Abstract

We present an optimal-estimation-based retrieval framework, the microphysical aerosol properties from polarimetry (MAPP) algorithm, designed for simultaneous retrieval of aerosol microphysical properties and ocean color bio-optical parameters using multi-angular total and polarized radiances. Polarimetric measurements from the airborne NASA Research Scanning Polarimeter (RSP) were inverted by MAPP to produce atmosphere and ocean products. The RSP MAPP results are compared with co-incident lidar measurements made by the NASA High-Spectral-Resolution Lidar HSRL-1 and HSRL-2 instruments. Comparisons are made of the aerosol optical depth (AOD) at 355 and 532 nm, lidar column-averaged measurements of the aerosol lidar ratio and Ångstrøm exponent, and lidar ocean measurements of the particulate hemispherical backscatter coefficient and the diffuse attenuation coefficient. The measurements were collected during the 2012 Two-Column Aerosol Project (TCAP) campaign and the 2014 Ship-Aircraft Bio-Optical Research (SABOR) campaign. For the SABOR campaign, 73% RSP MAPP retrievals fall within ±0.04 AOD at 532 nm as measured by HSRL-1, with an R value of 0.933 and root-mean-square deviation of 0.0372. For the TCAP campaign, 53% of RSP MAPP retrievals are within 0.04 AOD as measured by HSRL-2, with an R value of 0.927 and root-mean-square deviation of 0.0673. Comparisons with HSRL-2 AOD at 355 nm during TCAP result in an R value of 0.959 and a root-mean-square deviation of 0.0694. The RSP retrievals using the MAPP optimal estimation framework represent a key milestone on the path to a combined lidar+polarimeter retrieval using both HSRL and RSP measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

In this paper, we present a retrieval framework, microphysical aerosol properties from polarimetry (MAPP), designed to simultaneously retrieve aerosol microphysical properties and ocean color bio-optical parameters using multi-angular total and polarized radiances from the NASA GISS Research Scanning Polarimeter (RSP [1]). The atmosphere/ocean products are compared against NASA Langley High-Spectral-Resolution Lidar (HSRL-1 and HSRL-2 [2]) aerosol optical depths and lidar ocean measurements as well as lidar-intensive parameters (the lidar ratio and Ångstrøm exponent). The co-incident polarimeter and lidar measurements that are presented were collected during the 2012 Two-Column Aerosol Project (TCAP [3]) campaign and the 2014 Ship-Aircraft Bio-Optical Research (SABOR) campaign. TCAP was a Department of Energy campaign conducted off the coast of Cape Cod to address knowledge gaps in aerosol and cloud temporal evolution and uncertainties in direct and indirect aerosol forcing by improving remote sensing retrievals of aerosol optical and microphysical properties and studying aerosol–cloud interactions. Thus, the TCAP study sampled the atmosphere between and within two atmospheric columns: one fixed near the coast of North America (over Cape Cod, MA) and a second moveable column over the Atlantic Ocean several hundred kilometers from the coast. The NASA-led SABOR campaign was designed to assess the applicability of lidar and polarimetry for ocean biogeochemistry and involved ship-based in situ measurements as well as airborne remote sensors. The SABOR campaign provides a wide range of ocean optical properties from aircraft overflights of the ship, spanning ocean conditions from the eutrophic waters of the Gulf of Maine to oligotrophic waters near Bermuda.

The aircraft-based RSP instrument can retrieve aerosol/ocean products by measuring the upwelling total and polarized reflectance using six paired refractive telescopes, with each pair making measurements in three spectral bands. One telescope in each pair makes simultaneous measurements of the linear polarization components of the intensity in orthogonal planes at 0° and 90° to the meridional plane of the instrument, while the other telescope simultaneously measures equivalent intensities in orthogonal planes at 45° and 135°. The RSP instrument has nine spectral channels that are divided into two groups based on the type of detector used: visible/near infrared (VNIR) bands at approximate wavelengths (full width at half-maximum, FWHM, in parentheses) 410 (30), 469 (20), 555 (20), 670 (20), 864 (20), and 960 (20) nm and shortwave infrared (SWIR) bands at 1594 (60), 1880 (90), and 2264 (120) nm. The set of four measurements in a particular band are denoted S1L and S1R for the two orthogonal polarization states in the telescope observing at polarization azimuths of 0° and 90° and S2L and S2R for the two orthogonal polarizations in the second telescope of each pair. The Stokes parameters I, Q, and U can be derived from these four measurements, and the corresponding orthogonal (parallel and perpendicular) components are obtained as IL=(I+Q)/2 and IR=(IQ)/2, respectively. With appropriate normalization [see Eqs. (22), (23), and (24)], we can also define corresponding reflectances RI, RQ, RU, RIL, and RIR.

Waquet et al. (2009) [4] used polarized reflectance (RQ) observations in seven spectral spectral bands (excluding the 960 and 1880 nm bands) obtained during the 2005 ALIVE campaign in the Southern Great Plains and in 2003 over the Simi Valley in the Mojave desert to retrieve aerosol microphysical parameters. The 2.26 μm polarized reflectances were primarily used to characterize the polarized surface reflectance as a function of scan angle, which to a good approximation is spectrally invariant. Knobelspiesse et al. (2011) [5] used polarized reflectances rotated into the scattering plane in the same bands used by Waquet et al. (2009) and two total reflectance measurements at 410 nm and 2264 nm from RSP to retrieve aerosol microphysical parameters of thick smoke over land during the 2008 ARCTAS campaign. Over water, Chowdhary et al. (C2006, C2012) [6,7] performed simultaneous aerosol and ocean retrievals using total and polarized reflectance observations for RSP observations collected off the coast of Veracruz, Mexico during the 2006 MILAGRO campaign, but focused mainly on development of an ocean bio-optical model for polarized reflectances. Wu et al. (2015) [8] used all seven RSP window channels for total reflectance (RI) and the degree of linear polarization, DoLP=RQ2+RU2/RI, to retrieve properties of fine- and coarse-mode aerosol retrievals over land.

One of the main ideas in the “MAPP” algorithm is that the retrieval is “coupled,” in the sense that the atmosphere and ocean products are simultaneously retrieved, and that all seven RSP window channels are used, including polarization through both the reflectances RIL, RIR, and the degree of linear polarization. Similar “coupled” atmosphere and surface retrieval approaches have also been developed for the POLarization and Directionality of Earth Reflectances (POLDER) instrument on the PARASOL satellite, [9,10]. While MAPP may not work as well as “hand-tuned” retrievals one might conduct for a few cases, the goal is to produce an algorithm that is capable of automated processing of polarimeter (RSP) data. Also, MAPP was designed not only as a standalone polarimeter retrieval algorithm, but as the foundation for a combined HSRL+RSP retrieval (or arbitrary lidar+polarimeter configuration). The focus of this paper, and a key milestone on the path to the combined HSRL+RSP retrieval, is a MAPP RSP (polarimeter-only) retrieval that provides the framework for processing polarimeter data, and a baseline retrieval that the combined MAPP HSRL+RSP retrieval is expected to improve upon. Thus, for the RSP MAPP retrievals in this paper, we use lidar only to provide the aerosol top height and cloud screening to identify Aerosol-Above-Ocean (AAO) scenes. We present RSP MAPP results for all TCAP Phase 1 and SABOR AAO scenes, after screening for clouds and aircraft altitude/roll.

A unique feature of MAPP is the focus on coupled retrievals of aerosol microphysical properties and ocean color parameters using optimal estimation driven by on-the-fly vector radiative transfer and Mie calculations. The RSP instrument makes coupled retrievals easier in that, unlike an imager that has many scenes (pixels) but fewer measurements per scene, the RSP instrument scans along the track so that a single scene contains many measurements per pixel, with fewer scenes to process. Fewer scenes make it possible to perform Mie and vector radiative transfer calculations on the fly, rather than relying on lookup tables (LUTs) of pre-computed results. Performing the vector radiative transfer computations on the fly is advantageous for aircraft platforms where the sensor altitude varies and the aerosol location (top height, layering, etc.) is allowed to vary, whereas precomputed Mie LUTs would provide a speed benefit at the cost of reduced flexibility. Over 90% of the signal measured by a spectroradiometer or polarimeter is due to the molecular and aerosol scattering in the atmosphere and the Fresnel reflection of the ocean surface, so that less than 10% of the signal is due to subsurface ocean inherent optical properties (particulate and dissolved matter) [11]. RSP measurements of the polarized reflectance at multiple angles can lead to improved retrievals of underwater properties by enabling accurate characterization of the aerosol signal through retrieval of aerosol optical depth, microphysical aerosol properties including aerosol effective radius, single-scattering albedo, and the real part of the refractive index. Another advantage is that RSP does not saturate due to sunglint, which is a significant issue for instruments like MODIS.

The overall methodology is described in Section 2 and is summarized by the retrieval parameters, which determine the state of the atmosphere (aerosol) and ocean models. In Section 3, we present the retrieval framework based on principles of optimal estimation, while Section 4 includes descriptions of the instruments, direct measurements, lidar ocean products, and noise profiles. Section 5 discusses simulated retrievals, and Sections 6 and 7 present results for measurements collected during the SABOR and TCAP campaigns, respectively. Section 8 provides an error analysis, and a conclusion is provided in Section 9. The RSP MAPP products are summarized on the NASA LaRC HSRL website (https://science.larc.nasa.gov/hsrl/) [12] and are available for download at the NASA GISS RSP website (https://data.giss.nasa.gov/pub/rsp) [13].

2. METHODOLOGY

The MAPP algorithm consists of an optimal-estimation-based solver, where the forward model consists of a vector radiative transfer code and a Mie scattering code. In optimal-estimation theory, the forward model input is specified by the state vector, and the forward model output matches the instrument, in this case, RSP’s total and polarized radiances. Each MAPP retrieval takes approximately 60 min to run on a single core of a Sandy Bridge Intel Xeon processor, although we expect to reduce processing (CPU) time by a factor of 2–3. The NASA LaRC K cluster was used to perform the retrievals in parallel, and since the CPU time scales linearly with the number of cores, then 1,000 cores enables processing of approximately 24,000 scenes per 24 h. Assuming an RSP-like along-track polarimeter was scanning continuously at 1 Hz, averaging to 10 s per measurement would result in 8,640 scenes per 24 h. Hence, MAPP is already fast enough to process 10-second-averaged RSP-like data within 60 min, given a dedicated resource of approximately 500 Sandy Bridge cores (allowing for some overhead).

A. Overview of MAPP Retrieval Parameters

The state vector of MAPP retrieval parameters is defined as

x=τ555frnfσgfnrfnifτ555crncσgcnrcnicvCHLzczf,
where τ555f is the fine (accumulation) mode aerosol optical depth at 555 nm, rnf is the number-density mean radius with geometric width σgf, nrf+inif is the fine-mode refractive index (assumed to be spectrally invariant), τ555c is the aerosol optical depth of the coarse mode, and rnc is the coarse-mode number-density mean radius with geometric width σgc. The coarse-mode refractive index, nrc+inic, was assumed a priori to be equal to that of water to represent hydrated sea salt (marine) aerosols. The aerosol top heights for the coarse and fine mode were set to be the same (zf=zc), and were obtained by finding the altitude that represented an integral of 95% of the lidar backscatter or extinction at 532 nm. For the simulated retrieval, zf and zc were fixed and assumed to be known. While it is possible to use polarimetric observations to retrieve the aerosol layer height [14], here we assume that high-quality lidar observations are available to constrain this aspect of aerosol variability. The ocean surface roughness is described by the wind speed v [m/s], and the subsurface absorption and scattering is parameterized in terms of the chlorophyll concentration CHL [mg/m3]. The ranges allowed for each of the parameters in this 10-parameter retrieval are as follows:
105τ555f0.60.075rnf0.15μm1.36nrf1.65105nif0.03105τ555c0.40.5rnc1.5μm0.3σgf0.70.3σgc0.70.01v7.0m/s0.001CHL10mg/m3.

The maximum allowed optical depth for the fine and coarse modes is up to 0.6 for the fine mode and up to 0.4 for the coarse mode, which are reasonable values for conditions encountered over the Atlantic Ocean off the East coast of the United States, but which need to be increased in areas with higher aerosol loading. The choices for all the aerosol parameters are explained in Section 2B.2. The allowed ranges for the wind speed and chlorophyll concentration are explained in Section 2C.

B. Atmosphere Models

1. Atmospheric Gases

The atmosphere is assumed to consist of five layers between 0 and 100 km to account for the vertical distribution of molecules that scatter and absorb sunlight. For retrievals of real data we used five layers with [0, zaerosol, zaircraft, 12, 22, 100] km, where zaerosol is the aerosol top height and zaircraft is the aircraft altitude, followed by three additional layers to allow for some vertical variation in molecular absorption. The molecular absorption is due mainly to trace gases plus O2, while molecular scattering is driven by N2 and O2 gas, which comprise the bulk of the atmosphere. For the calculation of absorption by gases in each window channel (band), MODTRAN [15] was used with the Mid-latitude Summer model atmosphere. In addition to the gases N2 and O2, the following trace gases were considered: H2O, H2O continuum, CO2, O3, N2O, CO, CH4, NO, SO2, NO2, NH3, HNO3. The Mid-latitude Summer model was created in the 1980s, and as a result the well-mixed gases that absorb in the RSP channels need to be scaled to current values. The default value of 330 ppmv of CO2 is scaled to a 2012–2014 value of 400 ppmv of CO2 using a scaling factor of 1.2. Absorption by water vapor is turned off in the MODTRAN model, and is instead derived using measurements from RSP’s 960 nm channel and the following parameterization for the water vapor column amount, wcol [cm] [16,17]:

wcol=11|μg|+1|μ0|[lnI864(μg)I960(μg)α]1/β,
where μg is the cosine of the glint angle, μ0 is the cosine of the solar zenith angle, and α=0.31607, β=0.595575 are empirical constants that depend upon RSP’s 960 nm filter response function. The normalized radiances [see Eq. (23) and discussion in Section 4.A] at the 1594 nm and 2264 nm shortwave infrared (SWIR) channels are converted to reflectances [Eq. (24)] by the factor ds2μ0 and scaled by T, the transmission due to water vapor,
f=ds2μ01T,
where ds=Earth-to-Sun distance1AU is the ratio of the actual Earth-to-Sun distance to one astronomical unit. The band integrated total transmittance in the RSP SWIR channels is modeled by dividing the radiation into two parts. The first part can be regarded as the fraction of radiation that is in the centers of the absorption lines and which represents a negligible (<1%) fraction of the radiation reflected back to the sensor. The second part is the fraction of radiation that is representative of atmospheric windows together with absorption by line wings and the water vapor continuum. The absorption of this second part of the radiation is well represented by a single absorption coefficient with contributions from both water vapor and well-mixed gases. The model for total transmittance therefore only depends on this second part, and the total transmittance in the SWIR bands, T, is given by the product of two terms, T=T0(wcol)×TB(wcol,μ0,μv). In this equation T0(wcol) is the fraction of radiation that contributes to the RSP observation, which does not depend on viewing geometry, and TB(wcol,μ0,μv), which is a Beer’s law model for the transmittance of this radiation. The fraction of radiation that contributes to RSP SWIR channel observations is given by T0(wcol)=i=02[ciwcoli] for the 1594 and 2264 nm channels. The absorption optical depth for the Beer’s law model is given by τtot(wcol)awcol+τwellmixed where τtot,1594=0.00106669wcol+0.0146353 and τtot,2264=0.00438348wcol+0.03664. (Since we used MODTRAN to compute the absorption optical depth from well-mixed gases to use directly in the radiative transfer calculation, τwellmixed was set to zero.) The Beer’s law equation for transmittance is Ttot(wcol,μ0,μv)=exp[(1/μ0+1/|μv|)τtot]. The coefficients for the fraction of radiation T0 and the absorption optical depth τtot in this model are derived from calculations of transmittance at 1 nm resolution using a correlated-k distribution model for line absorption that is derived from HITRAN2008 and a physically based water vapor continuum model [18]. The 1 nm resolution transmittances are integrated with a solar spectral weighting over the RSP spectral bands for a wide range of water vapor amounts (0–5 precipitable cm) and air masses (2–5), and the coefficient in the model for RSP SWIR channel total transmittances provide a least mean square best fit to these calculations.

