We present a new strategy to validate modeled spectral irradiance of shallow cumulus cloud fields in a polluted background with airborne measurements. The concept is based on a spectral distinction of effects associated with heterogeneous clouds, aerosol particles, and surface albedo. We use measurements from the Gulf of Mexico Atmospheric Composition and Climate Study, conducted in the urban-industrial Houston area. Modeled irradiance fields were obtained from extensive three-dimensional radiative transfer calculations applied to the output of large eddy simulations. We show that the measurements below clouds or cloud gaps can only be reproduced by the calculations when including the aerosol radiative effects. The technique enables the derivation of measurement-based spectral forcing and absorption of the cloud-aerosol system which will help substantiate model calculations. At 400 nm wavelength, the inclusion of aerosol increases forcing of the cloud-aerosol system by 8%, and absorption by 20%.
 The climatic effects of aerosol particles on cloud microphysics and cloud radiative forcing are largely unknown [Forster et al., 2007], at least in part because aerosols and clouds are usually inseparable and occur on a large range of scales. Recent studies have emphasized the need to consider aerosol particles and clouds as an entity rather than artificially separating aerosol and cloud radiative forcing [Koren et al., 2007; Charlson et al., 2007]. Combined effects of heterogeneous clouds and aerosol particles are not currently considered in assessments of aerosol or cloud radiative forcing. Modeling work [Marshak et al., 2008; Wen et al., 2007] has resulted in a better understanding of solar radiation scattered and absorbed by heterogeneous cloud scenes in polluted environments. However observations are sorely lacking. It is often argued that when aerosol particles and clouds are present simultaneously, clouds dominate the radiative field as long as the cloud optical thickness is much larger than that of the aerosol layer. However, there are at least two important exceptions where aerosol particles may significantly alter the cloud radiative signature: (a) when the aerosol residing in or above an overcast cloud layer is strongly absorbing, and (b) under broken cloud conditions. We focus on the latter, and demonstrate that aerosol particles have a considerable effect on spectral irradiance fields.
 In the past, cloud radiative closure studies have been hampered by the fact that only broadband, rather than spectral, solar radiation was measured or that cloud heterogeneity was not taken into account [e.g., Cess et al., 1995]. Since then, considerable progress has been made. On the modeling side, various three-dimensional radiative transfer models (3D-RTM) [e.g., Mayer, 2009], large eddy simulations including detailed microphysics (LES) [e.g., Jiang and Feingold, 2006] and cloud stochastic generators [e.g., Venema et al., 2006] have been developed. On the measurement side, solar spectral radiation measurements have been introduced [Pilewskie et al., 2003; Wendisch et al., 2001]. Only with such spectral measurements, is it possible to distinguish the effects of aerosol and clouds and to study their forcing and absorption.
 This study presents a new methodology for validating the irradiance fields from cloud-aerosol systems, predicted by a combination of LES and 3D-RTM calculations, with airborne measurements of solar spectral radiation using the Solar Spectral Flux Radiometer (SSFR) [Pilewskie et al., 2003]. It demonstrates how spectral information can be used to identify contributions from clouds, hydrated aerosol particles, and the surface, to the irradiance field and shows that aerosol particles represent a significant component. Spectral forcing calculations for the cloud-aerosol system are compared with measurements of the “apparent forcing,” which excludes 3D effects, and the differences are shown to be significant.
2. Experimental Setup and Strategy
 The measurements were acquired in August and September, 2006, during the Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS) which targeted broken, shallow cumulus clouds in the polluted, urban-industrial Houston region [Lu et al., 2008]. GoMACCS included multiple aircraft, ground-based and ship activities (http://esrl.noaa.gov/csd/2006/). The Center for Interdisciplinary Remotely-Piloted Aircraft Studies (CIRPAS) Twin Otter (http://www.cirpas.org) performed 22 research flights. It carried instruments to characterize (i) aerosol size distributions, optical properties, and composition, (ii) cloud drop size distributions, (iii) standard meteorological data; and (iv) spectral irradiance over the solar spectral range from 380 nm to 2150 nm.
