Updated MISR dark water research aerosol retrieval algorithm – Part 1 : Coupled 1 . 1 km ocean surface chlorophyll a retrievals with empirical calibration corrections

As aerosol amount and type are key factors in the “atmospheric correction” required for remote-sensing chlorophyll a concentration (Chl) retrievals, the Multi-angle Imaging SpectroRadiometer (MISR) can contribute to ocean color analysis despite a lack of spectral channels optimized for this application. Conversely, an improved ocean surface constraint should also improve MISR aerosol-type products, especially spectral single-scattering albedo (SSA) retrievals. We introduce a coupled, self-consistent retrieval of Chl together with aerosol over dark water. There are time-varying MISR radiometric calibration errors that significantly affect key spectral reflectance ratios used in the retrievals. Therefore, we also develop and apply new calibration corrections to the MISR top-of-atmosphere (TOA) reflectance data, based on comparisons with coincident MODIS (Moderate Resolution Imaging Spectroradiometer) observations and trend analysis of the MISR TOA bidirectional reflectance factors (BRFs) over three pseudo-invariant desert sites. We run the MISR research retrieval algorithm (RA) with the corrected MISR reflectances to generate MISR-retrieved Chl and compare the MISR Chl values to a set of 49 coincident SeaBASS (SeaWiFS Bio-optical Archive and Storage System) in situ observations. Where Chlin situ < 1.5 mg m−3, the results from our Chl model are expected to be of highest quality, due to algorithmic assumption validity. Comparing MISR RA Chl to the 49 coincident SeaBASS observations, we report a correlation coefficient (r) of 0.86, a root-meansquare error (RMSE) of 0.25, and a median absolute error (MAE) of 0.10. Statistically, a two-sample Kolmogorov– Smirnov test indicates that it is not possible to distinguish between MISR Chl and available SeaBASS in situ Chl values (p > 0.1). We also compare MODIS–Terra and MISR RA Chl statistically, over much broader regions. With about 1.5 million MISR–MODIS collocations having MODIS Chl < 1.5 mg m−3, MISR and MODIS show very good agreement: r = 0.96, MAE= 0.09, and RMSE= 0.15. The new dark water aerosol/Chl RA can retrieve Chl in low-Chl, case I waters, independent of other imagers such as MODIS, via a largely physical algorithm, compared to the commonly applied statistical ones. At a minimum, MISR’s multi-angle data should help reduce uncertainties in the MODIS–Terra ocean color retrieval where coincident measurements are made, while also allowing for a more robust retrieval of particle properties such as spectral single-scattering albedo.

Abstract.As aerosol amount and type are key factors in the "atmospheric correction" required for remote-sensing chlorophyll a concentration (Chl) retrievals, the Multi-angle Imaging SpectroRadiometer (MISR) can contribute to ocean color analysis despite a lack of spectral channels optimized for this application.Conversely, an improved ocean surface constraint should also improve MISR aerosol-type products, especially spectral single-scattering albedo (SSA) retrievals.We introduce a coupled, self-consistent retrieval of Chl together with aerosol over dark water.There are time-varying MISR radiometric calibration errors that significantly affect key spectral reflectance ratios used in the retrievals.Therefore, we also develop and apply new calibration corrections to the MISR top-of-atmosphere (TOA) reflectance data, based on comparisons with coincident MODIS (Moderate Resolution Imaging Spectroradiometer) observations and trend analysis of the MISR TOA bidirectional reflectance factors (BRFs) over three pseudo-invariant desert sites.
We run the MISR research retrieval algorithm (RA) with the corrected MISR reflectances to generate MISR-retrieved Chl and compare the MISR Chl values to a set of 49 coincident SeaBASS (SeaWiFS Bio-optical Archive and Storage System) in situ observations.Where Chl in situ < 1.5 mg m −3 , the results from our Chl model are expected to be of highest quality, due to algorithmic assumption validity.Comparing MISR RA Chl to the 49 coincident SeaBASS observations, we report a correlation coefficient (r) of 0.86, a root-meansquare error (RMSE) of 0.25, and a median absolute error (MAE) of 0.10.Statistically, a two-sample Kolmogorov-Smirnov test indicates that it is not possible to distinguish between MISR Chl and available SeaBASS in situ Chl values (p > 0.1).We also compare MODIS-Terra and MISR RA Chl statistically, over much broader regions.With about 1.5 million MISR-MODIS collocations having MODIS Chl < 1.5 mg m −3 , MISR and MODIS show very good agreement: r = 0.96, MAE = 0.09, and RMSE = 0.15.
The new dark water aerosol/Chl RA can retrieve Chl in low-Chl, case I waters, independent of other imagers such as MODIS, via a largely physical algorithm, compared to the commonly applied statistical ones.At a minimum, MISR's multi-angle data should help reduce uncertainties in the MODIS-Terra ocean color retrieval where coincident measurements are made, while also allowing for a more robust retrieval of particle properties such as spectral single-scattering albedo.
1 Introduction Among the geophysical quantities routinely produced from the NASA Earth Observing System's Multi-angle Imaging SpectroRadiometer (MISR) instrument are aerosol optical depth (AOD) and aerosol type.MISR measures upwelling shortwave radiance from Earth in four spectral bands centered at 446 (blue), 558 (green), 672 (red), and 866 nm (nearinfrared, NIR) at each of nine view angles spread out in the forward (f ) and aft (a) directions along the flight path, at 70.5, 60.0, 45.6, 26.1 • , and nadir (Diner et al., 1998).The three near-nadir cameras are designated "Af", "Aa", and "An", and successively steeper-viewing pairs are "B", "C", and "D" cameras.MISR's multi-angle, multispectral radiance data sample air mass factors ranging systematically from one to three, making AOD retrieval possible even over bright desert surfaces, and improving retrieval sensitivity at low AOD compared to single-view instruments.In low-AOD situations, which are common over ocean, poor representation of the surface reflectance can limit aerosol retrieval accuracy, as the relative contribution of ocean under-light can be large, especially at shorter wavelengths.Therefore, applying a physical retrieval to constrain the ocean surface reflectance, of interest in itself as an indicator of ocean biological activity and its impact on the global carbon cycle (e.g., Behrenfeld et al., 2006), should also reduce the uncertainties in the concomitant aerosol retrievals, assuming the aerosol and ocean signals do not co-vary substantially over MISR's 36 channels.
A second factor directly affecting the quality of almost every MISR geophysical data product is the accuracy of the instrument's radiometric calibration.As the MISR data record now exceeds 17 years of near-global coverage about once per week, the advantages of further refining the MISR calibration have increased multifold.This applies to determining AOD trends and is especially true in the context of MISR's ability to retrieve aerosol type (Kahn and Gaitley, 2015).In addition to AOD and aerosol type, retrievals of ocean bio-optical properties from space are extremely sensitive to the calibration of the instrument, because only 5 to 20 % of the topof-atmosphere (TOA) reflected signal in the blue and green spectral bands, where ocean color is retrieved, arises from scattering related to ocean under-light (e.g., Fig. 2; more generally, Gordon and Wang, 1994).We find that not only the absolute radiometric calibration, but also the MISR blue/green ratio, critical for ocean color applications, has changed over time.
This paper is organized as follows: Sect. 2 reviews the datasets used in our analysis and the methodology adopted, Sect. 3 presents the Chl retrievals and initial validation of the results, example retrievals are shown in Sect.4, and conclusions are given in Sect. 5. MISR radiometric calibration corrections, including details of the observed temporal trends, are described in Appendix A.