2. Aerosol Models

Aerosols are assumed to be bimodally distributed, with a fine mode and a coarse mode. The complex refractive index of the fine mode is retrieved. The refractive index of the coarse mode is fixed to that of water, which is a reasonable assumption for hydrated sea-salt particles, particularly considering that the desired retrieval accuracy of the real refractive index is ±0.02.

The atmospheric layer that contains up to 95% of the lidar-backscattered signal above the ocean is assumed to contain all of the aerosol particles, distributed homogeneously. The bimodal lognormal volume-density size distribution is defined by

v(r)=1rdV(r)dlnr=1ri=12Vi2πσgiexp[(lnrlnrvi2σgi)2],
where the subscript i represents the particle mode, Vi [m1] is the total volume of particles per unit volume per unit radius, rvi is the volume geometric mean radius, and σgi is the geometric standard deviation. In terms of the number-density, Eq. (5) becomes
n(r)=1rdN(r)dlnr=1ri=12Ni2πσgiexp[(lnrlnrni2σgi)2],
where the total number of particles Ni [m4] per unit volume per unit radius and the mode radius rni in number-density space are related to Vi and rvi by
Ni=Vi43πrni3exp(4.5σgi2),
rni=rviexp(3σgi2).

If we use the subscript i=f to denote the fine mode and the subscript i=c to denote the coarse mode, we have V=Vf+Vc, and the fraction of fine mode particles in volume-density becomes fv=Vf/V. The definition of effective radius is

reff=rminrmaxr3n(r)drrminrmaxr2n(r)drlognormalrnexp(2.5σg2),
where the right-most expression is for a lognormal distribution. The corresponding effective variance is defined by
veff=rminrmax(rreff)2πr2n(r)drreff2rminrmaxπr2n(r)drlognormalexp(σg2)1,
where the right-most expression is for a lognormal distribution.

The effective radius [Eq. (9)] is a more useful parameter than the mode radius because the single-scattering properties depend on the geometrical cross section πr2 [19,20], and for weak absorption the single-scattering albedo is proportional to the effective radius. Thus, aerosols with the same effective radius and effective variance tend to have similar scattering properties independent of size distribution. The aerosol scattering is therefore described more concisely by the effective radius, which is a function of both the mode radius and mode width, rather than by the mode radius alone.

The assumption of a single homogenous aerosol layer was applied to both the simulated data (Section 5) and real data (Sections 6 and 7). For real data we rely on lidar data to identify the aerosol location; otherwise, information about the aerosol location would also have to be retrieved. The inversions of real/simulated data are described in Section 3. For inversions of real RSP data, we determined the aerosol height in kilometers (km) from collocated HSRL data, by integrating the measured backscatter from the surface to 95% of the total measured aerosol backscatter, and used the height corresponding to the 95th percentile as the aerosol top height. Thus, the aerosols were approximated as being homogeneously distributed between 0 km and the aerosol top height, representing a column aerosol retrieval.

The MAPP aerosol model consists of a Lorenz–Mie [19,2123] code that is run on the fly—at each step in the iterative retrieval—to calculate the scattering properties of spherical particles, i.e., the single-scattering albedo and scattering phase matrix needed for polarized radiative transfer calculations. The MAPP aerosol model incorporates fine-mode effective radii in the range [0.094 μm, 0.51 μm] and coarse-mode effective radii in the range [0.626 μm, 5.1 μm], which extends the size range used in the SeaDAS aerosol model for both modes (see Table 1). The goal is to capture most types of aerosols that can be modeled using spheres. Therefore, nonspherical dust particles, as well as aerosol particles with an effective radius above 5.1 μm, are not considered. Smoke particles are captured if the (ambient) refractive index is less than 1.65, and the (ambient) imaginary part is less than 0.03. Since the Mie code is run on the fly, MAPP retrieves aerosol optical depth and aerosol microphysical parameters directly. We found it useful to preserve a gap in the effective radius [2426] between 0.51 to 0.626 μm for the fine and coarse modes to reduce crosstalk in the retrieval.

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Table 1. Aerosol Fine/Coarse Mode Ranges (Low, High)a

Comparisons with the MODIS SeaDAS Aerosol Model: The SeaDAS aerosol model [25] currently being used in the atmospheric correction for MODIS/SeaWiFS ocean color retrievals parameterizes the particle size of the coarse and fine modes, the real refractive index, and the single-scattering albedo, to vary with relative humidity. For example, at a relative humidity of 70% or RH=0.7, rvf=0.158μm, and rvc=2.927μm. The standard deviations for both modes are kept fixed at all relative humidities: σgf=0.437, corresponding to an effective variance of veff,f=0.21, and σgc=0.672, corresponding to an effective variance of veff,c=0.57. For the atmospheric correction, one of 10 possible fine-mode fractions in volume-density, fv, can be retrieved: 0, 0.01, 0.02, 0.05, 0.10, 0.20, 0.30, 0.50, 0.80, 0.95. Compared to using the SeaDAS aerosol model to retrieve a three-parameter set of {RH, τf, τc}, MAPP retrieves the two optical depths {τf, τc} and directly retrieves six aerosol microphysical parameters: {rnf, rnc, nrf, nif, σgf, σgc}.

C. Ocean Model

The ocean surface roughness is modeled by a one-dimensional Gaussian (Cox–Munk) distribution of surface slopes, parameterized by wind speed [27]. The underwater scattering and absorption properties are described by the one-parameter Chowdhary polarized ocean bio-optical model (C2012, C2006) [6,7], which is parameterized by the chlorophyll concentration, CHL [mg/m3]. The one-parameter C2012 model was originally designed for chlorophyll concentrations 0CHL3 [mg/m3], but we found it useful to allow chlorophyll concentrations up to 10mg/m3 in order to represent more productive waters. Results from inversions of RSP polarimeter data collected during the SABOR campaign demonstrated the limitations of the original model and the improvement resulting from its extension to CHL values as large as 10 [mg/m3]. These results are presented in Section 6. The C2012 model is summarized in Appendix B.

D. Vector Radiative Transfer Model

The vector radiative transfer code we used is based on doubling-adding principles first proposed by H.C. van de Hulst (1963) [28] and developed starting in the late 1960s by James Hansen and Joop W. Hovenier [19,2931], which has been continuously upgraded [32,33]. Adding refers to combining two inhomogeneous layers, while doubling refers to combining two homogenous layers. Full polarization is available (all four Stokes parameters). The details are given in Appendix A.

3. OPTIMAL ESTIMATION

To test the MAPP algorithm, we generated simulated data for the seven RSP window channels at λ=410, 469, 555, 670, 864, 1594, and 2264 nm, and added noise as discussed in Section 4.B. The complete list of RSP channels is described in Section 4.A. The 960 nm channel to determine the water vapor absorption uses Eq. (3).

The cost function is defined as [34]

χ2(x)=ϕ(x)=ϕ(x)data+ϕ(x)prior=12(fy)TSε1(fy)+12(xxa)TSa1(xxa).

The vector radiative transfer model, described in Section 2.D, is our forward model, providing RIL, RIR, and DoLP, represented by f, which are a function of the state vector x, Eq. (1), and which provide a suitable model for the measured RIL, RIR, and DoLP, represented by y (either real measurements from RSP or synthetic measurements generated by the forward model with noise added). The first term may be called the data term since it depends on residuals of the forward model and the measurement, taking into account measurement error through its covariance matrix Sε. The second term may be considered the a priori term since it is the departure of the state vector x from the a priori state vector xa, with a priori uncertainty provided by the covariance matrix Sa. The a priori state vector and covariance matrices for our problem are defined below. It is convenient to define the normalized cost function of the data term by dividing by the number of measurements, m,

χ=1mϕ(x)data=1m12(fy)TSε1(fy).

Generally speaking, for a successful retrieval, 1mϕ(x)<1, and if there happen to be redundant measurements, then 1mϕ(x)1. For inversions of real RSP data in this paper, we consider retrievals successful if χ<0.1.

The optimal-estimation method used in this paper follows a method that has been used for inverting atmospheric temperature and water vapor vertical profiles, cloud, and surface properties from hyperspectral infrared sounders [35]. It was found to be reliable and efficient in terms of the number of forward model evaluations required. The inversion results from real and simulated data presented in this paper used this method. The state vector x is transformed into fifth-root-space x1 to smooth changes in the state parameters, analogous to a transformation into log-space,

x1=x1/5.

In order to ensure that the state vector does not go out of bounds [described by xlow and xhigh using the ranges in Eq. (2)], we found that the following transformation to b-space works well:

b=logx1x1lowx1highx1.

If x is out of bounds, the argument of the log will be negative, and will evaluate to an imaginary number. In order to transform from b-space to x1-space, we can use the transformation

x1=x1high1+eb+x1low1+eb.

Then x is given by x=x15. The retrieval is performed in b-space. Therefore, by definition, x1R+, and thus x will also be positive and real-valued. The m×n Jacobian matrix Kxf is expressed in b-space by

Kb=dfdb=dxdbdfdx=dxdbK=dxdx1dx1dbK.

The scaled cost function is a scalar value χs2, defined by

χs2=12(fy)TSε1(fy)+12(bba)TS1a1(bba),
where ba is the a priori state vector in b-space, and S1a is the a priori covariance in b-space proportional to the Jacobian. The following iteration over i is performed until x1 converges,
bi+1=ba+Si[(fy)+Kb(biba)],
where Si is the iteration-dependent constraint matrix [35].

We used a conservative and simple way to specify the a priori state vector, xa, using the mean of the allowable range of each retrieval parameter, which is also used as the first guess xi,

xa=(xlow+xhigh)/2xi.

The a priori covariance matrix, defined as a diagonal matrix, is given by

Sa=diag(σaσa),
where σa is a vector representing the standard deviations of the a priori values, which represent 1σ uncertainties, and is set equal to the a priori state vector, so that σa=xa and σaσa denotes the Schur product. [Also known as the Hadamard product, it is simply the element-by-element product. See https://en.wikipedia.org/wiki/Hadamard_product_(matrices).] The measurement error covariance matrix Sε is given in Section 4.B.

Once the retrieval has converged to x^, we calculate the posterior covariance matrix at x^, or the state error covariance matrix, given by

S^1(x^)=K(x^)TSε1K(x^)+Sa1.

The square root of the diagonals of S^1 give the 1σ uncertainty estimates of the retrieval accuracy, and the non-diagonal elements indicate how correlated the retrieval parameters are to each other. A diagonal or nearly-diagonal S^1(x^) indicates that the retrieval parameters are orthogonal to each other, without overlapping impacts on the modeled measurements. The RSP MAPP data files with the retrievals provide the uncertainty estimates of the state vector given by Eq. (21), and the propagated uncertainty for the fine- and coarse-mode effective radii, effective variances, and the fine-mode single-scattering albedo.

A. Desired Uncertainty Targets

The desired [36] one-standard-deviation (1σ) target accuracies for each aerosol retrieval parameter are summarized in Table 2. As the aerosol optical depth becomes small, it becomes difficult to retrieve aerosol properties.

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Table 2. Aerosol Uncertainty Targets for One Standard Deviation (1σ)a

4. MEASUREMENTS

A. Polarimeter Measurements

The RSP instrument [1] is capable of measuring the I, Q, and U Stokes parameters from multiple viewing angles and at multiple wavelengths. However, for this capability to be realized, the vector of aircraft motion must be parallel (or near-parallel) to the scanning direction. Data where the aircraft has substantial yaw is therefore excluded from this study. The exact nine RSP channel wavelengths, with FWHM in parentheses (nanometer, nm), are 410.27 (30), 469.13 (20), 554.96 (20), 670.01 (20), 863.51 (20), 960.0 (20), 1593.51 (60), 1880.0 (90), 2263.51 (120) nm, with angles measured between ±65° from zenith. These FWHM values are used to integrate the gaseous absorption in each channel, assuming a rectangular response function centered at the channel wavelength (see Section 2.B.1 and Chen et al., 2017 [37]).

The upwelling (reflected) total and polarized radiances (Stokes parameters) measured in the Earth’s atmosphere are defined by

Total Radiance=μ0F0πds2RI,Q,U[W/m2/sr],
where the ratio ds2=[Earth-to-Sun distance1AU]2 depends on day of year, μ0 is the solar zenith angle, and F0 is the solar irradiance at the top of the atmosphere [W/m2]. Thus, the actual solar irradiance that depends on time of year is given by F0/ds2. RI,Q,Uπ{I,Q,U}/μ0[1/sr] is the reflectance of the I, Q, or U Stokes parameter, respectively. The RSP L1B files contain measurements of calibrated normalized radiances, which are defined by (πF0×Total Radiance),
RSPL1BNormalized Radiance=μ0ds2RI,Q,U[1/sr].

Therefore, the RSP measurement is related to the reflectance calculated from vector radiative transfer programs by

RI,Q,U=ds2μ0(RSPL1BNormalized Radiance)[1/sr].