 The LES model [Jiang and Feingold, 2006] provided size-resolved cloud drop size distributions and ambient aerosol particle size distributions. It was initialized with rawinsondes from Houston University and run until convection had developed. Model input included aerosol profiles from the Twin Otter and land-use characteristics for the soil and vegetation model. Grid size was 100 m in the horizontal and 50 m in the vertical. The frequency distributions of microphysical and dynamical cloud fields (specifically cloud liquid water content, drop concentration and updraft velocity) were compared with the observed fields [Jiang et al., 2008], providing confidence in the LES model performance.
 We used the cloud and aerosol fields from LES runs for a case from September 15, 2006, as input to the 3D-RTM MYSTIC (Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres [Mayer, 2009]). Further input included atmospheric profiles from the Houston rawinsondes and spectral surface albedo - obtained from SSFR measurements above a similar land surface as encountered on September 15. For atmospheric correction, an iterative approach was used [Coddington et al., 2008; Wendisch et al., 2004] with aerosol extinction profiles from the NASA B-200 High Spectral Resolution Lidar (HSRL) [Hair et al., 2008]. Calculations were performed with 108 to 109 photons per wavelength for fifty wavelengths distributed throughout the SSFR spectral range (380–2150 nm) for a solar zenith angle of 28°. Cloud drop phase-functions were obtained from Mie calculations. Aerosol particle extinction was calculated from the ambient (humidified) particle size distributions while spectral single scattering albedo and asymmetry parameter were taken from Aerosol Robotic Network (AERONET) retrievals. A ground-based single scattering albedo was also derived from a cavity ring-down spectrometer [Wright et al., 2009] in conjunction with a nephelometer. Simulations included 3D-RTM (with and without aerosol) and the independent pixel approximation (IPA). Furthermore, the sensitivity of the irradiance fields to spectral surface albedo and aerosol single scattering albedo was examined.
 We used below-cloud measurements of the spectral downward irradiance F↓ for our LES/3D-RTM evaluation in the same way as Schmidt et al. . In addition, we compared the net irradiance F = F↓ − F↑ and the spectral radiative forcing f defined as the difference between net irradiance when clouds and aerosol particles are included (Fcld) and the unperturbed case (Fclr) (normalized by the unperturbed downward irradiance at the same altitude). We define the apparent forcing at flight altitude by replacing Fcld with cF1 + (1 − c)F2 where c is the cloud fraction, F1 the net irradiance below clouds (directly transmitted solar irradiance is attenuated), and F2 the net irradiance in cloud-free areas (directly transmitted and scattered irradiance), and by replacing Fclr with F2:
The apparent forcing fapparent is equivalent to the true forcing f for zero horizontal flux divergence, which is usually not the case for broken cumulus clouds, particularly in the regions between cloud elements. The difference between fapparent and f is therefore a measure of 3D effects.
 For our analysis, we used SSFR data from 16.4–16.8 h UTC, normalized to a solar zenith angle of 28°. Figure 1 shows histograms of the downward irradiance at 500 nm. Two modes can be distinguished: low irradiance values (0.4 W m−2 nm−1) correspond to measurements below clouds where the direct beam of solar radiation is attenuated and only scattered, i.e. diffuse, radiation is measured (“CLD” mode, F1↓); high values (1.6 W m−2 nm−1) stem from measurements in cloud-free areas (“GAP” mode, directly transmitted and scattered irradiance: F2↓). These cloud-free areas may comprise small cloud fragments and aerosol particles, both of which do not entirely attenuate the directly transmitted irradiance. Since the “CLD” and the “GAP” peak are different in amplitude we plotted them separately. The results of the LES/3D-RTM pertain to the cloud field at 19.8 h UTC when the measurement-derived cloud cover (20%) is slightly above the cloud cover from LES (16.5%). We did not seek to match model and measurement times but rather, similar cloud fractions. The afternoon advection of humidity by the sea breeze caused the observed cloud fraction to increase above that modeled by the LES, which did not consider the sea breeze. Within the LES domain (13 km × 13 km), the mean cloud base was at 1440 m, the mean cloud top at 1738 m, and the cloud-averaged LWP was 214 g m−2. The aerosol optical thickness in cloud-free areas ranged from 0.10–0.17 (ambient conditions) at 500 nm wavelength.
