Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado, USA
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, USA
Corresponding author: S. E. LeBlanc, Department of Atmospheric and Oceanic Sciences, University of Colorado, 311 UCB, Folsom Stadium, Rm 255, Gate 7, Boulder, CO 80309-0311, USA. (firstname.lastname@example.org)
 This study presents the aerosol radiative forcing derived from airborne measurements of shortwave spectral irradiance during the 2010 Research at the Nexus of Air Quality and Climate Change (CalNex). Relative forcing efficiency, the radiative forcing normalized by aerosol optical thickness and incident irradiance, is a means of comparing the aerosol radiative forcing for different conditions. In this study, it is used to put the aerosol radiative effects of an air mass in the Los Angeles basin in context with case studies from three field missions that targeted other regions and aerosol types, including a case study from the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS). For CalNex, we relied on irradiance measurements onboard the NOAA P-3 aircraft during a flight on 19 May 2010 over a ground station. CalNex presented a difficulty for determining forcing efficiency since one of the input parameters, optical thickness, was not available from the same aircraft. However, extinction profiles were available from a nearby aircraft. An existing retrieval algorithm was modified to use those measurements as initial estimate for the missing optical thickness. In addition, single scattering albedo and asymmetry parameter (secondary products of the method), were compared with CalNex in situ measurements. The CalNex relative forcing efficiency spectra agreed with earlier studies that found this parameter to be constrained at each wavelength within 20% per unit of aerosol optical thickness at 500 nm regardless of aerosol type and experiment, except for highly absorbing aerosols sampled near Mexico City. The diurnally averaged below-layer forcing efficiency integrated over the wavelength range of 350–700 nm for CalNex is estimated to be −58.6 ± 13.8 W/m2, whereas for the ARCTAS case it is −48.7 ± 11.5 W/m2.
 Aerosols contribute the largest uncertainty to the net anthropogenic radiative forcing of climate [Forster et al., 2007]. Aerosol particles can directly modify the net irradiance, which is a measure of the net radiative energy density. This is termed the aerosol direct radiative forcing. Aerosol direct radiative forcing may offset global carbon dioxide forcing by 5 to 50% [Forster et al., 2007], making its understanding crucial for characterizing climate change. The global annually averaged aerosol direct radiative forcing at the top of the atmosphere is determined by models utilizing in situ and satellite measurements [Bellouin et al., 2005; Chung et al., 2005]. However, the use of models with their associated uncertainties largely contribute to the uncertainty of this forcing [Yu et al., 2006; Remer and Kaufman, 2006; Forster et al., 2007]. The forcing uncertainties are large in part because they are often derived indirectly from remote sensing or in situ measurements of aerosol optical thickness, single scattering albedo, and asymmetry parameter [Massoli et al., 2009]. Reducing model uncertainties, improving satellite observations, and continuing intensive airborne studies are all needed to reduce forcing uncertainty.
 In the past, multiple airborne studies directly measured atmospheric irradiance and aerosol optical thickness, which provided a more accurate estimation of the local aerosol direct radiative forcing [Redemann et al., 2006]. One such method is presented in this current work. These studies determined the aerosol direct radiative forcing for some specific time, region, and prevailing aerosol type [Redemann et al., 2006; Schmidt et al., 2010; Bergstrom et al., 2003]. Uncertainties of simulated aerosol radiative forcing can be minimized by tying these values to measurements of irradiance at specific levels of the atmosphere and regions, or by validating the simulated aerosol radiative forcing with observations [Magi et al., 2008].
1.1. Radiative Forcing
 Instrument uncertainties and various assumptions in aerosol retrieval models propagate to uncertainties in calculated radiative forcing [Magi et al., 2008]. Although direct measurement of aerosol direct radiative forcing would be the preferred path to reduce these uncertainties, it is impossible to measure forcing directly. Aerosol radiative forcing is the change to net radiation due to aerosols. Its determination would require simultaneous measurements of atmospheric radiation in the presence and absence of aerosols, which is physically impossible. Previously, the radiative forcing was estimated by measuring the change of net irradiance along a gradient in aerosol optical thickness, with the restriction that aerosol intensive properties and surface albedo stay constant [e.g., Redemann et al., 2006].
 Another method to obtain aerosol direct radiative forcing was developed by Schmidt et al. , adapted from Bergstrom et al. . Schmidt et al.  used airborne spectral irradiance (F) and spectral aerosol optical thickness (τ), which, if not measured directly [e.g., Redemann et al., 2006], can be determined by a combination of aerosol optical thickness at one wavelength and the extinction Ångström exponent (a). These measurements of irradiance above and below an aerosol layer were used to derive aerosol radiative properties and surface albedo (α). The derived aerosol radiative properties (described in detail in Appendix B) were the aerosol single scattering albedo (ϖ) and the asymmetry parameter (g). These radiative properties along with the aerosol optical thickness were then used as inputs in a radiative transfer model to calculate spectral irradiance in the presence of the aerosol layer under study, while the clear sky spectral irradiance was calculated using only the retrieved surface albedo. The difference between the simulated irradiance with and without aerosol gives the aerosol direct radiative forcing. A comparison of the different methods used to obtain aerosol direct radiative forcing, including the one presented in this work, is presented in Table 1.
Table 1. Input and Output of Different Methods Used to Obtain Layer-Averaged Aerosol Optical Properties as Well as Relative Forcing Efficiency (fe) From Airborne Spectral Irradiance (F) and Aerosol Optical Thickness (τ) Measurements
 Aerosol direct radiative forcing (f) is the change in net irradiance due to aerosols, f = Fnet,aerosols − Fnet,clear. It can be defined at different time scales (such as instantaneous, diurnal, or since the pre-industrial period) and at different levels of the atmosphere (top of the atmosphere, at the tropopause, top of the layer, below a layer, or at the surface). In this study, the focus is on instantaneous radiative forcing above and below aerosol layers. Aerosol direct radiative forcing depends on aerosol optical thickness and incident irradiance at the top of the layer. Forcing efficiency, the radiative forcing normalized by aerosol optical thickness at 500 nm, was introduced byMeywerk and Ramanathan  to reduce large variability in aerosol loading which affects the comparison of forcing for different cases. Relative forcing efficiency (fe) [Redemann et al., 2006]:
is a measure of the radiative forcing as a percentage of the incident irradiance and per unit of midvisible aerosol optical thickness (τ500 nm) (normalized by the incident irradiance at the top of the layer [Ftop↓]).
