due to molecular scattering (the spread function associated with aerosols is effective over a relatively small distance, typically 1–2 km). As a result, the accuracy, quality, and daily coverage of ocean-color products should be improved substantially over water surfaces contiguous to land surfaces, sea-ice, and clouds, and in the open ocean where spatial variability may be large (e.g., upwelling regions). Otherwise, non-negligible errors would affect the retrieval of water reflectance, with a significant change in spatial structure and correlation scales (may alter the interpretation of mesoscale variability patterns, see Doney et al., 2003).

## Whitecaps

### Importance

Whitecaps generated by breaking waves, generally composed of surface foam (large bubbles separated by a thin layer of water) and underwater bubbles, have a pronounced effect on the intensity and shape of visible light diffusively reflected by the ocean surface (e.g., Frouin et al., 1996; Moore et al., 2000; Stramski and Tegowski, 2001; Terrill et al., 2001; Zhang et al., 2002; Randolph et al., 2014). They may enhance dramatically water-leaving radiance on temporal scales of seconds to minutes (Frouin et al., 1996; Randolph et al., 2017) and affect large areas such as the windy Southern oceans. This is illustrated in **Figures 41, 42**, which display, respectively, pictures of seas with whitecaps and a time series of surface reflectance affected by whitecaps. In the presence of whitecaps, the dark ocean appears much brighter (**Figure 41**). At a local scale, the water reflectance, about 0.08 in the blue in the absence of whitecaps, is increased to 0.4–0.7 (i.e., by a factor of 5–11) depending on the breaking event, and variability is large over time scales of 5 to 10 s (**Figure 42**). The frequency and intensity of such breaking wave features over a 1-km pixel would determine the enhanced reflectance observed by the PACE sensor.

When present, the enhanced reflectance from whitecaps needs to be removed in order to produce estimates of water reflectance suitable for standard ocean-optics applications. From space, since whitecap reflectivity is high, even a small fraction of whitecaps within the instrument's elementary field of view (i.e., within a pixel) may be problematic. The pixel reflectance is affected directly, but more importantly the spectral dependence of the whitecap reflectance skews the extrapolation to the visible of the aerosol signal determined in the near infrared, which may lead to water reflectance errors much larger (i.e., by an order of magnitude) than the requirements (Frouin et al., 1996).

Whitecap corrections are conducted as part of the overall “atmospheric correction” process, even though the signal does not originate in the atmosphere and can be considered a component of the water signal. The aim is to remove the signal due to actively breaking waves (Stage A), which includes surface foam (i.e., large bubbles separated by a thin layer of water) and underwater bubbles injected in the water column. It is not designed to remove enhancements due to the quiescent or mature phase of the whitecap (Stage B), when surface foam has dissipated, but bubbles are still present in the upper layer. In practice, much of the whitecap and the bubble plume signal is removed as part of the aerosol correction, since both

foam and bubbles act to enhance near infrared reflectance and the current aerosol routines (heritage atmospheric correction) cannot distinguish between different sources of near infrared reflectance. However, some problems may arise due to the spectral dependence of whitecaps (mentioned above) and the coupling between molecular and aerosol scattering processes, which may differ significantly (since the amount of aerosols is artificially increased).

## Current Approach to Whitecap Correction

The current approach is designed to remove the reflectance due to the actively breaking wave or bright white portion of the wave (Monahan, 1993) within each pixel. As part of that effort, an estimate of the fraction of the sea surface covered by whitecaps is generated for each pixel based on ancillary wind speed data. Whitecap fractions are commonly estimated using automated processing of digital photography of the sea surface (Brumer et al., 2017). However, comparisons of digital photography with radiometric approaches have shown that photographs capture primarily Stage A whitecaps and miss much of the Stage B bubble plumes that also enhance the surface reflectance. Many relations between whitecap fraction and wind speed have been developed over the last three decades for different ranges of wind speeds (Anguelova and Webster, 2006; Brumer et al., 2017). However, whitecap coverage can vary by several orders of magnitude at the same wind speed. At different locations in the world ocean, various environmental and meteorological factors act in concert but with different strengths and form a composite effect that either enhances or suppresses the effect of wind alone. These other factors include fetch and duration and the wind, water temperature, air temperature and stability of the lower atmosphere defined by the air/water temperature differential, salinity, current shear and long wave interaction, wave age, and the presence of surfactants such as organic films (reviewed in Scanlon and Ward, 2016). Hence, wind speed parameterizations should be viewed as “climatological” and cannot represent the instantaneous whitecap field required by remote sensing applications. In addition, other factors not related to wind speed could cause foam on water surfaces. High concentrations of the phytoplankton *Phaeocystis globosa*, for example, are associated with foam formation in coastal waters and on beaches (Armonies, 1989).

