Radiative transfer calculations were performed using software built to use the method of . AFRT treats the model atmosphere as consisting of plane-parallel layers, which are homogeneous horizontally but inhomogeneous vertically. It rests on an optically smooth ocean surface or a rough ocean surface where the slope orientation of the capillary waves follows Cox and Munk's probability distribution . In addition, the model atmosphere is non-emitting and consists of standard gas, aerosols, and absorbing gases like ozone (although in this implementation we do not test sensitivity to such gases). It accounts for all orders of scattering in the atmosphere and outputs the four Stokes parameters of the diffused radiation, leaving the top and bottom of the atmosphere. Also, it accounts for Fresnel reflection from the ocean surface but neglects the scattering and absorption in the ocean itself. In benchmark studies against other radiative transfer calculations (), the relative accuracy of AFRT for a Rayleigh-scattering-only atmosphere is 0.15 %.

AFRT is used to generate atmospheric correction LUTs in operational use by the NASA Ocean Biology Processing Group (OBPG) for processing of data from instruments such as the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), MODIS, the Visible and Infrared Imager/Radiometer Suite (VIIRS), and others (see , for a detailed tutorial). As mentioned previously, contributions from the ocean body beneath the air–water interface are not included, but this is a reasonable approximation for the open ocean at the NIR channel for which we are performing our retrieval (865 nm) (e.g., ).

Aerosols are modeled in AFRT as described in , by treating them as bi-modal combinations of fine- and coarse-sized particles. The coarse size mode is optically spherical and minimally absorbing (consistent with sea salt), while the size and real refractive index of both modes are defined by water uptake associated with eight relative humidity values between 30 % and 95 %. While this relative humidity may or may not be the same as ambient scene relative humidity, it is a convenient means to represent most of the range of microphysical properties encountered over the ocean. The exception is non-spherical dust aerosols (), which are encountered at some locations over the ocean). These eight fine-mode aerosols are combined with the coarse mode at 10 different fractions for a total of 80 aerosol models. These fractions are expressed as the relative volume concentration of the fine mode to the total particle volume concentration, with values of 0 %, 1 %, 2 %, 5 %, 10 %, 20 %, 30 %, 50 %, 80 %, or 95 %. Table  lists the optical properties of these aerosol models.

In AFRT, the ocean roughness is characterized by wind speed, which in turn is related to the Cox and Munk slope probability distribution of the capillary waves on ocean surface (). Not included in the computations are shadowing, and the multiple reflection effects between wave facets. It should be noted that the reflections of both the direct and diffused radiation at the base of the atmosphere (that is, Fresnel reflection properly weighted by the Cox–Munk slope probability distribution) are properly accounted for.

AFRT was used to calculate top-of-atmosphere (TOA) radiance at a variety of solar and observation geometries, at a density sufficient such that interpolation to a specific scene geometry has minimal error. Each combination of view zenith angle, θv (the observation vector's angle from nadir), solar zenith angle, θs (the solar illumination vector's angle from nadir), and relative azimuth angle, ϕ (the solar minus observation azimuth angles) is simulated. This means that there are 7744 (22 × 22 × 16; see Table ) observations simulated for each geophysical state. For analysis, these geometries are interpolated to provide a simulated observation for a specified MISR geometry (see Sect.  for a description). Also, note that in our implementation of AFRT azimuthal symmetry was preserved, so simulations from ϕ=0∘ to ϕ=180∘ mirror those from ϕ=360∘ to ϕ=180∘.

AFRT simulations were varied across four dimensions of parameter space. These dimensions, and the values over which the simulations were performed, are described in Table . A total of 1008 (6 × 8 × 7 × 3, table edge values omitted) geophysical states were simulated for each of the geometries.