 The aerosol direct radiative forcing can vary considerably between different types of aerosol and their regions. Since the first-order dependence of this forcing on aerosol optical thickness and incident irradiance above the aerosol layer is removed in the relative forcing efficiency, this enables us to compare the forcing from various different regions of the world on the same scale. Although the relative forcing efficiency removes much of the dependencies to the solar zenith angle, there are still some second order effects related to the optical path, such as differences in multiple scattering. Regardless of these second order effects, relative forcing efficiency provides a more uniform basis of comparison of the aerosol's effect on radiation from various regions than the aerosol's direct forcing itself.
1.3. This Study
 This study focuses on the derived relative forcing efficiency from data collected during an intensive field campaign in the Los Angeles basin. In addition, this study shows a comparison of the CalNex relative forcing efficiency to that from other similar regional studies. Using measurements of spectral irradiance from the Solar Spectral Flux Radiometer (SSFR; presented in section 2.1) and profiles of aerosol extinction from the High Spectral Resolution Lidar (HSRL) (presented in section 2.2), relative forcing efficiency is determined from measurements taken during the Research at the Nexus of Air Quality and Climate Change (CalNex) (presented in section 3) intensive field campaign. Relative forcing efficiency is derived via a modified retrieval of aerosol single scattering albedo, optical thickness, asymmetry parameter and surface albedo (presented in Appendix C). These new analysis tools are introduced to accommodate the incomplete (spectrally) and non-concurrent measurements of aerosol optical thickness. These tools are tested with concurrent measurements of aerosol optical thickness and spectral irradiance taken during another intensive field mission with similar instrumentation, the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) based in Cold Lake, Alberta, Canada. Relative forcing efficiency spectra calculated from the measurements taken during these two field campaigns (CalNex and ARCTAS) and other field campaigns are presented insection 4.
2. Instrumentation and Radiative Transfer Model
 Measurements of solar spectral irradiance taken during CalNex are used as input to a retrieval algorithm that determines the relative forcing efficiency. Both the SSFR, which measures solar spectral irradiance, and the radiative transfer model, which is used in the retrieval algorithm, are presented below. Ancillary instruments are also presented below.
2.1. Solar Spectral Flux Radiometer
 The SSFR [Pilewskie et al., 2003] is a moderate spectral-resolution (8 to 12 nm) instrument designed to measure solar spectral irradiance under varying atmospheric conditions. The SSFR is composed of two pairs of spectrometers for acquiring zenith and nadir irradiance over the near-complete shortwave spectrum (350–2150 nm). The SSFR has a precision of 0.1–0.2%, represented by the standard deviation of a collection of spectra with SSFR illuminated by a stable lamp source. Radiometric uncertainty is 3 to 5% across the spectrum, determined primarily by a NIST-traceable lamp used for calibration. Fiber optic bundles connect aircraft skin-mounted hemispheric light collectors to the rack-mounted spectrometers in the aircraft cabin. The light collectors measure full hemispheric (2πsr) downwelling and upwelling spectral irradiance. Spectral irradiance measurements are subject to larger uncertainty when fix-mounted on an aircraft surface that deviates from level attitude in flight. Sample irradiance spectra from the SSFR from a scene over Ontario, California, during CalNex are shown inFigure 1.
2.2. Ancillary Instruments
 Measurements of spectral irradiance alone are not sufficient to be able to quantify the relative forcing efficiency of aerosols. Measurements of the aerosol layer optical thickness are also required. During CalNex, the HSRL [Hair et al., 2008] provided profiles of aerosol extinction coefficients at a wavelength of 532 nm. This highly robust downward pointing lidar, which is radiometrically calibrated internally, also provides aerosol backscatter and aerosol depolarization at two wavelengths. During ARCTAS, the NASA Ames 14-channel Airborne Tracking Sunphotometer (AATS-14) [Redemann et al., 2005; Shinozuka et al., 2011] was used to determine the aerosol optical thickness above the aircraft level. Additionally, measurements of the entire column's aerosol optical thickness, single scattering albedo, asymmetry parameter, and Ångström exponent is returned from an Aerosol Robotic Network (AERONET) sunphotometer [Holben et al., 1998].
 In situ measurements of microphysical and optical properties of aerosol particles are used to compare secondary products (single scattering albedo and asymmetry parameter) obtained when determining relative forcing efficiency. Optical aerosol properties were provided by five instruments onboard the NOAA P-3. The Cavity Ring Down aerosol extinction Spectrometer (CRDS) [Langridge et al., 2011] measured total dry aerosol light extinction at 532, 405 and 662 nm and the dependence of extinction on relative humidity. The Photoacoustic Absorption Spectrometer (PAS) [Lack et al., 2012] measured total dry aerosol light absorption at the same wavelengths as the CRDS. Aerosol size distributions with particle diameters of 4–6300 nm were measured using the combination of a White-Light Optical Particle Counter (WLOPC) [Brock et al., 2003], an Ultra High Sensitivity Aerosol Size spectrometer (UHSAS) [Brock et al., 2004], and a Nucleation Mode Aerosol Size Spectrometer (NMASS) [Brock et al., 2004]. Aerosol extinction at ambient humidity conditions is derived from these measurements using kappa-Köhler theory [Petters and Kreidenweis, 2007].
2.3. Radiative Transfer Model
 The radiative transfer model used in this retrieval is the N-stream DISORT [Wiscombe and Grams, 1976] with SBDART [Ricchiazzi et al., 1998] for atmospheric molecular absorption, which is publicly available within LibRadtran [Mayer and Kylling, 2005]. The extraterrestrial solar spectral irradiance was taken from Kurucz at 1-nm spectral resolution. Mie scattering calculations were used to obtain the optical properties of aerosol particles using the in situ measurements.Wiscombe  describes the code that calculates Mie scattering.
3. Research at the Nexus of Air Quality and Climate Change
 CalNex was conducted in California during May and June 2010. Its primary focus was the impact of trace gases and aerosols from urban-industrial pollution on air quality and climate-relevant parameters (specifically, direct and indirect aerosol radiative forcing) in the state of California and the eastern Pacific coastal regions. Multiple aircraft, one research ship, two major ground measurement sites, tall instrumented towers, ozone sondes, satellite instruments, and forecast models were involved in this multiagency effort. Data taken from instruments situated on two of the research aircrafts and one of the major ground sites are presented in this study.