Satellite ocean color algorithms currently employ an expression for undeveloped seas based on wind speed at 10 m ($U_{10}$) where $f_{wc} = 8.75 \times 10^{-5}(U_{10} - 6.33)^{-3}$ (Stramska and Petelski, 2003), see **Figure 43**. This correction produces negative values below $6.33 \text{ m s}^{-1}$ and is much higher than with other parameterizations at high wind speeds. To avoid overestimation, NASA implements a lower threshold of $6.33 \text{ m s}^{-1}$ and an upper threshold equivalent to the whitecap fraction at $12 \text{ m s}^{-1}$ in the operational code (**Figure 43**). Hence the highest fraction of the sea surface covered by whitecaps that is currently used is 1.6%. Although this range may cover the average conditions, whitecaps can occur at wind speeds as low as $3-4 \text{ m s}^{-1}$ and the fractional whitecap coverage can approach 10% at wind speeds greater than $12 \text{ m s}^{-1}$ (Brumer et al., 2017).
Measurement of the spectral reflectance of whitecaps is challenging due to the many types and stages of whitecaps, the rapid time scale on the order of seconds, determining the contribution of foam and background water, and potential contamination from reflectance of sun and skylight. Reflectance of whitecaps varies with the type of breaking wave (e.g., rolling breakers and plunging breakers) and the layers of foam produced. From historic data (Whitlock et al., 1982; Koepke, 1984), an age-averaged effective reflectance, $\rho_{wc}$, of 22% is used in the NASA standard whitecap algorithm for visible wavelengths up to 550 nm. Frouin et al. (1996) studied the visible and near infrared reflectance of sea foam found in the turbulent surf zone. Sea foam reflectance was found to monotonically decrease into the near infrared wavelengths due to enhanced water absorption in these wavelengths. The spectral dependence was confirmed from aircraft measurements of whitecaps in the open ocean (Nicolas et al., 2001). From this work, a reduction factor is applied for red and near infrared wavelengths such that whitecap reflectance is 0.889, 0.760, and 0.645 at 670, 765, and 865 nm respectively and interpolated between these values. Whitecap reflectance can be approximated for wavelengths between 555 and 865 nm as: $\rho_{wc} (\lambda > 555) = 0.22(-1.162 \times 10^{-3}\lambda + 1.653)$. For MODIS bands, this translates to whitecap reflectance of 22% from 412 to 555 nm and 19.3, 19.0, 17.2, and 14.1% at 667, 678, 748, and 869.5 nm, respectively.

Following the discussions above, the standard reflectance for actively breaking waves, $\rho_{wc}$, is multiplied by the estimated fraction of the sea surface covered by whitecaps, $f_{wc}$, to generate the within-pixel reflectance attributable to whitecaps. An important distinction must be made at this point. Whitecap reflectance is not treated as an “augmented” reflectance above the background reflectance, as is commonly interpreted. Because whitecaps are so bright, the signal is believed to dwarf the contributions from water reflectance and surface reflectance (skylight and glint). The estimate $\rho_{wc}$ represents the total upwelling signal above the sea surface of a breaking wave, $E_u(0^+)$, normalized to the downwelling irradiance incident on the sea surface, $E_d(0^+)$. Hence, the $\rho_{wc}$ used in this context is considered invariant of the water reflectance and sky conditions. However, the actual enhancements due to whitecap reflectance can be influenced by many other factors including the intensity of the wave breaking and the concentrations of optical constituents in the water.

This whitecap contribution to reflectance is propagated through the atmosphere to estimate the enhancement $\rho_{wc}^{TOA}$ at the satellite. Assuming that whitecap reflectance is isotropic, we have:

$$ \rho_{wc}^{TOA} = f_{wc} \rho_{wc} t_d(\theta_s) t_u(\theta) \quad (23) $$

The at-sensor signal due to whitecaps ($\rho_{wc}^{TOA}$) is then subtracted from the TOA reflectance measured at the satellite. This effectively accounts for the reflectance from the area of the sea surface that is covered by whitecaps. The whitecap-free area should also be weighted by $(1-f_{wc})$ following Gordon (1997). Ignoring this weighting term is generally not important in

the currently implementation of the whitecap correction where whitecap fractions are <2%, but area-weighting the whitecap-free sea surface would be important if higher whitecap fractions were modeled like in the Southern Ocean or for applications to high spatial resolution satellites.

## Future Possibilities

Several issues must be considered going forward into the PACE era. The algorithm discussed above is a very crude and inaccurate representation of the impact of foam and bubbles on water-leaving radiance. Data collected to date show that wind speed can only roughly approximate the whitecap coverage in a climatological sense and cannot provide accurate real-time estimates of fractional whitecap coverage. The current wind speed thresholds used in the whitecap approach provide a minimal and largely inaccurate estimate of whitecap fraction that can be an order of magnitude lower or higher in the environment. Furthermore, use of a single reflectance value for all whitecaps does not represent the large amount of variability in the types of breaking waves and foam that can occur on the sea surface. Reflectance of whitecaps is variable based on the strength of the wave breaking and is not necessarily invariant of water reflectance signal. The bubbles plume or Stage B also serves to enhance reflectance substantially above background reflectance and this component is not explicitly treated in the model. Finally, the PACE mission is proposed to be hyperspectral from the ultraviolet (350 nm) to near-infrared (885 nm) and have shortwave infrared bands at 940, 1,038, 1,250, 1,378, 1,615, 2,130, 2,260 nm. The current simplified spectral model of whitecaps will need modification to account for the spectral variability of whitecap reflectance in the near and shortwave infrared (see below).

The PACE mission aims to provide a better separation of atmosphere and ocean processes. Currently, much of the whitecap and bubble correction, particularly during high wind conditions, is inaccurately modeled as an aerosol. Whitecaps and bubble serve to enhance reflectance across the near and short wave infrared and cannot be easily separated using the current aerosol routines. Aerosol modeling assumes that water-leaving radiance at two near infrared wavebands are zero or can be estimated with sufficient accuracy using a bio-optical model. The presence of foam and bubbles is not explicit to this formulation and can lead to errors in retrievals when incorrectly treated as spectrally dependent backscattering from waterborne hydrosols or from airborne aerosols.

With more spectral information, the contribution of whitecaps may be measurable in the hyper-spectral signal and removed as part of the data processing scheme without relying on wind speed measurements and single reflectance values (see Dierssen, 2019, this issue). Measured reflectances of whitecaps and generated foam reveal identifiable spectral features from visible to short wave infrared (Figure 44). These new values are largely consistent with the diminishing reflectance in NIR wavebands measured by Frouin et al. (1996), but also reveal many features in the signal that cannot be dealt with as a simple linear decrease into the near infrared. Reflectance dips occur particularly at 750, 980, and 1,150 nm that have enhanced liquid
water absorption, a result of multiple scattering in and around
the bubbles and foam.