Relative humidity (r), as described above, modifies the size distribution and complex refractive index of the aerosols to parameterize water update as described in Table . Aerosols are treated as bimodal, lognormal distributions of fine- and coarse-size aerosols, represented in volume space as 1dV(R)dln⁡R=Vf2πσfexp⁡-ln⁡R-ln⁡Rf2σf2+Vc2πσcexp⁡-ln⁡R-ln⁡Rc2σc2, where V is volume, R particle radius, Vf and Vc the volumes of the fine- and coarse-size-mode particles, Rf and Rc their geometric mean radius (in micrometers), and σf and σc their geometric standard deviation. Thus, the fine-size-mode fraction parameter is f=VfVf+Vc. Aerosol optical depth (τ) is defined at 865 nm, while the wind speed parameterizes the distribution of specular reflection from the sun by the ocean's surface, as described above.

Other geophysical parameters were held constant for all simulations, implying expectations of minimal impact on parameterization capability. These included trace gas absorption (for which we are minimally sensitive in the MISR NIR channel and can be accounted for in operational processing), total atmospheric pressure (which can also be accounted for in operational processing), and the ocean body contribution as mentioned previously. Surface reflectance contribution due to sea foam was not included in our simulations, but a subsequent analysis found that its inclusion in select cases had a negligible impact on our results.

There is a rich literature describing MISR's technical characteristics (e.g., ) and retrieval algorithms (e.g., ), so our description is limited to brief details relevant to this study.

The NASA Terra spacecraft, for which MISR is one of the instruments, is in an orbit with an altitude of 705 km and inclination angle of 98.2∘, and the ground track repeats every 16 d. It has nine push-broom cameras that are oriented along the satellite track direction, with nominal angles with respect to the Earth surface of 0, ±26.1, ±45.6, ±60.0, and ±70.5∘. In the terminology of MISR data users, cameras are denoted [Df, Cf, Bf, Af, An, Aa, Ba, Ca, Da] in order from the most forward camera to the most aft; roughly 7 min pass from the first image of a ground location to the last. Each camera has four spectral channels, with center wavelengths at 446.6 nm (blue), 557.5 nm (green), 671.7 nm (red), and 866.4 nm (NIR; note we approximate this channel at 865 nm). Although there is some variation in camera and channel swath width and inherent spatial resolution, the common resolution to which MISR data are typically analyzed is 1.1 km. In this paper, we assume all camera observations have the same spatial resolution and that systematic uncertainties such as out-of-band instrument response () have been corrected.

As mentioned previously, we assess the retrieval capability utilizing only the NIR channel. By doing so, we reduce the dimensionality of our parameter retrieval space by making the assumption that the water body does not contribute to the observations. This assumption has a long history in the ocean color remote sensing community (e.g., ) and is appropriate for most of the open ocean. It is also assumed to be the case for both the red and NIR channels in the most recent operational MISR aerosol retrieval algorithm, V23 (). Treatment of turbid or coastal water bodies would require a more extensive parameter space that we will not address in this work.

By using all NIR multi-angle observations, including those made at geometries with reflected sun glint, we can retrieve a somewhat unique set of parameters: those describing the nature of that sun glint and the atmospheric aerosols above it. The ultimate goal is to aid the atmospheric correction for ocean color observations for the other instrument on Terra, MODIS. Standard atmospheric correction for that instrument has access to single-view observations at two NIR channels and also utilizes the dark ocean assumption. While future missions may make use of a greater number of channels (), this means that only two pieces of information are used to select an aerosol type (model) and magnitude (τ). With the MISR NIR multi-angle observations, however, we have nine pieces of information from which to identify the aerosol magnitude (τ), two parameters defining aerosol type (r and f), and a measure for the distribution of reflected sun glint (w). How well we expect to retrieve these parameters, given measurement and model uncertainty, is the goal of this work.

Retrievals of aerosol properties with multi-angle instruments such as MISR are sensitive to the specific observation geometry (e.g., ), which varies with location, orbit, and season. In order to span the range of potential geometries, we selected seven scenes from the MISR archive. Specifically, we used the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) (https://seabass.gsfc.nasa.gov/, last access: 30 April 2021, ) to identify cloud-free coincident observations by MISR and ground instruments from AERONET-OC (). AERONET-OC is a network of ground-based instruments that are often mounted on platforms at sea and measure both aerosol properties and ocean reflectance. In a future work, we will compare MISR retrievals from the algorithm we develop to the optical properties observed by AERONET-OC and consider the differences between them in the context of this ICA.