 Radiative measurements were taken onboard the NOAA WP-3D research aircraft (hereafter, P-3), along with the contingent of cloud probes, gas-phase chemistry, aerosol optical properties, and meteorological instruments. The P-3 flew a suite of radiation instruments that measured solar spectral irradiance, spectral actinic flux, as well as solar and infrared broadband irradiance. The primary radiation measurements applied in this study were spectral irradiance, acquired from the SSFR.
 In situ measurements of microphysical and optical properties of aerosol particles were acquired from the CRDS, PAS, WLOPC, UHSAS, and NMASS located on the P-3. Other measurements were taken by the HSRL onboard the NASA King Air B-200 (hereafter, NASA King Air) and by AERONET at the Caltech ground site in Pasadena, California.
 In this work we focus on one case on 19 May 2010 (flight track in Figure 2), when the P-3 encountered cloud-free conditions and high aerosol concentrations, which is compared to flights from other field missions. On this day, the plane sampled the outflow of pollution from the Los Angeles basin across the San Gabriel mountain range, which runs east-west just north of San Bernardino. Flight legs in smog conditions over the Caltech ground site in Pasadena were coordinated with the NASA King Air. Above the Caltech ground site, the P-3 flew a series of stacked level legs within 30 min of the NASA King Air. A comparison between ambient aerosol extinction, derived from in situ measurements, and the aerosol extinction profile from the HSRL on board the NASA King Air (stacked-level flight legs, shown inFigures 3a and 3b) shows general agreement. General agreement has also been observed during CalNex between the integrated aerosol extinction profile measured by HSRL and aerosol optical thickness measured by AERONET. We note that in situ measurements of aerosol extinction were generally lower than extinction measured remotely by the HSRL. This was possibly due to the influence of particles larger than 2 microns diameter, which were not sampled by the CRDS but were often present during CALNEX. The layer-integrated aerosol extinction profile (between 400 and 800 m) measured by HSRL was equivalent to an aerosol optical thickness of approximately 0.13; the layer-integrated aerosol extinction measured by CRDS is approximately 0.16. In contrast, the total column aerosol optical thickness at 500 nm measured by AERONET is approximately 0.34. Since AERONET samples the entire column, including the near surface layer, while the other measurement methods sample the 400–800 m layer, a higher aerosol optical thickness is expected. In this layer, the measured depolarization values (at 532 nm) were <0.05, therefore the majority of aerosol particles were spherical.
4. Results and Discussion from CalNex: 19 May 2010
 Relative forcing efficiency has been retrieved for the CalNex case study on 19 May 2010 and for the ARCTAS case on 9 July 2008 and compared to values from different regions. For the CalNex case study secondary products of aerosol optical properties and surface albedo have been retrieved using the algorithm modified from Schmidt et al.  described in Appendix C. In this algorithm, aerosol optical thickness is retrieved when the values of the asymmetry parameter determined from transmittance and reflectance converge to a single value. These properties, along with single scattering albedo and surface albedo are determined by matching modeled spectral irradiance to its measurement above and below an aerosol layer. To measure upwelling and downwelling irradiance above and below an aerosol layer with a single aircraft, a flight path of stacked level legs is required. A diagram of the measurement geometry used in this method is presented in Figure 4. This method can be applied to the entire spectral range of SSFR, from 350 to 2150 nm. However, above 1050 nm the aerosol radiative effect is not significant compared to the radiometric uncertainty. Therefore, we only analyzed a limited wavelength range from 350 to 1050 nm.
4.1. Spectra of Retrieved Aerosol Properties
 The spectra of retrieved parameters for 19 May 2010 over the Caltech ground site are presented in Figure 5. Aerosol single scattering albedo (ϖ), asymmetry parameter (g), optical thickness (τ), and surface albedo (α) all lie within plausible ranges (see Figure 5a). Single scattering albedo values (black) lie within the range 0.85–0.98 throughout most of the spectrum. In comparison, various types of aerosol show different spectral single scattering albedo, both in shape and value, as compared to those sampled during CalNex. For the aerosol sampled during ARCTAS, its single scattering albedo increases from 0.85 to 0.92 and then decreases to 0.8 at 350 nm, 550 nm, and 1050 nm respectively. For another field mission, the Megacity Initiative: Local and Global Research Observations (MILAGRO) near Mexico City [Schmidt et al., 2010], the single scattering albedo for freshly emitted highly absorbing aerosol decreases from 0.85 at 350 nm to 0.7 at 1050 nm. For slightly aged aerosols sampled during MILAGRO, the single scattering albedo increases from 0.85 at 350 nm to a near constant 0.9 at longer wavelengths. A broadband estimate of single scattering albedo from another field mission, the Intercontinental Chemical Transport Experiment - North America (INTEX-NA) over the Gulf of Maine [Redemann et al., 2006], reports values between 0.88 to 1.00, which is similar to the range of spectral values reported for CalNex. The retrieved spectral asymmetry parameter for aerosol sampled during CalNex decreases from 0.8 at 350 nm to a constant 0.6 at 700–1050 nm. A decreasing asymmetry parameter with increasing wavelength is also observed during MILAGRO, where slightly aged and highly absorbing aerosol's asymmetry parameter decreased from 0.8 at 350 nm to 0.55 at 850 nm and 0.95 at 350 nm to 0.74 at 600 nm respectively. For the ARCTAS case, the asymmetry parameter decreases from 0.75 at 350 nm to 0.65 at 550 nm and then increases to 0.95 at 1050 nm. For CalNex, the surface albedo spectrum (blue) shows a pattern that resembles a mixed vegetation scene (increase in near infrared [Horler et al., 1983]). The aerosol optical thickness (red curve, right axis) exponentially decreases with increasing wavelength, typical for ambient aerosol particle extinction. A similar spectral shape of aerosol optical thickness is also observed for cases from ARCTAS, MILAGRO and INTEX-NA. The spectral absorption, measured during CalNex (red spectrum inFigure 5b), matches the modeled spectral absorption at the wavelengths denoted by the black dots, as required for a successful retrieval. Since we assume a plane parallel, horizontally homogeneous aerosol layer, there is no net horizontal transport of photons, thus the absorbed spectral irradiance of a layer is equivalent to the vertical flux divergence. The difference between above- and below-layer net spectral irradiance (derived from the irradiances shown inFigure 1) is the absorbed spectral irradiance of this layer. The absorbed spectral irradiance at longer wavelengths (>600 nm) is lower than the absorbed spectral irradiance at shorter wavelengths (<600 nm). Although the measurement uncertainty over this range is nearly constant, the relative uncertainty increases with lower absorbed spectral irradiance, consequently the relative uncertainty in the retrieve properties is also increased (larger shaded area at higher wavelengths in Figure 5a).