To retrieve aerosol microphysical and ocean color parameters, MAPP used all seven of RSP’s window channels, and the 960 nm water vapor detection channel was used to correct the measurements for water vapor absorption as described in Section 2.B. RSP also has a channel at 1880 nm for cirrus detection using water vapor absorption, but that channel was used only for cloud screening. The RSP field of view (FOV) is 14 mrad corresponding to a horizontal resolution of about 100 m with measurements occurring about every 0.8 s corresponding to 72 revolutions per minute. The RSP measurements were horizontally averaged ±30s, or 6.6 km assuming an aircraft cruising speed of about 110 m/s, since aerosol properties would not be normally expected to vary significantly over this distance. The measurements are then mapped to the same point on the ocean surface. As a pre-processing step, a cloud mask was constructed using HSRL/RSP cloud products to screen for clouds within ±160s of a particular scene, to mitigate contamination from cloud 3D side illumination effects. Thus, no RSP MAPP retrievals should have been attempted within 160 s of a cloud, or about 17 km, but clouds to the side of the aircraft could currently go undetected.

B. Polarimeter Measurement Noise

Optimal estimation fits the forward model to the measurements while accounting for measurement errors via the measurement covariance matrix Sε. The form of Sε depends upon the measurements and the instrument calibration. We adopted the commonly used approximation that the measurements are independent [38,39], so that the measurements are uncorrelated and Sε is a diagonal matrix, which is valid to the first order for RSP. For all channels, RSP has an accuracy in the Stokes parameters {RI, RQ, RU} of 3.5%, an accuracy of 0.2% for the degree of linear polarization, and polarization azimuth within 0.5°.

Simulated data RSP error model: For simulated data, we assumed an error of 2% normally distributed for each Stokes parameter in the set {RI, RQ, RU}. Thus, for each simulated measurement {RI, RQ, RU}, there is a 99.7% probability that the measurement will be found within ±6% of the measured value. The simulated RSP measurement error covariance thus used CIsim=CQsim=CUsim=(0.02RI,Q,U)2, and which was then propagated to RIL=(RI+RQ)/2, RIR=(RIRQ)/2, and the degree of linear polarization, DoLP=RQ2+RU2RI: SϵsimCRSPsim=diag(CILsim,CIRsim,CDoLPsim).

Real data RSP error model: The actual RSP measurement error covariances on RI, RQ, RU, RIL, RIR, and RDoLP are given in Appendix C.

C. Lidar Measurements

The NASA Langley airborne High-Spectral-Resolution Lidar (HSRL-1 and HSRL-2) beam is linearly h-polarized (i.e., horizontal or ∥) and both the h-polarized and v-polarized (i.e., vertical polarization or ⊥) components of the returned signal are measured, the latter of which provides the “depolarization” of the returned transmitted signal.

The lidar equation [2] for the measured total scattering (TS) signal [W/m2/sr] for each channel is

PTS(r)=ΨCTSr2[βm(r)+βa(r)]e20r[αm(r)+αa(r)]dr,
where r is the distance the light has traveled, corresponding to the time when the signal traveling at speed c is measured. The two unknowns are the aerosol (particulate) backscattering coefficient βa(r) [km1sr1] and the aerosol extinction coefficient αa(r) [km1]. The molecular backscattering coefficient βm(r) and the molecular extinction coefficient αm(r) depend on the (known) molecular number-density. CTS is a system calibration constant and Ψ is the transmitter-to-receiver overlap function.

High-spectral-resolution lidars like HSRL-1 and HSRL-2 have an additional 532-nm channel which is sensitive to only the molecular (m) backscatter and thereby provides a means to retrieve the profile of extinction [2]:

Pm,532(r)=FΨCm,532r2βm(r)e20r[αm(r)+αa(r)]dr.

Here F is the transmission through the iodine filter employed in the molecular channel to optically remove aerosol backscatter, and Cm,532 is a system calibration constant. The iodine is kept at high temperature so that it is always in the gas phase. Then the aerosol extinction coefficient can be obtained by differentiating Eq. (26) [2]. HSRL-2 has an additional high-spectral-resolution channel at 355 nm. Thus HSRL-2 can measure five aerosol parameters in each vertically resolved bin: three backscatter values at 355, 532, and 1064 nm, denoted β, and two extinction values at the high-spectral-resolution channels, 355 and 532 nm, denoted α. These five HSRL-2 measurements (3β+2α) allow us to make comparisons of AOD at 532 and 355 nm, the 355/532 Ångstrøm exponent, the aerosol lidar ratio at 532 and 355 nm, and can also be used to retrieve microphysical aerosol parameters directly [40]. The three HSRL-1 measurements (2β+1α) allow us to compare AOD and the lidar ratio at 532 nm and contain significant information about aerosol vertical distribution and type. In 2012, HSRL-1 completed upgrades to make underwater measurements of the diffuse attenuation coefficient, Kd, and the hemispherical backscatter coefficient, bbp.

1. HSRL AOD

HSRL lidars can measure aerosol optical depth by calculating the transmittance at a point near the aircraft (r1) and near the surface (r2) using the molecular lidar return Pm,532(r) and the theoretical molecular lidar backscattering coefficient βm at the two points [2]

HSRLAOD=τHSRL=12lnT(r2)T(r1)=12lnr22Pm,532(r2)βm(r1)r12Pm,532(r1)βm(r2).

2. HSRL Column-Averaged Intensive and Extensive Parameters

The HSRL-intensive parameters, such as the lidar ratio [sr] and the lidar aerosol depolarization ratio (in the single-scattering limit) do not depend on aerosol concentration, but only the aerosol scattering and absorption cross sections [41]. By contrast, extensive parameters, such as the aerosol backscatter [1/km/sr] and aerosol extinction km1, depend on the aerosol concentration. Note that both lidar-intensive and lidar-extensive parameters are inherent optical properties, since they depend on the aerosol concentration and cross sections, but not on the light field itself. We found it useful to compare the HSRL “column-averaged” lidar ratio Sa and Ångstrøm exponent at 355/532 (available on HSRL-2) to the RSP MAPP retrieved column-average values of lidar ratio and Ångstrøm exponent. The HSRL “column-averaged” lidar ratio is calculated as follows:

Sa=i=0Nαii=0Nβi[sr],
where i=0 corresponds to the lidar measurement bin closest to the surface (0.15km), i=N corresponds to the bin closest to the aircraft, and Δzi is the height interval of each lidar bin [km]. To compute Sa, both extinction and backscatter need to be defined and on the same resolution.

3. MAPP Aerosol Top Height and Lidar Parameter Mixing Rules

The aerosol top height, ht, is defined as the height at which

0htαdz=0.950hαdzor0htβdz=0.950hβdz.

This definition of aerosol top height has the advantage of being simple and powerful, although complex, multi-layered aerosol scenes may require a more sophisticated approach.

The corresponding RSP MAPP column-averaged values for backscattering and extinction coefficients and lidar ratio were calculated using the same equations for each mode separately. Since the MAPP retrieval assumes the aerosols to be distributed homogeneously between the surface h=0 and the aerosol top height h=ht, the integration is from 0 to ht, and the backscattering and extinction coefficients are assumed to be constant with height. Thus, we have β=β, α=α, Sa=αβ for each aerosol mode, fine and coarse. The following mixing rules are applied to calculate the RSP estimate of the column lidar ratio, which is the ratio of the total extinction to the total backscatter,

β=βf+βc,βfc=τfchtωfcp180;fc4π,
α=αf+αc,αfc=τfc/ht,
Sa=αf+αcβf+βc,
where the backscattering and extinction coefficients are defined for both aerosol modes by choosing f or c for fine or coarse. τ denotes the aerosol optical depth, ht denotes the aerosol layer height, ω denotes the aerosol single-scattering albedo, and p180 denotes the aerosol phase function at 180°.

4. HSRL Ocean Products

The HSRL-1 instrument was upgraded [42] with detectors that quickly recover from the strong Fresnel surface reflection and detect the underwater signal [43]. The lidar beam diffuse attenuation coefficient, Kbeam, is measured along the direction of the lidar beam by using the molecular backscatter channel, normalized to the molecular signal directly above the water. The slope of the molecular backscatter channel with depth, z, is directly related to the diffuse attenuation coefficient [42,44],

Kd(z)=Kbeam(z)cosθlidar,ocn=12dln[Pm,532(r)r2]dz[m1],
where r=H+z/n, H is the distance from the aircraft to the ocean surface, and n is the refractive index of water. The ratio of the particulate to molecular backscatter is then related to βp, the ocean particulate backscattering coefficient at 180° ([44,42]),
βp(z)=βw[Pa,532(z)+Pa,532(z)Pm,532(z)+Pm,532(z)][m1sr1],
where βw is the theoretical value of the backscattering coefficient for water at 180° [45], and the four terms inside the brackets are the measured signals in the 532 nm channel as indicated. The ocean particulate backscatter is related to the hemispherical backscattering coefficient, bbp through use of a factor χp,180 [sr], which represents the average of the 180° backscattering coefficient to the integral over the backward hemisphere, i.e., the integral in Eq. (B5) can be approximated by
qp2π=π/2πFp(Θ)4πsinΘdΘχp,180Fp(Θ=180°)[unitless],
where qp is the hemispherical particulate backscattering ratio. It has been found empirically that setting χp,180=12sr yields good agreement with in situ measurements of bbp ([44,42]) so that
bbp(z)=bpqp=bp2π[χp,180Fp(Θ=180°)]=π(1sr)·βp(z)[m1]
using the definition of the lidar particulate backscatter coefficient, βp=bpFp(Θ=180°). Thus, setting χp,180=12sr assumes that the integral of the phase function over the backward hemisphere is half the phase function at 180°. In order to compare to RSP ocean color retrievals, we define ocean column-averaged values,
Kd=1hz=6z=17Kddzandbbp=1hz=6z=17bbpdz[m1],
where the limits of 6 to 17 m were determined by a desire to avoid the near-surface measurements, which can have artifacts, and to average over at least two-thirds of an optical depth of lidar measurements in the water.

5. SIMULATED RESULTS

Simulations were performed using the 10-parameter state vector defined by Eq. (1), and the MAPP retrieved results using a simulated dataset are depicted in Fig. 1. The truth values were selected by using a random uniform distribution to select each retrieval parameter, independently. The ranges for the 10 parameters are given by Eq. (2). The aerosols were distributed homogeneously in a single layer between [0, 4 km]. The sensor geometry was fixed to a solar cosine zenith angle of 0.936 and relative azimuth of 105.27°. For each scene of simulated data, we randomly added Gaussian noise (one standard deviation=2% of signal) to the Stokes parameters {RI, RIQ, RU} and propagated the noise to the set of Stokes parameters {RIL, RIR, DoLP}. The simulated retrieval then used all seven RSP window channels simultaneously using the set {RIL, RIR, DoLP} and the optimal estimation method described in Section 3.

 figure: Fig. 1.

Fig. 1. Simulated retrievals using 10-parameter state space. The two lines surrounding the 1-to-1 line represent ±3σ, or three standard deviations. The red line represents the least-squares bisector. The units are micrometers (μm) for effective radius, meters per second (m/s) for wind speed, and milligrams per meter cubed (mg/m3) for chlorophyll concentration: the optical depth, effective variance, real refractive index, and single-scattering albedo are unitless. The ranges for the retrieval parameters used in this simulated study are slightly different than the finalized ranges defined by Eq. (2) for real data, but illustrate that the algorithm can successfully retrieve the 8 aerosol and wind speed parameters in 87% of the cases, and chlorophyll concentration in 67% of the cases, using simulated data where all 10 parameters are randomized.

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For the simulated study, 1024 scenes were randomly constructed, and then the retrieval was performed on each of them. Out of the 1024 scenes, 902 fit the criteria where τ555f0.05 and τ555c0.02. Of these retrievals, 87% of the scenes were successful in that the eight retrieved aerosol and wind speed parameters were all within 3σ (relative to the 1σ uncertainty goals listed in Table 2) of the true values. And 67% of the cases successfully retrieved chlorophyll concentration to 3σ, or 2.1mg/m3. Note that for some scenes we would not expect to be able to retrieve all 10 parameters within 3 standard deviations (for example, it is difficult to retrieve coarse-mode aerosol properties when the coarse-mode optical depth is small, especially if the fine-mode optical depth is large).

6. RESULTS FROM SABOR, 31 JULY 2014

In this section we present the results from SABOR 31 July 2014, which included both shallow- (less than 30 m ocean depth) and deep-water ocean measurements, and the flight track is shown in green in Fig. 2 together with the MODIS Aqua true color image. The other flight tracks and the ship track are also shown for reference. The HSRL extinction and aerosol typing for this day are given in Figs. 3(a) and 3(b), respectively. The resulting RSP MAPP retrievals of aerosol optical depth, τ, bbp, and Kd, are depicted in Fig. 3(c). There was heavy cirrus reported as the aircraft ascended until its cruising altitude at around 14 UTC, and became thinner, broken cirrus from 14.03 UTC onwards, with clear skies reported at 14.52 UTC. The influence of the cirrus (which could also be super-cooled liquid water droplets or mixed-phase cloud) appears to erroneously increase the aerosol optical depth. For this day and the TCAP case presented in the next section, all successful retrievals based on the magnitude of the cost function are displayed, without the altitude mask or clouds-above-aircraft mask used for the correlation plots. To help illustrate possible factors for discrepancies, the following masks are also displayed: clouds-above-aircraft (cyan), aircraft not at cruising altitude (magenta), aircraft turns/course corrections (yellow), and clouds below the aircraft (blue). According to the flight logs, there should have been clear sky conditions without significant clouds above the aircraft, as indicated by the lack of a cyan mask in Fig. 3(c). The variability of the ocean color measurements on this day, in addition to the complex, absorbing aerosols, make it a challenging and interesting case to study. Over the ocean, there was a tiny cloud spotted at 15:29 UTC below the aircraft, and a few small, low-level cumulus clouds were detected at around 15:38 through 15:42 UTC, followed by tiny, rogue clouds sprinkled here and there. Starting at around 16:02 UTC, the aircraft flew into a low-level field of cumulus clouds, and it can be seen that the AOD begins to drop significantly and the aerosol type changes from predominantly smoke to polluted marine. (Where clouds are detected by the cloud mask based on the HSRL-1 and RSP products, RSP MAPP retrievals were not attempted.) There were also some very thin clouds near the aircraft at around 16:03 and 16:06 UTC. Another thin cloud was near the aircraft, which grew thicker starting at 16:20 through 16:28 UTC, with the aircraft brocken spectre and surrounding glory clearly visible in the aircraft’s nadir camera, followed by another thin cloud at 16:29 through 16:34 UTC. The RSP retrievals for these thin, opaque clouds show optical depths between 1 and 3 with droplet sizes of 5 μm or smaller [46], and the cloud top is at 8 km, so they are significantly super-cooled.

 figure: Fig. 2.