The MISR research algorithm (RA)
The aerosol/Chl retrieval algorithm (RA) is summarized as a flow chart in Fig. 1.An in-depth description of the main RA components can be found in Limbacher andKahn (2014, 2015).Briefly, the algorithm finds the set of aerosol optical models, associated aerosol amounts, and Chl values that minimize the difference between the observed TOA reflectances (identical to bidirectional reflectance factors, BRFs, described in Appendix A, but without the solar-zenith normalization) and simulated values that are stored in a lookup table (LUT).The overall aim is to derive AOD and Chl over 1.1 km retrieval regions, conditioned on aerosol-type mixtures that produce TOA reflectances meeting certain χ 2 criteria.In the current study, we compare the MISR RA Chl retrievals to coincident validation data taken at the surface, after all MISR calibration corrections are applied (Appendix A), and also identify the impact the refined ocean surface model has on the retrieved aerosol results for a few scenes, in Sect. 4 below.

MISR RA enhanced ocean reflectance model
Prior to Limbacher and Kahn (2014), the MISR RA simulated ocean surface was modeled as an isotropic (wind-speed-dependent only) Fresnel reflector (Cox-Munk), with whitecap reflectance included.In Limbacher and Kahn (2014), we made adjustments to the whitecap reflectance and added an ocean under-light term that includes molecular and particulate attenuation.In Limbacher andKahn (2014, 2015), we used wind and ocean color constraints from the Cross-Calibrated Multi-Platform (CCMP; Atlas et al., 2011) and GlobColour (Barrot et al., 2010) products (and a climatology where these products were unavailable), respectively, to prescribe the ocean's color.
For the current analysis, we continue using CCMP data for 10 m wind speed where available, otherwise we use the MISR version 22 standard aerosol retrieval algorithm (SA) wind data, which comes from monthly averaged values of QuikSCAT and the Special Sensor Microwave/Imager (SSM/I; Michael Garay, personal communication).We set the surface pressure to 1013.25 mbar, as we find a number of cases where the MISR standard product surface pressure over ocean is aliased from nearby mountains.This results from the different footprint sizes of the SA vs. the RA; the SA has a 17.6 km footprint, whereas the RA has a 1.1 km footprint.Additionally, instead of prescribing Chl, we now retrieve it directly in the algorithm by inverting our ocean color model.To do this, we use all four MISR spectral bands to simultaneously retrieve aerosol and Chl, with equal weighting, whereas the SA (Martonchik et al., 2009) and past versions of the RA retrieved only aerosol amount and type and used only the red and NIR bands, where the ocean surface is darkest, except at high AOD.However, empirical camera weighting is applied here to mitigate the effects of sunglint, and different uncertainties are assigned to the 36 MISR channels when evaluating the χ 2 acceptance criteria, as discussed below.
Colored dissolved organic matter (CDOM) absorption is assumed to co-vary with Chl (Morel and Gentili, 2009).Relationships connecting Chl to absorption and backscattering coefficients can be found in many places; the ones we used (Chen et al., 2003;Devred et al., 2006;Morel and Prieur, 1977;Morel, 1988) are summarized in Sayer et al. (2010).For our ocean under-light model, we modify the absorption of light by seawater for the blue spectral band from Morel and Prieur (1977), which was used previously in the RA, to more recent results from Lee et al. (2015).
The following equation gives a bidirectional water-leaving radiance: The following explanation of the terms in Eq. ( 1) is basically a summary of Morel et al. (2002), which is also where the LUT for f/Q and was obtained.Variable dependences are included here only if they are given in the Morel et al. (2002) LUT.
-L + w represents the water-leaving radiance, which is the upward-directed radiance just above the water surface (excluding sunglint).It is a function of the cosine of the solar zenith angle (µ 0 ), the cosine of the view (camera) zenith angle (µ), the relative azimuth between the Sun and the sensor ( φ), the wavelength (λ), the wind speed (WS), the total column optical depth (τ ), the aerosol optical model (mix), and the chlorophyll a concentration (Chl).
-E d represents the downward-directed solar irradiance at the bottom of the atmosphere.
is a reflectance factor, the product of two effects: the fraction of the downward-directed bottom-ofatmosphere irradiance (E d ) transmitted through the airsea interface, and the fraction of the upward-directed radiance from just beneath the air-sea interface transmitted through the interface.
b b represents the total backscattering coefficient of the water plus other material within the water.
a represents the total absorption coefficient of the water plus the other material within the water.
f represents an empirical correction to the ratio of the backscattering to absorption (essentially a modification to the upward-directed under-light irradiance).
www.atmos-meas-tech.net/10/1539/2017/Atmos.Meas.Tech., 10, 1539-1555, 2017 -Q represents the ratio of the upward-directed irradiance to radiance just below the air-sea interface.This term (along with f ) is responsible for creating the directional dependence of the under-light on solar and viewing geometry.
L + w is multiplied by the transmittance from the bottom of atmosphere to the camera (T a,up ) to get the surface contribution to the TOA reflectances.Because the integrated waterleaving radiance, L + w E d (i.e., the under-light albedo), is small, the probability that a photon will be multiply reflected due to under-light is very small, regardless of atmospheric loading, and is ignored, given other, larger uncertainties in the algorithm.However, multiple surface reflections due to sunglint and whitecaps are directly accounted for in the radiative transfer code.
As we aim to extract both surface and aerosol information from the MISR data, we apply new camera weights when calculating the χ 2 test variables used to assess the agreement between the observed reflectances and those derived for various aerosol component and mixture options.In the SA and previous versions of the RA, a glitter mask was applied arbitrarily to all cameras viewing within 40 • of the specular direction.Instead, we now use a combination of glitterangle and Rayleigh NIR reflectance, calculated assuming Chl = 0.1 mg m −3 to assess glint contamination in each camera.The new camera weights are the product of the following two empirically derived equations: glitter weight,i = min max (G i − 25.0) 40.0 − 25.0 , 0.0 , 1.0 Here ρ NIR model represents the modeled NIR Rayleigh reflectance over an ocean surface for a particular MISR camera (i), and G is the glitter angle relative to the same MISR camera.The minimum and maximum reflectances were taken via forward modeling, and 25 • was set as the minimum because as glitter angle decreases, a small error in wind speed could substantially impact the retrieval.Equation (2) returns a value of unity if the modeled NIR reflectance is ≤ 0.0075; this weight decreases linearly to zero if the modeled reflectance is ≥ 0.0125.Essentially, as the modeled glint strength increases, camera weighting decreases.Similarly, Eq. (3) produces a value of unity if the glitter angle ≥ 40 • , decreasing linearly to zero for G ≤ 25 • .The product of these weights provides better glint masking than using an arbitrary cutoff, and the quality of these new weights should improve with the quality of the input wind speed data.Further, as we improve our ability to determine if a camera is glint contaminated in the future, we will likely lower this minimum glitter-angle threshold.
Figure 2 illustrates the impact of including under-light in the MISR RA, for the blue-and green-band retrieval TOA reflectance results.For this figure, MISR aerosol retrievals over dark water were performed using the multi-angular data for the NIR band only, because the ocean surface tends to be darkest at this wavelength (i.e., where under-light makes its smallest spectral contribution).When the retrieved aerosol properties are used in the forward radiative transfer model to simulate the MISR top-of-atmosphere reflectances in the blue and green bands, but under-light is not included, there are large discrepancies in the modeled TOA reflectances compared to the original MISR observations (Fig. 2a, b).However, when under-light is accounted for in the simulations (in this illustration using coincident Moderate Resolution Imaging Spectroradiometer (MODIS)-Terra Chl as input), the biases are substantially reduced, as shown in the lower two panels of Fig. 2. As the MODIS-constrained Chl was included when the aerosol retrieval was performed (using only the multi-angle NIR data), this example demonstrates the magnitude of the surface contribution to the TOA reflectances in the blue and green spectral bands.If surface contributions are not explicitly included, the aerosol retrievals would be skewed, and the spectral dependence of the anomaly could impact the derived aerosol type (e.g., Kahn and Gaitley, 2015), especially when the blue or green bands are included in the aerosol retrieval.In Sect. 4 we demonstrate the use of MISR to constrain Chl self-consistently with the retrieval of aerosol over ocean.