4.2. Retrieved Along-Path Aerosol Properties
 Spatial variations of the retrieved parameters at two wavelengths can be seen by the colored lines as a function of the distance from the Caltech ground site along the flight path in Figure 6. The single scattering albedo, evaluated at 380 nm, ranges from 0.84 (high absorption) to 0.96 (moderate absorption). The mean asymmetry parameter of this aerosol layer, evaluated at 380 nm, is around 0.85, which is higher than the value typically associated with an urban environment of 0.74 (determined at 440 nm [Dubovik et al., 2002, Figure 10a]). Nevertheless, the spectral shape of asymmetry parameter (decreasing with longer wavelengths) does coincide with observations from urban environments observed in worldwide locations from AERONET [Dubovik et al., 2002]. The higher value, compared to AERONET asymmetry parameter indicates stronger forward scattering and suggests larger aerosol particles than found from other urban environments (Greenbelt, Maryland, USA; Crete-Paris, France; Mexico City, Mexico; Maldives). Aerosol optical thickness, single scattering albedo, and asymmetry parameter exhibit variability throughout the flight leg, while the surface albedo stays fairly constant. In some cases, such as about 6 km east from the Caltech ground site, a noticeable change in the single scattering albedo and the asymmetry parameter at 500 nm coincide with the location of major roads in Pasadena. At this location, and a few others, single scattering albedo is lower than the average, thus signifying an increase in light absorption of these aerosol particles. Toward the west of the Caltech ground site, the airborne video of the surface shows an increase in vegetation. This increase in vegetation can be seen by the increased separation between the surface albedo at 380 nm and 870 nm, which is indicative of vegetation's spectral reflectance feature, the near-IR edge. This retrieved surface albedo thus reflects the changes in the physical environment.
4.3. Retrieved Relative Forcing Efficiency
 The aerosol direct radiative forcing is derived by calculating the spectral irradiance with and without aerosols, following the method described by Schmidt et al. . A negative direct radiative forcing represents a negative change in the net irradiance, and therefore cooling, while a positive direct radiative forcing represents heating. The same is true for relative forcing efficiency. The resulting aerosol relative forcing efficiency from CalNex is shown in Figure 7. The separation between the above- and below-layer relative forcing efficiency is a relative indication of the amount of absorption of within that layer. Even though the above- and below-layer forcing evaluated at 500 nm (Figure 7a) vary considerably, their difference remains fixed, except when there is increased absorption. The dips of relative forcing efficiency and the increased absorption coincide with the lower values of single scattering albedo at 500 nm, specifically near a major road in Pasadena (6 km east of Caltech). These dips of relative forcing efficiency are related to cooling, both above the layer and more significantly below the layer. At the same time, they are indicator of increased warming within the layer.
 The relative spectral forcing efficiency from measurements taken during CalNex and other field missions, including ARCTAS, is shown in Figure 7b. The relative forcing efficiency spectra from CalNex are compared to those from MILAGRO over the Gulf of Mexico, INTEX-NA off the coast of Maine, and ARCTAS in northern Alberta. The comparison reveals that the general spectral shape of the above- and below-layer forcing during CalNex is similar to those derived for the other field missions. For example, near the pollution sources during MILAGRO, freshly emitted and highly absorbing aerosols were measured. There were also slightly aged aerosols, measured at a larger distance from the same aerosol source. The relative forcing efficiency from an aged aerosol plume measured during MILAGRO agrees with the average relative forcing efficiency from the urban aerosols measured during CalNex.
 The relative forcing-efficiency spectra from the various experiments have similar magnitude and spectral shapes. These similarities suggest that for the field experiments under study, relative forcing efficiency at any one wavelength between 350–1050 nm is constrained within 20% per unit of midvisible aerosol optical thickness regardless of aerosol type, except for highly absorbing aerosol.
 The below-layer relative forcing efficiency spectra increases with increasing wavelength, but always represents cooling, even when the value and spectral shape of single scattering albedo, asymmetry parameter and surface albedo differs. The recurring spectral shape of the relative forcing efficiency may be due to aerosol optical thickness since it is the only optical property that does not change spectral shape between the various experiments. The relative forcing efficiency at each wavelength varies by no more than 20% per unit of midvisible aerosol optical thickness for all missions indicated inFigure 7b, with the exception of the freshly emitted aerosols shown for the MILAGRO case. The entire range of below-layer relative forcing efficiency at all wavelengths goes from −5 to −60% per unit of midvisible aerosol optical thickness. The above-layer relative-forcing efficiencies also have similar spectral shapes. Starting from near 0% at 350 nm, the above-layer relative forcing efficiencies decreases to their lowest values near 500 nm and then increases with increasing wavelength. These values all lie between −15 to +5% per unit of midvisible aerosol optical thickness with the largest spread between experiments at the lowest wavelengths. These above-layer forcings are modulated by the change in the upwelling irradiance. For aerosol similar to those sampled during CalNex, a modeled change in upwelling irradiance at 500 nm due to the aerosols is about −7.5% per unit of midvisible aerosol optical thickness [Russell et al., 1997]. Although this is only an approximation, the modeled change in upwelling irradiance per unit of midvisible aerosol optical thickness is within one standard deviation of the measured mean above-layer relative forcing efficiency.
