wang et al.  present a careful analysis of the uncertainty of their SMPS measurements for the ACE-Asia field campaign; they note that the concentration and size measurements are the most important source of uncertainty in calculating extinction from size distribution measurements and may have contributed up to ±30% uncertainty in the calculated extinction during the ACE-Asia study.
 In addition to aerosol size distributions, the GIF TDMA also measured size-resolved hygroscopic growth for a subset of diameters. The combination of these measurements can be used to derive a compositionally resolved size distribution consisting of four solubility categories: soluble, mixed soluble, mixed insoluble, and insoluble [Gasparini et al., 2004]. Each solubility category is assigned a representative refractive index and the optical properties are calculated on the basis of the size- and solubility-resolved concentration of particles. We will use this GIF TDMA inferred composition to investigate the sensitivity of the asymmetry factor to aerosol composition.
 The Aerosol Robotic Network (AERONET) Cimel Sun/sky scanning radiometer is located at the surface near the AOS and GIF trailers. The basic AERONET data product is spectral aerosol optical depth in the wavelength range (340–1020 nm). Other data products such as column-averaged aerosol size distributions and asymmetry parameters are derived for four wavelengths (440, 670, 870, and 1020 nm) using Dubovik's algorithm [Dubovik and King, 2000] and are available on the AERONET website. Here level 2.0, cloud-screened data were used. The minimum AOD for the Dubovik retrievals to work is 0.4 at 440 nm. Uncertainties in the retrieval of asymmetry parameter from AERONET data are in the range 3–5%; these small uncertainties reflect the fact that g is an integral characteristic of the aerosol (A. Smirnov, personal communication, 2005).
2.2. Airborne Aerosol Instrumentation
 During the IOP, two aircraft with aerosol optical and microphysical instrumentation flew various flight tracks over the site in order to make measurements of aerosol properties aloft. One airplane was the in situ aerosol profiling (IAP) Cessna, which has been making routine profile flights to measure aerosol optical properties over SGP since 2000 (over 530 flights as of December 2004). The second airplane was the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS) Twin Otter (TO) which was deployed specifically for the IOP.
 The IAP program routinely (2–3 times per week) measures aerosol optical property profiles over SGP using a small airplane (Cessna 172-N). The aerosol package on the airplane is similar to that in the AOS trailer (i.e., nephelometer, PSAP at low RH) and is described in more detail by Andrews et al. . There is a 1 μm impactor upstream of the aerosol instruments (corresponding to a geometric size cut of approximately 0.79 μm) on the Cessna to eliminate uncertainties due to particle losses and inlet transmission inefficiency for larger particles. During the IOP the Cessna flew 14 of its standard profile flights. The uncertainties in the nephelometer measurements for the IAP airplane depend primarily on the flight segment length (∼10 min for the four highest levels, ∼5 min for the five lowest levels) and on the amount of aerosol present [Clarke et al., 2002]. For very clean (σsp ∼ 1 Mm−1) upper flight levels the uncertainty in the scattering measurement is approximately 40%, while for flight levels with more aerosol (σsp > 20 Mm−1) the uncertainty will be less than 10%.
 The Twin Otter (TO) can carry a much larger payload than the Cessna and as such had a larger suite of measurements [e.g., Schmid et al., 2004; A. W. Strawa et al., In situ measurement of aerosol optical properties made during the DOE Aerosol IOP: 1. Comparison of extinction and scattering coefficients, submitted to Journal of Geophysical Research, 2005, hereinafter referred to as Strawa et al., submitted manuscript, 2005]. The instrumentation on board the TO included a humidograph system consisting of three Radiance Research nephelometers (Model M903), TSI nephelometer, 3-wavelength PSAP, PCASP, SMPS, and the AATS-14 sunphotometer (Table 1). The Twin Otter instrumentation will be preceded by TO to differentiate it from similar instruments on the IAP aircraft and at the surface. The TO did not have an impactor or other size cut device on its sampling inlet and thus was not limited to sampling submicrometer aerosol. The TO flew 17 flights during the IOP, five of which were side-by-side profile flights with the IAP aircraft.