MODIS-Terra top-of-atmosphere reflectances
The MODIS TOA reflectances are key to several radiometric calibration adjustments detailed in Appendix A. As in Limbacher and Kahn (2014), MODIS-Terra equivalent reflectance data are used as a baseline to compare against MISR, especially for the nadir camera.We use the latest MODIS collection 6 TOA reflectances (Sun et al., 2012) with additional corrections implemented via an algorithm provided by Alexi Lyapustin (Lyapustin et al., 2014;elaborated in Limbacher and Kahn, 2015).Primarily, we are interested in the following MODIS bands: 9 (443 nm, as compared to MISR's 446 nm blue), 4 (555 nm, as compared to MISR's 558 nm green), an average of bands 13 and 14 (effectively 672 nm, as compared to MISR's 672 nm red), and 2 (856 nm, as compared to MISR's 866 nm NIR).In the current study, MODIS reflectances are used only to remove flat-fielding artifacts in the MISR imagery and to make modifications to the ghosting parameterization described in Limbacher and Kahn (2015), so the absolute calibration accuracy of MODIS is not critical here.The most critical assumptions are that MODIS swath-edge and scan-angle issues are minimal for the scenes of interest and that pixel-to-pixel relative precision is high.Fortunately, because the MISR swath samples about 380 km around the center of the 2300 km MODIS swath, the effects of MODIS swath-edge and scan-angle artifacts on the coincident data are minimal.

The SeaWiFS Bio-optical Archive and Storage
System (SeaBASS) dataset The SeaBASS dataset (Werdell and Bailey, 2002; https:// seabass.gsfc.nasa.gov)was originally developed to compare products retrieved from sensors such as the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) and MODIS with in situ bio-optical observations.We use SeaBASS chlorophyll validation data generated either by fluorometry or by highperformance liquid chromatography (HPLC).Uncertainties for HPLC and fluorometry Chl measurements are 5 and 8 %, respectively (Heukelem et al., 2002).If HPLC (Chl) and fluorometry (Chl) data were acquired at the same location and time, we use the HPLC (Chl) data; otherwise we use the fluorometry data.Because the MISR standard algorithm does not retrieve Chl, the MISR-SeaBASS coincidences were found by locating MODIS-Terra validation matchups (Bailey and Werdell, 2006) and setting the view-ing zenith angle maximum to 16 • , which corresponds to the edge of the MISR nadir (AN) camera field of view.To assure meaningful SeaBASS observations for MISR Chl validation purposes, we also applied the following criteria: (1) minimum sea floor depth was set to 30 m to mitigate errors due to sea floor reflections, especially in the blue band, (2) maximum wind speed was set to 7 m s −1 to avoid whitecaps (eliminating ∼ 25 % of data), (3) maximum solar zenith angle was set to 70 • to eliminate steep-incidence-angle effects, (4) maximum coefficient of variation for MODIS Chl was set to 0.15 to avoid aliasing due to spatial variability of the scene, (5) maximum SeaBASS-MISR time difference was set to 3 h, and (6) minimum number of valid MODIS pixels was set to 25 %.This produced 75 coincidences that have valid MISR aerosol/Chl retrievals.Of these 75 coincidences, 49 correspond to Chl < 1.5 (the Chl regime where the MISR retrievals are expected to show good performance) and also have at least one valid MISR RA retrieval in a 5.5 × 5.5 km area surrounding the SeaBASS station passing our quality tests.