Fig. 2. Overview of the NASA 2014 SABOR campaign. The ship track is highlighted in blue, and the flight tracks are highlighted in magenta. The 31 July 2014 flight track is highlighted in green, together with the superimposed MODIS Aqua true color reflectance.

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 figure: Fig. 3.

Fig. 3. SABOR 31 July 2014 flight. (a) HSRL-1 atmosphere backscattering coefficient and ocean diffuse attenuation coefficient. (b) HSRL-1 aerosol typing algorithm, where we can see that the aerosol structure for this day is complex with multiple layers and a lofted smoke plume. (c) The atmosphere/ocean results from RSP MAPP and HSRL for this entire day. The following masks are also displayed, where the color indicates the presence of: clouds-above-aircraft (cyan), aircraft not at cruising altitude (magenta), aircraft turns/course corrections (yellow), and clouds below the aircraft (blue).

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The atmosphere (aerosols and molecules) is responsible for the major part of the signal measured by RSP. Therefore, when the aerosol retrieval is successful, the aerosol optical depth in Fig. 3(c) should match within 0.02 between RSP and HSRL, but not necessarily for all cases (see Section 8 for a discussion of discrepancies, error sources, and retrieval comparisons for the entire SABOR campaign). HSRL-1 can measure plankton and underwater particulate matter, but does not have the extra 355 nm channel available on HSRL-2. It is difficult to compare to the column-averaged HSRL-1 532 nm lidar ratio since the scenes on this day consisted of multi-layered aerosols.

A. SABOR 532 nm AOD Comparison

The HSRL ocean profiling capability allows us to test whether the extended one-parameter ocean model is helpful in improving our AOD retrievals, and we can compare the RSP MAPP retrieved AOD at 555 nm to the HSRL-1 AOD at 532 nm [see Fig. 3(c)] in order to validate our aerosol retrievals. We note that in most cases the agreement is within 0.02–0.04. Aerosols that happen to be near or above the airplane can explain larger RSP MAPP retrieved values compared to HSRL-1 but not smaller values.

B. SABOR Ocean Product Comparison

The HSRL-1 ocean measurements indicate that a significant amount of complex, coastal-type water was encountered, in that Kd and bbp do not covary closely with chlorophyll, i.e., they do not lie along a curve in Fig. 4, even for deeper waters (defined here as having an ocean bottom greater than 30 m). However, we can also see that a curve is not an entirely unreasonable approximation, where we have used the HSRL column-averaged values for Kd and bbp, suggesting that the one-to-one relationship between Kd and bbp in our simplified one-parameter bio-optical model is not without merit.

 figure: Fig. 4.

Fig. 4. RSP MAPP ocean retrievals and HSRL-1 ocean products plotted as Kd versus bbp. The RSP C2012 ocean bio-optical model retrieval result is super-imposed against the HSRL-1 measurements HSRL-1 column-averaged Kd and bbp. Only scenes for deeper waters, defined as having an ocean bottom greater than 30 m, are included.

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C. Bio-optical Model Impact on Aerosol Microphysics

Figure 5 illustrates how the aerosol microphysics products are “coupled” to the ocean bio-optical model, since changing the bio-optical model changes the aerosol microphysics retrievals. The set of retrievals labeled “v1.21” was performed using the [0,3]mg/m3 chlorophyll concentration ocean model (colored in cyan), while the set of retrievals labeled “v1.22” was performed using the extended [0,10]mg/m3 ocean model (colored in red). The [0,3]mg/m3 chlorophyll concentration was saturated in high-sediment/mesotrophic waters (Kd>0.15), since this situation corresponds to the maximum allowable chlorophyll concentration value of 3.0mg/m3. The saturation shows how bio-optical modeling errors can propagate into the aerosol retrievals (not just vice versa). We found that the extended [0,10]mg/m3 one-parameter ocean model helped to smooth out some of the oscillations in the aerosol single-scattering albedo and real part of the refractive index, although it had less impact on the aerosol optical depth and aerosol effective radius, which tend to be easier to retrieve. Bio-optical models designed with three (or more) parameters can address the limitations in the one-parameter model, and potentially improve match-ups with the HSRL-1 ocean measurements and the quality of the aerosol microphysical retrievals.

 figure: Fig. 5.

Fig. 5. RSP MAPP aerosol retrievals versus HSRL-1 aerosol products for a time-series of retrievals between 14 UTC and 17 UTC on 31 July 2014. From top: aerosol (a) optical depth, (b) single-scattering albedo at 555 nm, (c), (b) effective radius, (d) real part of the refractive index at 555 nm. The first set of results (v1.21) employed the one-parameter Chowdhary ocean model from 0 to 3mg/m3 chlorophyll concentration, while the second set of results (v1.22) employed the extended range from 0 to 10mg/m3.

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7. RESULTS FROM TCAP, 17 JULY 2012

The NASA Langley HSRL-2 instrument flew together with the NASA GISS RSP during the 2012 TCAP mission. In this section we present the results from the TCAP flight on 17 July 2012, which is highlighted in green, together with the MODIS Aqua true color image, in Fig. 6.

 figure: Fig. 6.

Fig. 6. Overview of the Department of Energy 2012 TCAP campaign. The flight tracks are highlighted in magenta. The 17 July 2012 flight track is highlighted in green, together with the superimposed MODIS Aqua true color reflectance.

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As the aircraft flew out over the ocean, and before turning point back to Cape Cod, there was a low-altitude fog observed near the ocean surface at 14.75 (and again 16.25 UTC) in the RSP TCAP cloud retrievals [46], which is also apparent in the lidar backscatter in Fig. 7(a). The fog had an optical depth generally between 2 and 3 with a multi-modal size distribution dominated by large drops of 10–17 μm [47] in effective radius, so it is more like a surface cloud than a classic radiation fog [48]. Above the fog, clouds at around 2 km are also apparent in the RSP cloud retrievals and in the HSRL-1 backscatter. The HSRL-1 AOD increases near the clouds, which could be due to hydrated aerosol or small cloud droplets. RSP also detected clouds near 15.5 UTC when the aircraft flew over Cape Cod as it was turning back for its return leg out over the ocean.

 figure: Fig. 7.

Fig. 7. TCAP 17 July 2012. (a) HSRL direct measurement of extinction km1 at 532 nm. (b) HSRL-1 aerosol typing product. (c) Atmosphere retrieval results from the RSP instrument for this entire day. RSP MAPP 532 nm aerosol optical depth and aerosol microphysics retrievals versus HSRL-2 532 nm aerosol optical depth (direct measurement) and HSRL-2 aerosol microphysics products for a time-series of retrievals between 14.5 UTC and 17.5 UTC on 17 July 2012. Aerosol products: (i) optical depth, (ii) single-scattering albedo, (iii) effective radius, (iv) real part of the refractive index. The following masks are also displayed, where the color indicates the presence of: clouds-above-aircraft (cyan), aircraft not at cruising altitude (magenta), aircraft turns/course corrections (yellow), and clouds below the aircraft (blue).

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A. TCAP 532 nm AOD Comparison

Both HSRL-1 and HSRL-2 are able to directly and accurately measure extinction km1 at 532 nm, and thus optical depth, which is extremely useful for validation and improvement of atmospheric correction algorithms for passive instruments like radiometers and polarimeters. The HSRL-2 extinction product is plotted in Fig. 7(a). The HSRL aerosol typing product [41] is depicted in Fig. 7(b), which uses the wavelength-dependent lidar-intensive parameters to discriminate between aerosol types: on this day, the aerosol was characterized by a homogenous layer of urban aerosol outflow, but the plume or lofted aerosol layer overflown at 15.5 UTC and again at 17 UTC may have different properties than the aerosol below it, despite being categorized as the same type.

B. TCAP Aerosol Microphysics

In Fig. 7(c), top panel, we compare the RSP-MAPP-retrieved aerosol optical depth at 532 nm to the HSRL-2 directly measured optical depth at 532 nm. The aerosol optical depths for this day generally agree within 0.02, despite thin cirrus (or super-cooled liquid clouds) reported above the aircraft during the beginning of the flight. In the second panel from top in Fig. 7(c), we plot the aerosol RSP-MAPP-retrieved single-scattering albedo (SSA), which quantifies how much the aerosols absorb. Defined as the scattering coefficient divided by the extinction coefficient, an SSA value of 1.0 represents a completely non-absorbing aerosol, values close to 1 represent weakly absorbing aerosols, while values smaller than 0.95 represent absorbing aerosols. Thus, the aerosols were found to be weakly to moderately absorbing, with retrieved aerosol SSA values between 0.9 and 1.0. Note that for a fine mode optical depth of 0.2, an SSA value of 0.95 corresponds to an aerosol absorption optical depth of 0.01, which makes it challenging to detect. The RSP-MAPP-retrieved aerosol effective radius (third panel from top) is about 0.15–0.17 μm for these urban aerosols. The fourth panel depicts the fine-mode real part of the refractive index, which is found to vary between 1.5 and 1.6, although becoming closer to 1.4 later in the day.

C. TCAP Intensive/Extensive Product Comparison

In the first panel of Fig. 8, the optical depths measured by the HSRL-2 at 355 and 532 nm are plotted, compared to the RSP MAPP retrieved aerosol product at 532 nm and 355 nm. In the second panel, the 532 nm HSRL-2 directly measured aerosol lidar ratio, or the extinction-to-backscatter ratio, is plotted in black. The HSRL-2 column aerosol lidar ratio varies from about 50 to 70 sr on this day. The RSP-MAPP-retrieved lidar ratio is plotted for comparison at 555 nm (red) and at 532 nm (cyan). The RSP aerosol lidar ratio is generally within 20% of the HSRL-2 extinction-weighted aerosol lidar ratio, and although in most cases it is within 5–15 sr, it can vary up to 25 sr. Note that the polarimeter will be influenced by aerosols or ice/liquid clouds above the aircraft (see Section 8 for a discussion of discrepancies, sources of error, and retrieval comparisons for the entire TCAP campaign). In the third panel, the Ångstrøm exponent (355/532) measured by the HSRL-2 is compared to the RSP MAPP retrieval. We note that it is important to calculate it at 355/532, since when a size distribution is bimodal, the Ångstrøm exponent can change substantially, depending on which wavelength pair is used. The HSRL-2 Ångstrøm exponent is generally quite stable (1.3–1.6), while the RSP Ångstrøm exponent is generally lower (0.9–1.46), which would correspond to larger particles. Note that the HSRL-1 and HSRL-2 column aerosol lidar ratio will not include a contribution from aerosols near the surface, e.g. sea-salt aerosols in the (low) marine boundary layer, but the HSRL-2 Ångstrøm exponent represents all aerosols between the lidar and the surface.

 figure: Fig. 8.

Fig. 8. TCAP 17 July 2012: RSP MAPP retrieved lidar intensive/extensive parameters versus HSRL-2 extinction-weighted lidar intensive/extensive parameters from top: optical depth for reference; Sa, aerosol lidar ratio [sr] (intensive parameter); Ångstrøm exponent.

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8. STATISTICAL OVERVIEW OF RESULTS AND ERROR ANALYSIS

In the following correlation plots, a clouds-above-aircraft mask was applied, and an altitude mask was applied to select only cases when the aircraft was flying a remote sensing leg at cruising altitude. For the SABOR comparisons, only the “deep-water” scenes were selected, defined as having an ocean bottom of 30 m or greater, to avoid complications from ocean bottom reflectance and/or very turbid coastal waters. Although there was no instrument to specifically detect clouds above the aircraft during TCAP or SABOR, the flight logs facilitated construction of a clouds-above-aircraft mask, particularly for SABOR.

A. SABOR and TCAP AOD Correlations

Correlations of the SABOR and TCAP Aerosol-Above-Ocean (AAO) RSP MAPP 532 nm AOD results compared to the HSRL AOD measurements are given in Figs. 9 and 10. The one-to-one line is colored in black, and the dashed black lines represent the desired ±1σ accuracy of the RSP MAPP algorithm, which is ±0.02 for the aerosol optical depth (AOD) at 532 nm. The HSRL-1 and HSRL-2 can measure AOD below the aircraft within ±0.02 at 532 nm. The red line represents the least-squares bisector.

 figure: Fig. 9.

Fig. 9. SABOR campaign RSP MAPP and HSRL-1 optical depth correlations at 532 nm using HSRL AOD product after a clouds-above-aircraft mask was applied. Each color represents a different day between 18 July to 4 August 2014. The one-to-one line is colored in black, and the dashed black lines represent the desired ±1σ accuracy. The red line represents the least-squares bisector.

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 figure: Fig. 10.

Fig. 10. TCAP campaign RSP MAPP and HSRL-2 optical depth correlations using HSRL AOD product at 532 nm and 355 nm. For TCAP there was no instrument that could detect clouds above the aircraft onboard the aircraft during TCAP, and there was limited reporting of above aircraft clouds, which made clouds-above-aircraft screening difficult. Each color represents a different day in July 2012.

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The majority of RSP MAPP retrievals fall within ±0.04 HSRL-1 or HSRL-2 AOD at 532 nm. For the SABOR campaign, which had better reporting of clouds above the aircraft, of the 532 nm AOD comparisons in Fig. 9, 73% are within 0.04, 88% are within 0.06, and 98% are within 0.08, and R is 0.933 with a root-mean-square deviation of about 0.0372. For the TCAP 532 nm AOD comparisons in Fig. 10(a), 53% are within 0.04, 74% are within 0.06, and 81% are within 0.08, and R is 0.927 with a root-mean-square deviation of about 0.0673.

Correlations of the TCAP RSP MAPP 355 nm AOD results compared to the HSRL-2 355 nm AOD measurements are given in Fig. 10(b). The RSP MAPP retrievals are generally within ±0.04 AOD at 355 nm (red lines), and R is 0.959 and the root-mean-square deviation of about 0.0694.