A potential approach for PACE and other missions is to identify spectral features associated with whitecaps that are unique from atmospheric and oceanic spectral properties. Water absorbs differently based on whether it is in vapor, liquid or solid form. As discussed above, unique peaks and dips occur in the near infrared portion of the reflectance spectrum that are associated with weak absorbing features of liquid water. The measured spectrum of intense foam and bubbles at the sea surface associated with the wake of a ship with a peak reflectance of 40% in visible wavelengths, As derived in Dierssen (2019, this issue), the general shape of this reflectance can be modeled from the logarithm of water absorption.

The overall shape of whitecap reflectance is directly related to liquid water absorption from visible through shortwave infrared. Some divergence at ultraviolet and violet wavelengths is apparent and likely due to colored substances such as absorption due to colored dissolved organic matter in these coastal waters. However, the overall shape can be used to assess the contribution of whitecaps into the near infrared and shortwave infrared. Parameterizations based on other physical considerations (e.g., vertical structure) should be contemplated to allow a direct estimation of the whitecap effect on water reflectance.

One approach would be to measure the depth of a liquid water absorption feature (e.g., 980 nm) to estimate the “effective” contribution of whitecaps to the total pixel reflectance. If we presume that the water reflectance does not contain this liquid water feature, then the line-depth of the water-absorption feature at 980 nm, for example, can be related to a linear mixing of unaffected sea surface with different intensities and areas with foam and bubble plumes. If the background water is highly scattering due to sediments or floating vegetation, for example, then this water absorption feature may also be present in the background signal and such water types would need to be identified prior to assessing the whitecap contribution (Dierssen, 2019, this issue). Candidate algorithms to model the whitecap factor, $A_{wc}$, from the hyper-spectral radiance rather than the area-weighted whitecap fraction derived from wind speed are provided in Dierssen (2019, this issue). The whitecap factor is the fraction of a standard whitecap reflectance that accounts for enhancements in spectral reflectance of the sea surface above the background reflectance. Since $A_{wc}$ is optically derived, it is better suited for atmospheric correction techniques because it specifically incorporates different levels of foam and bubbles associated with breaking waves and requires no implicit spatial scale.

In summary, decades of data have shown that wind speed models will not be able to predict the whitecap fraction with sufficient accuracy to use in daily remote sensing imagery. Use of other ancillary parameters such as fetch, air, and water temperature, and currents may have utility in further refining estimates of whitecap fraction. In the least, the Stramska and Petelski (2003) model should be replaced with a more recent parameterization that better fits both high and low wind speed conditions (e.g., Brumer et al., 2017). However, it is unlikely that the whitecap

fraction and particularly the associated bubble plume will be predictable from wind speed data for any given image to within an order of magnitude (see scatter of data points in Figure 43 above).

We should continue to refine spectral models of foam and bubbles to understand their impact on upwelling irradiance at the pixel level. As part of that effort, more hyper-spectral datasets are critical that provide a means to estimate reflectance of whitecaps over time and space under a wide variety of water types and whitecap conditions. New methods that seek to use the measured spectral information in near infrared wavelengths to estimate the contribution of whitecaps directly will provide a means to separate whitecaps from aerosols and other conditions where near infrared reflectance is non-negligible. Preliminary results have been conducted at the sea surface and more research is warranted to model the transmission of hyper-spectral reflectance from whitecaps through the atmosphere. Moreover, uncertainties need to be assessed when aerosol products are derived from at-sensor radiance that is “contaminated” by whitecaps and bubble plumes. Continuing to propagate such errors impacts the selection of spectral aerosol model and magnitude of aerosols, as well as impacts the spectral shape and magnitude of retrieved water-leaving radiance and associated ocean color products. Until correction methods with sufficient accuracy are found and tested widely across ocean provinces, we recommend that PACE images collected under high wind conditions, which may contain significant whitecap coverage, be flagged such that users will recognize higher uncertainty in the water reflectance and aerosol retrievals.

Finally, breaking waves on the ocean surface are areas of significant importance to air-sea interaction. Whitecaps foster climate-relevant physical and chemical processes in the ocean, including the production of sea salt aerosols, mixing processes, and the exchange of gas (e.g., CO₂, CH₄, DMS, water vapor) and heat with the atmosphere (Monahan and Spillane, 1984; Woolf, 1997; Asher and Wanninkhof, 1998; Woolf et al., 2007). Wave breaking generates turbulent kinetic energy in the surface ocean, driving upper ocean mixing, and transferring energy to currents and longer waves (Cavaleri et al., 2007). Visible manifestations of breaking waves (i.e., foam and bubbles) are related to the energy injected into the surface ocean. Using imagery to assess whitecaps directly will open up new science directions.