MODIS-Terra chlorophyll a
Although we validate our Chl retrieval against the SeaBASS dataset for Chl < 1.5, we also cross-compare our Chl results with those from MODIS-Terra (OBPG, 2014;OB.DAAC, 2014) to increase the number of coincidences (especially needed for Chl < 1.5) and because MISR and MODIS share a common platform.This ensures that the solar geometry is the same for MODIS and MISR and minimizes potential collocation errors.To do this, we compare MISR RA-retrieved Chl with the corresponding MODIS-Terra-retrieved values (Hu et al., 2012).Details of the algorithm used to generate the MODIS data can be found at http://oceancolor.gsfc.nasa.gov/cms/atbd/chlor_a. Briefly, a training dataset containing collocated in situ Chl and spectral water-leaving radiance (L + w ) is used to empirically relate the ratio of blue-to-green MODIS L + w to near-surface Chl (Werdell and Bailey, 2005).This same relationship is then used to retrieve MODIS Chl elsewhere, although the quality of the result also depends in part on the quality of the associated atmospheric correction (e.g., Kahn et al., 2016).

The AErosol RObotic NETwork (AERONET)
Although the main purpose of this paper is to demonstrate and validate our Chl retrieval, we also compare the new algorithm against AErosol RObotic NETwork observations for a few selected scenes.AERONET sun photometers (Holben et al., 1998) provide very accurate measurements of AOD (Eck et al., 1999) and Ångström exponent (ANG).The almucantar inversions (Dubovik and King, 2000) can provide constraints on particle sphericity (Dubovik et al., 2006; which we convert to fraction mid-visible AOD assigned to non-spherical particles, or Fr.Non-Sph), and for aerosol single-scattering albedo (SSA), provided the aerosol loading is high (AOD at 440 nm > 0.4), the scattering angle range for the inversions is large, and the aerosol is relatively uniform over the range of view angles used for the inversion (Holben et al., 2016).

Validation of MISR RA Chl retrievals against
SeaBASS, and comparisons with MODIS Collocation of the MISR and SeaBASS observations is of course critical to achieving meaningful comparisons.So for each SeaBASS-MISR coincidence, the corresponding location within an MISR orbit is identified as a block (180 blocks per orbit), line (128 along-track lines per block), and sample (512 across-track samples per block) at 1.1 × 1.1 km.We run the RA, as described in Sect.2.1, over three blocks of data per coincidence, centered on the MISR block that contains the MISR-SeaBASS coincidence.We then interpolate the MODIS-Terra Chl data, as well as the associated MODIS flags, to the MISR grid via nearest-neighbor interpolation.In an attempt to ensure the highest quality retrieval possible, we flag all MISR-MODIS data based on the following criteria: -Any MISR-MODIS data where the MODIS Chl flag data is masked (at level 3) according to https:// oceancolor.gsfc.nasa.gov/atbd/ocl2flags/.
-Any MISR-MODIS data where the MISR aerosol retrieval acceptance criterion is violated.In this case the criterion, χ 2 > 1.0, is calculated over all the four wavelengths for all glint-free cameras (see Sect. 2.1 above).This should help prevent poor aerosol retrievals impacting the MISR Chl retrieval.
-Any MISR-MODIS data where MISR 446 nm AOD > 1.0.AOD above this value over ocean tends to occur only in cases of dust, smoke, pollution plumes, or unmasked clouds.As the surface signal is very small for these cases, especially for the off-nadir cameras, MISR should have little or no sensitivity to Chl in these situations.
-Any MISR-MODIS data where the MISR Chl χ 2 > 1.0, calculated over the blue and green "A" and "B" glintfree cameras, as these cameras contain the most information about the surface.
-Any MISR-MODIS data where in situ Chl > 10 mg m −3 , as our Chl model is not expected to work at all in this regime.
For comparisons with SeaBASS, we average (in log 10 space) up to 5 × 5 MISR 1.1 km/MODIS 1 km Chl retrievals centered on the SeaBASS location and compare each of the MISR and MODIS-Terra Chl to the corresponding SeaBASS value.Following conventional practice, log 10 of MISR, MODIS, and SeaBASS Chl data are taken before any statistics are computed, except the mean relative error (MRE).

Validation against SeaBASS
Figure 3 shows scatterplots for MISR and MODIS-Terraretrieved Chl vs. SeaBASS coincident in situ Chl.Points left of the black vertical line in Fig. 3, and Table 1, demonstrate MISR sensitivity to retrieving chlorophyll a when the in situ value is less than 1.5 mg m −3 , which represents an upper bound on where we expect good-quality results.Statistics for Chl in situ ≤ 10 in Table 1 are shown for completeness.Compared to SeaBASS, for in situ Chl values ≤ 1.5 mg m −3 , MISR reports a correlation coefficient (r) of 0.86, a median absolute error (MAE) of 0.10, root-mean-square error (RMSE) of 0.25, and an MRE of 0.52.We also performed three sets of the two-sample Kolmogorov-Smirnov test to compare whether these MISR, MODIS, and SeaBASS populations are distinguishable.The null hypothesis that the MISR and MODIS datasets are taken from the same distribution cannot be rejected (p = 0.96), likely a result of having too few data points and/or strong covariance.Not surprisingly, statistics for the 49 SeaBASS coincidences that meet our criteria indicate that the MISR RA performs almost as well as MODIS-Terra for these cases.P -values of 0.25 and 0.37 also indicate that although the MISR and MODIS Chl data (respectively) are not statistically distinguishable from SeaBASS, they appear more similar to each other than they are to SeaBASS.Given the small sample size, it is not possible to draw strong conclusions about whether MISR could in general add value to the MODIS-Terra ocean color product in regions where MODIS-Terra reports Chl, despite the likelihood that MISR aerosol retrieval constraints would produce a more accurate atmospheric correction.However, MISR can add value in the glint-contaminated portion of the MODIS-Terra orbit, and probably in regions of medium-high aerosol loading (both of which are shown subsequently), where aerosol-type information could improve surface retrieval results (e.g., Kahn et al., 2016).