 As mentioned above, during the IOP the IAP aircraft continued to fly its normal flight profiles and the Twin Otter occasionally flew a profile side-by-side with the Cessna as part of longer flight tracks. For the comparison purposes here, we focus on the five side-by-side profile flights flown by the two aircraft on 7, 9, 17, 25 and 29 May. For each side-by-side profile flight, the Cessna flew nine level legs over (or near) the surface site. The legs were flown at altitudes of 467, 610, 915, 1220, 1525, 1830, 2440, 3050, 3660 m asl (these altitudes correspond to flight levels of 1500, 2000, 3000, 4000, 5000, 6000, 8000, 10000 and 12000 feet). The Twin Otter did not fly the lowest flight level side-by-side with the IAP Cessna because of safety constraints. Three of the side-by-side flights contained the maximum possible eight legs for comparison (7, 9, and 17 May), unfortunately in one of those flights (17 May) the IAP plane recorded data at 1 min resolution, which limits its value for comparison. The other two flights (25 and 29 May) had seven and two side-by-side legs respectively.
 Comparisons of low-RH, light scattering measurements by TSI nephelometers aboard the two airplanes during side-by-side flight legs showed the observations were correlated (R2 between 0.60 and 0.97 for the three flights with seven or more side-by-side legs), with the ratio of σsp(IAP)/σsp(TO) ranging from 0.6 to 1.1. Some of the observed differences between the two airplanes are due to differences in the sample inlet size cut for the two airplanes; better agreement was found between the two platforms when the aerosol Ångström exponent was large, indicating the predominance of submicrometer particles (Strawa et al., submitted manuscript, 2005). Overall uncertainties in the TO TSI nephelometer measurements will be slightly higher than those for the IAP nephelometer because it is measuring supermicron as well as submicron aerosol. A detailed discussion of uncertainty issues for a previous deployment of the in situ aerosol optical system on the Twin Otter is provided by Anderson et al. .
 The TO SMPS [Wang et al., 2003] measured dry aerosol size distributions in the range 0.02–0.73 μm. Humidity in the TO SMPS was always less than 30%. On the basis of segment averages, the calculated scattering from the TO SMPS is approximately 85% of the submicrometer scattering measured on the IAP airplane but the values were well correlated (R2 = 0.93). Some of the difference between the two scattering values may be due to the difference in inlet size cut for the TO SMPS and IAP nephelometer. The uncertainty for the TO SMPS is as described for the GIF SMPS.
 The TO PCASP (PMS Inc., Boulder, Colorado) with a SPP-200 data system (DMT Inc., Boulder, Colorado) measured particles in the size range 0.11–2.69 μm. The data from the TO PCASP are reported at ambient temperature and pressure conditions but low RH. Scattering calculated from the TO PCASP is significantly lower (34%) than the submicrometer scattering measured by the IAP nephelometer, but again the correlation between measured and calculated scattering is excellent (R2 = 0.96). TO PCASP-derived scattering is also much lower than that measured by the TO nephelometer. The Twin Otter PCASP was calibrated using spheres of three different refractive indices (1.33, 1.42 and 1.58) using the methodology described by Liu et al. . The bin diameters used in this study were based on the RI = 1.58 calibration. On the basis of the calibrations, there is a 20–30% shift in diameter for the TO PCASP between RI = 1.33 and RI = 1.58. Previous deployments of this instrument report uncertainties in the size range measurements of ±6% [Hegg and Jonsson, 2000].
 The Ames airborne tracking 14-channel sunphotometer (AATS-14) was deployed on the Twin Otter to measure aerosol optical depth and spectral extinction in the range 354–2139 nm [Schmid et al., 2006]. Schmid et al.  found the TO AATS-14 measurements during the IOP to be well correlated with the in situ instruments aboard the Twin Otter (R2 > 0.8), but the AATS AOD was 18% higher (at 519 nm) than the AOD estimated from TO nephelometer and PSAP instruments. They note that possible explanations for the lower in situ AOD include: losses of large particles due to inlet effects, uncertainties in humidity correction, change in particle size due to evaporation of volatile materials other than water and issues with filter-based measurements (i.e., PSAP). Here, because we are just looking at side-by-side TO and IAP data, we look at how AATS derived and measured scattering compare for the level flight legs. The King inversion routine [King et al., 1978] was used to process the TO AATS-14 spectral aerosol optical depth measurements (see next section for details) and derive aerosol size distributions. Although the King inversion was able to reproduce the input TO AATS-14 spectral AOD measurements within 5% over a wide range of AOD conditions (0.05 < AOD < 0.35 at 519 nm), the light scattering values calculated from the derived size distributions were often significantly different (factor of 3) than the scattering measured by the TO nephelometer. This is likely due to differences in vertical resolution; Schmid et al.  used smooth continuous ascents or descents in their comparisons allowing for much higher vertical resolution of the aerosol profile, while here the relatively coarse side-by-side flight levels (separated by 300–600 m) were used. If the aerosol is not vertically homogeneous from one flight level to the next, the comparison with in situ measurements may not be in good agreement. Looking at the ambient scattering values for the descents between flight levels for the TO nephelometer suggests that there is indeed vertical inhomogeneity between levels. Whether these differences in scattering between the in situ and remote instruments correspond with differences in asymmetry parameter will be discussed in the results section. The uncertainty in the spectral AOD measurements ranged from approximately 0.002 to 0.02, depending on wavelength and flight. More discussion of the uncertainty in the TO AATS-14 AOD measurements are given by Schmid et al. [2006, and references therein].