## Earth's Curvature

It was mentioned in section From Multi-Spectral to Hyper-Spectral Remote Sensing that assuming a plane-parallel atmosphere might introduce significant atmospheric correction errors for Sun zenith angles > 70°. This was also the conclusion of Ding and Gordon (1995), who suggested that for those angles a sufficient treatment would be to compute the molecular reflectance with a spherical-shell atmosphere RT code. It is important to emphasize, however, that the effect of Earth's curvature is not only to increase intensity at grazing Sun zenith angles due to the smaller attenuation of the direct solar beam, but also to lower intensity at low Sun zenith angles due to a smaller illumination volume (e.g., Chowdhary et al., 2019, this issue;
Ramon et al., 2019). This second effect is generally understated, but critical for accurate atmospheric correction. **Figure 45** displays, as an example, Monte Carlo simulations of molecular reflectance, $ρ_r$, and aerosol reflectance, $ρ_a$, at 446, 558, 672, and 867 nm as a function of Sun zenith angle for a view zenith angle of 15° and a relative azimuth angle of 90°. Aerosols are of maritime type with optical thickness 0.1 at 550 nm. In the 0–75° Sun zenith angle range, differences between plane-parallel and spherical-shell calculations are relatively small (0.3–0.5%) for $ρ_r$, and reach 1.5% for $ρ_a$. However, since molecular scattering may be large and dominate the TOA signal, especially in the blue and UV, even a small fraction of 1% error in $ρ_r$ would affect the water reflectance retrieval significantly (i.e., with resulting uncertainty above requirements). On the other hand, the impact of 1.5% differences in $ρ_a$ is comparatively inconsequential for the aerosol loading considered (relatively small aerosol signal). But one expects non-negligible effects for higher view zenith angle and aerosol optical thickness. Thus Earth's curvature should be taken into account in generating at least Rayleigh LUTs (it is also recommended to use spherical-shell RT code for aerosol LUTs), and this for all solar and viewing geometries, not only large Sun zenith angles.

## Multiple Scattering

Although the atmosphere is relatively thin optically compared with the water body, multiple scattering effects are not negligible in the atmosphere, especially at wavelengths for which scattering is effective (blue and UV). These effects are taken into account in atmospheric correction schemes, but their dependence on aerosol altitude is often neglected (case of the heritage algorithm in particular). It is generally assumed that aerosol altitude has a significant effect on the TOA signal only when aerosols are absorbing, which was discussed in section Estimation of Aerosol Vertical Profile. The coupling between scattering by molecules and aerosols, however, depends on their relative vertical distribution.

This is illustrated in **Figure 46**, which displays the coupling term of the aerosol reflectance at 443 nm for two very weakly absorbing models, i.e., Maritime with 98% humidity (M98) and Tropospheric with 70% humidity (T70). These models are part of the Shettle and Fenn (1979) suite used in early two-step atmospheric correction algorithms (e.g., Gordon and Wang, 1994; Gordon, 1997). Aerosol optical thickness is 0.1 at 865 nm, and aerosol concentration decreases exponentially with increasing altitude with scale height from 2 to 8 km. Sun zenith angle is 36.2°, and the results are presented as a function of viewing zenith angle (0 to 75°) in the principal plane of the Sun. Note that the coupling term can be negative since computed as the difference between the total atmospheric reflectance and the molecular component (i.e., with no aerosols) and the aerosol component (i.e., with no molecules) (Deschamps et al., 1983). It would always be positive if the molecular and aerosol components were computed for molecules only but in the presence of aerosols and for aerosols only but in the presence of molecules (Antoine and Morel, 1999). For some remote sensing geometries the effect of aerosol scale height reaches 0.002 (M98) and over 0.01 (T70) in amplitude, which in the case of T70 is

one order of magnitude larger than the required accuracy on water reflectance. Thus it is important to include the effect of aerosol altitude when correcting the TOA signal for atmospheric effects, even when aerosols are little or not absorbing. This can be done using PACE observations at 5 nm resolution in the oxygen A-band, especially using the sub-5nm spectral sampling capabilities of the OCI, which allow an estimate of aerosol altitude or scale height (see section Estimation of Aerosol Vertical Profile).

## UV Observations

Observing in the UV is important to separate absorption by CDOM and phytoplankton pigments, to distinguish hydrosol types (e.g., sediments from organic particles) in optically complex waters, to allow the discrimination of functional, taxonomic, and harmful algal groups, and to improve atmospheric correction in the presence of absorbing aerosols. Hence measurements in the UV (from 350 nm) constitute a key PACE mission requirement. Retrieving accurately the water signal in the UV, however, presents a number of specific challenges that originate chiefly from the large optical thickness of the atmosphere. These challenges are emphasized in the following; see also Chowdhary et al. (2019, this issue) for a discussion of the UV regime in the context of RT modeling for atmospheric correction.

(1) The water reflectance contribution to the TOA signal is small in the UV, often much smaller than in the visible, especially when CDOM absorption is strong. This can be exploited in some situations (i.e., when the water signal is negligible) to constrain the aerosol signal estimated from NIR to SWIR wavelengths in a classic atmospheric correction scheme, but in general the water reflectance retrieval is more difficult. In addition, errors in estimating the spectral shape and magnitude of reflected sky radiance off of wind-roughened seas are enhanced in the UV. Currently this component is modeled as part of the Rayleigh LUTs for wind-roughened surfaces and is not validated with field data. A further complication is that aerosol and CDOM absorption may act similarly, i.e., their effects on the TOA signal may not be easy to separate. Also the steep decrease of solar irradiance due to absorption bands in this spectral range makes radiometric calibration difficult.

(2) Multiple scattering and coupling processes between molecular scattering and aerosol absorption are effective, and the resulting effect strongly depends on the relative vertical distribution of molecules and aerosols. This significantly complicates the atmospheric correction problem, for which knowledge of aerosol altitude becomes necessary. This will be possible with OCI (see section Estimation of Aerosol Vertical Profile and Remer et al., 2019, this issue). In one-step deterministic and statistical schemes, however, aerosol altitude can be variable, i.e., taken into account in determining the best solution.

(3) The influence of the environment, and in general spatial heterogeneities in the atmosphere, surface, and water body properties, is substantial (since depending on atmospheric transmittance, which itself depends exponentially on optical thickness see section Adjacency Effects and **Figure 40**, left), and
the “large target” formalism may not yield acceptable water reflectance retrievals in coastal oceanic regions and water bodies surrounded by land (lakes, ponds, rivers).