Comparison against MODIS-Terra
Because the SeaBASS validation dataset contains very few matchups with MISR, in part due to the relatively narrow MISR swath, we compare MISR 1.1 km Chl retrievals with collocated MODIS 1 km Chl retrievals over much larger regions surrounding the MISR-SeaBASS coincidence locations, using the method described above.We compare to MODIS-Terra for this regional context exercise due to the assessments already performed on the MODIS Chl data Table 1.Statistics of chlorophyll a retrievals as compared to SeaBASS.In this table, r is the Pearson correlation coefficient, MAE is the median absolute error, RMSE is the root-mean-square error between the satellite retrieval and in situ data, Fr.Err is the mean absolute fractional error of the retrieval with respect to the measurement, and # is the number of validation cases included.The last row for Chl in situ < 1.5 and Chl in situ < 1.5 represents the statistics of MISR vs. MODIS.with the much larger number of MODIS-SeaBASS coincidences (e.g., Franz et al., 2012).As such, we compare the MISR RA Chl data with all valid pixels for which MODIS Chl ≤ 10 mg m −3 .Figure 4 shows comparisons between the MISR RA and MODIS-retrieved Chl, for MODIS Chl ≤ 10.0 mg m −3 .The black vertical line indicates 1.5 mg m −3 , as we expect higher-quality MISR Chl retrievals to the left of this line.The agreement between MISR and MODIS is best below MISR-retrieved Chl values of 0.5 mg m −3 .For MISR Chl between 0.5 and 3.0 mg m −3 , Fig. 4 indicates that a scale factor could be applied to the MISR data to bring the data into better agreement with MODIS (and likely SeaBASS as well).Statistics for the MISR-MODIS Chl comparisons, as a function of MODIS-retrieved Chl, are summarized in Table 2. Comparing MISR vs. MODIS for the ∼ 1.5 million data points with MODIS Chl < 1.5 mg m −3 , r = 0.96, MAE = 0.09, RMSE = 0.15, and MRE = 0.23.A two-sample Kolmogorov-Smirnov test comparing these two datasets demonstrates that they are statistically different (p 0.001).Overall, although Fig. 4 and Table 2 indicate that the agreement between MISR and MODIS appears to be much better than the agreement between either MISR or MODIS and SeaBASS (Fig. 3 and Table 1), it is possible that this is an artifact of a small MISR-SeaBASS sample size.However, comparisons between MODIS-Terra, SeaW-IFS, and SeaBASS on the SeaBASS website suggest that this behavior is real, as SeaWIFS and MODIS-Terra agree much better with each other than with SeaBASS (https://seabass.gsfc.nasa.gov/search#bio).This strongly suggests that satellite remote-sensing covariation is playing a substantial role in the comparisons between MISR, MODIS, and SeaBASS.Interestingly, SeaWIFS also agrees better with MODIS-Terra than MISR does.Regardless, Figures 3 and 4

indicate that
Table 2. Statistics of MISR vs. MODIS regional chlorophyll a retrievals.In this table, r is the Pearson correlation coefficient, MAE is the median absolute error, RMSE is the root-mean-square error between MISR and MODIS-Terra, Fr.Err is the mean absolute fractional error of the MISR RA retrieval with respect to MODIS-Terra, and # is the number of validation cases included.there is skill in the MISR Chl retrieval, which could be exploited.

Example MISR aerosol surface retrievals over ocean
We present here two examples of individual MISR RA joint surface and atmosphere retrievals and comparisons with the corresponding MISR SA retrievals, MODIS Chl results, and embedded AERONET AOD measurements and particle property retrievals.Figure 5 presents both the SA and RA aerosol retrievals, along with the MISR RA and MODIS Chl results for a region of the Atlantic along the east coast of the US that includes the Chesapeake Bay and two coastal AERONET sites, in August 2003.Weakly to non-absorbing, relatively small, pollution particles are expected in this region and season, as confirmed by the AERONET inversion results.Both the SA (Diner et al., 2008;Kahn et al., 2010) and RA also identify the scene as dominated by small, spherical particles.Although the RA finds weakly or nonabsorbing particles spread fairly uniformly over the entire scene, the SA appears to incorrectly identify part of the scene as contaminated by moderately absorbing aerosol.The MISR SA best estimate preferentially selects lower SSA (Fig. 5, ∼ 0.91) aerosol mixtures near the coast, where both MODIS and the MISR RA report elevated Chl.In this same region, AERONET and the MISR RA find that the SSA falls within the range of 0.98 to 1.0.For particle size, represented here by ANG, the MISR RA tends to pick slightly larger aerosol models (ANG ∼ 1.72), in poorer agreement with AERONET (ANG ∼ 2.05) than the SA (ANG ∼ 2.00).This is probably related to the aerosol optical model options in the RA (e.g., Limbacher and Kahn, 2014), which are being reconsidered as part of continuing work.Ultimately, we are hoping to systematically acquire direct, in situ measurements of the particle optical and chemical properties for the major aerosol air mass types to put these remote-sensing algorithm assumptions on more solid footing (Kahn et al., 2017).Note also that the MISR Chl results compare very well with the corresponding MODIS values where coincident retrievals were obtained, and here the multi-angle data offer an advantage, as the MODIS camera is in sunglint over the eastern half of the scene, whereas the MISR off-nadir cameras make it possible to perform Chl and aerosol retrievals over the entire area.Figure 6 captures a scene in the mid-South Atlantic Ocean near Ascension Island, where smoke advected from southern Africa is commonly found.Both the SA and RA identify much of the scene as dominated by small, spherical absorbing aerosol, consistent with both the Ascension Island AERONET station and expectation.The scene is covered in broken cloud, typical of much of this ocean region, which makes aerosol remote-sensing retrievals especially challenging.Both the SA and the RA results exhibit 3-D light-scattering effects near cloud edges.Here the difference between the SA and RA retrieval-region sizes has significant consequences: the SA appears to have more coverage, whereas the cloud-edge anomalies are more localized in the higher-resolution RA retrievals, and the SA shows substantially more SSA (and hence retrieved aerosol-type) variability (0.92 ± 0.08) compared to the RA (0.91 ± 0.04).The variability artifacts due to 3-D effects also show up in the ANG and Fr.Non-Sph for both the SA and RA, and are re- flected in the MISR RA-retrieved Chl, giving an indication of the impact aerosol type has on retrieved ocean color.