Table  contains the details about the seven geometries we use for this study, while Fig.  is a polar plot of the corresponding MISR observation geometries. The seven cases were chosen to span the range of measurement geometries and include two at “high” θs (70∘), two at “medium” θs (45∘), and two at “low” θs (30∘). We also included a less common extremely low θs (20∘) for which the glint was centered about the An (nadir) viewing direction. Among these geometries, the high-θs scenes are minimally impacted by glint, while its influence progressively increases for lower θs. These locations are used to provide realistic geometries for observation only; information content is assessed for each of 1008 combinations of parameter values from Table  (see Sect.  for more details).

There are multiple techniques for assessing information content in a remote sensing retrieval. Inherent to all techniques is the need to connect measurement space to geophysical parameter (often denoted state) space, in a manner that incorporates measurement and model characteristics plus a priori knowledge. While such efforts can not incorporate “unknown unknowns”, they provide a useful ceiling for potential retrieval success and a means to compare different measurement and retrieval systems.

The aerosol remote sensing community has often utilized a technique popularized by , which projects model and measurement uncertainty from the measurement to parameter spaces. This technique is fast and convenient, as it uses Jacobian matrices (K) calculated as the partial derivatives of the simulated signal in the vicinity of the retrieved parameters. This is performed using a radiative transfer forward model (F), which represents geophysical reality by calculating a simulated observation (y) for a given set of parameters (m), i.e., y=F(m) and Ki,j=∂Fi∂mj (where i and j are indices for the measurement and parameter vectors, respectively). Like all information content assessments, it relies on the suitability of the forward model and uncertainty estimate fidelity. Because of its speed and flexibility, it has become a common tool in the multi-angle aerosol remote sensing to identify optimal instrument characteristics (e.g., ). Furthermore, since Jacobians are often used in optimal estimation or similar iterative retrieval algorithms, this technique can also reuse the Jacobians of the final iterative step to provide an estimate of parameter retrieval uncertainty (e.g., ). It has also been shown to produce similar results to other assessment techniques, such as in .

However, the technique does make several assumptions that may influence the analysis. The use of Jacobians implies that the forward model connecting parameter to measurement space is locally continuous. Furthermore, PDFs are assumed to be Gaussian, as uncertainty is characterized by a simple distribution width metric (although an advantage of that technique is the simplicity with which it accounts for uncertainty correlation for multiple measurements). For information-rich, well-posed problems, this is most likely not an issue, as measurement uncertainties are well characterized by Gaussian distributions and because a posteriori PDFs are usually sufficiently compact that the local linearity assumed in the use of Jacobians is preserved. Additionally, computational efficiency is important in the case of large measurement and parameter space dimensionality. For example, in the assessment of the Aerosol Polarimetry Sensor (APS) in , the measurement vector had 3570 elements for the retrieval of 12 parameters. This contrasts with the current study, which has a measurement vector with nine elements for the retrieval of four parameters.

The smaller dimensionality of this retrieval allows us to explore other techniques that do not make the same approximations as . The GENRA technique () is attractive because it does not make the same assumptions of forward model linearity and the Gaussian nature of uncertainty. Developed for the assessment of cloud remote sensing (), GENRA is similar to Bayesian inference in its treatment of all components of the retrieval system as stochastic with associated PDFs. The result is a posterior which represents the best understanding of the expected parameter PDF for a synthetic measurement. The technique is computationally inexpensive and can utilize pre-computed LUTs to represent the forward model (the primary expense is the typical need to interpolate these LUTs to a finer grid). Metrics for the reduction in entropy from the prior to posterior PDF, such as the Shannon information content (), can be used to characterize the overall quality of a retrieval, while marginal PDFs (the posterior PDF integrated to one parameter dimension) indicate the capability for an individual parameter.