(4) The spherical albedo of the atmosphere becomes large (e.g., 0.37 at 350 nm for a clear atmosphere) and neglecting the multiple interactions between the water body and the atmosphere may introduce errors of up to 2% (case of oligotrophic waters) on water reflectance estimates.

(5) Errors in the spectral dependence of aerosol scattering in the NIR and SWIR, by propagating through the standard algorithm, may translate into large errors in the UV (since further away than the visible). This and the complex RT processes in the UV make it difficult to achieve via “system” vicarious calibration (Franz et al., 2007) radiometric accuracy within a small fraction of 1%.

**Figure 47** displays various components of the TOA signal and their relative importance for typical conditions, i.e., a WMO maritime atmosphere (aerosol optical thickness of 0.2 at 550 nm) over waters with chlorophyll-a concentration of 0.1 mgm⁻³ and CDOM absorption of 0.02 m⁻¹ at 440 nm. Spectral range is 350-400 nm, Sun and view zenith angles are 30 and 15°, respectively, relative azimuth angle is 90°, aerosol scale height is 2 km, and wind speed is 7 m s⁻¹. The water signal represents only 3 to 5% of the TOA signal and 34 to 42% of the TOA signal corrected for molecular scattering effects, with the lower values at 350 nm and the higher values at 400 nm. For waters with the same chlorophyll concentration but zero CDOM absorption, however, the contribution of the water signal would be larger, i.e., 8 to 12% and about 62%, respectively. For smaller aerosols, e.g., tropospheric type, the relative importance of the water signal would be reduced at shorter wavelengths. The small contribution of the water signal to the TOA signal stresses the importance of accurate radiometric calibration and modeling of molecular effects. In the case of **Figure 47**, an error as small as 0.1% on the TOA reflectance would already translate into a 3.3% error on the water reflectance at 350 nm.

**Figure 48** displays the absorption effect of a continental aerosol with scale height of 2, 5, and 8 km on the TOA signal and the effect of CDOM absorption (0.01, 0.02, and 0.1 m⁻¹ at 440 nm) on the water signal observed at TOA. The absorption effect is the difference between the atmospheric reflectance at TOA in the presence of aerosol absorption and without absorption (see section Estimation of Aerosol Vertical Profile and Equation 14). Chlorophyll-a concentration is 1 mgm⁻³. Spectral range, angular geometry, wind speed, and aerosol optical thickness are the same as in **Figure 47**. For the CDOM absorption effect, i.e., the difference between the water signal with and without CDOM absorption, aerosol scale height (slightly affects the atmospheric transmittance) is 2 km. The spectral dependence of the aerosol and CDOM absorption effects is comparable, making distinction of the two signals difficult in some one-step atmospheric correction schemes (e.g., spectral-matching). For example, 0.01 m⁻¹ of CDOM absorption has nearly the same effect as aerosol

absorption when scale height is 2 km, i.e., about -0.002 over 50 nm.

## STRATEGY FOR ATMOSPHERIC CORRECTION

The standard, 2-step approach to atmospheric correction of satellite ocean-color imagery has been used operationally by space agencies since the CZCS was launched in 1978 to process data from major large-scale ocean color missions into water reflectance. The approach has proved to be robust, sufficiently accurate, and useful for many applications, scientific and societal (IOCCG, 2008). Its chief advantage over a variety of alternatives, as pointed out in sections Heritage Atmospheric Correction Algorithm and Alternative Algorithms, is that essentially minimal assumptions about water reflectance, the signal to be retrieved, are made. Algorithms have evolved and improved to account for new capabilities (e.g., observations in the shortwave infrared to deal with turbid waters) and take advantage of new knowledge (e.g., aerosol optical properties, whitecap reflectance), but have followed the same principle of using a spectral region where the water body is not or little reflecting to isolate the perturbing influence of the atmosphere and surface. In view of the success of this heritage approach, and the fact that it has been selected and applied systematically to correct imagery from most ocean color sensors, it is highly desirable to continue its usage in current and future processing lines, in particular for the PACE OCI. The adaptation to hyper-spectral OCI would address the challenges associated with observing in the ultraviolet and dealing with strong gaseous absorption bands; see section From Multi-Spectral to Hyper-Spectral Remote Sensing. Observing in the UV, even with hyper-spectral capability, continues to be an open question and area of active research, but does not negate the overall benefit of proceeding with a heritage 2-step retrieval for OCI. This continuity would maintain a certain level of consistency across sensors from different missions, allowing for a long-term record of water reflectance relatively free of algorithm-related discrepancies and biases. Furthermore, new methodologies may not be applicable to some sensors, complicating the generation of accurate long-term time series.

The heritage algorithm, however, has important limitations, as discussed in section Procedures. In particular it cannot handle properly situations of absorbing aerosols (i.e., dust, biomass burning and pollution particles), which are encountered over large oceanic regions and the coastal zone, reducing the spatiotemporal coverage of ocean color products, therefore their utility for scientific investigations and operational oceanography. It also does not work in Sun glint regions and in the presence of clouds, resulting in a typical 10-15% daily spatial coverage. To resolve these issues, one needs to move to further explore and implement alternative algorithms, deterministic or statistical, such as those described in section Alternative Algorithms. These algorithms exploit observations in the entire set of available spectral bands and eventually include, depending on the sensor, bidirectional and polarization information, either directly or
indirectly (e.g., to constrain the set of possible aerosol models). So far only a few new algorithms have been checked thoroughly and applied systematically (i.e., at the scale of a satellite mission), notably the Steinmetz et al. (2011) spectral matching POLYMER algorithm and the Schroeder et al. (2007) neural network algorithm. Neural network atmospheric correction including sun glint correction was part of MERIS standard processing for Case 2 waters during the whole lifetime of the mission. Most of the advanced algorithms have been only tested on a few images, and they need to be further evaluated theoretically and experimentally and examined for robustness, reliability, and general applicability in an operational context. Their potential, however, as demonstrated in the examples presented in section Alternative Algorithms, is undoubtedly great to improve atmospheric correction in difficult situations (i.e., absorbing aerosols, turbid waters, Sun glint, whitecaps, land proximity, sea ice, thin clouds), offering the opportunity to generate more accurate ocean color products with wider coverage (i.e., less gaps) that will allow a better description of ocean properties (IOPs, concentrations) and biogeochemical phenomena.