Conclusions
In Limbacher and Kahn (2014), we detailed extensive modifications to the MISR research aerosol retrieval algorithm over ocean that reduced the 0.024 AOD high bias for AOD 558 nm < 0.10 to ∼ 0.01 or less.The modifications also improved the results of the RA in general, compared to a set of about 1100 ground-truth observations from coincident AERONET sun photometer observations.We also found that the success of MISR aerosol retrieval algorithm refinements depends in part on the accuracy of instrument radiometric calibration.So, in Limbacher and Kahn (2015), we implemented a stray-light correction for the near-nadir cameras based on empirical image analysis with MODIS.This further reduced the remaining high bias at low AOD and also improved statistical comparisons to the validation data overall.Here, we introduce a coupled surface component to the RA over water.More accurately accounting for ocean surface contributions to TOA reflectance should improve aerosoltype retrievals (which will be explored in part 2 of this paper).As part of the MISR calibration refinement effort, we also performed a radiometric trend analysis over three stable, relatively homogeneous desert sites to identify and quantify temporal radiometric drift in each of the 36 MISR channels (Appendix A, below).
Validation of the MISR RA-retrieved Chl, with all radiometric corrections applied, was performed in part by comparison with coincident SeaBASS in situ observations.Further comparisons were made against the previously validated MODIS-Terra ocean color Chl retrievals, because of the relatively small MISR-SeaBASS coincident dataset.Results show that the MISR RA can retrieve Chl reliably if the MODIS-reported Chl ≤ 1.5 mg m −3 , which represents a large fraction of the Earth's ocean area (Fig. 4).Compared to SeaBASS, for in situ Chl values ≤ 1.5 mg m −3 , MISR reports a correlation coefficient of 0.86, MAE is 0.10, RMSE is 0.25, and MRE is 0.52.A comparison of the 49 coincident MISR, MODIS, and SeaBASS Chl observations (Fig. 3), using three two-sample Kolmogorov-Smirnov tests, indicates that it is not possible to distinguish statistically between any of these three small Chl datasets.For the larger (n = 1 499 610) MISR-MODIS dataset with MODISretrieved Chl ≤ 1.5 mg m −3 , we find r = 0.96, MAE = 0.09, RMSE = 0.15, and MRE = 0.23.Although the MISR RA as implemented here lacks much sensitivity to retrieved Chl above 1.5 mg m −3 , and especially above about 3 mg m −3 , this result was anticipated, due to the lack of MISR spectral bands between 446 and 558 nm (Diner et al, 1998).However, with further work, adjustments to the scattering and absorption terms in Eq. ( 1) might improve the results in the higher Chl regime, particularly if MODIS-Terra reflectances can be integrated into the algorithm.
Obtaining MISR Chl retrievals can help fill in the glint-contaminated regions in the single-view MODIS-Terra swath near the solar equator, as only a few of MISR's nine view angles will be contaminated by glint in any one location, allowing the others to be used for the aerosol/Chl retrieval.In addition, these MISR Chl results are derived self-consistently with aerosol amount and type in a physical retrieval, which from the ocean color perspective provides a more robust "atmospheric correction" for the surface retrieval.This work formally opens the door for the use of MISR data in ocean color, complementing the betterconstrained and more extensive spectral coverage of MODIS ocean color retrievals.With the improved ocean surface boundary condition, the MISR multi-angular data should also allow for better-constrained aerosol products, particularly non-sphericity and single-scattering albedo.In the future, it might be possible to ingest collocated MISR and MODIS-Terra reflectances and use the strengths of each instrument in a complementary manner.
Data availability.The main data used for the temporal trending analysis are the MISR L1B2 Terrain projected data (MISR Science Team, 2015d).The MISR RA uses MISR L1B2 Ellipsoid projected data (MISR Science Team, 2015b) as its primary input.Additionally, MISR ancillary data, MISR L1 geometric parameter data, and ancillary MISR L2 data are required to run the RA (MISR Science Team, 2015a, c, e).MISR SA L2 aerosol output can be found in the MISR MIL2ASAE_L2 files (MISR Science Team, 2015e).These data can be obtained from the NASA Langley Atmospheric Sciences Data Center (ASDC) at http://eosweb.larc.nasa.gov.The MISR research aerosol retrieval algorithm is documented in the current paper (Fig. 1) and in previous publications (Limbacher andKahn, 2014, 2015).Radiometric calibration data were obtained in part from the Jet Propulsion Laboratory, Caltech.Access to MODIS data, ocean color products, etc. used in this study are included in the text.