4.4. Corresponding Diurnal Average of Forcing Efficiency
 In order to compare the instantaneous spectral relative forcing efficiency to other often reported values of broadband diurnally averaged forcing efficiency, we used a conversion method described below. The instantaneous spectral relative forcing efficiency was multiplied with the downwelling irradiance above the aerosol layer to compute the instantaneous spectral forcing efficiency. The instantaneous broadband forcing efficiency is then calculated by integrating the resulting spectral forcing efficiency over the wavelength range of 350–700 nm. The conversion of the instantaneous broadband forcing efficiency to its diurnal average was done by using the well-confined ratios calculated byRedemann et al. . These ratios represent the below-layer relationship between instantaneous broadband forcing efficiency at various solar zenith angles to diurnally averaged values. The diurnally averaged broadband forcing efficiency at the bottom of the aerosol layer for the CalNex case is −58.6 ± 13.8 W/m2, whereas for the ARCTAS case it is −48.7 ± 11.5 W/m2. Other radiometrically determined estimates of diurnally averaged forcing efficiency show −45.8 ± 13.1 W/m2for INTEX-NA, −48 W/m2 from broadband (400–700 nm) irradiance measured during an Indian ocean experiment by Meywerk and Ramanathan , 38.5 ± 4.0 W/m2 and 42.2 ± 4.8 W/m2from ground-based radiometer measurements of broadband (400–700 nm) irradiance taken during the Indian ocean experiment and another in Asia byBush and Valero [2002, 2003]. Although CalNex represents the highest below-layer diurnally averaged forcing efficiency presented here, its uncertainty falls within the reported values from ARCTAS, INTEX-NA, and the Indian Ocean experiment.
5. Summary and Discussion
 Measurements by SSFR deployed on the P-3 during the field mission CalNex were used to derive relative forcing efficiency and its spectral dependence. A comparison of this spectral relative forcing efficiency to those from other field missions, including ARCTAS, reveals that for these cases, the relative forcing efficiency at each wavelength vary by no more than 20% per unit of midvisible aerosol optical thickness, with the exception of highly absorbing urban-industrial aerosol.
 Previous algorithms for determining relative forcing efficiency required measurements of spectral irradiance and optical thickness as inputs. During CalNex, no concurrent measurements of aerosol optical thickness were available on one aircraft (P-3). Instead, profiles of aerosol extinction coefficients were available from an HSRL onboard a separate platform (NASA King Air). To derive relative forcing efficiency, an existing algorithm was modified to use the extinction-coefficient profile from HSRL. We adjusted this profile for the temporal and spatial displacement of the P-3 and the NASA King Air and to extend this profile to other wavelengths. In addition to relative forcing efficiency, the algorithm provides spectral single scattering albedo, the asymmetry parameter, and the effective surface albedo. We tested our retrieval with data from the ARCTAS field mission where, in addition to HSRL and SSFR measurements, the spectral aerosol optical thickness was available from a sunphotometer (AATS-14). A comparison of the adjusted aerosol optical thickness from HSRL and the true aerosol optical thickness from AATS-14 was used to assess the accuracy of the new algorithm. Beyond this simple comparison, the accuracy of the retrieval was estimated by determining the uncertainty of the retrieved properties, as well as the sensitivity of the retrieved aerosol optical thickness to its initial estimate. The accuracy of this retrieval during CalNex is also evaluated by comparing retrieved single scattering albedo and asymmetry parameter to their in situ measured counterparts. Although the secondary retrieved products differ slightly from in situ measurements and from measurements of aerosol optical thickness, the relative forcing efficiency derived for CalNex compares at each wavelength to within 20% per unit of midvisible aerosol optical thickness of other field missions, with the exception of freshly emitted aerosol. This result indicates that different aerosol types can be characterized by quite similar relative forcing-efficiency spectra.
 The variation between these different aerosol types can be understood more thoroughly with more measurements of airborne spectral irradiance from different field missions. Although the relative forcing efficiency removes most regionally dependent factors, the regional effect of surface albedo, among others, still influence the relative forcing efficiency. By understanding this and other effects a more thorough comparison, and possibly a better constraint on the relative forcing efficiency, can be achieved. Since relative forcing efficiency is mostly constrained within 20% per unit of midvisible aerosol optical thickness for these cases it can be used as a parameterization of the aerosol direct radiative forcing of climate with the midvisible aerosol optical thickness as the only parameter. To obtain the value of the aerosol direct radiative forcing for these cases, you can simply multiply the spectrally resolved downwelling short-wave irradiance and the aerosol optical thickness at 500 nm to the average relative forcing efficiency described in this paper. Climate models, which show disagreement of aerosol absorption [Forster et al., 2007], can integrate these below-layer forcings and therefore help constrain the aerosol direct radiative forcing of climate.
Appendix A:: Acronyms
 In this section we present the various acronyms, organized alphabetically, used throughout this work.
 Presented here are the various definitions of measured and derived radiative quantities. All quantities introduced here are wavelength dependent, unless specifically mentioned.
B1. Spectral Irradiance
 Spectral irradiance (F) is the hemispherically integrated cosine-weighted radiative energy per unit time per unit area per wavelength. The net irradiance (Fnet) is defined as the difference between the downwelling (F↓) and upwelling (F↑) irradiance (Fnet = F↓ − F↑). The albedo (α) is the ratio of the upwelling-to-downwelling irradiance (α = F↑/F↓). In absence of net horizontal photon transport, the difference of net irradiance at the top of the layer (Ftopnet) and at the bottom of the layer (Fbotnet) can be used to derive the layer-absorbed irradiance. Absorptance (A) is defined as absorbed irradiance normalized by incident irradiance (A = ).
B2. Aerosol Optical Thickness
 Aerosol optical thickness (τ) is a measure of the total mean free path of photons through a layer. Scattering (β) and absorption (κ) coefficients are the inverse of the distance that a photon must travel before it is either scattered or absorbed. The sum of these coefficients is the extinction coefficient (σext). Aerosol optical thickness is obtained from integrating the extinction coefficient over a column:
B3. Single Scattering Albedo
 Single scattering albedo (ϖ) is the ratio of scattering and extinction coefficients:
 The single scattering albedo of a nonabsorptive layer would be unity. It describes the absorption properties of an aerosol layer.
B4. Asymmetry Parameter
 The asymmetry parameter (g) is the first moment of the scattering phase function (P(θ)) and describes the overall direction of photon scattering [Hansen and Hovenier, 1974]:
 This parameter can be used in the Henyey-Greenstein (HG) phase-function approximation, which adequately represents the actual phase function for a spherical particle within the N-stream radiative model code DISORT [Bohren and Clothiaux, 2006; Wiscombe and Grams, 1976]. The asymmetry parameter ranges from −1 for backscattering to 1 for forward scattering. At a given wavelength, the largest particles scatter light more in the forward direction, and thus have a larger asymmetry parameter than the smallest particles.