GENRA can be represented by a single, perhaps deceptively simple, equation: 2po(m)=pr(m)γ∑ypd(y)pl(F(m)|m), where po(m) is a multi-dimensional a posteriori PDF for the m parameter vector (bold-italic indicates vector), pr(m) is the a priori PDF, pd(y) is the stochastic measurement distribution (d for data), and pl(y) is the same for the likelihood function. Instead of an integration over measurement space (y), we use a summation, as we represent all PDFs as discrete functions. γ is a normalization factor such that 3γ=∑mpo(m), which ensures the summation of the posterior PDF is 1. The result is a multidimensional a posteriori PDF that incorporates all known information. In the context of GENRA the “data” (pd) are a PDF created from a single node in the LUT and expectations of measurement and model uncertainty, while the likelihood (pl) is created from the entire LUT, which is used as a forward model (y=F(m)). In our implementation, the a priori PDF (pr(m)) is a weakly informative prior defined as uniform within the boundaries of the LUT and zero outsize those boundaries.

A full assessment of retrieval space involves the calculation of the a posteriori PDF for each LUT node. The result will have n+n dimensions, where n is the number of dimensions in m. In our case, this is a rather unwieldy eight dimensions. Marginal PDFs (pm) ease this analysis by calculating the summation of po(m) over each retrieval parameter: 4pmr(r′,r,f,τ,w)=∑f∑τ∑wpo(m),5pmf(f′,r,f,τ,w)=∑r∑τ∑wpo(m),6pmτ(τ′,r,f,τ,w)=∑r∑f∑wpo(m),7pmw(w′,r,f,τ,w)=∑r∑f∑τpo(m), where we have now reduced the total number of dimensions to five, meaning a marginal PDF (with the associated dimension indicated by ′) for each parameter in each node of the LUT.

A useful metric to indicate the overall success of a measurement is the Shannon information content, SIC (). Derived from the concepts of entropy, SIC indicates the reduction in the volume of possible solutions in po(m) from the original pr(m) and is calculated 8Sposterior=-∑Lpo(m)log⁡2po(m),9Sprior=-∑Lpr(m)log⁡2pr(m),10SIC=Sprior-Sposterior,11SICH=Sprior-Sposterior/Sprior. Here, S represents entropy and we have performed summations of discrete PDFs. Like in and , we choose to use a base 2 logarithm so that the entropy values are represented in bits. SIC is the change in that entropy between prior and posterior. It is bounded by zero, which indicates no information in a measurement, and an upper value which is log⁡2(k), where k is the number of bins in the discrete PDF. SIC can be calculated for the entire multi-dimensional space (using po(m) and pr(m)), or for specific parameters using the marginal PDFs and the corresponding subset of pr. However, we will not be able to compare SIC since the number of bins in the discrete PDF k varies among parameters. For that purpose, we define a relative Shannon information content, SICH, for which the maximum is 1.

Finally, we should note that a disadvantage of our implementation of GENRA is that it does not account for uncertainty correlation in the data. However, we expect MISR observations for each camera to be largely uncorrelated (). The resulting posterior PDF expresses covariance between parameters but cannot account for model uncertainties that are correlated in parameter space.

Our ICA incorporates expectations of both measurement and model uncertainty. The former are based upon the MISR instrument characteristics, while the latter are derived from our knowledge of radiative transfer model accuracy and estimates for uncertainty due to simplifications of that model compared to geophysical reality. We test the relative importance of those simplifications compared to other sources of uncertainty as part of this work. Furthermore, appropriate estimates of measurement and model uncertainty provide for the means to assess retrieval performance with varying observation geometries and retrieval parameter values.

Additional sources of error (unknown unknowns) can be due to conditions outside of the simulated parameter LUT boundaries (e.g., τ≫0.5) or optically relevant complexity (such as non-spherical aerosols described in ) that are not incorporated into the analysis because we are unable to estimate their specific impact in either measurement or parameter space. In this sense, the ICA can be considered the best-case scenario, as additional sources of error can only degrade performance.