 The thick black line in Figure 1 shows the 3D-RTM results when including aerosol particles (at various stages of hydration) along with clouds. The location and shape of both peaks are close to the measurements. When not including them (blue line), the “CLD” peak is shifted to smaller, and the “GAP” peak to larger values. Thus, aerosol particles between cloud elements reduce irradiance (by scattering radiation out of the direct beam) and increase irradiance below clouds (by increasing the diffuse irradiance). This effect cannot be modeled with IPA (results not shown): Horizontal photon transport and thus full 3D-RTM is required to reproduce the positions and shapes of the measured histograms. The width of the “GAP” mode is larger in the SSFR measurements than in the LES/3D-RTM simulations because the measured PDFs are accumulated by flying through a potentially heterogeneous area while the simulations depict the values throughout the model grid at a fixed time. The length of the measurement time series is a compromise between sufficient sampling statistics on the one hand and natural variability of cloud and aerosol properties on the other. The measured PDFs depend on the flight track and may not be representative of the entire area. For example, the measured peak at 1.8 W m−2 nm−1 is due to the irradiance scattered from the edge of an individual cloud (or of multiple clouds with similar size within the sampled area), increasing the clear-sky irradiance by a certain factor. In the calculations, this enhancement presents itself as a tail towards values above the clear-sky value - an effect of all cloud edges throughout the model domain.
 The temporal variability of the measurements is illustrated by showing the histogram of the measured GAP irradiance just six minutes prior to the measurement explained above (16:24 h UTC, open bars). The additional mode at 1.38 W m−2 nm−1 can be traced to a measurement area with lower particle single scattering albedo (ωo ≈ 0.7) and thus more absorption. Simulations with ωo = 0.7 (red lines in Figure 1) show a consistent shift toward smaller values for both peaks. Increasing aerosol optical thickness instead results in a decrease in direct irradiance below cloud gaps and an increase in diffuse radiation below clouds. The low ωo value corresponds to the in-situ measurements on the ground. The value of ωo ≈ 0.8 from AERONET (used for the base case) is more representative of the entire atmospheric column.
 The green line in Figure 1 shows the effect of surface albedo (α ≈ 0.10 versus the standard value of α ≈ 0.035) on the downward irradiance at 500 nm. As expected, the GAP peak remains unchanged with respect to the base case, but the diffuse irradiance below clouds is shifted to slightly higher values because of the increased upward irradiance, reflected back down from cloud base. Although in this case the downward irradiance below clouds is only weakly dependent on the surface albedo, surface albedo may have a larger effect for cloud-aerosol studies under different conditions.
 In Figure 2, the location of the two peaks from Figure 1 is plotted as a function of wavelength. The red lines show the measured spectral irradiance for the “CLD” mode, the blue ones for the “GAP” mode; the dotted lines correspond to the downward irradiance, the solid lines to the net irradiance. Near 680 nm wavelength, the difference between downward and net irradiance becomes much larger because of the increase in surface albedo from vegetated surfaces. The full circles show the location of the peaks of the calculated downward irradiance in the histograms; the triangles correspond to the aerosol-free 3D-RTM runs (shown only for the visible part of the spectrum where the aerosol has a sizeable effect). For most wavelengths across the visible range, the model results are in agreement with the measurements only when aerosol particles are included in the calculations. The same applies for net irradiance (open symbols). Noticeable disagreement occurs at 1180 nm and (less obviously) at other water vapor absorption wavelengths. The model predicts a higher water vapor absorption than measured. We used the original values from the rawinsonde so the source of this discrepancy is unclear. Nevertheless the good spectral agreement between observations and calculations provides further confidence in the ability of the model to represent the cloud-aerosol system.