In view of the above, a suitable strategy for atmospheric correction during the PACE era would be to continue performing atmospheric correction with the standard, 2-step heritage algorithm, adapted/adjusted as necessary, but at the same time applying the best advanced algorithm that fits the characteristics and capabilities of a given sensor, or a suitable combination of sensors. In the case of PACE, it is expected (by mission design) that OCI and polarimeters will be used synergistically. The selected methodology may be different, indeed, for a sensor that only measures spectrally total TOA radiance and a sensor that also measures directionally polarized TOA radiance. Whenever possible satellite data from previous missions would be re-processed with the new algorithm. An elaborate flagging system, although not easy to define and validate, is necessary to warn the user about doubtful algorithm performance. The quality of the atmospheric correction processors, therefore selection of the best one, could be assessed following procedures developed by Müller et al. (2015a,b) for the ESA Ocean Color-Climate change Initiative (OC-CCI), which include in a straightforward fashion not only comparisons with *in situ* measurements, but also analysis of image quality and processor behavior along scan line (e.g., spatial and temporal homogeneity and consistency in water reflectance retrieval). Since individual advanced algorithms may lead to improved products (or may perform similarly) in some situations, or have advantageous features, their implementation in data analyzing systems such as SeaDAS would provide the user community with best options depending on the study or application. This strategy would generate two separate water reflectance products, which is not a problem as long as respective advantages and limitations are understood and uncertainties specified, preferentially on a pixel-by-pixel basis. Thus we would end up with a continuity product and an advanced product that fully exploits the mission capabilities, which for PACE will combine hyper-spectral radiometry and multi-angle polarimetry. The two products could be merged optimally, at the Level 3 highest resolution possible, i.e., native resolution, taking into account their uncertainties (bias and standard

deviation). Various merging procedures exist (see IOCCG, 2007 for a review), and choosing the best procedure will depend critically on the representation of algorithm performance and uncertainties (expected to be better and smaller, respectively, for the advanced algorithm).

## CONCLUSIONS

Substantial progress in atmospheric correction of ocean-color imagery has been made since the proof-of-concept CZCS mission that demonstrated the feasibility of retrieving water reflectance from space and led to the first generation of operational ocean-color sensors (SeaWiFS, MODIS, MERIS, VIIRS, etc). Compared with CZCS, the new sensors have higher radiometric sensitivity and they measure in more and better-defined spectral bands in the visible. They also have spectral bands in the near infrared and (for some sensors) shortwave infrared, facilitating the removal of atmosphere and surface effects. This has generated a flurry of activities aimed at developing efficient atmospheric correction algorithms that exploit the new capabilities, which has contributed to a better understanding of the problem and resulted in significant improvements and new avenues.

Since the first attempts, the approach to atmospheric correction has essentially remained a 2-step process, in which the perturbing effects of the atmosphere and surface are determined in spectral bands where the signal from the water body can be considered negligible (i.e., in the near infrared and/or shortwave infrared) and propagated or extrapolated to the shorter spectral bands. Definite improvements to algorithms based on this approach have been made, notably in the specification of the aerosol models (based on AERONET measurements), the correction of gaseous absorption (e.g., nitrous oxide influence in the blue), and the processing of imagery over optically complex waters, where the water-leaving signal in the near infrared (or even SWIR) is not negligible and must be estimated through iterative bio-optical modeling. A number of approximations and issues have been identified and studied, such as whitecaps, Sun glint, aerosol vertical structure, polarization, sea surface roughness, Earth curvature, in-water radiance angular distribution, diffuse transmittance, absorbing atmospheric gases, absorbing aerosols, stratospheric aerosols, optically thin clouds, highly turbid waters, and adjacency effects. For some of these issues, satisfactory solutions have been proposed and implemented operationally, but not for others (e.g., absorbing aerosols, whitecaps, adjacency effects). In the absence of satisfactory solutions for a given observing condition, the operational approach has been to allow the atmospheric correction to fail, or to flag the water reflectance retrievals as suspect quality. This has resulted in large data gaps in some regions, preventing the efficient utilization of ocean color products.

Alternative approaches, deterministic and statistical, which aim at inverting the top-of-atmosphere signal (i.e., retrieving the water reflectance) in a single step, have been developed with varied degrees of success. The information in all available spectral bands is generally used, which is advantageous in some situations
(e.g., absorbing aerosols), but the main drawback is that water reflectance, i.e., the signal to retrieve, is often constrained by a model (which may not represent well the environmental conditions of a given observation). Some algorithms have been able to handle situations of Sun glint and thin clouds, increasing significantly the daily coverage of ocean color products. All the proposed methods, however, have been based on multi-spectral observations, the information generally available; few attempts have been made to exploit the polarized and/or directional properties of reflected sunlight (available for some sensors, e.g., POLDER and MISR), but the potential of these properties to improve atmospheric correction (e.g., to enhance the contribution of water reflectance, to deal effectively with Sun glint, and to determine absorption effects) has been recognized and, to some extent, demonstrated. The improvements revealed in the selected examples, however, need to be confirmed (e.g., by analyzing other situations) before drawing final conclusions.