Lacking more detailed information about our uncertainties, we treat them as Gaussian and construct measurement PDFs (pd) as follows: 12pd(y)=1σ2πexp⁡(y-y′)2-2σ2, where y′ is the simulated LUT value and σ represents the squared sum of all sources of uncertainty. In this representation we express the pd for each measurement (i.e., each camera observation) individually.

Measurement uncertainties for MISR are based upon the comprehensive literature that has characterized various sources of uncertainty (e.g., ) from which we chose the following model of MISR radiometric uncertainty 13σMISR=0.03max⁡y′,0.04cos⁡θsπ, where y′ is expressed in units of radiance. For all of our simulations, the LUT radiance was calculated such that the exo-atmospheric irradiance is 1 W m-2 and the solar distance in astronomical units is 1. While this convention is not the same as geophysical reality, it is easily converted to the appropriate values if needed and irrelevant for the purposes of this study so long as we are consistent. The relationship between reflectance (ρ) and radiance (y′) is thus 14ρ=πy′cos⁡θs, so the right-most portion of Eq. () is a conversion from reflectance units to the version of radiance in use in this work. In most cases, this was the smaller of the pair of values in that equation and not incorporated into the uncertainty estimate.

We consider three sources of model uncertainty. The first is the AFRT numerical uncertainty established by benchmark comparisons to be σRT=0.001y′ (). Next, we include expectations of uncertainty due to the atmospheric plane-parallel assumption inherent to AFRT. While this assumption has minimal impact for most solar and viewing geometries, it becomes relevant at oblique angles, such as the MISR Df and Da cameras. Recently, conducted an analysis of the difference between plane-parallel and pseudo-spherical radiative transfer. We use this as the basis for an estimate of the plane-parallel model uncertainty (σpp), described in Table . Later, we will use this camera-specific uncertainty estimate to test whether the information content of a retrieval is higher when using all nine cameras or when omitting the two most oblique angle cameras (Df and Da).

AFRT uses a scalar (unidirectional) treatment of sun glint with a single wind speed parameter. Because this represents a potential oversimplification by the forward model, we include this as an additional model uncertainty term. The magnitude of this uncertainty depends on geometry, wind speed, and atmospheric transmittance, so it is derived individually for each measurement by comparing the scalar and vector (based on wind speed and direction) sun glint models of . Figure  illustrates the differences between the scalar and vector parameterizations as they would be observed by MISR for a viewing geometry similar to test case A, a wind speed of 1.68 m s-1, and τ=0.05. The left panel shows how the greatest differences between the scalar and vector representations of sun glint occur at the peak angle of that glint, while the right panel shows the sinusoidal nature of the scalar and vector difference. To determine the uncertainty term, σcm, we calculate the cumulative distribution function of the differences between scalar and vector glint radiance at the top of atmosphere for a full 360∘ cycle. We then assume the differences are Gaussian distributed and estimate σcm based on the shape of the cumulative distribution function. This conservative assessment was chosen because we do not account for the wave shadow effect, although we expect that to be small for MISR geometries ().

To summarize, we use radiative transfer simulations to create a LUT, which we interpolate to each of the geometries described in Sect. . This LUT is again interpolated to a finer parameter grid and used to generate the likelihood function. It is also used, in combination with uncertainty estimates, to determine individual measurement distributions for each node in the LUT. In practice, this involves the following steps.

Generate LUT(θv,θs,ϕ,r,f,τ,w) using AFRT.

The product of this analysis is a multidimensional a posteriori PDF, po(r,f,τ,w,r′,f′,τ′,w′), where the first four dimensions index each node in the LUT, while the latter four represent the interpolated parameter values. An overall estimate of Shannon information content has four dimensions, SICR(r,f,τ,w), and there are corresponding Shannon information content values derived from the marginal PDFs that have the same dimensionality. These products are generated for each test case geometry, so comparisons among them can be used to determine the impact of changes in geometry. Slight modifications to this procedure can be used to address specific questions. For example, we test the importance of scalar wind and glint parameterization by omitting the σcm term from the σ calculation in step B. We also test the value of discarding the most oblique view angles and their corresponding increased model uncertainty due to the plane-parallel approximation, by simply omitting those measurements in the loop in step ii. The multi-dimensional nature of these products is a challenge we hope to address successfully in the next section.