B. SABOR Kd and bbp Ocean Product Correlation

Correlations of SABOR RSP MAPP Kd and bbp at 532 nm compared to HSRL-1 ocean measurements are given in Fig. 11. The one-to-one line is colored in black, and the dashed black lines represent the desired ±1σ accuracies of the RSP MAPP algorithm, which are ±0.1m1 for Kd and ±0.0005m1 for bbp. The Kd root-mean-square deviation is 0.0221 and R is 0.867. At the lower limit for clearer waters, the RSP Kd is 0.05m1 when the HSRL Kd 0.060.075, a 20%–45% bias. At the lower limit, the RSP bbp approaches 0m1, whereas the HSRL bbp is 0.001m1. At RSP MAPP retrieved bbp values of 0.0005m1, the HSRL bbp generally varies between 0.0010.0015m1, which is a bias of 200%–300%, or in absolute terms, 0.00050.001m1, which is close to the root-mean-square of about 0.000102. R for bbp is 0.759. There is a discrepancy in Kd and bbp for clearer waters that could be due to simplifications in the RSP MAPP ocean bio-optical model, which currently has only one parameter (chlorophyll concentration). The RSP MAPP passive ocean color retrieval uses multiple wavelengths to retrieve the bulk properties of the water assuming a single homogenous layer, whereas the HSRL measurement is at a single wavelength and is capable of providing vertical profiles in the water. We simply stress that the RSP ocean color retrieval correlates well with the average of the HSRL measurements, and therefore shows significant potential. In the future we plan to use a more advanced ocean bio-optical model to reconcile the differences at the low end (clear/oligotrophic waters) and at the high end (coastal and mesotrophic/eutrophic waters) between the ocean RSP retrieval and the HSRL measurement.

 figure: Fig. 11.

Fig. 11. SABOR campaign RSP MAPP and HSRL-1 ocean product correlations of (a) Kd[m1] and (b) bbp[m1], both at 532 nm, for all AAO (Aerosol-Above-Ocean) scenes with an ocean bottom greater than 30 m. Each color represents a different day between 18 July to 4 August 2014. The one-to-one line is colored in black, and the dashed black lines represent the desired ±1σ accuracy. The red line represents the least-squares bisector.

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C. Active/Passive Discrepancies

The following conditions will lead to discrepancies between RSP passive retrievals and HSRL active measurements: (i) aerosols near the aircraft, (ii) aerosols within 100 m of the surface, (iii) two or more layers of different aerosol types in the column, (iv) lofted or multi-layered absorbing aerosols, (v) non-spherical aerosols, (vi) three-dimensional effects caused by clouds above or in the vicinity of the aircraft, including cloud shadowing and cloud brightening [49,50], (vii) aerosol above the aircraft, (viii) cloud above the aircraft, and (ix) inherent retrieval and measurement uncertainties including those for viewing geometry caused by variations in the aircraft pitch, yaw and roll, and ocean modeling errors.

The HSRL is able to detect the vertical extinction and backscatter profile of aerosols, but has larger uncertainties when aerosols are in the near field of the lidar or if the aerosols are very close to the surface, since contamination from the surface return becomes a concern (i and ii). But we note that the HSRL AOD product uses the lidar two-way transmittance to accurately measure aerosol AOD from the aircraft all the way down to the surface. The HSRL typing algorithm can potentially determine how many aerosol types are present, and the HSRL depolarization measurement can be used to identify the presence of non-spherical aerosols. Thus items (iii) through (vi) are largely avoidable from co-incident HSRL measurements, although three-dimensional effects from nearby clouds can be difficult to detect and will potentially require ancillary data and improved screening techniques. Aerosols and clouds above the aircraft will both hamper the algorithm’s performance, but we would not typically expect significant amounts of aerosol above the airplane. Therefore we focus on (viii) liquid or ice clouds above the aircraft as a probable cause of the horizontal “streamers” in the correlation plots for RSP AOD and (ix) retrieval uncertainties. For the latter, simplifications or unrealistic assumptions can cause the retrieval to diverge or converge to an erroneous solution. The current MAPP polarimeter retrieval is approximate in that it assumes that the aerosols are located in a single layer and modeled as a bimodal aerosol distribution, whereas in reality we know that aerosols can be layered in complex structures with different aerosol types. Also, the ocean bio-optical model is simplistic in that it depends on only a single parameter. The RSP versus HSRL correlation plots provide important campaign-wide aerosol and ocean product statistics, and the discrepancies indicate where the RSP MAPP retrievals can be further improved, such as enhanced above-aircraft-cloud and nearby cloud detection and ocean bio-optical modeling.

9. CONCLUSION

A new algorithm called MAPP has been created that can invert polarimetric data to retrieve detailed aerosol microphysical parameters such as aerosol single-scattering albedo and complex refractive index, in addition to ocean color products such as the diffuse attenuation coefficient. The MAPP algorithm is fully automated and capable of bulk processing entire field campaigns of data (thousands of scenes), and the entire framework is described in this paper. The MAPP algorithm has some unique advantages, since it does not rely on look-up tables and simultaneously retrieves aerosol and ocean products. For the first time, hundreds of aerosol microphysics retrievals from the RSP polarimeter have been compared to HSRL-1/HSRL-2 AOD at multiple wavelengths, and also comparisons have been made to the HSRL-1 ocean measurements.

The MAPP algorithm was tested on simulated data and used to analyze field data from AAO (Aerosol-Above-Ocean) scenes. These high-density retrievals from polarimeter measurements were collected during two aircraft campaigns, SABOR and TCAP. RSP MAPP retrievals were validated by comparing them to co-incident high-spectral-resolution lidar measurements obtained by the Langley airborne High-Spectral-Resolution Lidars HSRL-1 and HSRL-2. The AOD at 532 and 355 nm (when available) are compared, as are the 532-nm ocean measurements of the diffuse attenuation coefficient, Kd, and the hemispherical particulate backscattering coefficient, bbp.

The co-incident HSRL-1/HSRL-2 measurements of AOD and column-averaged intensive parameters (lidar ratio and the Ångstrøm exponent) were useful for evaluating the MAPP algorithm, and they show significant promise as additional validation tools for atmospheric correction algorithms for passive ocean color remote sensing. We found that the HSRL aerosol optical depth at 532 nm is an extremely useful and accurate check on the aerosol retrieval, i.e., the atmospheric correction, which is important, because accurate atmospheric correction is a prerequisite for retrieval of marine parameters with reliable accuracy from passive ocean color sensors. In addition, HSRL-1’s underwater measurement capability of the diffuse attenuation coefficient, the hemispherical backscattering coefficient, and potentially the hydrosol depolarization ratio are groundbreaking measurements for evaluating polarimeter- (e.g., RSP) and radiometer-retrieved (e.g. MODIS) ocean products. Taken together, these measurements have significant potential to advance the next stage of ocean color retrievals using data obtained by passive ocean color sensors. The agreement between the polarimeter and lidar observations, despite being very different measurement systems, underscores the importance of developing joint polarimeter/HSRL observations of the atmosphere/ocean system, since the two types of instruments are in many ways complementary. The RSP MAPP products are summarized on the NASA LaRC website [12] and are available for download at the NASA GISS RSP website [13].

Future work involves implementing a more advanced three- or four-parameter ocean bio-optical model into MAPP that has, for example, not only a chlorophyll concentration parameter (CHL), but also an independently varying color dissolved organic matter parameter (CDOM]), together with its spectral slope, SCDOM, and a hemispherical backscatter parameter, (bbp) to allow for the effects of scattering by non-algal particles. A more comprehensive ocean model would allow us to model the two-dimensional ocean complexities detected by lidar as depicted in Fig. 4 and to potentially retrieve the CDOM and/or hemispherical backscatter wavelength-dependent slope, which can then be also compared against ship-based and buoy in situ ocean and underwater radiance-based measurements. It is also of interest to compare the MAPP aerosol retrievals to in situ measurements of aerosols made during SABOR and TCAP. We plan to add the capability to retrieve the aerosol layer height independently from RSP, since collocated lidar measurements are not always available. Another task is to include scattering by non-spherical aerosols, such as dust.

Lastly, the MAPP framework was designed with the ultimate goal of being able to use HSRL-2 measurements directly in a joint polarimeter+lidar retrieval. The joint HSRL+RSP retrieval algorithm is expected to improve upon the column-averaged microphysics of the polarimeter-only version presented in this paper, while simultaneously improving the vertically resolved microphysics retrievals of the HSRL-2-only retrievals [40,51].

APPENDIX A: VECTOR RADIATIVE TRANSFER

The solution to the vector radiative transfer equation is given by the following recipe:

Q1=Ra*Rb*,
Qn=Q1Qn1,
S=n=1Qn,
U=Rbeτa/μ0+RbD,
D=Ta+Seτa/μ0+STa,
R(τa+τb)=Ra+eτa/μU+Ta*U,
T(τa+τb)=eτb/μD+Tbeτa/μ0+TbD.

τa is the optical thickness of the first layer, and τb is the optical thickness of the second layer. The exponential terms represent direct beam attenuation at solar zenith cosine μ0, while T is the diffuse transmission matrix. The bold-faced uppercase letters are 4×4 matrices that represent diffuse scattering matrices, the reflection matrix, R, the transmission matrix, T, and the downwelling and upwelling (D and U) matrices between the two layers. By multiplying the above reflection, transmission, upwelling, and downwelling matrices by the incident beam flux πμ0f0, and by including the direct beam exponential term, we can find the Stokes vector components representing the reflection at the top, μ0πf0R, the transmission at the bottom, μ0πf0T(τa+τb)+μ0πf0e(τa+τb)μ0, and the downwelling and upwelling (μ0πf0D and μ0πf0U) between the two layers. The superscript * denotes reflection (or transmission) matrices when illuminated from below, and for homogenous layers, R*(μ,μ0,Δϕ)=R*(μ,μ0,Δϕ), where μ is the polar angle cosine and Δϕ=ϕϕ0 is the difference between the azimuthal angle ϕ and the azimuthal solar angle ϕ0.

APPENDIX B: C2012 ONE-PARAMETER POLARIZED OCEAN BIO-OPTICAL MODEL

1. Scattering Coefficient of the Ocean

The total scattering coefficient for the ocean as a function of wavelength, λ [nm], is given by

b=bsw(λ)+bp(λ,CHL)[m1],
where the scattering coefficient for seawater, bsw, is given by SB1981 [52]. The scattering coefficient, bp, for the ocean particles is given by (Morel and Maritorena (MM2001) [53], Huot (2007) [54])
bp(λ,CHL)=0.347[CHL]0.766(λ660)k[m1],
where the chlorophyll concentration, CHL [mg/m3], and k is given by (MM2001):
k={10CHL<0.02,0.5(log10[CHL]0.3)0.02CHL2,0CHL>2.

The hemispherical backscattering coefficient bbpbpqp for ocean particles is parameterized as [53]

bbp(λ,CHL)=bp(λ,CHL)qp(CHL),
where qp is the hemispherical particulate backscattering ratio, defined as the integral over the backward hemisphere of the combined particulate scattering phase function Fp(Θ),
qp2ππ/2πFp(Θ)4πsinΘdΘ[unitless].

The normalization of Fp differs by a factor 14π to that commonly used by the ocean color community. The C2012 ocean model was constructed by constraining Eq. (B5) using the following empirical relation for qp (C2006, MM2001), which has been modified so that there is no (λ660)k wavelength dependence (C2012) for the particulate backscattering ratio,

qp(CHL)(0.0070.0025log10[CHL]))[unitless].

Thus, in this model, the hemispherical backscattering coefficient bpbp(λ,CHL) has wavelength dependence, but not the hemispherical backscattering ratio, qpqp(CHL). Then the particulate hemispherical backscattering coefficient becomes

bbp(λ,CHL)=bp(λ,CHL)(0.0070.0025log10[CHL]))[m1],
and the total hemispherical backscattering coefficient for the ocean is then given by
bb(λ,CHL)=bb,sw+bbp=0.5bsw(λ)+bbp(λ,CHL)[m1].

2. Hydrosol Mie Computations and Scattering Matrix

The ocean particles are modeled as a bimodal mixture (D–P) of detritus (D) and plankton (P) spherical particles. Each mode is assumed to have a Junge (power-law) size distribution with radii between 0.01 and 100 μm and Junge-exponents γdet and γplk, respectively. The real part of the refractive indices relative to water, nr,det and nr,plk, are assumed to be wavelength independent. Mie computations are used to calculate the resulting scattering matrices fdet(Θ), fplk(Θ), scattering cross sections σdet, σplk, and the backscattering ratios qdet, qplk. The imaginary part of the refractive index is set to zero, since its impact on the backscattering ratio is negligible (C2012). Note that we use an empirical relation, Eq. (B17), to determine the total D–P particle absorption and also use an empirical relation to calculate the particulate scattering coefficient from Eq. (B2), so that the hydrosol particulate single-scattering albedo is

ωp(λ,CHL)=bp(λ,CHL)ap(λ,CHL)+bp(λ,CHL).

But the combined D–P Stokes scattering matrix is given by the Mie-computed scattering cross sections and scattering Stokes matrices,

fp(Θ)=(1fdet)σplkfplk(Θ)+fdetσdetfdet(Θ)(1fdet)σplk+fdetσdet,
where fdet=NdetNdet+Nplk, and Ndet and Nplk are the number of detritus and plankton particles, respectively. Therefore, the hemispherical backscattering ratio due to the D–P mixture is given by (using the definition in Eq. (B5) for qdet, qplk)
qp=(1fdet)σplkqplk+fdetσdetqdet(1fdet)σplk+fdetσdet.

For each mode, the values are determined to be (nr,det=1.15, γdet=4.4) and (nr,plk=1.04, γplk=3.7). The detritus fraction of the D–P mixture, fdet, then depends on the chlorophyll concentration, and can be fitted by the following polynomial to within ±0.003:

fdet(CHL)=0.610.099χCHL0.009χCHL2,
where χCHL=log10CHL0.03. By using the real part of the refractive index and the Junge exponent for detritus and plankton, we can then compute the scattering cross sections from Mie theory as σdet=1.388×105μm2 and σplk=8.874×105μm2.

The values above were determined as follows (C2012):

  • (1) For a given refractive index nr, the Junge exponent γ was varied to minimize d=1Ni=1Nh(phyd(Θi)pw(Θi))2, where p=F21(Θ)F11(Θ), phyd is for the plankton or detritus, pw is for water using a depolarization ratio of δ=0.09, and the scaling factor h=4 when phyd0.85 and 1 otherwise.
  • (2) A linear fit formula was derived from the results of (1): γhyd=6.63nhyd3.25.
  • (3) The minimum and maximum values, qp,min and qp,max, are obtained by using CHL=0.03 and 3.0mg/m3 in Eq. (B6), respectively. Thus qp,min=0.01081 and qp,max=0.00581 for the four RSP ocean color channels at 410, 469, 555, and 670 nm.
  • (4) Based on applying the constraint in (3), the real refractive indices are found to be nr,det=1.15 and nr,plk=1.04. Then Junge exponents γdet=4.4 and γplk=3.7 are obtained from the fit in (2). The resulting effective radii are small, at 0.35 μm (plankton) and 0.034 μm (detritus), since the emphasis is to reproduce variations in qp corresponding to the MM2001 bio-optical model, and smaller particles contribute more to backscattering than larger particles.
  • (5) Using the refractive index and Junge exponent values in (4), we can calculate the scattering matrices fdet(Θ),fplk(Θ), scattering cross sections σdet and σplk, and backscattering ratios qdet and qplk.
  • (6) The empirical relationship between qp as a function of CHL, Eq. (B6), is used with Eq. (B11) given values in (5) for σdet, σplk, qdet, qplk, to provide fdet as a function of CHL [Eq. (B12)]. The resulting D–P scattering matrix is consistent with a wavelength-dependent Fournier–Forand phase function (C2012).