Appendix A: MISR radiometric calibration adjustments
As mentioned in the introduction, instrument calibration can affect retrieval products such as AOD, aerosol type, and ocean surface properties (Limbacher and Kahn, 2015).Calibration includes determination of (1) the absolute radiometric scale as well as (2) the relative band-to-band response among the four MISR spectral bands, (3) the camera-tocamera response among the nine MISR cameras, (4) flatfielding across the MISR imagery (i.e., CCD detector-based gain errors, which show up as across-track biases in reflectance), and (5) temporal trends in these quantities.Considerable effort has been expended to assess MISR radiometric calibration (Chrien et al., 2001) and to meet the standards of approximately 3 % absolute and 1 % channelto-channel, established prelaunch.Previous work involved prelaunch laboratory studies (Bruegge et al., 1999), onboard-calibrator analysis and lunar calibration, along with vicarious calibration over bright land targets (Bruegge et al., 2004(Bruegge et al., , 2007(Bruegge et al., , 2014)), symmetry tests comparing the forward and aft-viewing cameras across the solar equator (Diner et al., 2004), and over-ocean dark target vicarious calibration (Kahn et al., 2005).Cross-calibration analysis has been performed over bright and dark land and ocean surfaces with the Moderate Resolution Imaging Spectroradiometer, that flies aboard the Terra satellite with MISR (Lyapustin et al., 2007), and MODIS combined with the MEdium Resolution Imaging Spectrometer (MERIS), the AirMISR (airborne MISR) instrument, the Landsat-7 ETM+ (Enhanced Thematic Mapper Plus; Bruegge et al., 2007), and the Polarization and Directionality of the Earth's Reflectances 2 (POLDER 2; Lallart et al., 2008).A synthesis of much of this work is given in Bruegge et al. (2014).Limbacher and Kahn (2015) used image analysis, including comparisons with coincident MODIS observations, to characterize flat-fielding errors and to identify empirical relationships that correct anomalies exhibiting spatial structure in high-contrast scenes, an aggregate of "ghosting" light reflections (or stray light) within the cameras.Here we make minor adjustments to our earlier ghosting and flat-fielding corrections.For the flat-fielding characterization, we select only low-contrast scenes, where ghosting artifacts are minimal, and we then normalize the mean MISR-MODIS ratios for the entire scene to unity.For the ghosting modifications, we normalize the MISR-MODIS ratios to an area of little contrast, where stray light is unlikely to be an issue.In the course of that analysis, we also observed systematic, temporal drifts in the measured reflectances, addressed in Appendix A2 below.

A1 TOA reflectance pre-processing and stray light corrections
In the RA pre-processing, all MISR L1B2 reflectance data are first averaged to 1.1 km.The reflectances are then rotated to the L1B1 format, as described in Limbacher and Kahn (2015), and updated stray-light and flat-fielding corrections are applied before being rotated back to L1B2 format.Compared to Limbacher and Kahn (2015), we modify the stray-light corrections in the following way: -The primary ghost term has been divided into a discrete ghosting component (reflected images of features in the scene) and an unstructured veiling-light component.
-This revised primary ghost has a band-and-cameradependent along-track offset applied, as indicated by MISR lunar observations acquired on 14 April 2003 (e.g., Bruegge et al., 2004).
-The primary ghost image is also stretched or squeezed across-track (for the near-nadir A cameras only), based on further comparisons with MODIS-Terra, following the same approach as our earlier work.
-Via ray tracing, it was found that the "secondary ghosting" term in Limbacher and Kahn (2015) distributes light uniformly from the left-or rightmost ∼ 1/3 of the scene to the remainder of that half of the scene (A. Davis, personal communication, 2016), and the correction has been modified accordingly.
-All stray-light terms are now represented as convolutions, which are much quicker to compute than applying the functions pixel by pixel as was done in our earlier work.
-The magnitudes of all stray-light terms have been adjusted as a result of adding the unstructured veiling-light component.
-The stray-light model for the An camera (all four bands) is used for all off-nadir cameras.Only the along-track offset and primary ghost stretching are varied by camera.
We then correct for temporal degradation in the MISR calibration (see Appendix A2 below) and revise the bandto-band calibration.We change the band-to-band calibration by increasing the red reflectance 0.75 % and decreasing the near-infrared reflectance 0.75 %, adjustments that are within the calibration uncertainty and are required to match a global set of coincident, spectral aerosol optical depth validation data (Limbacher andKahn, 2014, 2015).We also apply corrections to the radiance data to smooth out apparent anomalies in the instrument gain (C.Bruegge, personal communication, 2016).

A2 Temporal trend characterization and correction
We characterize here temporal trends in the instrument calibration, again using an empirical image-analysis approach.Bruegge et al. (2014) identified temporal trends in the MISR bidirectional reflectance factor (BRF; computed as described in Step 1a below) data, based on a time series of mean BRFs for a region approximately 10 × 20 high-resolution (275 m) MISR pixels, a region roughly 2.5 × 6 km in size, centered at (27.21 • N, 26.10 • E) within the Egypt-1 desert site.Although this site is stable over time, we adopt a different methodology, similar to Lyapustin et al. (2014), but without performing an atmospheric correction (thus we assume no trend in TOA reflectance due to changes in AOD and aerosol type).The temporal trending analysis is done here based on BRFs averaged over larger areas and at three stable desert sites (Egypt-1, Libya-1, and Libya-4).Compared to Bruegge et al. (2014), both techniques are valid, but we limit geolocation error by averaging, and we reduce the influence of clouds by selecting the median BRF pixel from each case.
The first challenge to performing the temporal trend analysis is finding suitable homogeneous regions.The following was done to select study regions within each of the three sites: (a) the spectral coefficients of variation (standard deviation divided by the mean) were calculated for rolling 50 × 50 pixel patches, in each spectral band of the nadir camera, for three or more orbits and (b) the 50 × 50 pixel patch having the smallest maximum coefficient of variation among all four bands was chosen for subsequent time-series analysis.The central coordinates for the sites selected are Egypt-1 (26.62 • N, 26.18 • E), Libya-1 (24.73 • N, 13.52 • E), and Libya-4 (28.77 • N, 23.50 • E).Information about these calibration sites can be found at http://calval.cr.usgs.gov/rst-resources/sites_catalog/radiometric-sites/test-site-gallery/.
The central coordinate of each study site is imaged repeatedly by MISR along at least two distinct paths having different sub-spacecraft ground tracks and therefore different viewing geometries at the site.(A "path" is one of 233 ground tracks that the Terra satellite covers, repeatedly, once every 16 days.)Therefore, the following procedure was applied separately to each path and camera (6 paths × 9 cameras), for data acquired between 1 January 2002 and 31 December 2014, giving 13 full years of MISR data.(Prior to 1 January 2002, the spacecraft equator-crossing time was not yet stable, so solar geometry varied too much for this timeseries analysis.)All observations of each site, about four per month, were initially included.Note that we also apply flat-fielding corrections to the nadir camera (Limbacher and Kahn, 2015) and additional corrections to the radiance data in all cameras to smooth the instrument gain temporal samples (C.Bruegge, personal communication, 2016).We characterize the temporal trends as follows: 1. Calculate median patch reflectance for each orbit.Median BRF values for at least 193 orbits, and up to 229 orbits, were retained for 6 paths, 4 spectral bands, and 9 cameras at this step.
2. Remove outliers for each path/site and spectral band.
a. Arrange the saved median BRFs by acquisition date, fit a line to the values, and subtract the linear trend from the data (to be added back after outliers are removed and the data are de-seasonalized).
b. Aggregate the data by day of year (DOY) and smooth the sorted, de-trended BRFs using a 21point (i.e., ±10 data point) rolling average.(The data are sufficiently dense that dividing each data point with the mean of 21 surrounding data points does not create significant artifacts in the time series.)This removes the seasonality but does not remove outliers from the data, therefore allowing us to identify them.
c. Identify BRFs that fall outside 2σ from the time series.
d. Remove the identified outliers from the original data.
This step removed 3-14 % of data outliers from each time series.
3. De-seasonalize the data for each site and spectral band.Step 3 is illustrated in Fig. A1 for the Libya-4 site.
a. Normalize the data so the time-series mean for each spectral band at each site is 1.0, which retains the linear trends in each time series but allows data from multiple sites and paths to be compared.The result is 216 normalized time series, one for each MISR camera and band, for two paths at each of the three sites.
Table A1.Decadal trend values (in percent) aggregated over three stable desert sites for the 36 MISR channels.The first four rows present the decadal trends for all four MISR wavelengths and nine cameras.The second four rows represent the 95 % confidence intervals (CI) for the corresponding trends.The final row gives the number of events for each camera.b.These time series are then aggregated across all paths to produce 36 time series, one for each MISR channel (Fig. A2).
The linear percent change per decade and its 95th percent confidence interval are then calculated for each channel, and the results are presented in Table A1 and Fig. A3.The trends are all negative, as might be expected due to sensor degradation over time.They are smallest in the blue band for all but the forward-viewing 70.5 • (Df) and 60.0 • (Cf) cameras, smallest for the aft-viewing 70.5 • (Da) and 60.0 • (Ca) cameras for all bands except the NIR, and largest for the An and 26.1 • forward (Af) and aft-viewing (Aa) cameras.The largest drift overall is about −1.5 % per decade for the An camera red and NIR bands, and the uncertainty in these results ranges from ∼ 0.1 % per decade to ∼ 0.4 % per decade, depending on wavelength and camera.The apparent stability of the MISR blue band is probably due to the use of the blue diode to assess degradation of the MISR on-board calibration panels (Bruegge et al., 2007).Because MISR calibration assumes that the panel degrades in a spectrally invariant way (likely a poor assumption), this subsequently results in a spectrally varying TOA reflectance drift with time.