 In general, comparison of measured and calculated scattering showed these values were well correlated among the different platforms, R2 > 0.9, with the exception of the GIF TDMA (R2 = 0.78) and AATS-14 (R2 = 0.8, based on Schmid et al. ). The actual values of the scattering intercomparisons did not suggest quite as good agreement. However, for deriving g, the correlation rather than the absolute value of scattering is the critical factor because g is an intensive parameter [Ogren, 1995] and thus is independent of the absolute amount of aerosol present. As we show in the following section it is the size distribution (size and width) and wavelength which are the most important factors for determining g.
2.3. Methods for Deriving g From Various Aerosol Measurements
 The information needed to calculate g on the basis of aerosol physical properties includes the aerosol size distribution, refractive index and particle shape. With these data in hand, Mie theory (in the case of spherical particles) or discrete dipole approximation (DDA) or T-matrix calculations (for nonspherical particles) can be used to calculate the aerosol optical properties. Size distributions can be measured directly with in situ aerosol size instrumentation, but another way to obtain a size distribution is the inversion of spectral aerosol optical depth or light extinction measurements [e.g., King et al., 1978; Fiebig et al., 2005]. Refractive index values can be estimated from aerosol chemistry and/or size-resolved hygroscopicity (e.g., R. Gasparini et al., Comparison of humidity-dependent optical properties and CCN spectra derived using size-resolved hygroscopicity with direct measurements made at the ARM Southern Great Plains site, submitted to Journal of Geophysical Research, 2005, hereinafter referred to as Gasparini et al., submitted manuscript, 2005) measurements. In the case of chemical measurements, the low time resolution and limited number of species analyzed often make this method no better than assuming a reasonable value for the refractive index. As is shown later, assuming a reasonable refractive index for dry aerosol does not have a significant effect (less than 3%) on the calculated light scattering. At ambient humidities, the change in refractive index and particle size due to water uptake can be significant and will influence the calculated optical properties. Hartley and Hobbs , for example, show the strong influence of RH on g, where g increases with RH.
 For the aerosol size distribution measurements made during the IOP (and for size distributions derived from spectral AOD or scattering measurements), homogeneous, spherical particles are assumed, and Mie theory is used to calculate an asymmetry parameter at 550 nm. This provides for convenient comparison to the nephelometer-derived g at 550 nm. A refractive index of 1.55 + 0.015i is assumed for measurements made below 40% RH. This value results in good agreement between measured and calculated scattering as noted in the instrument descriptions. To go from an asymmetry parameter for a single particle to an asymmetry parameter representing the aerosol size distribution the following equation [d'Almeida et al., 1991] is used:
where i indicates the aerosol size bin.
 If both σsp and σbsp are measured then the backscattering fraction b can be calculated. Here the backscatter fraction (b) refers to the ratio of light scattered into the backward hemisphere (backscatter, σbsp)) to total light scattering (σsp) measured by the nephelometer. With b an alternative approach for deriving asymmetry parameter applying the Henyey-Greenstein approximation [e.g., Wiscombe and Grams, 1976] can be used. Wiscombe and Grams  plot a smooth relationship between b (which they call β(1)) and g in their Figure 3. The fit equation based on that plot relating b to g is (P. Arnott, personal communication, 2002):
Marshall et al.  suggest a more complex relationship between b and g which depends on the imaginary part of the refractive index and the width of the aerosol size distribution.