3. Absorption Coefficient of the Ocean

In order to calculate the absorption coefficient of the ocean, C2012 uses a model of the diffuse attenuation coefficient Kd(λ,CHL). The diffuse attenuation coefficient is a quasi inherent optical property defined as [55]

Kd=ddz[lnFν(z)]=1FνdFν(z)dz,
where Fν is the diffuse downwelling irradiance. One may approximate Kd as follows (MM2001):
Kd(λ,CHL)Kw(λ)+Kbio(λ,CHL)[aw(λ)+0.5bw(λ)]+χ(λ)[CHL]e(λ),
where Kwaw(λ)+0.5bw(λ) is the apparent attenuation coefficient due to pure ocean water, and aw and bw are the absorption [56] and scattering coefficients, respectively, from SB1981 [52]. Kbio is the apparent attenuation coefficient for all other scattering and absorbing species in the ocean, which are assumed to covary with the chlorophyll concentration (CHL). The parameters χ(λ) and e(λ) are regression coefficients [53]. In principle, we are only allowed to add inherent optical properties, but since Kd is a quasi inherent optical property, the error resulting from the addition in Eq. (B14) is assumed to be small (MM2001).

The total absorption coefficient for the ocean is then given by solving the following equation for aocn (C2006):

aocn(λ,CHL)=Kd(λ,CHL)[1α(λ,CHL,θ0)bb(λ,CHL)aocn]×μd(λ,CHL,θ0)μuμd(λ,CHL,θ0)α(λ,CHL,θ0)bb(λ,CHL)aocn+μu[m1],
where μd(λ,CHL) and μu=0.4 are the average upward and downward cosine directions, so that (suppressing the functional dependencies),
aocn(λ,CHL)=12μd(Kdαbb)±12μd2(Kdαbbμu)24Kdαbb.

The quantity α(λ,CHL,θ0)bb(λ,CHL)aocnEu(λ)Ed(λ) is the ratio of the upwelling to downwelling irradiance measured just below the ocean surface and is equal to α(1+bbaocn)(bbaocn+bb) when bb is large compared to aocn [57].

Since we know the absorption for pure water, we can then find the particulate absorption (by plankton and implicitly CDOM),

ap(λ,CHL)=aocn(λ,CHL)aw(λ).

Thus the C2012 bio-optical model depends only on chlorophyll concentration (one parameter), and is consistent with (i) the commonly used Fournier–Forand phase function for scattering by plankton particles, (ii) empirical measurements of scattering and absorption coefficients, and (iii) provides the full 4×4 scattering matrix for polarized light calculations. The goal of a bio-optical model should be to capture the relevant changes in the inherent optical properties in the ultraviolet (UV) and visible with as few parameters as possible, and ideally to be as general and realistic as possible to allow application to as many different regions as possible. In that context, the C2012 model works well for having only a single parameter. Future work would reduce assumptions and increase the number of parameters to allow more detailed retrieval of in-water inherent optical properties.

4. Example C2012 IOP Calculation (λ=555nm, CHL=1mg/m3)

From Morel and Mueller (2002) [57], α(λ,CHL,θ0)0.38. Kd(λ,CHL)=0.09857 (MM2001). bb(λ,CHL)=0.00431 since bb,sw(λ)=0.0019 [52] and bbp(λ,CHL)=0.00236 (MM2001). At SZA=30°, μd(SZA,λ,CHL)=0.832. μu=0.4 for all wavelengths and chlorophyll concentrations (MM2001). Thus, aocn(λ,CHL)=0.077515m1.

APPENDIX C: RSP UNCERTAINTY MODEL

The actual RSP measurement error covariances are given as follows, substituting in the values σfloor=0.00002, a=1×107, σlnK1=0.005 (0.5%), σlnαc=0.015 (1.5%), σlnα1=0.002 (0.2%):

CI=σRI2=(2σfloorμ0)2+(aμ0RI)2+(RQ2σlnK1)2+(RIσlnαc)2.CQ=σRQ2=(σfloor2μ0)2+(aRIμ0)2+(12RIσlnK1)2+(RQσlnαc)2+(RQσlnα1)2.CU=σRU2=(σfloor2μ0)2+(aRI2μ0)2(12RI2σlnK1)2+(RUσlnαc)2+(RUσlnα1)2.CIL=σRIL2=CI4+CQ4+(RI+RQ2σlnαc)2+(RI+RQ4σlnK1)2+(RQ2σlnα1)2.CIR=σRIR2=CI4+CQ4+(RIRQ2σlnαc)2+(RIRQ4σlnK1)2+(RQ2σlnα1)2.CDoLP=σDoLP2=(2σfloorμ0RI2+DoLP2)2+(aμ0RI2DoLP2)2+(12σlnK11DoLP2)2+(σlnα1DoLP)2+(12σlnK1RQ4+RU4RI2)2.

Funding

Langley Research Center; Goddard Space Flight Center (GSFC); National Aeronautics and Space Administration (NASA); U.S. Department of Energy (DOE) (DE-A06-76RLO 1830, DE-SC0006730, KP1701000/57131).

Acknowledgment

This paper was funded by the NASA Aerosols-Clouds-Ecosystems (ACE) project, NASA ROSES Remote Sensing Theory for Earth Science, the NASA Ocean Biology and Biogeochemistry Program, and the NASA Science Innovation Fund 2015-2016. The SABOR campaign was funded by the NASA Ocean Biology and Biogeochemistry Program. Support for the RSP and HSRL-2 flight operations during TCAP was provided by the Department of Energy Atmospheric Radiation Measurement Climate Research Facility (DOE ARM): Interagency Agreement. Larry Berg was supported by the U.S. DOE’s Atmospheric System Research (ASR) Program, and TCAP was supported by ARM. The Pacific Northwest National Laboratory is operated for DOE by the Battelle Memorial Institute.

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31. J. Hovenier, “Multiple scattering of polarized light in planetary atmospheres,” Astron. Astrophys. 13, 7–29 (1971).

32. J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

33. B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).

34. C. Rodgers, Inverse Methods for Atmospheric Sounding (World Scientific, 2000).

35. W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017). [CrossRef]  

36. M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004). [CrossRef]  

37. N. Chen, W. Li, T. Tanikawa, M. Hori, R. Shimada, T. Aoki, and K. Stamnes, “Fast yet accurate computation of radiances in shortwave infrared satellite remote sensing channels,” Opt. Express 25, A649–A664 (2017). [CrossRef]  

38. O. Hasekamp, “Capability of multi-viewing-angle photo-polarimetric measurements for the simultaneous retrieval of aerosol and cloud properties,” Atmos. Meas. Tech. 3, 1229–1262 (2010). [CrossRef]  

39. M. D. Lebsock, T. S. L’Ecuyer, and G. L. Stephens, “Information content of near-infrared spaceborne multiangular polarization measurements for aerosol retrievals,” J. Geophys. Res. Atmos. 112, D14206 (2007). [CrossRef]  

40. D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014). [CrossRef]  

41. S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014). [CrossRef]  

42. J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

43. J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017). [CrossRef]  

44. M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013). [CrossRef]  

45. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009). [CrossRef]  

46. M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012). [CrossRef]  

47. M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012). [CrossRef]  

48. M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015). [CrossRef]  

49. T. Várnai and A. Marshak, “Analysis of co-located MODIS and CALIPSO observations near clouds,” Atmos. Meas. Tech. 5, 389–396 (2012). [CrossRef]  

50. F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016). [CrossRef]  

51. P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017). [CrossRef]  

52. R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981). [CrossRef]  

53. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters—a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]  

54. Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007). [CrossRef]  

55. K. Stamnes, G. E. Thomas, and J. J. Stamnes, Radiative Transfer in the Atmosphere and Ocean, 2nd ed. (Cambridge University, 2017).

56. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997). [CrossRef]  

57. A. Morel and J. L. Mueller, “Normalized water-leaving radiance and remote sensing reflectance: bidirectional reflectance and other factors,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation (2002), Vol. 2, pp. 183–210.

References

  • View by:

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  4. F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
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  5. K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
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  8. L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
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  9. O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
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  26. R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
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    [Crossref]
  30. J. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres part ii. sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
    [Crossref]
  31. J. Hovenier, “Multiple scattering of polarized light in planetary atmospheres,” Astron. Astrophys. 13, 7–29 (1971).
  32. J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).
  33. B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).
  34. C. Rodgers, Inverse Methods for Atmospheric Sounding (World Scientific, 2000).
  35. W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
    [Crossref]
  36. M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
    [Crossref]
  37. N. Chen, W. Li, T. Tanikawa, M. Hori, R. Shimada, T. Aoki, and K. Stamnes, “Fast yet accurate computation of radiances in shortwave infrared satellite remote sensing channels,” Opt. Express 25, A649–A664 (2017).
    [Crossref]
  38. O. Hasekamp, “Capability of multi-viewing-angle photo-polarimetric measurements for the simultaneous retrieval of aerosol and cloud properties,” Atmos. Meas. Tech. 3, 1229–1262 (2010).
    [Crossref]
  39. M. D. Lebsock, T. S. L’Ecuyer, and G. L. Stephens, “Information content of near-infrared spaceborne multiangular polarization measurements for aerosol retrievals,” J. Geophys. Res. Atmos. 112, D14206 (2007).
    [Crossref]
  40. D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
    [Crossref]
  41. S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
    [Crossref]
  42. J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.
  43. J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
    [Crossref]
  44. M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
    [Crossref]
  45. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009).
    [Crossref]
  46. M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
    [Crossref]
  47. M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012).
    [Crossref]
  48. M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
    [Crossref]
  49. T. Várnai and A. Marshak, “Analysis of co-located MODIS and CALIPSO observations near clouds,” Atmos. Meas. Tech. 5, 389–396 (2012).
    [Crossref]
  50. F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016).
    [Crossref]
  51. P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
    [Crossref]
  52. R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
    [Crossref]
  53. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters—a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
    [Crossref]
  54. Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
    [Crossref]
  55. K. Stamnes, G. E. Thomas, and J. J. Stamnes, Radiative Transfer in the Atmosphere and Ocean, 2nd ed. (Cambridge University, 2017).
  56. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
    [Crossref]
  57. A. Morel and J. L. Mueller, “Normalized water-leaving radiance and remote sensing reflectance: bidirectional reflectance and other factors,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation (2002), Vol. 2, pp. 183–210.

2017 (4)

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
[Crossref]

N. Chen, W. Li, T. Tanikawa, M. Hori, R. Shimada, T. Aoki, and K. Stamnes, “Fast yet accurate computation of radiances in shortwave infrared satellite remote sensing channels,” Opt. Express 25, A649–A664 (2017).
[Crossref]

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

2016 (3)

F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016).
[Crossref]

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

2015 (3)

L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
[Crossref]

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

2014 (2)

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
[Crossref]

2013 (1)

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

2012 (4)

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

T. Várnai and A. Marshak, “Analysis of co-located MODIS and CALIPSO observations near clouds,” Atmos. Meas. Tech. 5, 389–396 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012).
[Crossref]

2011 (3)

K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from parasol multiangle photopolarimetric measurements,” J. Geophys. Res. Atmos. 116, D14204 (2011).

2010 (2)

2009 (2)

X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
[Crossref]

2008 (1)

2007 (2)

M. D. Lebsock, T. S. L’Ecuyer, and G. L. Stephens, “Information content of near-infrared spaceborne multiangular polarization measurements for aerosol retrievals,” J. Geophys. Res. Atmos. 112, D14206 (2007).
[Crossref]

Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
[Crossref]

2006 (1)

2004 (2)

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[Crossref]

H. Du, “Mie-scattering calculation,” Appl. Opt. 43, 1951–1956 (2004).
[Crossref]

2003 (1)

B. Cairns, B. E. Carlson, R. Ying, A. A. Lacis, and V. Oinas, “Atmospheric correction and its application to an analysis of hyperion data,” IEEE Trans. Geosci. Remote Sens. 41, 1232–1244 (2003).
[Crossref]

2001 (2)

1999 (1)

B. Cairns, E. E. Russell, and L. D. Travis, “Research scanning polarimeter: calibration and ground-based measurements,” Proc. SPIE 3754, 186–196 (1999).
[Crossref]

1997 (3)

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth observing system era,” J. Geophys. Res. Atmos. 102, 17081–17106 (1997).
[Crossref]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. Atmos. 102, 16831–16847 (1997).
[Crossref]

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
[Crossref]

1995 (1)

J. Michalsky, J. Liljegren, and L. Harrison, “A comparison of sun photometer derivations of total column water vapor and ozone to standard measures of same at the southern great plains atmospheric radiation measurement site,” J. Geophys. Res. 100, 25995–26003 (1995).
[Crossref]

1987 (1)

J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

1981 (1)

1980 (1)

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1971 (3)

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11, 809–812 (1971).
[Crossref]

J. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres part ii. sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
[Crossref]

J. Hovenier, “Multiple scattering of polarized light in planetary atmospheres,” Astron. Astrophys. 13, 7–29 (1971).

1954 (1)

Ackerman, A. S.

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

Ahlm, L.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Ahmad, Z.

Alexandrov, M. D.

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

Alexandrov, M. L.

B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).

Aoki, T.

Arnold, G. T.

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

Baker, K. S.

Barnard, J. C.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

B. Schmid, J. J. Michalsky, D. W. Slater, J. C. Barnard, R. N. Halthore, J. C. Liljegren, B. N. Holben, T. F. Eck, J. M. Livingston, and P. B. Russell, “Comparison of columnar water-vapor measurements from solar transmittance methods,” Appl. Opt. 40, 1886–1896 (2001).
[Crossref]

Behrenfeld, M.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Behrenfeld, M. J.

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Berg, L. K.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Berk, A.

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN,” Technical report, (1987).

Berkoff, T.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Bernstein, L. S.

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN,” Technical report, (1987).

Bertram, A.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Beyersdorf, A. J.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

Bosma, P.

J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Burg, R.

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[Crossref]

Burton, S.

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
[Crossref]

Burton, S. P.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Butler, C.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Butz, A.

O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from parasol multiangle photopolarimetric measurements,” J. Geophys. Res. Atmos. 116, D14204 (2011).

Cairns, B.