B5. Ångström Exponent
 An Ångström exponent (a) is often used to parameterize the wavelength dependence of optical thickness. A power law approximates the relationship between wavelength (λ) and aerosol optical thickness to a reference aerosol optical thickness (τ0) given at a reference wavelength (λ0):
 The Ångström exponent is often used as a qualitative indicator of aerosol particle size. Values of a ≤ 1 indicate size distributions dominated by larger aerosols (radii ≥ 0.5 μm), which are typically associated with dust and sea salt. Values of a ≥ 2 indicate size distributions dominated by smaller aerosols (radii ≤ 0.5 μm), which are usually associated with urban pollution and biomass burning [Eck et al., 1999; Westphal and Toon, 1991]. This relationship is used in this work to extrapolate aerosol optical thickness measured at a single wavelength to aerosol optical thickness at multiple wavelengths.
Appendix C:: Aerosol Retrieval
 The aerosol retrieval method described in Schmidt et al. , used as an intermediate step to get the relative forcing efficiency, is based on minimizing the difference between modeled and measured upwelling and downwelling spectral irradiance at the top and bottom of a layer. Figure 4shows the measurement geometry. Model input parameters, i.e., single scattering albedo, asymmetry parameter, and surface albedo, are varied in a radiative transfer model until the calculated spectral irradiances match the measured values. This method requires concurrent measurements of aerosol optical thickness from a sunphotometer (e.g., AATS-14) or from HSRL and spectral irradiance (e.g., from SSFR).
 The retrieval algorithm applied to the observations from CalNex required a modification to the one developed by Schmidt et al. because spectral aerosol optical thickness was not measured onboard the P-3. In lieu of directly measured spectral aerosol optical thickness onboard the same aircraft, the modified retrieval method uses the layer-integrated extinction from HSRL on the King air as initial estimate of optical thickness at 532 nm. This estimate is then adjusted iteratively to account for the temporal (30 min) and spatial (up to 2.5 km) mismatch between P-3 and King Air. The initial estimate at other wavelengths is extrapolated from the HSRL measurements using the AERONET optical thickness (that is, full-column) measurements at the Caltech ground site via the Ångström exponent.
 By varying the initial estimate of aerosol optical thickness, the aerosol asymmetry parameter, derived with two different methods (transmittance and reflectance) described by Schmidt et al. , can converge to a single value. Only a correct combination of aerosol optical thickness, single scattering albedo, and surface albedo will produce convergent asymmetry parameters from the two methods.
 To evaluate the accuracy of the retrieved relative forcing efficiency, the uncertainty has been determined for both the relative forcing efficiency and the secondary products (aerosol optical thickness, single scattering albedo, asymmetry parameter, and surface albedo). These uncertainties are determined by varying the inputs of the retrieval (spectral irradiance) within their uncertainty range. While the uncertainty has been determined by varying the input spectral irradiance within its uncertainty range, the uniqueness of the retrieved properties is determined by varying the initial estimate of the aerosol optical thickness within a wide range of values. This uniqueness test presents the retrieved products' sensitivity to the initial estimate of aerosol optical thickness and at which initial estimate the retrieved products are no longer unique. Another evaluation of the accuracy of the retrieval is based on the comparison of in situ measurements of the asymmetry parameter and the single scattering albedo, taken during CalNex with their retrieved counterparts. An independent way to determine the accuracy of the relative forcing efficiency uses data taken during another field mission (ARCTAS) where concurrent measurements of aerosol optical thickness and spectral irradiance were in fact available. By applying this retrieval to ARCTAS, a comparison of retrieved-to-measured aerosol optical thickness is used to evaluate the accuracy of the retrieved relative forcing efficiency.
C1. Retrieval Description
 A conceptual map of the modified Schmidt et al.  retrieval algorithm is shown in Figure C1. This algorithm is sequentially iterative, where one aerosol property is modified within each step to obtain matching modeled and measured spectral irradiance at each selected wavelength. Single scattering albedo (ϖ) is determined by matching the absorbed spectral irradiance (A), similar to the method described in Bergstrom et al. . The surface albedo (α) is derived from the reflected spectral irradiance (Fbot↑). The asymmetry parameter can be obtained from layer-transmitted spectral irradiance (Fbot↓) or from layer-reflected spectral irradiance (Ftop↑) [Schmidt et al., 2010], resulting in two values for the asymmetry parameter, g, from transmittance and , from the reflectance. In the original algorithm [Schmidt et al., 2010], the consistency of g and indicates whether the retrieval is successful. If g ≠ , the retrieval is discarded. For the modified algorithm applied here, the consistency of g and is used as the basis for modifying the initial estimate for the optical thickness from HSRL. The aerosol optical thickness is modified by a factor (Δτ) until g and converge within a specified limit.
 The modeled top-of-layer incident irradiance spectra do not always coincide with the measurements. These in turn affect all the modeled irradiance spectra. To address this issue, we introduce a correction factor, the ratio of the modeled and measured incident spectral irradiance on top of the aerosol layer. The correction factor rescales all four spectral irradiance components. This correction factor rarely differs by more than 5% from unity. When it does, then the retrieval is discarded. A pre-defined measurement-model convergence threshold,ε, is based on measurement uncertainty and an empirical optimization of computing time. When the modeled spectral irradiances are equal to the spectral irradiance measurements (within ε), the convergence criterion is satisfied.
 The following paragraphs describe the retrieval algorithm. In the retrieval algorithm description, the subscript i denotes the current iteration value, while i − 1 denotes the previous iteration value, and i + 1, the next iteration step. Modeled values are denoted by a “∼.” The numbered steps correspond to the numbers in the Figure C1.
 1. Input the pairs of above-layer and below-layer measured spectral irradiance.
 2. Initialization routine sets ϖ to 0.9, g and to 0.6, α to the ratio of Fbot↑ and Fbot↓, and τ to the initial estimate of aerosol optical thickness from HSRL and AERONET.