The final product of our analysis is an a posteriori PDF (po) that has eight dimensions. There are individual PDFs calculated for each test case geometry. As this is difficult to visualize, we calculate aggregate metrics such as the SICH and marginal PDFs. Figure  is an example uncertainty assessment for test case G, parameter set r=90 %, f=0.10, τ=0.10, and w=1.87 m s-1. In this geometry, the influence of the sun glint is obvious (panel a), so we would expect to be able to retrieve all parameters. Indeed, this is the case: marginal PDFs (panels i, j, k and l) are narrow and peaked near the simulated parameter value. Slices through po (panels c, d, e, f, g, and h) show a small volume centered about the simulated parameter values. τ and w have the narrowest marginal PDFs, while those of the aerosol intensive parameters r and f are wider. What is striking is that the shape of the marginal PDFs is often non-Gaussian, especially for the wider PDFs. This indicates that single-parameter retrieval uncertainty estimates based upon Gaussian assumptions may not adequately represent the nature of that uncertainty. To some extent, this is to be expected for the wider PDFs, as they are more influenced by the uniform prior.

Figure  shows another slice of po for test case  G. The parameter set is r=75 %, f=0.50, τ=0.30, and w=7.49 m s-1, and overall performance is worse than in Fig. . The larger τ obscured the sun glint feature, leading to reduced retrieval capability for all parameters (among other changes). This is shown in the wider marginal PDFs, which are clearly non-Gaussian; the larger volumes in the a posteriori PDF slices; and the lower SICH values. The change in SICH helps us understand relative differences between the two cases. In this case, the overall metric for SICH decreases to 0.35 from 0.54, and all four of the marginal SICH values decrease. This is especially true for w, which decreases to 0.27 from 0.82.

Next, we consider the results for a different test case. Figure  is for test case D, where θs=69.7∘, and the same parameter set as in Fig. . At this geometry, sun glint is not present in the simulated observations. The overall impact is a degradation in w retrieval capability, as expected, and improvement in the aerosol parameters. Despite the lack of sun glint in the simulation, the marginal PDF for w does correctly exclude large wind speeds, which perhaps might have influenced the observations. In any case, the total SICH decreases only slightly, to 0.48.

While these three figures only show results for three test case and parameter set examples, they express the range of potential results, and the relationship between a posteriori PDF volumes, marginal PDFs, and SICH. In the following subsections we will focus on the change in information content with geometry, parameter value, and sensitivity to model assumptions. To do so, we only plot SICH, which is the most compact means to express information content. However, figures similar to those in this section were made for all test cases and parameter sets and can be found in the archive at https://data.nasa.gov/Earth-Science/MISR_MODIS_AtmCorrection/sg4r-ftwb .

Multi-angle observations, especially those that contain sun glint, should be very sensitive to sun and observation geometry (e.g., ). This is because the atmospheric radiative transfer is largely governed by the scattering angle (the angle between illumination and observation vectors; ), while the glint is controlled by both sun and observation geometry (). This means that what is observed by MISR's nine cameras changes with location, time of day, and season, factors which define geometry. It also means that the nature of the sun glint pattern does not change in tandem with that of atmospheric scattering.