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).
[Crossref]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[Crossref]

B. Cairns, B. E. Carlson, R. Ying, A. A. Lacis, and V. Oinas, “Atmospheric correction and its application to an analysis of hyperion data,” IEEE Trans. Geosci. Remote Sens. 41, 1232–1244 (2003).
[Crossref]

B. Cairns, E. E. Russell, and L. D. Travis, “Research scanning polarimeter: calibration and ground-based measurements,” Proc. SPIE 3754, 186–196 (1999).
[Crossref]

B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).

Carlson, B.

B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).

Carlson, B. E.

B. Cairns, B. E. Carlson, R. Ying, A. A. Lacis, and V. Oinas, “Atmospheric correction and its application to an analysis of hyperion data,” IEEE Trans. Geosci. Remote Sens. 41, 1232–1244 (2003).
[Crossref]

Chand, D.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Chemyakin, E.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Chen, N.

Chowdhary, J.

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).
[Crossref]

Collins, J.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Comstock, J. M.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Cook, A.

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

J. Hair, C. Hostetler, A. Cook, D. Harper, R. Ferrare, T. Mack, W. Welch, L. Izquierdo, and F. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
[Crossref]

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Corrigan, C.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Cox, C.

Dall’Olmo, G.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

De Haan, J.

J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Deuzé, J.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Diedenhoven, B.

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

Du, H.

Dubovik, O.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Ducos, F.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Dunagan, S.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Eck, T. F.

Emde, C.

F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

Fast, J. D.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Ferrare, R.

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
[Crossref]

K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

J. Hair, C. Hostetler, A. Cook, D. Harper, R. Ferrare, T. Mack, W. Welch, L. Izquierdo, and F. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
[Crossref]

Ferrare, R. A.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Flynn, C. J.

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
[Crossref]

Franz, B. A.

Frossard, A.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Fry, E. S.

Gordon, H. R.

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Hair, J. W.

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
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M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
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Harper, D.

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
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J. Hair, C. Hostetler, A. Cook, D. Harper, R. Ferrare, T. Mack, W. Welch, L. Izquierdo, and F. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
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J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

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J. Michalsky, J. Liljegren, and L. Harrison, “A comparison of sun photometer derivations of total column water vapor and ozone to standard measures of same at the southern great plains atmospheric radiation measurement site,” J. Geophys. Res. 100, 25995–26003 (1995).
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L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
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R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
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He, M.-X.

Herman, M.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
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M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
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Holdak, A.

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[Crossref]

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[Crossref]

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

Hostetler, C. A.

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
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[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
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Hu, L.

Hu, Y.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
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J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (EDP Sciences, 2016), Vol. 119, p. 22001.

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Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
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Kahn, R. A.

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J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
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W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
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Litvinov, P.

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Liu, Q.

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
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Liu, X.

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
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Lopatin, A.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
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J. Michalsky, J. Liljegren, and L. Harrison, “A comparison of sun photometer derivations of total column water vapor and ozone to standard measures of same at the southern great plains atmospheric radiation measurement site,” J. Geophys. Res. 100, 25995–26003 (1995).
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Mishchenko, M.

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P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
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Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
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Müller, D.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
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K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
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Redemann, J.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
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Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
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R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
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C. Rodgers, Inverse Methods for Atmospheric Sounding (World Scientific, 2000).

Rodier, S. D.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Rogers, R.

D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

Russell, E. E.

B. Cairns, E. E. Russell, and L. D. Travis, “Research scanning polarimeter: calibration and ground-based measurements,” Proc. SPIE 3754, 186–196 (1999).
[Crossref]

Russell, L.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Russell, P. B.

Sawamura, P.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

Schmid, B.

Schroder, J.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Schulien, J. A.

Seinfeld, J.

J. Seinfeld and S. Pandis, Atmospheric Chemistry and Physics: from Air Pollution to Climate Change (Wiley, 2006).

Shettle, E. P.

Z. Ahmad, B. A. Franz, C. R. McClain, E. J. Kwiatkowska, J. Werdell, E. P. Shettle, and B. N. Holben, “New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving radiances from the SeaWiFS and MODIS sensors over coastal regions and open oceans,” Appl. Opt. 49, 5545–5560 (2010).
[Crossref]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[Crossref]

Shimada, R.

Shinozuka, Y.

K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

Sinyuk, A.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Slater, D. W.

Smith, R. C.

Stamnes, J. J.

K. Stamnes, G. E. Thomas, and J. J. Stamnes, Radiative Transfer in the Atmosphere and Ocean, 2nd ed. (Cambridge University, 2017).

Stamnes, K.

Stap, F.

F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016).
[Crossref]

Stephens, G. L.

M. D. Lebsock, T. S. L’Ecuyer, and G. L. Stephens, “Information content of near-infrared spaceborne multiangular polarization measurements for aerosol retrievals,” J. Geophys. Res. Atmos. 112, D14206 (2007).
[Crossref]

Stramski, D.

Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
[Crossref]

Tanikawa, T.

Tanré, D.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Thomas, G. E.

K. Stamnes, G. E. Thomas, and J. J. Stamnes, Radiative Transfer in the Atmosphere and Ocean, 2nd ed. (Cambridge University, 2017).

Travis, L.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
[Crossref]

Travis, L. D.

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).
[Crossref]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
[Crossref]

B. Cairns, E. E. Russell, and L. D. Travis, “Research scanning polarimeter: calibration and ground-based measurements,” Proc. SPIE 3754, 186–196 (1999).
[Crossref]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. Atmos. 102, 16831–16847 (1997).
[Crossref]

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Trepte, C. R.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Twardowski, M.

Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
[Crossref]

Twardowski, M. S.

Van de Hulst, H. C.

H. C. Van de Hulst, A New Look at Multiple Scattering (NASA Institute for Space Studies, Goddard Space Flight Center, 1963).

Van Diedenhoven, B.

L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

Várnai, T.

T. Várnai and A. Marshak, “Analysis of co-located MODIS and CALIPSO observations near clouds,” Atmos. Meas. Tech. 5, 389–396 (2012).
[Crossref]

Vaughan, M.

S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
[Crossref]

Waquet, F.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
[Crossref]

Wasilewski, A. P.

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

Welch, W.

Werdell, J.

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. Atmos. 102, 16831–16847 (1997).
[Crossref]

Wiscombe, W. J.

Wu, L.

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
[Crossref]

Wu, W.

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
[Crossref]

Yang, Q.

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
[Crossref]

Ying, R.

B. Cairns, B. E. Carlson, R. Ying, A. A. Lacis, and V. Oinas, “Atmospheric correction and its application to an analysis of hyperion data,” IEEE Trans. Geosci. Remote Sens. 41, 1232–1244 (2003).
[Crossref]

Yorks, J. E.

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
[Crossref]

Zhang, X.

Zhao, R.

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

Zhou, D. K.

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
[Crossref]

Ziemba, L. D.

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

Appl. Opt. (8)

J. Hair, C. Hostetler, A. Cook, D. Harper, R. Ferrare, T. Mack, W. Welch, L. Izquierdo, and F. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
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J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45, 5542–5567 (2006).
[Crossref]

B. Schmid, J. J. Michalsky, D. W. Slater, J. C. Barnard, R. N. Halthore, J. C. Liljegren, B. N. Holben, T. F. Eck, J. M. Livingston, and P. B. Russell, “Comparison of columnar water-vapor measurements from solar transmittance methods,” Appl. Opt. 40, 1886–1896 (2001).
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W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
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H. Du, “Mie-scattering calculation,” Appl. Opt. 43, 1951–1956 (2004).
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Z. Ahmad, B. A. Franz, C. R. McClain, E. J. Kwiatkowska, J. Werdell, E. P. Shettle, and B. N. Holben, “New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving radiances from the SeaWiFS and MODIS sensors over coastal regions and open oceans,” Appl. Opt. 49, 5545–5560 (2010).
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R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
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R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
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Astron. Astrophys. (2)

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J. De Haan, P. Bosma, and J. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

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K. Knobelspiesse, B. Cairns, M. Ottaviani, R. Ferrare, J. Hair, C. Hostetler, M. Obland, R. Rogers, J. Redemann, and Y. Shinozuka, “Combined retrievals of boreal forest fire aerosol properties with a polarimeter and lidar,” Atmos. Chem. Phys. 11, 7045–7067 (2011).
[Crossref]

P. Sawamura, R. H. Moore, S. P. Burton, E. Chemyakin, D. Müller, A. Kolgotin, R. A. Ferrare, C. A. Hostetler, L. D. Ziemba, and A. J. Beyersdorf, “HSRL-2 aerosol optical measurements and microphysical retrievals vs. airborne in situ measurements during discover-aq 2013: an intercomparison study,” Atmos. Chem. Phys. 17, 7229–7243 (2017).
[Crossref]

Atmos. Meas. Tech. (6)

T. Várnai and A. Marshak, “Analysis of co-located MODIS and CALIPSO observations near clouds,” Atmos. Meas. Tech. 5, 389–396 (2012).
[Crossref]

O. Hasekamp, “Capability of multi-viewing-angle photo-polarimetric measurements for the simultaneous retrieval of aerosol and cloud properties,” Atmos. Meas. Tech. 3, 1229–1262 (2010).
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D. Müller, C. A. Hostetler, R. Ferrare, S. Burton, E. Chemyakin, A. Kolgotin, J. Hair, A. Cook, D. Harper, and R. Rogers, “Airborne multiwavelength high spectral resolution lidar (hsrl-2) observations during tcap 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the us,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

S. Burton, M. Vaughan, R. Ferrare, and C. Hostetler, “Separating mixtures of aerosol types in airborne high spectral resolution lidar data,” Atmos. Meas. Tech. 7, 419–436 (2014).
[Crossref]

L. Wu, O. Hasekamp, B. Van Diedenhoven, and B. Cairns, “Aerosol retrieval from multiangle multispectral photopolarimetric measurements: importance of spectral range and angular resolution,” Atmos. Meas. Tech. 8, 2625–2638 (2015).
[Crossref]

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4, 975–1018 (2011).
[Crossref]

Biogeosciences (1)

Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern south Pacific Ocean,” Biogeosciences 4, 4571–4604 (2007).
[Crossref]

Geophys. Res. Lett. (2)

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

L. Wu, O. Hasekamp, B. Diedenhoven, B. Cairns, J. E. Yorks, and J. Chowdhary, “Passive remote sensing of aerosol layer height using near-uv multiangle polarization measurements,” Geophys. Res. Lett. 43, 8783–8790 (2016).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (2)

B. Cairns, B. E. Carlson, R. Ying, A. A. Lacis, and V. Oinas, “Atmospheric correction and its application to an analysis of hyperion data,” IEEE Trans. Geosci. Remote Sens. 41, 1232–1244 (2003).
[Crossref]

W. Wu, X. Liu, D. K. Zhou, A. M. Larar, Q. Yang, S. H. Kizer, and Q. Liu, “The application of PCRTM physical retrieval methodology for IASI cloudy scene analysis,” IEEE Trans. Geosci. Remote Sens. 55, 5042–5056 (2017).
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F. Stap, O. Hasekamp, C. Emde, and T. Röckmann, “Multiangle photopolarimetric aerosol retrievals in the vicinity of clouds: synthetic study based on a large eddy simulation,” J. Geophys Res. Atmos. 121, 12914–12935 (2016).
[Crossref]

J. Geophys. Res (1)

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res 114, D01206 (2009).
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J. Michalsky, J. Liljegren, and L. Harrison, “A comparison of sun photometer derivations of total column water vapor and ozone to standard measures of same at the southern great plains atmospheric radiation measurement site,” J. Geophys. Res. 100, 25995–26003 (1995).
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J. Geophys. Res. Atmos. (6)

M. D. Lebsock, T. S. L’Ecuyer, and G. L. Stephens, “Information content of near-infrared spaceborne multiangular polarization measurements for aerosol retrievals,” J. Geophys. Res. Atmos. 112, D14206 (2007).
[Crossref]

L. K. Berg, J. D. Fast, J. C. Barnard, S. P. Burton, B. Cairns, D. Chand, J. M. Comstock, S. Dunagan, R. A. Ferrare, and C. J. Flynn, “The two-column aerosol project: phase i-overview and impact of elevated aerosol layers on aerosol optical depth,” J. Geophys. Res. Atmos. 121, 336–350 (2016).
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O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from parasol multiangle photopolarimetric measurements,” J. Geophys. Res. Atmos. 116, D14204 (2011).

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M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. Atmos. 102, 16831–16847 (1997).
[Crossref]

R. Modini, A. Frossard, L. Ahlm, L. Russell, C. Corrigan, G. Roberts, L. Hawkins, J. Schroder, A. Bertram, and R. Zhao, “Primary marine aerosol-cloud interactions off the coast of California,” J. Geophys. Res. Atmos. 120, 4282–4303 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (2)

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11, 809–812 (1971).
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M. D. Alexandrov, B. Cairns, and M. I. Mishchenko, “Rainbow fourier transform,” J. Quant. Spectrosc. Radiat. Transfer 113, 2521–2535 (2012).
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J. Quantum Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, “Monitoring of aerosol forcing of climate from space: analysis of measurement requirements,” J. Quantum Spectrosc. Radiat. Transfer 88, 149–161 (2004).
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Opt. Express (3)

Proc. SPIE (1)

B. Cairns, E. E. Russell, and L. D. Travis, “Research scanning polarimeter: calibration and ground-based measurements,” Proc. SPIE 3754, 186–196 (1999).
[Crossref]

Remote Sens. Environ. (3)

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, C. Emde, A. S. Ackerman, and B. van Diedenhoven, “Accuracy assessments of cloud droplet size retrievals from polarized reflectance measurements by the research scanning polarimeter,” Remote Sens. Environ. 125, 92–111 (2012).
[Crossref]

M. D. Alexandrov, B. Cairns, A. P. Wasilewski, A. S. Ackerman, M. J. McGill, J. E. Yorks, D. L. Hlavka, S. E. Platnick, G. T. Arnold, and B. Van Diedenhoven, “Liquid water cloud properties during the polarimeter definition experiment (podex),” Remote Sens. Environ. 169, 20–36 (2015).
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J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
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C. Hostetler, J. Hair, R. Ferrare, S. Burton, and S. Stamnes, “NASA Langley Airborne HSRL microphysics website,” 2017, https://science.larc.nasa.gov/hsrl/ .

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B. Cairns, M. L. Alexandrov, and B. Carlson, “Inversion of multi-angle radiation measurement,” Technical report (Columbia University; NASA Goddard Institute for Space Studies, 2005).

C. Rodgers, Inverse Methods for Atmospheric Sounding (World Scientific, 2000).

H. C. Van de Hulst, A New Look at Multiple Scattering (NASA Institute for Space Studies, Goddard Space Flight Center, 1963).