The PACE mission, which will carry into space a spectrometer measuring at 5 nm resolution in the UV to NIR with additional spectral bands in the SWIR and two multi-angle polarimeters, has great potential for improving estimates of water reflectance in the post-EOS era. The improved instrument capabilities offer opportunities, but retrieving a continuous water reflectance spectrum at 5 nm resolution in the UV to NIR, a chief mission objective, poses new challenges. First, measurements in the UV, where molecular scattering is effective (and may dominate the signal), are strongly affected by the vertical structure of atmospheric scatterers, and adjacency effects are large. Second, correcting measurements in spectral regions where gaseous absorption is strong may be difficult when absorbers are located in lower atmospheric levels (e.g., water vapor) due to coupling between scattering and absorption. Observing in the UV to SWIR, however, is adapted to the problem since observations in the UV are sensitive to absorbing aerosols, those in the SWIR to coarse aerosols (and they allow a better separation of the atmospheric/surface signal), and those in the oxygen-A band (763 nm) to aerosol altitude, a parameter controlling aerosol absorption effects. This is especially useful for inversion schemes that incorporate all the available information to retrieve water reflectance. Polarized and multi-angular measurements, sensitive to aerosol type, increase the information content in the inversion process and, therefore, are expected to yield more accurate retrievals, but the possibilities and improvements have yet to be fully investigated.

During the PACE era one may envision an approach to atmospheric correction that is based primarily on the heritage 2-step algorithm, taking into account and extending past accomplishments, yet exploiting as much as possible new capabilities (observations in the UV and in oxygen-A band) and multi-angular polarimetry (e.g., to constrain the aerosol model ensemble or estimate directly aerosol absorption effects). It should be clear that polarized and directional measurements are essential here, due to the inherent limitations of the heritage algorithm, in particular its inability to handle absorbing aerosols, which may affect large oceanic areas. This strategy, aimed at ensuring continuity with previous ocean-color missions, should be complemented by the development and implementation of

more sophisticated inversion schemes (deterministic, Bayesian) that, by the nature of their construction, their robustness, and their generalization capabilities, have the undeniable potential to become the new standard in the near future.

Despite the progress made and the major improvements in atmospheric correction expected during PACE, important gaps/issues still remain to be filled/tackled. They include (1) improving the accuracy of whitecap corrections, for which coverage and optical properties are highly variable and difficult to model, (2) accounting for Earth curvature effects in atmospheric radiative transfer, which may be significant even at small zenith angles, (3) correcting for adjacency effects (influential near land, sea ice, and clouds) and cloud shadows, (4) accounting for the coupling between scattering and absorption (especially important in the UV where the molecular scattering signal is large), (5) modeling accurately water reflectance, including polarization (too little is known about the polarization properties of hydrosols), and (6) acquiring a sufficiently representative data set of water reflectance in the UV to SWIR to describe the variety of water bodies (such prior information is needed in Bayesian approaches). Dedicated efforts, experimental as well as theoretical, are in order to gather the necessary information and resolve inadequacies. Ideas and solutions exist and have been put forward to address the unsolved issues, thanks especially to the new capabilities provided by PACE, which will mark the beginning of a new era of accurate ocean-color radiometry from space.

## AUTHOR CONTRIBUTIONS

This work was a statement of findings by the Atmospheric Correction subgroup of the first NASA PACE Science Team (Principal Investigators and Associates). All the authors contributed to the conception and organization of the study, the analysis of the results, and the writing of the sections. They critically revised the manuscript and helped to bring about the final version. RF developed the overall structure of the manuscript and arranged the contents of the sections. He also led the writing of sections Introduction, Improvements Using Super-sampling in Selected Spectral Intervals, Significant Issues, Strategy for Atmospheric Correction, and Conclusions. LR, EB, OD, and AO contributed to the section Introduction and provided invaluable comments to the other sections. BF, AI, KK, ZA, and B-CG wrote the section Heritage Atmospheric Correction Algorithm. BC, JC, OD, XH, DT, OK, AD, RF, and P-WZ wrote the section Alternative Algorithms. LG, BP, FS, RF, and DR provided results for that section. KK, OK, LR, LG, OC, AO, and AD wrote or contributed to the section Enhancements Using Multi-Angular and/or Polarimetric Information. JT, P-YD, LR, OK, OC, AO, and AD provided useful insight for the section Improvements Using Super-sampling in Selected Spectral Intervals. HD, DR, P-YD, JT, and JC contributed to the section Significant Issues. BF, AI, and LR helped to work out the atmospheric correction strategy (section Strategy for Atmospheric Correction) and to form the conclusions of the study (section Conclusions).
## FUNDING

The National Aeronautics and Space Administration's Ocean Biology and Biogeochemistry Program, managed by Dr. Paula Bontempi, provided funding for the study under solicitation NNH13ZDA001N-PACEST.