 A new data inversion technique [Fiebig et al., 2005] is also applied to derive the asymmetry parameter from the low-humidity AOS and IAP aerosol system measurements (aerosol light absorption and spectral light scattering and backscattering). The 1 and 10 μm impactors upstream of the nephelometer provide geometric aerosol size cuts of 0.79 and 7.9 μm respectively, which allows for separation of the aerosol into fine (dp < 0.79 μm) and coarse (0.79 μm < dp < 7.9 μm) size modes. The particles are represented by homogenous, internally mixed spheres composed of ammonium sulfate, soot and water over the entire size range. (Note: not including organic aerosol as one of the components is unlikely to affect the inversion results for dry aerosol as the organics can be assumed to have similar RI as ammonium sulfate.) The aerosol chemical composition is parameterized by a soot volume fraction fsoot and a water volume fraction fH2O for the absorbing and nonabsorbing portions of the aerosol. The algorithm does not assume an initial guess for the aerosol size distribution, rather it requires knowledge of the instrument transfer function, i.e., what fraction of particles of each size are sensed by the instrument. During the inversion, the PSAP and nephelometer (including angular truncation effects) responses are calculated for each size mode. The measured particle scattering coefficients are used to derive a particle size distribution and the inversion algorithm discretizes the particle size distribution into logarithmic equidistant bins. In an iterative process, the values for fsoot and fH2O are varied so that the measured light absorption and backscattering coefficients, respectively, are reproduced by the inversion result. Iterations are done first for the fine mode and then for the coarse mode. For an inversion to be deemed successful, the calculated responses must match the measurements. The inversion's final output is an aerosol size distribution and chemical composition from which refractive index can be determined and thus the asymmetry parameter can be calculated using Mie theory. The median RI retrieved for the IOP aerosol was 1.55 + 0.015i. The inversion does not retrieve information about the state of mixture of the soot component, the soot size distribution and the particle density and this results in a systematic uncertainty in the retrieved asymmetry parameter of approximately 1% at 550 nm in both size ranges (M. Fiebig and J. A. Ogren, Retrieval and climatology of the aerosol asymmetry parameter at the CMDL aerosol baseline stations, submitted to Journal of Geophysical Research, 2005). For the surface and airborne CMDL measurements, we will use both equation (4) and the Fiebig inversion scheme to derive values for asymmetry parameters.
 For the remote sensing instruments (AERONET and TO AATS-14) different data inversion techniques are employed to derive an asymmetry parameter. For the AERONET measurements, the data inversion algorithm [Dubovik and King, 2000; Dubovik et al., 2000] assumes that the particles are homogenous spheres, although the composition (i.e., index of refraction) is not fixed. Both of these remote sensing instruments make measurements at ambient conditions so that no relative humidity adjustment is needed.
 For the TO AATS-14 data, the inversion algorithm by King et al.  is used to calculate aerosol size distributions consistent with the measured optical depths. The basic requirements of the inversion are spectral AOD and their associated uncertainties, an assumed refractive index, and diameter limits for the size distribution. It is up to the user to choose which of the many aerosol size distributions output by the inversion algorithm is most representative of the actual aerosol. King  shows successful application of the inversion for 0.01 < AOD < 2.0. The measurements of in situ size distributions and aerosol optical properties made on the Twin Otter simultaneous with the TO AATS-14 observations are used here to constrain the choice of size distribution. The King algorithm assumes spherical, homogenous particles and a constant refractive index over the entire size range, the same assumptions used in the Mie theory calculations. Because the input data to the inversion algorithm is aerosol optical depth the result is a “columnar” aerosol size distribution, i.e., “number of particles per unit area per unit log radius interval in a vertical column in the atmosphere” and has units of cm−2. To correctly compare asymmetry parameters derived from the TO AATS-14 with those derived from in situ instruments during a flight leg two things must be done. First, the AOD contribution from each flight leg must be determined. Because the TO AATS-14 measures AOD in the atmospheric column between the aircraft and the top of the atmosphere, this calculation is straightforward: AODΔi = AODi − AODi+1 where i is the level of interest and i + 1 is the level above it. Second, the size distribution resulting from the inversion must be divided by the assumed vertical thickness of the flight leg (Δi), i.e., the portion of the column over which AOD was calculated, e.g., Δi = zi+1 − zi. Here zi is the altitude of the level of interest and zi+1 is the altitude of the level above it. This division gives the calculated number concentration in units of cm−3 and thus should make the number concentration comparable to other size distributions and also can be directly input into Mie scattering code.
 The King inversion can be used to derive a value for g [Gonzalez-Jorge and Ogren, 1996] for the total column at ambient conditions by using the TO AATS-14 measurements for the lowest flight leg. Likewise, the AERONET g is a column value at ambient conditions. Calculating g for the total column for the in situ airborne instruments first requires calculation of g for the individual flight layers weighted by the scattering coefficient and then summing over the flight levels normalized by level thickness Δi and scattering coefficient:
We will do this for all of the profile flights over SGP during the IOP: all the IAP flights during the IOP and the three TO flights (DOY 127, 129 and 145) that were side-by-side with IAP plane for seven or more flight levels for both ambient and low-RH conditions.