 3. Step ϖ. (a) Model the absorptance, Ã, defined in Appendix B1, with current values of ϖ, g, α, and τ. (b) If |Ã − A| < ε, where ε = 0.001, proceed to step (4). (c) Modify ϖ for next iteration while keeping all other variables constant using:
 4. Step g and α. (a) Model the transmitted spectral irradiance, , and below-layer upwelling spectral irradiance, . (b) If | − Fbot↓| < ε, where ε = Fbot↓ ⋅ 0.01, proceed to step (5). (c) Modify both g and α for the next iteration, using
 5. Step . (a) Model above the layer upwelling spectral irradiance, . (b) If | − Ftop↑| < ε, where ε = 0.002, proceed to step (6). (c) Modify for the next iteration, using:
 6. Consistency of g and − Δτ step. (a) If |g − | < ε, where ε = 0.02, proceed to step (7). (b) Variation of τ by ±4% of τ (Δτ = 0.04 τ):
 (c) Return to step (4), keeping ϖ constant, using the new τ.
 7. Final consistency test of Δτ. (a) The new variation of Δτi must be equal to the last derived variation Δτi−1. If Δτi = Δτi−1, then return the values of ϖ, g, α, and Δτ. (b) If Δτi − Δτi−1 ≠ 0 return to step (3) starting with the current values of ϖ, g, , and α, while initializing τ to its original value.
 The exponent in step (3c) is determined from tests designed to minimize the time of convergence while still having convergence. During these test, there was no evidence that the exponent influenced the results. In step (6), agreement between the two methods of evaluating the asymmetry parameter indicated convergence of the aerosol optical thickness. If the retrieval is successful, the values of the asymmetry parameter retrieved by the two different methods match (g − ε < < g + ε). If the two values do not match (g + ε < or g − ε > ), then the aerosol optical thickness is either increased or decreased by 4%. The 4% optical thickness modification increment was based on the uncertainty of the inputs and empirical tests aimed at minimizing computing time.
 If the aerosol properties between the lower leg and the surface are unknown, the retrieved surface albedo may not be representative of the true value. However, in the sense of an effective surface albedo, it is sufficient to use it when deriving the aerosol radiative forcing of the layer, which depends on the albedo at the low flight level, regardless of the actual surface albedo. The effective surface albedo encompasses contributions from the surface and the aerosol layer of unknown properties between the bottom flight leg and the surface.
C2. Retrieval Uncertainty
 To quantify uncertainties, an approximation of the total derivative method [Bevington and Robinson, 2003] is used for deriving the error associated with this retrieval. For a function y(x1, …, xi), the uncertainty (Δy) is:
where ( , ⋯, ) are partial derivatives of this function with respect to the variables (x1, …, xi), and the uncertainties of the independent variables are (Δx1, …, Δxi). For the aerosol retrieval, changes in the input irradiances (Ftop↓, Ftop↑, Fbot↓, Fbot↑) produce a change in the retrieved single scattering albedo, asymmetry parameter, and surface albedo. This numerically derived change is used to approximate partial derivatives. For example, the change in ϖ due to a change in Ftop↓, , is:
where denotes the single scattering albedo that has been retrieved from the downwelling spectral irradiance measured above the layer that corresponds to Ftop↓ + ΔFtop↓ (Ftop↓ − ΔFtop↓). This approximation is also used for all the other input parameters. The total uncertainty in ϖ:
combined with the approximations for the partial derivatives as described above is
 The uncertainties of the asymmetry parameter and surface albedo can be derived in the same way.
 The uncertainty of the aerosol optical thickness is determined by using a case from ARCTAS [Jacob et al., 2009] on 9 July 2008 where a boreal forest fire plume was sampled. During the summer component of ARCTAS, based out of Cold Lake, Alberta, Canada, measurements from SSFR and the AATS-14 were taken, where both instruments were mounted on the NASA P-3. AATS-14 provided aerosol optical thickness measurements simultaneously with spectral irradiance measurements from SSFR. Some NASA King Air flights, with the HSRL onboard, were coordinated with the NASA P-3, as they were during the CalNex case study. The relevant radiative measurements available during CalNex and ARCTAS are presented inTable C1.
Table C1. Available Spectral Radiative Measurements on Board Aircrafts During CalNex and ARCTAS Field Missions
SSFR on board NASA P-3
Airborne sunphotometer (AATS-14) on board NASA P-3
Coordinated measurements with HSRL on board NASA King Air
SSFR on board NOAA P-3
Coordinated measurements with HSRL on board NASA King Air
 Using data obtained during ARCTAS, the retrieval of aerosol optical thickness and its uncertainty was possible. The two asymmetry parameter values (g and ) and their absolute difference vary with a change of the assumed (and a priori unknown) optical thickness (Figures C2a and C2b). The aerosol optical thickness which minimizes the difference between these two asymmetry parameter retrievals (within ε) represents the best estimate for the optical thickness given all irradiance measurements. In the case of the ARCTAS measurements where the true aerosol optical thickness was known from AATS-14, the irradiance-derived optical thickness is in agreement with the AATS-14 derived value. In contrast to the uncertainty estimation of the single scattering albedo and the asymmetry parameter,equations (C6)–(C8) cannot be used to determine the range of uncertainty in the aerosol optical thickness, since the relationship of τi versus |g − | exhibits discontinuities over the range of observed aerosol optical thickness; note the jump of |g − | near optical thickness 0.65 in Figure C2b. These discontinuities, which arise from determining g and | either from increasing or decreasing aerosol optical depth, represent a change in the solution set of single scattering albedo and asymmetry parameter at one aerosol optical depth.
 The range of aerosol optical thickness that leads to consistent values of g and within their uncertainties, i.e., |g − | ≤ , is represented by values of |g − | < ε (marked in red in Figure C2b).