Figure 1 .
Figure 1.Flow chart describing the MISR RA aerosol/Chl retrieval process.

Figure 2 .
Figure 2. The effect of including under-light, assessed by comparing the MISR-observed TOA reflectances with model-simulated values, not including (a, b) and including (c, d) under-light calculated with independently retrieved MODIS Chl values.These joint histograms show (MISR-Model)/MISR TOA reflectance for the blue (446 nm, a, c) and green (558 nm, b, d) spectral bands, as a function of MODIS Chl.All glint-free cameras are aggregated for this analysis.The solid blue (or green) lines represent the smoothed mean bias, and the dashed lines indicate ±1 smoothed standard deviation.AOD and mixture were obtained by running the RA with under-light included, based on the MODIS Chl, and finding the best-fitting mixture and AOD (using only the NIR band, but up to 9 cameras).Once AOD and mixture were obtained, the TOA reflectances were calculated with the forward model, both with and without under-light.Results show that including under-light dramatically lowers the bias in both the blue and green bands for all Chl up to 10 mg m −3 .As expected, because chlorophyll a strongly absorbs in the spectral response range of the MISR blue wavelength, the contribution of under-light to the TOA reflectance decreases with Chl in the blue, whereas it increases with Chl in the green due to the enhanced scattering from phytoplankton.

Figure 3 .
Figure 3. MISR (red points) and MODIS (blue) Chl plotted against SeaBASS validation data for Chl in situ ≤ 10. Results are presented if both MODIS and MISR have at least one valid retrieval in a 5 × 5 pixel box surrounding the central SeaBASS location.The vertical black line represents Chl in situ = 1.5.We expect better-quality MISR Chl retrievals to the left of this line.

MISRFigure 4 .
Figure 4. MISR-MODIS Chl scatter-density plot for Chl MODIS ≤ 10.The green line represents the mean MISR Chl value for each MODIS Chl bin, and the vertical black line represents Chl MODIS = 1.5.The bin size used for the green line is roughly 0.03 in log 10 space.

Figure 5 .
Figure 5. MISR imagery acquired on 26 August 2003, 15:51 Z: Terra orbit 19620, MISR blocks 60-63, along the US east coast.Plots compare the MISR SA (at 17.6 km resolution, top row) to the RA that includes retrieved Chl (at 1.1 km resolution, row 2).AOD and particle properties correspond to the MISR green band (558 nm).AERONET direct-sun and inversion values are shown for the COVE and Wallops stations as embedded circles.AERONET Fr.Non-Sph may not be informative when aerosol extinction is dominated by the fine mode.In the lower left, MISR An and Df RGB images are shown for context.MISR-retrieved Chl and MODIS-retrieved Chl are shown in the bottom right two panels.
a. Perform Earth-Sun and solar zenith normalization according to BRF= L × ([π × D 2 ]/[E(i) × cos(SZA)]), where L is the top-of-atmosphere radiance, D is the Sun-Earth distance in AU, E(i) is the band-weighted exoatmospheric solar irradiance for band (i), and SZA is the solar zenith angle.b.Calculate the median (and mean) BRF and standard deviation over a region 25 km in radius surrounding the central latitude and longitude coordinate.c.If the wavelength-maximized coefficient of variation is less than 0.02, save the median BRF for use in the time series, otherwise discard the data.
a. Fit a line to the original, time-ordered BRFs (for all 13 years), with outliers removed, and again linearly de-trend the data.b.Reaggregate the data by DOY and divide the BRFs by their 21-point (±10 data point) rolling average.c.Rearrange the data by time and add back the linear trend from Step 3a.