 The measurement-validated calculated net irradiance allowed us to reliably derive the absorption (the difference between net irradiance above and below clouds) that cannot be measured directly. The total absorption within the SSFR spectral range was 158 W m−2 for the aerosol-cloud continuum and 129 W m−2 excluding aerosol. Thus the aerosol particles increased the total absorption by about 20%.
 The measured and modeled spectral radiative forcing for the cloud-aerosol system is shown in Figure 3. From the measurements, only the apparent forcing at 0.5 km altitude can be obtained (black line). The calculated apparent forcing (black full circles) reproduces these measurements. This justifies using the calculations to obtain the true forcing (red full circles) which is inaccessible from the measurements alone. At longer wavelengths, the true forcing levels off at about −2%. The apparent forcing is much more pronounced (−12%). One reason for this significant difference lies in 3D effects: They increase the “GAP” irradiance, which consequently cannot be used as a proxy for clear-sky conditions. It is also possible that contributions from small cloud fragments might explain the difference between apparent and true forcing. The open red circles show the results for the aerosol-free 3D-RTM runs. The spectral forcing has a constant value of −5% between 400 nm and 600 nm. Around the vegetation step at 680 nm, it changes to about −2%. The addition of aerosol changes the spectral shape in the visible wavelength range and increases the amount of forcing especially for short wavelengths: at 400 nm, the difference is almost 8%. The blue triangles show the true forcing at 5 km altitude, above the cloud-aerosol layer. It is smaller in magnitude than the forcing below the layer. The difference between the top-of-layer and bottom-of-layer forcing can be ascribed to aerosol absorption at short wavelengths and cloud absorption at long wavelengths.
4. Summary and Conclusions
 We introduced a strategy to validate model calculations of spectral radiative quantities for polluted cumulus cloud fields using measurements. We showed that aerosols alter the irradiance, forcing, and absorption of broken cloud fields significantly, and that the spectral measurements can be reproduced only by including aerosol in the radiative transfer calculations. Extensive LES and 3D-RTM calculations were performed to model the irradiance fields at fifty wavelengths throughout the spectral range of SSFR. The independent pixel approximation could not be used because horizontal photon transport is essential to the processes under study. The effects of 3D cloud structure, surface albedo and aerosol properties were distinguished by using the spectral signature of measured and calculated irradiance fields. Validating the LES/3D-RTM calculations with measurements allowed us to derive measurement-based spectral forcing and absorption of the cloud-aerosol system.
 The various calculations performed above provide strong indication that the cloud-aerosol system is correctly represented by the LES. They do not, however, constitute proof of this because of the large number of degrees of freedom of the system. Future work must continue to address the questions raised here. To this end our scheme is currently being extended to spectral radiance. This will enable inclusion of spectral radiance measurements from, e.g., the cloud absorption radiometer (CAR) [Gatebe et al., 2007] as a further constraint for forthcoming cloud-aerosol studies.
 We are grateful to the CIRPAS Twin-Otter and California Institute of Technology for their help during GoMACCS. This work was supported by NOAA grants NA06OAR4310085 and NA06OAR4310082. We thank Warren Gore and Tony Trias, NASA Ames Research Center, for their technical support before and during GoMACCS. We thank Barry Lefer and staff for establishing and maintaining the Houston University AERONET site and Dean Atkinson from Portland State University for the in-situ aerosol data. Acquisition of the aerosol extinction profiles with the NASA LaRC HSRL was supported by NASA's Radiation Sciences Program and the Office of Science (BER), U. S. Department of Energy, interagency agreement DE-AI02-05ER63985. Bernhard Mayer, DLR Oberpfaffenhofen, Germany, provided the 3D-RTM MYSTIC.