 The uncertainty in relative forcing efficiency fe is determined by τ500 nm, Ftop↓, forcing (f), and their uncertainties (from equation (1) and equation (C6)):
where the uncertainty in the radiative forcing (Δf) is determined by:
C3. Retrieval Testing
 One of the intermediate steps of the new relative forcing efficiency retrieval is tested by applying this retrieval to the ARCTAS case, described above, and comparing the retrieved aerosol optical thickness to the measured aerosol optical thickness. We compared the retrieved aerosol optical thickness to measurements acquired from AATS-14 (Figure C3). The initial estimate of aerosol optical thickness used the 532 nm aerosol extinction profile from HSRL extrapolated to the entire spectrum with the Ångström exponent from AATS-14. Differently from CalNex, AATS-14 is used to obtain the Ångström exponent in lieu of a surface AERONET station, since there was none in the flight vicinity. At wavelengths near 532 nm, the irradiance-derived aerosol optical thickness agrees with the AATS-14 aerosol optical thickness within 15%. At the shorter and longer wavelengths (<452 nm, >675 nm respectively), the irradiance-derived aerosol optical thickness deviates from the AATS-14 derived values by an average of up to 35%. Although the disagreement is considerably larger than AATS uncertainty (∼0.013) [Redemann et al., 2005], the range of uncertainty in the irradiance-derived optical thickness is consistent with the AATS retrievals. Where the range of retrieved values doesn't overlap with the measurements, they are only separated by up to 0.1, which can be said to be the minimum uncertainty. Therefore, this retrieval can be used even when concurrent aerosol optical thickness measurements are unavailable, albeit with a reduced accuracy in aerosol optical thickness.
C4. Retrieval Sensitivity and Uniqueness
 The retrieval of aerosol optical thickness, single scattering albedo, asymmetry parameter, and surface albedo may not be unique, given the irradiance measurements alone. For example, while Figure C2bshows only one solution for optical thickness, the absolute difference between the two values for the asymmetry parameter may have multiple minima as a function of optical thickness. In this case, a-priori information, i.e., an initial estimate for the optical thickness parameter (for example, from a nearby platform) is required. To retrieve a unique solution of aerosol optical thickness, single scattering albedo, asymmetry parameter, and surface albedo, the initial estimate has to be within a factor of 0.55 to 1.30 to the true aerosol optical thickness to ensure a unique solution.
 To determine this range, we used the data gathered during the ARCTAS case where the actual value of aerosol optical thickness is known as input to retrieve relative forcing efficiency and its secondary products. The sensitivity of the retrieved aerosol optical thickness to its initial estimate indicates the maximum deviation of the initial estimate from the true aerosol optical thickness. This sensitivity is determined by considering the range of solutions for the optical thickness when varying the initial estimate for the aerosol optical thickness (e.g., 0 to 2.5 at 500 nm). If the initial estimate is either larger than a factor 1.3 or smaller than a factor 0.55 of the actual optical thickness, the solutions become multimodal. Therefore, an initial estimate within a reasonable range of the true optical thickness is essential.
C5. Retrieval Comparisons of Secondary Aerosol Optical Properties
 Tests for the secondary retrieved parameters were conducted by comparing them to their in situ measured counterparts (Figure C4). In situ measurements of single scattering albedo and asymmetry parameter were not available at ambient humidity. Instead, the humidified single scattering albedo was obtained by combing measurements of dry-particle absorption from the PAS and calculations of extinction at elevated humidity, based upon measurements of dry particle extinction made by the CRDS. This approach assumed that absorption was independent of relative humidity. A combination of kappa-Köhler [Petters and Kreidenweis, 2007] and Mie theories [Wiscombe, 1979] were used to calculate the degree to which scattering was enhanced at elevated relative humidity with respect to dry conditions. This scattering enhancement is determined by evaluating the hygroscopicity parameter (the growth of a particle due to an uptake of water vapor). The hygroscopicity parameters for aerosol of ambient composition were derived by volume-weighting the hygroscopicity parameter assigned to each of the non-refractory components measured by an aerosol mass spectrometer aboard the P3 (ammonium nitrate: 0.59, ammonium sulphate: 0.53, organics 0.01) and to black carbon (0). This calculation-based approach was preferred to using direct measurements of the relative humidity enhancement made by the CRDS as it provided slightly more data during the period of interest. Comparison of calculated and measured enhancement factors during periods of concurrent coverage showed excellent agreement. For obtaining the asymmetry parameter, Mie scattering calculations were based on the ambient relative humidity aerosol particle size distribution, which was calculated from the measured dry particle size distributions using kappa-Köhler theory as described above. These Mie scattering calculations represent spherical aerosol particles at a constant refractive index. Variations in both the aerosol particles' geometrical shape and refractive index can add more variability to the resulting asymmetry parameter.
 The frequency distribution of the retrieved asymmetry parameter and single scattering albedo is compared to the distribution of their in situ and AERONET retrieved counterparts (Figure C4). The retrieved asymmetry parameter distribution (Figure C4a) derived from SSFR measurements seems to overlap with both the distributions from AERONET and in situ based Mie scattering calculations, even though these two distributions do not mutually overlap, albeit the AERONET distribution of asymmetry parameter only contains 7 points. Similarly to previous studies [Esteve et al., 2012], the asymmetry parameter values derived from AERONET measurements are higher than those derived from in situ measurements. Although the distributions overlap, there are large differences between the distributions of these aerosol properties. Differences between aerosol properties derived from radiative measurements and in situ measurements may be due to a difference in the sampling volume. The aerosol properties derived from SSFR measurements represent the column-integrated values between the two flight legs, equivalent to about 100 000 000 m3/s, while the aerosol properties derived from the in situ measurements represent point-like measurements along the flight path, equivalent to about 0.0005 m3/s. In this view, the calculated single scattering albedo and asymmetry parameter, along with their uncertainty (not shown here) represent an effective aerosol property of the whole layer rather than a few aerosol particles. Although this can account for some of the differences, there may be also errors in the aerosol particles' humidification process, described above, which may also contribute to the differences. This humidification process and the Mie scattering calculations therein use some approximations that may not always hold, such as constant refractive indices and spherical aerosol particles.
 This work was supported through NOAA CalNex (grant NA06OAR4310085) and NASA ARCTAS (grant NNX08AF93G). The authors would like to recognize the efforts from Warren Gore and Antony Trias from NASA Ames for their continued and reliable support of the SSFR during these deployments. We thank the NASA Langley B200 King Air and NOAA WP-3D flight crews for their outstanding work in support of these measurements. Support for the HSRL measurements came from the NASA HQ Science Mission Directorate Radiation Sciences Program, the NASA CALIPSO project, and the Department of Energy's Atmospheric Science Program Atmospheric System Research, an Office of Science, Office of Biological and Environmental Research program, under grant DE-AI02-05ER63985.