## ACKNOWLEDGMENTS

The PRISM flight over Santa Monica Bay was enabled by a PRISM AITT grant from NASA ESTO. We thank other sponsors including: the NASA Earth Science Division for the AVIRIS-NG instrument and the data analysis program Utilization of Airborne Visible/Infrared Imaging Spectrometer Next Generation Data from an Airborne Campaign in India NNH16ZDA001N-AVRSNG, managed by Dr. Woody Turner;

the Jet Propulsion Laboratory and California Institute of Technology President and Director's Fund; the Jet Propulsion Laboratory 20 Research and Technology Development Program; and the NASA Center Innovation Fund managed in conjunction with the Jet Propulsion Laboratory Office of the Chief Scientist and Technologist. RF acknowledges the technical support of Mr. John McPherson, Scripps Institution of Oceanography. A portion of this research took place at the Jet Propulsion Laboratory, California Institute of Technology.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2019.00145/full#supplementary-material

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**Conflict of Interest Statement:** LG is employed by company Pixstart, and DR and FS are employed by company HYGEOS.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Frouin, Franz, Ibrahim, Knobelspiesse, Ahmad, Cairns, Chowdhary, Dierssen, Tan, Dubovik, Huang, Davis, Kalashnikova, Thompson, Remer, Boss, Coddington, Deschamps, Gao, Gross, Hasekamp, Omar, Pelletier, Ramon, Steinmetz and Zhai. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
# APPENDIX A: METHODOLOGY FOR INFORMATION CONTENT ASSESSMENT

The information content assessment described in section Information Content Assessment uses a Bayesian approach with Gaussian distributions as described in Rodgers (2000), and implemented for aerosol remote sensing by Knobelspiesse et al. (2012) and references therein. This method estimates retrieval uncertainty given an observational configuration and uncertainty with the Equation:

$$ \hat{S}^{-1} = K^T S_{\epsilon} K + S_a^{-1} $$

where $\hat{S}$ is the retrieval error covariance matrix, $S_{\epsilon}$ is the observation error covariance matrix, $S_a$ is the a priori error covariance matrix, $K$ is the Jacobian (forward model sensitivity) matrix, $^T$ denotes the transpose, and $^{-1}$ denotes the inverse. The observation error covariance matrix represents measurement uncertainty and is square, with the dimension of the number of measurements [m x m], made with each observation. The retrieval error covariance matrix, $\hat{S}$, has a similar structure, but represents the uncertainty in parameters retrieved from the data and has the dimension of the number of retrieved parameters [n x n]. Essentially, it is the projection of observational uncertainties into state (parameter) space. The Jacobian matrix, $K$, expresses the sensitivity of the atmosphere/ocean radiative transfer model to changes in the parameters to be retrieved, and has the dimension [m x n]. Radiative transfer simulations, indicated by the function $F(x) = y$ (where $x$ is a vector atmospheric and surface optical parameters, often called the state space, and $y$ is the measurement vector), are used to estimate the Jacobian matrix

$$ K_{i,j}(x) = \frac{\partial F_i(x)}{\partial x_j} \approx \frac{F_i(x') - F_i(x)}{x' - x_j} $$

where the partial derivative of the radiative transfer model for the simulated set of parameters, $x$, is computed for each observation, $i$, and each parameter, $j$. We approximate the Jacobian using the forward difference technique, where the radiative transfer model is rerun with a perturbed parameter $x'_{j}$, and the forward model is assumed linear over that perturbation.

This method provides the means to relate measurement characteristics to expected retrieval success. Instrument capability is defined by the contents of the measurement vector, $y$, and the measurement uncertainty defined in $S_{\epsilon}$. The a priori error covariance matrix, $S_a$, describes what we know about state parameters $x$ prior to a measurement. The Jacobian, $K$, is the product of a radiative transfer model and thus computationally expensive to generate. It is, however, crucial since it links parameter to measurement space. In practice, we generate a Jacobian matrix for a very large measurement vector, encompassing all possible measurement spectral sensitivities, geometries, and polarimetric states, and then make a subset corresponding to the instrument system in question. Since the

atmosphere/ocean system is highly nonlinear, we also need to repeat this analysis for a variety of states, and express the results as an aggregate of many states. For example, we might expect the ability to determine ocean properties decreases as the amount of aerosol loading increases, so we must test with a variety of aerosol amounts.

The averaging kernel matrix, $A$ (also known as the model resolution matrix), is a useful reformulation that is an identity matrix for perfect retrieval ability. It is calculated as:

$$ A = [K^T S_{\epsilon} K + S_a^{-1}]^{-1} K^T S_{\epsilon} K $$

where a null matrix indicates no ability to determine the state parameters beyond what is already known from the a priori matrix. The Degrees of Freedom for Signal is a scalar, representation of measurement system capability, calculated as $DFS=trace(A)$, and has the property $0 \le DFS \le n$. We use DFS to compactly show system capability for many simulated states.

We used a forward model that defines the measurement state with ocean and atmospheric physical and optical properties. However, PACE SDT requirements were expressed as the water reflectance [$\rho_w$], which is instead a byproduct of the model. We must therefore project the results $\hat{S}$ into this space. To do so, we first determine the Jacobian matrix, $J$, for water reflectance in the same manner as $K$:

$$ J_{i,j}(x) = \frac{\partial M_i(x)}{\partial x_j} \approx \frac{M_i(x') - M_i(x)}{x' - x_j} $$

where $\lambda$ corresponds to each wavelength in [$\rho_w$], and $M$ is the forward model component that produces the water reflectance. To project the retrieval error covariance matrix we therefore use

$$ \hat{S}_b^{-1} = J^T K^T S_{\epsilon} K J + J^T S_a^{-1} J $$

Where $\hat{S}_b$ is the byproduct error covariance matrix. The indirect nature of this matrix may mean that it has an implicit regularization. Comparison of $\hat{S}_b$ and the projection of the a priori error covariance matrix $J^T S_a^{-1} J$ can provide clues to the intermediate step constraints.

section Information Content Assessment contains an implementation of these techniques for several prototypical MAP designs for a variety of geophysical conditions. In practice, this means we construct Jacobian matrices to include all possible measurement spectral channels and geometries, and subset the Jacobian to represent the measurement system of interest. This is repeated for a variety of geophysical cases, and results presented in aggregate. In section Information Content Assessment we show the DFS as an overall metric of measurement capability, and $\hat{S}_b$ for water reflectance to show atmospheric correction capability.