As we can see from Fig. , MISR cameras observe a scene in a generally constant relative azimuth angle plane, indicated by straight lines in that figure. While the significance of such behavior is explored more fully in , we would like to note that if this plane is aligned with the solar principal plane, i.e., ϕ=0,180∘, then a multi-angle measurement would see the widest possible range of scattering angles, presumably containing more information about the atmospheric state. It would also be more influenced by reflected sun glint, which is centered about that plane. Observations along the cross principal plane (ϕ=90,270∘), in contrast, see a narrower range of scattering angles and are less likely to observe sun glint (which is also defined by θs). MISR observations fall between these two extremes. The test cases with the largest θs (cases D and E) are closest to the solar principal plane, meaning that they observe the largest scattering angle range. However, θs is high enough that the sun glint is for the most part not observed. MISR, θs, and ϕ mostly change in tandem, so as θs decreases, the observation plane becomes closer to the cross principal plane. For these observation (A, B, and F), a narrower scattering range, yet greater glint influence, is to be expected.

Figure  shows the impact of different observation geometries on SICH. In this figure, we have plotted the median SICH for each test case/geometry as diamonds connected by dashed lines. Vertical lines are the inter-quartile SICH range. This has been done for the total SICH, shown in black, along with the marginal SICH for relative humidity (blue), fine mode fraction (red), aerosol optical depth (green), and wind speed (magenta). The overall SICH is relatively insensitive to geometry, perhaps because SICH improvement for some parameters comes at the expense of others. For the aerosol parameters, SICH increases with θs (and consequently, a decrease in ϕ), confirming our expectation that access to a greater scattering angle range improves the information content. By contrast, wind speed, which is the parameter retrieved from the sun glint pattern, shows the highest SICH for moderate θs (test cases A, B, C, and G) and is nearly zero for the largest θs (test cases D and E). This is to be expected, since the sun glint has minimal impact on those scenes.

Test case F is somewhat unique, as it is among the lowest SICH for nearly all parameters. While this is due in part to the most restricted scattering angle range of a nearly cross principal plane geometry, this scene also exhibits a form of symmetry, since the highest glint is in the nadir view (camera An). The other camera angles are mirrored in the forward or aft views, implying a reduction in information content. Figure  demonstrates this for the same parameter set as in Figs.  and . In this figure we can see the aforementioned nearly mirror symmetry in panel (a). While w and τ still have narrow marginal PDFs, those for r and f have grown. Panel (e) indicates that there is the some non-uniqueness between the pair of parameters, which has a detrimental effect on information content. This is similar to the lowered information content found in some low-latitude observations by .

In addition to geometry, the retrieval parameters defining a scene also impact information content. For example, for low aerosol loads, the information content of aerosol intensive properties (in this parameterization scheme, r and f) should be less than that for higher aerosol loads. However, with highly nonlinear systems such as ours, it can be difficult to make predictions beyond simplistic assumptions such as these. GENRA, however, provides the means to systematically assess the relationship between parameter value and retrieval information content.

Figure  shows the sensitivity of both the total and marginal SICH values for each of the retrieved parameters. For clarity, only median values of SICH are presented. For the aerosol intensive parameters (r and f, top row) we see only small changes in SICH as those parameters change. This is consistent with , who also found little to no information content dependence on aerosol intensive properties (see Fig. 4 in that paper). That study was an analysis using different parameterization schemes, radiative transfer, and information content assessment. This tells us that the range of aerosol intensive property values has minimal impact on the information content assessment result. Furthermore, so long as the paramaterization scheme correctly represents geophysical reality, retrieval success will depend more on observation geometry and other parameters. However, we should note that this assessment does not include non-spherical aerosols, such as dust, for which information content (and required parameterization scheme) differs.

The bottom panels in Fig.  do show SICH sensitivity to parameter value. The SICH of aerosol intensive properties, as noted above, is lowest for small amounts of aerosols and increases with aerosol optical depth. This is to be expected, since there will be a greater radiative impact of the aerosol intensive parameters as the quantity of aerosols increases. Conversely, the ability to determine w is best for low aerosol loads and decreases as the aerosol magnitude increases and obscures the reflected sun glint. SICH for τ has a more complicated relationship with the value of τ itself, in part because this is an extensive parameter. The total SICH shows relatively small change with τ, indicating a balance between aerosol intensive and w information content with changing τ. In contrast, SICH uniformly decreases for all parameters as w increases. Increasing w serves to broaden the sun glint pattern, which may be a source of information content reducing ambiguity.