M. Mishchenko, “Lorenz-Mie code,” 2010, http://www.giss.nasa.gov/staff/mmishchenko/ .

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Figures (11)

Fig. 1.
Fig. 1. Simulated retrievals using 10-parameter state space. The two lines surrounding the 1-to-1 line represent ± 3 σ , or three standard deviations. The red line represents the least-squares bisector. The units are micrometers (μm) for effective radius, meters per second (m/s) for wind speed, and milligrams per meter cubed ( mg / m 3 ) for chlorophyll concentration: the optical depth, effective variance, real refractive index, and single-scattering albedo are unitless. The ranges for the retrieval parameters used in this simulated study are slightly different than the finalized ranges defined by Eq. (2) for real data, but illustrate that the algorithm can successfully retrieve the 8 aerosol and wind speed parameters in 87% of the cases, and chlorophyll concentration in 67% of the cases, using simulated data where all 10 parameters are randomized.
Fig. 2.
Fig. 2. Overview of the NASA 2014 SABOR campaign. The ship track is highlighted in blue, and the flight tracks are highlighted in magenta. The 31 July 2014 flight track is highlighted in green, together with the superimposed MODIS Aqua true color reflectance.
Fig. 3.
Fig. 3. SABOR 31 July 2014 flight. (a) HSRL-1 atmosphere backscattering coefficient and ocean diffuse attenuation coefficient. (b) HSRL-1 aerosol typing algorithm, where we can see that the aerosol structure for this day is complex with multiple layers and a lofted smoke plume. (c) The atmosphere/ocean results from RSP MAPP and HSRL for this entire day. The following masks are also displayed, where the color indicates the presence of: clouds-above-aircraft (cyan), aircraft not at cruising altitude (magenta), aircraft turns/course corrections (yellow), and clouds below the aircraft (blue).
Fig. 4.
Fig. 4. RSP MAPP ocean retrievals and HSRL-1 ocean products plotted as K d versus b bp . The RSP C2012 ocean bio-optical model retrieval result is super-imposed against the HSRL-1 measurements HSRL-1 column-averaged K d and b bp . Only scenes for deeper waters, defined as having an ocean bottom greater than 30 m, are included.
Fig. 5.
Fig. 5. RSP MAPP aerosol retrievals versus HSRL-1 aerosol products for a time-series of retrievals between 14 UTC and 17 UTC on 31 July 2014. From top: aerosol (a) optical depth, (b) single-scattering albedo at 555 nm, (c), (b) effective radius, (d) real part of the refractive index at 555 nm. The first set of results (v1.21) employed the one-parameter Chowdhary ocean model from 0 to 3 mg / m 3 chlorophyll concentration, while the second set of results (v1.22) employed the extended range from 0 to 10 mg / m 3 .
Fig. 6.
Fig. 6. Overview of the Department of Energy 2012 TCAP campaign. The flight tracks are highlighted in magenta. The 17 July 2012 flight track is highlighted in green, together with the superimposed MODIS Aqua true color reflectance.
Fig. 7.
Fig. 7. TCAP 17 July 2012. (a) HSRL direct measurement of extinction km 1 at 532 nm. (b) HSRL-1 aerosol typing product. (c) Atmosphere retrieval results from the RSP instrument for this entire day. RSP MAPP 532 nm aerosol optical depth and aerosol microphysics retrievals versus HSRL-2 532 nm aerosol optical depth (direct measurement) and HSRL-2 aerosol microphysics products for a time-series of retrievals between 14.5 UTC and 17.5 UTC on 17 July 2012. Aerosol products: (i) optical depth, (ii) single-scattering albedo, (iii) effective radius, (iv) real part of the refractive index. The following masks are also displayed, where the color indicates the presence of: clouds-above-aircraft (cyan), aircraft not at cruising altitude (magenta), aircraft turns/course corrections (yellow), and clouds below the aircraft (blue).
Fig. 8.
Fig. 8. TCAP 17 July 2012: RSP MAPP retrieved lidar intensive/extensive parameters versus HSRL-2 extinction-weighted lidar intensive/extensive parameters from top: optical depth for reference; S a , aerosol lidar ratio [sr] (intensive parameter); Ångstrøm exponent.
Fig. 9.
Fig. 9. SABOR campaign RSP MAPP and HSRL-1 optical depth correlations at 532 nm using HSRL AOD product after a clouds-above-aircraft mask was applied. Each color represents a different day between 18 July to 4 August 2014. The one-to-one line is colored in black, and the dashed black lines represent the desired ± 1 σ accuracy. The red line represents the least-squares bisector.
Fig. 10.
Fig. 10. TCAP campaign RSP MAPP and HSRL-2 optical depth correlations using HSRL AOD product at 532 nm and 355 nm. For TCAP there was no instrument that could detect clouds above the aircraft onboard the aircraft during TCAP, and there was limited reporting of above aircraft clouds, which made clouds-above-aircraft screening difficult. Each color represents a different day in July 2012.
Fig. 11.
Fig. 11. SABOR campaign RSP MAPP and HSRL-1 ocean product correlations of (a)  K d [ m 1 ] and (b)  b bp [ m 1 ] , both at 532 nm, for all AAO (Aerosol-Above-Ocean) scenes with an ocean bottom greater than 30 m. Each color represents a different day between 18 July to 4 August 2014. The one-to-one line is colored in black, and the dashed black lines represent the desired ± 1 σ accuracy. The red line represents the least-squares bisector.

Tables (2)

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Table 1. Aerosol Fine/Coarse Mode Ranges (Low, High) a

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Table 2. Aerosol Uncertainty Targets for One Standard Deviation ( 1 σ ) a

Equations (62)

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x = τ 555 f r n f σ g f n r f n i f τ 555 c r n c σ g c n r c n i c v CHL z c z f ,
10 5 τ 555 f 0.6 0.075 r n f 0.15 μm 1.36 n r f 1.65 10 5 n i f 0.03 10 5 τ 555 c 0.4 0.5 r n c 1.5 μm 0.3 σ g f 0.7 0.3 σ g c 0.7 0.01 v 7.0 m / s 0.001 CHL 10 mg / m 3 .
w col = 1 1 | μ g | + 1 | μ 0 | [ ln I 864 ( μ g ) I 960 ( μ g ) α ] 1 / β ,
f = d s 2 μ 0 1 T ,
v ( r ) = 1 r d V ( r ) d ln r = 1 r i = 1 2 V i 2 π σ g i exp [ ( ln r ln r v i 2 σ g i ) 2 ] ,
n ( r ) = 1 r d N ( r ) d ln r = 1 r i = 1 2 N i 2 π σ g i exp [ ( ln r ln r n i 2 σ g i ) 2 ] ,
N i = V i 4 3 π r n i 3 exp ( 4.5 σ g i 2 ) ,
r n i = r v i exp ( 3 σ g i 2 ) .
r eff = r min r max r 3 n ( r ) d r r min r max r 2 n ( r ) d r lognormal r n exp ( 2.5 σ g 2 ) ,
v eff = r min r max ( r r eff ) 2 π r 2 n ( r ) d r r eff 2 r min r max π r 2 n ( r ) d r lognormal exp ( σ g 2 ) 1 ,
χ 2 ( x ) = ϕ ( x ) = ϕ ( x ) data + ϕ ( x ) prior = 1 2 ( f y ) T S ε 1 ( f y ) + 1 2 ( x x a ) T S a 1 ( x x a ) .
χ = 1 m ϕ ( x ) data = 1 m 1 2 ( f y ) T S ε 1 ( f y ) .
x 1 = x 1 / 5 .
b = log x 1 x 1 low x 1 high x 1 .
x 1 = x 1 high 1 + e b + x 1 low 1 + e b .
K b = d f d b = d x d b d f d x = d x d b K = d x d x 1 d x 1 d b K .
χ s 2 = 1 2 ( f y ) T S ε 1 ( f y ) + 1 2 ( b b a ) T S 1 a 1 ( b b a ) ,
b i + 1 = b a + S i [ ( f y ) + K b ( b i b a ) ] ,
x a = ( x low + x high ) / 2 x i .
S a = diag ( σ a σ a ) ,
S ^ 1 ( x ^ ) = K ( x ^ ) T S ε 1 K ( x ^ ) + S a 1 .
Total Radiance = μ 0 F 0 π d s 2 R I , Q , U [ W / m 2 / sr ] ,
RSP L 1 B Normalized Radiance = μ 0 d s 2 R I , Q , U [ 1 / sr ] .
R I , Q , U = d s 2 μ 0 ( RSP L 1 B Normalized Radiance ) [ 1 / sr ] .
P TS ( r ) = Ψ C TS r 2 [ β m ( r ) + β a ( r ) ] e 2 0 r [ α m ( r ) + α a ( r ) ] d r ,
P m , 532 ( r ) = F Ψ C m , 532 r 2 β m ( r ) e 2 0 r [ α m ( r ) + α a ( r ) ] d r .
HSRL AOD = τ HSRL = 1 2 ln T ( r 2 ) T ( r 1 ) = 1 2 ln r 2 2 P m , 532 ( r 2 ) β m ( r 1 ) r 1 2 P m , 532 ( r 1 ) β m ( r 2 ) .
S a = i = 0 N α i i = 0 N β i [ sr ] ,
0 h t α d z = 0.95 0 h α d z or 0 h t β d z = 0.95 0 h β d z .
β = β f + β c , β f c = τ f c h t ω f c p 180 ; f c 4 π ,
α = α f + α c , α f c = τ f c / h t ,
S a = α f + α c β f + β c ,
K d ( z ) = K beam ( z ) cos θ lidar , ocn = 1 2 d ln [ P m , 532 ( r ) r 2 ] d z [ m 1 ] ,
β p ( z ) = β w [ P a , 532 ( z ) + P a , 532 ( z ) P m , 532 ( z ) + P m , 532 ( z ) ] [ m 1 sr 1 ] ,
q p 2 π = π / 2 π F p ( Θ ) 4 π sin Θ d Θ χ p , 180 F p ( Θ = 180 ° ) [ unitless ] ,
b bp ( z ) = b p q p = b p 2 π [ χ p , 180 F p ( Θ = 180 ° ) ] = π ( 1 sr ) · β p ( z ) [ m 1 ]
K d = 1 h z = 6 z = 17 K d d z and b bp = 1 h z = 6 z = 17 b bp d z [ m 1 ] ,
Q 1 = R a * R b * ,
Q n = Q 1 Q n 1 ,
S = n = 1 Q n ,
U = R b e τ a / μ 0 + R b D ,
D = T a + S e τ a / μ 0 + ST a ,
R ( τ a + τ b ) = R a + e τ a / μ U + T a * U ,
T ( τ a + τ b ) = e τ b / μ D + T b e τ a / μ 0 + T b D .
b = b sw ( λ ) + b p ( λ , CHL ) [ m 1 ] ,
b p ( λ , CHL ) = 0.347 [ CHL ] 0.766 ( λ 660 ) k [ m 1 ] ,
k = { 1 0 CHL < 0.02 , 0.5 ( log 10 [ CHL ] 0.3 ) 0.02 CHL 2 , 0 CHL > 2 .
b bp ( λ , CHL ) = b p ( λ , CHL ) q p ( CHL ) ,
q p 2 π π / 2 π F p ( Θ ) 4 π sin Θ d Θ [ unitless ] .
q p ( CHL ) ( 0.007 0.0025 log 10 [ CHL ] ) ) [ unitless ] .
b bp ( λ , CHL ) = b p ( λ , CHL ) ( 0.007 0.0025 log 10 [ CHL ] ) ) [ m 1 ] ,
b b ( λ , CHL ) = b b , sw + b bp = 0.5 b sw ( λ ) + b bp ( λ , CHL ) [ m 1 ] .
ω p ( λ , CHL ) = b p ( λ , CHL ) a p ( λ , CHL ) + b p ( λ , CHL ) .
f p ( Θ ) = ( 1 f det ) σ plk f plk ( Θ ) + f det σ det f det ( Θ ) ( 1 f det ) σ plk + f det σ det ,
q p = ( 1 f det ) σ plk q plk + f det σ det q det ( 1 f det ) σ plk + f det σ det .
f det ( CHL ) = 0.61 0.099 χ CHL 0.009 χ CHL 2 ,
K d = d d z [ ln F ν ( z ) ] = 1 F ν d F ν ( z ) d z ,
K d ( λ , CHL ) K w ( λ ) + K bio ( λ , CHL ) [ a w ( λ ) + 0.5 b w ( λ ) ] + χ ( λ ) [ CHL ] e ( λ ) ,
a ocn ( λ , CHL ) = K d ( λ , CHL ) [ 1 α ( λ , CHL , θ 0 ) b b ( λ , CHL ) a ocn ] × μ d ( λ , CHL , θ 0 ) μ u μ d ( λ , CHL , θ 0 ) α ( λ , CHL , θ 0 ) b b ( λ , CHL ) a ocn + μ u [ m 1 ] ,
a ocn ( λ , CHL ) = 1 2 μ d ( K d α b b ) ± 1 2 μ d 2 ( K d α b b μ u ) 2 4 K d α b b .
a p ( λ , CHL ) = a ocn ( λ , CHL ) a w ( λ ) .
C I = σ R I 2 = ( 2 σ floor μ 0 ) 2 + ( a μ 0 R I ) 2 + ( R Q 2 σ ln K 1 ) 2 + ( R I σ ln α c ) 2 . C Q = σ R Q 2 = ( σ floor 2 μ 0 ) 2 + ( a R I μ 0 ) 2 + ( 1 2 R I σ ln K 1 ) 2 + ( R Q σ ln α c ) 2 + ( R Q σ ln α 1 ) 2 . C U = σ R U 2 = ( σ floor 2 μ 0 ) 2 + ( a R I 2 μ 0 ) 2 ( 1 2 R I 2 σ ln K 1 ) 2 + ( R U σ ln α c ) 2 + ( R U σ ln α 1 ) 2 . C I L = σ R I L 2 = C I 4 + C Q 4 + ( R I + R Q 2 σ ln α c ) 2 + ( R I + R Q 4 σ ln K 1 ) 2 + ( R Q 2 σ ln α 1 ) 2 . C I R = σ R I R 2 = C I 4 + C Q 4 + ( R I R Q 2 σ ln α c ) 2 + ( R I R Q 4 σ ln K 1 ) 2 + ( R Q 2 σ ln α 1 ) 2 . C DoLP = σ DoLP 2 = ( 2 σ floo r μ 0 R I 2 + DoLP 2 ) 2 + ( a μ 0 R I 2 DoLP 2 ) 2 + ( 1 2 σ ln K 1 1 DoLP 2 ) 2 + ( σ ln α 1 DoLP ) 2 + ( 1 2 σ ln K 1 R Q 4 + R U 4 R I 2 ) 2 .

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