In Sect. , we discuss the uncertainty associated with the use of a (computationally efficient) radiative transfer model that simulates the atmosphere as parallel layers. assessed that uncertainty, which we incorporate into our overall uncertainty estimate independently for each MISR camera (Table ). As we can see, the Df and Da cameras, whose θv=±70.5∘, have the largest uncertainty, roughly an order of magnitude less than the overall instrumental uncertainty (Eq. ).

This raises the following question: is it better to omit those two camera views when performing retrievals with plane-parallel radiative transfer? To test this, we compare our overall results, described in the previous subsections, to those for a modified GENRA test. The modified test does not incorporate simulated observations from the Df and Da cameras, such that the iteration described in step b.iii in Sect.  does not include those views. In other words, we are testing whether cameras Df and Da, when including expectations of their uncertainty due to the plane-parallel assumption, contain information that does not already exist in the other views.

We find that it is indeed best to include all nine MISR cameras, so long as the expectations of the plane-parallel model uncertainty are a part of the retrieval algorithm. Figure  illustrates the differences between the SICH for the case using all nine MISR cameras and for the seven-camera case excluding the most extreme view zenith angles. The top panel is the histogram of the SICH,9 views - SICH,7 views difference. Positive values indicate that the SICH is higher for the case using all cameras than when the Df and Da camera views are omitted. The vast majority are positive, and in some instances significantly so. This is true for both the overall SICH and the parameter-specific marginal SICH values. In an effort to understand the consistency of these differences, we plotted in the lower panel the median SICH for each test case. While these are all positive, the SICH for test case C is higher than the others. This is unexpected because test case G has similar θs but less positive SICH,9 views - SICH,7 views values. If we refer to Fig. , we see that the plane of observations in test case C is farther from nadir than that of test case G. This means that the sun glint is observed at higher θv angles, so the omission of the most extreme θv cameras has a more significant impact upon information content. This also illustrates that the geometry differences between the nadir portion of the image swath and points far from that direction can in some cases be significant.

In a similar fashion, we test sensitivity to the parameterization model of reflected sun glint. As described in Sect. , provided two sun glint parameterization models. The simplest, which we use, treats wind as scalar and unidirectional. A more complicated model uses wind speed and direction (or the equivalent zonal and meridional winds). The latter is difficult to use in our current implementation of AFRT because that model assumes azimuthal symmetry (180∘<ϕ<360∘ is a mirror reflection of 0∘<ϕ<180∘). It also implies the retrieval of two, not one, parameters.

We do account for the additional model uncertainty due to the use of scalar instead of the vector representation of wind speed, and the results thus far include that uncertainty. To test its significance, we performed another GENRA analysis without that source of uncertainty and compare to our original test case. The results are shown in Fig. . Like Fig. , this shows the histogram of the SICH change, in this case without and with the scalar uncertainty term. For most cases, but not all, the information content difference is minimal. The lower panel, which has median SICH values broken down by test case geometry, shows that the lowest θs test cases are most affected by this form of uncertainty, which makes sense since they are most influenced by sun glint.

From a practical perspective, how significant are these impacts? While SICH is a useful differentiation metric, examination of the marginal PDFs can help place them in the context of retrieval success. Figure  shows the change in the marginal PDF for each parameter for the set of parameters illustrated in Figs. , , and (r=90 %, f=0.10, τ=0.10, and w=1.87 m s-1). In this figure, dashed lines indicate the marginal PDF without the vector wind uncertainty; lack of visible dashed lines means they overlap the solid line PDFs representing use of the vector wind uncertainty. As we can expect based on Fig. , the lowest-θs cases are more impacted by this uncertainty term. However, the impacts appear constrained primarily to the aerosol intensive parameters (r and f) with minimal impact on τ and no impact on w. This indicates that determination of wind speed is largely unaffected by the use of the wind parameterization scheme, while the scalar scheme only degrades the ability to determine aerosol intensive parameters moderately and at low-θs geometries.